Merge pull request #44 from AeneasVerif/son_traits_types

Add support for traits

168 files changed, 25526 insertions, 13173 deletions

diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml
index 664dc674..6b5aacf0 100644
--- a/.github/workflows/ci.yml
+++ b/.github/workflows/ci.yml
@@ -15,5 +15,20 @@ jobs:
       - run: nix build -L .#checks.x86_64-linux.aeneas-tests
       - run: nix build -L .#checks.x86_64-linux.aeneas-verify-fstar
       - run: nix build -L .#checks.x86_64-linux.aeneas-verify-coq
-      #- run: nix build -L .#checks.x86_64-linux.aeneas-verify-lean
       - run: nix build -L .#checks.x86_64-linux.aeneas-verify-hol4
+      # Lean doesn't work with Nix
+      #- run: nix build -L .#checks.x86_64-linux.aeneas-verify-lean
+  lean: # Lean isn't supported by Nix, so we put it in a different job
+    runs-on: [ubuntu-latest]
+    steps:
+      # Install curl
+      - run: sudo apt update && sudo apt install curl
+      # Install Elan (https://leanprover-community.github.io/install/linux.html) and Lean in
+      # non-interactive mode:
+      - run: curl https://raw.githubusercontent.com/leanprover/elan/master/elan-init.sh -sSf | bash -s -- -y
+      # Checkout the repo and download it to the runner
+      - name: Checkout
+        uses: actions/checkout@v4
+      # Verify - note that we need to update the environment with `source` so
+      # that the lake binary is in the path.
+      - run: source ~/.profile && cd tests/lean && make
diff --git a/Makefile b/Makefile
index a0111b37..4660ac83 100644
--- a/Makefile
+++ b/Makefile
@@ -27,7 +27,7 @@ CHARON_TESTS_POLONIUS_DIR ?= $(CHARON_HOME)/tests-polonius
 
 # The path to the Aeneas executable to run the tests - we need the ability to
 # change this path for the Nix package.
-AENEAS_EXE ?= bin/aeneas.exe
+AENEAS_EXE ?= bin/aeneas
 
 # The user can specify additional translation options for Aeneas.
 # By default we do:
@@ -71,9 +71,12 @@ build-lib:
 .PHONY: build-bin-dir
 build-bin-dir: build-driver build-lib
 	mkdir -p bin
-	cp -f compiler/_build/default/driver.exe bin/aeneas.exe
+	cp -f compiler/_build/default/driver.exe bin/aeneas
 	cp -f compiler/_build/default/driver.exe bin/aeneas.cmxs
-	cp -rf backends bin
+	mkdir -p bin/backends/fstar
+	mkdir -p bin/backends/coq
+	cp -rf backends/fstar/*.fst* bin/backends/fstar/
+	cp -rf backends/coq/*.v bin/backends/coq/
 
 .PHONY: doc
 doc:
@@ -85,13 +88,13 @@ clean:
 
 # Test the project by translating test files to F*
 .PHONY: tests
-tests: trans-no_nested_borrows trans-paper \
-	trans-hashmap trans-hashmap_main \
-	trans-external trans-constants \
-	transp-polonius_list transp-betree_main \
-	test-transp-betree_main \
-	trans-loops \
-	trans-array # TODO: generalize to all backends
+tests: test-no_nested_borrows test-paper \
+	test-hashmap test-hashmap_main \
+	test-external test-constants \
+	testp-polonius_list testp-betree_main \
+	ctest-testp-betree_main \
+	test-loops \
+	test-array test-traits # TODO: generalize to all backends
 
 # Verify the F* files generated by the translation
 .PHONY: verify
@@ -114,51 +117,65 @@ AENEAS_CMD = $(AENEAS_EXE) $(CHARON_TEST_DIR)/llbc/$(FILE).llbc -dest tests/$(BA
 
 
 # Add specific options to some tests
-trans-no_nested_borrows trans-paper: \
-	OPTIONS += -test-units -test-trans-units -no-split-files -no-state
-trans-no_nested_borrows trans-paper: SUBDIR := misc
+test-no_nested_borrows test-paper: \
+	OPTIONS += -test-trans-units
+test-no_nested_borrows test-paper: SUBDIR := misc
 tfstar-no_nested_borrows tfstar-paper:
 tlean-no_nested_borrows: SUBDIR :=
 tlean-paper: SUBDIR :=
 thol4-no_nested_borrows: SUBDIR := misc-no_nested_borrows
 thol4-paper: SUBDIR := misc-paper
 
-trans-array: OPTIONS += -no-state
-trans-array: SUBDIR := array
-tfstar-array: OPTIONS += -decreases-clauses -template-clauses
+test-array: OPTIONS +=
+test-array: SUBDIR := array
+tfstar-array: OPTIONS += -decreases-clauses -template-clauses -split-files
 tcoq-array: OPTIONS += -use-fuel
 tlean-array: SUBDIR :=
 tlean-array: OPTIONS +=
 thol4-array: OPTIONS +=
 
+test-traits: OPTIONS +=
+test-traits: SUBDIR := traits
+tfstar-traits: OPTIONS += -decreases-clauses -template-clauses
+tcoq-traits: OPTIONS +=
+tlean-traits: SUBDIR :=
+tlean-traits: OPTIONS +=
+thol4-traits: OPTIONS +=
+
 # TODO: activate the arrays for all the backends
 thol4-array:
 	echo "Ignoring the array test for HOL4"
 
-trans-loops: OPTIONS += -no-state
-trans-loops: SUBDIR := misc
-tfstar-loops: OPTIONS += -decreases-clauses -template-clauses
-tcoq-loops: OPTIONS += -use-fuel -no-split-files
+# TODO: activate the traits for all the backends
+thol4-traits:
+	echo "Ignoring the traits test for HOL4"
+
+test-loops: OPTIONS +=
+test-loops: SUBDIR := misc
+tfstar-loops: OPTIONS += -decreases-clauses -template-clauses -split-files
+tcoq-loops: OPTIONS += -use-fuel
 tlean-loops: SUBDIR :=
 thol4-loops: SUBDIR := misc-loops
 
-trans-hashmap: OPTIONS += -no-state -test-trans-units
-trans-hashmap: SUBDIR := hashmap
+# TODO: reactivate -test-trans-units
+test-hashmap: OPTIONS += -split-files
+test-hashmap: SUBDIR := hashmap
 tfstar-hashmap: OPTIONS += -decreases-clauses -template-clauses
 tcoq-hashmap: OPTIONS += -use-fuel
 tlean-hashmap: SUBDIR :=
 tlean-hashmap: OPTIONS += -no-gen-lib-entry # We add a custom import in the Hashmap.lean file: we do not want to overwrite it
 thol4-hashmap: OPTIONS +=
 
-trans-hashmap_main: OPTIONS += -test-trans-units
-trans-hashmap_main: SUBDIR := hashmap_on_disk
+# TODO: reactivate -test-trans-units
+test-hashmap_main: OPTIONS += -state -split-files
+test-hashmap_main: SUBDIR := hashmap_on_disk
 tfstar-hashmap_main: OPTIONS += -decreases-clauses -template-clauses
 tcoq-hashmap_main: OPTIONS += -use-fuel
 tlean-hashmap_main: SUBDIR :=
 thol4-hashmap_main: OPTIONS +=
 
-transp-polonius_list: OPTIONS += -test-units -test-trans-units -no-split-files -no-state
-transp-polonius_list: SUBDIR := misc
+testp-polonius_list: OPTIONS += -test-trans-units
+testp-polonius_list: SUBDIR := misc
 tfstarp-polonius_list: OPTIONS +=
 tcoqp-polonius_list: OPTIONS +=
 tleanp-polonius_list: SUBDIR :=
@@ -166,8 +183,8 @@ tleanp-polonius_list: OPTIONS +=
 thol4p-polonius_list: SUBDIR := misc-polonius_list
 thol4p-polonius_list: OPTIONS +=
 
-trans-constants: OPTIONS += -test-units -test-trans-units -no-split-files -no-state
-trans-constants: SUBDIR := misc
+test-constants: OPTIONS += -test-trans-units
+test-constants: SUBDIR := misc
 tfstar-constants: OPTIONS +=
 tcoq-constants: OPTIONS +=
 tlean-constants: SUBDIR :=
@@ -175,8 +192,8 @@ tlean-constants: OPTIONS +=
 thol4-constants: SUBDIR := misc-constants
 thol4-constants: OPTIONS +=
 
-trans-external: OPTIONS += -test-trans-units
-trans-external: SUBDIR := misc
+test-external: OPTIONS += -test-trans-units -state -split-files
+test-external: SUBDIR := misc
 tfstar-external: OPTIONS +=
 tcoq-external: OPTIONS +=
 tlean-external: SUBDIR :=
@@ -185,25 +202,25 @@ thol4-external: SUBDIR := misc-external
 thol4-external: OPTIONS +=
 
 BETREE_FSTAR_OPTIONS = -decreases-clauses -template-clauses
-transp-betree_main: OPTIONS += -backward-no-state-update -test-trans-units
-transp-betree_main: SUBDIR:=betree
+testp-betree_main: OPTIONS += -backward-no-state-update -test-trans-units -state -split-files
+testp-betree_main: SUBDIR:=betree
 tfstarp-betree_main: OPTIONS += $(BETREE_FSTAR_OPTIONS)
 tcoqp-betree_main: OPTIONS += -use-fuel
 tleanp-betree_main: SUBDIR :=
 tleanp-betree_main: OPTIONS +=
 thol4-betree_main: OPTIONS +=
 
-# Additional test on the betree: translate it without `-backward-no-state-update`.
+# Additional, *c*ustom test on the betree: translate it without `-backward-no-state-update`.
 # This generates very ugly code, but is good to test the translation.
-.PHONY: test-transp-betree_main
-test-transp-betree_main: transp-betree_main
-test-transp-betree_main: OPTIONS += -backend fstar -test-trans-units
-test-transp-betree_main: OPTIONS += $(BETREE_FSTAR_OPTIONS)
-test-transp-betree_main: BACKEND_SUBDIR := "fstar"
-test-transp-betree_main: SUBDIR:=betree_back_stateful
-test-transp-betree_main: CHARON_TEST_DIR = $(CHARON_TESTS_POLONIUS_DIR)
-test-transp-betree_main: FILE = betree_main
-test-transp-betree_main:
+.PHONY: ctest-testp-betree_main
+ctest-testp-betree_main: testp-betree_main
+ctest-testp-betree_main: OPTIONS += -backend fstar -test-trans-units -state -split-files
+ctest-testp-betree_main: OPTIONS += $(BETREE_FSTAR_OPTIONS)
+ctest-testp-betree_main: BACKEND_SUBDIR := "fstar"
+ctest-testp-betree_main: SUBDIR:=betree_back_stateful
+ctest-testp-betree_main: CHARON_TEST_DIR = $(CHARON_TESTS_POLONIUS_DIR)
+ctest-testp-betree_main: FILE = betree_main
+ctest-testp-betree_main:
 	$(AENEAS_CMD)
 
 # Generic rules to extract the LLBC from a rust file
@@ -220,20 +237,20 @@ gen-llbcp-%: CHARON_TEST_DIR = $(CHARON_TESTS_POLONIUS_DIR)
 gen-llbcp-%:
 	$(CHARON_CMD)
 
-# Generic rules to test the translation of an LLBC file.
+# Generic rules to test the testlation of an LLBC file.
 # Note that the files requiring the Polonius borrow-checker are generated
 # in the tests-polonius subdirectory.
-.PHONY: trans-%
-trans-%: CHARON_TEST_DIR = $(CHARON_TESTS_REGULAR_DIR)
-trans-%: FILE = $*
-trans-%: gen-llbc-% tfstar-% tcoq-% tlean-% thol4-%
+.PHONY: test-%
+test-%: CHARON_TEST_DIR = $(CHARON_TESTS_REGULAR_DIR)
+test-%: FILE = $*
+test-%: gen-llbc-% tfstar-% tcoq-% tlean-% thol4-%
 	echo "# Test $* done"
 
 # "p" stands for "Polonius"
-.PHONY: transp-%
-transp-%: CHARON_TEST_DIR = $(CHARON_TESTS_POLONIUS_DIR)
-transp-%: FILE = $*
-transp-%: gen-llbcp-% tfstarp-% tcoqp-% tleanp-% thol4p-%
+.PHONY: testp-%
+testp-%: CHARON_TEST_DIR = $(CHARON_TESTS_POLONIUS_DIR)
+testp-%: FILE = $*
+testp-%: gen-llbcp-% tfstarp-% tcoqp-% tleanp-% thol4p-%
 	echo "# Test $* done"
 
 .PHONY: tfstar-%
@@ -276,17 +293,25 @@ tleanp-%: BACKEND_SUBDIR := lean
 tleanp-%:
 	$(AENEAS_CMD)
 
+# TODO: reactivate HOL4 once traits are parameterized by their associated types
 .PHONY: thol4-%
 thol4-%: OPTIONS += -backend hol4
 thol4-%: BACKEND_SUBDIR := hol4
 thol4-%:
-	$(AENEAS_CMD)
+	echo Ignoring the $* test for HOL4
 
+#thol4-%:
+#	$(AENEAS_CMD)
+
+# TODO: reactivate HOL4 once traits are parameterized by their associated types
 .PHONY: thol4p-%
 thol4p-%: OPTIONS += -backend hol4
 thol4p-%: BACKEND_SUBDIR := hol4
 thol4p-%:
-	$(AENEAS_CMD)
+	echo Ignoring the $* test for HOL4
+
+#thol4p-%:
+#	$(AENEAS_CMD)
 
 # Nix - TODO: add the lean tests
 .PHONY: nix
diff --git a/backends/coq/Primitives.v b/backends/coq/Primitives.v
index 71a2d9c3..85e38f01 100644
--- a/backends/coq/Primitives.v
+++ b/backends/coq/Primitives.v
@@ -63,13 +63,15 @@ Check (if true then Return (1 + 2) else Fail_ Failure)%global = 3.
 
 (*** Misc *)
 
-
 Definition string := Coq.Strings.String.string.
 Definition char := Coq.Strings.Ascii.ascii.
 Definition char_of_byte := Coq.Strings.Ascii.ascii_of_byte.
 
-Definition mem_replace_fwd (a : Type) (x : a) (y : a) : a := x .
-Definition mem_replace_back (a : Type) (x : a) (y : a) : a := y .
+Definition core_mem_replace (a : Type) (x : a) (y : a) : a := x .
+Definition core_mem_replace_back (a : Type) (x : a) (y : a) : a := y .
+
+Record mut_raw_ptr (T : Type) := { mut_raw_ptr_v : T }.
+Record const_raw_ptr (T : Type) := { const_raw_ptr_v : T }.
 
 (*** Scalars *)
 
@@ -394,12 +396,89 @@ Notation "x s< y" := (scalar_ltb x y)  (at level 80) : Primitives_scope.
 Notation "x s>= y" := (scalar_geb x y)  (at level 80) : Primitives_scope.
 Notation "x s> y" := (scalar_gtb x y)  (at level 80) : Primitives_scope.
 
-(*** Range *)
-Record range (T : Type) := mk_range {
-  start: T;
-  end_: T;
+(** Constants *)
+Definition core_u8_max    := u8_max %u32.
+Definition core_u16_max   := u16_max %u32.
+Definition core_u32_max   := u32_max %u32.
+Definition core_u64_max   := u64_max %u64.
+Definition core_u128_max  := u64_max %u128.
+Axiom core_usize_max : usize. (** TODO *)
+Definition core_i8_max    := i8_max %i32.
+Definition core_i16_max   := i16_max %i32.
+Definition core_i32_max   := i32_max %i32.
+Definition core_i64_max   := i64_max %i64.
+Definition core_i128_max  := i64_max %i128.
+Axiom core_isize_max : isize. (** TODO *)
+
+(*** core::ops *)
+
+(* Trait declaration: [core::ops::index::Index] *)
+Record core_ops_index_Index (Self Idx : Type) := mk_core_ops_index_Index {
+  core_ops_index_Index_Output : Type;
+  core_ops_index_Index_index : Self -> Idx -> result core_ops_index_Index_Output;
+}.
+Arguments mk_core_ops_index_Index {_ _}.
+Arguments core_ops_index_Index_Output {_ _}.
+Arguments core_ops_index_Index_index {_ _}.
+
+(* Trait declaration: [core::ops::index::IndexMut] *)
+Record core_ops_index_IndexMut (Self Idx : Type) := mk_core_ops_index_IndexMut {
+  core_ops_index_IndexMut_indexInst : core_ops_index_Index Self Idx;
+  core_ops_index_IndexMut_index_mut : Self -> Idx -> result core_ops_index_IndexMut_indexInst.(core_ops_index_Index_Output);
+  core_ops_index_IndexMut_index_mut_back : Self -> Idx -> core_ops_index_IndexMut_indexInst.(core_ops_index_Index_Output) -> result Self;
+}.
+Arguments mk_core_ops_index_IndexMut {_ _}.
+Arguments core_ops_index_IndexMut_indexInst {_ _}.
+Arguments core_ops_index_IndexMut_index_mut {_ _}.
+Arguments core_ops_index_IndexMut_index_mut_back {_ _}.
+
+(* Trait declaration [core::ops::deref::Deref] *)
+Record core_ops_deref_Deref (Self : Type) := mk_core_ops_deref_Deref {
+  core_ops_deref_Deref_target : Type;
+  core_ops_deref_Deref_deref : Self -> result core_ops_deref_Deref_target;
+}.
+Arguments mk_core_ops_deref_Deref {_}.
+Arguments core_ops_deref_Deref_target {_}.
+Arguments core_ops_deref_Deref_deref {_}.
+
+(* Trait declaration [core::ops::deref::DerefMut] *)
+Record core_ops_deref_DerefMut (Self : Type) := mk_core_ops_deref_DerefMut {
+  core_ops_deref_DerefMut_derefInst : core_ops_deref_Deref Self;
+  core_ops_deref_DerefMut_deref_mut : Self -> result core_ops_deref_DerefMut_derefInst.(core_ops_deref_Deref_target);
+  core_ops_deref_DerefMut_deref_mut_back : Self -> core_ops_deref_DerefMut_derefInst.(core_ops_deref_Deref_target) -> result Self;
 }.
-Arguments mk_range {_}.
+Arguments mk_core_ops_deref_DerefMut {_}.
+Arguments core_ops_deref_DerefMut_derefInst {_}.
+Arguments core_ops_deref_DerefMut_deref_mut {_}.
+Arguments core_ops_deref_DerefMut_deref_mut_back {_}.
+
+Record core_ops_range_Range (T : Type) := mk_core_ops_range_Range {
+  core_ops_range_Range_start : T;
+  core_ops_range_Range_end_ : T;
+}.
+Arguments mk_core_ops_range_Range {_}.
+Arguments core_ops_range_Range_start {_}.
+Arguments core_ops_range_Range_end_ {_}.
+
+(*** [alloc] *)
+
+Definition alloc_boxed_Box_deref (T : Type) (x : T) : result T := Return x.
+Definition alloc_boxed_Box_deref_mut (T : Type) (x : T) : result T := Return x.
+Definition alloc_boxed_Box_deref_mut_back (T : Type) (_ : T) (x : T) : result T := Return x.
+
+(* Trait instance *)
+Definition alloc_boxed_Box_coreOpsDerefInst (Self : Type) : core_ops_deref_Deref Self := {|
+  core_ops_deref_Deref_target := Self;
+  core_ops_deref_Deref_deref := alloc_boxed_Box_deref Self;
+|}.
+
+(* Trait instance *)
+Definition alloc_boxed_Box_coreOpsDerefMutInst (Self : Type) : core_ops_deref_DerefMut Self := {|
+  core_ops_deref_DerefMut_derefInst := alloc_boxed_Box_coreOpsDerefInst Self;
+  core_ops_deref_DerefMut_deref_mut := alloc_boxed_Box_deref_mut Self;
+  core_ops_deref_DerefMut_deref_mut_back := alloc_boxed_Box_deref_mut_back Self;
+|}.
+
 
 (*** Arrays *)
 Definition array T (n : usize) := { l: list T | Z.of_nat (length l) = to_Z n}.
@@ -419,51 +498,50 @@ Qed.
 (* TODO: finish the definitions *)
 Axiom mk_array : forall (T : Type) (n : usize) (l : list T), array T n.
 
-Axiom array_index_shared : forall (T : Type) (n : usize) (x : array T n) (i : usize), result T.
-Axiom array_index_mut_fwd : forall (T : Type) (n : usize) (x : array T n) (i : usize), result T.
-Axiom array_index_mut_back : forall (T : Type) (n : usize) (x : array T n) (i : usize) (nx : T), result (array T n).
+(* For initialization *)
+Axiom array_repeat : forall (T : Type) (n : usize) (x : T), array T n.
+
+Axiom array_index_usize : forall (T : Type) (n : usize) (x : array T n) (i : usize), result T.
+Axiom array_update_usize : forall (T : Type) (n : usize) (x : array T n) (i : usize) (nx : T), result (array T n).
 
 (*** Slice *)
 Definition slice T := { l: list T | Z.of_nat (length l) <= usize_max}.
 
 Axiom slice_len : forall (T : Type) (s : slice T), usize.
-Axiom slice_index_shared : forall (T : Type) (x : slice T) (i : usize), result T.
-Axiom slice_index_mut_fwd : forall (T : Type) (x : slice T) (i : usize), result T.
-Axiom slice_index_mut_back : forall (T : Type) (x : slice T) (i : usize) (nx : T), result (slice T).
+Axiom slice_index_usize : forall (T : Type) (x : slice T) (i : usize), result T.
+Axiom slice_update_usize : forall (T : Type) (x : slice T) (i : usize) (nx : T), result (slice T).
 
 (*** Subslices *)
 
-Axiom array_to_slice_shared : forall (T : Type) (n : usize) (x : array T n), result (slice T).
-Axiom array_to_slice_mut_fwd : forall (T : Type) (n : usize) (x : array T n), result (slice T).
-Axiom array_to_slice_mut_back : forall (T : Type) (n : usize) (x : array T n) (s : slice T), result (array T n).
+Axiom array_to_slice : forall (T : Type) (n : usize) (x : array T n), result (slice T).
+Axiom array_from_slice : forall (T : Type) (n : usize) (x : array T n) (s : slice T), result (array T n).
+
+Axiom array_subslice: forall (T : Type) (n : usize) (x : array T n) (r : core_ops_range_Range usize), result (slice T).
+Axiom array_update_subslice: forall (T : Type) (n : usize) (x : array T n) (r : core_ops_range_Range usize) (ns : slice T), result (array T n).
 
-Axiom array_subslice_shared: forall (T : Type) (n : usize) (x : array T n) (r : range usize), result (slice T).
-Axiom array_subslice_mut_fwd: forall (T : Type) (n : usize) (x : array T n) (r : range usize), result (slice T).
-Axiom array_subslice_mut_back: forall (T : Type) (n : usize) (x : array T n) (r : range usize) (ns : slice T), result (array T n).
-Axiom slice_subslice_shared: forall (T : Type) (x : slice T) (r : range usize), result (slice T).
-Axiom slice_subslice_mut_fwd: forall (T : Type) (x : slice T) (r : range usize), result (slice T).
-Axiom slice_subslice_mut_back: forall (T : Type) (x : slice T) (r : range usize) (ns : slice T), result (slice T).
+Axiom slice_subslice: forall (T : Type) (x : slice T) (r : core_ops_range_Range usize), result (slice T).
+Axiom slice_update_subslice: forall (T : Type) (x : slice T) (r : core_ops_range_Range usize) (ns : slice T), result (slice T).
 
 (*** Vectors *)
 
-Definition vec T := { l: list T | Z.of_nat (length l) <= usize_max }.
+Definition alloc_vec_Vec T := { l: list T | Z.of_nat (length l) <= usize_max }.
 
-Definition vec_to_list {T: Type} (v: vec T) : list T := proj1_sig v.
+Definition alloc_vec_Vec_to_list {T: Type} (v: alloc_vec_Vec T) : list T := proj1_sig v.
 
-Definition vec_length {T: Type} (v: vec T) : Z := Z.of_nat (length (vec_to_list v)).
+Definition alloc_vec_Vec_length {T: Type} (v: alloc_vec_Vec T) : Z := Z.of_nat (length (alloc_vec_Vec_to_list v)).
 
-Definition vec_new (T: Type) : vec T := (exist _ [] le_0_usize_max).
+Definition alloc_vec_Vec_new (T: Type) : alloc_vec_Vec T := (exist _ [] le_0_usize_max).
 
-Lemma vec_len_in_usize {T} (v: vec T) : usize_min <= vec_length v <= usize_max.
+Lemma alloc_vec_Vec_len_in_usize {T} (v: alloc_vec_Vec T) : usize_min <= alloc_vec_Vec_length v <= usize_max.
 Proof.
-  unfold vec_length, usize_min.
+  unfold alloc_vec_Vec_length, usize_min.
   split.
   - lia.
   - apply (proj2_sig v).
 Qed.
 
-Definition vec_len (T: Type) (v: vec T) : usize :=
-  exist _ (vec_length v) (vec_len_in_usize v).
+Definition alloc_vec_Vec_len (T: Type) (v: alloc_vec_Vec T) : usize :=
+  exist _ (alloc_vec_Vec_length v) (alloc_vec_Vec_len_in_usize v).
 
 Fixpoint list_update {A} (l: list A) (n: nat) (a: A)
   : list A :=
@@ -474,50 +552,271 @@ Fixpoint list_update {A} (l: list A) (n: nat) (a: A)
     | S m => x :: (list_update t m a)
 end end.
 
-Definition vec_bind {A B} (v: vec A) (f: list A -> result (list B)) : result (vec B) :=
-  l <- f (vec_to_list v) ;
+Definition alloc_vec_Vec_bind {A B} (v: alloc_vec_Vec A) (f: list A -> result (list B)) : result (alloc_vec_Vec B) :=
+  l <- f (alloc_vec_Vec_to_list v) ;
   match sumbool_of_bool (scalar_le_max Usize (Z.of_nat (length l))) with
   | left H => Return (exist _ l (scalar_le_max_valid _ _ H))
   | right _ => Fail_ Failure
   end.
 
 (* The **forward** function shouldn't be used *)
-Definition vec_push_fwd (T: Type) (v: vec T) (x: T) : unit := tt.
+Definition alloc_vec_Vec_push_fwd (T: Type) (v: alloc_vec_Vec T) (x: T) : unit := tt.
 
-Definition vec_push_back (T: Type) (v: vec T) (x: T) : result (vec T) :=
-  vec_bind v (fun l => Return (l ++ [x])).
+Definition alloc_vec_Vec_push (T: Type) (v: alloc_vec_Vec T) (x: T) : result (alloc_vec_Vec T) :=
+  alloc_vec_Vec_bind v (fun l => Return (l ++ [x])).
 
 (* The **forward** function shouldn't be used *)
-Definition vec_insert_fwd (T: Type) (v: vec T) (i: usize) (x: T) : result unit :=
-  if to_Z i <? vec_length v then Return tt else Fail_ Failure.
+Definition alloc_vec_Vec_insert_fwd (T: Type) (v: alloc_vec_Vec T) (i: usize) (x: T) : result unit :=
+  if to_Z i <? alloc_vec_Vec_length v then Return tt else Fail_ Failure.
 
-Definition vec_insert_back (T: Type) (v: vec T) (i: usize) (x: T) : result (vec T) :=
-  vec_bind v (fun l =>
+Definition alloc_vec_Vec_insert (T: Type) (v: alloc_vec_Vec T) (i: usize) (x: T) : result (alloc_vec_Vec T) :=
+  alloc_vec_Vec_bind v (fun l =>
     if to_Z i <? Z.of_nat (length l)
     then Return (list_update l (usize_to_nat i) x)
     else Fail_ Failure).
 
-(* The **backward** function shouldn't be used *)
-Definition vec_index_fwd (T: Type) (v: vec T) (i: usize) : result T :=
-  match nth_error (vec_to_list v) (usize_to_nat i) with
-  | Some n => Return n
-  | None   => Fail_ Failure
-  end.
-
-Definition vec_index_back (T: Type) (v: vec T) (i: usize) (x: T) : result unit :=
-  if to_Z i <? vec_length v then Return tt else Fail_ Failure.
-
-(* The **backward** function shouldn't be used *)
-Definition vec_index_mut_fwd (T: Type) (v: vec T) (i: usize) : result T :=
-  match nth_error (vec_to_list v) (usize_to_nat i) with
-  | Some n => Return n
-  | None   => Fail_ Failure
+(* Helper *)
+Axiom alloc_vec_Vec_index_usize : forall {T : Type} (v : alloc_vec_Vec T) (i : usize) (x : T), result T.
+
+(* Helper *)
+Axiom alloc_vec_Vec_update_usize : forall {T : Type} (v : alloc_vec_Vec T) (i : usize) (x : T), result (alloc_vec_Vec T).
+
+(* Trait declaration: [core::slice::index::private_slice_index::Sealed] *)
+Definition core_slice_index_private_slice_index_Sealed (self : Type) := unit.
+
+(* Trait declaration: [core::slice::index::SliceIndex] *)
+Record core_slice_index_SliceIndex (Self T : Type) := mk_core_slice_index_SliceIndex {
+  core_slice_index_SliceIndex_sealedInst : core_slice_index_private_slice_index_Sealed Self;
+  core_slice_index_SliceIndex_Output : Type;
+  core_slice_index_SliceIndex_get : Self -> T -> result (option core_slice_index_SliceIndex_Output);
+  core_slice_index_SliceIndex_get_mut : Self -> T -> result (option core_slice_index_SliceIndex_Output);
+  core_slice_index_SliceIndex_get_mut_back : Self -> T -> option core_slice_index_SliceIndex_Output -> result T;
+  core_slice_index_SliceIndex_get_unchecked : Self -> const_raw_ptr T -> result (const_raw_ptr core_slice_index_SliceIndex_Output);
+  core_slice_index_SliceIndex_get_unchecked_mut : Self -> mut_raw_ptr T -> result (mut_raw_ptr core_slice_index_SliceIndex_Output);
+  core_slice_index_SliceIndex_index : Self -> T -> result core_slice_index_SliceIndex_Output;
+  core_slice_index_SliceIndex_index_mut : Self -> T -> result core_slice_index_SliceIndex_Output;
+  core_slice_index_SliceIndex_index_mut_back : Self -> T -> core_slice_index_SliceIndex_Output -> result T;
+}.
+Arguments mk_core_slice_index_SliceIndex {_ _}.
+Arguments core_slice_index_SliceIndex_sealedInst {_ _}.
+Arguments core_slice_index_SliceIndex_Output {_ _}.
+Arguments core_slice_index_SliceIndex_get {_ _}.
+Arguments core_slice_index_SliceIndex_get_mut {_ _}.
+Arguments core_slice_index_SliceIndex_get_mut_back {_ _}.
+Arguments core_slice_index_SliceIndex_get_unchecked {_ _}.
+Arguments core_slice_index_SliceIndex_get_unchecked_mut {_ _}.
+Arguments core_slice_index_SliceIndex_index {_ _}.
+Arguments core_slice_index_SliceIndex_index_mut {_ _}.
+Arguments core_slice_index_SliceIndex_index_mut_back {_ _}.
+
+(* [core::slice::index::[T]::index]: forward function *)
+Definition core_slice_index_Slice_index
+  (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T))
+  (s : slice T) (i : Idx) : result inst.(core_slice_index_SliceIndex_Output) :=
+  x <- inst.(core_slice_index_SliceIndex_get) i s;
+  match x with
+  | None => Fail_ Failure
+  | Some x => Return x
   end.
 
-Definition vec_index_mut_back (T: Type) (v: vec T) (i: usize) (x: T) : result (vec T) :=
-  vec_bind v (fun l =>
-    if to_Z i <? Z.of_nat (length l)
-    then Return (list_update l (usize_to_nat i) x)
-    else Fail_ Failure).
+(* [core::slice::index::Range:::get]: forward function *)
+Axiom core_slice_index_Range_get : forall (T : Type) (i : core_ops_range_Range usize) (s : slice T), result (option (slice T)).
+
+(* [core::slice::index::Range::get_mut]: forward function *)
+Axiom core_slice_index_Range_get_mut :
+  forall (T : Type), core_ops_range_Range usize -> slice T -> result (option (slice T)).
+
+(* [core::slice::index::Range::get_mut]: backward function 0 *)
+Axiom core_slice_index_Range_get_mut_back :
+  forall (T : Type), core_ops_range_Range usize -> slice T -> option (slice T) -> result (slice T).
+
+(* [core::slice::index::Range::get_unchecked]: forward function *)
+Definition core_slice_index_Range_get_unchecked
+  (T : Type) :
+  core_ops_range_Range usize -> const_raw_ptr (slice T) -> result (const_raw_ptr (slice T)) :=
+  (* Don't know what the model should be - for now we always fail to make
+     sure code which uses it fails *)
+  fun _ _ => Fail_ Failure.
+
+(* [core::slice::index::Range::get_unchecked_mut]: forward function *)
+Definition core_slice_index_Range_get_unchecked_mut
+  (T : Type) :
+  core_ops_range_Range usize -> mut_raw_ptr (slice T) -> result (mut_raw_ptr (slice T)) :=
+  (* Don't know what the model should be - for now we always fail to make
+    sure code which uses it fails *)
+  fun _ _ => Fail_ Failure.
+
+(* [core::slice::index::Range::index]: forward function *)
+Axiom core_slice_index_Range_index :
+  forall (T : Type), core_ops_range_Range usize -> slice T -> result (slice T).
+
+(* [core::slice::index::Range::index_mut]: forward function *)
+Axiom core_slice_index_Range_index_mut :
+  forall (T : Type), core_ops_range_Range usize -> slice T -> result (slice T).
+
+(* [core::slice::index::Range::index_mut]: backward function 0 *)
+Axiom core_slice_index_Range_index_mut_back :
+  forall (T : Type), core_ops_range_Range usize -> slice T -> slice T -> result (slice T).
+
+(* [core::slice::index::[T]::index_mut]: forward function *)
+Axiom core_slice_index_Slice_index_mut :
+  forall (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T)),
+  slice T -> Idx -> result inst.(core_slice_index_SliceIndex_Output).
+
+(* [core::slice::index::[T]::index_mut]: backward function 0 *)
+Axiom core_slice_index_Slice_index_mut_back :
+  forall (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T)),
+  slice T -> Idx -> inst.(core_slice_index_SliceIndex_Output) -> result (slice T).
+
+(* [core::array::[T; N]::index]: forward function *)
+Axiom core_array_Array_index :
+  forall (T Idx : Type) (N : usize) (inst : core_ops_index_Index (slice T) Idx)
+  (a : array T N) (i : Idx), result inst.(core_ops_index_Index_Output).
+
+(* [core::array::[T; N]::index_mut]: forward function *)
+Axiom core_array_Array_index_mut :
+  forall (T Idx : Type) (N : usize) (inst : core_ops_index_IndexMut (slice T) Idx)
+  (a : array T N) (i : Idx), result inst.(core_ops_index_IndexMut_indexInst).(core_ops_index_Index_Output).
+
+(* [core::array::[T; N]::index_mut]: backward function 0 *)
+Axiom core_array_Array_index_mut_back :
+  forall (T Idx : Type) (N : usize) (inst : core_ops_index_IndexMut (slice T) Idx)
+  (a : array T N) (i : Idx) (x : inst.(core_ops_index_IndexMut_indexInst).(core_ops_index_Index_Output)), result (array T N).
+
+(* Trait implementation: [core::slice::index::[T]] *)
+Definition core_slice_index_Slice_coreopsindexIndexInst (T Idx : Type)
+  (inst : core_slice_index_SliceIndex Idx (slice T)) :
+  core_ops_index_Index (slice T) Idx := {|
+  core_ops_index_Index_Output := inst.(core_slice_index_SliceIndex_Output);
+  core_ops_index_Index_index := core_slice_index_Slice_index T Idx inst;
+|}.
+
+(* Trait implementation: [core::slice::index::private_slice_index::Range] *)
+Definition core_slice_index_private_slice_index_Range_coresliceindexprivate_slice_indexSealedInst
+  : core_slice_index_private_slice_index_Sealed (core_ops_range_Range usize) := tt.
+
+(* Trait implementation: [core::slice::index::Range] *)
+Definition core_slice_index_Range_coresliceindexSliceIndexInst (T : Type) :
+  core_slice_index_SliceIndex (core_ops_range_Range usize) (slice T) := {|
+  core_slice_index_SliceIndex_sealedInst := core_slice_index_private_slice_index_Range_coresliceindexprivate_slice_indexSealedInst;
+  core_slice_index_SliceIndex_Output := slice T;
+  core_slice_index_SliceIndex_get := core_slice_index_Range_get T;
+  core_slice_index_SliceIndex_get_mut := core_slice_index_Range_get_mut T;
+  core_slice_index_SliceIndex_get_mut_back := core_slice_index_Range_get_mut_back T;
+  core_slice_index_SliceIndex_get_unchecked := core_slice_index_Range_get_unchecked T;
+  core_slice_index_SliceIndex_get_unchecked_mut := core_slice_index_Range_get_unchecked_mut T;
+  core_slice_index_SliceIndex_index := core_slice_index_Range_index T;
+  core_slice_index_SliceIndex_index_mut := core_slice_index_Range_index_mut T;
+  core_slice_index_SliceIndex_index_mut_back := core_slice_index_Range_index_mut_back T;
+|}.
+
+(* Trait implementation: [core::slice::index::[T]] *)
+Definition core_slice_index_Slice_coreopsindexIndexMutInst (T Idx : Type)
+  (inst : core_slice_index_SliceIndex Idx (slice T)) :
+  core_ops_index_IndexMut (slice T) Idx := {|
+  core_ops_index_IndexMut_indexInst := core_slice_index_Slice_coreopsindexIndexInst T Idx inst;
+  core_ops_index_IndexMut_index_mut := core_slice_index_Slice_index_mut T Idx inst;
+  core_ops_index_IndexMut_index_mut_back := core_slice_index_Slice_index_mut_back T Idx inst;
+|}.
+
+(* Trait implementation: [core::array::[T; N]] *)
+Definition core_array_Array_coreopsindexIndexInst (T Idx : Type) (N : usize)
+  (inst : core_ops_index_Index (slice T) Idx) :
+  core_ops_index_Index (array T N) Idx := {|
+  core_ops_index_Index_Output := inst.(core_ops_index_Index_Output);
+  core_ops_index_Index_index := core_array_Array_index T Idx N inst;
+|}.
+
+(* Trait implementation: [core::array::[T; N]] *)
+Definition core_array_Array_coreopsindexIndexMutInst (T Idx : Type) (N : usize)
+  (inst : core_ops_index_IndexMut (slice T) Idx) :
+  core_ops_index_IndexMut (array T N) Idx := {|
+  core_ops_index_IndexMut_indexInst := core_array_Array_coreopsindexIndexInst T Idx N inst.(core_ops_index_IndexMut_indexInst);
+  core_ops_index_IndexMut_index_mut := core_array_Array_index_mut T Idx N inst;
+  core_ops_index_IndexMut_index_mut_back := core_array_Array_index_mut_back T Idx N inst;
+|}.
+
+(* [core::slice::index::usize::get]: forward function *)
+Axiom core_slice_index_usize_get : forall (T : Type), usize -> slice T -> result (option T).
+
+(* [core::slice::index::usize::get_mut]: forward function *)
+Axiom core_slice_index_usize_get_mut : forall (T : Type), usize -> slice T -> result (option T).
+
+(* [core::slice::index::usize::get_mut]: backward function 0 *)
+Axiom core_slice_index_usize_get_mut_back :
+  forall (T : Type), usize -> slice T -> option T -> result (slice T).
+
+(* [core::slice::index::usize::get_unchecked]: forward function *)
+Axiom core_slice_index_usize_get_unchecked :
+  forall (T : Type), usize -> const_raw_ptr (slice T) -> result (const_raw_ptr T).
+
+(* [core::slice::index::usize::get_unchecked_mut]: forward function *)
+Axiom core_slice_index_usize_get_unchecked_mut :
+  forall (T : Type), usize -> mut_raw_ptr (slice T) -> result (mut_raw_ptr T).
+
+(* [core::slice::index::usize::index]: forward function *)
+Axiom core_slice_index_usize_index : forall (T : Type), usize -> slice T -> result T.
+
+(* [core::slice::index::usize::index_mut]: forward function *)
+Axiom core_slice_index_usize_index_mut : forall (T : Type), usize -> slice T -> result T.
+
+(* [core::slice::index::usize::index_mut]: backward function 0 *)
+Axiom core_slice_index_usize_index_mut_back :
+  forall (T : Type), usize -> slice T -> T -> result (slice T).
+
+(* Trait implementation: [core::slice::index::private_slice_index::usize] *)
+Definition core_slice_index_private_slice_index_usize_coresliceindexprivate_slice_indexSealedInst
+  : core_slice_index_private_slice_index_Sealed usize := tt.
+
+(* Trait implementation: [core::slice::index::usize] *)
+Definition core_slice_index_usize_coresliceindexSliceIndexInst (T : Type) :
+  core_slice_index_SliceIndex usize (slice T) := {|
+  core_slice_index_SliceIndex_sealedInst := core_slice_index_private_slice_index_usize_coresliceindexprivate_slice_indexSealedInst;
+  core_slice_index_SliceIndex_Output := T;
+  core_slice_index_SliceIndex_get := core_slice_index_usize_get T;
+  core_slice_index_SliceIndex_get_mut := core_slice_index_usize_get_mut T;
+  core_slice_index_SliceIndex_get_mut_back := core_slice_index_usize_get_mut_back T;
+  core_slice_index_SliceIndex_get_unchecked := core_slice_index_usize_get_unchecked T;
+  core_slice_index_SliceIndex_get_unchecked_mut := core_slice_index_usize_get_unchecked_mut T;
+  core_slice_index_SliceIndex_index := core_slice_index_usize_index T;
+  core_slice_index_SliceIndex_index_mut := core_slice_index_usize_index_mut T;
+  core_slice_index_SliceIndex_index_mut_back := core_slice_index_usize_index_mut_back T;
+|}.
+
+(* [alloc::vec::Vec::index]: forward function *)
+Axiom alloc_vec_Vec_index : forall (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T))
+  (Self : alloc_vec_Vec T) (i : Idx), result inst.(core_slice_index_SliceIndex_Output).
+
+(* [alloc::vec::Vec::index_mut]: forward function *)
+Axiom alloc_vec_Vec_index_mut : forall (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T))
+  (Self : alloc_vec_Vec T) (i : Idx), result inst.(core_slice_index_SliceIndex_Output).
+
+(* [alloc::vec::Vec::index_mut]: backward function 0 *)
+Axiom alloc_vec_Vec_index_mut_back :
+  forall (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T))
+  (Self : alloc_vec_Vec T) (i : Idx) (x : inst.(core_slice_index_SliceIndex_Output)), result (alloc_vec_Vec T).
+
+(* Trait implementation: [alloc::vec::Vec] *)
+Definition alloc_vec_Vec_coreopsindexIndexInst (T Idx : Type)
+  (inst : core_slice_index_SliceIndex Idx (slice T)) :
+  core_ops_index_Index (alloc_vec_Vec T) Idx := {|
+  core_ops_index_Index_Output := inst.(core_slice_index_SliceIndex_Output);
+  core_ops_index_Index_index := alloc_vec_Vec_index T Idx inst;
+|}.
+
+(* Trait implementation: [alloc::vec::Vec] *)
+Definition alloc_vec_Vec_coreopsindexIndexMutInst (T Idx : Type)
+  (inst : core_slice_index_SliceIndex Idx (slice T)) :
+  core_ops_index_IndexMut (alloc_vec_Vec T) Idx := {|
+  core_ops_index_IndexMut_indexInst := alloc_vec_Vec_coreopsindexIndexInst T Idx inst;
+  core_ops_index_IndexMut_index_mut := alloc_vec_Vec_index_mut T Idx inst;
+  core_ops_index_IndexMut_index_mut_back := alloc_vec_Vec_index_mut_back T Idx inst;
+|}.
+
+(*** Theorems *)
+
+Axiom alloc_vec_Vec_index_mut_back_eq : forall {a : Type} (v : alloc_vec_Vec a) (i : usize) (x : a),
+  alloc_vec_Vec_index_mut_back a usize (core_slice_index_usize_coresliceindexSliceIndexInst a) v i x =
+    alloc_vec_Vec_update_usize v i x.
 
 End Primitives.
diff --git a/backends/fstar/Primitives.fst b/backends/fstar/Primitives.fst
index 9db82069..3297803c 100644
--- a/backends/fstar/Primitives.fst
+++ b/backends/fstar/Primitives.fst
@@ -55,8 +55,12 @@ type string = string
 let is_zero (n: nat) : bool = n = 0
 let decrease (n: nat{n > 0}) : nat = n - 1
 
-let mem_replace_fwd (a : Type0) (x : a) (y : a) : a = x
-let mem_replace_back (a : Type0) (x : a) (y : a) : a = y
+let core_mem_replace (a : Type0) (x : a) (y : a) : a = x
+let core_mem_replace_back (a : Type0) (x : a) (y : a) : a = y
+
+// We don't really use raw pointers for now
+type mut_raw_ptr (t : Type0) = { v : t }
+type const_raw_ptr (t : Type0) = { v : t }
 
 (*** Scalars *)
 /// Rem.: most of the following code was partially generated
@@ -100,6 +104,11 @@ type scalar_ty =
 | U64
 | U128
 
+let is_unsigned = function
+  | Isize | I8 | I16 | I32 | I64 | I128 -> false
+  | Usize | U8 | U16 | U32 | U64 | U128 -> true
+
+
 let scalar_min (ty : scalar_ty) : int =
   match ty with
   | Isize -> isize_min
@@ -162,6 +171,15 @@ let scalar_sub (#ty : scalar_ty) (x : scalar ty) (y : scalar ty) : result (scala
 let scalar_mul (#ty : scalar_ty) (x : scalar ty) (y : scalar ty) : result (scalar ty) =
   mk_scalar ty (x * y)
 
+let scalar_lxor (#ty : scalar_ty { is_unsigned ty && ty <> Usize })
+    (x : scalar ty) (y : scalar ty) : scalar ty =
+  match ty with
+  | U8 -> FStar.UInt.logxor #8 x y
+  | U16 -> FStar.UInt.logxor #16 x y
+  | U32 -> FStar.UInt.logxor #32 x y
+  | U64 -> FStar.UInt.logxor #64 x y
+  | U128 -> FStar.UInt.logxor #128 x y
+
 (** Cast an integer from a [src_ty] to a [tgt_ty] *)
 // TODO: check the semantics of casts in Rust
 let scalar_cast (src_ty : scalar_ty) (tgt_ty : scalar_ty) (x : scalar src_ty) : result (scalar tgt_ty) =
@@ -169,17 +187,44 @@ let scalar_cast (src_ty : scalar_ty) (tgt_ty : scalar_ty) (x : scalar src_ty) :
 
 /// The scalar types
 type isize : eqtype = scalar Isize
-type i8 : eqtype = scalar I8
-type i16 : eqtype = scalar I16
-type i32 : eqtype = scalar I32
-type i64 : eqtype = scalar I64
-type i128 : eqtype = scalar I128
+type i8    : eqtype = scalar I8
+type i16   : eqtype = scalar I16
+type i32   : eqtype = scalar I32
+type i64   : eqtype = scalar I64
+type i128  : eqtype = scalar I128
 type usize : eqtype = scalar Usize
-type u8 : eqtype = scalar U8
-type u16 : eqtype = scalar U16
-type u32 : eqtype = scalar U32
-type u64 : eqtype = scalar U64
-type u128 : eqtype = scalar U128
+type u8    : eqtype = scalar U8
+type u16   : eqtype = scalar U16
+type u32   : eqtype = scalar U32
+type u64   : eqtype = scalar U64
+type u128  : eqtype = scalar U128
+
+
+let core_isize_min : isize = isize_min
+let core_isize_max : isize = isize_max
+let core_i8_min    : i8 = i8_min
+let core_i8_max    : i8 = i8_max
+let core_i16_min   : i16 = i16_min
+let core_i16_max   : i16 = i16_max
+let core_i32_min   : i32 = i32_min
+let core_i32_max   : i32 = i32_max
+let core_i64_min   : i64 = i64_min
+let core_i64_max   : i64 = i64_max
+let core_i128_min  : i128 = i128_min
+let core_i128_max  : i128 = i128_max
+
+let core_usize_min : usize = usize_min
+let core_usize_max : usize = usize_max
+let core_u8_min    : u8 = u8_min
+let core_u8_max    : u8 = u8_max
+let core_u16_min   : u16 = u16_min
+let core_u16_max   : u16 = u16_max
+let core_u32_min   : u32 = u32_min
+let core_u32_max   : u32 = u32_max
+let core_u64_min   : u64 = u64_min
+let core_u64_max   : u64 = u64_max
+let core_u128_min  : u128 = u128_min
+let core_u128_max  : u128 = u128_max
 
 /// Negation
 let isize_neg = scalar_neg #Isize
@@ -231,7 +276,7 @@ let u32_add = scalar_add #U32
 let u64_add = scalar_add #U64
 let u128_add = scalar_add #U128
 
-/// Substraction
+/// Subtraction
 let isize_sub = scalar_sub #Isize
 let i8_sub = scalar_sub #I8
 let i16_sub = scalar_sub #I16
@@ -259,12 +304,65 @@ let u32_mul = scalar_mul #U32
 let u64_mul = scalar_mul #U64
 let u128_mul = scalar_mul #U128
 
-(*** Range *)
-type range (a : Type0) = {
+/// Logical operators, defined for unsigned types only, so far
+let u8_xor = scalar_lxor #U8
+let u16_xor = scalar_lxor #U16
+let u32_xor = scalar_lxor #U32
+let u64_xor = scalar_lxor #U64
+let u128_xor = scalar_lxor #U128
+
+(*** core::ops *)
+
+// Trait declaration: [core::ops::index::Index]
+noeq type core_ops_index_Index (self idx : Type0) = {
+  output : Type0;
+  index : self → idx → result output
+}
+
+// Trait declaration: [core::ops::index::IndexMut]
+noeq type core_ops_index_IndexMut (self idx : Type0) = {
+  indexInst : core_ops_index_Index self idx;
+  index_mut : self → idx → result indexInst.output;
+  index_mut_back : self → idx → indexInst.output → result self;
+}
+
+// Trait declaration [core::ops::deref::Deref]
+noeq type core_ops_deref_Deref (self : Type0) = {
+  target : Type0;
+  deref : self → result target;
+}
+
+// Trait declaration [core::ops::deref::DerefMut]
+noeq type core_ops_deref_DerefMut (self : Type0) = {
+  derefInst : core_ops_deref_Deref self;
+  deref_mut : self → result derefInst.target;
+  deref_mut_back : self → derefInst.target → result self;
+}
+
+type core_ops_range_Range (a : Type0) = {
   start : a;
   end_ : a;
 }
 
+(*** [alloc] *)
+
+let alloc_boxed_Box_deref (t : Type0) (x : t) : result t = Return x
+let alloc_boxed_Box_deref_mut (t : Type0) (x : t) : result t = Return x
+let alloc_boxed_Box_deref_mut_back (t : Type) (_ : t) (x : t) : result t = Return x
+
+// Trait instance
+let alloc_boxed_Box_coreOpsDerefInst (self : Type0) : core_ops_deref_Deref self = {
+  target = self;
+  deref = alloc_boxed_Box_deref self;
+}
+
+// Trait instance
+let alloc_boxed_Box_coreOpsDerefMutInst (self : Type0) : core_ops_deref_DerefMut self = {
+  derefInst = alloc_boxed_Box_coreOpsDerefInst self;
+  deref_mut = alloc_boxed_Box_deref_mut self;
+  deref_mut_back = alloc_boxed_Box_deref_mut_back self;
+}
+
 (*** Array *)
 type array (a : Type0) (n : usize) = s:list a{length s = n}
 
@@ -278,15 +376,11 @@ let mk_array (a : Type0) (n : usize)
   normalize_term_spec (FStar.List.Tot.length l);
   l
 
-let array_index_shared (a : Type0) (n : usize) (x : array a n) (i : usize) : result a =
-  if i < length x then Return (index x i)
-  else Fail Failure
-
-let array_index_mut_fwd (a : Type0) (n : usize) (x : array a n) (i : usize) : result a =
+let array_index_usize (a : Type0) (n : usize) (x : array a n) (i : usize) : result a =
   if i < length x then Return (index x i)
   else Fail Failure
 
-let array_index_mut_back (a : Type0) (n : usize) (x : array a n) (i : usize) (nx : a) : result (array a n) =
+let array_update_usize (a : Type0) (n : usize) (x : array a n) (i : usize) (nx : a) : result (array a n) =
   if i < length x then Return (list_update x i nx)
   else Fail Failure
 
@@ -295,55 +389,54 @@ type slice (a : Type0) = s:list a{length s <= usize_max}
 
 let slice_len (a : Type0) (s : slice a) : usize = length s
 
-let slice_index_shared (a : Type0) (x : slice a) (i : usize) : result a =
+let slice_index_usize (a : Type0) (x : slice a) (i : usize) : result a =
   if i < length x then Return (index x i)
   else Fail Failure
 
-let slice_index_mut_fwd (a : Type0) (x : slice a) (i : usize) : result a =
-  if i < length x then Return (index x i)
-  else Fail Failure
-
-let slice_index_mut_back (a : Type0) (x : slice a) (i : usize) (nx : a) : result (slice a) =
+let slice_update_usize (a : Type0) (x : slice a) (i : usize) (nx : a) : result (slice a) =
   if i < length x then Return (list_update x i nx)
   else Fail Failure
 
 (*** Subslices *)
 
-let array_to_slice_shared (a : Type0) (n : usize) (x : array a n) : result (slice a) = Return x
-let array_to_slice_mut_fwd (a : Type0) (n : usize) (x : array a n) : result (slice a) = Return x
-let array_to_slice_mut_back (a : Type0) (n : usize) (x : array a n) (s : slice a) : result (array a n) =
+let array_to_slice (a : Type0) (n : usize) (x : array a n) : result (slice a) = Return x
+let array_from_slice (a : Type0) (n : usize) (x : array a n) (s : slice a) : result (array a n) =
   if length s = n then Return s
   else Fail Failure
 
 // TODO: finish the definitions below (there lacks [List.drop] and [List.take] in the standard library *)
-let array_subslice_shared (a : Type0) (n : usize) (x : array a n) (r : range usize) : result (slice a) =
-  admit()
-
-let array_subslice_mut_fwd (a : Type0) (n : usize) (x : array a n) (r : range usize) : result (slice a) =
+let array_subslice (a : Type0) (n : usize) (x : array a n) (r : core_ops_range_Range usize) : result (slice a) =
   admit()
 
-let array_subslice_mut_back (a : Type0) (n : usize) (x : array a n) (r : range usize) (ns : slice a) : result (array a n) =
+let array_update_subslice (a : Type0) (n : usize) (x : array a n) (r : core_ops_range_Range usize) (ns : slice a) : result (array a n) =
   admit()
 
-let slice_subslice_shared (a : Type0) (x : slice a) (r : range usize) : result (slice a) =
+let array_repeat (a : Type0) (n : usize) (x : a) : array a n =
   admit()
 
-let slice_subslice_mut_fwd (a : Type0) (x : slice a) (r : range usize) : result (slice a) =
+let slice_subslice (a : Type0) (x : slice a) (r : core_ops_range_Range usize) : result (slice a) =
   admit()
 
-let slice_subslice_mut_back (a : Type0) (x : slice a) (r : range usize) (ns : slice a) : result (slice a) =
+let slice_update_subslice (a : Type0) (x : slice a) (r : core_ops_range_Range usize) (ns : slice a) : result (slice a) =
   admit()
 
 (*** Vector *)
-type vec (a : Type0) = v:list a{length v <= usize_max}
+type alloc_vec_Vec (a : Type0) = v:list a{length v <= usize_max}
 
-let vec_new (a  : Type0) : vec a = assert_norm(length #a [] == 0); []
-let vec_len (a : Type0) (v : vec a) : usize = length v
+let alloc_vec_Vec_new (a  : Type0) : alloc_vec_Vec a = assert_norm(length #a [] == 0); []
+let alloc_vec_Vec_len (a : Type0) (v : alloc_vec_Vec a) : usize = length v
+
+// Helper
+let alloc_vec_Vec_index_usize (#a : Type0) (v : alloc_vec_Vec a) (i : usize) : result a =
+  if i < length v then Return (index v i) else Fail Failure
+// Helper
+let alloc_vec_Vec_update_usize (#a : Type0) (v : alloc_vec_Vec a) (i : usize) (x : a) : result (alloc_vec_Vec a) =
+  if i < length v then Return (list_update v i x) else Fail Failure
 
 // The **forward** function shouldn't be used
-let vec_push_fwd (a  : Type0) (v : vec a) (x : a) : unit = ()
-let vec_push_back (a  : Type0) (v : vec a) (x : a) :
-  Pure (result (vec a))
+let alloc_vec_Vec_push_fwd (a  : Type0) (v : alloc_vec_Vec a) (x : a) : unit = ()
+let alloc_vec_Vec_push (a  : Type0) (v : alloc_vec_Vec a) (x : a) :
+  Pure (result (alloc_vec_Vec a))
   (requires True)
   (ensures (fun res ->
     match res with
@@ -358,18 +451,279 @@ let vec_push_back (a  : Type0) (v : vec a) (x : a) :
   else Fail Failure
 
 // The **forward** function shouldn't be used
-let vec_insert_fwd (a : Type0) (v : vec a) (i : usize) (x : a) : result unit =
+let alloc_vec_Vec_insert_fwd (a : Type0) (v : alloc_vec_Vec a) (i : usize) (x : a) : result unit =
   if i < length v then Return () else Fail Failure
-let vec_insert_back (a : Type0) (v : vec a) (i : usize) (x : a) : result (vec a) =
+let alloc_vec_Vec_insert (a : Type0) (v : alloc_vec_Vec a) (i : usize) (x : a) : result (alloc_vec_Vec a) =
   if i < length v then Return (list_update v i x) else Fail Failure
 
-// The **backward** function shouldn't be used
-let vec_index_fwd (a : Type0) (v : vec a) (i : usize) : result a =
-  if i < length v then Return (index v i) else Fail Failure
-let vec_index_back (a : Type0) (v : vec a) (i : usize) (x : a) : result unit =
-  if i < length v then Return () else Fail Failure
+// Trait declaration: [core::slice::index::private_slice_index::Sealed]
+type core_slice_index_private_slice_index_Sealed (self : Type0) = unit
+
+// Trait declaration: [core::slice::index::SliceIndex]
+noeq type core_slice_index_SliceIndex (self t : Type0) = {
+  sealedInst : core_slice_index_private_slice_index_Sealed self;
+  output : Type0;
+  get : self → t → result (option output);
+  get_mut : self → t → result (option output);
+  get_mut_back : self → t → option output → result t;
+  get_unchecked : self → const_raw_ptr t → result (const_raw_ptr output);
+  get_unchecked_mut : self → mut_raw_ptr t → result (mut_raw_ptr output);
+  index : self → t → result output;
+  index_mut : self → t → result output;
+  index_mut_back : self → t → output → result t;
+}
 
-let vec_index_mut_fwd (a : Type0) (v : vec a) (i : usize) : result a =
-  if i < length v then Return (index v i) else Fail Failure
-let vec_index_mut_back (a : Type0) (v : vec a) (i : usize) (nx : a) : result (vec a) =
-  if i < length v then Return (list_update v i nx) else Fail Failure
+// [core::slice::index::[T]::index]: forward function
+let core_slice_index_Slice_index
+  (t idx : Type0) (inst : core_slice_index_SliceIndex idx (slice t))
+  (s : slice t) (i : idx) : result inst.output =
+  let* x = inst.get i s in
+  match x with
+  | None -> Fail Failure
+  | Some x -> Return x
+
+// [core::slice::index::Range:::get]: forward function
+let core_slice_index_Range_get (t : Type0) (i : core_ops_range_Range usize) (s : slice t) :
+  result (option (slice t)) =
+  admit () // TODO
+
+// [core::slice::index::Range::get_mut]: forward function
+let core_slice_index_Range_get_mut
+  (t : Type0) : core_ops_range_Range usize → slice t → result (option (slice t)) =
+  admit () // TODO
+
+// [core::slice::index::Range::get_mut]: backward function 0
+let core_slice_index_Range_get_mut_back
+  (t : Type0) :
+  core_ops_range_Range usize → slice t → option (slice t) → result (slice t) =
+  admit () // TODO
+
+// [core::slice::index::Range::get_unchecked]: forward function
+let core_slice_index_Range_get_unchecked
+  (t : Type0) :
+  core_ops_range_Range usize → const_raw_ptr (slice t) → result (const_raw_ptr (slice t)) =
+  // Don't know what the model should be - for now we always fail to make
+  // sure code which uses it fails
+  fun _ _ -> Fail Failure
+
+// [core::slice::index::Range::get_unchecked_mut]: forward function
+let core_slice_index_Range_get_unchecked_mut
+  (t : Type0) :
+  core_ops_range_Range usize → mut_raw_ptr (slice t) → result (mut_raw_ptr (slice t)) =
+  // Don't know what the model should be - for now we always fail to make
+  // sure code which uses it fails
+  fun _ _ -> Fail Failure
+
+// [core::slice::index::Range::index]: forward function
+let core_slice_index_Range_index
+  (t : Type0) : core_ops_range_Range usize → slice t → result (slice t) =
+  admit () // TODO
+
+// [core::slice::index::Range::index_mut]: forward function
+let core_slice_index_Range_index_mut
+  (t : Type0) : core_ops_range_Range usize → slice t → result (slice t) =
+  admit () // TODO
+
+// [core::slice::index::Range::index_mut]: backward function 0
+let core_slice_index_Range_index_mut_back
+  (t : Type0) : core_ops_range_Range usize → slice t → slice t → result (slice t) =
+  admit () // TODO
+
+// [core::slice::index::[T]::index_mut]: forward function
+let core_slice_index_Slice_index_mut
+  (t idx : Type0) (inst : core_slice_index_SliceIndex idx (slice t)) :
+  slice t → idx → result inst.output =
+  admit () // 
+
+// [core::slice::index::[T]::index_mut]: backward function 0
+let core_slice_index_Slice_index_mut_back
+  (t idx : Type0) (inst : core_slice_index_SliceIndex idx (slice t)) :
+  slice t → idx → inst.output → result (slice t) =
+  admit () // TODO
+
+// [core::array::[T; N]::index]: forward function
+let core_array_Array_index
+  (t idx : Type0) (n : usize) (inst : core_ops_index_Index (slice t) idx)
+  (a : array t n) (i : idx) : result inst.output =
+  admit () // TODO
+
+// [core::array::[T; N]::index_mut]: forward function
+let core_array_Array_index_mut
+  (t idx : Type0) (n : usize) (inst : core_ops_index_IndexMut (slice t) idx)
+  (a : array t n) (i : idx) : result inst.indexInst.output =
+  admit () // TODO
+
+// [core::array::[T; N]::index_mut]: backward function 0
+let core_array_Array_index_mut_back
+  (t idx : Type0) (n : usize) (inst : core_ops_index_IndexMut (slice t) idx)
+  (a : array t n) (i : idx) (x : inst.indexInst.output) : result (array t n) =
+  admit () // TODO
+
+// Trait implementation: [core::slice::index::[T]]
+let core_slice_index_Slice_coreopsindexIndexInst (t idx : Type0)
+  (inst : core_slice_index_SliceIndex idx (slice t)) :
+  core_ops_index_Index (slice t) idx = {
+  output = inst.output;
+  index = core_slice_index_Slice_index t idx inst;
+}
+
+// Trait implementation: [core::slice::index::private_slice_index::Range]
+let core_slice_index_private_slice_index_Range_coresliceindexprivate_slice_indexSealedInst
+  : core_slice_index_private_slice_index_Sealed (core_ops_range_Range usize) = ()
+
+// Trait implementation: [core::slice::index::Range]
+let core_slice_index_Range_coresliceindexSliceIndexInst (t : Type0) :
+  core_slice_index_SliceIndex (core_ops_range_Range usize) (slice t) = {
+  sealedInst = core_slice_index_private_slice_index_Range_coresliceindexprivate_slice_indexSealedInst;
+  output = slice t;
+  get = core_slice_index_Range_get t;
+  get_mut = core_slice_index_Range_get_mut t;
+  get_mut_back = core_slice_index_Range_get_mut_back t;
+  get_unchecked = core_slice_index_Range_get_unchecked t;
+  get_unchecked_mut = core_slice_index_Range_get_unchecked_mut t;
+  index = core_slice_index_Range_index t;
+  index_mut = core_slice_index_Range_index_mut t;
+  index_mut_back = core_slice_index_Range_index_mut_back t;
+}
+
+// Trait implementation: [core::slice::index::[T]]
+let core_slice_index_Slice_coreopsindexIndexMutInst (t idx : Type0)
+  (inst : core_slice_index_SliceIndex idx (slice t)) :
+  core_ops_index_IndexMut (slice t) idx = {
+  indexInst = core_slice_index_Slice_coreopsindexIndexInst t idx inst;
+  index_mut = core_slice_index_Slice_index_mut t idx inst;
+  index_mut_back = core_slice_index_Slice_index_mut_back t idx inst;
+}
+
+// Trait implementation: [core::array::[T; N]]
+let core_array_Array_coreopsindexIndexInst (t idx : Type0) (n : usize)
+  (inst : core_ops_index_Index (slice t) idx) :
+  core_ops_index_Index (array t n) idx = {
+  output = inst.output;
+  index = core_array_Array_index t idx n inst;
+}
+
+// Trait implementation: [core::array::[T; N]]
+let core_array_Array_coreopsindexIndexMutInst (t idx : Type0) (n : usize)
+  (inst : core_ops_index_IndexMut (slice t) idx) :
+  core_ops_index_IndexMut (array t n) idx = {
+  indexInst = core_array_Array_coreopsindexIndexInst t idx n inst.indexInst;
+  index_mut = core_array_Array_index_mut t idx n inst;
+  index_mut_back = core_array_Array_index_mut_back t idx n inst;
+}
+
+// [core::slice::index::usize::get]: forward function
+let core_slice_index_usize_get
+  (t : Type0) : usize → slice t → result (option t) =
+  admit () // TODO
+
+// [core::slice::index::usize::get_mut]: forward function
+let core_slice_index_usize_get_mut
+  (t : Type0) : usize → slice t → result (option t) =
+  admit () // TODO
+
+// [core::slice::index::usize::get_mut]: backward function 0
+let core_slice_index_usize_get_mut_back
+  (t : Type0) : usize → slice t → option t → result (slice t) =
+  admit () // TODO
+
+// [core::slice::index::usize::get_unchecked]: forward function
+let core_slice_index_usize_get_unchecked
+  (t : Type0) : usize → const_raw_ptr (slice t) → result (const_raw_ptr t) =
+  admit () // TODO
+
+// [core::slice::index::usize::get_unchecked_mut]: forward function
+let core_slice_index_usize_get_unchecked_mut
+  (t : Type0) : usize → mut_raw_ptr (slice t) → result (mut_raw_ptr t) =
+  admit () // TODO
+
+// [core::slice::index::usize::index]: forward function
+let core_slice_index_usize_index (t : Type0) : usize → slice t → result t =
+  admit () // TODO
+
+// [core::slice::index::usize::index_mut]: forward function
+let core_slice_index_usize_index_mut (t : Type0) : usize → slice t → result t =
+  admit () // TODO
+
+// [core::slice::index::usize::index_mut]: backward function 0
+let core_slice_index_usize_index_mut_back
+  (t : Type0) : usize → slice t → t → result (slice t) =
+  admit () // TODO
+
+// Trait implementation: [core::slice::index::private_slice_index::usize]
+let core_slice_index_private_slice_index_usize_coresliceindexprivate_slice_indexSealedInst
+  : core_slice_index_private_slice_index_Sealed usize = ()
+
+// Trait implementation: [core::slice::index::usize]
+let core_slice_index_usize_coresliceindexSliceIndexInst (t : Type0) :
+  core_slice_index_SliceIndex usize (slice t) = {
+  sealedInst = core_slice_index_private_slice_index_usize_coresliceindexprivate_slice_indexSealedInst;
+  output = t;
+  get = core_slice_index_usize_get t;
+  get_mut = core_slice_index_usize_get_mut t;
+  get_mut_back = core_slice_index_usize_get_mut_back t;
+  get_unchecked = core_slice_index_usize_get_unchecked t;
+  get_unchecked_mut = core_slice_index_usize_get_unchecked_mut t;
+  index = core_slice_index_usize_index t;
+  index_mut = core_slice_index_usize_index_mut t;
+  index_mut_back = core_slice_index_usize_index_mut_back t;
+}
+
+// [alloc::vec::Vec::index]: forward function
+let alloc_vec_Vec_index (t idx : Type0) (inst : core_slice_index_SliceIndex idx (slice t))
+  (self : alloc_vec_Vec t) (i : idx) : result inst.output =
+  admit () // TODO
+
+// [alloc::vec::Vec::index_mut]: forward function
+let alloc_vec_Vec_index_mut (t idx : Type0) (inst : core_slice_index_SliceIndex idx (slice t))
+  (self : alloc_vec_Vec t) (i : idx) : result inst.output =
+  admit () // TODO
+
+// [alloc::vec::Vec::index_mut]: backward function 0
+let alloc_vec_Vec_index_mut_back
+  (t idx : Type0) (inst : core_slice_index_SliceIndex idx (slice t))
+  (self : alloc_vec_Vec t) (i : idx) (x : inst.output) : result (alloc_vec_Vec t) =
+  admit () // TODO
+
+// Trait implementation: [alloc::vec::Vec]
+let alloc_vec_Vec_coreopsindexIndexInst (t idx : Type0)
+  (inst : core_slice_index_SliceIndex idx (slice t)) :
+  core_ops_index_Index (alloc_vec_Vec t) idx = {
+  output = inst.output;
+  index = alloc_vec_Vec_index t idx inst;
+}
+
+// Trait implementation: [alloc::vec::Vec]
+let alloc_vec_Vec_coreopsindexIndexMutInst (t idx : Type0)
+  (inst : core_slice_index_SliceIndex idx (slice t)) :
+  core_ops_index_IndexMut (alloc_vec_Vec t) idx = {
+  indexInst = alloc_vec_Vec_coreopsindexIndexInst t idx inst;
+  index_mut = alloc_vec_Vec_index_mut t idx inst;
+  index_mut_back = alloc_vec_Vec_index_mut_back t idx inst;
+}
+
+(*** Theorems *)
+
+let alloc_vec_Vec_index_eq (#a : Type0) (v : alloc_vec_Vec a) (i : usize) :
+  Lemma (
+    alloc_vec_Vec_index a usize (core_slice_index_usize_coresliceindexSliceIndexInst a) v i ==
+      alloc_vec_Vec_index_usize v i)
+  [SMTPat (alloc_vec_Vec_index a usize (core_slice_index_usize_coresliceindexSliceIndexInst a) v i)]
+  =
+  admit()
+
+let alloc_vec_Vec_index_mut_eq (#a : Type0) (v : alloc_vec_Vec a) (i : usize) :
+  Lemma (
+    alloc_vec_Vec_index_mut a usize (core_slice_index_usize_coresliceindexSliceIndexInst a) v i ==
+      alloc_vec_Vec_index_usize v i)
+  [SMTPat (alloc_vec_Vec_index_mut a usize (core_slice_index_usize_coresliceindexSliceIndexInst a) v i)]
+  =
+  admit()
+
+let alloc_vec_Vec_index_mut_back_eq (#a : Type0) (v : alloc_vec_Vec a) (i : usize) (x : a) :
+  Lemma (
+    alloc_vec_Vec_index_mut_back a usize (core_slice_index_usize_coresliceindexSliceIndexInst a) v i x ==
+      alloc_vec_Vec_update_usize v i x)
+  [SMTPat (alloc_vec_Vec_index_mut_back a usize (core_slice_index_usize_coresliceindexSliceIndexInst a) v i x)]
+  =
+  admit()
diff --git a/backends/hol4/primitivesScript.sml b/backends/hol4/primitivesScript.sml
index 82da4de9..916988be 100644
--- a/backends/hol4/primitivesScript.sml
+++ b/backends/hol4/primitivesScript.sml
@@ -555,6 +555,32 @@ Proof
 QED
 val _ = evalLib.add_unfold_thm "mk_isize_unfold"
 
+(** Constants *)
+val core_i8_min_def    = Define ‘core_i8_min     = int_to_i8 i8_min’
+val core_i8_max_def    = Define ‘core_i8_max     = int_to_i8 i8_max’
+val core_i16_min_def   = Define ‘core_i16_min    = int_to_i16 i16_min’
+val core_i16_max_def   = Define ‘core_i16_max    = int_to_i16 i16_max’
+val core_i32_min_def   = Define ‘core_i32_min    = int_to_i32 i32_min’
+val core_i32_max_def   = Define ‘core_i32_max    = int_to_i32 i32_max’
+val core_i64_min_def   = Define ‘core_i64_min    = int_to_i64 i64_min’
+val core_i64_max_def   = Define ‘core_i64_max    = int_to_i64 i64_max’
+val core_i128_min_def  = Define ‘core_i128_min   = int_to_i128 i128_min’
+val core_i128_max_def  = Define ‘core_i128_max   = int_to_i128 i128_max’
+val core_isize_min_def = Define ‘core_isize_min  = int_to_isize isize_min’
+val core_isize_max_def = Define ‘core_isize_max  = int_to_isize isize_max’
+val core_u8_min_def    = Define ‘core_u8_min     = int_to_u8 0’
+val core_u8_max_def    = Define ‘core_u8_max     = int_to_u8 u8_max’
+val core_u16_min_def   = Define ‘core_u16_min    = int_to_u16 0’
+val core_u16_max_def   = Define ‘core_u16_max    = int_to_u16 u16_max’
+val core_u32_min_def   = Define ‘core_u32_min    = int_to_u32 0’
+val core_u32_max_def   = Define ‘core_u32_max    = int_to_u32 u32_max’
+val core_u64_min_def   = Define ‘core_u64_min    = int_to_u64 0’
+val core_u64_max_def   = Define ‘core_u64_max    = int_to_u64 u64_max’
+val core_u128_min_def  = Define ‘core_u128_min   = int_to_u128 0’
+val core_u128_max_def  = Define ‘core_u128_max   = int_to_u128 u128_max’
+val core_usize_min_def = Define ‘core_usize_min  = int_to_usize 0’
+val core_usize_max_def = Define ‘core_usize_max  = int_to_usize usize_max’
+
 val isize_neg_def = Define ‘isize_neg x = mk_isize (- (isize_to_int x))’
 val i8_neg_def    = Define ‘i8_neg x    = mk_i8 (- (i8_to_int x))’
 val i16_neg_def   = Define ‘i16_neg x   = mk_i16 (- (i16_to_int x))’
diff --git a/backends/hol4/primitivesTheory.sig b/backends/hol4/primitivesTheory.sig
index 6660b02d..4ae6bb3e 100644
--- a/backends/hol4/primitivesTheory.sig
+++ b/backends/hol4/primitivesTheory.sig
@@ -46,6 +46,30 @@ sig
   
   (*  Definitions  *)
     val bind_def : thm
+    val core_i128_max_def : thm
+    val core_i128_min_def : thm
+    val core_i16_max_def : thm
+    val core_i16_min_def : thm
+    val core_i32_max_def : thm
+    val core_i32_min_def : thm
+    val core_i64_max_def : thm
+    val core_i64_min_def : thm
+    val core_i8_max_def : thm
+    val core_i8_min_def : thm
+    val core_isize_max_def : thm
+    val core_isize_min_def : thm
+    val core_u128_max_def : thm
+    val core_u128_min_def : thm
+    val core_u16_max_def : thm
+    val core_u16_min_def : thm
+    val core_u32_max_def : thm
+    val core_u32_min_def : thm
+    val core_u64_max_def : thm
+    val core_u64_min_def : thm
+    val core_u8_max_def : thm
+    val core_u8_min_def : thm
+    val core_usize_max_def : thm
+    val core_usize_min_def : thm
     val error_BIJ : thm
     val error_CASE : thm
     val error_TY_DEF : thm
@@ -566,6 +590,102 @@ sig
           monad_bind x f =
           case x of Return y => f y | Fail e => Fail e | Diverge => Diverge
    
+   [core_i128_max_def]  Definition
+      
+      ⊢ core_i128_max = int_to_i128 i128_max
+   
+   [core_i128_min_def]  Definition
+      
+      ⊢ core_i128_min = int_to_i128 i128_min
+   
+   [core_i16_max_def]  Definition
+      
+      ⊢ core_i16_max = int_to_i16 i16_max
+   
+   [core_i16_min_def]  Definition
+      
+      ⊢ core_i16_min = int_to_i16 i16_min
+   
+   [core_i32_max_def]  Definition
+      
+      ⊢ core_i32_max = int_to_i32 i32_max
+   
+   [core_i32_min_def]  Definition
+      
+      ⊢ core_i32_min = int_to_i32 i32_min
+   
+   [core_i64_max_def]  Definition
+      
+      ⊢ core_i64_max = int_to_i64 i64_max
+   
+   [core_i64_min_def]  Definition
+      
+      ⊢ core_i64_min = int_to_i64 i64_min
+   
+   [core_i8_max_def]  Definition
+      
+      ⊢ core_i8_max = int_to_i8 i8_max
+   
+   [core_i8_min_def]  Definition
+      
+      ⊢ core_i8_min = int_to_i8 i8_min
+   
+   [core_isize_max_def]  Definition
+      
+      ⊢ core_isize_max = int_to_isize isize_max
+   
+   [core_isize_min_def]  Definition
+      
+      ⊢ core_isize_min = int_to_isize isize_min
+   
+   [core_u128_max_def]  Definition
+      
+      ⊢ core_u128_max = int_to_u128 u128_max
+   
+   [core_u128_min_def]  Definition
+      
+      ⊢ core_u128_min = int_to_u128 0
+   
+   [core_u16_max_def]  Definition
+      
+      ⊢ core_u16_max = int_to_u16 u16_max
+   
+   [core_u16_min_def]  Definition
+      
+      ⊢ core_u16_min = int_to_u16 0
+   
+   [core_u32_max_def]  Definition
+      
+      ⊢ core_u32_max = int_to_u32 u32_max
+   
+   [core_u32_min_def]  Definition
+      
+      ⊢ core_u32_min = int_to_u32 0
+   
+   [core_u64_max_def]  Definition
+      
+      ⊢ core_u64_max = int_to_u64 u64_max
+   
+   [core_u64_min_def]  Definition
+      
+      ⊢ core_u64_min = int_to_u64 0
+   
+   [core_u8_max_def]  Definition
+      
+      ⊢ core_u8_max = int_to_u8 u8_max
+   
+   [core_u8_min_def]  Definition
+      
+      ⊢ core_u8_min = int_to_u8 0
+   
+   [core_usize_max_def]  Definition
+      
+      ⊢ core_usize_max = int_to_usize usize_max
+   
+   [core_usize_min_def]  Definition
+      
+      ⊢ core_usize_min = int_to_usize 0
+   
    [error_BIJ]  Definition
       
       ⊢ (∀a. num2error (error2num a) = a) ∧
diff --git a/backends/lean/Base/Arith/Base.lean b/backends/lean/Base/Arith/Base.lean
index 9c11ed45..8ada4171 100644
--- a/backends/lean/Base/Arith/Base.lean
+++ b/backends/lean/Base/Arith/Base.lean
@@ -57,4 +57,16 @@ theorem int_pos_ind (p : Int → Prop) :
 -- TODO: there is probably something more general to do
 theorem nat_zero_eq_int_zero : (0 : Nat) = (0 : Int) := by simp
 
+-- This is mostly used in termination proofs
+theorem to_int_to_nat_lt (x y : ℤ) (h0 : 0 ≤ x) (h1 : x < y) :
+  ↑(x.toNat) < y := by
+  simp [*]
+
+-- This is mostly used in termination proofs
+theorem to_int_sub_to_nat_lt (x y : ℤ) (x' : ℕ)
+  (h0 : ↑x' ≤ x) (h1 : x - ↑x' < y) :
+  ↑(x.toNat - x') < y := by
+  have : 0 ≤ x := by linarith
+  simp [Int.toNat_sub_of_le, *]
+
 end Arith
diff --git a/backends/lean/Base/Arith/Int.lean b/backends/lean/Base/Arith/Int.lean
index 3359ecdb..a57f8bb1 100644
--- a/backends/lean/Base/Arith/Int.lean
+++ b/backends/lean/Base/Arith/Int.lean
@@ -162,7 +162,7 @@ def introInstances (declToUnfold : Name) (lookup : Expr → MetaM (Option Expr))
     -- Add a declaration
     let nval ← Utils.addDeclTac name e type (asLet := false)
     -- Simplify to unfold the declaration to unfold (i.e., the projector)
-    Utils.simpAt [declToUnfold] [] [] (Tactic.Location.targets #[mkIdent name] false)
+    Utils.simpAt true [declToUnfold] [] [] (Location.targets #[mkIdent name] false)
     -- Return the new value
     pure nval
 
@@ -240,7 +240,7 @@ def intTac (splitGoalConjs : Bool) (extraPreprocess :  Tactic.TacticM Unit) : Ta
   -- the goal. I think before leads to a smaller proof term?
   Tactic.allGoals (intTacPreprocess extraPreprocess)
   -- More preprocessing
-  Tactic.allGoals (Utils.tryTac (Utils.simpAt [] [``nat_zero_eq_int_zero] [] .wildcard))
+  Tactic.allGoals (Utils.tryTac (Utils.simpAt true [] [``nat_zero_eq_int_zero] [] .wildcard))
   -- Split the conjunctions in the goal
   if splitGoalConjs then Tactic.allGoals (Utils.repeatTac Utils.splitConjTarget)
   -- Call linarith
@@ -270,6 +270,17 @@ elab "int_tac" args:(" split_goal"?): tactic =>
   let split := args.raw.getArgs.size > 0
   intTac split (do pure ())
 
+-- For termination proofs
+syntax "int_decr_tac" : tactic
+macro_rules
+  | `(tactic| int_decr_tac) =>
+    `(tactic|
+      simp_wf;
+      -- TODO: don't use a macro (namespace problems)
+      (first | apply Arith.to_int_to_nat_lt
+             | apply Arith.to_int_sub_to_nat_lt) <;>
+      simp_all <;> int_tac)
+
 example (x : Int) (h0: 0 ≤ x) (h1: x ≠ 0) : 0 < x := by
   int_tac_preprocess
   linarith
diff --git a/backends/lean/Base/Arith/Scalar.lean b/backends/lean/Base/Arith/Scalar.lean
index 47751c8a..2342cce6 100644
--- a/backends/lean/Base/Arith/Scalar.lean
+++ b/backends/lean/Base/Arith/Scalar.lean
@@ -17,7 +17,7 @@ def scalarTacExtraPreprocess : Tactic.TacticM Unit := do
    add (← mkAppM ``Scalar.cMax_bound #[.const ``ScalarTy.Usize []])
    add (← mkAppM ``Scalar.cMax_bound #[.const ``ScalarTy.Isize []])
    -- Reveal the concrete bounds, simplify calls to [ofInt]
-   Utils.simpAt [``Scalar.min, ``Scalar.max, ``Scalar.cMin, ``Scalar.cMax,
+   Utils.simpAt true [``Scalar.min, ``Scalar.max, ``Scalar.cMin, ``Scalar.cMax,
                  ``I8.min, ``I16.min, ``I32.min, ``I64.min, ``I128.min,
                  ``I8.max, ``I16.max, ``I32.max, ``I64.max, ``I128.max,
                  ``U8.min, ``U16.min, ``U32.min, ``U64.min, ``U128.min,
@@ -36,6 +36,17 @@ def scalarTac (splitGoalConjs : Bool) : Tactic.TacticM Unit := do
 elab "scalar_tac" : tactic =>
   scalarTac false
 
+-- For termination proofs
+syntax "scalar_decr_tac" : tactic
+macro_rules
+  | `(tactic| scalar_decr_tac) =>
+    `(tactic|
+      simp_wf;
+      -- TODO: don't use a macro (namespace problems)
+      (first | apply Arith.to_int_to_nat_lt
+             | apply Arith.to_int_sub_to_nat_lt) <;>
+      simp_all <;> scalar_tac)
+
 instance (ty : ScalarTy) : HasIntProp (Scalar ty) where
   -- prop_ty is inferred
   prop := λ x => And.intro x.hmin x.hmax
diff --git a/backends/lean/Base/IList/IList.lean b/backends/lean/Base/IList/IList.lean
index a940da25..f71f2de2 100644
--- a/backends/lean/Base/IList/IList.lean
+++ b/backends/lean/Base/IList/IList.lean
@@ -112,7 +112,13 @@ def pairwise_rel
 
 section Lemmas
 
-variable {α : Type u} 
+variable {α : Type u}
+
+def ireplicate {α : Type u} (i : ℤ) (x : α) : List α :=
+  if i ≤ 0 then []
+  else x :: ireplicate (i - 1) x
+termination_by ireplicate i x => i.toNat
+decreasing_by int_decr_tac
 
 @[simp] theorem update_nil : update ([] : List α) i y = [] := by simp [update]
 @[simp] theorem update_zero_cons : update ((x :: tl) : List α) 0 y = y :: tl := by simp [update]
@@ -129,6 +135,10 @@ variable {α : Type u}
 @[simp] theorem slice_nil : slice i j ([] : List α) = [] := by simp [slice]
 @[simp] theorem slice_zero : slice 0 0 (ls : List α) = [] := by cases ls <;> simp [slice]
 
+@[simp] theorem ireplicate_zero : ireplicate 0 x = [] := by rw [ireplicate]; simp
+@[simp] theorem ireplicate_nzero_cons (hne : 0 < i) : ireplicate i x = x :: ireplicate (i - 1) x := by
+  rw [ireplicate]; simp [*]; intro; linarith
+
 @[simp]
 theorem slice_nzero_cons (i j : Int) (x : α) (tl : List α) (hne : i ≠ 0) : slice i j ((x :: tl) : List α) = slice (i - 1) (j - 1) tl :=
   match tl with
@@ -144,6 +154,33 @@ theorem slice_nzero_cons (i j : Int) (x : α) (tl : List α) (hne : i ≠ 0) : s
         conv at this => lhs; simp [slice, *]
         simp [*, slice]
 
+@[simp]
+theorem ireplicate_replicate {α : Type u} (l : ℤ) (x : α) (h : 0 ≤ l) :
+  ireplicate l x = replicate l.toNat x :=
+  if hz: l = 0 then by
+    simp [*]
+  else by
+    have : 0 < l := by int_tac
+    have hr := ireplicate_replicate (l - 1) x (by int_tac)
+    simp [*]
+    have hl : l.toNat = .succ (l.toNat - 1) := by
+      cases hl: l.toNat <;> simp_all
+    conv => rhs; rw[hl]
+termination_by ireplicate_replicate l x h => l.toNat
+decreasing_by int_decr_tac
+
+@[simp]
+theorem ireplicate_len {α : Type u} (l : ℤ) (x : α) (h : 0 ≤ l) :
+  (ireplicate l x).len = l :=
+  if hz: l = 0 then by
+    simp [*]
+  else by
+    have : 0 < l := by int_tac
+    have hr := ireplicate_len (l - 1) x (by int_tac)
+    simp [*]
+termination_by ireplicate_len l x h => l.toNat
+decreasing_by int_decr_tac
+
 theorem len_eq_length (ls : List α) : ls.len = ls.length := by
   induction ls
   . rfl
diff --git a/backends/lean/Base/Primitives.lean b/backends/lean/Base/Primitives.lean
index 6b7b0792..613b6076 100644
--- a/backends/lean/Base/Primitives.lean
+++ b/backends/lean/Base/Primitives.lean
@@ -1,4 +1,6 @@
 import Base.Primitives.Base
 import Base.Primitives.Scalar
-import Base.Primitives.Array
+import Base.Primitives.ArraySlice
 import Base.Primitives.Vec
+import Base.Primitives.Alloc
+import Base.Primitives.CoreOps
diff --git a/backends/lean/Base/Primitives/Alloc.lean b/backends/lean/Base/Primitives/Alloc.lean
new file mode 100644
index 00000000..34590499
--- /dev/null
+++ b/backends/lean/Base/Primitives/Alloc.lean
@@ -0,0 +1,37 @@
+import Lean
+import Base.Primitives.Base
+import Base.Primitives.CoreOps
+
+open Primitives
+open Result
+
+namespace alloc
+
+namespace boxed -- alloc.boxed
+
+namespace Box -- alloc.boxed.Box
+
+def deref (T : Type) (x : T) : Result T := ret x
+def deref_mut (T : Type) (x : T) : Result T := ret x
+def deref_mut_back (T : Type) (_ : T) (x : T) : Result T := ret x
+
+/-- Trait instance -/
+def coreOpsDerefInst (Self : Type) :
+  core.ops.deref.Deref Self := {
+  Target := Self
+  deref := deref Self
+}
+
+/-- Trait instance -/
+def coreOpsDerefMutInst (Self : Type) :
+  core.ops.deref.DerefMut Self := {
+  derefInst := coreOpsDerefInst Self
+  deref_mut := deref_mut Self
+  deref_mut_back := deref_mut_back Self
+}
+
+end Box -- alloc.boxed.Box
+
+end boxed -- alloc.boxed
+
+end alloc
diff --git a/backends/lean/Base/Primitives/Array.lean b/backends/lean/Base/Primitives/Array.lean
deleted file mode 100644
index 6c95fd78..00000000
--- a/backends/lean/Base/Primitives/Array.lean
+++ /dev/null
@@ -1,394 +0,0 @@
-/- Arrays/slices -/
-import Lean
-import Lean.Meta.Tactic.Simp
-import Init.Data.List.Basic
-import Mathlib.Tactic.RunCmd
-import Mathlib.Tactic.Linarith
-import Base.IList
-import Base.Primitives.Scalar
-import Base.Primitives.Range
-import Base.Arith
-import Base.Progress.Base
-
-namespace Primitives
-
-open Result Error
-
-def Array (α : Type u) (n : Usize) := { l : List α // l.length = n.val }
-
-instance (a : Type u) (n : Usize) : Arith.HasIntProp (Array a n) where
-  prop_ty := λ v => v.val.len = n.val
-  prop := λ ⟨ _, l ⟩ => by simp[Scalar.max, List.len_eq_length, *]
-
-instance {α : Type u} {n : Usize} (p : Array α n → Prop) : Arith.HasIntProp (Subtype p) where
-  prop_ty := λ x => p x
-  prop := λ x => x.property
-
-@[simp]
-abbrev Array.length {α : Type u} {n : Usize} (v : Array α n) : Int := v.val.len
-
-@[simp]
-abbrev Array.v {α : Type u} {n : Usize} (v : Array α n) : List α := v.val
-
-example {α: Type u} {n : Usize} (v : Array α n) : v.length ≤ Scalar.max ScalarTy.Usize := by
-  scalar_tac
-
-def Array.make (α : Type u) (n : Usize) (init : List α) (hl : init.len = n.val := by decide) :
-  Array α n := ⟨ init, by simp [← List.len_eq_length]; apply hl ⟩
-
-example : Array Int (Usize.ofInt 2) := Array.make Int (Usize.ofInt 2) [0, 1]
-
-@[simp]
-abbrev Array.index {α : Type u} {n : Usize} [Inhabited α] (v : Array α n) (i : Int) : α :=
-  v.val.index i
-
-@[simp]
-abbrev Array.slice {α : Type u} {n : Usize} [Inhabited α] (v : Array α n) (i j : Int) : List α :=
-  v.val.slice i j
-
-def Array.index_shared (α : Type u) (n : Usize) (v: Array α n) (i: Usize) : Result α :=
-  match v.val.indexOpt i.val with
-  | none => fail .arrayOutOfBounds
-  | some x => ret x
-
-/- In the theorems below: we don't always need the `∃ ..`, but we use one
-   so that `progress` introduces an opaque variable and an equality. This
-   helps control the context.
- -/
-
-@[pspec]
-theorem Array.index_shared_spec {α : Type u} {n : Usize} [Inhabited α] (v: Array α n) (i: Usize)
-  (hbound : i.val < v.length) :
-  ∃ x, v.index_shared α n i = ret x ∧ x = v.val.index i.val := by
-  simp only [index_shared]
-  -- TODO: dependent rewrite
-  have h := List.indexOpt_eq_index v.val i.val (by scalar_tac) (by simp [*])
-  simp [*]
-
--- This shouldn't be used
-def Array.index_shared_back (α : Type u) (n : Usize) (v: Array α n) (i: Usize) (_: α) : Result Unit :=
-  if i.val < List.length v.val then
-    .ret ()
-  else
-    .fail arrayOutOfBounds
-
-def Array.index_mut (α : Type u) (n : Usize) (v: Array α n) (i: Usize) : Result α :=
-  match v.val.indexOpt i.val with
-  | none => fail .arrayOutOfBounds
-  | some x => ret x
-
-@[pspec]
-theorem Array.index_mut_spec {α : Type u} {n : Usize} [Inhabited α] (v: Array α n) (i: Usize)
-  (hbound : i.val < v.length) :
-  ∃ x, v.index_mut α n i = ret x ∧ x = v.val.index i.val := by
-  simp only [index_mut]
-  -- TODO: dependent rewrite
-  have h := List.indexOpt_eq_index v.val i.val (by scalar_tac) (by simp [*])
-  simp [*]
-
-def Array.index_mut_back (α : Type u) (n : Usize) (v: Array α n) (i: Usize) (x: α) : Result (Array α n) :=
-  match v.val.indexOpt i.val with
-  | none => fail .arrayOutOfBounds
-  | some _ =>
-    .ret ⟨ v.val.update i.val x, by have := v.property; simp [*] ⟩
-
-@[pspec]
-theorem Array.index_mut_back_spec {α : Type u} {n : Usize} (v: Array α n) (i: Usize) (x : α)
-  (hbound : i.val < v.length) :
-  ∃ nv, v.index_mut_back α n i x = ret nv ∧
-  nv.val = v.val.update i.val x
-  := by
-  simp only [index_mut_back]
-  have h := List.indexOpt_bounds v.val i.val
-  split
-  . simp_all [length]; cases h <;> scalar_tac
-  . simp_all
-
-def Slice (α : Type u) := { l : List α // l.length ≤ Usize.max }
-
-instance (a : Type u) : Arith.HasIntProp (Slice a) where
-  prop_ty := λ v => 0 ≤ v.val.len ∧ v.val.len ≤ Scalar.max ScalarTy.Usize
-  prop := λ ⟨ _, l ⟩ => by simp[Scalar.max, List.len_eq_length, *]
-
-instance {α : Type u} (p : Slice α → Prop) : Arith.HasIntProp (Subtype p) where
-  prop_ty := λ x => p x
-  prop := λ x => x.property
-
-@[simp]
-abbrev Slice.length {α : Type u} (v : Slice α) : Int := v.val.len
-
-@[simp]
-abbrev Slice.v {α : Type u} (v : Slice α) : List α := v.val
-
-example {a: Type u} (v : Slice a) : v.length ≤ Scalar.max ScalarTy.Usize := by
-  scalar_tac
-
-def Slice.new (α : Type u): Slice α := ⟨ [], by apply Scalar.cMax_suffices .Usize; simp ⟩
-
--- TODO: very annoying that the α is an explicit parameter
-def Slice.len (α : Type u) (v : Slice α) : Usize :=
-  Usize.ofIntCore v.val.len (by scalar_tac) (by scalar_tac)
-
-@[simp]
-theorem Slice.len_val {α : Type u} (v : Slice α) : (Slice.len α v).val = v.length :=
-  by rfl
-
-@[simp]
-abbrev Slice.index {α : Type u} [Inhabited α] (v: Slice α) (i: Int) : α :=
-  v.val.index i
-
-@[simp]
-abbrev Slice.slice {α : Type u} [Inhabited α] (s : Slice α) (i j : Int) : List α :=
-  s.val.slice i j
-
-def Slice.index_shared (α : Type u) (v: Slice α) (i: Usize) : Result α :=
-  match v.val.indexOpt i.val with
-  | none => fail .arrayOutOfBounds
-  | some x => ret x
-
-/- In the theorems below: we don't always need the `∃ ..`, but we use one
-   so that `progress` introduces an opaque variable and an equality. This
-   helps control the context.
- -/
-
-@[pspec]
-theorem Slice.index_shared_spec {α : Type u} [Inhabited α] (v: Slice α) (i: Usize)
-  (hbound : i.val < v.length) :
-  ∃ x, v.index_shared α i = ret x ∧ x = v.val.index i.val := by
-  simp only [index_shared]
-  -- TODO: dependent rewrite
-  have h := List.indexOpt_eq_index v.val i.val (by scalar_tac) (by simp [*])
-  simp [*]
-
--- This shouldn't be used
-def Slice.index_shared_back (α : Type u) (v: Slice α) (i: Usize) (_: α) : Result Unit :=
-  if i.val < List.length v.val then
-    .ret ()
-  else
-    .fail arrayOutOfBounds
-
-def Slice.index_mut (α : Type u) (v: Slice α) (i: Usize) : Result α :=
-  match v.val.indexOpt i.val with
-  | none => fail .arrayOutOfBounds
-  | some x => ret x
-
-@[pspec]
-theorem Slice.index_mut_spec {α : Type u} [Inhabited α] (v: Slice α) (i: Usize)
-  (hbound : i.val < v.length) :
-  ∃ x, v.index_mut α i = ret x ∧ x = v.val.index i.val := by
-  simp only [index_mut]
-  -- TODO: dependent rewrite
-  have h := List.indexOpt_eq_index v.val i.val (by scalar_tac) (by simp [*])
-  simp [*]
-
-def Slice.index_mut_back (α : Type u) (v: Slice α) (i: Usize) (x: α) : Result (Slice α) :=
-  match v.val.indexOpt i.val with
-  | none => fail .arrayOutOfBounds
-  | some _ =>
-    .ret ⟨ v.val.update i.val x, by have := v.property; simp [*] ⟩
-
-@[pspec]
-theorem Slice.index_mut_back_spec {α : Type u} (v: Slice α) (i: Usize) (x : α)
-  (hbound : i.val < v.length) :
-  ∃ nv, v.index_mut_back α i x = ret nv ∧
-  nv.val = v.val.update i.val x
-  := by
-  simp only [index_mut_back]
-  have h := List.indexOpt_bounds v.val i.val
-  split
-  . simp_all [length]; cases h <;> scalar_tac
-  . simp_all
-
-/- Array to slice/subslices -/
-
-/- We could make this function not use the `Result` type. By making it monadic, we
-   push the user to use the `Array.to_slice_shared_spec` spec theorem below (through the
-   `progress` tactic), meaning `Array.to_slice_shared` should be considered as opaque.
-   All what the spec theorem reveals is that the "representative" lists are the same. -/
-def Array.to_slice_shared (α : Type u) (n : Usize) (v : Array α n) : Result (Slice α) :=
-  ret ⟨ v.val, by simp [← List.len_eq_length]; scalar_tac ⟩
-
-@[pspec]
-theorem Array.to_slice_shared_spec {α : Type u} {n : Usize} (v : Array α n) :
-  ∃ s, to_slice_shared α n v = ret s ∧ v.val = s.val := by simp [to_slice_shared]
-
-def Array.to_slice_mut (α : Type u) (n : Usize) (v : Array α n) : Result (Slice α) :=
-  to_slice_shared α n v
-
-@[pspec]
-theorem Array.to_slice_mut_spec {α : Type u} {n : Usize} (v : Array α n) :
-  ∃ s, Array.to_slice_shared α n v = ret s ∧ v.val = s.val := to_slice_shared_spec v
-
-def Array.to_slice_mut_back (α : Type u) (n : Usize) (_ : Array α n) (s : Slice α) : Result (Array α n) :=
-  if h: s.val.len = n.val then
-    ret ⟨ s.val, by simp [← List.len_eq_length, *] ⟩
-  else fail panic
-
-@[pspec]
-theorem Array.to_slice_mut_back_spec {α : Type u} {n : Usize} (a : Array α n) (ns : Slice α) (h : ns.val.len = n.val) :
-  ∃ na, to_slice_mut_back α n a ns = ret na ∧ na.val = ns.val
-  := by simp [to_slice_mut_back, *]
-
-def Array.subslice_shared (α : Type u) (n : Usize) (a : Array α n) (r : Range Usize) : Result (Slice α) :=
-  -- TODO: not completely sure here
-  if r.start.val < r.end_.val ∧ r.end_.val ≤ a.val.len then
-    ret ⟨ a.val.slice r.start.val r.end_.val,
-          by
-            simp [← List.len_eq_length]
-            have := a.val.slice_len_le r.start.val r.end_.val
-            scalar_tac ⟩
-  else
-    fail panic
-
-@[pspec]
-theorem Array.subslice_shared_spec {α : Type u} {n : Usize} [Inhabited α] (a : Array α n) (r : Range Usize)
-  (h0 : r.start.val < r.end_.val) (h1 : r.end_.val ≤ a.val.len) :
-  ∃ s, subslice_shared α n a r = ret s ∧
-  s.val = a.val.slice r.start.val r.end_.val ∧
-  (∀ i, 0 ≤ i → i + r.start.val < r.end_.val → s.val.index i = a.val.index (r.start.val + i))
-  := by
-  simp [subslice_shared, *]
-  intro i _ _
-  have := List.index_slice r.start.val r.end_.val i a.val (by scalar_tac) (by scalar_tac) (by trivial) (by scalar_tac)
-  simp [*]
-
-def Array.subslice_mut (α : Type u) (n : Usize) (a : Array α n) (r : Range Usize) : Result (Slice α) :=
-  Array.subslice_shared α n a r
-
-@[pspec]
-theorem Array.subslice_mut_spec {α : Type u} {n : Usize} [Inhabited α] (a : Array α n) (r : Range Usize)
-  (h0 : r.start.val < r.end_.val) (h1 : r.end_.val ≤ a.val.len) :
-  ∃ s, subslice_mut α n a r = ret s ∧
-  s.val = a.slice r.start.val r.end_.val ∧
-  (∀ i, 0 ≤ i → i + r.start.val < r.end_.val → s.val.index i = a.val.index (r.start.val + i))
-  := subslice_shared_spec a r h0 h1
-
-def Array.subslice_mut_back (α : Type u) (n : Usize) (a : Array α n) (r : Range Usize) (s : Slice α) : Result (Array α n) :=
-  -- TODO: not completely sure here
-  if h: r.start.val < r.end_.val ∧ r.end_.val ≤ a.length ∧ s.val.len = r.end_.val - r.start.val then
-    let s_beg := a.val.itake r.start.val
-    let s_end := a.val.idrop r.end_.val
-    have : s_beg.len = r.start.val := by
-      apply List.itake_len
-      . simp_all; scalar_tac
-      . scalar_tac
-    have : s_end.len = a.val.len - r.end_.val := by
-      apply List.idrop_len
-      . scalar_tac
-      . scalar_tac
-    let na := s_beg.append (s.val.append s_end)
-    have : na.len = a.val.len := by simp [*]
-    ret ⟨ na, by simp_all [← List.len_eq_length]; scalar_tac ⟩
-  else
-    fail panic
-
--- TODO: it is annoying to write `.val` everywhere. We could leverage coercions,
--- but: some symbols like `+` are already overloaded to be notations for monadic
--- operations/
--- We should introduce special symbols for the monadic arithmetic operations
--- (the use will never write those symbols directly).
-@[pspec]
-theorem Array.subslice_mut_back_spec {α : Type u} {n : Usize} [Inhabited α] (a : Array α n) (r : Range Usize) (s : Slice α)
-  (_ : r.start.val < r.end_.val) (_ : r.end_.val ≤ a.length) (_ : s.length = r.end_.val - r.start.val) :
-  ∃ na, subslice_mut_back α n a r s = ret na ∧
-  (∀ i, 0 ≤ i → i < r.start.val → na.index i = a.index i) ∧
-  (∀ i, r.start.val ≤ i → i < r.end_.val → na.index i = s.index (i - r.start.val)) ∧
-  (∀ i, r.end_.val ≤ i → i < n.val → na.index i = a.index i) := by
-  simp [subslice_mut_back, *]
-  have h := List.replace_slice_index r.start.val r.end_.val a.val s.val
-    (by scalar_tac) (by scalar_tac) (by scalar_tac) (by scalar_tac)
-  simp [List.replace_slice] at h
-  have ⟨ h0, h1, h2 ⟩ := h
-  clear h
-  split_conjs
-  . intro i _ _
-    have := h0 i (by int_tac) (by int_tac)
-    simp [*]
-  . intro i _ _
-    have := h1 i (by int_tac) (by int_tac)
-    simp [*]
-  . intro i _ _
-    have := h2 i (by int_tac) (by int_tac)
-    simp [*]
-
-def Slice.subslice_shared (α : Type u) (s : Slice α) (r : Range Usize) : Result (Slice α) :=
-  -- TODO: not completely sure here
-  if r.start.val < r.end_.val ∧ r.end_.val ≤ s.length then
-    ret ⟨ s.val.slice r.start.val r.end_.val,
-          by
-            simp [← List.len_eq_length]
-            have := s.val.slice_len_le r.start.val r.end_.val
-            scalar_tac ⟩
-  else
-    fail panic
-
-@[pspec]
-theorem Slice.subslice_shared_spec {α : Type u} [Inhabited α] (s : Slice α) (r : Range Usize)
-  (h0 : r.start.val < r.end_.val) (h1 : r.end_.val ≤ s.val.len) :
-  ∃ ns, subslice_shared α s r = ret ns ∧
-  ns.val = s.slice r.start.val r.end_.val ∧
-  (∀ i, 0 ≤ i → i + r.start.val < r.end_.val → ns.index i = s.index (r.start.val + i))
-  := by
-  simp [subslice_shared, *]
-  intro i _ _
-  have := List.index_slice r.start.val r.end_.val i s.val (by scalar_tac) (by scalar_tac) (by trivial) (by scalar_tac)
-  simp [*]
-
-def Slice.subslice_mut (α : Type u) (s : Slice α) (r : Range Usize) : Result (Slice α) :=
-  Slice.subslice_shared α s r
-
-@[pspec]
-theorem Slice.subslice_mut_spec {α : Type u} [Inhabited α] (s : Slice α) (r : Range Usize)
-  (h0 : r.start.val < r.end_.val) (h1 : r.end_.val ≤ s.val.len) :
-  ∃ ns, subslice_mut α s r = ret ns ∧
-  ns.val = s.slice r.start.val r.end_.val ∧
-  (∀ i, 0 ≤ i → i + r.start.val < r.end_.val → ns.index i = s.index (r.start.val + i))
-  := subslice_shared_spec s r h0 h1
-
-attribute [pp_dot] List.len List.length List.index -- use the dot notation when printing
-set_option pp.coercions false -- do not print coercions with ↑ (this doesn't parse)
-
-def Slice.subslice_mut_back (α : Type u) (s : Slice α) (r : Range Usize) (ss : Slice α) : Result (Slice α) :=
-  -- TODO: not completely sure here
-  if h: r.start.val < r.end_.val ∧ r.end_.val ≤ s.length ∧ ss.val.len = r.end_.val - r.start.val then
-    let s_beg := s.val.itake r.start.val
-    let s_end := s.val.idrop r.end_.val
-    have : s_beg.len = r.start.val := by
-      apply List.itake_len
-      . simp_all; scalar_tac
-      . scalar_tac
-    have : s_end.len = s.val.len - r.end_.val := by
-      apply List.idrop_len
-      . scalar_tac
-      . scalar_tac
-    let ns := s_beg.append (ss.val.append s_end)
-    have : ns.len = s.val.len := by simp [*]
-    ret ⟨ ns, by simp_all [← List.len_eq_length]; scalar_tac ⟩
-  else
-    fail panic
-
-@[pspec]
-theorem Slice.subslice_mut_back_spec {α : Type u} [Inhabited α] (a : Slice α) (r : Range Usize) (ss : Slice α)
-  (_ : r.start.val < r.end_.val) (_ : r.end_.val ≤ a.length) (_ : ss.length = r.end_.val - r.start.val) :
-  ∃ na, subslice_mut_back α a r ss = ret na ∧
-  (∀ i, 0 ≤ i → i < r.start.val → na.index i = a.index i) ∧
-  (∀ i, r.start.val ≤ i → i < r.end_.val → na.index i = ss.index (i - r.start.val)) ∧
-  (∀ i, r.end_.val ≤ i → i < a.length → na.index i = a.index i) := by
-  simp [subslice_mut_back, *]
-  have h := List.replace_slice_index r.start.val r.end_.val a.val ss.val
-    (by scalar_tac) (by scalar_tac) (by scalar_tac) (by scalar_tac)
-  simp [List.replace_slice, *] at h
-  have ⟨ h0, h1, h2 ⟩ := h
-  clear h
-  split_conjs
-  . intro i _ _
-    have := h0 i (by int_tac) (by int_tac)
-    simp [*]
-  . intro i _ _
-    have := h1 i (by int_tac) (by int_tac)
-    simp [*]
-  . intro i _ _
-    have := h2 i (by int_tac) (by int_tac)
-    simp [*]
-
-end Primitives
diff --git a/backends/lean/Base/Primitives/ArraySlice.lean b/backends/lean/Base/Primitives/ArraySlice.lean
new file mode 100644
index 00000000..cfc9a6b2
--- /dev/null
+++ b/backends/lean/Base/Primitives/ArraySlice.lean
@@ -0,0 +1,553 @@
+/- Arrays/Slices -/
+import Lean
+import Lean.Meta.Tactic.Simp
+import Init.Data.List.Basic
+import Mathlib.Tactic.RunCmd
+import Mathlib.Tactic.Linarith
+import Base.IList
+import Base.Primitives.Scalar
+import Base.Primitives.Range
+import Base.Primitives.CoreOps
+import Base.Arith
+import Base.Progress.Base
+
+namespace Primitives
+
+open Result Error core.ops.range
+
+def Array (α : Type u) (n : Usize) := { l : List α // l.length = n.val }
+
+instance (a : Type u) (n : Usize) : Arith.HasIntProp (Array a n) where
+  prop_ty := λ v => v.val.len = n.val
+  prop := λ ⟨ _, l ⟩ => by simp[Scalar.max, List.len_eq_length, *]
+
+instance {α : Type u} {n : Usize} (p : Array α n → Prop) : Arith.HasIntProp (Subtype p) where
+  prop_ty := λ x => p x
+  prop := λ x => x.property
+
+@[simp]
+abbrev Array.length {α : Type u} {n : Usize} (v : Array α n) : Int := v.val.len
+
+@[simp]
+abbrev Array.v {α : Type u} {n : Usize} (v : Array α n) : List α := v.val
+
+example {α: Type u} {n : Usize} (v : Array α n) : v.length ≤ Scalar.max ScalarTy.Usize := by
+  scalar_tac
+
+def Array.make (α : Type u) (n : Usize) (init : List α) (hl : init.len = n.val := by decide) :
+  Array α n := ⟨ init, by simp [← List.len_eq_length]; apply hl ⟩
+
+example : Array Int (Usize.ofInt 2) := Array.make Int (Usize.ofInt 2) [0, 1]
+
+@[simp]
+abbrev Array.index_s {α : Type u} {n : Usize} [Inhabited α] (v : Array α n) (i : Int) : α :=
+  v.val.index i
+
+@[simp]
+abbrev Array.slice {α : Type u} {n : Usize} [Inhabited α] (v : Array α n) (i j : Int) : List α :=
+  v.val.slice i j
+
+def Array.index_usize (α : Type u) (n : Usize) (v: Array α n) (i: Usize) : Result α :=
+  match v.val.indexOpt i.val with
+  | none => fail .arrayOutOfBounds
+  | some x => ret x
+
+-- For initialization
+def Array.repeat (α : Type u) (n : Usize) (x : α) : Array α n :=
+  ⟨ List.ireplicate n.val x, by have h := n.hmin; simp_all [Scalar.min] ⟩
+
+@[pspec]
+theorem Array.repeat_spec {α : Type u} (n : Usize) (x : α) :
+  ∃ a, Array.repeat α n x = a ∧ a.val = List.ireplicate n.val x := by
+  simp [Array.repeat]
+
+/- In the theorems below: we don't always need the `∃ ..`, but we use one
+   so that `progress` introduces an opaque variable and an equality. This
+   helps control the context.
+ -/
+
+@[pspec]
+theorem Array.index_usize_spec {α : Type u} {n : Usize} [Inhabited α] (v: Array α n) (i: Usize)
+  (hbound : i.val < v.length) :
+  ∃ x, v.index_usize α n i = ret x ∧ x = v.val.index i.val := by
+  simp only [index_usize]
+  -- TODO: dependent rewrite
+  have h := List.indexOpt_eq_index v.val i.val (by scalar_tac) (by simp [*])
+  simp [*]
+
+def Array.update_usize (α : Type u) (n : Usize) (v: Array α n) (i: Usize) (x: α) : Result (Array α n) :=
+  match v.val.indexOpt i.val with
+  | none => fail .arrayOutOfBounds
+  | some _ =>
+    .ret ⟨ v.val.update i.val x, by have := v.property; simp [*] ⟩
+
+@[pspec]
+theorem Array.update_usize_spec {α : Type u} {n : Usize} (v: Array α n) (i: Usize) (x : α)
+  (hbound : i.val < v.length) :
+  ∃ nv, v.update_usize α n i x = ret nv ∧
+  nv.val = v.val.update i.val x
+  := by
+  simp only [update_usize]
+  have h := List.indexOpt_bounds v.val i.val
+  split
+  . simp_all [length]; cases h <;> scalar_tac
+  . simp_all
+
+def Slice (α : Type u) := { l : List α // l.length ≤ Usize.max }
+
+instance (a : Type u) : Arith.HasIntProp (Slice a) where
+  prop_ty := λ v => 0 ≤ v.val.len ∧ v.val.len ≤ Scalar.max ScalarTy.Usize
+  prop := λ ⟨ _, l ⟩ => by simp[Scalar.max, List.len_eq_length, *]
+
+instance {α : Type u} (p : Slice α → Prop) : Arith.HasIntProp (Subtype p) where
+  prop_ty := λ x => p x
+  prop := λ x => x.property
+
+@[simp]
+abbrev Slice.length {α : Type u} (v : Slice α) : Int := v.val.len
+
+@[simp]
+abbrev Slice.v {α : Type u} (v : Slice α) : List α := v.val
+
+example {a: Type u} (v : Slice a) : v.length ≤ Scalar.max ScalarTy.Usize := by
+  scalar_tac
+
+def Slice.new (α : Type u): Slice α := ⟨ [], by apply Scalar.cMax_suffices .Usize; simp ⟩
+
+-- TODO: very annoying that the α is an explicit parameter
+def Slice.len (α : Type u) (v : Slice α) : Usize :=
+  Usize.ofIntCore v.val.len (by scalar_tac) (by scalar_tac)
+
+@[simp]
+theorem Slice.len_val {α : Type u} (v : Slice α) : (Slice.len α v).val = v.length :=
+  by rfl
+
+@[simp]
+abbrev Slice.index_s {α : Type u} [Inhabited α] (v: Slice α) (i: Int) : α :=
+  v.val.index i
+
+@[simp]
+abbrev Slice.slice {α : Type u} [Inhabited α] (s : Slice α) (i j : Int) : List α :=
+  s.val.slice i j
+
+def Slice.index_usize (α : Type u) (v: Slice α) (i: Usize) : Result α :=
+  match v.val.indexOpt i.val with
+  | none => fail .arrayOutOfBounds
+  | some x => ret x
+
+/- In the theorems below: we don't always need the `∃ ..`, but we use one
+   so that `progress` introduces an opaque variable and an equality. This
+   helps control the context.
+ -/
+
+@[pspec]
+theorem Slice.index_usize_spec {α : Type u} [Inhabited α] (v: Slice α) (i: Usize)
+  (hbound : i.val < v.length) :
+  ∃ x, v.index_usize α i = ret x ∧ x = v.val.index i.val := by
+  simp only [index_usize]
+  -- TODO: dependent rewrite
+  have h := List.indexOpt_eq_index v.val i.val (by scalar_tac) (by simp [*])
+  simp [*]
+
+-- This shouldn't be used
+def Slice.index_shared_back (α : Type u) (v: Slice α) (i: Usize) (_: α) : Result Unit :=
+  if i.val < List.length v.val then
+    .ret ()
+  else
+    .fail arrayOutOfBounds
+
+def Slice.update_usize (α : Type u) (v: Slice α) (i: Usize) (x: α) : Result (Slice α) :=
+  match v.val.indexOpt i.val with
+  | none => fail .arrayOutOfBounds
+  | some _ =>
+    .ret ⟨ v.val.update i.val x, by have := v.property; simp [*] ⟩
+
+@[pspec]
+theorem Slice.update_usize_spec {α : Type u} (v: Slice α) (i: Usize) (x : α)
+  (hbound : i.val < v.length) :
+  ∃ nv, v.update_usize α i x = ret nv ∧
+  nv.val = v.val.update i.val x
+  := by
+  simp only [update_usize]
+  have h := List.indexOpt_bounds v.val i.val
+  split
+  . simp_all [length]; cases h <;> scalar_tac
+  . simp_all
+
+/- Array to slice/subslices -/
+
+/- We could make this function not use the `Result` type. By making it monadic, we
+   push the user to use the `Array.to_slice_spec` spec theorem below (through the
+   `progress` tactic), meaning `Array.to_slice` should be considered as opaque.
+   All what the spec theorem reveals is that the "representative" lists are the same. -/
+def Array.to_slice (α : Type u) (n : Usize) (v : Array α n) : Result (Slice α) :=
+  ret ⟨ v.val, by simp [← List.len_eq_length]; scalar_tac ⟩
+
+@[pspec]
+theorem Array.to_slice_spec {α : Type u} {n : Usize} (v : Array α n) :
+  ∃ s, to_slice α n v = ret s ∧ v.val = s.val := by simp [to_slice]
+
+def Array.from_slice (α : Type u) (n : Usize) (_ : Array α n) (s : Slice α) : Result (Array α n) :=
+  if h: s.val.len = n.val then
+    ret ⟨ s.val, by simp [← List.len_eq_length, *] ⟩
+  else fail panic
+
+@[pspec]
+theorem Array.from_slice_spec {α : Type u} {n : Usize} (a : Array α n) (ns : Slice α) (h : ns.val.len = n.val) :
+  ∃ na, from_slice α n a ns = ret na ∧ na.val = ns.val
+  := by simp [from_slice, *]
+
+def Array.subslice (α : Type u) (n : Usize) (a : Array α n) (r : Range Usize) : Result (Slice α) :=
+  -- TODO: not completely sure here
+  if r.start.val < r.end_.val ∧ r.end_.val ≤ a.val.len then
+    ret ⟨ a.val.slice r.start.val r.end_.val,
+          by
+            simp [← List.len_eq_length]
+            have := a.val.slice_len_le r.start.val r.end_.val
+            scalar_tac ⟩
+  else
+    fail panic
+
+@[pspec]
+theorem Array.subslice_spec {α : Type u} {n : Usize} [Inhabited α] (a : Array α n) (r : Range Usize)
+  (h0 : r.start.val < r.end_.val) (h1 : r.end_.val ≤ a.val.len) :
+  ∃ s, subslice α n a r = ret s ∧
+  s.val = a.val.slice r.start.val r.end_.val ∧
+  (∀ i, 0 ≤ i → i + r.start.val < r.end_.val → s.val.index i = a.val.index (r.start.val + i))
+  := by
+  simp [subslice, *]
+  intro i _ _
+  have := List.index_slice r.start.val r.end_.val i a.val (by scalar_tac) (by scalar_tac) (by trivial) (by scalar_tac)
+  simp [*]
+
+def Array.update_subslice (α : Type u) (n : Usize) (a : Array α n) (r : Range Usize) (s : Slice α) : Result (Array α n) :=
+  -- TODO: not completely sure here
+  if h: r.start.val < r.end_.val ∧ r.end_.val ≤ a.length ∧ s.val.len = r.end_.val - r.start.val then
+    let s_beg := a.val.itake r.start.val
+    let s_end := a.val.idrop r.end_.val
+    have : s_beg.len = r.start.val := by
+      apply List.itake_len
+      . simp_all; scalar_tac
+      . scalar_tac
+    have : s_end.len = a.val.len - r.end_.val := by
+      apply List.idrop_len
+      . scalar_tac
+      . scalar_tac
+    let na := s_beg.append (s.val.append s_end)
+    have : na.len = a.val.len := by simp [*]
+    ret ⟨ na, by simp_all [← List.len_eq_length]; scalar_tac ⟩
+  else
+    fail panic
+
+-- TODO: it is annoying to write `.val` everywhere. We could leverage coercions,
+-- but: some symbols like `+` are already overloaded to be notations for monadic
+-- operations/
+-- We should introduce special symbols for the monadic arithmetic operations
+-- (the use will never write those symbols directly).
+@[pspec]
+theorem Array.update_subslice_spec {α : Type u} {n : Usize} [Inhabited α] (a : Array α n) (r : Range Usize) (s : Slice α)
+  (_ : r.start.val < r.end_.val) (_ : r.end_.val ≤ a.length) (_ : s.length = r.end_.val - r.start.val) :
+  ∃ na, update_subslice α n a r s = ret na ∧
+  (∀ i, 0 ≤ i → i < r.start.val → na.index_s i = a.index_s i) ∧
+  (∀ i, r.start.val ≤ i → i < r.end_.val → na.index_s i = s.index_s (i - r.start.val)) ∧
+  (∀ i, r.end_.val ≤ i → i < n.val → na.index_s i = a.index_s i) := by
+  simp [update_subslice, *]
+  have h := List.replace_slice_index r.start.val r.end_.val a.val s.val
+    (by scalar_tac) (by scalar_tac) (by scalar_tac) (by scalar_tac)
+  simp [List.replace_slice] at h
+  have ⟨ h0, h1, h2 ⟩ := h
+  clear h
+  split_conjs
+  . intro i _ _
+    have := h0 i (by int_tac) (by int_tac)
+    simp [*]
+  . intro i _ _
+    have := h1 i (by int_tac) (by int_tac)
+    simp [*]
+  . intro i _ _
+    have := h2 i (by int_tac) (by int_tac)
+    simp [*]
+
+def Slice.subslice (α : Type u) (s : Slice α) (r : Range Usize) : Result (Slice α) :=
+  -- TODO: not completely sure here
+  if r.start.val < r.end_.val ∧ r.end_.val ≤ s.length then
+    ret ⟨ s.val.slice r.start.val r.end_.val,
+          by
+            simp [← List.len_eq_length]
+            have := s.val.slice_len_le r.start.val r.end_.val
+            scalar_tac ⟩
+  else
+    fail panic
+
+@[pspec]
+theorem Slice.subslice_spec {α : Type u} [Inhabited α] (s : Slice α) (r : Range Usize)
+  (h0 : r.start.val < r.end_.val) (h1 : r.end_.val ≤ s.val.len) :
+  ∃ ns, subslice α s r = ret ns ∧
+  ns.val = s.slice r.start.val r.end_.val ∧
+  (∀ i, 0 ≤ i → i + r.start.val < r.end_.val → ns.index_s i = s.index_s (r.start.val + i))
+  := by
+  simp [subslice, *]
+  intro i _ _
+  have := List.index_slice r.start.val r.end_.val i s.val (by scalar_tac) (by scalar_tac) (by trivial) (by scalar_tac)
+  simp [*]
+
+attribute [pp_dot] List.len List.length List.index -- use the dot notation when printing
+set_option pp.coercions false -- do not print coercions with ↑ (this doesn't parse)
+
+def Slice.update_subslice (α : Type u) (s : Slice α) (r : Range Usize) (ss : Slice α) : Result (Slice α) :=
+  -- TODO: not completely sure here
+  if h: r.start.val < r.end_.val ∧ r.end_.val ≤ s.length ∧ ss.val.len = r.end_.val - r.start.val then
+    let s_beg := s.val.itake r.start.val
+    let s_end := s.val.idrop r.end_.val
+    have : s_beg.len = r.start.val := by
+      apply List.itake_len
+      . simp_all; scalar_tac
+      . scalar_tac
+    have : s_end.len = s.val.len - r.end_.val := by
+      apply List.idrop_len
+      . scalar_tac
+      . scalar_tac
+    let ns := s_beg.append (ss.val.append s_end)
+    have : ns.len = s.val.len := by simp [*]
+    ret ⟨ ns, by simp_all [← List.len_eq_length]; scalar_tac ⟩
+  else
+    fail panic
+
+@[pspec]
+theorem Slice.update_subslice_spec {α : Type u} [Inhabited α] (a : Slice α) (r : Range Usize) (ss : Slice α)
+  (_ : r.start.val < r.end_.val) (_ : r.end_.val ≤ a.length) (_ : ss.length = r.end_.val - r.start.val) :
+  ∃ na, update_subslice α a r ss = ret na ∧
+  (∀ i, 0 ≤ i → i < r.start.val → na.index_s i = a.index_s i) ∧
+  (∀ i, r.start.val ≤ i → i < r.end_.val → na.index_s i = ss.index_s (i - r.start.val)) ∧
+  (∀ i, r.end_.val ≤ i → i < a.length → na.index_s i = a.index_s i) := by
+  simp [update_subslice, *]
+  have h := List.replace_slice_index r.start.val r.end_.val a.val ss.val
+    (by scalar_tac) (by scalar_tac) (by scalar_tac) (by scalar_tac)
+  simp [List.replace_slice, *] at h
+  have ⟨ h0, h1, h2 ⟩ := h
+  clear h
+  split_conjs
+  . intro i _ _
+    have := h0 i (by int_tac) (by int_tac)
+    simp [*]
+  . intro i _ _
+    have := h1 i (by int_tac) (by int_tac)
+    simp [*]
+  . intro i _ _
+    have := h2 i (by int_tac) (by int_tac)
+    simp [*]
+
+/- Trait declaration: [core::slice::index::private_slice_index::Sealed] -/
+structure core.slice.index.private_slice_index.Sealed (Self : Type) where
+
+/- Trait declaration: [core::slice::index::SliceIndex] -/
+structure core.slice.index.SliceIndex (Self T : Type) where
+  sealedInst : core.slice.index.private_slice_index.Sealed Self
+  Output : Type
+  get : Self → T → Result (Option Output)
+  get_mut : Self → T → Result (Option Output)
+  get_mut_back : Self → T → Option Output → Result T
+  get_unchecked : Self → ConstRawPtr T → Result (ConstRawPtr Output)
+  get_unchecked_mut : Self → MutRawPtr T → Result (MutRawPtr Output)
+  index : Self → T → Result Output
+  index_mut : Self → T → Result Output
+  index_mut_back : Self → T → Output → Result T
+
+/- [core::slice::index::[T]::index]: forward function -/
+def core.slice.index.Slice.index
+  (T I : Type) (inst : core.slice.index.SliceIndex I (Slice T))
+  (slice : Slice T) (i : I) : Result inst.Output := do
+  let x ← inst.get i slice
+  match x with
+  | none => fail panic
+  | some x => ret x
+
+/- [core::slice::index::Range:::get]: forward function -/
+def core.slice.index.Range.get (T : Type) (i : Range Usize) (slice : Slice T) :
+  Result (Option (Slice T)) :=
+  sorry -- TODO
+
+/- [core::slice::index::Range::get_mut]: forward function -/
+def core.slice.index.Range.get_mut
+  (T : Type) : Range Usize → Slice T → Result (Option (Slice T)) :=
+  sorry -- TODO
+
+/- [core::slice::index::Range::get_mut]: backward function 0 -/
+def core.slice.index.Range.get_mut_back
+  (T : Type) :
+  Range Usize → Slice T → Option (Slice T) → Result (Slice T) :=
+  sorry -- TODO
+
+/- [core::slice::index::Range::get_unchecked]: forward function -/
+def core.slice.index.Range.get_unchecked
+  (T : Type) :
+  Range Usize → ConstRawPtr (Slice T) → Result (ConstRawPtr (Slice T)) :=
+  -- Don't know what the model should be - for now we always fail to make
+  -- sure code which uses it fails
+  fun _ _ => fail panic
+
+/- [core::slice::index::Range::get_unchecked_mut]: forward function -/
+def core.slice.index.Range.get_unchecked_mut
+  (T : Type) :
+  Range Usize → MutRawPtr (Slice T) → Result (MutRawPtr (Slice T)) :=
+  -- Don't know what the model should be - for now we always fail to make
+  -- sure code which uses it fails
+  fun _ _ => fail panic
+
+/- [core::slice::index::Range::index]: forward function -/
+def core.slice.index.Range.index
+  (T : Type) : Range Usize → Slice T → Result (Slice T) :=
+  sorry -- TODO
+
+/- [core::slice::index::Range::index_mut]: forward function -/
+def core.slice.index.Range.index_mut
+  (T : Type) : Range Usize → Slice T → Result (Slice T) :=
+  sorry -- TODO
+
+/- [core::slice::index::Range::index_mut]: backward function 0 -/
+def core.slice.index.Range.index_mut_back
+  (T : Type) : Range Usize → Slice T → Slice T → Result (Slice T) :=
+  sorry -- TODO
+
+/- [core::slice::index::[T]::index_mut]: forward function -/
+def core.slice.index.Slice.index_mut
+  (T I : Type) (inst : core.slice.index.SliceIndex I (Slice T)) :
+  Slice T → I → Result inst.Output :=
+  sorry -- TODO
+
+/- [core::slice::index::[T]::index_mut]: backward function 0 -/
+def core.slice.index.Slice.index_mut_back
+  (T I : Type) (inst : core.slice.index.SliceIndex I (Slice T)) :
+  Slice T → I → inst.Output → Result (Slice T) :=
+  sorry -- TODO
+
+/- [core::array::[T; N]::index]: forward function -/
+def core.array.Array.index
+  (T I : Type) (N : Usize) (inst : core.ops.index.Index (Slice T) I)
+  (a : Array T N) (i : I) : Result inst.Output :=
+  sorry -- TODO
+
+/- [core::array::[T; N]::index_mut]: forward function -/
+def core.array.Array.index_mut
+  (T I : Type) (N : Usize) (inst : core.ops.index.IndexMut (Slice T) I)
+  (a : Array T N) (i : I) : Result inst.indexInst.Output :=
+  sorry -- TODO
+
+/- [core::array::[T; N]::index_mut]: backward function 0 -/
+def core.array.Array.index_mut_back
+  (T I : Type) (N : Usize) (inst : core.ops.index.IndexMut (Slice T) I)
+  (a : Array T N) (i : I) (x : inst.indexInst.Output) : Result (Array T N) :=
+  sorry -- TODO
+
+/- Trait implementation: [core::slice::index::[T]] -/
+def core.slice.index.Slice.coreopsindexIndexInst (T I : Type)
+  (inst : core.slice.index.SliceIndex I (Slice T)) :
+  core.ops.index.Index (Slice T) I := {
+  Output := inst.Output
+  index := core.slice.index.Slice.index T I inst
+}
+
+/- Trait implementation: [core::slice::index::private_slice_index::Range] -/
+def core.slice.index.private_slice_index.Range.coresliceindexprivate_slice_indexSealedInst
+  : core.slice.index.private_slice_index.Sealed (Range Usize) := {}
+
+/- Trait implementation: [core::slice::index::Range] -/
+def core.slice.index.Range.coresliceindexSliceIndexInst (T : Type) :
+  core.slice.index.SliceIndex (Range Usize) (Slice T) := {
+  sealedInst :=
+    core.slice.index.private_slice_index.Range.coresliceindexprivate_slice_indexSealedInst
+  Output := Slice T
+  get := core.slice.index.Range.get T
+  get_mut := core.slice.index.Range.get_mut T
+  get_mut_back := core.slice.index.Range.get_mut_back T
+  get_unchecked := core.slice.index.Range.get_unchecked T
+  get_unchecked_mut := core.slice.index.Range.get_unchecked_mut T
+  index := core.slice.index.Range.index T
+  index_mut := core.slice.index.Range.index_mut T
+  index_mut_back := core.slice.index.Range.index_mut_back T
+}
+
+/- Trait implementation: [core::slice::index::[T]] -/
+def core.slice.index.Slice.coreopsindexIndexMutInst (T I : Type)
+  (inst : core.slice.index.SliceIndex I (Slice T)) :
+  core.ops.index.IndexMut (Slice T) I := {
+  indexInst := core.slice.index.Slice.coreopsindexIndexInst T I inst
+  index_mut := core.slice.index.Slice.index_mut T I inst
+  index_mut_back := core.slice.index.Slice.index_mut_back T I inst
+}
+
+/- Trait implementation: [core::array::[T; N]] -/
+def core.array.Array.coreopsindexIndexInst (T I : Type) (N : Usize)
+  (inst : core.ops.index.Index (Slice T) I) :
+  core.ops.index.Index (Array T N) I := {
+  Output := inst.Output
+  index := core.array.Array.index T I N inst
+}
+
+/- Trait implementation: [core::array::[T; N]] -/
+def core.array.Array.coreopsindexIndexMutInst (T I : Type) (N : Usize)
+  (inst : core.ops.index.IndexMut (Slice T) I) :
+  core.ops.index.IndexMut (Array T N) I := {
+  indexInst := core.array.Array.coreopsindexIndexInst T I N inst.indexInst
+  index_mut := core.array.Array.index_mut T I N inst
+  index_mut_back := core.array.Array.index_mut_back T I N inst
+}
+
+/- [core::slice::index::usize::get]: forward function -/
+def core.slice.index.Usize.get
+  (T : Type) : Usize → Slice T → Result (Option T) :=
+  sorry -- TODO
+
+/- [core::slice::index::usize::get_mut]: forward function -/
+def core.slice.index.Usize.get_mut
+  (T : Type) : Usize → Slice T → Result (Option T) :=
+  sorry -- TODO
+
+/- [core::slice::index::usize::get_mut]: backward function 0 -/
+def core.slice.index.Usize.get_mut_back
+  (T : Type) : Usize → Slice T → Option T → Result (Slice T) :=
+  sorry -- TODO
+
+/- [core::slice::index::usize::get_unchecked]: forward function -/
+def core.slice.index.Usize.get_unchecked
+  (T : Type) : Usize → ConstRawPtr (Slice T) → Result (ConstRawPtr T) :=
+  sorry -- TODO
+
+/- [core::slice::index::usize::get_unchecked_mut]: forward function -/
+def core.slice.index.Usize.get_unchecked_mut
+  (T : Type) : Usize → MutRawPtr (Slice T) → Result (MutRawPtr T) :=
+  sorry -- TODO
+
+/- [core::slice::index::usize::index]: forward function -/
+def core.slice.index.Usize.index (T : Type) : Usize → Slice T → Result T :=
+  sorry -- TODO
+
+/- [core::slice::index::usize::index_mut]: forward function -/
+def core.slice.index.Usize.index_mut (T : Type) : Usize → Slice T → Result T :=
+  sorry -- TODO
+
+/- [core::slice::index::usize::index_mut]: backward function 0 -/
+def core.slice.index.Usize.index_mut_back
+  (T : Type) : Usize → Slice T → T → Result (Slice T) :=
+  sorry -- TODO
+
+/- Trait implementation: [core::slice::index::private_slice_index::usize] -/
+def core.slice.index.private_slice_index.usize.coresliceindexprivate_slice_indexSealedInst
+  : core.slice.index.private_slice_index.Sealed Usize := {}
+
+/- Trait implementation: [core::slice::index::usize] -/
+def core.slice.index.usize.coresliceindexSliceIndexInst (T : Type) :
+  core.slice.index.SliceIndex Usize (Slice T) := {
+  sealedInst := core.slice.index.private_slice_index.usize.coresliceindexprivate_slice_indexSealedInst
+  Output := T
+  get := core.slice.index.Usize.get T
+  get_mut := core.slice.index.Usize.get_mut T
+  get_mut_back := core.slice.index.Usize.get_mut_back T
+  get_unchecked := core.slice.index.Usize.get_unchecked T
+  get_unchecked_mut := core.slice.index.Usize.get_unchecked_mut T
+  index := core.slice.index.Usize.index T
+  index_mut := core.slice.index.Usize.index_mut T
+  index_mut_back := core.slice.index.Usize.index_mut_back T
+}
+
+end Primitives
diff --git a/backends/lean/Base/Primitives/Base.lean b/backends/lean/Base/Primitives/Base.lean
index 7c0fa3bb..7fc33251 100644
--- a/backends/lean/Base/Primitives/Base.lean
+++ b/backends/lean/Base/Primitives/Base.lean
@@ -120,11 +120,18 @@ def Result.attach {α: Type} (o : Result α): Result { x : α // o = ret x } :=
 -- MISC --
 ----------
 
-@[simp] def mem.replace (a : Type) (x : a) (_ : a) : a := x
-@[simp] def mem.replace_back (a : Type) (_ : a) (y : a) : a := y
+@[simp] def core.mem.replace (a : Type) (x : a) (_ : a) : a := x
+@[simp] def core.mem.replace_back (a : Type) (_ : a) (y : a) : a := y
 
 /-- Aeneas-translated function -- useful to reduce non-recursive definitions.
  Use with `simp [ aeneas ]` -/
 register_simp_attr aeneas
 
+-- We don't really use raw pointers for now
+structure MutRawPtr (T : Type) where
+  v : T
+
+structure ConstRawPtr (T : Type) where
+  v : T
+
 end Primitives
diff --git a/backends/lean/Base/Primitives/CoreOps.lean b/backends/lean/Base/Primitives/CoreOps.lean
new file mode 100644
index 00000000..da458f66
--- /dev/null
+++ b/backends/lean/Base/Primitives/CoreOps.lean
@@ -0,0 +1,37 @@
+import Lean
+import Base.Primitives.Base
+
+open Primitives
+open Result
+
+namespace core.ops
+
+namespace index -- core.ops.index
+
+/- Trait declaration: [core::ops::index::Index] -/
+structure Index (Self Idx : Type) where
+  Output : Type
+  index : Self → Idx → Result Output
+
+/- Trait declaration: [core::ops::index::IndexMut] -/
+structure IndexMut (Self Idx : Type) where
+  indexInst : Index Self Idx
+  index_mut : Self → Idx → Result indexInst.Output
+  index_mut_back : Self → Idx → indexInst.Output → Result Self
+
+end index -- core.ops.index
+
+namespace deref -- core.ops.deref
+
+structure Deref (Self : Type) where
+  Target : Type
+  deref : Self → Result Target
+
+structure DerefMut (Self : Type) where
+  derefInst : Deref Self
+  deref_mut : Self → Result derefInst.Target
+  deref_mut_back : Self → derefInst.Target → Result Self
+
+end deref -- core.ops.deref
+
+end core.ops
diff --git a/backends/lean/Base/Primitives/Range.lean b/backends/lean/Base/Primitives/Range.lean
index 26cbee42..a268bcba 100644
--- a/backends/lean/Base/Primitives/Range.lean
+++ b/backends/lean/Base/Primitives/Range.lean
@@ -11,7 +11,7 @@ import Base.Progress.Base
 
 namespace Primitives
 
-structure Range (α : Type u) where
+structure core.ops.range.Range (α : Type u) where
   mk ::
   start: α
   end_: α
diff --git a/backends/lean/Base/Primitives/Scalar.lean b/backends/lean/Base/Primitives/Scalar.lean
index 55227a9f..ec9665a5 100644
--- a/backends/lean/Base/Primitives/Scalar.lean
+++ b/backends/lean/Base/Primitives/Scalar.lean
@@ -230,6 +230,20 @@ def Scalar.cMax (ty : ScalarTy) : Int :=
   | .Usize => Scalar.max .U32
   | _ => Scalar.max ty
 
+theorem Scalar.min_lt_max (ty : ScalarTy) : Scalar.min ty < Scalar.max ty := by
+  cases ty <;> simp [Scalar.min, Scalar.max]
+  . simp [Isize.min, Isize.max]
+    have h1 := Isize.refined_min.property
+    have h2 := Isize.refined_max.property
+    cases h1 <;> cases h2 <;> simp [*]
+  . simp [Usize.max]
+    have h := Usize.refined_max.property
+    cases h <;> simp [*]
+
+theorem Scalar.min_le_max (ty : ScalarTy) : Scalar.min ty ≤ Scalar.max ty := by
+  have := Scalar.min_lt_max ty
+  int_tac
+
 theorem Scalar.cMin_bound ty : Scalar.min ty ≤ Scalar.cMin ty := by
   cases ty <;> simp [Scalar.min, Scalar.max, Scalar.cMin, Scalar.cMax] at *
   have h := Isize.refined_min.property
@@ -395,6 +409,34 @@ def Scalar.cast {src_ty : ScalarTy} (tgt_ty : ScalarTy) (x : Scalar src_ty) : Re
 @[reducible] def U64   := Scalar .U64
 @[reducible] def U128  := Scalar .U128
 
+-- TODO: reducible?
+@[reducible] def core_isize_min : Isize := Scalar.ofInt Isize.min (by simp [Scalar.min, Scalar.max]; apply (Scalar.min_le_max .Isize))
+@[reducible] def core_isize_max : Isize := Scalar.ofInt Isize.max (by simp [Scalar.min, Scalar.max]; apply (Scalar.min_le_max .Isize))
+@[reducible] def core_i8_min : I8 := Scalar.ofInt I8.min
+@[reducible] def core_i8_max : I8 := Scalar.ofInt I8.max
+@[reducible] def core_i16_min : I16 := Scalar.ofInt I16.min
+@[reducible] def core_i16_max : I16 := Scalar.ofInt I16.max
+@[reducible] def core_i32_min : I32 := Scalar.ofInt I32.min
+@[reducible] def core_i32_max : I32 := Scalar.ofInt I32.max
+@[reducible] def core_i64_min : I64 := Scalar.ofInt I64.min
+@[reducible] def core_i64_max : I64 := Scalar.ofInt I64.max
+@[reducible] def core_i128_min : I128 := Scalar.ofInt I128.min
+@[reducible] def core_i128_max : I128 := Scalar.ofInt I128.max
+
+-- TODO: reducible?
+@[reducible] def core_usize_min : Usize := Scalar.ofInt Usize.min
+@[reducible] def core_usize_max : Usize := Scalar.ofInt Usize.max (by simp [Scalar.min, Scalar.max]; apply (Scalar.min_le_max .Usize))
+@[reducible] def core_u8_min : U8 := Scalar.ofInt U8.min
+@[reducible] def core_u8_max : U8 := Scalar.ofInt U8.max
+@[reducible] def core_u16_min : U16 := Scalar.ofInt U16.min
+@[reducible] def core_u16_max : U16 := Scalar.ofInt U16.max
+@[reducible] def core_u32_min : U32 := Scalar.ofInt U32.min
+@[reducible] def core_u32_max : U32 := Scalar.ofInt U32.max
+@[reducible] def core_u64_min : U64 := Scalar.ofInt U64.min
+@[reducible] def core_u64_max : U64 := Scalar.ofInt U64.max
+@[reducible] def core_u128_min : U128 := Scalar.ofInt U128.min
+@[reducible] def core_u128_max : U128 := Scalar.ofInt U128.max
+
 -- TODO: below: not sure this is the best way.
 -- Should we rather overload operations like +, -, etc.?
 -- Also, it is possible to automate the generation of those definitions
@@ -861,33 +903,33 @@ theorem Scalar.rem_unsigned_spec {ty} (s: ¬ ty.isSigned) (x : Scalar ty) {y : S
 
 -- ofIntCore
 -- TODO: typeclass?
-@[reducible] def Isize.ofIntCore := @Scalar.ofIntCore .Isize
-@[reducible] def I8.ofIntCore    := @Scalar.ofIntCore .I8
-@[reducible] def I16.ofIntCore   := @Scalar.ofIntCore .I16
-@[reducible] def I32.ofIntCore   := @Scalar.ofIntCore .I32
-@[reducible] def I64.ofIntCore   := @Scalar.ofIntCore .I64
-@[reducible] def I128.ofIntCore  := @Scalar.ofIntCore .I128
-@[reducible] def Usize.ofIntCore := @Scalar.ofIntCore .Usize
-@[reducible] def U8.ofIntCore    := @Scalar.ofIntCore .U8
-@[reducible] def U16.ofIntCore   := @Scalar.ofIntCore .U16
-@[reducible] def U32.ofIntCore   := @Scalar.ofIntCore .U32
-@[reducible] def U64.ofIntCore   := @Scalar.ofIntCore .U64
-@[reducible] def U128.ofIntCore  := @Scalar.ofIntCore .U128
+def Isize.ofIntCore := @Scalar.ofIntCore .Isize
+def I8.ofIntCore    := @Scalar.ofIntCore .I8
+def I16.ofIntCore   := @Scalar.ofIntCore .I16
+def I32.ofIntCore   := @Scalar.ofIntCore .I32
+def I64.ofIntCore   := @Scalar.ofIntCore .I64
+def I128.ofIntCore  := @Scalar.ofIntCore .I128
+def Usize.ofIntCore := @Scalar.ofIntCore .Usize
+def U8.ofIntCore    := @Scalar.ofIntCore .U8
+def U16.ofIntCore   := @Scalar.ofIntCore .U16
+def U32.ofIntCore   := @Scalar.ofIntCore .U32
+def U64.ofIntCore   := @Scalar.ofIntCore .U64
+def U128.ofIntCore  := @Scalar.ofIntCore .U128
 
 --  ofInt
 -- TODO: typeclass?
-@[reducible] def Isize.ofInt := @Scalar.ofInt .Isize
-@[reducible] def I8.ofInt    := @Scalar.ofInt .I8
-@[reducible] def I16.ofInt   := @Scalar.ofInt .I16
-@[reducible] def I32.ofInt   := @Scalar.ofInt .I32
-@[reducible] def I64.ofInt   := @Scalar.ofInt .I64
-@[reducible] def I128.ofInt  := @Scalar.ofInt .I128
-@[reducible] def Usize.ofInt := @Scalar.ofInt .Usize
-@[reducible] def U8.ofInt    := @Scalar.ofInt .U8
-@[reducible] def U16.ofInt   := @Scalar.ofInt .U16
-@[reducible] def U32.ofInt   := @Scalar.ofInt .U32
-@[reducible] def U64.ofInt   := @Scalar.ofInt .U64
-@[reducible] def U128.ofInt  := @Scalar.ofInt .U128
+abbrev Isize.ofInt := @Scalar.ofInt .Isize
+abbrev I8.ofInt    := @Scalar.ofInt .I8
+abbrev I16.ofInt   := @Scalar.ofInt .I16
+abbrev I32.ofInt   := @Scalar.ofInt .I32
+abbrev I64.ofInt   := @Scalar.ofInt .I64
+abbrev I128.ofInt  := @Scalar.ofInt .I128
+abbrev Usize.ofInt := @Scalar.ofInt .Usize
+abbrev U8.ofInt    := @Scalar.ofInt .U8
+abbrev U16.ofInt   := @Scalar.ofInt .U16
+abbrev U32.ofInt   := @Scalar.ofInt .U32
+abbrev U64.ofInt   := @Scalar.ofInt .U64
+abbrev U128.ofInt  := @Scalar.ofInt .U128
 
 postfix:max "#isize" => Isize.ofInt
 postfix:max "#i8"    => I8.ofInt
@@ -905,9 +947,46 @@ postfix:max "#u128"  => U128.ofInt
 -- Testing the notations
 example : Result Usize := 0#usize + 1#usize
 
+-- TODO: factor those lemmas out
 @[simp] theorem Scalar.ofInt_val_eq {ty} (h : Scalar.min ty ≤ x ∧ x ≤ Scalar.max ty) : (Scalar.ofInt x h).val = x := by
   simp [Scalar.ofInt, Scalar.ofIntCore]
 
+@[simp] theorem Isize.ofInt_val_eq (h : Scalar.min ScalarTy.Isize ≤ x ∧ x ≤ Scalar.max ScalarTy.Isize) : (Isize.ofInt x h).val = x := by
+  apply Scalar.ofInt_val_eq h
+
+@[simp] theorem I8.ofInt_val_eq (h : Scalar.min ScalarTy.I8 ≤ x ∧ x ≤ Scalar.max ScalarTy.I8) : (I8.ofInt x h).val = x := by
+  apply Scalar.ofInt_val_eq h
+
+@[simp] theorem I16.ofInt_val_eq (h : Scalar.min ScalarTy.I16 ≤ x ∧ x ≤ Scalar.max ScalarTy.I16) : (I16.ofInt x h).val = x := by
+  apply Scalar.ofInt_val_eq h
+
+@[simp] theorem I32.ofInt_val_eq (h : Scalar.min ScalarTy.I32 ≤ x ∧ x ≤ Scalar.max ScalarTy.I32) : (I32.ofInt x h).val = x := by
+  apply Scalar.ofInt_val_eq h
+
+@[simp] theorem I64.ofInt_val_eq (h : Scalar.min ScalarTy.I64 ≤ x ∧ x ≤ Scalar.max ScalarTy.I64) : (I64.ofInt x h).val = x := by
+  apply Scalar.ofInt_val_eq h
+
+@[simp] theorem I128.ofInt_val_eq (h : Scalar.min ScalarTy.I128 ≤ x ∧ x ≤ Scalar.max ScalarTy.I128) : (I128.ofInt x h).val = x := by
+  apply Scalar.ofInt_val_eq h
+
+@[simp] theorem Usize.ofInt_val_eq (h : Scalar.min ScalarTy.Usize ≤ x ∧ x ≤ Scalar.max ScalarTy.Usize) : (Usize.ofInt x h).val = x := by
+  apply Scalar.ofInt_val_eq h
+
+@[simp] theorem U8.ofInt_val_eq (h : Scalar.min ScalarTy.U8 ≤ x ∧ x ≤ Scalar.max ScalarTy.U8) : (U8.ofInt x h).val = x := by
+  apply Scalar.ofInt_val_eq h
+
+@[simp] theorem U16.ofInt_val_eq (h : Scalar.min ScalarTy.U16 ≤ x ∧ x ≤ Scalar.max ScalarTy.U16) : (U16.ofInt x h).val = x := by
+  apply Scalar.ofInt_val_eq h
+
+@[simp] theorem U32.ofInt_val_eq (h : Scalar.min ScalarTy.U32 ≤ x ∧ x ≤ Scalar.max ScalarTy.U32) : (U32.ofInt x h).val = x := by
+  apply Scalar.ofInt_val_eq h
+
+@[simp] theorem U64.ofInt_val_eq (h : Scalar.min ScalarTy.U64 ≤ x ∧ x ≤ Scalar.max ScalarTy.U64) : (U64.ofInt x h).val = x := by
+  apply Scalar.ofInt_val_eq h
+
+@[simp] theorem U128.ofInt_val_eq (h : Scalar.min ScalarTy.U128 ≤ x ∧ x ≤ Scalar.max ScalarTy.U128) : (U128.ofInt x h).val = x := by
+  apply Scalar.ofInt_val_eq h
+
 -- Comparisons
 instance {ty} : LT (Scalar ty) where
   lt a b := LT.lt a.val b.val
diff --git a/backends/lean/Base/Primitives/Vec.lean b/backends/lean/Base/Primitives/Vec.lean
index c4c4d9f2..bbed6082 100644
--- a/backends/lean/Base/Primitives/Vec.lean
+++ b/backends/lean/Base/Primitives/Vec.lean
@@ -6,7 +6,7 @@ import Mathlib.Tactic.RunCmd
 import Mathlib.Tactic.Linarith
 import Base.IList
 import Base.Primitives.Scalar
-import Base.Primitives.Array
+import Base.Primitives.ArraySlice
 import Base.Arith
 import Base.Progress.Base
 
@@ -14,6 +14,8 @@ namespace Primitives
 
 open Result Error
 
+namespace alloc.vec
+
 def Vec (α : Type u) := { l : List α // l.length ≤ Usize.max }
 
 instance (a : Type u) : Arith.HasIntProp (Vec a) where
@@ -79,7 +81,7 @@ theorem Vec.insert_spec {α : Type u} (v: Vec α) (i: Usize) (x: α)
   ∃ nv, v.insert α i x = ret nv ∧ nv.val = v.val.update i.val x := by
   simp [insert, *]
 
-def Vec.index_shared (α : Type u) (v: Vec α) (i: Usize) : Result α :=
+def Vec.index_usize {α : Type u} (v: Vec α) (i: Usize) : Result α :=
   match v.val.indexOpt i.val with
   | none => fail .arrayOutOfBounds
   | some x => ret x
@@ -90,51 +92,83 @@ def Vec.index_shared (α : Type u) (v: Vec α) (i: Usize) : Result α :=
  -/
 
 @[pspec]
-theorem Vec.index_shared_spec {α : Type u} [Inhabited α] (v: Vec α) (i: Usize)
-  (hbound : i.val < v.length) :
-  ∃ x, v.index_shared α i = ret x ∧ x = v.val.index i.val := by
-  simp only [index_shared]
-  -- TODO: dependent rewrite
-  have h := List.indexOpt_eq_index v.val i.val (by scalar_tac) (by simp [*])
-  simp [*]
-
--- This shouldn't be used
-def Vec.index_back (α : Type u) (v: Vec α) (i: Usize) (_: α) : Result Unit :=
-  if i.val < List.length v.val then
-    .ret ()
-  else
-    .fail arrayOutOfBounds
-
-def Vec.index_mut (α : Type u) (v: Vec α) (i: Usize) : Result α :=
-  match v.val.indexOpt i.val with
-  | none => fail .arrayOutOfBounds
-  | some x => ret x
-
-@[pspec]
-theorem Vec.index_mut_spec {α : Type u} [Inhabited α] (v: Vec α) (i: Usize)
+theorem Vec.index_usize_spec {α : Type u} [Inhabited α] (v: Vec α) (i: Usize)
   (hbound : i.val < v.length) :
-  ∃ x, v.index_mut α i = ret x ∧ x = v.val.index i.val := by
-  simp only [index_mut]
+  ∃ x, v.index_usize i = ret x ∧ x = v.val.index i.val := by
+  simp only [index_usize]
   -- TODO: dependent rewrite
   have h := List.indexOpt_eq_index v.val i.val (by scalar_tac) (by simp [*])
   simp [*]
 
-def Vec.index_mut_back (α : Type u) (v: Vec α) (i: Usize) (x: α) : Result (Vec α) :=
+def Vec.update_usize {α : Type u} (v: Vec α) (i: Usize) (x: α) : Result (Vec α) :=
   match v.val.indexOpt i.val with
   | none => fail .arrayOutOfBounds
   | some _ =>
     .ret ⟨ v.val.update i.val x, by have := v.property; simp [*] ⟩
 
 @[pspec]
-theorem Vec.index_mut_back_spec {α : Type u} (v: Vec α) (i: Usize) (x : α)
+theorem Vec.update_usize_spec {α : Type u} (v: Vec α) (i: Usize) (x : α)
   (hbound : i.val < v.length) :
-  ∃ nv, v.index_mut_back α i x = ret nv ∧
+  ∃ nv, v.update_usize i x = ret nv ∧
   nv.val = v.val.update i.val x
   := by
-  simp only [index_mut_back]
+  simp only [update_usize]
   have h := List.indexOpt_bounds v.val i.val
   split
   . simp_all [length]; cases h <;> scalar_tac
   . simp_all
 
+/- [alloc::vec::Vec::index]: forward function -/
+def Vec.index (T I : Type) (inst : core.slice.index.SliceIndex I (Slice T))
+  (self : Vec T) (i : I) : Result inst.Output :=
+  sorry -- TODO
+
+/- [alloc::vec::Vec::index_mut]: forward function -/
+def Vec.index_mut (T I : Type) (inst : core.slice.index.SliceIndex I (Slice T))
+  (self : Vec T) (i : I) : Result inst.Output :=
+  sorry -- TODO
+
+/- [alloc::vec::Vec::index_mut]: backward function 0 -/
+def Vec.index_mut_back
+  (T I : Type) (inst : core.slice.index.SliceIndex I (Slice T))
+  (self : Vec T) (i : I) (x : inst.Output) : Result (alloc.vec.Vec T) :=
+  sorry -- TODO
+
+/- Trait implementation: [alloc::vec::Vec] -/
+def Vec.coreopsindexIndexInst (T I : Type)
+  (inst : core.slice.index.SliceIndex I (Slice T)) :
+  core.ops.index.Index (alloc.vec.Vec T) I := {
+  Output := inst.Output
+  index := Vec.index T I inst
+}
+
+/- Trait implementation: [alloc::vec::Vec] -/
+def Vec.coreopsindexIndexMutInst (T I : Type)
+  (inst : core.slice.index.SliceIndex I (Slice T)) :
+  core.ops.index.IndexMut (alloc.vec.Vec T) I := {
+  indexInst := Vec.coreopsindexIndexInst T I inst
+  index_mut := Vec.index_mut T I inst
+  index_mut_back := Vec.index_mut_back T I inst
+}
+
+@[simp]
+theorem Vec.index_slice_index {α : Type} (v : Vec α) (i : Usize) :
+  Vec.index α Usize (core.slice.index.usize.coresliceindexSliceIndexInst α) v i =
+  Vec.index_usize v i :=
+  sorry
+
+@[simp]
+theorem Vec.index_mut_slice_index {α : Type} (v : Vec α) (i : Usize) :
+  Vec.index_mut α Usize (core.slice.index.usize.coresliceindexSliceIndexInst α) v i =
+  Vec.index_usize v i :=
+  sorry
+
+@[simp]
+theorem Vec.index_mut_back_slice_index {α : Type} (v : Vec α) (i : Usize) (x : α) :
+  Vec.index_mut_back α Usize (core.slice.index.usize.coresliceindexSliceIndexInst α) v i x =
+  Vec.update_usize v i x :=
+  sorry
+
+end alloc.vec
+
 end Primitives
diff --git a/backends/lean/Base/Progress/Progress.lean b/backends/lean/Base/Progress/Progress.lean
index 8b0759c5..ba63f09d 100644
--- a/backends/lean/Base/Progress/Progress.lean
+++ b/backends/lean/Base/Progress/Progress.lean
@@ -8,6 +8,27 @@ namespace Progress
 open Lean Elab Term Meta Tactic
 open Utils
 
+-- TODO: the scalar types annoyingly often get reduced when we use the progress
+-- tactic. We should find a way of controling reduction. For now we use rewriting
+-- lemmas to make sure the goal remains clean, but this complexifies proof terms.
+-- It seems there used to be a `fold` tactic.
+theorem scalar_isize_eq : Primitives.Scalar .Isize = Primitives.Isize := by rfl
+theorem scalar_i8_eq    : Primitives.Scalar .I8 = Primitives.I8 := by rfl
+theorem scalar_i16_eq   : Primitives.Scalar .I16 = Primitives.I16 := by rfl
+theorem scalar_i32_eq   : Primitives.Scalar .I32 = Primitives.I32 := by rfl
+theorem scalar_i64_eq   : Primitives.Scalar .I64 = Primitives.I64 := by rfl
+theorem scalar_i128_eq  : Primitives.Scalar .I128 = Primitives.I128 := by rfl
+theorem scalar_usize_eq : Primitives.Scalar .Usize = Primitives.Usize := by rfl
+theorem scalar_u8_eq    : Primitives.Scalar .U8 = Primitives.U8 := by rfl
+theorem scalar_u16_eq   : Primitives.Scalar .U16 = Primitives.U16 := by rfl
+theorem scalar_u32_eq   : Primitives.Scalar .U32 = Primitives.U32 := by rfl
+theorem scalar_u64_eq   : Primitives.Scalar .U64 = Primitives.U64 := by rfl
+theorem scalar_u128_eq  : Primitives.Scalar .U128 = Primitives.U128 := by rfl
+def scalar_eqs := [
+  ``scalar_isize_eq, ``scalar_i8_eq, ``scalar_i16_eq, ``scalar_i32_eq, ``scalar_i64_eq, ``scalar_i128_eq,
+  ``scalar_usize_eq, ``scalar_u8_eq, ``scalar_u16_eq, ``scalar_u32_eq, ``scalar_u64_eq, ``scalar_u128_eq
+]
+
 inductive TheoremOrLocal where
 | Theorem (thName : Name)
 | Local (asm : LocalDecl)
@@ -111,8 +132,11 @@ def progressWith (fExpr : Expr) (th : TheoremOrLocal)
     splitEqAndPost fun hEq hPost ids => do
     trace[Progress] "eq and post:\n{hEq} : {← inferType hEq}\n{hPost}"
     tryTac (
-      simpAt [] [``Primitives.bind_tc_ret, ``Primitives.bind_tc_fail, ``Primitives.bind_tc_div]
+      simpAt true []
+             [``Primitives.bind_tc_ret, ``Primitives.bind_tc_fail, ``Primitives.bind_tc_div]
              [hEq.fvarId!] (.targets #[] true))
+    -- TODO: remove this (some types get unfolded too much: we "fold" them back)
+    tryTac (simpAt true [] scalar_eqs [] .wildcard_dep)
     -- Clear the equality, unless the user requests not to do so
     let mgoal ← do
       if keep.isSome then getMainGoal
@@ -359,6 +383,7 @@ namespace Test
   -- #eval showStoredPSpec
   -- #eval showStoredPSpecClass
   -- #eval showStoredPSpecExprClass
+  open alloc.vec
 
   example {ty} {x y : Scalar ty}
     (hmin : Scalar.min ty ≤ x.val + y.val)
@@ -384,7 +409,7 @@ namespace Test
      `α : Type u` where u is quantified, while here we use `α : Type 0` -/
   example {α : Type} (v: Vec α) (i: Usize) (x : α)
     (hbounds : i.val < v.length) :
-    ∃ nv, v.index_mut_back α i x = ret nv ∧
+    ∃ nv, v.update_usize i x = ret nv ∧
     nv.val = v.val.update i.val x := by
     progress
     simp [*]
diff --git a/backends/lean/Base/Utils.lean b/backends/lean/Base/Utils.lean
index 5224e1c3..b917a789 100644
--- a/backends/lean/Base/Utils.lean
+++ b/backends/lean/Base/Utils.lean
@@ -604,16 +604,12 @@ example (h : ∃ x y z, x + y + z ≥ 0) : ∃ x, x ≥ 0 := by
   rename_i x y z
   exists x + y + z
 
-/- Call the simp tactic.
-   The initialization of the context is adapted from Tactic.elabSimpArgs.
-   Something very annoying is that there is no function which allows to
-   initialize a simp context without doing an elaboration - as a consequence
-   we write our own here. -/
-def simpAt (declsToUnfold : List Name) (thms : List Name) (hypsToUse : List FVarId)
-  (loc : Tactic.Location) :
-  Tactic.TacticM Unit := do
-  -- Initialize with the builtin simp theorems
-  let simpThms ← Tactic.simpOnlyBuiltins.foldlM (·.addConst ·) ({} : SimpTheorems)
+def mkSimpCtx (simpOnly : Bool) (declsToUnfold : List Name) (thms : List Name) (hypsToUse : List FVarId) :
+  Tactic.TacticM Simp.Context := do
+  -- Initialize either with the builtin simp theorems or with all the simp theorems
+  let simpThms ←
+    if simpOnly then Tactic.simpOnlyBuiltins.foldlM (·.addConst ·) ({} : SimpTheorems)
+    else getSimpTheorems
   -- Add the equational theorem for the declarations to unfold
   let simpThms ←
     declsToUnfold.foldlM (fun thms decl => thms.addDeclToUnfold decl) simpThms
@@ -637,8 +633,63 @@ def simpAt (declsToUnfold : List Name) (thms : List Name) (hypsToUse : List FVar
         throwError "Not a proposition: {thmName}"
       ) simpThms
   let congrTheorems ← getSimpCongrTheorems
-  let ctx : Simp.Context := { simpTheorems := #[simpThms], congrTheorems }
+  pure { simpTheorems := #[simpThms], congrTheorems }
+
+
+inductive Location where
+  /-- Apply the tactic everywhere. Same as `Tactic.Location.wildcard` -/
+  | wildcard
+  /-- Apply the tactic everywhere, including in the variable types (i.e., in
+      assumptions which are not propositions).  --/
+  | wildcard_dep
+  /-- Same as Tactic.Location -/
+  | targets (hypotheses : Array Syntax) (type : Bool)
+
+-- Comes from Tactic.simpLocation
+def customSimpLocation (ctx : Simp.Context) (discharge? : Option Simp.Discharge := none)
+  (loc : Location) : TacticM Simp.UsedSimps := do
+  match loc with
+  | Location.targets hyps simplifyTarget =>
+    withMainContext do
+      let fvarIds ← Lean.Elab.Tactic.getFVarIds hyps
+      go fvarIds simplifyTarget
+  | Location.wildcard =>
+    withMainContext do
+      go (← (← getMainGoal).getNondepPropHyps) (simplifyTarget := true)
+  | Location.wildcard_dep =>
+    withMainContext do
+      let ctx ← Lean.MonadLCtx.getLCtx
+      let decls ← ctx.getDecls
+      let tgts := (decls.map (fun d => d.fvarId)).toArray
+      go tgts (simplifyTarget := true)
+where
+  go (fvarIdsToSimp : Array FVarId) (simplifyTarget : Bool) : TacticM Simp.UsedSimps := do
+    let mvarId ← getMainGoal
+    let (result?, usedSimps) ← simpGoal mvarId ctx (simplifyTarget := simplifyTarget) (discharge? := discharge?) (fvarIdsToSimp := fvarIdsToSimp)
+    match result? with
+    | none => replaceMainGoal []
+    | some (_, mvarId) => replaceMainGoal [mvarId]
+    return usedSimps
+
+/- Call the simp tactic.
+   The initialization of the context is adapted from Tactic.elabSimpArgs.
+   Something very annoying is that there is no function which allows to
+   initialize a simp context without doing an elaboration - as a consequence
+   we write our own here. -/
+def simpAt (simpOnly : Bool) (declsToUnfold : List Name) (thms : List Name) (hypsToUse : List FVarId)
+  (loc : Location) :
+  Tactic.TacticM Unit := do
+  -- Initialize the simp context
+  let ctx ← mkSimpCtx simpOnly declsToUnfold thms hypsToUse
+  -- Apply the simplifier
+  let _ ← customSimpLocation ctx (discharge? := .none) loc
+
+-- Call the simpAll tactic
+def simpAll (declsToUnfold : List Name) (thms : List Name) (hypsToUse : List FVarId) :
+  Tactic.TacticM Unit := do
+  -- Initialize the simp context
+  let ctx ← mkSimpCtx false declsToUnfold thms hypsToUse
   -- Apply the simplifier
-  let _ ← Tactic.simpLocation ctx (discharge? := .none) loc
+  let _ ← Lean.Meta.simpAll (← getMainGoal) ctx
 
 end Utils
diff --git a/compiler/AssociatedTypes.ml b/compiler/AssociatedTypes.ml
new file mode 100644
index 00000000..581e218c
--- /dev/null
+++ b/compiler/AssociatedTypes.ml
@@ -0,0 +1,681 @@
+(** This file implements utilities to handle trait associated types, in
+    particular with normalization helpers.
+
+    When normalizing a type, we simplify the references to the trait associated
+    types, and choose a representative when there are equalities between types
+    enforced by local clauses (i.e., clauses of the shape [where Trait1::T = Trait2::U]).
+ *)
+
+module T = Types
+module TU = TypesUtils
+module V = Values
+module E = Expressions
+module A = LlbcAst
+module C = Contexts
+module Subst = Substitute
+module L = Logging
+module UF = UnionFind
+module PA = Print.EvalCtxLlbcAst
+
+(** The local logger *)
+let log = L.associated_types_log
+
+let trait_type_ref_substitute (subst : ('r, 'r1) Subst.subst)
+    (r : 'r C.trait_type_ref) : 'r1 C.trait_type_ref =
+  let { C.trait_ref; type_name } = r in
+  let trait_ref = Subst.trait_ref_substitute subst trait_ref in
+  { C.trait_ref; type_name }
+
+(* TODO: how not to duplicate below? *)
+module RTyOrd = struct
+  type t = T.rty
+
+  let compare = T.compare_rty
+  let to_string = T.show_rty
+  let pp_t = T.pp_rty
+  let show_t = T.show_rty
+end
+
+module STyOrd = struct
+  type t = T.sty
+
+  let compare = T.compare_sty
+  let to_string = T.show_sty
+  let pp_t = T.pp_sty
+  let show_t = T.show_sty
+end
+
+module RTyMap = Collections.MakeMap (RTyOrd)
+module STyMap = Collections.MakeMap (STyOrd)
+
+(* TODO: is it possible not to have this? *)
+module type TypeWrapper = sig
+  type t
+end
+
+(* TODO: don't manage to get the syntax right so using a functor *)
+module MakeNormalizer
+    (R : TypeWrapper)
+    (RTyMap : Collections.Map with type key = R.t T.region T.ty)
+    (M : Collections.Map with type key = R.t T.region C.trait_type_ref) =
+struct
+  let compute_norm_trait_types_from_preds
+      (trait_type_constraints : R.t T.region T.trait_type_constraint list) :
+      R.t T.region T.ty M.t =
+    (* Compute a union-find structure by recursively exploring the predicates and clauses *)
+    let norm : R.t T.region T.ty UF.elem RTyMap.t ref = ref RTyMap.empty in
+    let get_ref (ty : R.t T.region T.ty) : R.t T.region T.ty UF.elem =
+      match RTyMap.find_opt ty !norm with
+      | Some r -> r
+      | None ->
+          let r = UF.make ty in
+          norm := RTyMap.add ty r !norm;
+          r
+    in
+    let add_trait_type_constraint (c : R.t T.region T.trait_type_constraint) =
+      let trait_ty = T.TraitType (c.trait_ref, c.generics, c.type_name) in
+      let trait_ty_ref = get_ref trait_ty in
+      let ty_ref = get_ref c.ty in
+      let new_repr = UF.get ty_ref in
+      let merged = UF.union trait_ty_ref ty_ref in
+      (* Not sure the set operation is necessary, but I want to control which
+         representative is chosen *)
+      UF.set merged new_repr
+    in
+    (* Explore the local predicates *)
+    List.iter add_trait_type_constraint trait_type_constraints;
+    (* TODO: explore the local clauses *)
+    (* Compute the norm maps *)
+    let rbindings =
+      List.map (fun (k, v) -> (k, UF.get v)) (RTyMap.bindings !norm)
+    in
+    (* Filter the keys to keep only the trait type aliases *)
+    let rbindings =
+      List.filter_map
+        (fun (k, v) ->
+          match k with
+          | T.TraitType (trait_ref, generics, type_name) ->
+              assert (generics = TypesUtils.mk_empty_generic_args);
+              Some ({ C.trait_ref; type_name }, v)
+          | _ -> None)
+        rbindings
+    in
+    M.of_list rbindings
+end
+
+(** Compute the representative classes of trait associated types, for normalization *)
+let compute_norm_trait_stypes_from_preds
+    (trait_type_constraints : T.strait_type_constraint list) :
+    T.sty C.STraitTypeRefMap.t =
+  (* Compute the normalization map for the types with regions *)
+  let module R = struct
+    type t = T.region_var_id
+  end in
+  let module M = C.STraitTypeRefMap in
+  let module Norm = MakeNormalizer (R) (STyMap) (M) in
+  Norm.compute_norm_trait_types_from_preds trait_type_constraints
+
+(** Compute the representative classes of trait associated types, for normalization *)
+let compute_norm_trait_types_from_preds
+    (trait_type_constraints : T.rtrait_type_constraint list) :
+    T.ety C.ETraitTypeRefMap.t * T.rty C.RTraitTypeRefMap.t =
+  (* Compute the normalization map for the types with regions *)
+  let module R = struct
+    type t = T.region_id
+  end in
+  let module M = C.RTraitTypeRefMap in
+  let module Norm = MakeNormalizer (R) (RTyMap) (M) in
+  let rbindings =
+    Norm.compute_norm_trait_types_from_preds trait_type_constraints
+  in
+  (* Compute the normalization map for the types with erased regions *)
+  let ebindings =
+    List.map
+      (fun (k, v) ->
+        ( trait_type_ref_substitute Subst.erase_regions_subst k,
+          Subst.erase_regions v ))
+      (M.bindings rbindings)
+  in
+  (C.ETraitTypeRefMap.of_list ebindings, rbindings)
+
+let ctx_add_norm_trait_stypes_from_preds (ctx : C.eval_ctx)
+    (trait_type_constraints : T.strait_type_constraint list) : C.eval_ctx =
+  let norm_trait_stypes =
+    compute_norm_trait_stypes_from_preds trait_type_constraints
+  in
+  { ctx with C.norm_trait_stypes }
+
+let ctx_add_norm_trait_types_from_preds (ctx : C.eval_ctx)
+    (trait_type_constraints : T.rtrait_type_constraint list) : C.eval_ctx =
+  let norm_trait_etypes, norm_trait_rtypes =
+    compute_norm_trait_types_from_preds trait_type_constraints
+  in
+  { ctx with C.norm_trait_etypes; norm_trait_rtypes }
+
+(** A trait instance id refers to a local clause if it only uses the variants:
+    [Self], [Clause], [ParentClause], [ItemClause] *)
+let rec trait_instance_id_is_local_clause (id : 'r T.trait_instance_id) : bool =
+  match id with
+  | T.Self | Clause _ -> true
+  | TraitImpl _ | BuiltinOrAuto _ | TraitRef _ | UnknownTrait _ | FnPointer _ ->
+      false
+  | ParentClause (id, _, _) | ItemClause (id, _, _, _) ->
+      trait_instance_id_is_local_clause id
+
+(** About the conversion functions: for now we need them (TODO: merge ety, rty, etc.),
+    but they should be applied to types without regions.
+ *)
+type 'r norm_ctx = {
+  ctx : C.eval_ctx;
+  get_ty_repr : 'r C.trait_type_ref -> 'r T.ty option;
+  convert_ety : T.ety -> 'r T.ty; (* TODO: remove? *)
+  convert_etrait_ref : T.etrait_ref -> 'r T.trait_ref; (* TODO: remove? *)
+  ty_to_string : 'r T.ty -> string;
+  generic_params_to_string : T.generic_params -> string;
+  generic_args_to_string : 'r T.generic_args -> string;
+  trait_ref_to_string : 'r T.trait_ref -> string;
+  trait_instance_id_to_string : 'r T.trait_instance_id -> string;
+  pp_r : Format.formatter -> 'r -> unit;
+}
+
+(** Small utility to lookup trait impls, together with a substitution.
+
+    Remark: one reason we have those small helpers is that all functions are
+    parameterized by a type variable 'r. The OCaml type inferencer and type
+    checker are however not very good at generating precise error messages in
+    this context: if in the body of the function we have an overly constrained
+    usage of 'r (for instance, the type inferencer deduces 'r should be
+    [T.erased_region]), it will not be able to pinpoint the location which
+    introduced the constraints and we just get a type-checking error for the
+    whole function. The fact that we have mutually recursive functions makes it
+    worse (the type-checker sometimes indicates a well-typed function as not
+    well-typed, because it calls a not well-typed function...).
+    By isolating the places where such errors typically happen in small helpers
+    (i.e., the places where we convert between different types of regions by
+    performing substitutions), we make maintenance a lot easier.
+ *)
+let ctx_lookup_trait_impl :
+      'r.
+      'r norm_ctx ->
+      T.TraitImplId.id ->
+      'r T.generic_args ->
+      A.trait_impl * (T.region_var_id T.region, 'r) Subst.subst =
+ fun ctx impl_id generics ->
+  (* Lookup the implementation *)
+  let trait_impl = C.ctx_lookup_trait_impl ctx.ctx impl_id in
+  (* The substitution *)
+  let tr_self = T.UnknownTrait __FUNCTION__ in
+  let subst =
+    Subst.make_subst_from_generics_no_regions trait_impl.generics generics
+      tr_self
+  in
+  (* Return *)
+  (trait_impl, subst)
+
+let ctx_lookup_trait_impl_ty :
+      'r.
+      'r norm_ctx -> T.TraitImplId.id -> 'r T.generic_args -> string -> 'r T.ty
+    =
+ fun ctx impl_id generics type_name ->
+  (* Lookup the implementation *)
+  let trait_impl, subst = ctx_lookup_trait_impl ctx impl_id generics in
+  (* Lookup the type *)
+  let ty = snd (List.assoc type_name trait_impl.types) in
+  (* Annoying: convert etype to an stype - TODO: how to avoid that? *)
+  let ty : T.sty = TypesUtils.ety_no_regions_to_gr_ty ty in
+  (* Substitute *)
+  Subst.ty_substitute subst ty
+
+let ctx_lookup_trait_impl_parent_clause :
+      'r.
+      'r norm_ctx ->
+      T.TraitImplId.id ->
+      'r T.generic_args ->
+      T.TraitClauseId.id ->
+      'r T.trait_ref =
+ fun ctx impl_id generics clause_id ->
+  (* Lookup the implementation *)
+  let trait_impl, subst = ctx_lookup_trait_impl ctx impl_id generics in
+  (* Lookup the clause *)
+  let clause = T.TraitClauseId.nth trait_impl.parent_trait_refs clause_id in
+  (* Sanity check: the clause necessarily refers to an impl *)
+  let _ = TypesUtils.trait_instance_id_as_trait_impl clause.trait_id in
+  (* Substitute *)
+  Subst.trait_ref_substitute subst clause
+
+let ctx_lookup_trait_impl_item_clause :
+      'r.
+      'r norm_ctx ->
+      T.TraitImplId.id ->
+      'r T.generic_args ->
+      string ->
+      T.TraitClauseId.id ->
+      'r T.trait_ref =
+ fun ctx impl_id generics item_name clause_id ->
+  (* Lookup the implementation *)
+  let trait_impl, subst = ctx_lookup_trait_impl ctx impl_id generics in
+  (* Lookup the item then its clause *)
+  let item = List.assoc item_name trait_impl.types in
+  let clause = T.TraitClauseId.nth (fst item) clause_id in
+  (* Sanity check: the clause necessarily refers to an impl *)
+  let _ = TypesUtils.trait_instance_id_as_trait_impl clause.trait_id in
+  (* Annoying: convert etype to an stype - TODO: how to avoid that? *)
+  let clause : T.strait_ref =
+    TypesUtils.etrait_ref_no_regions_to_gr_trait_ref clause
+  in
+  (* Substitute *)
+  Subst.trait_ref_substitute subst clause
+
+(** Normalize a type by simplifying the references to trait associated types
+    and choosing a representative when there are equalities between types
+    enforced by local clauses (i.e., `where Trait1::T = Trait2::U`.
+
+    See the comments for {!ctx_normalize_trait_instance_id}.
+  *)
+let rec ctx_normalize_ty : 'r. 'r norm_ctx -> 'r T.ty -> 'r T.ty =
+ fun ctx ty ->
+  log#ldebug (lazy ("ctx_normalize_ty: " ^ ctx.ty_to_string ty));
+  match ty with
+  | T.Adt (id, generics) -> Adt (id, ctx_normalize_generic_args ctx generics)
+  | TypeVar _ | Literal _ | Never -> ty
+  | Ref (r, ty, rkind) ->
+      let ty = ctx_normalize_ty ctx ty in
+      T.Ref (r, ty, rkind)
+  | RawPtr (ty, rkind) ->
+      let ty = ctx_normalize_ty ctx ty in
+      RawPtr (ty, rkind)
+  | Arrow (inputs, output) ->
+      let inputs = List.map (ctx_normalize_ty ctx) inputs in
+      let output = ctx_normalize_ty ctx output in
+      Arrow (inputs, output)
+  | TraitType (trait_ref, generics, type_name) -> (
+      log#ldebug
+        (lazy
+          ("ctx_normalize_ty:\n- trait type: " ^ ctx.ty_to_string ty
+         ^ "\n- trait_ref: "
+          ^ ctx.trait_ref_to_string trait_ref
+          ^ "\n- raw trait ref:\n"
+          ^ T.show_trait_ref ctx.pp_r trait_ref
+          ^ "\n- generics:\n"
+          ^ ctx.generic_args_to_string generics));
+      (* Normalize and attempt to project the type from the trait ref *)
+      let trait_ref = ctx_normalize_trait_ref ctx trait_ref in
+      let generics = ctx_normalize_generic_args ctx generics in
+      (*  For now, we don't support higher order types *)
+      assert (generics = TypesUtils.mk_empty_generic_args);
+      let ty : 'r T.ty =
+        match trait_ref.trait_id with
+        | T.TraitRef
+            { T.trait_id = T.TraitImpl impl_id; generics = ref_generics; _ } ->
+            assert (ref_generics = TypesUtils.mk_empty_generic_args);
+            log#ldebug
+              (lazy
+                ("ctx_normalize_ty: trait type: trait ref: "
+               ^ ctx.ty_to_string ty));
+            (* Lookup the type *)
+            let ty =
+              ctx_lookup_trait_impl_ty ctx impl_id trait_ref.generics type_name
+            in
+            (* Normalize *)
+            ctx_normalize_ty ctx ty
+        | T.TraitImpl impl_id ->
+            log#ldebug
+              (lazy
+                ("ctx_normalize_ty (trait impl):\n- trait type: "
+               ^ ctx.ty_to_string ty ^ "\n- trait_ref: "
+                ^ ctx.trait_ref_to_string trait_ref
+                ^ "\n- raw trait ref:\n"
+                ^ T.show_trait_ref ctx.pp_r trait_ref));
+            (* This happens. This doesn't come from the substitutions
+               performed by Aeneas (the [TraitImpl] would be wrapped in a
+               [TraitRef] but from non-normalized traits translated from
+               the Rustc AST.
+               TODO: factor out with the branch above.
+            *)
+            (* Lookup the type *)
+            let ty =
+              ctx_lookup_trait_impl_ty ctx impl_id trait_ref.generics type_name
+            in
+            (* Normalize *)
+            ctx_normalize_ty ctx ty
+        | _ ->
+            log#ldebug
+              (lazy
+                ("ctx_normalize_ty: trait type: not a trait ref: "
+               ^ ctx.ty_to_string ty ^ "\n- trait_ref: "
+                ^ ctx.trait_ref_to_string trait_ref
+                ^ "\n- raw trait ref:\n"
+                ^ T.show_trait_ref ctx.pp_r trait_ref));
+            (* We can't project *)
+            assert (trait_instance_id_is_local_clause trait_ref.trait_id);
+            T.TraitType (trait_ref, generics, type_name)
+      in
+      let tr : 'r C.trait_type_ref = { C.trait_ref; type_name } in
+      (* Lookup the representative, if there is *)
+      match ctx.get_ty_repr tr with None -> ty | Some ty -> ty)
+
+(** This returns the normalized trait instance id together with an optional
+    reference to a trait **implementation** (the `trait_ref` we return has
+    necessarily for instance id a [TraitImpl]).
+
+    We need this in particular to simplify the trait instance ids after we
+    performed a substitution.
+
+    Example:
+    ========
+    {[
+      trait Trait {
+        type S
+      }
+
+      impl TraitImpl for Foo {
+        type S = usize
+      }
+
+      fn f<T : Trait>(...) -> T::S;
+
+      ...
+      let x = f<Foo>[TraitImpl](...);
+      (* The return type of the call to f is:
+         T::S ~~> TraitImpl::S ~~> usize
+       *)
+    ]}
+
+    Several remarks:
+    - as we do not allow higher-order types (yet) then local clauses (and
+      sub-clauses) can't have generic arguments
+    - the [TraitRef] case only happens because of substitution, the role of
+      the normalization is in particular to eliminate it. Inside a [TraitRef]
+      there is necessarily:
+      - an id referencing a local (sub-)clause, that is an id using the variants
+        [Self], [Clause], [ItemClause] and [ParentClause] exclusively. We can't
+        simplify those cases: all we can do is remove the [TraitRef] wrapper
+        by leveraging the fact that the generic arguments must be empty.
+      - a [TraitImpl]. Note that the [TraitImpl] is necessarily just a [TraitImpl],
+        it can't be for instance a [ParentClause(TraitImpl ...)] because the
+        trait resolution would then directly reference the implementation
+        designated by [ParentClause(TraitImpl ...)] (and same for the other cases).
+        In this case we can lookup the trait implementation and recursively project
+        over it.
+ *)
+and ctx_normalize_trait_instance_id :
+      'r.
+      'r norm_ctx ->
+      'r T.trait_instance_id ->
+      'r T.trait_instance_id * 'r T.trait_ref option =
+ fun ctx id ->
+  match id with
+  | Self -> (id, None)
+  | TraitImpl _ ->
+      (* The [TraitImpl] shouldn't be inside any projection - we check this
+         elsewhere by asserting that whenever we return [None] for the impl
+         trait ref, then the id actually refers to a local clause. *)
+      (id, None)
+  | Clause _ -> (id, None)
+  | BuiltinOrAuto _ -> (id, None)
+  | ParentClause (inst_id, decl_id, clause_id) -> (
+      let inst_id, impl = ctx_normalize_trait_instance_id ctx inst_id in
+      (* Check if the inst_id refers to a specific implementation, if yes project *)
+      match impl with
+      | None ->
+          (* This is actually a local clause *)
+          assert (trait_instance_id_is_local_clause inst_id);
+          (ParentClause (inst_id, decl_id, clause_id), None)
+      | Some impl ->
+          (* We figure out the parent clause by doing the following:
+             {[
+               // The implementation we are looking at
+               impl Impl1 : Trait1 { ... }
+
+               // Check the trait it implements
+               trait Trait1 : ParentTrait1 + ParentTrait2 { ... }
+                              ^^^^^^^^^^^^^^^^^^^^^^^^^^^
+                              those are the parent clauses
+             ]}
+          *)
+          (* Lookup the clause *)
+          let impl_id =
+            TypesUtils.trait_instance_id_as_trait_impl impl.trait_id
+          in
+          let clause =
+            ctx_lookup_trait_impl_parent_clause ctx impl_id impl.generics
+              clause_id
+          in
+          (* Normalize the clause *)
+          let clause = ctx_normalize_trait_ref ctx clause in
+          (TraitRef clause, Some clause))
+  | ItemClause (inst_id, decl_id, item_name, clause_id) -> (
+      let inst_id, impl = ctx_normalize_trait_instance_id ctx inst_id in
+      (* Check if the inst_id refers to a specific implementation, if yes project *)
+      match impl with
+      | None ->
+          (* This is actually a local clause *)
+          assert (trait_instance_id_is_local_clause inst_id);
+          (ItemClause (inst_id, decl_id, item_name, clause_id), None)
+      | Some impl ->
+          (* We figure out the item clause by doing the following:
+             {[
+               // The implementation we are looking at
+               impl Impl1 : Trait1<R> {
+                  type S = ...
+                     with Impl2 : Trait2 ... // Instances satisfying the declared bounds
+                          ^^^^^^^^^^^^^^^^^^
+                      Lookup the clause from here
+               }
+             ]}
+          *)
+          (* Lookup the impl *)
+          let impl_id =
+            TypesUtils.trait_instance_id_as_trait_impl impl.trait_id
+          in
+          let clause =
+            ctx_lookup_trait_impl_item_clause ctx impl_id impl.generics
+              item_name clause_id
+          in
+          (* Normalize the clause *)
+          let clause = ctx_normalize_trait_ref ctx clause in
+          (TraitRef clause, Some clause))
+  | TraitRef { T.trait_id = T.TraitImpl trait_id; generics; trait_decl_ref } ->
+      (* We can't simplify the id *yet* : we will simplify it when projecting.
+         However, we have an implementation to return *)
+      (* Normalize the generics *)
+      let generics = ctx_normalize_generic_args ctx generics in
+      let trait_decl_ref = ctx_normalize_trait_decl_ref ctx trait_decl_ref in
+      let trait_ref : 'r T.trait_ref =
+        { T.trait_id = T.TraitImpl trait_id; generics; trait_decl_ref }
+      in
+      (TraitRef trait_ref, Some trait_ref)
+  | TraitRef trait_ref ->
+      (* The trait instance id necessarily refers to a local sub-clause. We
+         can't project over it and can only peel off the [TraitRef] wrapper *)
+      assert (trait_instance_id_is_local_clause trait_ref.trait_id);
+      assert (trait_ref.generics = TypesUtils.mk_empty_generic_args);
+      (trait_ref.trait_id, None)
+  | FnPointer ty ->
+      let ty = ctx_normalize_ty ctx ty in
+      (* TODO: we might want to return the ref to the function pointer,
+         in order to later normalize a call to this function pointer *)
+      (FnPointer ty, None)
+  | UnknownTrait _ ->
+      (* This is actually an error case *)
+      (id, None)
+
+and ctx_normalize_generic_args (ctx : 'r norm_ctx)
+    (generics : 'r T.generic_args) : 'r T.generic_args =
+  let { T.regions; types; const_generics; trait_refs } = generics in
+  let types = List.map (ctx_normalize_ty ctx) types in
+  let trait_refs = List.map (ctx_normalize_trait_ref ctx) trait_refs in
+  { T.regions; types; const_generics; trait_refs }
+
+and ctx_normalize_trait_ref (ctx : 'r norm_ctx) (trait_ref : 'r T.trait_ref) :
+    'r T.trait_ref =
+  log#ldebug
+    (lazy
+      ("ctx_normalize_trait_ref: "
+      ^ ctx.trait_ref_to_string trait_ref
+      ^ "\n- raw trait ref:\n"
+      ^ T.show_trait_ref ctx.pp_r trait_ref));
+  let { T.trait_id; generics; trait_decl_ref } = trait_ref in
+  (* Check if the id is an impl, otherwise normalize it *)
+  let trait_id, norm_trait_ref = ctx_normalize_trait_instance_id ctx trait_id in
+  match norm_trait_ref with
+  | None ->
+      log#ldebug
+        (lazy
+          ("ctx_normalize_trait_ref: no norm: "
+          ^ ctx.trait_instance_id_to_string trait_id));
+      let generics = ctx_normalize_generic_args ctx generics in
+      let trait_decl_ref = ctx_normalize_trait_decl_ref ctx trait_decl_ref in
+      { T.trait_id; generics; trait_decl_ref }
+  | Some trait_ref ->
+      log#ldebug
+        (lazy
+          ("ctx_normalize_trait_ref: normalized to: "
+          ^ ctx.trait_ref_to_string trait_ref));
+      assert (generics = TypesUtils.mk_empty_generic_args);
+      trait_ref
+
+(* Not sure this one is really necessary *)
+and ctx_normalize_trait_decl_ref (ctx : 'r norm_ctx)
+    (trait_decl_ref : 'r T.trait_decl_ref) : 'r T.trait_decl_ref =
+  let { T.trait_decl_id; decl_generics } = trait_decl_ref in
+  let decl_generics = ctx_normalize_generic_args ctx decl_generics in
+  { T.trait_decl_id; decl_generics }
+
+let ctx_normalize_trait_type_constraint (ctx : 'r norm_ctx)
+    (ttc : 'r T.trait_type_constraint) : 'r T.trait_type_constraint =
+  let { T.trait_ref; generics; type_name; ty } = ttc in
+  let trait_ref = ctx_normalize_trait_ref ctx trait_ref in
+  let generics = ctx_normalize_generic_args ctx generics in
+  let ty = ctx_normalize_ty ctx ty in
+  { T.trait_ref; generics; type_name; ty }
+
+let generic_params_to_string ctx x =
+  "<" ^ String.concat ", " (fst (PA.generic_params_to_strings ctx x)) ^ ">"
+
+let mk_snorm_ctx (ctx : C.eval_ctx) : T.RegionVarId.id T.region norm_ctx =
+  let get_ty_repr x = C.STraitTypeRefMap.find_opt x ctx.norm_trait_stypes in
+  {
+    ctx;
+    get_ty_repr;
+    convert_ety = TypesUtils.ety_no_regions_to_sty;
+    convert_etrait_ref = TypesUtils.etrait_ref_no_regions_to_gr_trait_ref;
+    ty_to_string = PA.sty_to_string ctx;
+    generic_params_to_string = generic_params_to_string ctx;
+    generic_args_to_string = PA.sgeneric_args_to_string ctx;
+    trait_ref_to_string = PA.strait_ref_to_string ctx;
+    trait_instance_id_to_string = PA.strait_instance_id_to_string ctx;
+    pp_r = T.pp_region T.pp_region_var_id;
+  }
+
+let mk_rnorm_ctx (ctx : C.eval_ctx) : T.RegionId.id T.region norm_ctx =
+  let get_ty_repr x = C.RTraitTypeRefMap.find_opt x ctx.norm_trait_rtypes in
+  {
+    ctx;
+    get_ty_repr;
+    convert_ety = TypesUtils.ety_no_regions_to_rty;
+    convert_etrait_ref = TypesUtils.etrait_ref_no_regions_to_gr_trait_ref;
+    ty_to_string = PA.rty_to_string ctx;
+    generic_params_to_string = generic_params_to_string ctx;
+    generic_args_to_string = PA.rgeneric_args_to_string ctx;
+    trait_ref_to_string = PA.rtrait_ref_to_string ctx;
+    trait_instance_id_to_string = PA.rtrait_instance_id_to_string ctx;
+    pp_r = T.pp_region T.pp_region_id;
+  }
+
+let mk_enorm_ctx (ctx : C.eval_ctx) : T.erased_region norm_ctx =
+  let get_ty_repr x = C.ETraitTypeRefMap.find_opt x ctx.norm_trait_etypes in
+  {
+    ctx;
+    get_ty_repr;
+    convert_ety = (fun x -> x);
+    convert_etrait_ref = (fun x -> x);
+    ty_to_string = PA.ety_to_string ctx;
+    generic_params_to_string = generic_params_to_string ctx;
+    generic_args_to_string = PA.egeneric_args_to_string ctx;
+    trait_ref_to_string = PA.etrait_ref_to_string ctx;
+    trait_instance_id_to_string = PA.etrait_instance_id_to_string ctx;
+    pp_r = T.pp_erased_region;
+  }
+
+let ctx_normalize_sty (ctx : C.eval_ctx) (ty : T.sty) : T.sty =
+  ctx_normalize_ty (mk_snorm_ctx ctx) ty
+
+let ctx_normalize_rty (ctx : C.eval_ctx) (ty : T.rty) : T.rty =
+  ctx_normalize_ty (mk_rnorm_ctx ctx) ty
+
+let ctx_normalize_ety (ctx : C.eval_ctx) (ty : T.ety) : T.ety =
+  ctx_normalize_ty (mk_enorm_ctx ctx) ty
+
+let ctx_normalize_rtrait_type_constraint (ctx : C.eval_ctx)
+    (ttc : T.rtrait_type_constraint) : T.rtrait_type_constraint =
+  ctx_normalize_trait_type_constraint (mk_rnorm_ctx ctx) ttc
+
+(** Same as [type_decl_get_instantiated_variants_fields_rtypes] but normalizes the types *)
+let type_decl_get_inst_norm_variants_fields_rtypes (ctx : C.eval_ctx)
+    (def : T.type_decl) (generics : T.rgeneric_args) :
+    (T.VariantId.id option * T.rty list) list =
+  let res =
+    Subst.type_decl_get_instantiated_variants_fields_rtypes def generics
+  in
+  List.map
+    (fun (variant_id, types) ->
+      (variant_id, List.map (ctx_normalize_rty ctx) types))
+    res
+
+(** Same as [type_decl_get_instantiated_field_rtypes] but normalizes the types *)
+let type_decl_get_inst_norm_field_rtypes (ctx : C.eval_ctx) (def : T.type_decl)
+    (opt_variant_id : T.VariantId.id option) (generics : T.rgeneric_args) :
+    T.rty list =
+  let types =
+    Subst.type_decl_get_instantiated_field_rtypes def opt_variant_id generics
+  in
+  List.map (ctx_normalize_rty ctx) types
+
+(** Same as [ctx_adt_value_get_instantiated_field_rtypes] but normalizes the types *)
+let ctx_adt_value_get_inst_norm_field_rtypes (ctx : C.eval_ctx)
+    (adt : V.adt_value) (id : T.type_id) (generics : T.rgeneric_args) :
+    T.rty list =
+  let types =
+    Subst.ctx_adt_value_get_instantiated_field_rtypes ctx adt id generics
+  in
+  List.map (ctx_normalize_rty ctx) types
+
+(** Same as [ctx_adt_value_get_instantiated_field_etypes] but normalizes the types *)
+let type_decl_get_inst_norm_field_etypes (ctx : C.eval_ctx) (def : T.type_decl)
+    (opt_variant_id : T.VariantId.id option) (generics : T.egeneric_args) :
+    T.ety list =
+  let types =
+    Subst.type_decl_get_instantiated_field_etypes def opt_variant_id generics
+  in
+  List.map (ctx_normalize_ety ctx) types
+
+(** Same as [ctx_adt_get_instantiated_field_etypes] but normalizes the types *)
+let ctx_adt_get_inst_norm_field_etypes (ctx : C.eval_ctx)
+    (def_id : T.TypeDeclId.id) (opt_variant_id : T.VariantId.id option)
+    (generics : T.egeneric_args) : T.ety list =
+  let types =
+    Subst.ctx_adt_get_instantiated_field_etypes ctx def_id opt_variant_id
+      generics
+  in
+  List.map (ctx_normalize_ety ctx) types
+
+(** Same as [substitute_signature] but normalizes the types *)
+let ctx_subst_norm_signature (ctx : C.eval_ctx)
+    (asubst : T.RegionGroupId.id -> V.AbstractionId.id)
+    (r_subst : T.RegionVarId.id -> T.RegionId.id)
+    (ty_subst : T.TypeVarId.id -> T.rty)
+    (cg_subst : T.ConstGenericVarId.id -> T.const_generic)
+    (tr_subst : T.TraitClauseId.id -> T.rtrait_instance_id)
+    (tr_self : T.rtrait_instance_id) (sg : A.fun_sig) : A.inst_fun_sig =
+  let sg =
+    Subst.substitute_signature asubst r_subst ty_subst cg_subst tr_subst tr_self
+      sg
+  in
+  let { A.regions_hierarchy; inputs; output; trait_type_constraints } = sg in
+  let inputs = List.map (ctx_normalize_rty ctx) inputs in
+  let output = ctx_normalize_rty ctx output in
+  let trait_type_constraints =
+    List.map (ctx_normalize_rtrait_type_constraint ctx) trait_type_constraints
+  in
+  { regions_hierarchy; inputs; output; trait_type_constraints }
diff --git a/compiler/Assumed.ml b/compiler/Assumed.ml
index 11cd5666..79f6b0d4 100644
--- a/compiler/Assumed.ml
+++ b/compiler/Assumed.ml
@@ -63,200 +63,52 @@ module Sig = struct
 
   let empty_const_generic_params : T.const_generic_var list = []
 
+  let mk_generic_args regions types const_generics : T.sgeneric_args =
+    { regions; types; const_generics; trait_refs = [] }
+
+  let mk_generic_params regions types const_generics : T.generic_params =
+    { regions; types; const_generics; trait_clauses = [] }
+
   let mk_ref_ty (r : T.RegionVarId.id T.region) (ty : T.sty) (is_mut : bool) :
       T.sty =
     let ref_kind = if is_mut then T.Mut else T.Shared in
     mk_ref_ty r ty ref_kind
 
   let mk_array_ty (ty : T.sty) (cg : T.const_generic) : T.sty =
-    Adt (Assumed Array, [], [ ty ], [ cg ])
+    Adt (Assumed Array, mk_generic_args [] [ ty ] [ cg ])
 
-  let mk_slice_ty (ty : T.sty) : T.sty = Adt (Assumed Slice, [], [ ty ], [])
-  let range_ty : T.sty = Adt (Assumed Range, [], [ usize_ty ], [])
+  let mk_slice_ty (ty : T.sty) : T.sty =
+    Adt (Assumed Slice, mk_generic_args [] [ ty ] [])
 
-  (** [fn<T>(&'a mut T, T) -> T] *)
-  let mem_replace_sig : A.fun_sig =
-    (* The signature fields *)
-    let region_params = [ region_param_0 ] (* <'a> *) in
-    let regions_hierarchy = [ region_group_0 ] (* [{<'a>}] *) in
-    let type_params = [ type_param_0 ] (* <T> *) in
-    let inputs =
-      [ mk_ref_ty rvar_0 tvar_0 true (* &'a mut T *); tvar_0 (* T *) ]
+  let mk_sig generics regions_hierarchy inputs output : A.fun_sig =
+    let preds : T.predicates =
+      { regions_outlive = []; types_outlive = []; trait_type_constraints = [] }
     in
-    let output = tvar_0 (* T *) in
     {
-      region_params;
-      num_early_bound_regions = 0;
+      is_unsafe = false;
+      generics;
+      preds;
+      parent_params_info = None;
       regions_hierarchy;
-      type_params;
-      const_generic_params = empty_const_generic_params;
       inputs;
       output;
     }
 
   (** [fn<T>(T) -> Box<T>] *)
   let box_new_sig : A.fun_sig =
-    {
-      region_params = [];
-      num_early_bound_regions = 0;
-      regions_hierarchy = [];
-      type_params = [ type_param_0 ] (* <T> *);
-      const_generic_params = empty_const_generic_params;
-      inputs = [ tvar_0 (* T *) ];
-      output = mk_box_ty tvar_0 (* Box<T> *);
-    }
+    let generics = mk_generic_params [] [ type_param_0 ] [] (* <T> *) in
+    let regions_hierarchy = [] in
+    let inputs = [ tvar_0 (* T *) ] in
+    let output = mk_box_ty tvar_0 (* Box<T> *) in
+    mk_sig generics regions_hierarchy inputs output
 
   (** [fn<T>(Box<T>) -> ()] *)
   let box_free_sig : A.fun_sig =
-    {
-      region_params = [];
-      num_early_bound_regions = 0;
-      regions_hierarchy = [];
-      type_params = [ type_param_0 ] (* <T> *);
-      const_generic_params = empty_const_generic_params;
-      inputs = [ mk_box_ty tvar_0 (* Box<T> *) ];
-      output = mk_unit_ty (* () *);
-    }
-
-  (** Helper for [Box::deref_shared] and [Box::deref_mut].
-      Returns:
-      [fn<'a, T>(&'a (mut) Box<T>) -> &'a (mut) T]
-  *)
-  let box_deref_gen_sig (is_mut : bool) : A.fun_sig =
-    (* The signature fields *)
-    let region_params = [ region_param_0 ] in
-    let regions_hierarchy = [ region_group_0 ] (* <'a> *) in
-    {
-      region_params;
-      num_early_bound_regions = 0;
-      regions_hierarchy;
-      type_params = [ type_param_0 ] (* <T> *);
-      const_generic_params = empty_const_generic_params;
-      inputs =
-        [ mk_ref_ty rvar_0 (mk_box_ty tvar_0) is_mut (* &'a (mut) Box<T> *) ];
-      output = mk_ref_ty rvar_0 tvar_0 is_mut (* &'a (mut) T *);
-    }
-
-  (** [fn<'a, T>(&'a Box<T>) -> &'a T] *)
-  let box_deref_shared_sig = box_deref_gen_sig false
-
-  (** [fn<'a, T>(&'a mut Box<T>) -> &'a mut T] *)
-  let box_deref_mut_sig = box_deref_gen_sig true
-
-  (** [fn<T>() -> Vec<T>] *)
-  let vec_new_sig : A.fun_sig =
-    let region_params = [] in
+    let generics = mk_generic_params [] [ type_param_0 ] [] (* <T> *) in
     let regions_hierarchy = [] in
-    let type_params = [ type_param_0 ] (* <T> *) in
-    let inputs = [] in
-    let output = mk_vec_ty tvar_0 (* Vec<T> *) in
-    {
-      region_params;
-      num_early_bound_regions = 0;
-      regions_hierarchy;
-      type_params;
-      const_generic_params = empty_const_generic_params;
-      inputs;
-      output;
-    }
-
-  (** [fn<T>(&'a mut Vec<T>, T)] *)
-  let vec_push_sig : A.fun_sig =
-    (* The signature fields *)
-    let region_params = [ region_param_0 ] in
-    let regions_hierarchy = [ region_group_0 ] (* <'a> *) in
-    let type_params = [ type_param_0 ] (* <T> *) in
-    let inputs =
-      [
-        mk_ref_ty rvar_0 (mk_vec_ty tvar_0) true (* &'a mut Vec<T> *);
-        tvar_0 (* T *);
-      ]
-    in
+    let inputs = [ mk_box_ty tvar_0 (* Box<T> *) ] in
     let output = mk_unit_ty (* () *) in
-    {
-      region_params;
-      num_early_bound_regions = 0;
-      regions_hierarchy;
-      type_params;
-      const_generic_params = empty_const_generic_params;
-      inputs;
-      output;
-    }
-
-  (** [fn<T>(&'a mut Vec<T>, usize, T)] *)
-  let vec_insert_sig : A.fun_sig =
-    (* The signature fields *)
-    let region_params = [ region_param_0 ] in
-    let regions_hierarchy = [ region_group_0 ] (* <'a> *) in
-    let type_params = [ type_param_0 ] (* <T> *) in
-    let inputs =
-      [
-        mk_ref_ty rvar_0 (mk_vec_ty tvar_0) true (* &'a mut Vec<T> *);
-        mk_usize_ty (* usize *);
-        tvar_0 (* T *);
-      ]
-    in
-    let output = mk_unit_ty (* () *) in
-    {
-      region_params;
-      num_early_bound_regions = 0;
-      regions_hierarchy;
-      type_params;
-      const_generic_params = empty_const_generic_params;
-      inputs;
-      output;
-    }
-
-  (** [fn<T>(&'a Vec<T>) -> usize] *)
-  let vec_len_sig : A.fun_sig =
-    (* The signature fields *)
-    let region_params = [ region_param_0 ] in
-    let regions_hierarchy = [ region_group_0 ] (* <'a> *) in
-    let type_params = [ type_param_0 ] (* <T> *) in
-    let inputs =
-      [ mk_ref_ty rvar_0 (mk_vec_ty tvar_0) false (* &'a Vec<T> *) ]
-    in
-    let output = mk_usize_ty (* usize *) in
-    {
-      region_params;
-      num_early_bound_regions = 0;
-      regions_hierarchy;
-      type_params;
-      const_generic_params = empty_const_generic_params;
-      inputs;
-      output;
-    }
-
-  (** Helper:
-      [fn<T>(&'a (mut) Vec<T>, usize) -> &'a (mut) T]
-   *)
-  let vec_index_gen_sig (is_mut : bool) : A.fun_sig =
-    (* The signature fields *)
-    let region_params = [ region_param_0 ] in
-    let regions_hierarchy = [ region_group_0 ] (* <'a> *) in
-    let type_params = [ type_param_0 ] (* <T> *) in
-    let inputs =
-      [
-        mk_ref_ty rvar_0 (mk_vec_ty tvar_0) is_mut (* &'a (mut) Vec<T> *);
-        mk_usize_ty (* usize *);
-      ]
-    in
-    let output = mk_ref_ty rvar_0 tvar_0 is_mut (* &'a (mut) T *) in
-    {
-      region_params;
-      num_early_bound_regions = 0;
-      regions_hierarchy;
-      type_params;
-      const_generic_params = empty_const_generic_params;
-      inputs;
-      output;
-    }
-
-  (** [fn<T>(&'a Vec<T>, usize) -> &'a T] *)
-  let vec_index_shared_sig : A.fun_sig = vec_index_gen_sig false
-
-  (** [fn<T>(&'a mut Vec<T>, usize) -> &'a mut T] *)
-  let vec_index_mut_sig : A.fun_sig = vec_index_gen_sig true
+    mk_sig generics regions_hierarchy inputs output
 
   (** Array/slice functions *)
 
@@ -275,10 +127,10 @@ module Sig = struct
   let mk_array_slice_borrow_sig (cgs : T.const_generic_var list)
       (input_ty : T.TypeVarId.id -> T.sty) (index_ty : T.sty option)
       (output_ty : T.TypeVarId.id -> T.sty) (is_mut : bool) : A.fun_sig =
-    (* The signature fields *)
-    let region_params = [ region_param_0 ] in
+    let generics =
+      mk_generic_params [ region_param_0 ] [ type_param_0 ] cgs (* <'a, T> *)
+    in
     let regions_hierarchy = [ region_group_0 ] (* <'a> *) in
-    let type_params = [ type_param_0 ] (* <T> *) in
     let inputs =
       [
         mk_ref_ty rvar_0
@@ -294,15 +146,7 @@ module Sig = struct
         (output_ty type_param_0.index)
         is_mut (* &'a (mut) output_ty<T> *)
     in
-    {
-      region_params;
-      num_early_bound_regions = 0;
-      regions_hierarchy;
-      type_params;
-      const_generic_params = cgs;
-      inputs;
-      output;
-    }
+    mk_sig generics regions_hierarchy inputs output
 
   let mk_array_slice_index_sig (is_array : bool) (is_mut : bool) : A.fun_sig =
     (* Array<T, N> *)
@@ -328,50 +172,53 @@ module Sig = struct
     let cgs = [ cg_param_0 ] in
     mk_array_slice_borrow_sig cgs input_ty None output_ty is_mut
 
-  let mk_array_slice_subslice_sig (is_array : bool) (is_mut : bool) : A.fun_sig
-      =
-    (* Array<T, N> *)
-    let input_ty id =
-      if is_array then mk_array_ty (T.TypeVar id) cgvar_0
-      else mk_slice_ty (T.TypeVar id)
+  let array_repeat_sig =
+    let generics =
+      (* <T, N> *)
+      mk_generic_params [] [ type_param_0 ] [ cg_param_0 ]
     in
-    (* Range *)
-    let index_ty = range_ty in
-    (* Slice<T> *)
-    let output_ty id = mk_slice_ty (T.TypeVar id) in
-    let cgs = if is_array then [ cg_param_0 ] else [] in
-    mk_array_slice_borrow_sig cgs input_ty (Some index_ty) output_ty is_mut
-
-  let array_subslice_sig (is_mut : bool) =
-    mk_array_slice_subslice_sig true is_mut
-
-  let slice_subslice_sig (is_mut : bool) =
-    mk_array_slice_subslice_sig false is_mut
+    let regions_hierarchy = [] (* <> *) in
+    let inputs = [ tvar_0 (* T *) ] in
+    let output =
+      (* [T; N] *)
+      mk_array_ty tvar_0 cgvar_0
+    in
+    mk_sig generics regions_hierarchy inputs output
 
   (** Helper:
       [fn<T>(&'a [T]) -> usize]
    *)
   let slice_len_sig : A.fun_sig =
-    (* The signature fields *)
-    let region_params = [ region_param_0 ] in
+    let generics =
+      mk_generic_params [ region_param_0 ] [ type_param_0 ] [] (* <'a, T> *)
+    in
     let regions_hierarchy = [ region_group_0 ] (* <'a> *) in
-    let type_params = [ type_param_0 ] (* <T> *) in
     let inputs =
       [ mk_ref_ty rvar_0 (mk_slice_ty tvar_0) false (* &'a [T] *) ]
     in
     let output = mk_usize_ty (* usize *) in
-    {
-      region_params;
-      num_early_bound_regions = 0;
-      regions_hierarchy;
-      type_params;
-      const_generic_params = empty_const_generic_params;
-      inputs;
-      output;
-    }
+    mk_sig generics regions_hierarchy inputs output
 end
 
-type assumed_info = A.assumed_fun_id * A.fun_sig * bool * name
+type raw_assumed_fun_info =
+  A.assumed_fun_id * A.fun_sig * bool * name * bool list option
+
+type assumed_fun_info = {
+  fun_id : A.assumed_fun_id;
+  fun_sig : A.fun_sig;
+  can_fail : bool;
+  name : name;
+  keep_types : bool list option;
+      (** We may want to filter some type arguments.
+
+          For instance, all the `Vec` functions (and the `Vec` type itself) take
+          an `Allocator` type as argument, that we ignore.
+       *)
+}
+
+let mk_assumed_fun_info (raw : raw_assumed_fun_info) : assumed_fun_info =
+  let fun_id, fun_sig, can_fail, name, keep_types = raw in
+  { fun_id; fun_sig; can_fail; name; keep_types }
 
 (** The list of assumed functions and all their information:
     - their signature
@@ -384,94 +231,72 @@ type assumed_info = A.assumed_fun_id * A.fun_sig * bool * name
     a [usize], we have to make sure that vectors are bounded by the max usize.
     As a consequence, [Vec::push] is monadic.
  *)
-let assumed_infos : assumed_info list =
-  let deref_pre = [ "core"; "ops"; "deref" ] in
-  let vec_pre = [ "alloc"; "vec"; "Vec" ] in
-  let index_pre = [ "core"; "ops"; "index" ] in
+let raw_assumed_fun_infos : raw_assumed_fun_info list =
   [
-    (A.Replace, Sig.mem_replace_sig, false, to_name [ "core"; "mem"; "replace" ]);
-    (BoxNew, Sig.box_new_sig, false, to_name [ "alloc"; "boxed"; "Box"; "new" ]);
+    ( BoxNew,
+      Sig.box_new_sig,
+      false,
+      to_name [ "alloc"; "boxed"; "Box"; "new" ],
+      Some [ true; false ] );
+    (* BoxFree shouldn't be used *)
     ( BoxFree,
       Sig.box_free_sig,
       false,
-      to_name [ "alloc"; "boxed"; "Box"; "free" ] );
-    ( BoxDeref,
-      Sig.box_deref_shared_sig,
-      false,
-      to_name (deref_pre @ [ "Deref"; "deref" ]) );
-    ( BoxDerefMut,
-      Sig.box_deref_mut_sig,
-      false,
-      to_name (deref_pre @ [ "DerefMut"; "deref_mut" ]) );
-    (VecNew, Sig.vec_new_sig, false, to_name (vec_pre @ [ "new" ]));
-    (VecPush, Sig.vec_push_sig, true, to_name (vec_pre @ [ "push" ]));
-    (VecInsert, Sig.vec_insert_sig, true, to_name (vec_pre @ [ "insert" ]));
-    (VecLen, Sig.vec_len_sig, false, to_name (vec_pre @ [ "len" ]));
-    ( VecIndex,
-      Sig.vec_index_shared_sig,
-      true,
-      to_name (index_pre @ [ "Index"; "index" ]) );
-    ( VecIndexMut,
-      Sig.vec_index_mut_sig,
-      true,
-      to_name (index_pre @ [ "IndexMut"; "index_mut" ]) );
+      to_name [ "alloc"; "boxed"; "Box"; "free" ],
+      Some [ true; false ] );
     (* Array Index *)
     ( ArrayIndexShared,
       Sig.array_index_sig false,
       true,
-      to_name [ "@ArrayIndexShared" ] );
-    (ArrayIndexMut, Sig.array_index_sig true, true, to_name [ "@ArrayIndexMut" ]);
+      to_name [ "@ArrayIndexShared" ],
+      None );
+    ( ArrayIndexMut,
+      Sig.array_index_sig true,
+      true,
+      to_name [ "@ArrayIndexMut" ],
+      None );
     (* Array to slice*)
     ( ArrayToSliceShared,
       Sig.array_to_slice_sig false,
       true,
-      to_name [ "@ArrayToSliceShared" ] );
+      to_name [ "@ArrayToSliceShared" ],
+      None );
     ( ArrayToSliceMut,
       Sig.array_to_slice_sig true,
       true,
-      to_name [ "@ArrayToSliceMut" ] );
-    (* Array Subslice *)
-    ( ArraySubsliceShared,
-      Sig.array_subslice_sig false,
-      true,
-      to_name [ "@ArraySubsliceShared" ] );
-    ( ArraySubsliceMut,
-      Sig.array_subslice_sig true,
-      true,
-      to_name [ "@ArraySubsliceMut" ] );
+      to_name [ "@ArrayToSliceMut" ],
+      None );
+    (* Array Repeat *)
+    (ArrayRepeat, Sig.array_repeat_sig, false, to_name [ "@ArrayRepeat" ], None);
     (* Slice Index *)
     ( SliceIndexShared,
       Sig.slice_index_sig false,
       true,
-      to_name [ "@SliceIndexShared" ] );
-    (SliceIndexMut, Sig.slice_index_sig true, true, to_name [ "@SliceIndexMut" ]);
-    (* Slice Subslice *)
-    ( SliceSubsliceShared,
-      Sig.slice_subslice_sig false,
-      true,
-      to_name [ "@SliceSubsliceShared" ] );
-    ( SliceSubsliceMut,
-      Sig.slice_subslice_sig true,
+      to_name [ "@SliceIndexShared" ],
+      None );
+    ( SliceIndexMut,
+      Sig.slice_index_sig true,
       true,
-      to_name [ "@SliceSubsliceMut" ] );
-    (SliceLen, Sig.slice_len_sig, false, to_name [ "@SliceLen" ]);
+      to_name [ "@SliceIndexMut" ],
+      None );
+    (SliceLen, Sig.slice_len_sig, false, to_name [ "@SliceLen" ], None);
   ]
 
-let get_assumed_info (id : A.assumed_fun_id) : assumed_info =
-  match List.find_opt (fun (id', _, _, _) -> id = id') assumed_infos with
+let assumed_fun_infos : assumed_fun_info list =
+  List.map mk_assumed_fun_info raw_assumed_fun_infos
+
+let get_assumed_fun_info (id : A.assumed_fun_id) : assumed_fun_info =
+  match List.find_opt (fun x -> id = x.fun_id) assumed_fun_infos with
   | Some info -> info
   | None ->
       raise
-        (Failure ("get_assumed_info: not found: " ^ A.show_assumed_fun_id id))
+        (Failure ("get_assumed_fun_info: not found: " ^ A.show_assumed_fun_id id))
 
-let get_assumed_sig (id : A.assumed_fun_id) : A.fun_sig =
-  let _, sg, _, _ = get_assumed_info id in
-  sg
+let get_assumed_fun_sig (id : A.assumed_fun_id) : A.fun_sig =
+  (get_assumed_fun_info id).fun_sig
 
-let get_assumed_name (id : A.assumed_fun_id) : fun_name =
-  let _, _, _, name = get_assumed_info id in
-  name
+let get_assumed_fun_name (id : A.assumed_fun_id) : fun_name =
+  (get_assumed_fun_info id).name
 
-let assumed_can_fail (id : A.assumed_fun_id) : bool =
-  let _, _, b, _ = get_assumed_info id in
-  b
+let assumed_fun_can_fail (id : A.assumed_fun_id) : bool =
+  (get_assumed_fun_info id).can_fail
diff --git a/compiler/Config.ml b/compiler/Config.ml
index bd80769f..a487f9e2 100644
--- a/compiler/Config.ml
+++ b/compiler/Config.ml
@@ -124,7 +124,7 @@ let always_deconstruct_adts_with_matches = ref false
 (** Controls whether we need to use a state to model the external world
     (I/O, for instance).
  *)
-let use_state = ref true
+let use_state = ref false
 
 (** Controls whether we use fuel to control termination.
  *)
@@ -160,7 +160,7 @@ let backward_no_state_update = ref false
     files for the types, clauses and functions, or if we group them in
     one file.
  *)
-let split_files = ref true
+let split_files = ref false
 
 (** Generate the library entry point, if the crate is split between different files.
 
@@ -306,13 +306,6 @@ let filter_useless_monadic_calls = ref true
  *)
 let filter_useless_functions = ref true
 
-(** Obsolete. TODO: remove.
-
-    For Lean we used to parameterize the entire development by a section variable
-    called opaque_defs, of type OpaqueDefs.
-  *)
-let wrap_opaque_in_sig = ref false
-
 (** Use short names for the record fields.
 
     Some backends can't disambiguate records when their field names have collisions.
@@ -323,3 +316,23 @@ let wrap_opaque_in_sig = ref false
     information), we use short names (i.e., the original field names).
  *)
 let record_fields_short_names = ref false
+
+(** Parameterize the traits with their associated types, so as not to use
+    types as first class objects.
+
+    This is useful for some backends with limited expressiveness like HOL4,
+    and to account for type constraints (like [fn f<T : Foo>(...) where T::bar = usize]).
+ *)
+let parameterize_trait_types = ref false
+
+(** For sanity check: type check the generated pure code (activates checks in
+    several places).
+
+    TODO: deactivated for now because we need to implement the normalization of
+    trait associated types in the pure code.
+ *)
+let type_check_pure_code = ref false
+
+(** Shall we fail hard if we encounter an issue, or should we attempt to go
+    as far as possible while leaving "holes" in the generated code? *)
+let fail_hard = ref true
diff --git a/compiler/Contexts.ml b/compiler/Contexts.ml
index 2ca5653d..dac64a9a 100644
--- a/compiler/Contexts.ml
+++ b/compiler/Contexts.ml
@@ -5,6 +5,7 @@ open LlbcAst
 module V = Values
 open ValuesUtils
 open Identifiers
+module L = Logging
 
 (** The [Id] module for dummy variables.
 
@@ -17,6 +18,9 @@ IdGen ()
 
 type dummy_var_id = DummyVarId.id [@@deriving show, ord]
 
+(** The local logger *)
+let log = L.contexts_log
+
 (** Some global counters.
 
   Note that those counters were initially stored in {!eval_ctx} values,
@@ -40,6 +44,7 @@ type dummy_var_id = DummyVarId.id [@@deriving show, ord]
     fn f x : fun_type =
       let id = fresh_id () in
       ...
+      fun () -> ...
    
     let g = f x in   // <-- the fresh identifier gets generated here
     let x1 = g () in // <-- no fresh generation here
@@ -250,27 +255,127 @@ type type_context = {
 }
 [@@deriving show]
 
-type fun_context = { fun_decls : fun_decl FunDeclId.Map.t } [@@deriving show]
+type fun_context = {
+  fun_decls : fun_decl FunDeclId.Map.t;
+  fun_infos : FunsAnalysis.fun_info FunDeclId.Map.t;
+}
+[@@deriving show]
 
 type global_context = { global_decls : global_decl GlobalDeclId.Map.t }
 [@@deriving show]
 
+type trait_decls_context = { trait_decls : trait_decl TraitDeclId.Map.t }
+[@@deriving show]
+
+type trait_impls_context = { trait_impls : trait_impl TraitImplId.Map.t }
+[@@deriving show]
+
+type decls_ctx = {
+  type_ctx : type_context;
+  fun_ctx : fun_context;
+  global_ctx : global_context;
+  trait_decls_ctx : trait_decls_context;
+  trait_impls_ctx : trait_impls_context;
+}
+[@@deriving show]
+
+(** A reference to a trait associated type *)
+type 'r trait_type_ref = { trait_ref : 'r trait_ref; type_name : string }
+[@@deriving show, ord]
+
+type etrait_type_ref = erased_region trait_type_ref [@@deriving show, ord]
+
+type rtrait_type_ref = Types.RegionId.id Types.region trait_type_ref
+[@@deriving show, ord]
+
+type strait_type_ref = Types.RegionVarId.id Types.region trait_type_ref
+[@@deriving show, ord]
+
+(* TODO: correctly use the functors so as not to have a duplication below *)
+module ETraitTypeRefOrd = struct
+  type t = etrait_type_ref
+
+  let compare = compare_etrait_type_ref
+  let to_string = show_etrait_type_ref
+  let pp_t = pp_etrait_type_ref
+  let show_t = show_etrait_type_ref
+end
+
+module RTraitTypeRefOrd = struct
+  type t = rtrait_type_ref
+
+  let compare = compare_rtrait_type_ref
+  let to_string = show_rtrait_type_ref
+  let pp_t = pp_rtrait_type_ref
+  let show_t = show_rtrait_type_ref
+end
+
+module STraitTypeRefOrd = struct
+  type t = strait_type_ref
+
+  let compare = compare_strait_type_ref
+  let to_string = show_strait_type_ref
+  let pp_t = pp_strait_type_ref
+  let show_t = show_strait_type_ref
+end
+
+module ETraitTypeRefMap = Collections.MakeMap (ETraitTypeRefOrd)
+module RTraitTypeRefMap = Collections.MakeMap (RTraitTypeRefOrd)
+module STraitTypeRefMap = Collections.MakeMap (STraitTypeRefOrd)
+
 (** Evaluation context *)
 type eval_ctx = {
   type_context : type_context;
   fun_context : fun_context;
   global_context : global_context;
+  trait_decls_context : trait_decls_context;
+  trait_impls_context : trait_impls_context;
   region_groups : RegionGroupId.id list;
   type_vars : type_var list;
   const_generic_vars : const_generic_var list;
+  const_generic_vars_map : typed_value Types.ConstGenericVarId.Map.t;
+      (** The map from const generic vars to their values. Those values
+          can be symbolic values or concrete values (in the latter case:
+          if we run in interpreter mode) *)
+  norm_trait_etypes : ety ETraitTypeRefMap.t;
+      (** The normalized trait types (a map from trait types to their representatives).
+          Note that this doesn't support account higher-order types. *)
+  norm_trait_rtypes : rty RTraitTypeRefMap.t;
+      (** We need this because we manipulate two kinds of types.
+          Note that we actually forbid regions from appearing both in the trait
+          references and in the constraints given to the associated types,
+          meaning that we don't have to worry about mismatches due to changes
+          in region ids.
+
+          TODO: how not to duplicate?
+       *)
+  norm_trait_stypes : sty STraitTypeRefMap.t;
+      (** We sometimes need to normalize types in non-instantiated signatures.
+
+          Note that we either need to use the etypes/rtypes maps, or the stypes map.
+          This means that we either compute the maps for etypes and rtypes, or compute
+          the one for stypes (we don't always compute and carry all the maps).
+       *)
   env : env;
   ended_regions : RegionId.Set.t;
 }
 [@@deriving show]
 
+let lookup_type_var_opt (ctx : eval_ctx) (vid : TypeVarId.id) : type_var option
+    =
+  if TypeVarId.to_int vid < List.length ctx.type_vars then
+    Some (TypeVarId.nth ctx.type_vars vid)
+  else None
+
 let lookup_type_var (ctx : eval_ctx) (vid : TypeVarId.id) : type_var =
   TypeVarId.nth ctx.type_vars vid
 
+let lookup_const_generic_var_opt (ctx : eval_ctx) (vid : ConstGenericVarId.id) :
+    const_generic_var option =
+  if ConstGenericVarId.to_int vid < List.length ctx.const_generic_vars then
+    Some (ConstGenericVarId.nth ctx.const_generic_vars vid)
+  else None
+
 let lookup_const_generic_var (ctx : eval_ctx) (vid : ConstGenericVarId.id) :
     const_generic_var =
   ConstGenericVarId.nth ctx.const_generic_vars vid
@@ -304,6 +409,12 @@ let ctx_lookup_global_decl (ctx : eval_ctx) (gid : GlobalDeclId.id) :
     global_decl =
   GlobalDeclId.Map.find gid ctx.global_context.global_decls
 
+let ctx_lookup_trait_decl (ctx : eval_ctx) (id : TraitDeclId.id) : trait_decl =
+  TraitDeclId.Map.find id ctx.trait_decls_context.trait_decls
+
+let ctx_lookup_trait_impl (ctx : eval_ctx) (id : TraitImplId.id) : trait_impl =
+  TraitImplId.Map.find id ctx.trait_impls_context.trait_impls
+
 (** Retrieve a variable's value in the current frame *)
 let env_lookup_var_value (env : env) (vid : VarId.id) : typed_value =
   snd (env_lookup_var env vid)
@@ -312,6 +423,11 @@ let env_lookup_var_value (env : env) (vid : VarId.id) : typed_value =
 let ctx_lookup_var_value (ctx : eval_ctx) (vid : VarId.id) : typed_value =
   env_lookup_var_value ctx.env vid
 
+(** Retrieve a const generic value in an evaluation context *)
+let ctx_lookup_const_generic_value (ctx : eval_ctx) (vid : ConstGenericVarId.id)
+    : typed_value =
+  Types.ConstGenericVarId.Map.find vid ctx.const_generic_vars_map
+
 (** Update a variable's value in the current frame.
 
     This is a helper function: it can break invariants and doesn't perform
@@ -361,6 +477,15 @@ let ctx_push_var (ctx : eval_ctx) (var : var) (v : typed_value) : eval_ctx =
 *)
 let ctx_push_vars (ctx : eval_ctx) (vars : (var * typed_value) list) : eval_ctx
     =
+  log#ldebug
+    (lazy
+      ("push_vars:\n"
+      ^ String.concat "\n"
+          (List.map
+             (fun (var, value) ->
+               (* We can unfortunately not use Print because it depends on Contexts... *)
+               show_var var ^ " -> " ^ V.show_typed_value value)
+             vars)));
   assert (
     List.for_all
       (fun (var, (value : typed_value)) -> var.var_ty = value.ty)
diff --git a/compiler/Driver.ml b/compiler/Driver.ml
index b646a53d..128ae890 100644
--- a/compiler/Driver.ml
+++ b/compiler/Driver.ml
@@ -17,11 +17,15 @@ let log = main_log
 let _ =
   (* Set up the logging - for now we use default values - TODO: use the
    * command-line arguments *)
-  (* By setting a level for the main_logger_handler, we filter everything *)
+  (* By setting a level for the main_logger_handler, we filter everything.
+     To have a good trace: one should switch between Info and Debug.
+  *)
   Easy_logging.Handlers.set_level main_logger_handler EL.Debug;
   main_log#set_level EL.Info;
   llbc_of_json_logger#set_level EL.Info;
   pre_passes_log#set_level EL.Info;
+  associated_types_log#set_level EL.Info;
+  contexts_log#set_level EL.Info;
   interpreter_log#set_level EL.Info;
   statements_log#set_level EL.Info;
   loops_match_ctxs_log#set_level EL.Info;
@@ -37,7 +41,7 @@ let _ =
   pure_utils_log#set_level EL.Info;
   symbolic_to_pure_log#set_level EL.Info;
   pure_micro_passes_log#set_level EL.Info;
-  pure_to_extract_log#set_level EL.Info;
+  extract_log#set_level EL.Info;
   translate_log#set_level EL.Info;
   scc_log#set_level EL.Info;
   reorder_decls_log#set_level EL.Info
@@ -62,6 +66,9 @@ let () =
   (* Read the command line arguments *)
   let dest_dir = ref "" in
 
+  (* Print the imported llbc *)
+  let print_llbc = ref false in
+
   let spec =
     [
       ( "-backend",
@@ -86,9 +93,9 @@ let () =
         Arg.Set extract_decreases_clauses,
         " Use decreases clauses/termination measures for the recursive \
          definitions" );
-      ( "-no-state",
-        Arg.Clear use_state,
-        " Do not use state-error monads, simply use error monads" );
+      ( "-state",
+        Arg.Set use_state,
+        " Use a *state*-error monads, instead of an error monads" );
       ( "-use-fuel",
         Arg.Set use_fuel,
         " Use a fuel parameter to control divergence" );
@@ -99,10 +106,10 @@ let () =
         Arg.Set extract_template_decreases_clauses,
         " Generate templates for the required decreases clauses/termination \
          measures, in a dedicated file. Implies -decreases-clauses" );
-      ( "-no-split-files",
-        Arg.Clear split_files,
-        " Do not split the definitions between different files for types, \
-         functions, etc." );
+      ( "-split-files",
+        Arg.Set split_files,
+        " Split the definitions between different files for types, functions, \
+         etc." );
       ( "-no-check-inv",
         Arg.Clear check_invariants,
         " Deactivate the invariant sanity checks performed at every evaluation \
@@ -114,6 +121,8 @@ let () =
       ( "-lean-default-lakefile",
         Arg.Clear lean_gen_lakefile,
         " Generate a default lakefile.lean (Lean only)" );
+      ("-print-llbc", Arg.Set print_llbc, " Print the imported LLBC");
+      ("-k", Arg.Clear fail_hard, " Do not fail hard in case of error");
     ]
   in
 
@@ -127,6 +136,7 @@ let () =
   in
 
   if !extract_template_decreases_clauses then extract_decreases_clauses := true;
+  if !print_llbc then main_log#set_level EL.Debug;
 
   (* Sanity check (now that the arguments are parsed!): -template-clauses ==> decrease-clauses *)
   assert (!extract_decreases_clauses || not !extract_template_decreases_clauses);
@@ -158,14 +168,14 @@ let () =
     | FStar ->
         (* Some patterns are not supported *)
         decompose_monadic_let_bindings := false;
-        decompose_nested_let_patterns := false
+        decompose_nested_let_patterns := false;
+        (* F* can disambiguate the field names *)
+        record_fields_short_names := true
     | Coq ->
         (* Some patterns are not supported *)
         decompose_monadic_let_bindings := true;
         decompose_nested_let_patterns := true
     | Lean ->
-        (* The Lean backend is experimental: print a warning *)
-        log#lwarning (lazy "The Lean backend is experimental");
         (* We don't support fuel for the Lean backend *)
         if !use_fuel then (
           log#error "The Lean backend doesn't support the -use-fuel option";
@@ -212,28 +222,6 @@ let () =
       log#linfo (lazy ("Imported: " ^ filename));
       log#ldebug (lazy ("\n" ^ Print.Crate.crate_to_string m ^ "\n"));
 
-      (* Print a warning if the crate contains loops (loops are experimental for now) *)
-      let has_loops =
-        A.FunDeclId.Map.exists
-          (fun _ -> Aeneas.LlbcAstUtils.fun_decl_has_loops)
-          m.functions
-      in
-      if has_loops then log#lwarning (lazy "Support for loops is experimental");
-
-      (* If we target Lean, we request the crates to be split into several files
-         whenever there are opaque functions *)
-      if
-        !backend = Lean
-        && A.FunDeclId.Map.exists
-             (fun _ (d : A.fun_decl) -> d.body = None)
-             m.functions
-        && not !split_files
-      then (
-        log#error
-          "For Lean, we request the -split-file option whenever using opaque \
-           functions";
-        fail ());
-
       (* We don't support mutually recursive definitions with decreases clauses in Lean *)
       if
         !backend = Lean && !extract_decreases_clauses
diff --git a/compiler/Extract.ml b/compiler/Extract.ml
index c4238d83..d04f5c1d 100644
--- a/compiler/Extract.ml
+++ b/compiler/Extract.ml
@@ -3,2102 +3,104 @@
    the formatter everywhere...
 *)
 
-open Utils
 open Pure
 open PureUtils
 open TranslateCore
 open ExtractBase
-open StringUtils
 open Config
-module F = Format
-
-(** Small helper to compute the name of an int type *)
-let int_name (int_ty : integer_type) =
-  let isize, usize, i_format, u_format =
-    match !backend with
-    | FStar | Coq | HOL4 ->
-        ("isize", "usize", format_of_string "i%d", format_of_string "u%d")
-    | Lean -> ("Isize", "Usize", format_of_string "I%d", format_of_string "U%d")
-  in
-  match int_ty with
-  | Isize -> isize
-  | I8 -> Printf.sprintf i_format 8
-  | I16 -> Printf.sprintf i_format 16
-  | I32 -> Printf.sprintf i_format 32
-  | I64 -> Printf.sprintf i_format 64
-  | I128 -> Printf.sprintf i_format 128
-  | Usize -> usize
-  | U8 -> Printf.sprintf u_format 8
-  | U16 -> Printf.sprintf u_format 16
-  | U32 -> Printf.sprintf u_format 32
-  | U64 -> Printf.sprintf u_format 64
-  | U128 -> Printf.sprintf u_format 128
-
-(** Small helper to compute the name of a unary operation *)
-let unop_name (unop : unop) : string =
-  match unop with
-  | Not -> (
-      match !backend with FStar | Lean -> "not" | Coq -> "negb" | HOL4 -> "~")
-  | Neg (int_ty : integer_type) -> (
-      match !backend with Lean -> "-" | _ -> int_name int_ty ^ "_neg")
-  | Cast _ ->
-      (* We never directly use the unop name in this case *)
-      raise (Failure "Unsupported")
-
-(** Small helper to compute the name of a binary operation (note that many
-    binary operations like "less than" are extracted to primitive operations,
-    like [<]).
- *)
-let named_binop_name (binop : E.binop) (int_ty : integer_type) : string =
-  let binop =
-    match binop with
-    | Div -> "div"
-    | Rem -> "rem"
-    | Add -> "add"
-    | Sub -> "sub"
-    | Mul -> "mul"
-    | Lt -> "lt"
-    | Le -> "le"
-    | Ge -> "ge"
-    | Gt -> "gt"
-    | _ -> raise (Failure "Unreachable")
-  in
-  (* Remark: the Lean case is actually not used *)
-  match !backend with
-  | Lean -> int_name int_ty ^ "." ^ binop
-  | FStar | Coq | HOL4 -> int_name int_ty ^ "_" ^ binop
-
-(** A list of keywords/identifiers used by the backend and with which we
-    want to check collision.
-
-    Remark: this is useful mostly to look for collisions when generating
-    names for *variables*.
- *)
-let keywords () =
-  let named_unops =
-    unop_name Not
-    :: List.map (fun it -> unop_name (Neg it)) T.all_signed_int_types
-  in
-  let named_binops = [ E.Div; Rem; Add; Sub; Mul ] in
-  let named_binops =
-    List.concat_map
-      (fun bn -> List.map (fun it -> named_binop_name bn it) T.all_int_types)
-      named_binops
-  in
-  let misc =
-    match !backend with
-    | FStar ->
-        [
-          "assert";
-          "assert_norm";
-          "assume";
-          "else";
-          "fun";
-          "fn";
-          "FStar";
-          "FStar.Mul";
-          "if";
-          "in";
-          "include";
-          "int";
-          "let";
-          "list";
-          "match";
-          "not";
-          "open";
-          "rec";
-          "scalar_cast";
-          "then";
-          "type";
-          "Type0";
-          "Type";
-          "unit";
-          "val";
-          "with";
-        ]
-    | Coq ->
-        [
-          "assert";
-          "Arguments";
-          "Axiom";
-          "char_of_byte";
-          "Check";
-          "Declare";
-          "Definition";
-          "else";
-          "End";
-          "fun";
-          "Fixpoint";
-          "if";
-          "in";
-          "int";
-          "Inductive";
-          "Import";
-          "let";
-          "Lemma";
-          "match";
-          "Module";
-          "not";
-          "Notation";
-          "Proof";
-          "Qed";
-          "rec";
-          "Record";
-          "Require";
-          "Scope";
-          "Search";
-          "SearchPattern";
-          "Set";
-          "then";
-          (* [tt] is unit *)
-          "tt";
-          "type";
-          "Type";
-          "unit";
-          "with";
-        ]
-    | Lean ->
-        [
-          "by";
-          "class";
-          "decreasing_by";
-          "def";
-          "deriving";
-          "do";
-          "else";
-          "end";
-          "for";
-          "have";
-          "if";
-          "inductive";
-          "instance";
-          "import";
-          "let";
-          "macro";
-          "match";
-          "namespace";
-          "opaque";
-          "open";
-          "run_cmd";
-          "set_option";
-          "simp";
-          "structure";
-          "syntax";
-          "termination_by";
-          "then";
-          "Type";
-          "unsafe";
-          "where";
-          "with";
-          "opaque_defs";
-        ]
-    | HOL4 ->
-        [
-          "Axiom";
-          "case";
-          "Definition";
-          "else";
-          "End";
-          "fix";
-          "fix_exec";
-          "fn";
-          "fun";
-          "if";
-          "in";
-          "int";
-          "Inductive";
-          "let";
-          "of";
-          "Proof";
-          "QED";
-          "then";
-          "Theorem";
-        ]
-  in
-  List.concat [ named_unops; named_binops; misc ]
-
-let assumed_adts () : (assumed_ty * string) list =
-  match !backend with
-  | Lean ->
-      [
-        (State, "State");
-        (Result, "Result");
-        (Error, "Error");
-        (Fuel, "Nat");
-        (Option, "Option");
-        (Vec, "Vec");
-        (Array, "Array");
-        (Slice, "Slice");
-        (Str, "Str");
-        (Range, "Range");
-      ]
-  | Coq | FStar ->
-      [
-        (State, "state");
-        (Result, "result");
-        (Error, "error");
-        (Fuel, "nat");
-        (Option, "option");
-        (Vec, "vec");
-        (Array, "array");
-        (Slice, "slice");
-        (Str, "str");
-        (Range, "range");
-      ]
-  | HOL4 ->
-      [
-        (State, "state");
-        (Result, "result");
-        (Error, "error");
-        (Fuel, "num");
-        (Option, "option");
-        (Vec, "vec");
-        (Array, "array");
-        (Slice, "slice");
-        (Str, "str");
-        (Range, "range");
-      ]
-
-let assumed_struct_constructors () : (assumed_ty * string) list =
-  match !backend with
-  | Lean -> [ (Range, "Range.mk"); (Array, "Array.make") ]
-  | Coq -> [ (Range, "mk_range"); (Array, "mk_array") ]
-  | FStar -> [ (Range, "Mkrange"); (Array, "mk_array") ]
-  | HOL4 -> [ (Range, "mk_range"); (Array, "mk_array") ]
-
-let assumed_variants () : (assumed_ty * VariantId.id * string) list =
-  match !backend with
-  | FStar ->
-      [
-        (Result, result_return_id, "Return");
-        (Result, result_fail_id, "Fail");
-        (Error, error_failure_id, "Failure");
-        (Error, error_out_of_fuel_id, "OutOfFuel");
-        (* No Fuel::Zero on purpose *)
-        (* No Fuel::Succ on purpose *)
-        (Option, option_some_id, "Some");
-        (Option, option_none_id, "None");
-      ]
-  | Coq ->
-      [
-        (Result, result_return_id, "Return");
-        (Result, result_fail_id, "Fail_");
-        (Error, error_failure_id, "Failure");
-        (Error, error_out_of_fuel_id, "OutOfFuel");
-        (Fuel, fuel_zero_id, "O");
-        (Fuel, fuel_succ_id, "S");
-        (Option, option_some_id, "Some");
-        (Option, option_none_id, "None");
-      ]
-  | Lean ->
-      [
-        (Result, result_return_id, "ret");
-        (Result, result_fail_id, "fail");
-        (Error, error_failure_id, "panic");
-        (* No Fuel::Zero on purpose *)
-        (* No Fuel::Succ on purpose *)
-        (Option, option_some_id, "some");
-        (Option, option_none_id, "none");
-      ]
-  | HOL4 ->
-      [
-        (Result, result_return_id, "Return");
-        (Result, result_fail_id, "Fail");
-        (Error, error_failure_id, "Failure");
-        (* No Fuel::Zero on purpose *)
-        (* No Fuel::Succ on purpose *)
-        (Option, option_some_id, "SOME");
-        (Option, option_none_id, "NONE");
-      ]
-
-let assumed_llbc_functions () :
-    (A.assumed_fun_id * T.RegionGroupId.id option * string) list =
-  let rg0 = Some T.RegionGroupId.zero in
-  match !backend with
-  | FStar | Coq | HOL4 ->
-      [
-        (Replace, None, "mem_replace_fwd");
-        (Replace, rg0, "mem_replace_back");
-        (VecNew, None, "vec_new");
-        (VecPush, None, "vec_push_fwd") (* Shouldn't be used *);
-        (VecPush, rg0, "vec_push_back");
-        (VecInsert, None, "vec_insert_fwd") (* Shouldn't be used *);
-        (VecInsert, rg0, "vec_insert_back");
-        (VecLen, None, "vec_len");
-        (VecIndex, None, "vec_index_fwd");
-        (VecIndex, rg0, "vec_index_back") (* shouldn't be used *);
-        (VecIndexMut, None, "vec_index_mut_fwd");
-        (VecIndexMut, rg0, "vec_index_mut_back");
-        (ArrayIndexShared, None, "array_index_shared");
-        (ArrayIndexMut, None, "array_index_mut_fwd");
-        (ArrayIndexMut, rg0, "array_index_mut_back");
-        (ArrayToSliceShared, None, "array_to_slice_shared");
-        (ArrayToSliceMut, None, "array_to_slice_mut_fwd");
-        (ArrayToSliceMut, rg0, "array_to_slice_mut_back");
-        (ArraySubsliceShared, None, "array_subslice_shared");
-        (ArraySubsliceMut, None, "array_subslice_mut_fwd");
-        (ArraySubsliceMut, rg0, "array_subslice_mut_back");
-        (SliceIndexShared, None, "slice_index_shared");
-        (SliceIndexMut, None, "slice_index_mut_fwd");
-        (SliceIndexMut, rg0, "slice_index_mut_back");
-        (SliceSubsliceShared, None, "slice_subslice_shared");
-        (SliceSubsliceMut, None, "slice_subslice_mut_fwd");
-        (SliceSubsliceMut, rg0, "slice_subslice_mut_back");
-        (SliceLen, None, "slice_len");
-      ]
-  | Lean ->
-      [
-        (Replace, None, "mem.replace");
-        (Replace, rg0, "mem.replace_back");
-        (VecNew, None, "Vec.new");
-        (VecPush, None, "Vec.push_fwd") (* Shouldn't be used *);
-        (VecPush, rg0, "Vec.push");
-        (VecInsert, None, "Vec.insert_fwd") (* Shouldn't be used *);
-        (VecInsert, rg0, "Vec.insert");
-        (VecLen, None, "Vec.len");
-        (VecIndex, None, "Vec.index_shared");
-        (VecIndex, rg0, "Vec.index_shared_back") (* shouldn't be used *);
-        (VecIndexMut, None, "Vec.index_mut");
-        (VecIndexMut, rg0, "Vec.index_mut_back");
-        (ArrayIndexShared, None, "Array.index_shared");
-        (ArrayIndexMut, None, "Array.index_mut");
-        (ArrayIndexMut, rg0, "Array.index_mut_back");
-        (ArrayToSliceShared, None, "Array.to_slice_shared");
-        (ArrayToSliceMut, None, "Array.to_slice_mut");
-        (ArrayToSliceMut, rg0, "Array.to_slice_mut_back");
-        (ArraySubsliceShared, None, "Array.subslice_shared");
-        (ArraySubsliceMut, None, "Array.subslice_mut");
-        (ArraySubsliceMut, rg0, "Array.subslice_mut_back");
-        (SliceIndexShared, None, "Slice.index_shared");
-        (SliceIndexMut, None, "Slice.index_mut");
-        (SliceIndexMut, rg0, "Slice.index_mut_back");
-        (SliceSubsliceShared, None, "Slice.subslice_shared");
-        (SliceSubsliceMut, None, "Slice.subslice_mut");
-        (SliceSubsliceMut, rg0, "Slice.subslice_mut_back");
-        (SliceLen, None, "Slice.len");
-      ]
-
-let assumed_pure_functions () : (pure_assumed_fun_id * string) list =
-  match !backend with
-  | FStar ->
-      [
-        (Return, "return");
-        (Fail, "fail");
-        (Assert, "massert");
-        (FuelDecrease, "decrease");
-        (FuelEqZero, "is_zero");
-      ]
-  | Coq ->
-      (* We don't provide [FuelDecrease] and [FuelEqZero] on purpose *)
-      [ (Return, "return_"); (Fail, "fail_"); (Assert, "massert") ]
-  | Lean ->
-      (* We don't provide [FuelDecrease] and [FuelEqZero] on purpose *)
-      [ (Return, "return"); (Fail, "fail_"); (Assert, "massert") ]
-  | HOL4 ->
-      (* We don't provide [FuelDecrease] and [FuelEqZero] on purpose *)
-      [ (Return, "return"); (Fail, "fail"); (Assert, "massert") ]
-
-let names_map_init () : names_map_init =
-  {
-    keywords = keywords ();
-    assumed_adts = assumed_adts ();
-    assumed_structs = assumed_struct_constructors ();
-    assumed_variants = assumed_variants ();
-    assumed_llbc_functions = assumed_llbc_functions ();
-    assumed_pure_functions = assumed_pure_functions ();
-  }
-
-let extract_unop (extract_expr : bool -> texpression -> unit)
-    (fmt : F.formatter) (inside : bool) (unop : unop) (arg : texpression) : unit
-    =
-  match unop with
-  | Not | Neg _ ->
-      let unop = unop_name unop in
-      if inside then F.pp_print_string fmt "(";
-      F.pp_print_string fmt unop;
-      F.pp_print_space fmt ();
-      extract_expr true arg;
-      if inside then F.pp_print_string fmt ")"
-  | Cast (src, tgt) -> (
-      (* HOL4 has a special treatment: because it doesn't support dependent
-         types, we don't have a specific operator for the cast *)
-      match !backend with
-      | HOL4 ->
-          (* Casting, say, an u32 to an i32 would be done as follows:
-             {[
-               mk_i32 (u32_to_int x)
-             ]}
-          *)
-          if inside then F.pp_print_string fmt "(";
-          F.pp_print_string fmt ("mk_" ^ int_name tgt);
-          F.pp_print_space fmt ();
-          F.pp_print_string fmt "(";
-          F.pp_print_string fmt (int_name src ^ "_to_int");
-          F.pp_print_space fmt ();
-          extract_expr true arg;
-          F.pp_print_string fmt ")";
-          if inside then F.pp_print_string fmt ")"
-      | FStar | Coq | Lean ->
-          (* Rem.: the source type is an implicit parameter *)
-          if inside then F.pp_print_string fmt "(";
-          let cast_str =
-            match !backend with
-            | Coq | FStar -> "scalar_cast"
-            | Lean -> (* TODO: I8.cast, I16.cast, etc.*) "Scalar.cast"
-            | HOL4 -> raise (Failure "Unreachable")
-          in
-          F.pp_print_string fmt cast_str;
-          F.pp_print_space fmt ();
-          if !backend <> Lean then (
-            F.pp_print_string fmt
-              (StringUtils.capitalize_first_letter
-                 (PrintPure.integer_type_to_string src));
-            F.pp_print_space fmt ());
-          if !backend = Lean then F.pp_print_string fmt ("." ^ int_name tgt)
-          else
-            F.pp_print_string fmt
-              (StringUtils.capitalize_first_letter
-                 (PrintPure.integer_type_to_string tgt));
-          F.pp_print_space fmt ();
-          extract_expr true arg;
-          if inside then F.pp_print_string fmt ")")
-
-(** [extract_expr] : the boolean argument is [inside] *)
-let extract_binop (extract_expr : bool -> texpression -> unit)
-    (fmt : F.formatter) (inside : bool) (binop : E.binop)
-    (int_ty : integer_type) (arg0 : texpression) (arg1 : texpression) : unit =
-  if inside then F.pp_print_string fmt "(";
-  (* Some binary operations have a special notation depending on the backend *)
-  (match (!backend, binop) with
-  | HOL4, (Eq | Ne)
-  | (FStar | Coq | Lean), (Eq | Lt | Le | Ne | Ge | Gt)
-  | Lean, (Div | Rem | Add | Sub | Mul) ->
-      let binop =
-        match binop with
-        | Eq -> "="
-        | Lt -> "<"
-        | Le -> "<="
-        | Ne -> if !backend = Lean then "!=" else "<>"
-        | Ge -> ">="
-        | Gt -> ">"
-        | Div -> "/"
-        | Rem -> "%"
-        | Add -> "+"
-        | Sub -> "-"
-        | Mul -> "*"
-        | _ -> raise (Failure "Unreachable")
-      in
-      let binop =
-        match !backend with FStar | Lean | HOL4 -> binop | Coq -> "s" ^ binop
-      in
-      extract_expr false arg0;
-      F.pp_print_space fmt ();
-      F.pp_print_string fmt binop;
-      F.pp_print_space fmt ();
-      extract_expr false arg1
-  | _, (Lt | Le | Ge | Gt | Div | Rem | Add | Sub | Mul) ->
-      let binop = named_binop_name binop int_ty in
-      F.pp_print_string fmt binop;
-      F.pp_print_space fmt ();
-      extract_expr true arg0;
-      F.pp_print_space fmt ();
-      extract_expr true arg1
-  | _, (BitXor | BitAnd | BitOr | Shl | Shr) -> raise Unimplemented);
-  if inside then F.pp_print_string fmt ")"
-
-let type_decl_kind_to_qualif (kind : decl_kind)
-    (type_kind : type_decl_kind option) : string option =
-  match !backend with
-  | FStar -> (
-      match kind with
-      | SingleNonRec -> Some "type"
-      | SingleRec -> Some "type"
-      | MutRecFirst -> Some "type"
-      | MutRecInner -> Some "and"
-      | MutRecLast -> Some "and"
-      | Assumed -> Some "assume type"
-      | Declared -> Some "val")
-  | Coq -> (
-      match (kind, type_kind) with
-      | SingleNonRec, Some Enum -> Some "Inductive"
-      | SingleNonRec, Some Struct -> Some "Record"
-      | (SingleRec | MutRecFirst), Some _ -> Some "Inductive"
-      | (MutRecInner | MutRecLast), Some _ ->
-          (* Coq doesn't support groups of mutually recursive definitions which mix
-           * records and inducties: we convert everything to records if this happens
-           *)
-          Some "with"
-      | (Assumed | Declared), None -> Some "Axiom"
-      | _ -> raise (Failure "Unexpected"))
-  | Lean -> (
-      match kind with
-      | SingleNonRec ->
-          if type_kind = Some Struct then Some "structure" else Some "inductive"
-      | SingleRec -> Some "inductive"
-      | MutRecFirst -> Some "inductive"
-      | MutRecInner -> Some "inductive"
-      | MutRecLast -> Some "inductive"
-      | Assumed -> Some "axiom"
-      | Declared -> Some "axiom")
-  | HOL4 -> None
-
-let fun_decl_kind_to_qualif (kind : decl_kind) : string option =
-  match !backend with
-  | FStar -> (
-      match kind with
-      | SingleNonRec -> Some "let"
-      | SingleRec -> Some "let rec"
-      | MutRecFirst -> Some "let rec"
-      | MutRecInner -> Some "and"
-      | MutRecLast -> Some "and"
-      | Assumed -> Some "assume val"
-      | Declared -> Some "val")
-  | Coq -> (
-      match kind with
-      | SingleNonRec -> Some "Definition"
-      | SingleRec -> Some "Fixpoint"
-      | MutRecFirst -> Some "Fixpoint"
-      | MutRecInner -> Some "with"
-      | MutRecLast -> Some "with"
-      | Assumed -> Some "Axiom"
-      | Declared -> Some "Axiom")
-  | Lean -> (
-      match kind with
-      | SingleNonRec -> Some "def"
-      | SingleRec -> Some "divergent def"
-      | MutRecFirst -> Some "mutual divergent def"
-      | MutRecInner -> Some "divergent def"
-      | MutRecLast -> Some "divergent def"
-      | Assumed -> Some "axiom"
-      | Declared -> Some "axiom")
-  | HOL4 -> None
-
-(** The type of types.
-
-    TODO: move inside the formatter?
- *)
-let type_keyword () =
-  match !backend with
-  | FStar -> "Type0"
-  | Coq | Lean -> "Type"
-  | HOL4 -> raise (Failure "Unexpected")
-
-(**
-   [ctx]: we use the context to lookup type definitions, to retrieve type names.
-   This is used to compute variable names, when they have no basenames: in this
-   case we use the first letter of the type name.
-
-   [variant_concatenate_type_name]: if true, add the type name as a prefix
-   to the variant names.
-   Ex.:
-   In Rust:
-     {[
-       enum List = {
-         Cons(u32, Box<List>),x
-         Nil,
-       }
-     ]}
-
-   F*, if option activated:
-     {[
-       type list =
-       | ListCons : u32 -> list -> list
-       | ListNil : list
-     ]}
-
-   F*, if option not activated:
-     {[
-       type list =
-       | Cons : u32 -> list -> list
-       | Nil : list
-     ]}
-
-   Rk.: this should be true by default, because in Rust all the variant names
-   are actively uniquely identifier by the type name [List::Cons(...)], while
-   in other languages it is not necessarily the case, and thus clashes can mess
-   up type checking. Note that some languages actually forbids the name clashes
-   (it is the case of F* ).
- *)
-let mk_formatter (ctx : trans_ctx) (crate_name : string)
-    (variant_concatenate_type_name : bool) : formatter =
-  let int_name = int_name in
-
-  (* Prepare a name.
-   * The first id elem is always the crate: if it is the local crate,
-   * we remove it.
-   * We also remove all the disambiguators, then convert everything to strings.
-   * **Rmk:** because we remove the disambiguators, there may be name collisions
-   * (which is ok, because we check for name collisions and fail if there is any).
-   *)
-  let get_name (name : name) : string list =
-    (* Rmk.: initially we only filtered the disambiguators equal to 0 *)
-    let name = Names.filter_disambiguators name in
-    match name with
-    | Ident crate :: name ->
-        let name = if crate = crate_name then name else Ident crate :: name in
-        let name =
-          List.map
-            (function
-              | Names.Ident s -> s
-              | Disambiguator d -> Names.Disambiguator.to_string d)
-            name
-        in
-        name
-    | _ ->
-        raise (Failure ("Unexpected name shape: " ^ Print.name_to_string name))
-  in
-  let get_type_name = get_name in
-  let type_name_to_camel_case name =
-    let name = get_type_name name in
-    let name = List.map to_camel_case name in
-    String.concat "" name
-  in
-  let type_name_to_snake_case name =
-    let name = get_type_name name in
-    let name = List.map to_snake_case name in
-    let name = String.concat "_" name in
-    match !backend with
-    | FStar | Lean | HOL4 -> name
-    | Coq -> capitalize_first_letter name
-  in
-  let type_name name =
-    match !backend with
-    | FStar | Coq | HOL4 -> type_name_to_snake_case name ^ "_t"
-    | Lean -> String.concat "." (get_type_name name)
-  in
-  let field_name (def_name : name) (field_id : FieldId.id)
-      (field_name : string option) : string =
-    let field_name =
-      match field_name with
-      | Some field_name -> field_name
-      | None -> FieldId.to_string field_id
-    in
-    if !Config.record_fields_short_names then field_name
-    else
-      let def_name = type_name_to_snake_case def_name ^ "_" in
-      def_name ^ field_name
-  in
-  let variant_name (def_name : name) (variant : string) : string =
-    match !backend with
-    | FStar | Coq | HOL4 ->
-        let variant = to_camel_case variant in
-        if variant_concatenate_type_name then
-          type_name_to_camel_case def_name ^ variant
-        else variant
-    | Lean -> variant
-  in
-  let struct_constructor (basename : name) : string =
-    let tname = type_name basename in
-    let prefix =
-      match !backend with FStar -> "Mk" | Coq | HOL4 -> "mk" | Lean -> ""
-    in
-    let suffix =
-      match !backend with FStar | Coq | HOL4 -> "" | Lean -> ".mk"
-    in
-    prefix ^ tname ^ suffix
-  in
-  let get_fun_name fname =
-    let fname = get_name fname in
-    (* TODO: don't convert to snake case for Coq, HOL4, F* *)
-    match !backend with
-    | FStar | Coq | HOL4 -> String.concat "_" (List.map to_snake_case fname)
-    | Lean -> String.concat "." fname
-  in
-  let global_name (name : global_name) : string =
-    (* Converting to snake case also lowercases the letters (in Rust, global
-     * names are written in capital letters). *)
-    let parts = List.map to_snake_case (get_name name) in
-    String.concat "_" parts
-  in
-  let fun_name (fname : fun_name) (num_loops : int) (loop_id : LoopId.id option)
-      (num_rgs : int) (rg : region_group_info option) (filter_info : bool * int)
-      : string =
-    let fname = get_fun_name fname in
-    (* Compute the suffix *)
-    let suffix = default_fun_suffix num_loops loop_id num_rgs rg filter_info in
-    (* Concatenate *)
-    fname ^ suffix
-  in
-
-  let termination_measure_name (_fid : A.FunDeclId.id) (fname : fun_name)
-      (num_loops : int) (loop_id : LoopId.id option) : string =
-    let fname = get_fun_name fname in
-    let lp_suffix = default_fun_loop_suffix num_loops loop_id in
-    (* Compute the suffix *)
-    let suffix =
-      match !Config.backend with
-      | FStar -> "_decreases"
-      | Lean -> "_terminates"
-      | Coq | HOL4 -> raise (Failure "Unexpected")
-    in
-    (* Concatenate *)
-    fname ^ lp_suffix ^ suffix
-  in
-
-  let decreases_proof_name (_fid : A.FunDeclId.id) (fname : fun_name)
-      (num_loops : int) (loop_id : LoopId.id option) : string =
-    let fname = get_fun_name fname in
-    let lp_suffix = default_fun_loop_suffix num_loops loop_id in
-    (* Compute the suffix *)
-    let suffix =
-      match !Config.backend with
-      | Lean -> "_decreases"
-      | FStar | Coq | HOL4 -> raise (Failure "Unexpected")
-    in
-    (* Concatenate *)
-    fname ^ lp_suffix ^ suffix
-  in
-
-  let opaque_pre () =
-    match !Config.backend with
-    | FStar | Coq | HOL4 -> ""
-    | Lean -> if !Config.wrap_opaque_in_sig then "opaque_defs." else ""
-  in
-
-  let var_basename (_varset : StringSet.t) (basename : string option) (ty : ty)
-      : string =
-    (* If there is a basename, we use it *)
-    match basename with
-    | Some basename ->
-        (* This should be a no-op *)
-        to_snake_case basename
-    | None -> (
-        (* No basename: we use the first letter of the type *)
-        match ty with
-        | Adt (type_id, tys, _) -> (
-            match type_id with
-            | Tuple ->
-                (* The "pair" case is frequent enough to have its special treatment *)
-                if List.length tys = 2 then "p" else "t"
-            | Assumed Result -> "r"
-            | Assumed Error -> ConstStrings.error_basename
-            | Assumed Fuel -> ConstStrings.fuel_basename
-            | Assumed Option -> "opt"
-            | Assumed Vec -> "v"
-            | Assumed Array -> "a"
-            | Assumed Slice -> "s"
-            | Assumed Str -> "s"
-            | Assumed Range -> "r"
-            | Assumed State -> ConstStrings.state_basename
-            | AdtId adt_id ->
-                let def =
-                  TypeDeclId.Map.find adt_id ctx.type_context.type_decls
-                in
-                (* We do the following:
-                 * - compute the type name, and retrieve the last ident
-                 * - convert this to snake case
-                 * - take the first letter of every "letter group"
-                 * Ex.: ["hashmap"; "HashMap"] ~~> "HashMap" -> "hash_map" -> "hm"
-                 *)
-                (* Thename shouldn't be empty, and its last element should
-                 * be an ident *)
-                let cl = List.nth def.name (List.length def.name - 1) in
-                let cl = to_snake_case (Names.as_ident cl) in
-                let cl = String.split_on_char '_' cl in
-                let cl = List.filter (fun s -> String.length s > 0) cl in
-                assert (List.length cl > 0);
-                let cl = List.map (fun s -> s.[0]) cl in
-                StringUtils.string_of_chars cl)
-        | TypeVar _ -> (
-            (* TODO: use "t" also for F* *)
-            match !backend with
-            | FStar -> "x" (* lacking inspiration here... *)
-            | Coq | Lean | HOL4 -> "t" (* lacking inspiration here... *))
-        | Literal lty -> (
-            match lty with Bool -> "b" | Char -> "c" | Integer _ -> "i")
-        | Arrow _ -> "f")
-  in
-  let type_var_basename (_varset : StringSet.t) (basename : string) : string =
-    (* Rust type variables are snake-case and start with a capital letter *)
-    match !backend with
-    | FStar ->
-        (* This is *not* a no-op: this removes the capital letter *)
-        to_snake_case basename
-    | HOL4 ->
-        (* In HOL4, type variable names must start with "'" *)
-        "'" ^ to_snake_case basename
-    | Coq | Lean -> basename
-  in
-  let const_generic_var_basename (_varset : StringSet.t) (basename : string) :
-      string =
-    (* Rust type variables are snake-case and start with a capital letter *)
-    match !backend with
-    | FStar | HOL4 ->
-        (* This is *not* a no-op: this removes the capital letter *)
-        to_snake_case basename
-    | Coq | Lean -> basename
-  in
-  let append_index (basename : string) (i : int) : string =
-    basename ^ string_of_int i
-  in
-
-  let extract_literal (fmt : F.formatter) (inside : bool) (cv : literal) : unit
-      =
-    match cv with
-    | Scalar sv -> (
-        match !backend with
-        | FStar -> F.pp_print_string fmt (Z.to_string sv.PV.value)
-        | Coq | HOL4 ->
-            let print_brackets = inside && !backend = HOL4 in
-            if print_brackets then F.pp_print_string fmt "(";
-            (match !backend with
-            | Coq -> ()
-            | HOL4 ->
-                F.pp_print_string fmt ("int_to_" ^ int_name sv.PV.int_ty);
-                F.pp_print_space fmt ()
-            | _ -> raise (Failure "Unreachable"));
-            (* We need to add parentheses if the value is negative *)
-            if sv.PV.value >= Z.of_int 0 then
-              F.pp_print_string fmt (Z.to_string sv.PV.value)
-            else F.pp_print_string fmt ("(" ^ Z.to_string sv.PV.value ^ ")");
-            (match !backend with
-            | Coq -> F.pp_print_string fmt ("%" ^ int_name sv.PV.int_ty)
-            | HOL4 -> ()
-            | _ -> raise (Failure "Unreachable"));
-            if print_brackets then F.pp_print_string fmt ")"
-        | Lean ->
-            F.pp_print_string fmt "(";
-            F.pp_print_string fmt (int_name sv.int_ty);
-            F.pp_print_string fmt ".ofInt ";
-            (* Something very annoying: negated values like `-3` are
-               ambiguous in Lean because of conversions, so we have to
-               be extremely explicit with negative numbers.
-            *)
-            if Z.lt sv.value Z.zero then (
-              F.pp_print_string fmt "(";
-              F.pp_print_string fmt "-";
-              F.pp_print_string fmt "(";
-              Z.pp_print fmt (Z.neg sv.value);
-              F.pp_print_string fmt ":Int";
-              F.pp_print_string fmt ")";
-              F.pp_print_string fmt ")")
-            else Z.pp_print fmt sv.value;
-            F.pp_print_string fmt ")")
-    | Bool b ->
-        let b =
-          match !backend with
-          | HOL4 -> if b then "T" else "F"
-          | Coq | FStar | Lean -> if b then "true" else "false"
-        in
-        F.pp_print_string fmt b
-    | Char c -> (
-        match !backend with
-        | HOL4 ->
-            (* [#"a"] is a notation for [CHR 97] (97 is the ASCII code for 'a') *)
-            F.pp_print_string fmt ("#\"" ^ String.make 1 c ^ "\"")
-        | FStar | Lean -> F.pp_print_string fmt ("'" ^ String.make 1 c ^ "'")
-        | Coq ->
-            if inside then F.pp_print_string fmt "(";
-            F.pp_print_string fmt "char_of_byte";
-            F.pp_print_space fmt ();
-            (* Convert the the char to ascii *)
-            let c =
-              let i = Char.code c in
-              let x0 = i / 16 in
-              let x1 = i mod 16 in
-              "Coq.Init.Byte.x" ^ string_of_int x0 ^ string_of_int x1
-            in
-            F.pp_print_string fmt c;
-            if inside then F.pp_print_string fmt ")")
-  in
-  let bool_name = if !backend = Lean then "Bool" else "bool" in
-  let char_name = if !backend = Lean then "Char" else "char" in
-  let str_name = if !backend = Lean then "String" else "string" in
-  {
-    bool_name;
-    char_name;
-    int_name;
-    str_name;
-    type_decl_kind_to_qualif;
-    fun_decl_kind_to_qualif;
-    field_name;
-    variant_name;
-    struct_constructor;
-    type_name;
-    global_name;
-    fun_name;
-    termination_measure_name;
-    decreases_proof_name;
-    opaque_pre;
-    var_basename;
-    type_var_basename;
-    const_generic_var_basename;
-    append_index;
-    extract_literal;
-    extract_unop;
-    extract_binop;
-  }
-
-let mk_formatter_and_names_map (ctx : trans_ctx) (crate_name : string)
-    (variant_concatenate_type_name : bool) : formatter * names_map =
-  let fmt = mk_formatter ctx crate_name variant_concatenate_type_name in
-  let names_map = initialize_names_map fmt (names_map_init ()) in
-  (fmt, names_map)
-
-let is_single_opaque_fun_decl_group (dg : Pure.fun_decl list) : bool =
-  match dg with [ d ] -> d.body = None | _ -> false
-
-let is_single_opaque_type_decl_group (dg : Pure.type_decl list) : bool =
-  match dg with [ d ] -> d.kind = Opaque | _ -> false
-
-let is_empty_record_type_decl (d : Pure.type_decl) : bool = d.kind = Struct []
-
-let is_empty_record_type_decl_group (dg : Pure.type_decl list) : bool =
-  match dg with [ d ] -> is_empty_record_type_decl d | _ -> false
-
-(** In some provers, groups of definitions must be delimited.
-
-    - in Coq, *every* group (including singletons) must end with "."
-    - in Lean, groups of mutually recursive definitions must end with "end"
-    - in HOL4 (in most situations) the whole group must be within a `Define` command
-
-    Calls to {!extract_fun_decl} should be inserted between calls to
-    {!start_fun_decl_group} and {!end_fun_decl_group}.
-
-    TODO: maybe those [{start/end}_decl_group] functions are not that much a good
-    idea and we should merge them with the corresponding [extract_decl] functions.
- *)
-let start_fun_decl_group (ctx : extraction_ctx) (fmt : F.formatter)
-    (is_rec : bool) (dg : Pure.fun_decl list) =
-  match !backend with
-  | FStar | Coq | Lean -> ()
-  | HOL4 ->
-      (* In HOL4, opaque functions have a special treatment *)
-      if is_single_opaque_fun_decl_group dg then ()
-      else
-        let with_opaque_pre = false in
-        let compute_fun_def_name (def : Pure.fun_decl) : string =
-          ctx_get_local_function with_opaque_pre def.def_id def.loop_id
-            def.back_id ctx
-          ^ "_def"
-        in
-        let names = List.map compute_fun_def_name dg in
-        (* Add a break before *)
-        F.pp_print_break fmt 0 0;
-        (* Open the box for the delimiters *)
-        F.pp_open_vbox fmt 0;
-        (* Open the box for the definitions themselves *)
-        F.pp_open_vbox fmt ctx.indent_incr;
-        (* Print the delimiters *)
-        if is_rec then
-          F.pp_print_string fmt
-            ("val [" ^ String.concat ", " names ^ "] = DefineDiv ‘")
-        else (
-          assert (List.length names = 1);
-          let name = List.hd names in
-          F.pp_print_string fmt ("val " ^ name ^ " = Define ‘"));
-        F.pp_print_cut fmt ()
-
-(** See {!start_fun_decl_group}. *)
-let end_fun_decl_group (fmt : F.formatter) (is_rec : bool)
-    (dg : Pure.fun_decl list) =
-  match !backend with
-  | FStar -> ()
-  | Coq ->
-      (* For aesthetic reasons, we print the Coq end group delimiter directly
-         in {!extract_fun_decl}. *)
-      ()
-  | Lean ->
-      (* We must add the "end" keyword to groups of mutually recursive functions *)
-      if is_rec && List.length dg > 1 then (
-        F.pp_print_cut fmt ();
-        F.pp_print_string fmt "end";
-        (* Add breaks to insert new lines between definitions *)
-        F.pp_print_break fmt 0 0)
-      else ()
-  | HOL4 ->
-      (* In HOL4, opaque functions have a special treatment *)
-      if is_single_opaque_fun_decl_group dg then ()
-      else (
-        (* Close the box for the definitions *)
-        F.pp_close_box fmt ();
-        (* Print the end delimiter *)
-        F.pp_print_cut fmt ();
-        F.pp_print_string fmt "’";
-        (* Close the box for the delimiters *)
-        F.pp_close_box fmt ();
-        (* Add breaks to insert new lines between definitions *)
-        F.pp_print_break fmt 0 0)
-
-(** See {!start_fun_decl_group}: similar usage, but for the type declarations. *)
-let start_type_decl_group (ctx : extraction_ctx) (fmt : F.formatter)
-    (is_rec : bool) (dg : Pure.type_decl list) =
-  match !backend with
-  | FStar | Coq -> ()
-  | Lean ->
-      if is_rec && List.length dg > 1 then (
-        F.pp_print_space fmt ();
-        F.pp_print_string fmt "mutual";
-        F.pp_print_space fmt ())
-  | HOL4 ->
-      (* In HOL4, opaque types and empty records have a special treatment *)
-      if
-        is_single_opaque_type_decl_group dg
-        || is_empty_record_type_decl_group dg
-      then ()
-      else (
-        (* Add a break before *)
-        F.pp_print_break fmt 0 0;
-        (* Open the box for the delimiters *)
-        F.pp_open_vbox fmt 0;
-        (* Open the box for the definitions themselves *)
-        F.pp_open_vbox fmt ctx.indent_incr;
-        (* Print the delimiters *)
-        F.pp_print_string fmt "Datatype:";
-        F.pp_print_cut fmt ())
-
-(** See {!start_fun_decl_group}. *)
-let end_type_decl_group (fmt : F.formatter) (is_rec : bool)
-    (dg : Pure.type_decl list) =
-  match !backend with
-  | FStar -> ()
-  | Coq ->
-      (* For aesthetic reasons, we print the Coq end group delimiter directly
-         in {!extract_fun_decl}. *)
-      ()
-  | Lean ->
-      (* We must add the "end" keyword to groups of mutually recursive functions *)
-      if is_rec && List.length dg > 1 then (
-        F.pp_print_cut fmt ();
-        F.pp_print_string fmt "end";
-        (* Add breaks to insert new lines between definitions *)
-        F.pp_print_break fmt 0 0)
-      else ()
-  | HOL4 ->
-      (* In HOL4, opaque types and empty records have a special treatment *)
-      if
-        is_single_opaque_type_decl_group dg
-        || is_empty_record_type_decl_group dg
-      then ()
-      else (
-        (* Close the box for the definitions *)
-        F.pp_close_box fmt ();
-        (* Print the end delimiter *)
-        F.pp_print_cut fmt ();
-        F.pp_print_string fmt "End";
-        (* Close the box for the delimiters *)
-        F.pp_close_box fmt ();
-        (* Add breaks to insert new lines between definitions *)
-        F.pp_print_break fmt 0 0)
-
-let unit_name () =
-  match !backend with Lean -> "Unit" | Coq | FStar | HOL4 -> "unit"
-
-(** Small helper *)
-let extract_arrow (fmt : F.formatter) () : unit =
-  if !Config.backend = Lean then F.pp_print_string fmt "→"
-  else F.pp_print_string fmt "->"
-
-let extract_const_generic (ctx : extraction_ctx) (fmt : F.formatter)
-    (inside : bool) (cg : const_generic) : unit =
-  match cg with
-  | ConstGenericGlobal id ->
-      let s = ctx_get_global ctx.use_opaque_pre id ctx in
-      F.pp_print_string fmt s
-  | ConstGenericValue v -> ctx.fmt.extract_literal fmt inside v
-  | ConstGenericVar id ->
-      let s = ctx_get_const_generic_var id ctx in
-      F.pp_print_string fmt s
-
-let extract_literal_type (ctx : extraction_ctx) (fmt : F.formatter)
-    (ty : literal_type) : unit =
-  match ty with
-  | Bool -> F.pp_print_string fmt ctx.fmt.bool_name
-  | Char -> F.pp_print_string fmt ctx.fmt.char_name
-  | Integer int_ty -> F.pp_print_string fmt (ctx.fmt.int_name int_ty)
-
-(** [inside] constrols whether we should add parentheses or not around type
-    applications (if [true] we add parentheses).
-
-    [no_params_tys]: for all the types inside this set, do not print the type parameters.
-    This is used for HOL4. As polymorphism is uniform in HOL4, printing the
-    type parameters in the recursive definitions is useless (and actually
-    forbidden).
-
-    For instance, where in F* we would write:
-    {[
-      type list a = | Nil : list a | Cons : a -> list a -> list a
-    ]}
-
-    In HOL4 we would simply write:
-    {[
-      Datatype:
-        list = Nil 'a | Cons 'a list
-      End
-    ]}
- *)
-let rec extract_ty (ctx : extraction_ctx) (fmt : F.formatter)
-    (no_params_tys : TypeDeclId.Set.t) (inside : bool) (ty : ty) : unit =
-  let extract_rec = extract_ty ctx fmt no_params_tys in
-  match ty with
-  | Adt (type_id, tys, cgs) -> (
-      let has_params = tys <> [] || cgs <> [] in
-      match type_id with
-      | Tuple ->
-          (* This is a bit annoying, but in F*/Coq/HOL4 [()] is not the unit type:
-           * we have to write [unit]... *)
-          if tys = [] then F.pp_print_string fmt (unit_name ())
-          else (
-            F.pp_print_string fmt "(";
-            Collections.List.iter_link
-              (fun () ->
-                F.pp_print_space fmt ();
-                let product =
-                  match !backend with
-                  | FStar -> "&"
-                  | Coq -> "*"
-                  | Lean -> "×"
-                  | HOL4 -> "#"
-                in
-                F.pp_print_string fmt product;
-                F.pp_print_space fmt ())
-              (extract_rec true) tys;
-            F.pp_print_string fmt ")")
-      | AdtId _ | Assumed _ -> (
-          (* HOL4 behaves differently. Where in Coq/FStar/Lean we would write:
-             `tree a b`
-
-             In HOL4 we would write:
-             `('a, 'b) tree`
-          *)
-          let with_opaque_pre = false in
-          match !backend with
-          | FStar | Coq | Lean ->
-              let print_paren = inside && has_params in
-              if print_paren then F.pp_print_string fmt "(";
-              (* TODO: for now, only the opaque *functions* are extracted in the
-                 opaque module. The opaque *types* are assumed. *)
-              F.pp_print_string fmt (ctx_get_type with_opaque_pre type_id ctx);
-              if tys <> [] then (
-                F.pp_print_space fmt ();
-                Collections.List.iter_link (F.pp_print_space fmt)
-                  (extract_rec true) tys);
-              if cgs <> [] then (
-                F.pp_print_space fmt ();
-                Collections.List.iter_link (F.pp_print_space fmt)
-                  (extract_const_generic ctx fmt true)
-                  cgs);
-              if print_paren then F.pp_print_string fmt ")"
-          | HOL4 ->
-              (* Const generics are unsupported in HOL4 *)
-              assert (cgs = []);
-              let print_tys =
-                match type_id with
-                | AdtId id -> not (TypeDeclId.Set.mem id no_params_tys)
-                | Assumed _ -> true
-                | _ -> raise (Failure "Unreachable")
-              in
-              if tys <> [] && print_tys then (
-                let print_paren = List.length tys > 1 in
-                if print_paren then F.pp_print_string fmt "(";
-                Collections.List.iter_link
-                  (fun () ->
-                    F.pp_print_string fmt ",";
-                    F.pp_print_space fmt ())
-                  (extract_rec true) tys;
-                if print_paren then F.pp_print_string fmt ")";
-                F.pp_print_space fmt ());
-              F.pp_print_string fmt (ctx_get_type with_opaque_pre type_id ctx)))
-  | TypeVar vid -> F.pp_print_string fmt (ctx_get_type_var vid ctx)
-  | Literal lty -> extract_literal_type ctx fmt lty
-  | Arrow (arg_ty, ret_ty) ->
-      if inside then F.pp_print_string fmt "(";
-      extract_rec false arg_ty;
-      F.pp_print_space fmt ();
-      extract_arrow fmt ();
-      F.pp_print_space fmt ();
-      extract_rec false ret_ty;
-      if inside then F.pp_print_string fmt ")"
-
-(** Compute the names for all the top-level identifiers used in a type
-    definition (type name, variant names, field names, etc. but not type
-    parameters).
-
-    We need to do this preemptively, beforce extracting any definition,
-    because of recursive definitions.
- *)
-let extract_type_decl_register_names (ctx : extraction_ctx) (def : type_decl) :
-    extraction_ctx =
-  (* Compute and register the type def name *)
-  let ctx = ctx_add_type_decl def ctx in
-  (* Compute and register:
-   * - the variant names, if this is an enumeration
-   * - the field names, if this is a structure
-   *)
-  let ctx =
-    match def.kind with
-    | Struct fields ->
-        (* Add the fields *)
-        let ctx =
-          fst
-            (ctx_add_fields def (FieldId.mapi (fun id f -> (id, f)) fields) ctx)
-        in
-        (* Add the constructor name *)
-        fst (ctx_add_struct def ctx)
-    | Enum variants ->
-        fst
-          (ctx_add_variants def
-             (VariantId.mapi (fun id v -> (id, v)) variants)
-             ctx)
-    | Opaque ->
-        (* Nothing to do *)
-        ctx
-  in
-  (* Return *)
-  ctx
-
-(** Print the variants *)
-let extract_type_decl_variant (ctx : extraction_ctx) (fmt : F.formatter)
-    (type_decl_group : TypeDeclId.Set.t) (type_name : string)
-    (type_params : string list) (cg_params : string list) (cons_name : string)
-    (fields : field list) : unit =
-  F.pp_print_space fmt ();
-  (* variant box *)
-  F.pp_open_hvbox fmt ctx.indent_incr;
-  (* [| Cons :]
-   * Note that we really don't want any break above so we print everything
-   * at once. *)
-  let opt_colon = if !backend <> HOL4 then " :" else "" in
-  F.pp_print_string fmt ("| " ^ cons_name ^ opt_colon);
-  let print_field (fid : FieldId.id) (f : field) (ctx : extraction_ctx) :
-      extraction_ctx =
-    F.pp_print_space fmt ();
-    (* Open the field box *)
-    F.pp_open_box fmt ctx.indent_incr;
-    (* Print the field names, if the backend accepts it.
-     * [  x :]
-     * Note that when printing fields, we register the field names as
-     * *variables*: they don't need to be unique at the top level. *)
-    let ctx =
-      match !backend with
-      | FStar -> (
-          match f.field_name with
-          | None -> ctx
-          | Some field_name ->
-              let var_id = VarId.of_int (FieldId.to_int fid) in
-              let field_name =
-                ctx.fmt.var_basename ctx.names_map.names_set (Some field_name)
-                  f.field_ty
-              in
-              let ctx, field_name = ctx_add_var field_name var_id ctx in
-              F.pp_print_string fmt (field_name ^ " :");
-              F.pp_print_space fmt ();
-              ctx)
-      | Coq | Lean | HOL4 -> ctx
-    in
-    (* Print the field type *)
-    let inside = !backend = HOL4 in
-    extract_ty ctx fmt type_decl_group inside f.field_ty;
-    (* Print the arrow [->] *)
-    if !backend <> HOL4 then (
-      F.pp_print_space fmt ();
-      extract_arrow fmt ());
-    (* Close the field box *)
-    F.pp_close_box fmt ();
-    (* Return *)
-    ctx
-  in
-  (* Print the fields *)
-  let fields = FieldId.mapi (fun fid f -> (fid, f)) fields in
-  let _ =
-    List.fold_left (fun ctx (fid, f) -> print_field fid f ctx) ctx fields
-  in
-  (* Sanity check: HOL4 doesn't support const generics *)
-  assert (cg_params = [] || !backend <> HOL4);
-  (* Print the final type *)
-  if !backend <> HOL4 then (
-    F.pp_print_space fmt ();
-    F.pp_open_hovbox fmt 0;
-    F.pp_print_string fmt type_name;
-    List.iter
-      (fun p ->
-        F.pp_print_space fmt ();
-        F.pp_print_string fmt p)
-      (List.append type_params cg_params);
-    F.pp_close_box fmt ());
-  (* Close the variant box *)
-  F.pp_close_box fmt ()
-
-(* TODO: we don' need the [def_name] paramter: it can be retrieved from the context *)
-let extract_type_decl_enum_body (ctx : extraction_ctx) (fmt : F.formatter)
-    (type_decl_group : TypeDeclId.Set.t) (def : type_decl) (def_name : string)
-    (type_params : string list) (cg_params : string list)
-    (variants : variant list) : unit =
-  (* We want to generate a definition which looks like this (taking F* as example):
-     {[
-       type list a = | Cons : a -> list a -> list a | Nil : list a
-     ]}
-
-     If there isn't enough space on one line:
-     {[
-       type s =
-       | Cons : a -> list a -> list a
-       | Nil : list a
-     ]}
-
-     And if we need to write the type of a variant on several lines:
-     {[
-       type s =
-       | Cons :
-         a ->
-         list a ->
-         list a
-       | Nil : list a
-     ]}
-
-     Finally, it is possible to give names to the variant fields in Rust.
-     In this situation, we generate a definition like this:
-     {[
-       type s =
-       | Cons : hd:a -> tl:list a -> list a
-       | Nil : list a
-     ]}
-
-     Note that we already printed: [type s =]
-  *)
-  let print_variant _variant_id (v : variant) =
-    (* We don't lookup the name, because it may have a prefix for the type
-       id (in the case of Lean) *)
-    let cons_name = ctx.fmt.variant_name def.name v.variant_name in
-    let fields = v.fields in
-    extract_type_decl_variant ctx fmt type_decl_group def_name type_params
-      cg_params cons_name fields
-  in
-  (* Print the variants *)
-  let variants = VariantId.mapi (fun vid v -> (vid, v)) variants in
-  List.iter (fun (vid, v) -> print_variant vid v) variants
-
-let extract_type_decl_struct_body (ctx : extraction_ctx) (fmt : F.formatter)
-    (type_decl_group : TypeDeclId.Set.t) (kind : decl_kind) (def : type_decl)
-    (type_params : string list) (cg_params : string list) (fields : field list)
-    : unit =
-  (* We want to generate a definition which looks like this (taking F* as example):
-     {[
-       type t = { x : int; y : bool; }
-     ]}
-
-     If there isn't enough space on one line:
-     {[
-       type t =
-       {
-         x : int; y : bool;
-       }
-     ]}
-
-     And if there is even less space:
-     {[
-       type t =
-       {
-         x : int;
-         y : bool;
-       }
-     ]}
-
-     Also, in case there are no fields, we need to define the type as [unit]
-     ([type t = {}] doesn't work in F* ).
-
-     Coq:
-     ====
-     We need to define the constructor name upon defining the struct (record, in Coq).
-     The syntex is:
-     {[
-       Record Foo = mkFoo { x : int; y : bool; }.
-     }]
-
-     Also, Coq doesn't support groups of mutually recursive inductives and records.
-     This is fine, because we can then define records as inductives, and leverage
-     the fact that when record fields are accessed, the records are symbolically
-     expanded which introduces let bindings of the form: [let RecordCons ... = x in ...].
-     As a consequence, we never use the record projectors (unless we reconstruct
-     them in the micro passes of course).
-
-     HOL4:
-     =====
-     Type definitions are written as follows:
-     {[
-       Datatype:
-         tree =
-           TLeaf 'a
-         | TNode node ;
-
-         node =
-           Node (tree list)
-       End
-     ]}
-  *)
-  (* Note that we already printed: [type t =] *)
-  let is_rec = decl_is_from_rec_group kind in
-  let _ =
-    if !backend = FStar && fields = [] then (
-      F.pp_print_space fmt ();
-      F.pp_print_string fmt (unit_name ()))
-    else if !backend = Lean && fields = [] then ()
-      (* If the definition is recursive, we may need to extract it as an inductive
-         (instead of a record). We start with the "normal" case: we extract it
-         as a record. *)
-    else if (not is_rec) || (!backend <> Coq && !backend <> Lean) then (
-      if !backend <> Lean then F.pp_print_space fmt ();
-      (* If Coq: print the constructor name *)
-      (* TODO: remove superfluous test not is_rec below *)
-      if !backend = Coq && not is_rec then (
-        let with_opaque_pre = false in
-        F.pp_print_string fmt
-          (ctx_get_struct with_opaque_pre (AdtId def.def_id) ctx);
-        F.pp_print_string fmt " ");
-      (match !backend with
-      | Lean -> ()
-      | FStar | Coq -> F.pp_print_string fmt "{"
-      | HOL4 -> F.pp_print_string fmt "<|");
-      F.pp_print_break fmt 1 ctx.indent_incr;
-      (* The body itself *)
-      (* Open a box for the body *)
-      (match !backend with
-      | Coq | FStar | HOL4 -> F.pp_open_hvbox fmt 0
-      | Lean -> F.pp_open_vbox fmt 0);
-      (* Print the fields *)
-      let print_field (field_id : FieldId.id) (f : field) : unit =
-        let field_name = ctx_get_field (AdtId def.def_id) field_id ctx in
-        (* Open a box for the field *)
-        F.pp_open_box fmt ctx.indent_incr;
-        F.pp_print_string fmt field_name;
-        F.pp_print_space fmt ();
-        F.pp_print_string fmt ":";
-        F.pp_print_space fmt ();
-        extract_ty ctx fmt type_decl_group false f.field_ty;
-        if !backend <> Lean then F.pp_print_string fmt ";";
-        (* Close the box for the field *)
-        F.pp_close_box fmt ()
-      in
-      let fields = FieldId.mapi (fun fid f -> (fid, f)) fields in
-      Collections.List.iter_link (F.pp_print_space fmt)
-        (fun (fid, f) -> print_field fid f)
-        fields;
-      (* Close the box for the body *)
-      F.pp_close_box fmt ();
-      match !backend with
-      | Lean -> ()
-      | FStar | Coq ->
-          F.pp_print_space fmt ();
-          F.pp_print_string fmt "}"
-      | HOL4 ->
-          F.pp_print_space fmt ();
-          F.pp_print_string fmt "|>")
-    else (
-      (* We extract for Coq or Lean, and we have a recursive record, or a record in
-         a group of mutually recursive types: we extract it as an inductive type *)
-      assert (is_rec && (!backend = Coq || !backend = Lean));
-      let with_opaque_pre = false in
-      (* Small trick: in Lean we use namespaces, meaning we don't need to prefix
-         the constructor name with the name of the type at definition site,
-         i.e., instead of generating `inductive Foo := | MkFoo ...` like in Coq
-         we generate `inductive Foo := | mk ... *)
-      let cons_name =
-        if !backend = Lean then "mk"
-        else ctx_get_struct with_opaque_pre (AdtId def.def_id) ctx
-      in
-      let def_name = ctx_get_local_type with_opaque_pre def.def_id ctx in
-      extract_type_decl_variant ctx fmt type_decl_group def_name type_params
-        cg_params cons_name fields)
-  in
-  ()
-
-(** Extract a nestable, muti-line comment *)
-let extract_comment (fmt : F.formatter) (sl : string list) : unit =
-  (* Delimiters, space after we break a line *)
-  let ld, space, rd =
-    match !backend with
-    | Coq | FStar | HOL4 -> ("(** ", 4, " *)")
-    | Lean -> ("/- ", 3, " -/")
-  in
-  F.pp_open_vbox fmt space;
-  F.pp_print_string fmt ld;
-  (match sl with
-  | [] -> ()
-  | s :: sl ->
-      F.pp_print_string fmt s;
-      List.iter
-        (fun s ->
-          F.pp_print_space fmt ();
-          F.pp_print_string fmt s)
-        sl);
-  F.pp_print_string fmt rd;
-  F.pp_close_box fmt ()
-
-(** Extract a type declaration.
-
-    This function is for all type declarations and all backends **at the exception**
-    of opaque (assumed/declared) types format4 HOL4.
-
-    See {!extract_type_decl}.
- *)
-let extract_type_decl_gen (ctx : extraction_ctx) (fmt : F.formatter)
-    (type_decl_group : TypeDeclId.Set.t) (kind : decl_kind) (def : type_decl)
-    (extract_body : bool) : unit =
-  (* Sanity check *)
-  assert (extract_body || !backend <> HOL4);
-  let type_kind =
-    if extract_body then
-      match def.kind with
-      | Struct _ -> Some Struct
-      | Enum _ -> Some Enum
-      | Opaque -> None
-    else None
-  in
-  (* If in Coq and the declaration is opaque, it must have the shape:
-     [Axiom Ident : forall (T0 ... Tn : Type) (N0 : ...) ... (Nn : ...), ... -> ... -> ...].
-
-     The boolean [is_opaque_coq] is used to detect this case.
-  *)
-  let is_opaque = type_kind = None in
-  let is_opaque_coq = !backend = Coq && is_opaque in
-  let use_forall =
-    is_opaque_coq && (def.type_params <> [] || def.const_generic_params <> [])
-  in
-  (* Retrieve the definition name *)
-  let with_opaque_pre = false in
-  let def_name = ctx_get_local_type with_opaque_pre def.def_id ctx in
-  (* Add the type and const generic params - note that we need those bindings only for the
-   * body translation (they are not top-level) *)
-  let ctx_body, type_params, cg_params =
-    ctx_add_type_const_generic_params def.type_params def.const_generic_params
-      ctx
-  in
-  let ty_cg_params = List.append type_params cg_params in
-  (* Add a break before *)
-  if !backend <> HOL4 || not (decl_is_first_from_group kind) then
-    F.pp_print_break fmt 0 0;
-  (* Print a comment to link the extracted type to its original rust definition *)
-  extract_comment fmt [ "[" ^ Print.name_to_string def.name ^ "]" ];
-  F.pp_print_break fmt 0 0;
-  (* Open a box for the definition, so that whenever possible it gets printed on
-   * one line. Note however that in the case of Lean line breaks are important
-   * for parsing: we thus use a hovbox. *)
-  (match !backend with
-  | Coq | FStar | HOL4 -> F.pp_open_hvbox fmt 0
-  | Lean -> F.pp_open_vbox fmt 0);
-  (* Open a box for "type TYPE_NAME (TYPE_PARAMS CONST_GEN_PARAMS) =" *)
-  F.pp_open_hovbox fmt ctx.indent_incr;
-  (* > "type TYPE_NAME" *)
-  let qualif = ctx.fmt.type_decl_kind_to_qualif kind type_kind in
-  (match qualif with
-  | Some qualif -> F.pp_print_string fmt (qualif ^ " " ^ def_name)
-  | None -> F.pp_print_string fmt def_name);
-  (* HOL4 doesn't support const generics *)
-  assert (cg_params = [] || !backend <> HOL4);
-  (* Print the type/const generic parameters *)
-  if ty_cg_params <> [] && !backend <> HOL4 then (
-    if use_forall then (
-      F.pp_print_space fmt ();
-      F.pp_print_string fmt ":";
-      F.pp_print_space fmt ();
-      F.pp_print_string fmt "forall");
-    (* Print the type parameters *)
-    if type_params <> [] then (
-      F.pp_print_space fmt ();
-      F.pp_print_string fmt "(";
-      List.iter
-        (fun s ->
-          F.pp_print_string fmt s;
-          F.pp_print_space fmt ())
-        type_params;
-      F.pp_print_string fmt ":";
-      F.pp_print_space fmt ();
-      F.pp_print_string fmt (type_keyword () ^ ")"));
-    (* Print the const generic parameters *)
-    List.iter
-      (fun (var : const_generic_var) ->
-        F.pp_print_space fmt ();
-        F.pp_print_string fmt "(";
-        let n = ctx_get_const_generic_var var.index ctx in
-        F.pp_print_string fmt n;
-        F.pp_print_space fmt ();
-        F.pp_print_string fmt ":";
-        F.pp_print_space fmt ();
-        extract_literal_type ctx fmt var.ty;
-        F.pp_print_string fmt ")")
-      def.const_generic_params);
-  (* Print the "=" if we extract the body*)
-  if extract_body then (
-    F.pp_print_space fmt ();
-    let eq =
-      match !backend with
-      | FStar -> "="
-      | Coq -> ":="
-      | Lean ->
-          if type_kind = Some Struct && kind = SingleNonRec then "where"
-          else ":="
-      | HOL4 -> "="
-    in
-    F.pp_print_string fmt eq)
-  else (
-    (* Otherwise print ": Type", unless it is the HOL4 backend (in
-       which case we declare the type with `new_type`) *)
-    if use_forall then F.pp_print_string fmt ","
-    else (
-      F.pp_print_space fmt ();
-      F.pp_print_string fmt ":");
-    F.pp_print_space fmt ();
-    F.pp_print_string fmt (type_keyword ()));
-  (* Close the box for "type TYPE_NAME (TYPE_PARAMS) =" *)
-  F.pp_close_box fmt ();
-  (if extract_body then
-     match def.kind with
-     | Struct fields ->
-         extract_type_decl_struct_body ctx_body fmt type_decl_group kind def
-           type_params cg_params fields
-     | Enum variants ->
-         extract_type_decl_enum_body ctx_body fmt type_decl_group def def_name
-           type_params cg_params variants
-     | Opaque -> raise (Failure "Unreachable"));
-  (* Add the definition end delimiter *)
-  if !backend = HOL4 && decl_is_not_last_from_group kind then (
-    F.pp_print_space fmt ();
-    F.pp_print_string fmt ";")
-  else if !backend = Coq && decl_is_last_from_group kind then (
-    (* This is actually an end of group delimiter. For aesthetic reasons
-       we print it here instead of in {!end_type_decl_group}. *)
-    F.pp_print_cut fmt ();
-    F.pp_print_string fmt ".");
-  (* Close the box for the definition *)
-  F.pp_close_box fmt ();
-  (* Add breaks to insert new lines between definitions *)
-  if !backend <> HOL4 || decl_is_not_last_from_group kind then
-    F.pp_print_break fmt 0 0
-
-(** Extract an opaque type declaration to HOL4.
-
-    Remark (SH): having to treat this specific case separately is very annoying,
-    but I could not find a better way.
- *)
-let extract_type_decl_hol4_opaque (ctx : extraction_ctx) (fmt : F.formatter)
-    (def : type_decl) : unit =
-  (* Retrieve the definition name *)
-  let with_opaque_pre = false in
-  let def_name = ctx_get_local_type with_opaque_pre def.def_id ctx in
-  (* Generic parameters are unsupported *)
-  assert (def.const_generic_params = []);
-  (* Count the number of parameters *)
-  let num_params = List.length def.type_params in
-  (* Generate the declaration *)
-  F.pp_print_space fmt ();
-  F.pp_print_string fmt
-    ("val _ = new_type (\"" ^ def_name ^ "\", " ^ string_of_int num_params ^ ")");
-  F.pp_print_space fmt ()
-
-(** Extract an empty record type declaration to HOL4.
-
-    Empty records are not supported in HOL4, so we extract them as type
-    abbreviations to the unit type.
-
-    Remark (SH): having to treat this specific case separately is very annoying,
-    but I could not find a better way.
- *)
-let extract_type_decl_hol4_empty_record (ctx : extraction_ctx)
-    (fmt : F.formatter) (def : type_decl) : unit =
-  (* Retrieve the definition name *)
-  let with_opaque_pre = false in
-  let def_name = ctx_get_local_type with_opaque_pre def.def_id ctx in
-  (* Sanity check *)
-  assert (def.type_params = []);
-  assert (def.const_generic_params = []);
-  (* Generate the declaration *)
-  F.pp_print_space fmt ();
-  F.pp_print_string fmt ("Type " ^ def_name ^ " = “: unit”");
-  F.pp_print_space fmt ()
-
-(** Extract a type declaration.
-
-    Note that all the names used for extraction should already have been
-    registered.
-
-    This function should be inserted between calls to {!start_type_decl_group}
-    and {!end_type_decl_group}.
- *)
-let extract_type_decl (ctx : extraction_ctx) (fmt : F.formatter)
-    (type_decl_group : TypeDeclId.Set.t) (kind : decl_kind) (def : type_decl) :
-    unit =
-  let extract_body =
-    match kind with
-    | SingleNonRec | SingleRec | MutRecFirst | MutRecInner | MutRecLast -> true
-    | Assumed | Declared -> false
-  in
-  if extract_body then
-    if !backend = HOL4 && is_empty_record_type_decl def then
-      extract_type_decl_hol4_empty_record ctx fmt def
-    else extract_type_decl_gen ctx fmt type_decl_group kind def extract_body
-  else
-    match !backend with
-    | FStar | Coq | Lean ->
-        extract_type_decl_gen ctx fmt type_decl_group kind def extract_body
-    | HOL4 -> extract_type_decl_hol4_opaque ctx fmt def
-
-(** Auxiliary function.
-
-    Generate [Arguments] instructions in Coq.
- *)
-let extract_type_decl_coq_arguments (ctx : extraction_ctx) (fmt : F.formatter)
-    (kind : decl_kind) (decl : type_decl) : unit =
-  assert (!backend = Coq);
-  (* Generating the [Arguments] instructions is useful only if there are type parameters *)
-  if decl.type_params = [] && decl.const_generic_params = [] then ()
-  else
-    (* Add the type params - note that we need those bindings only for the
-     * body translation (they are not top-level) *)
-    let _ctx_body, type_params, cg_params =
-      ctx_add_type_const_generic_params decl.type_params
-        decl.const_generic_params ctx
-    in
-    (* Auxiliary function to extract an [Arguments Cons {T} _ _.] instruction *)
-    let extract_arguments_info (cons_name : string) (fields : 'a list) : unit =
-      (* Add a break before *)
-      F.pp_print_break fmt 0 0;
-      (* Open a box *)
-      F.pp_open_hovbox fmt ctx.indent_incr;
-      (* Small utility *)
-      let print_vars () =
-        List.iter
-          (fun (var : string) ->
-            F.pp_print_space fmt ();
-            F.pp_print_string fmt ("{" ^ var ^ "}"))
-          (List.append type_params cg_params)
-      in
-      let print_fields () =
-        List.iter
-          (fun _ ->
-            F.pp_print_space fmt ();
-            F.pp_print_string fmt "_")
-          fields
-      in
-      F.pp_print_break fmt 0 0;
-      F.pp_print_string fmt "Arguments";
-      F.pp_print_space fmt ();
-      F.pp_print_string fmt cons_name;
-      print_vars ();
-      print_fields ();
-      F.pp_print_string fmt ".";
-
-      (* Close the box *)
-      F.pp_close_box fmt ()
-    in
-
-    (* Generate the [Arguments] instruction *)
-    match decl.kind with
-    | Opaque -> ()
-    | Struct fields ->
-        let adt_id = AdtId decl.def_id in
-        (* Generate the instruction for the record constructor *)
-        let with_opaque_pre = false in
-        let cons_name = ctx_get_struct with_opaque_pre adt_id ctx in
-        extract_arguments_info cons_name fields;
-        (* Generate the instruction for the record projectors, if there are *)
-        let is_rec = decl_is_from_rec_group kind in
-        if not is_rec then
-          FieldId.iteri
-            (fun fid _ ->
-              let cons_name = ctx_get_field adt_id fid ctx in
-              extract_arguments_info cons_name [])
-            fields;
-        (* Add breaks to insert new lines between definitions *)
-        F.pp_print_break fmt 0 0
-    | Enum variants ->
-        (* Generate the instructions *)
-        VariantId.iteri
-          (fun vid (v : variant) ->
-            let cons_name = ctx_get_variant (AdtId decl.def_id) vid ctx in
-            extract_arguments_info cons_name v.fields)
-          variants;
-        (* Add breaks to insert new lines between definitions *)
-        F.pp_print_break fmt 0 0
-
-(** Auxiliary function.
-
-    Generate field projectors in Coq.
-
-    Sometimes we extract records as inductives in Coq: when this happens we
-    have to define the field projectors afterwards.
- *)
-let extract_type_decl_record_field_projectors (ctx : extraction_ctx)
-    (fmt : F.formatter) (kind : decl_kind) (decl : type_decl) : unit =
-  assert (!backend = Coq);
-  match decl.kind with
-  | Opaque | Enum _ -> ()
-  | Struct fields ->
-      (* Records are extracted as inductives only if they are recursive *)
-      let is_rec = decl_is_from_rec_group kind in
-      if is_rec then
-        (* Add the type params *)
-        let ctx, type_params, cg_params =
-          ctx_add_type_const_generic_params decl.type_params
-            decl.const_generic_params ctx
-        in
-        let ctx, record_var = ctx_add_var "x" (VarId.of_int 0) ctx in
-        let ctx, field_var = ctx_add_var "x" (VarId.of_int 1) ctx in
-        let with_opaque_pre = false in
-        let def_name = ctx_get_local_type with_opaque_pre decl.def_id ctx in
-        let cons_name =
-          ctx_get_struct with_opaque_pre (AdtId decl.def_id) ctx
-        in
-        let extract_field_proj (field_id : FieldId.id) (_ : field) : unit =
-          F.pp_print_space fmt ();
-          (* Outer box for the projector definition *)
-          F.pp_open_hvbox fmt 0;
-          (* Inner box for the projector definition *)
-          F.pp_open_hvbox fmt ctx.indent_incr;
-          (* Open a box for the [Definition PROJ ... :=] *)
-          F.pp_open_hovbox fmt ctx.indent_incr;
-          F.pp_print_string fmt "Definition";
-          F.pp_print_space fmt ();
-          let field_name = ctx_get_field (AdtId decl.def_id) field_id ctx in
-          F.pp_print_string fmt field_name;
-          F.pp_print_space fmt ();
-          (* Print the type parameters *)
-          if type_params <> [] then (
-            F.pp_print_string fmt "{";
-            List.iter
-              (fun p ->
-                F.pp_print_string fmt p;
-                F.pp_print_space fmt ())
-              type_params;
-            F.pp_print_string fmt ":";
-            F.pp_print_space fmt ();
-            F.pp_print_string fmt "Type}";
-            F.pp_print_space fmt ());
-          (* Print the const generic parameters *)
-          if cg_params <> [] then
-            List.iter
-              (fun (v : const_generic_var) ->
-                F.pp_print_string fmt "{";
-                let n = ctx_get_const_generic_var v.index ctx in
-                F.pp_print_string fmt n;
-                F.pp_print_string fmt ":";
-                F.pp_print_space fmt ();
-                extract_literal_type ctx fmt v.ty;
-                F.pp_print_string fmt "}";
-                F.pp_print_space fmt ())
-              decl.const_generic_params;
-          (* Print the record parameter *)
-          F.pp_print_string fmt "(";
-          F.pp_print_string fmt record_var;
-          F.pp_print_space fmt ();
-          F.pp_print_string fmt ":";
-          F.pp_print_space fmt ();
-          F.pp_print_string fmt def_name;
-          List.iter
-            (fun p ->
-              F.pp_print_space fmt ();
-              F.pp_print_string fmt p)
-            type_params;
-          F.pp_print_string fmt ")";
-          (* *)
-          F.pp_print_space fmt ();
-          F.pp_print_string fmt ":=";
-          (* Close the box for the [Definition PROJ ... :=] *)
-          F.pp_close_box fmt ();
-          F.pp_print_space fmt ();
-          (* Open a box for the whole match *)
-          F.pp_open_hvbox fmt 0;
-          (* Open a box for the [match ... with] *)
-          F.pp_open_hovbox fmt ctx.indent_incr;
-          F.pp_print_string fmt "match";
-          F.pp_print_space fmt ();
-          F.pp_print_string fmt record_var;
-          F.pp_print_space fmt ();
-          F.pp_print_string fmt "with";
-          (* Close the box for the [match ... with] *)
-          F.pp_close_box fmt ();
-
-          (* Open a box for the branch *)
-          F.pp_open_hovbox fmt ctx.indent_incr;
-          (* Print the match branch *)
-          F.pp_print_space fmt ();
-          F.pp_print_string fmt "|";
-          F.pp_print_space fmt ();
-          F.pp_print_string fmt cons_name;
-          FieldId.iteri
-            (fun id _ ->
-              F.pp_print_space fmt ();
-              if field_id = id then F.pp_print_string fmt field_var
-              else F.pp_print_string fmt "_")
-            fields;
-          F.pp_print_space fmt ();
-          F.pp_print_string fmt "=>";
-          F.pp_print_space fmt ();
-          F.pp_print_string fmt field_var;
-          (* Close the box for the branch *)
-          F.pp_close_box fmt ();
-          (* Print the [end] *)
-          F.pp_print_space fmt ();
-          F.pp_print_string fmt "end";
-          (* Close the box for the whole match *)
-          F.pp_close_box fmt ();
-          (* Close the inner box projector *)
-          F.pp_close_box fmt ();
-          (* If Coq: end the definition with a "." *)
-          if !backend = Coq then (
-            F.pp_print_cut fmt ();
-            F.pp_print_string fmt ".");
-          (* Close the outer box projector  *)
-          F.pp_close_box fmt ();
-          (* Add breaks to insert new lines between definitions *)
-          F.pp_print_break fmt 0 0
-        in
-
-        let extract_proj_notation (field_id : FieldId.id) (_ : field) : unit =
-          F.pp_print_space fmt ();
-          (* Outer box for the projector definition *)
-          F.pp_open_hvbox fmt 0;
-          (* Inner box for the projector definition *)
-          F.pp_open_hovbox fmt ctx.indent_incr;
-          let ctx, record_var = ctx_add_var "x" (VarId.of_int 0) ctx in
-          F.pp_print_string fmt "Notation";
-          F.pp_print_space fmt ();
-          let field_name = ctx_get_field (AdtId decl.def_id) field_id ctx in
-          F.pp_print_string fmt ("\"" ^ record_var ^ " .(" ^ field_name ^ ")\"");
-          F.pp_print_space fmt ();
-          F.pp_print_string fmt ":=";
-          F.pp_print_space fmt ();
-          F.pp_print_string fmt "(";
-          F.pp_print_string fmt field_name;
-          F.pp_print_space fmt ();
-          F.pp_print_string fmt record_var;
-          F.pp_print_string fmt ")";
-          F.pp_print_space fmt ();
-          F.pp_print_string fmt "(at level 9)";
-          (* Close the inner box projector *)
-          F.pp_close_box fmt ();
-          (* If Coq: end the definition with a "." *)
-          if !backend = Coq then (
-            F.pp_print_cut fmt ();
-            F.pp_print_string fmt ".");
-          (* Close the outer box projector  *)
-          F.pp_close_box fmt ();
-          (* Add breaks to insert new lines between definitions *)
-          F.pp_print_break fmt 0 0
-        in
-
-        let extract_field_proj_and_notation (field_id : FieldId.id)
-            (field : field) : unit =
-          extract_field_proj field_id field;
-          extract_proj_notation field_id field
-        in
-
-        FieldId.iteri extract_field_proj_and_notation fields
-
-(** Extract extra information for a type (e.g., [Arguments] instructions in Coq).
-
-    Note that all the names used for extraction should already have been
-    registered.
- *)
-let extract_type_decl_extra_info (ctx : extraction_ctx) (fmt : F.formatter)
-    (kind : decl_kind) (decl : type_decl) : unit =
-  match !backend with
-  | FStar | Lean | HOL4 -> ()
-  | Coq ->
-      extract_type_decl_coq_arguments ctx fmt kind decl;
-      extract_type_decl_record_field_projectors ctx fmt kind decl
-
-(** Extract the state type declaration. *)
-let extract_state_type (fmt : F.formatter) (ctx : extraction_ctx)
-    (kind : decl_kind) : unit =
-  (* Add a break before *)
-  F.pp_print_break fmt 0 0;
-  (* Print a comment  *)
-  extract_comment fmt [ "The state type used in the state-error monad" ];
-  F.pp_print_break fmt 0 0;
-  (* Open a box for the definition, so that whenever possible it gets printed on
-   * one line *)
-  F.pp_open_hvbox fmt 0;
-  (* Retrieve the name *)
-  let state_name = ctx_get_assumed_type State ctx in
-  (* The syntax for Lean and Coq is almost identical. *)
-  let print_axiom () =
-    let axiom =
-      match !backend with
-      | Coq -> "Axiom"
-      | Lean -> "axiom"
-      | FStar | HOL4 -> raise (Failure "Unexpected")
-    in
-    F.pp_print_string fmt axiom;
-    F.pp_print_space fmt ();
-    F.pp_print_string fmt state_name;
-    F.pp_print_space fmt ();
-    F.pp_print_string fmt ":";
-    F.pp_print_space fmt ();
-    F.pp_print_string fmt "Type";
-    if !backend = Coq then F.pp_print_string fmt "."
-  in
-  (* The kind should be [Assumed] or [Declared] *)
-  (match kind with
-  | SingleNonRec | SingleRec | MutRecFirst | MutRecInner | MutRecLast ->
-      raise (Failure "Unexpected")
-  | Assumed -> (
-      match !backend with
-      | FStar ->
-          F.pp_print_string fmt "assume";
-          F.pp_print_space fmt ();
-          F.pp_print_string fmt "type";
-          F.pp_print_space fmt ();
-          F.pp_print_string fmt state_name;
-          F.pp_print_space fmt ();
-          F.pp_print_string fmt ":";
-          F.pp_print_space fmt ();
-          F.pp_print_string fmt "Type0"
-      | HOL4 ->
-          F.pp_print_string fmt ("val _ = new_type (\"" ^ state_name ^ "\", 0)")
-      | Coq | Lean -> print_axiom ())
-  | Declared -> (
-      match !backend with
-      | FStar ->
-          F.pp_print_string fmt "val";
-          F.pp_print_space fmt ();
-          F.pp_print_string fmt state_name;
-          F.pp_print_space fmt ();
-          F.pp_print_string fmt ":";
-          F.pp_print_space fmt ();
-          F.pp_print_string fmt "Type0"
-      | HOL4 ->
-          F.pp_print_string fmt ("val _ = new_type (\"" ^ state_name ^ "\", 0)")
-      | Coq | Lean -> print_axiom ()));
-  (* Close the box for the definition *)
-  F.pp_close_box fmt ();
-  (* Add breaks to insert new lines between definitions *)
-  F.pp_print_break fmt 0 0
+include ExtractTypes
 
 (** Compute the names for all the pure functions generated from a rust function
     (forward function and backward functions).
  *)
-let extract_fun_decl_register_names (ctx : extraction_ctx) (keep_fwd : bool)
+let extract_fun_decl_register_names (ctx : extraction_ctx)
     (has_decreases_clause : fun_decl -> bool) (def : pure_fun_translation) :
     extraction_ctx =
-  let (fwd, loop_fwds), back_ls = def in
-  (* Register the decrease clauses, if necessary *)
-  let register_decreases ctx def =
-    if has_decreases_clause def then
-      (* Add the termination measure *)
-      let ctx = ctx_add_termination_measure def ctx in
-      (* Add the decreases proof for Lean only *)
-      match !Config.backend with
-      | Coq | FStar -> ctx
-      | HOL4 -> raise (Failure "Unexpected")
-      | Lean -> ctx_add_decreases_proof def ctx
-    else ctx
-  in
-  let ctx = List.fold_left register_decreases ctx (fwd :: loop_fwds) in
-  let register_fun ctx f = ctx_add_fun_decl (keep_fwd, def) f ctx in
-  let register_funs ctx fl = List.fold_left register_fun ctx fl in
-  (* Register the forward functions' names *)
-  let ctx = register_funs ctx (fwd :: loop_fwds) in
-  (* Register the backward functions' names *)
-  let ctx =
-    List.fold_left
-      (fun ctx (back, loop_backs) ->
-        let ctx = register_fun ctx back in
-        register_funs ctx loop_backs)
-      ctx back_ls
-  in
-
-  (* Return *)
-  ctx
+  (* Ignore the trait methods **declarations** (rem.: we do not ignore the trait
+     method implementations): we do not need to refer to them directly. We will
+     only use their type for the fields of the records we generate for the trait
+     declarations *)
+  match def.fwd.f.kind with
+  | TraitMethodDecl _ -> ctx
+  | _ -> (
+      (* Check if the function is builtin *)
+      let builtin =
+        let open ExtractBuiltin in
+        let funs_map = builtin_funs_map () in
+        let sname = name_to_simple_name def.fwd.f.basename in
+        SimpleNameMap.find_opt sname funs_map
+      in
+      (* Use the builtin names if necessary *)
+      match builtin with
+      | Some (filter_info, info) ->
+          (* Register the filtering information, if there is *)
+          let ctx =
+            match filter_info with
+            | Some keep ->
+                {
+                  ctx with
+                  funs_filter_type_args_map =
+                    FunDeclId.Map.add def.fwd.f.def_id keep
+                      ctx.funs_filter_type_args_map;
+                }
+            | _ -> ctx
+          in
+          let backs = List.map (fun f -> f.f) def.backs in
+          let funs = if def.keep_fwd then def.fwd.f :: backs else backs in
+          List.fold_left
+            (fun ctx (f : fun_decl) ->
+              let open ExtractBuiltin in
+              let fun_id =
+                (Pure.FunId (Regular f.def_id), f.loop_id, f.back_id)
+              in
+              let fun_info =
+                List.find_opt
+                  (fun (x : builtin_fun_info) -> x.rg = f.back_id)
+                  info
+              in
+              match fun_info with
+              | Some fun_info ->
+                  ctx_add (FunId (FromLlbc fun_id)) fun_info.extract_name ctx
+              | None ->
+                  raise
+                    (Failure
+                       ("Not found: "
+                       ^ Names.name_to_string f.basename
+                       ^ ", "
+                       ^ Print.option_to_string Pure.show_loop_id f.loop_id
+                       ^ Print.option_to_string Pure.show_region_group_id
+                           f.back_id)))
+            ctx funs
+      | None ->
+          let fwd = def.fwd in
+          let backs = def.backs in
+          (* Register the decrease clauses, if necessary *)
+          let register_decreases ctx def =
+            if has_decreases_clause def then
+              (* Add the termination measure *)
+              let ctx = ctx_add_termination_measure def ctx in
+              (* Add the decreases proof for Lean only *)
+              match !Config.backend with
+              | Coq | FStar -> ctx
+              | HOL4 -> raise (Failure "Unexpected")
+              | Lean -> ctx_add_decreases_proof def ctx
+            else ctx
+          in
+          let ctx =
+            List.fold_left register_decreases ctx (fwd.f :: fwd.loops)
+          in
+          let register_fun ctx f = ctx_add_fun_decl def f ctx in
+          let register_funs ctx fl = List.fold_left register_fun ctx fl in
+          (* Register the names of the forward functions *)
+          let ctx =
+            if def.keep_fwd then register_funs ctx (fwd.f :: fwd.loops) else ctx
+          in
+          (* Register the names of the backward functions *)
+          List.fold_left
+            (fun ctx { f = back; loops = loop_backs } ->
+              let ctx = register_fun ctx back in
+              register_funs ctx loop_backs)
+            ctx backs)
 
 (** Simply add the global name to the context. *)
 let extract_global_decl_register_names (ctx : extraction_ctx)
@@ -2122,11 +124,11 @@ let extract_adt_g_value
     (inside : bool) (variant_id : VariantId.id option) (field_values : 'v list)
     (ty : ty) : extraction_ctx =
   match ty with
-  | Adt (Tuple, type_args, cg_args) ->
+  | Adt (Tuple, generics) ->
       (* Tuple *)
       (* For now, we only support fully applied tuple constructors *)
-      assert (List.length type_args = List.length field_values);
-      assert (cg_args = []);
+      assert (List.length generics.types = List.length field_values);
+      assert (generics.const_generics = [] && generics.trait_refs = []);
       (* This is very annoying: in Coq, we can't write [()] for the value of
          type [unit], we have to write [tt]. *)
       if !backend = Coq && field_values = [] then (
@@ -2144,7 +146,7 @@ let extract_adt_g_value
         in
         F.pp_print_string fmt ")";
         ctx)
-  | Adt (adt_id, _, _) ->
+  | Adt (adt_id, _) ->
       (* "Regular" ADT *)
 
       (* If we are generating a pattern for a let-binding and we target Lean,
@@ -2172,18 +174,14 @@ let extract_adt_g_value
          * [{ field0=...; ...; fieldn=...; }] in case of structures.
          *)
         let cons =
-          (* The ADT shouldn't be opaque *)
-          let with_opaque_pre = false in
           match variant_id with
           | Some vid -> (
               (* In the case of Lean, we might have to add the type name as a prefix *)
               match (!backend, adt_id) with
               | Lean, Assumed _ ->
-                  ctx_get_type with_opaque_pre adt_id ctx
-                  ^ "."
-                  ^ ctx_get_variant adt_id vid ctx
+                  ctx_get_type adt_id ctx ^ "." ^ ctx_get_variant adt_id vid ctx
               | _ -> ctx_get_variant adt_id vid ctx)
-          | None -> ctx_get_struct with_opaque_pre adt_id ctx
+          | None -> ctx_get_struct adt_id ctx
         in
         let use_parentheses = inside && field_values <> [] in
         if use_parentheses then F.pp_print_string fmt "(";
@@ -2202,8 +200,33 @@ let extract_adt_g_value
 (* Extract globals in the same way as variables *)
 let extract_global (ctx : extraction_ctx) (fmt : F.formatter)
     (id : A.GlobalDeclId.id) : unit =
-  let with_opaque_pre = ctx.use_opaque_pre in
-  F.pp_print_string fmt (ctx_get_global with_opaque_pre id ctx)
+  F.pp_print_string fmt (ctx_get_global id ctx)
+
+(* Filter the generics of a function if it is builtin *)
+let fun_builtin_filter_types (id : FunDeclId.id) (types : 'a list)
+    (ctx : extraction_ctx) : ('a list, 'a list * string) Result.result =
+  match FunDeclId.Map.find_opt id ctx.funs_filter_type_args_map with
+  | None -> Result.Ok types
+  | Some filter ->
+      if List.length filter <> List.length types then (
+        let decl = FunDeclId.Map.find id ctx.trans_funs in
+        let err =
+          "Ill-formed builtin information for function "
+          ^ Names.name_to_string decl.fwd.f.basename
+          ^ ": "
+          ^ string_of_int (List.length filter)
+          ^ " filtering arguments provided for "
+          ^ string_of_int (List.length types)
+          ^ " type arguments"
+        in
+        log#serror err;
+        Result.Error (types, err))
+      else
+        let types = List.combine filter types in
+        let types =
+          List.filter_map (fun (b, ty) -> if b then Some ty else None) types
+        in
+        Result.Ok types
 
 (** [inside]: see {!extract_ty}.
 
@@ -2218,7 +241,7 @@ let rec extract_typed_pattern (ctx : extraction_ctx) (fmt : F.formatter)
       ctx
   | PatVar (v, _) ->
       let vname =
-        ctx.fmt.var_basename ctx.names_map.names_set v.basename v.ty
+        ctx.fmt.var_basename ctx.names_maps.names_map.names_set v.basename v.ty
       in
       let ctx, vname = ctx_add_var vname v.id ctx in
       F.pp_print_string fmt vname;
@@ -2249,6 +272,9 @@ let rec extract_texpression (ctx : extraction_ctx) (fmt : F.formatter)
   | Var var_id ->
       let var_name = ctx_get_var var_id ctx in
       F.pp_print_string fmt var_name
+  | CVar var_id ->
+      let var_name = ctx_get_const_generic_var var_id ctx in
+      F.pp_print_string fmt var_name
   | Const cv -> ctx.fmt.extract_literal fmt inside cv
   | App _ ->
       let app, args = destruct_apps e in
@@ -2279,14 +305,26 @@ and extract_App (ctx : extraction_ctx) (fmt : F.formatter) (inside : bool)
       (* Top-level qualifier *)
       match qualif.id with
       | FunOrOp fun_id ->
-          extract_function_call ctx fmt inside fun_id qualif.type_args
-            qualif.const_generic_args args
+          extract_function_call ctx fmt inside fun_id qualif.generics args
       | Global global_id -> extract_global ctx fmt global_id
       | AdtCons adt_cons_id ->
-          extract_adt_cons ctx fmt inside adt_cons_id qualif.type_args
-            qualif.const_generic_args args
+          extract_adt_cons ctx fmt inside adt_cons_id qualif.generics args
       | Proj proj ->
-          extract_field_projector ctx fmt inside app proj qualif.type_args args)
+          extract_field_projector ctx fmt inside app proj qualif.generics args
+      | TraitConst (trait_ref, generics, const_name) ->
+          let use_brackets = generics <> empty_generic_args in
+          if use_brackets then F.pp_print_string fmt "(";
+          extract_trait_ref ctx fmt TypeDeclId.Set.empty false trait_ref;
+          extract_generic_args ctx fmt TypeDeclId.Set.empty generics;
+          let name =
+            ctx_get_trait_const trait_ref.trait_decl_ref.trait_decl_id
+              const_name ctx
+          in
+          let add_brackets (s : string) =
+            if !backend = Coq then "(" ^ s ^ ")" else s
+          in
+          if use_brackets then F.pp_print_string fmt ")";
+          F.pp_print_string fmt ("." ^ add_brackets name))
   | _ ->
       (* "Regular" expression *)
       (* Open parentheses *)
@@ -2309,8 +347,8 @@ and extract_App (ctx : extraction_ctx) (fmt : F.formatter) (inside : bool)
 
 (** Subcase of the app case: function call *)
 and extract_function_call (ctx : extraction_ctx) (fmt : F.formatter)
-    (inside : bool) (fid : fun_or_op_id) (type_args : ty list)
-    (cg_args : const_generic list) (args : texpression list) : unit =
+    (inside : bool) (fid : fun_or_op_id) (generics : generic_args)
+    (args : texpression list) : unit =
   match (fid, args) with
   | Unop unop, [ arg ] ->
       (* A unop can have *at most* one argument (the result can't be a function!).
@@ -2327,24 +365,124 @@ and extract_function_call (ctx : extraction_ctx) (fmt : F.formatter)
       if inside then F.pp_print_string fmt "(";
       (* Open a box for the function call *)
       F.pp_open_hovbox fmt ctx.indent_incr;
-      (* Print the function name *)
-      let with_opaque_pre = ctx.use_opaque_pre in
-      let fun_name = ctx_get_function with_opaque_pre fun_id ctx in
-      F.pp_print_string fmt fun_name;
-      (* Sanity check: HOL4 doesn't support const generics *)
-      assert (cg_args = [] || !backend <> HOL4);
-      (* Print the type parameters, if the backend is not HOL4 *)
-      if !backend <> HOL4 then (
-        List.iter
-          (fun ty ->
-            F.pp_print_space fmt ();
-            extract_ty ctx fmt TypeDeclId.Set.empty true ty)
-          type_args;
-        List.iter
-          (fun cg ->
+      (* Print the function name.
+
+         For the function name: the id is not the same depending on whether
+         we call a trait method and a "regular" function (remark: trait
+         method *implementations* are considered as regular functions here;
+         only calls to method of traits which are parameterized in a where
+         clause have a special treatment.
+
+         Remark: the reason why trait method declarations have a special
+         treatment is that, as traits are extracted to records, we may
+         allow collisions between trait item names and some other names,
+         while we do not allow collisions between function names.
+
+         # Impl trait refs:
+         ==================
+         When the trait ref refers to an impl, in
+         [InterpreterStatement.eval_transparent_function_call_symbolic] we
+         replace the call to the trait impl method to a call to the function
+         which implements the trait method (that is, we "forget" that we
+         called a trait method, and treat it as a regular function call).
+
+         # Provided trait methods:
+         =========================
+         Calls to provided trait methods also have a special treatment.
+         For now, we do not allow overriding provided trait methods (methods
+         for which a default implementation is provided in the trait declaration).
+         Whenever we translate a provided trait method, we translate it once as
+         a function which takes a trait ref as input. We have to handle this
+         case below.
+
+         With an example, if in Rust we write:
+         {[
+           fn Foo {
+             fn f(&self) -> u32; // Required
+             fn ret_true(&self) -> bool { true } // Provided
+           }
+         ]}
+
+         We generate:
+         {[
+           structure Foo (Self : Type) = {
+             f : Self -> result u32
+           }
+
+           let ret_true (Self : Type) (self_clause : Foo Self) (self : Self) : result bool =
+             true
+         ]}
+      *)
+      (match fun_id with
+      | FromLlbc
+          (TraitMethod (trait_ref, method_name, _fun_decl_id), lp_id, rg_id) ->
+          (* We have to check whether the trait method is required or provided *)
+          let trait_decl_id = trait_ref.trait_decl_ref.trait_decl_id in
+          let trait_decl =
+            TraitDeclId.Map.find trait_decl_id ctx.trans_trait_decls
+          in
+          let method_id =
+            PureUtils.trait_decl_get_method trait_decl method_name
+          in
+
+          if not method_id.is_provided then (
+            (* Required method *)
+            assert (lp_id = None);
+            extract_trait_ref ctx fmt TypeDeclId.Set.empty true trait_ref;
+            let fun_name =
+              ctx_get_trait_method trait_ref.trait_decl_ref.trait_decl_id
+                method_name rg_id ctx
+            in
+            let add_brackets (s : string) =
+              if !backend = Coq then "(" ^ s ^ ")" else s
+            in
+            F.pp_print_string fmt ("." ^ add_brackets fun_name))
+          else
+            (* Provided method: we see it as a regular function call, and use
+               the function name *)
+            let fun_id =
+              FromLlbc (FunId (Regular method_id.id), lp_id, rg_id)
+            in
+            let fun_name = ctx_get_function fun_id ctx in
+            F.pp_print_string fmt fun_name;
+
+            (* Note that we do not need to print the generics for the trait
+               declaration: they are always implicit as they can be deduced
+               from the trait self clause.
+
+               Print the trait ref (to instantate the self clause) *)
             F.pp_print_space fmt ();
-            extract_const_generic ctx fmt true cg)
-          cg_args);
+            extract_trait_ref ctx fmt TypeDeclId.Set.empty true trait_ref
+      | _ ->
+          let fun_name = ctx_get_function fun_id ctx in
+          F.pp_print_string fmt fun_name);
+
+      (* Sanity check: HOL4 doesn't support const generics *)
+      assert (generics.const_generics = [] || !backend <> HOL4);
+      (* Print the generics.
+
+         We might need to filter some of the type arguments, if the type
+         is builtin (for instance, we filter the global allocator type
+         argument for `Vec::new`).
+      *)
+      let types =
+        match fun_id with
+        | FromLlbc (FunId (Regular id), _, _) ->
+            fun_builtin_filter_types id generics.types ctx
+        | _ -> Result.Ok generics.types
+      in
+      (match types with
+      | Ok types ->
+          extract_generic_args ctx fmt TypeDeclId.Set.empty
+            { generics with types }
+      | Error (types, err) ->
+          extract_generic_args ctx fmt TypeDeclId.Set.empty
+            { generics with types };
+          if !Config.fail_hard then raise (Failure err)
+          else
+            F.pp_print_string fmt
+              "(\"ERROR: ill-formed builtin: invalid number of filtering \
+               arguments\")");
       (* Print the arguments *)
       List.iter
         (fun ve ->
@@ -2366,9 +504,9 @@ and extract_function_call (ctx : extraction_ctx) (fmt : F.formatter)
 
 (** Subcase of the app case: ADT constructor *)
 and extract_adt_cons (ctx : extraction_ctx) (fmt : F.formatter) (inside : bool)
-    (adt_cons : adt_cons_id) (type_args : ty list)
-    (cg_args : const_generic list) (args : texpression list) : unit =
-  let e_ty = Adt (adt_cons.adt_id, type_args, cg_args) in
+    (adt_cons : adt_cons_id) (generics : generic_args) (args : texpression list)
+    : unit =
+  let e_ty = Adt (adt_cons.adt_id, generics) in
   let is_single_pat = false in
   let _ =
     extract_adt_g_value
@@ -2382,7 +520,7 @@ and extract_adt_cons (ctx : extraction_ctx) (fmt : F.formatter) (inside : bool)
 (** Subcase of the app case: ADT field projector.  *)
 and extract_field_projector (ctx : extraction_ctx) (fmt : F.formatter)
     (inside : bool) (original_app : texpression) (proj : projection)
-    (_proj_type_params : ty list) (args : texpression list) : unit =
+    (_generics : generic_args) (args : texpression list) : unit =
   (* We isolate the first argument (if there is), in order to pretty print the
    * projection ([x.field] instead of [MkAdt?.field x] *)
   match args with
@@ -2734,9 +872,7 @@ and extract_StructUpdate (ctx : extraction_ctx) (fmt : F.formatter)
   let extract_as_unit =
     match (!backend, supd.struct_id) with
     | HOL4, AdtId adt_id ->
-        let d =
-          TypeDeclId.Map.find adt_id ctx.trans_ctx.type_context.type_decls
-        in
+        let d = TypeDeclId.Map.find adt_id ctx.trans_ctx.type_ctx.type_decls in
         d.kind = Struct []
     | _ -> false
   in
@@ -2835,17 +971,17 @@ and extract_StructUpdate (ctx : extraction_ctx) (fmt : F.formatter)
         F.pp_open_hvbox fmt ctx.indent_incr;
         let need_paren = inside in
         if need_paren then F.pp_print_string fmt "(";
-        (* Open the box for `Array.mk T N [` *)
+        (* Open the box for `Array.replicate T N [` *)
         F.pp_open_hovbox fmt ctx.indent_incr;
         (* Print the array constructor *)
-        let cs = ctx_get_struct false (Assumed Array) ctx in
+        let cs = ctx_get_struct (Assumed Array) ctx in
         F.pp_print_string fmt cs;
         (* Print the parameters *)
-        let _, tys, cgs = ty_as_adt e_ty in
-        let ty = Collections.List.to_cons_nil tys in
+        let _, generics = ty_as_adt e_ty in
+        let ty = Collections.List.to_cons_nil generics.types in
         F.pp_print_space fmt ();
         extract_ty ctx fmt TypeDeclId.Set.empty true ty;
-        let cg = Collections.List.to_cons_nil cgs in
+        let cg = Collections.List.to_cons_nil generics.const_generics in
         F.pp_print_space fmt ();
         extract_const_generic ctx fmt true cg;
         F.pp_print_space fmt ();
@@ -2872,17 +1008,15 @@ and extract_StructUpdate (ctx : extraction_ctx) (fmt : F.formatter)
         F.pp_close_box fmt ()
     | _ -> raise (Failure "Unreachable")
 
-(** Insert a space, if necessary *)
-let insert_req_space (fmt : F.formatter) (space : bool ref) : unit =
-  if !space then space := false else F.pp_print_space fmt ()
-
 (** A small utility to print the parameters of a function signature.
 
     We return two contexts:
-    - the context augmented with bindings for the type parameters
-    - the context augmented with bindings for the type parameters *and*
+    - the context augmented with bindings for the generics
+    - the context augmented with bindings for the generics *and*
       bindings for the input values
 
+    We also return names for the type parameters, const generics, etc.
+
     TODO: do we really need the first one? We should probably always use
     the second one.
     It comes from the fact that when we print the input values for the
@@ -2890,57 +1024,40 @@ let insert_req_space (fmt : F.formatter) (space : bool ref) : unit =
     patterns, not the variables). We should figure a cleaner way.
  *)
 let extract_fun_parameters (space : bool ref) (ctx : extraction_ctx)
-    (fmt : F.formatter) (def : fun_decl) : extraction_ctx * extraction_ctx =
+    (fmt : F.formatter) (def : fun_decl) :
+    extraction_ctx * extraction_ctx * string list =
+  (* First, add the associated types and constants if the function is a method
+     in a trait declaration.
+
+     About the order: we want to make sure the names are reserved for
+     those (variable names might collide with them but it is ok, we will add
+     suffixes to the variables).
+
+     TODO: micro-pass to update what happens when calling trait provided
+     functions.
+  *)
+  let ctx, trait_decl =
+    match def.kind with
+    | TraitMethodProvided (decl_id, _) ->
+        let trait_decl = T.TraitDeclId.Map.find decl_id ctx.trans_trait_decls in
+        let ctx, _ = ctx_add_trait_self_clause ctx in
+        let ctx = { ctx with is_provided_method = true } in
+        (ctx, Some trait_decl)
+    | _ -> (ctx, None)
+  in
   (* Add the type parameters - note that we need those bindings only for the
    * body translation (they are not top-level) *)
-  let ctx, type_params, cg_params =
-    ctx_add_type_const_generic_params def.signature.type_params
-      def.signature.const_generic_params ctx
+  let ctx, type_params, cg_params, trait_clauses =
+    ctx_add_generic_params def.signature.generics ctx
   in
-  (* Print the parameters - rem.: we should have filtered the functions
-   * with no input parameters *)
-  (* The type parameters.
-
-     Note that in HOL4 we don't print the type parameters.
-  *)
-  if (type_params <> [] || cg_params <> []) && !backend <> HOL4 then (
-    (* Open a box for the type and const generic parameters *)
-    F.pp_open_hovbox fmt 0;
-    (* The type parameters *)
-    if type_params <> [] then (
-      insert_req_space fmt space;
-      F.pp_print_string fmt "(";
-      List.iter
-        (fun (p : type_var) ->
-          let pname = ctx_get_type_var p.index ctx in
-          F.pp_print_string fmt pname;
-          F.pp_print_space fmt ())
-        def.signature.type_params;
-      F.pp_print_string fmt ":";
-      F.pp_print_space fmt ();
-      let type_keyword =
-        match !backend with
-        | FStar -> "Type0"
-        | Coq | Lean -> "Type"
-        | HOL4 -> raise (Failure "Unreachable")
-      in
-      F.pp_print_string fmt (type_keyword ^ ")"));
-    (* The const generic parameters *)
-    if cg_params <> [] then
-      List.iter
-        (fun (p : const_generic_var) ->
-          let pname = ctx_get_const_generic_var p.index ctx in
-          insert_req_space fmt space;
-          F.pp_print_string fmt "(";
-          F.pp_print_string fmt pname;
-          F.pp_print_space fmt ();
-          F.pp_print_string fmt ":";
-          F.pp_print_space fmt ();
-          extract_literal_type ctx fmt p.ty;
-          F.pp_print_string fmt ")")
-        def.signature.const_generic_params;
-    (* Close the box for the type parameters *)
-    F.pp_close_box fmt ());
+  (* Print the generics *)
+  (* Open a box for the generics *)
+  F.pp_open_hovbox fmt 0;
+  (let space = Some space in
+   extract_generic_params ctx fmt TypeDeclId.Set.empty ~space ~trait_decl
+     def.signature.generics type_params cg_params trait_clauses);
+  (* Close the box for the generics *)
+  F.pp_close_box fmt ();
   (* The input parameters - note that doing this adds bindings to the context *)
   let ctx_body =
     match def.body with
@@ -2963,7 +1080,7 @@ let extract_fun_parameters (space : bool ref) (ctx : extraction_ctx)
             ctx)
           ctx body.inputs_lvs
   in
-  (ctx, ctx_body)
+  (ctx, ctx_body, List.concat [ type_params; cg_params; trait_clauses ])
 
 (** A small utility to print the types of the input parameters in the form:
     [u32 -> list u32 -> ...]
@@ -2982,6 +1099,11 @@ let extract_fun_input_parameters_types (ctx : extraction_ctx)
   in
   List.iter extract_param def.signature.inputs
 
+let extract_fun_inputs_output_parameters_types (ctx : extraction_ctx)
+    (fmt : F.formatter) (def : fun_decl) : unit =
+  extract_fun_input_parameters_types ctx fmt def;
+  extract_ty ctx fmt TypeDeclId.Set.empty false def.signature.output
+
 let assert_backend_supports_decreases_clauses () =
   match !backend with
   | FStar | Lean -> ()
@@ -3032,7 +1154,7 @@ let extract_template_fstar_decreases_clause (ctx : extraction_ctx)
   F.pp_print_space fmt ();
   (* Extract the parameters *)
   let space = ref true in
-  let _, _ = extract_fun_parameters space ctx fmt def in
+  let _, _, _ = extract_fun_parameters space ctx fmt def in
   insert_req_space fmt space;
   F.pp_print_string fmt ":";
   (* Print the signature *)
@@ -3094,7 +1216,7 @@ let extract_template_lean_termination_and_decreasing (ctx : extraction_ctx)
   F.pp_print_space fmt ();
   (* Extract the parameters *)
   let space = ref true in
-  let _, ctx_body = extract_fun_parameters space ctx fmt def in
+  let _, ctx_body, _ = extract_fun_parameters space ctx fmt def in
   (* Print the ":=" *)
   F.pp_print_space fmt ();
   F.pp_print_string fmt ":=";
@@ -3164,7 +1286,7 @@ let extract_fun_comment (ctx : extraction_ctx) (fmt : F.formatter)
     (def : fun_decl) : unit =
   let { keep_fwd; num_backs } =
     PureUtils.RegularFunIdMap.find
-      (A.Regular def.def_id, def.loop_id, def.back_id)
+      (Pure.FunId (Regular def.def_id), def.loop_id, def.back_id)
       ctx.fun_name_info
   in
   let comment_pre = "[" ^ Print.fun_name_to_string def.basename ^ "]: " in
@@ -3205,10 +1327,8 @@ let extract_fun_decl_gen (ctx : extraction_ctx) (fmt : F.formatter)
     (kind : decl_kind) (has_decreases_clause : bool) (def : fun_decl) : unit =
   assert (not def.is_global_decl_body);
   (* Retrieve the function name *)
-  let with_opaque_pre = false in
   let def_name =
-    ctx_get_local_function with_opaque_pre def.def_id def.loop_id def.back_id
-      ctx
+    ctx_get_local_function def.def_id def.loop_id def.back_id ctx
   in
   (* Add a break before *)
   if !backend <> HOL4 || not (decl_is_first_from_group kind) then
@@ -3234,23 +1354,15 @@ let extract_fun_decl_gen (ctx : extraction_ctx) (fmt : F.formatter)
   *)
   let is_opaque_coq = !backend = Coq && is_opaque in
   let use_forall =
-    is_opaque_coq
-    && (def.signature.type_params <> []
-       || def.signature.const_generic_params <> [])
+    is_opaque_coq && def.signature.generics <> empty_generic_params
   in
-  (* Print the qualifier ("assume", etc.).
-
-     if `wrap_opaque_in_sig`: we generate a record of assumed funcions.
-     TODO: this is obsolete.
-  *)
-  (if not (!Config.wrap_opaque_in_sig && (kind = Assumed || kind = Declared))
-   then
-     let qualif = ctx.fmt.fun_decl_kind_to_qualif kind in
-     match qualif with
-     | Some qualif ->
-         F.pp_print_string fmt qualif;
-         F.pp_print_space fmt ()
-     | None -> ());
+  (* Print the qualifier ("assume", etc.). *)
+  let qualif = ctx.fmt.fun_decl_kind_to_qualif kind in
+  (match qualif with
+  | Some qualif ->
+      F.pp_print_string fmt qualif;
+      F.pp_print_space fmt ()
+  | None -> ());
   F.pp_print_string fmt def_name;
   F.pp_print_space fmt ();
   if use_forall then (
@@ -3262,7 +1374,7 @@ let extract_fun_decl_gen (ctx : extraction_ctx) (fmt : F.formatter)
   (* Open a box for "(PARAMS) :" *)
   F.pp_open_hovbox fmt 0;
   let space = ref true in
-  let ctx, ctx_body = extract_fun_parameters space ctx fmt def in
+  let ctx, ctx_body, all_params = extract_fun_parameters space ctx fmt def in
   (* Print the return type - note that we have to be careful when
    * printing the input values for the decrease clause, because
    * it introduces bindings in the context... We thus "forget"
@@ -3310,20 +1422,13 @@ let extract_fun_decl_gen (ctx : extraction_ctx) (fmt : F.formatter)
       (* The name of the decrease clause *)
       let decr_name = ctx_get_termination_measure def.def_id def.loop_id ctx in
       F.pp_print_string fmt decr_name;
-      (* Print the type/const generic parameters - TODO: we do this many
+      (* Print the generic parameters - TODO: we do this many
          times, we should have a helper to factor it out *)
       List.iter
-        (fun (p : type_var) ->
-          let pname = ctx_get_type_var p.index ctx in
+        (fun (name : string) ->
           F.pp_print_space fmt ();
-          F.pp_print_string fmt pname)
-        def.signature.type_params;
-      List.iter
-        (fun (p : const_generic_var) ->
-          let pname = ctx_get_const_generic_var p.index ctx in
-          F.pp_print_space fmt ();
-          F.pp_print_string fmt pname)
-        def.signature.const_generic_params;
+          F.pp_print_string fmt name)
+        all_params;
       (* Print the input values: we have to be careful here to print
        * only the input values which are in common with the *forward*
        * function (the additional input values "given back" to the
@@ -3410,19 +1515,12 @@ let extract_fun_decl_gen (ctx : extraction_ctx) (fmt : F.formatter)
     (* Open the box for [DECREASES] *)
     F.pp_open_hovbox fmt ctx.indent_incr;
     F.pp_print_string fmt terminates_name;
-    (* Print the type/const generic params - TODO: factor out *)
+    (* Print the generic params - TODO: factor out *)
     List.iter
-      (fun (p : type_var) ->
-        let pname = ctx_get_type_var p.index ctx in
+      (fun (name : string) ->
         F.pp_print_space fmt ();
-        F.pp_print_string fmt pname)
-      def.signature.type_params;
-    List.iter
-      (fun (p : const_generic_var) ->
-        let pname = ctx_get_const_generic_var p.index ctx in
-        F.pp_print_space fmt ();
-        F.pp_print_string fmt pname)
-      def.signature.const_generic_params;
+        F.pp_print_string fmt name)
+      all_params;
     (* Print the variables *)
     List.iter
       (fun v ->
@@ -3475,18 +1573,13 @@ let extract_fun_decl_gen (ctx : extraction_ctx) (fmt : F.formatter)
 let extract_fun_decl_hol4_opaque (ctx : extraction_ctx) (fmt : F.formatter)
     (def : fun_decl) : unit =
   (* Retrieve the definition name *)
-  let with_opaque_pre = false in
   let def_name =
-    ctx_get_local_function with_opaque_pre def.def_id def.loop_id def.back_id
-      ctx
+    ctx_get_local_function def.def_id def.loop_id def.back_id ctx
   in
-  assert (def.signature.const_generic_params = []);
+  assert (def.signature.generics.const_generics = []);
   (* Add the type/const gen parameters - note that we need those bindings
      only for the generation of the type (they are not top-level) *)
-  let ctx, _, _ =
-    ctx_add_type_const_generic_params def.signature.type_params
-      def.signature.const_generic_params ctx
-  in
+  let ctx, _, _, _ = ctx_add_generic_params def.signature.generics ctx in
   (* Add breaks to insert new lines between definitions *)
   F.pp_print_break fmt 0 0;
   (* Open a box for the whole definition *)
@@ -3635,8 +1728,13 @@ let extract_global_decl_hol4_opaque (ctx : extraction_ctx) (fmt : F.formatter)
   (* Print the type *)
   F.pp_open_hovbox fmt 0;
   extract_ty ctx fmt TypeDeclId.Set.empty false ty;
+  (* Close the definition *)
+  F.pp_print_string fmt ")";
+  F.pp_close_box fmt ();
+  (* Close the definition box *)
   F.pp_close_box fmt ();
-  (* Close the definition boxe *) F.pp_close_box fmt ()
+  (* Add a line *)
+  F.pp_print_space fmt ()
 
 (** Extract a global declaration.
 
@@ -3662,21 +1760,19 @@ let extract_global_decl (ctx : extraction_ctx) (fmt : F.formatter)
     (global : A.global_decl) (body : fun_decl) (interface : bool) : unit =
   assert body.is_global_decl_body;
   assert (Option.is_none body.back_id);
-  assert (List.length body.signature.inputs = 0);
+  assert (body.signature.inputs = []);
   assert (List.length body.signature.doutputs = 1);
-  assert (List.length body.signature.type_params = 0);
-  assert (List.length body.signature.const_generic_params = 0);
+  assert (body.signature.generics = empty_generic_params);
 
   (* Add a break then the name of the corresponding LLBC declaration *)
   F.pp_print_break fmt 0 0;
   extract_comment fmt [ "[" ^ Print.global_name_to_string global.name ^ "]" ];
   F.pp_print_space fmt ();
 
-  let with_opaque_pre = false in
-  let decl_name = ctx_get_global with_opaque_pre global.def_id ctx in
+  let decl_name = ctx_get_global global.def_id ctx in
   let body_name =
-    ctx_get_function with_opaque_pre
-      (FromLlbc (Regular global.body_id, None, None))
+    ctx_get_function
+      (FromLlbc (Pure.FunId (Regular global.body_id), None, None))
       ctx
   in
 
@@ -3713,6 +1809,807 @@ let extract_global_decl (ctx : extraction_ctx) (fmt : F.formatter)
       (* Add a break to insert lines between declarations *)
       F.pp_print_break fmt 0 0
 
+(** Similar to {!extract_trait_decl_register_names} *)
+let extract_trait_decl_register_parent_clause_names (ctx : extraction_ctx)
+    (trait_decl : trait_decl)
+    (builtin_info : ExtractBuiltin.builtin_trait_decl_info option) :
+    extraction_ctx =
+  (* Compute the clause names *)
+  let clause_names =
+    match builtin_info with
+    | None ->
+        List.map
+          (fun (c : trait_clause) ->
+            let name = ctx.fmt.trait_parent_clause_name trait_decl c in
+            (* Add a prefix if necessary *)
+            let name =
+              if !Config.record_fields_short_names then name
+              else ctx.fmt.trait_decl_name trait_decl ^ name
+            in
+            (c.clause_id, name))
+          trait_decl.parent_clauses
+    | Some info ->
+        List.map
+          (fun (c, name) -> (c.clause_id, name))
+          (List.combine trait_decl.parent_clauses info.parent_clauses)
+  in
+  (* Register the names *)
+  List.fold_left
+    (fun ctx (cid, cname) ->
+      ctx_add (TraitParentClauseId (trait_decl.def_id, cid)) cname ctx)
+    ctx clause_names
+
+(** Similar to {!extract_trait_decl_register_names} *)
+let extract_trait_decl_register_constant_names (ctx : extraction_ctx)
+    (trait_decl : trait_decl)
+    (builtin_info : ExtractBuiltin.builtin_trait_decl_info option) :
+    extraction_ctx =
+  let consts = trait_decl.consts in
+  (* Compute the names *)
+  let constant_names =
+    match builtin_info with
+    | None ->
+        List.map
+          (fun (item_name, _) ->
+            let name = ctx.fmt.trait_const_name trait_decl item_name in
+            (* Add a prefix if necessary *)
+            let name =
+              if !Config.record_fields_short_names then name
+              else ctx.fmt.trait_decl_name trait_decl ^ name
+            in
+            (item_name, name))
+          consts
+    | Some info ->
+        let const_map = StringMap.of_list info.consts in
+        List.map
+          (fun (item_name, _) ->
+            (item_name, StringMap.find item_name const_map))
+          consts
+  in
+  (* Register the names *)
+  List.fold_left
+    (fun ctx (item_name, name) ->
+      ctx_add (TraitItemId (trait_decl.def_id, item_name)) name ctx)
+    ctx constant_names
+
+(** Similar to {!extract_trait_decl_register_names} *)
+let extract_trait_decl_type_names (ctx : extraction_ctx)
+    (trait_decl : trait_decl)
+    (builtin_info : ExtractBuiltin.builtin_trait_decl_info option) :
+    extraction_ctx =
+  let types = trait_decl.types in
+  (* Compute the names *)
+  let type_names =
+    match builtin_info with
+    | None ->
+        let compute_type_name (item_name : string) : string =
+          let type_name = ctx.fmt.trait_type_name trait_decl item_name in
+          if !Config.record_fields_short_names then type_name
+          else ctx.fmt.trait_decl_name trait_decl ^ type_name
+        in
+        let compute_clause_name (item_name : string) (clause : trait_clause) :
+            TraitClauseId.id * string =
+          let name =
+            ctx.fmt.trait_type_clause_name trait_decl item_name clause
+          in
+          (* Add a prefix if necessary *)
+          let name =
+            if !Config.record_fields_short_names then name
+            else ctx.fmt.trait_decl_name trait_decl ^ name
+          in
+          (clause.clause_id, name)
+        in
+        List.map
+          (fun (item_name, (item_clauses, _)) ->
+            (* Type name *)
+            let type_name = compute_type_name item_name in
+            (* Clause names *)
+            let clauses =
+              List.map (compute_clause_name item_name) item_clauses
+            in
+            (item_name, (type_name, clauses)))
+          types
+    | Some info ->
+        let type_map = StringMap.of_list info.types in
+        List.map
+          (fun (item_name, (item_clauses, _)) ->
+            let type_name, clauses_info = StringMap.find item_name type_map in
+            let clauses =
+              List.map
+                (fun (clause, clause_name) -> (clause.clause_id, clause_name))
+                (List.combine item_clauses clauses_info)
+            in
+            (item_name, (type_name, clauses)))
+          types
+  in
+  (* Register the names *)
+  List.fold_left
+    (fun ctx (item_name, (type_name, clauses)) ->
+      let ctx =
+        ctx_add (TraitItemId (trait_decl.def_id, item_name)) type_name ctx
+      in
+      List.fold_left
+        (fun ctx (clause_id, clause_name) ->
+          ctx_add
+            (TraitItemClauseId (trait_decl.def_id, item_name, clause_id))
+            clause_name ctx)
+        ctx clauses)
+    ctx type_names
+
+(** Similar to {!extract_trait_decl_register_names} *)
+let extract_trait_decl_method_names (ctx : extraction_ctx)
+    (trait_decl : trait_decl)
+    (builtin_info : ExtractBuiltin.builtin_trait_decl_info option) :
+    extraction_ctx =
+  let required_methods = trait_decl.required_methods in
+  (* Compute the names *)
+  let method_names =
+    (* We add one field per required forward/backward function *)
+    let get_funs_for_id (id : fun_decl_id) : fun_decl list =
+      let trans : pure_fun_translation = FunDeclId.Map.find id ctx.trans_funs in
+      List.map (fun f -> f.f) (trans.fwd :: trans.backs)
+    in
+    match builtin_info with
+    | None ->
+        (* We add one field per required forward/backward function *)
+        let compute_item_names (item_name : string) (id : fun_decl_id) :
+            string * (RegionGroupId.id option * string) list =
+          let compute_fun_name (f : fun_decl) : RegionGroupId.id option * string
+              =
+            (* We do something special to reuse the [ctx_compute_fun_decl]
+               function. TODO: make it cleaner. *)
+            let basename : name = [ Ident item_name ] in
+            let f = { f with basename } in
+            let trans = A.FunDeclId.Map.find f.def_id ctx.trans_funs in
+            let name = ctx_compute_fun_name trans f ctx in
+            (* Add a prefix if necessary *)
+            let name =
+              if !Config.record_fields_short_names then name
+              else ctx.fmt.trait_decl_name trait_decl ^ "_" ^ name
+            in
+            (f.back_id, name)
+          in
+          let funs = get_funs_for_id id in
+          (item_name, List.map compute_fun_name funs)
+        in
+        List.map (fun (name, id) -> compute_item_names name id) required_methods
+    | Some info ->
+        let funs_map = StringMap.of_list info.methods in
+        List.map
+          (fun (item_name, fun_id) ->
+            let open ExtractBuiltin in
+            let info = StringMap.find item_name funs_map in
+            let trans_funs = get_funs_for_id fun_id in
+            let find (trans_fun : fun_decl) =
+              let info =
+                List.find_opt
+                  (fun (info : builtin_fun_info) -> info.rg = trans_fun.back_id)
+                  info
+              in
+              match info with
+              | Some info -> (info.rg, info.extract_name)
+              | None ->
+                  let err =
+                    "Ill-formed builtin information for trait decl \""
+                    ^ Names.name_to_string trait_decl.name
+                    ^ "\", method \"" ^ item_name
+                    ^ "\": could not find name for region "
+                    ^ Print.option_to_string Pure.show_region_group_id
+                        trans_fun.back_id
+                  in
+                  log#serror err;
+                  if !Config.fail_hard then raise (Failure err)
+                  else (trans_fun.back_id, "%ERROR_BUILTIN_NAME_NOT_FOUND%")
+            in
+            let rg_with_name_list = List.map find trans_funs in
+            (item_name, rg_with_name_list))
+          required_methods
+  in
+  (* Register the names *)
+  List.fold_left
+    (fun ctx (item_name, funs) ->
+      (* We add one field per required forward/backward function *)
+      List.fold_left
+        (fun ctx (rg, fun_name) ->
+          ctx_add
+            (TraitMethodId (trait_decl.def_id, item_name, rg))
+            fun_name ctx)
+        ctx funs)
+    ctx method_names
+
+(** Similar to {!extract_type_decl_register_names} *)
+let extract_trait_decl_register_names (ctx : extraction_ctx)
+    (trait_decl : trait_decl) : extraction_ctx =
+  (* Lookup the information if this is a builtin trait *)
+  let open ExtractBuiltin in
+  let sname = name_to_simple_name trait_decl.name in
+  let builtin_info =
+    SimpleNameMap.find_opt sname (builtin_trait_decls_map ())
+  in
+  let ctx =
+    let trait_name, trait_constructor =
+      match builtin_info with
+      | None ->
+          ( ctx.fmt.trait_decl_name trait_decl,
+            ctx.fmt.trait_decl_constructor trait_decl )
+      | Some info -> (info.extract_name, info.constructor)
+    in
+    let ctx = ctx_add (TraitDeclId trait_decl.def_id) trait_name ctx in
+    ctx_add (TraitDeclConstructorId trait_decl.def_id) trait_constructor ctx
+  in
+  (* Parent clauses *)
+  let ctx =
+    extract_trait_decl_register_parent_clause_names ctx trait_decl builtin_info
+  in
+  (* Constants *)
+  let ctx =
+    extract_trait_decl_register_constant_names ctx trait_decl builtin_info
+  in
+  (* Types *)
+  let ctx = extract_trait_decl_type_names ctx trait_decl builtin_info in
+  (* Required methods *)
+  let ctx = extract_trait_decl_method_names ctx trait_decl builtin_info in
+  ctx
+
+(** Similar to {!extract_type_decl_register_names} *)
+let extract_trait_impl_register_names (ctx : extraction_ctx)
+    (trait_impl : trait_impl) : extraction_ctx =
+  let decl_id = trait_impl.impl_trait.trait_decl_id in
+  let trait_decl = TraitDeclId.Map.find decl_id ctx.trans_trait_decls in
+  (* Check if the trait implementation is builtin *)
+  let builtin_info =
+    let open ExtractBuiltin in
+    let type_sname = name_to_simple_name trait_impl.name in
+    let trait_sname = name_to_simple_name trait_decl.name in
+    SimpleNamePairMap.find_opt (type_sname, trait_sname)
+      (builtin_trait_impls_map ())
+  in
+  (* Register some builtin information (if necessary) *)
+  let ctx, builtin_info =
+    match builtin_info with
+    | None -> (ctx, None)
+    | Some (filter, info) ->
+        let ctx =
+          match filter with
+          | None -> ctx
+          | Some filter ->
+              {
+                ctx with
+                trait_impls_filter_type_args_map =
+                  TraitImplId.Map.add trait_impl.def_id filter
+                    ctx.trait_impls_filter_type_args_map;
+              }
+        in
+        (ctx, Some info)
+  in
+
+  (* For now we do not support overriding provided methods *)
+  assert (trait_impl.provided_methods = []);
+  (* Everything is taken care of by {!extract_trait_decl_register_names} *but*
+     the name of the implementation itself *)
+  (* Compute the name *)
+  let name =
+    match builtin_info with
+    | None -> ctx.fmt.trait_impl_name trait_decl trait_impl
+    | Some name -> name
+  in
+  ctx_add (TraitImplId trait_impl.def_id) name ctx
+
+(** Small helper.
+
+    The type `ty` is to be understood in a very general sense.
+ *)
+let extract_trait_item (ctx : extraction_ctx) (fmt : F.formatter)
+    (item_name : string) (separator : string) (ty : unit -> unit) : unit =
+  F.pp_print_space fmt ();
+  F.pp_open_hovbox fmt ctx.indent_incr;
+  F.pp_print_string fmt item_name;
+  F.pp_print_space fmt ();
+  (* ":" or "=" *)
+  F.pp_print_string fmt separator;
+  ty ();
+  (match !Config.backend with Lean -> () | _ -> F.pp_print_string fmt ";");
+  F.pp_close_box fmt ()
+
+let extract_trait_decl_item (ctx : extraction_ctx) (fmt : F.formatter)
+    (item_name : string) (ty : unit -> unit) : unit =
+  extract_trait_item ctx fmt item_name ":" ty
+
+let extract_trait_impl_item (ctx : extraction_ctx) (fmt : F.formatter)
+    (item_name : string) (ty : unit -> unit) : unit =
+  let assign = match !Config.backend with Lean | Coq -> ":=" | _ -> "=" in
+  extract_trait_item ctx fmt item_name assign ty
+
+(** Small helper - TODO: move *)
+let generic_params_drop_prefix ~(drop_trait_clauses : bool)
+    (g1 : generic_params) (g2 : generic_params) : generic_params =
+  let open Collections.List in
+  let types = drop (length g1.types) g2.types in
+  let const_generics = drop (length g1.const_generics) g2.const_generics in
+  let trait_clauses =
+    if drop_trait_clauses then drop (length g1.trait_clauses) g2.trait_clauses
+    else g2.trait_clauses
+  in
+  { types; const_generics; trait_clauses }
+
+(** Small helper.
+
+    Extract the items for a method in a trait decl.
+ *)
+let extract_trait_decl_method_items (ctx : extraction_ctx) (fmt : F.formatter)
+    (decl : trait_decl) (item_name : string) (id : fun_decl_id) : unit =
+  (* Lookup the definition *)
+  let trans = A.FunDeclId.Map.find id ctx.trans_funs in
+  (* Extract the items *)
+  let funs = if trans.keep_fwd then trans.fwd :: trans.backs else trans.backs in
+  let extract_method (f : fun_and_loops) =
+    let f = f.f in
+    let fun_name = ctx_get_trait_method decl.def_id item_name f.back_id ctx in
+    let ty () =
+      (* Extract the generics *)
+      (* We need to add the generics specific to the method, by removing those
+         which actually apply to the trait decl *)
+      let generics =
+        let drop_trait_clauses = false in
+        generic_params_drop_prefix ~drop_trait_clauses decl.generics
+          f.signature.generics
+      in
+      let ctx, type_params, cg_params, trait_clauses =
+        ctx_add_generic_params generics ctx
+      in
+      let backend_uses_forall =
+        match !backend with Coq | Lean -> true | FStar | HOL4 -> false
+      in
+      let generics_not_empty = generics <> empty_generic_params in
+      let use_forall = generics_not_empty && backend_uses_forall in
+      let use_arrows = generics_not_empty && not backend_uses_forall in
+      let use_forall_use_sep = false in
+      extract_generic_params ctx fmt TypeDeclId.Set.empty ~use_forall
+        ~use_forall_use_sep ~use_arrows generics type_params cg_params
+        trait_clauses;
+      if use_forall then F.pp_print_string fmt ",";
+      (* Extract the inputs and output *)
+      F.pp_print_space fmt ();
+      extract_fun_inputs_output_parameters_types ctx fmt f
+    in
+    extract_trait_decl_item ctx fmt fun_name ty
+  in
+  List.iter extract_method funs
+
+(** Extract a trait declaration *)
+let extract_trait_decl (ctx : extraction_ctx) (fmt : F.formatter)
+    (decl : trait_decl) : unit =
+  (* Retrieve the trait name *)
+  let decl_name = ctx_get_trait_decl decl.def_id ctx in
+  (* Add a break before *)
+  F.pp_print_break fmt 0 0;
+  (* Print a comment to link the extracted type to its original rust definition *)
+  extract_comment fmt
+    [ "Trait declaration: [" ^ Print.name_to_string decl.name ^ "]" ];
+  F.pp_print_break fmt 0 0;
+  (* Open two outer boxes for the definition, so that whenever possible it gets printed on
+     one line and indents are correct.
+
+     There is just an exception with Lean: in this backend, line breaks are important
+     for the parsing, so we always open a vertical box.
+  *)
+  if !Config.backend = Lean then F.pp_open_vbox fmt ctx.indent_incr
+  else (
+    F.pp_open_hvbox fmt 0;
+    F.pp_open_hvbox fmt ctx.indent_incr);
+
+  (* `struct Trait (....) =` *)
+  (* Open the box for the name + generics *)
+  F.pp_open_hovbox fmt ctx.indent_incr;
+  let qualif =
+    Option.get (ctx.fmt.type_decl_kind_to_qualif SingleNonRec (Some Struct))
+  in
+  (* When checking if the trait declaration is empty: we ignore the provided
+     methods, because for now they are extracted separately *)
+  let is_empty = trait_decl_is_empty { decl with provided_methods = [] } in
+  if !backend = FStar && not is_empty then (
+    F.pp_print_string fmt "noeq";
+    F.pp_print_space fmt ());
+  F.pp_print_string fmt qualif;
+  F.pp_print_space fmt ();
+  F.pp_print_string fmt decl_name;
+  (* Print the generics *)
+  let generics = decl.generics in
+  (* Add the type and const generic params - note that we need those bindings only for the
+   * body translation (they are not top-level) *)
+  let ctx, type_params, cg_params, trait_clauses =
+    ctx_add_generic_params generics ctx
+  in
+  extract_generic_params ctx fmt TypeDeclId.Set.empty generics type_params
+    cg_params trait_clauses;
+
+  F.pp_print_space fmt ();
+  if is_empty && !backend = FStar then (
+    F.pp_print_string fmt "= unit";
+    (* Outer box *)
+    F.pp_close_box fmt ())
+  else if is_empty && !backend = Coq then (
+    (* Coq is not very good at infering constructors *)
+    let cons = ctx_get_trait_constructor decl.def_id ctx in
+    F.pp_print_string fmt (":= " ^ cons ^ "{}.");
+    (* Outer box *)
+    F.pp_close_box fmt ())
+  else (
+    (match !backend with
+    | Lean -> F.pp_print_string fmt "where"
+    | FStar -> F.pp_print_string fmt "= {"
+    | Coq ->
+        let cons = ctx_get_trait_constructor decl.def_id ctx in
+        F.pp_print_string fmt (":= " ^ cons ^ " {")
+    | _ -> F.pp_print_string fmt "{");
+
+    (* Close the box for the name + generics *)
+    F.pp_close_box fmt ();
+
+    (*
+     * Extract the items
+     *)
+
+    (* The constants *)
+    List.iter
+      (fun (name, (ty, _)) ->
+        let item_name = ctx_get_trait_const decl.def_id name ctx in
+        let ty () =
+          let inside = false in
+          F.pp_print_space fmt ();
+          extract_ty ctx fmt TypeDeclId.Set.empty inside ty
+        in
+        extract_trait_decl_item ctx fmt item_name ty)
+      decl.consts;
+
+    (* The types *)
+    List.iter
+      (fun (name, (clauses, _)) ->
+        (* Extract the type *)
+        let item_name = ctx_get_trait_type decl.def_id name ctx in
+        let ty () =
+          F.pp_print_space fmt ();
+          F.pp_print_string fmt (type_keyword ())
+        in
+        extract_trait_decl_item ctx fmt item_name ty;
+        (* Extract the clauses *)
+        List.iter
+          (fun clause ->
+            let item_name =
+              ctx_get_trait_item_clause decl.def_id name clause.clause_id ctx
+            in
+            let ty () =
+              F.pp_print_space fmt ();
+              extract_trait_clause_type ctx fmt TypeDeclId.Set.empty clause
+            in
+            extract_trait_decl_item ctx fmt item_name ty)
+          clauses)
+      decl.types;
+
+    (* The parent clauses - note that the parent clauses may refer to the types
+       and const generics: for this reason we extract them *after* *)
+    List.iter
+      (fun clause ->
+        let item_name =
+          ctx_get_trait_parent_clause decl.def_id clause.clause_id ctx
+        in
+        let ty () =
+          F.pp_print_space fmt ();
+          extract_trait_clause_type ctx fmt TypeDeclId.Set.empty clause
+        in
+        extract_trait_decl_item ctx fmt item_name ty)
+      decl.parent_clauses;
+
+    (* The required methods *)
+    List.iter
+      (fun (name, id) -> extract_trait_decl_method_items ctx fmt decl name id)
+      decl.required_methods;
+
+    (* Close the outer boxes for the definition *)
+    if !Config.backend <> Lean then F.pp_close_box fmt ();
+    (* Close the brackets *)
+    match !Config.backend with
+    | Lean -> ()
+    | Coq ->
+        F.pp_print_space fmt ();
+        F.pp_print_string fmt "}."
+    | _ ->
+        F.pp_print_space fmt ();
+        F.pp_print_string fmt "}");
+  F.pp_close_box fmt ();
+  (* Add breaks to insert new lines between definitions *)
+  F.pp_print_break fmt 0 0
+
+(** Generate the [Arguments] instructions for the trait declarationsin Coq, so
+    that we don't have to provide the implicit arguments when projecting the fields. *)
+let extract_trait_decl_coq_arguments (ctx : extraction_ctx) (fmt : F.formatter)
+    (decl : trait_decl) : unit =
+  (* Generating the [Arguments] instructions is useful only if there are parameters *)
+  let num_params =
+    List.length decl.generics.types
+    + List.length decl.generics.const_generics
+    + List.length decl.generics.trait_clauses
+  in
+  if num_params > 0 then (
+    (* The constructor *)
+    let cons_name = ctx_get_trait_constructor decl.def_id ctx in
+    extract_coq_arguments_instruction ctx fmt cons_name num_params;
+    (* The constants *)
+    List.iter
+      (fun (name, _) ->
+        let item_name = ctx_get_trait_const decl.def_id name ctx in
+        extract_coq_arguments_instruction ctx fmt item_name num_params)
+      decl.consts;
+    (* The types *)
+    List.iter
+      (fun (name, (clauses, _)) ->
+        (* The type *)
+        let item_name = ctx_get_trait_type decl.def_id name ctx in
+        extract_coq_arguments_instruction ctx fmt item_name num_params;
+        (* The type clauses *)
+        List.iter
+          (fun clause ->
+            let item_name =
+              ctx_get_trait_item_clause decl.def_id name clause.clause_id ctx
+            in
+            extract_coq_arguments_instruction ctx fmt item_name num_params)
+          clauses)
+      decl.types;
+    (* The parent clauses *)
+    List.iter
+      (fun clause ->
+        let item_name =
+          ctx_get_trait_parent_clause decl.def_id clause.clause_id ctx
+        in
+        extract_coq_arguments_instruction ctx fmt item_name num_params)
+      decl.parent_clauses;
+    (* The required methods *)
+    List.iter
+      (fun (item_name, id) ->
+        (* Lookup the definition *)
+        let trans = A.FunDeclId.Map.find id ctx.trans_funs in
+        (* Extract the items *)
+        let funs =
+          if trans.keep_fwd then trans.fwd :: trans.backs else trans.backs
+        in
+        let extract_for_method (f : fun_and_loops) =
+          let f = f.f in
+          let item_name =
+            ctx_get_trait_method decl.def_id item_name f.back_id ctx
+          in
+          extract_coq_arguments_instruction ctx fmt item_name num_params
+        in
+        List.iter extract_for_method funs)
+      decl.required_methods;
+    (* Add a space *)
+    F.pp_print_space fmt ())
+
+(** See {!extract_trait_decl_coq_arguments} *)
+let extract_trait_decl_extra_info (ctx : extraction_ctx) (fmt : F.formatter)
+    (trait_decl : trait_decl) : unit =
+  match !backend with
+  | Coq -> extract_trait_decl_coq_arguments ctx fmt trait_decl
+  | _ -> ()
+
+(** Small helper.
+
+    Extract the items for a method in a trait impl.
+ *)
+let extract_trait_impl_method_items (ctx : extraction_ctx) (fmt : F.formatter)
+    (impl : trait_impl) (item_name : string) (id : fun_decl_id)
+    (impl_generics : string list * string list * string list) : unit =
+  let trait_decl_id = impl.impl_trait.trait_decl_id in
+  (* Lookup the definition *)
+  let trans = A.FunDeclId.Map.find id ctx.trans_funs in
+  (* Extract the items *)
+  let funs = if trans.keep_fwd then trans.fwd :: trans.backs else trans.backs in
+  let extract_method (f : fun_and_loops) =
+    let f = f.f in
+    let fun_name = ctx_get_trait_method trait_decl_id item_name f.back_id ctx in
+    let ty () =
+      (* Filter the generics if the method is a builtin *)
+      let i_tys, _, _ = impl_generics in
+      let impl_types, i_tys, f_tys =
+        match FunDeclId.Map.find_opt f.def_id ctx.funs_filter_type_args_map with
+        | None -> (impl.generics.types, i_tys, f.signature.generics.types)
+        | Some filter ->
+            let filter_list filter ls =
+              let ls = List.combine filter ls in
+              List.filter_map (fun (b, ty) -> if b then Some ty else None) ls
+            in
+            let impl_types = impl.generics.types in
+            let impl_filter =
+              Collections.List.prefix (List.length impl_types) filter
+            in
+            let i_tys = i_tys in
+            let i_filter = Collections.List.prefix (List.length i_tys) filter in
+            ( filter_list impl_filter impl_types,
+              filter_list i_filter i_tys,
+              filter_list filter f.signature.generics.types )
+      in
+      let f_generics = { f.signature.generics with types = f_tys } in
+      (* Extract the generics - we need to quantify over the generics which
+         are specific to the method, and call it will all the generics
+         (trait impl + method generics) *)
+      let f_generics =
+        let drop_trait_clauses = true in
+        generic_params_drop_prefix ~drop_trait_clauses
+          { impl.generics with types = impl_types }
+          f_generics
+      in
+      (* Register and print the quantified generics *)
+      let ctx, f_tys, f_cgs, f_tcs = ctx_add_generic_params f_generics ctx in
+      let use_forall = f_generics <> empty_generic_params in
+      extract_generic_params ctx fmt TypeDeclId.Set.empty ~use_forall f_generics
+        f_tys f_cgs f_tcs;
+      if use_forall then F.pp_print_string fmt ",";
+      (* Extract the function call *)
+      F.pp_print_space fmt ();
+      let fun_name = ctx_get_local_function f.def_id None f.back_id ctx in
+      F.pp_print_string fmt fun_name;
+      let all_generics =
+        let _, i_cgs, i_tcs = impl_generics in
+        List.concat [ i_tys; f_tys; i_cgs; f_cgs; i_tcs; f_tcs ]
+      in
+
+      (* Filter the generics if the function is builtin *)
+      List.iter
+        (fun p ->
+          F.pp_print_space fmt ();
+          F.pp_print_string fmt p)
+        all_generics
+    in
+    extract_trait_impl_item ctx fmt fun_name ty
+  in
+  List.iter extract_method funs
+
+(** Extract a trait implementation *)
+let extract_trait_impl (ctx : extraction_ctx) (fmt : F.formatter)
+    (impl : trait_impl) : unit =
+  log#ldebug (lazy ("extract_trait_impl: " ^ Names.name_to_string impl.name));
+  (* Retrieve the impl name *)
+  let impl_name = ctx_get_trait_impl impl.def_id ctx in
+  (* Add a break before *)
+  F.pp_print_break fmt 0 0;
+  (* Print a comment to link the extracted type to its original rust definition *)
+  extract_comment fmt
+    [ "Trait implementation: [" ^ Print.name_to_string impl.name ^ "]" ];
+  F.pp_print_break fmt 0 0;
+
+  (* Open two outer boxes for the definition, so that whenever possible it gets printed on
+     one line and indents are correct.
+
+     There is just an exception with Lean: in this backend, line breaks are important
+     for the parsing, so we always open a vertical box.
+  *)
+  if !Config.backend = Lean then (
+    F.pp_open_vbox fmt 0;
+    F.pp_open_vbox fmt ctx.indent_incr)
+  else (
+    F.pp_open_hvbox fmt 0;
+    F.pp_open_hvbox fmt ctx.indent_incr);
+
+  (* `let (....) : Trait ... =` *)
+  (* Open the box for the name + generics *)
+  F.pp_open_hovbox fmt ctx.indent_incr;
+  (match ctx.fmt.fun_decl_kind_to_qualif SingleNonRec with
+  | Some qualif ->
+      F.pp_print_string fmt qualif;
+      F.pp_print_space fmt ()
+  | None -> ());
+  F.pp_print_string fmt impl_name;
+
+  (* Print the generics *)
+  (* Add the type and const generic params - note that we need those bindings only for the
+   * body translation (they are not top-level) *)
+  let ctx, type_params, cg_params, trait_clauses =
+    ctx_add_generic_params impl.generics ctx
+  in
+  let all_generics = (type_params, cg_params, trait_clauses) in
+  extract_generic_params ctx fmt TypeDeclId.Set.empty impl.generics type_params
+    cg_params trait_clauses;
+
+  (* Print the type *)
+  F.pp_print_space fmt ();
+  F.pp_print_string fmt ":";
+  F.pp_print_space fmt ();
+  extract_trait_decl_ref ctx fmt TypeDeclId.Set.empty false impl.impl_trait;
+
+  (* When checking if the trait impl is empty: we ignore the provided
+     methods, because for now they are extracted separately *)
+  let is_empty = trait_impl_is_empty { impl with provided_methods = [] } in
+
+  F.pp_print_space fmt ();
+  if is_empty && !Config.backend = FStar then (
+    F.pp_print_string fmt "= ()";
+    (* Outer box *)
+    F.pp_close_box fmt ())
+  else if is_empty && !Config.backend = Coq then (
+    (* Coq is not very good at infering constructors *)
+    let cons = ctx_get_trait_constructor impl.impl_trait.trait_decl_id ctx in
+    F.pp_print_string fmt (":= " ^ cons ^ ".");
+    (* Outer box *)
+    F.pp_close_box fmt ())
+  else (
+    if !Config.backend = Lean then F.pp_print_string fmt ":= {"
+    else if !Config.backend = Coq then F.pp_print_string fmt ":= {|"
+    else F.pp_print_string fmt "= {";
+
+    (* Close the box for the name + generics *)
+    F.pp_close_box fmt ();
+
+    (*
+     * Extract the items
+     *)
+    let trait_decl_id = impl.impl_trait.trait_decl_id in
+
+    (* The constants *)
+    List.iter
+      (fun (name, (_, id)) ->
+        let item_name = ctx_get_trait_const trait_decl_id name ctx in
+        let ty () =
+          F.pp_print_space fmt ();
+          F.pp_print_string fmt (ctx_get_global id ctx)
+        in
+
+        extract_trait_impl_item ctx fmt item_name ty)
+      impl.consts;
+
+    (* The types *)
+    List.iter
+      (fun (name, (trait_refs, ty)) ->
+        (* Extract the type *)
+        let item_name = ctx_get_trait_type trait_decl_id name ctx in
+        let ty () =
+          F.pp_print_space fmt ();
+          extract_ty ctx fmt TypeDeclId.Set.empty false ty
+        in
+        extract_trait_impl_item ctx fmt item_name ty;
+        (* Extract the clauses *)
+        TraitClauseId.iteri
+          (fun clause_id trait_ref ->
+            let item_name =
+              ctx_get_trait_item_clause trait_decl_id name clause_id ctx
+            in
+            let ty () =
+              F.pp_print_space fmt ();
+              extract_trait_ref ctx fmt TypeDeclId.Set.empty false trait_ref
+            in
+            extract_trait_impl_item ctx fmt item_name ty)
+          trait_refs)
+      impl.types;
+
+    (* The parent clauses *)
+    TraitClauseId.iteri
+      (fun clause_id trait_ref ->
+        let item_name =
+          ctx_get_trait_parent_clause trait_decl_id clause_id ctx
+        in
+        let ty () =
+          F.pp_print_space fmt ();
+          extract_trait_ref ctx fmt TypeDeclId.Set.empty false trait_ref
+        in
+        extract_trait_impl_item ctx fmt item_name ty)
+      impl.parent_trait_refs;
+
+    (* The required methods *)
+    List.iter
+      (fun (name, id) ->
+        extract_trait_impl_method_items ctx fmt impl name id all_generics)
+      impl.required_methods;
+
+    (* Close the outer boxes for the definition, as well as the brackets *)
+    F.pp_close_box fmt ();
+    if !backend = Coq then (
+      F.pp_print_space fmt ();
+      F.pp_print_string fmt "|}.")
+    else if (not (!backend = FStar)) || not is_empty then (
+      F.pp_print_space fmt ();
+      F.pp_print_string fmt "}"));
+  F.pp_close_box fmt ();
+  (* Add breaks to insert new lines between definitions *)
+  F.pp_print_break fmt 0 0
+
 (** Extract a unit test, if the function is a unit function (takes no
     parameters, returns unit).
 
@@ -3735,8 +2632,7 @@ let extract_unit_test_if_unit_fun (ctx : extraction_ctx) (fmt : F.formatter)
   (* Check if this is a unit function *)
   let sg = def.signature in
   if
-    sg.type_params = []
-    && sg.const_generic_params = []
+    sg.generics = empty_generic_params
     && (sg.inputs = [ mk_unit_ty ] || sg.inputs = [])
     && sg.output = mk_result_ty mk_unit_ty
   then (
@@ -3756,12 +2652,8 @@ let extract_unit_test_if_unit_fun (ctx : extraction_ctx) (fmt : F.formatter)
         F.pp_print_string fmt "assert_norm";
         F.pp_print_space fmt ();
         F.pp_print_string fmt "(";
-        (* Note that if the function is opaque, the unit test will fail
-           because the normalizer will get stuck *)
-        let with_opaque_pre = ctx.use_opaque_pre in
         let fun_name =
-          ctx_get_local_function with_opaque_pre def.def_id def.loop_id
-            def.back_id ctx
+          ctx_get_local_function def.def_id def.loop_id def.back_id ctx
         in
         F.pp_print_string fmt fun_name;
         if sg.inputs <> [] then (
@@ -3776,12 +2668,8 @@ let extract_unit_test_if_unit_fun (ctx : extraction_ctx) (fmt : F.formatter)
         F.pp_print_string fmt "Check";
         F.pp_print_space fmt ();
         F.pp_print_string fmt "(";
-        (* Note that if the function is opaque, the unit test will fail
-           because the normalizer will get stuck *)
-        let with_opaque_pre = ctx.use_opaque_pre in
         let fun_name =
-          ctx_get_local_function with_opaque_pre def.def_id def.loop_id
-            def.back_id ctx
+          ctx_get_local_function def.def_id def.loop_id def.back_id ctx
         in
         F.pp_print_string fmt fun_name;
         if sg.inputs <> [] then (
@@ -3793,12 +2681,8 @@ let extract_unit_test_if_unit_fun (ctx : extraction_ctx) (fmt : F.formatter)
         F.pp_print_string fmt "#assert";
         F.pp_print_space fmt ();
         F.pp_print_string fmt "(";
-        (* Note that if the function is opaque, the unit test will fail
-           because the normalizer will get stuck *)
-        let with_opaque_pre = ctx.use_opaque_pre in
         let fun_name =
-          ctx_get_local_function with_opaque_pre def.def_id def.loop_id
-            def.back_id ctx
+          ctx_get_local_function def.def_id def.loop_id def.back_id ctx
         in
         F.pp_print_string fmt fun_name;
         if sg.inputs <> [] then (
@@ -3812,12 +2696,8 @@ let extract_unit_test_if_unit_fun (ctx : extraction_ctx) (fmt : F.formatter)
     | HOL4 ->
         F.pp_print_string fmt "val _ = assert_return (";
         F.pp_print_string fmt "“";
-        (* Note that if the function is opaque, the unit test will fail
-           because the normalizer will get stuck *)
-        let with_opaque_pre = ctx.use_opaque_pre in
         let fun_name =
-          ctx_get_local_function with_opaque_pre def.def_id def.loop_id
-            def.back_id ctx
+          ctx_get_local_function def.def_id def.loop_id def.back_id ctx
         in
         F.pp_print_string fmt fun_name;
         if sg.inputs <> [] then (
diff --git a/compiler/ExtractBase.ml b/compiler/ExtractBase.ml
index d733c763..31b1a447 100644
--- a/compiler/ExtractBase.ml
+++ b/compiler/ExtractBase.ml
@@ -5,9 +5,10 @@ open TranslateCore
 module C = Contexts
 module RegionVarId = T.RegionVarId
 module F = Format
+open ExtractBuiltin
 
 (** The local logger *)
-let log = L.pure_to_extract_log
+let log = L.extract_log
 
 type region_group_info = {
   id : RegionGroupId.id;
@@ -21,8 +22,8 @@ type region_group_info = {
        *)
 }
 
-module StringSet = Collections.MakeSet (Collections.OrderedString)
-module StringMap = Collections.MakeMap (Collections.OrderedString)
+module StringSet = Collections.StringSet
+module StringMap = Collections.StringMap
 
 type name = Names.name
 type type_name = Names.type_name
@@ -77,6 +78,7 @@ type decl_kind =
           F*:  [val x : Type0]
           Coq: [Axiom x : Type.]
        *)
+[@@deriving show]
 
 (** Return [true] if the declaration is the last from its group of declarations.
 
@@ -111,9 +113,9 @@ let decl_is_first_from_group (kind : decl_kind) : bool =
 let decl_is_not_last_from_group (kind : decl_kind) : bool =
   not (decl_is_last_from_group kind)
 
-(* TODO: this should a module we give to a functor! *)
+type type_decl_kind = Enum | Struct [@@deriving show]
 
-type type_decl_kind = Enum | Struct
+(* TODO: this should be a module we give to a functor! *)
 
 (** A formatter's role is twofold:
     1. Come up with name suggestions.
@@ -125,6 +127,9 @@ type type_decl_kind = Enum | Struct
     snake case, adding prefixes/suffixes, etc.
 
     2. Format some specific terms, like constants.
+
+    TODO: unclear that this is useful now that all the backends are so much
+    entangled in Extract.ml
  *)
 type formatter = {
   bool_name : string;
@@ -239,37 +244,14 @@ type formatter = {
             the same purpose as in {!field:fun_name}.
           - loop identifier, if this is for a loop
        *)
-  opaque_pre : unit -> string;
-      (** TODO: obsolete, remove.
-
-          The prefix to use for opaque definitions.
-
-          We need this because for some backends like Lean and Coq, we group
-          opaque definitions in module signatures, meaning that using those
-          definitions requires to prefix them with a module parameter name (such
-          as "opaque_defs.").
-
-          For instance, if we have an opaque function [f : int -> int], which
-          is used by the non-opaque function [g], we would generate (in Coq):
-          {[
-            (* The module signature declaring the opaque definitions *)
-            module type OpaqueDefs = {
-              f_fwd : int -> int
-              ... (* Other definitions *)
-            }
-
-            (* The definitions generated for the non-opaque definitions *)
-            module Funs (opaque: OpaqueDefs) = {
-              let g ... =
-                ...
-                opaque_defs.f_fwd
-                ...
-            }
-          ]}
-
-          Upon using [f] in [g], we don't directly use the the name "f_fwd",
-          but prefix it with the "opaque_defs." identifier.
-       *)
+  trait_decl_name : trait_decl -> string;
+  trait_impl_name : trait_decl -> trait_impl -> string;
+  trait_decl_constructor : trait_decl -> string;
+  trait_parent_clause_name : trait_decl -> trait_clause -> string;
+  trait_const_name : trait_decl -> string -> string;
+  trait_type_name : trait_decl -> string -> string;
+  trait_method_name : trait_decl -> string -> string;
+  trait_type_clause_name : trait_decl -> string -> trait_clause -> string;
   var_basename : StringSet.t -> string option -> ty -> string;
       (** Generates a variable basename.
 
@@ -288,6 +270,14 @@ type formatter = {
       (** Generates a type variable basename. *)
   const_generic_var_basename : StringSet.t -> string -> string;
       (** Generates a const generic variable basename. *)
+  trait_self_clause_basename : string;
+  trait_clause_basename : StringSet.t -> trait_clause -> string;
+      (** Return a base name for a trait clause. We might add a suffix to prevent
+          collisions.
+
+          In the traduction we explicitely manipulate the trait clause instances,
+          that is we introduce one input variable for each trait clause.
+       *)
   append_index : string -> int -> string;
       (** Appends an index to a name - we use this to generate unique
           names: when doing so, the role of the formatter is just to concatenate
@@ -396,10 +386,60 @@ type id =
   | TypeVarId of TypeVarId.id
   | ConstGenericVarId of ConstGenericVarId.id
   | VarId of VarId.id
+  | TraitDeclId of TraitDeclId.id
+  | TraitImplId of TraitImplId.id
+  | LocalTraitClauseId of TraitClauseId.id
+  | TraitDeclConstructorId of TraitDeclId.id
+  | TraitMethodId of TraitDeclId.id * string * T.RegionGroupId.id option
+      (** Something peculiar with trait methods: because we have to take into
+          account forward/backward functions, we may need to generate fields
+          items per method.
+       *)
+  | TraitItemId of TraitDeclId.id * string
+      (** A trait associated item which is not a method *)
+  | TraitParentClauseId of TraitDeclId.id * TraitClauseId.id
+  | TraitItemClauseId of TraitDeclId.id * string * TraitClauseId.id
+  | TraitSelfClauseId
+      (** Specifically for the clause: [Self : Trait].
+
+          For now, we forbid provided methods (methods in trait declarations
+          with a default implementation) from being overriden in trait implementations.
+          We extract trait provided methods such that they take an instance of
+          the trait as input: this instance is given by the trait self clause.
+
+          For instance:
+          {[
+            //
+            // Rust
+            //
+            trait ToU64 {
+              fn to_u64(&self) -> u64;
+
+              // Provided method
+              fn is_pos(&self) -> bool {
+                self.to_u64() > 0
+              }
+            }
+
+            //
+            // Generated code
+            //
+            struct ToU64 (T : Type) {
+              to_u64 : T -> u64;
+            }
+
+            //                    The trait self clause
+            //                    vvvvvvvvvvvvvvvvvvvvvv
+            let is_pos (T : Type) (trait_self : ToU64 T) (self : T) : bool =
+              trait_self.to_u64 self > 0
+          ]}
+       *)
   | UnknownId
       (** Used for stored various strings like keywords, definitions which
           should always be in context, etc. and which can't be linked to one
           of the above.
+
+          TODO: rename to "keyword"
        *)
 [@@deriving show, ord]
 
@@ -429,69 +469,64 @@ type names_map = {
           precisely which identifiers are mapped to the same name...
        *)
   names_set : StringSet.t;
-  opaque_ids : IdSet.t;
-      (** TODO: this is obsolete. Remove.
+}
 
-          The set of opaque definitions.
+let empty_names_map : names_map =
+  {
+    id_to_name = IdMap.empty;
+    name_to_id = StringMap.empty;
+    names_set = StringSet.empty;
+  }
 
-          See {!formatter.opaque_pre} for detailed explanations about why
-          we need to know which definitions are opaque to compute names.
+(** Small helper to report name collision *)
+let report_name_collision (id_to_string : id -> string) (id1 : id) (id2 : id)
+    (name : string) : unit =
+  let id1 = "\n- " ^ id_to_string id1 in
+  let id2 = "\n- " ^ id_to_string id2 in
+  let err =
+    "Name clash detected: the following identifiers are bound to the same name \
+     \"" ^ name ^ "\":" ^ id1 ^ id2
+    ^ "\nYou may want to rename some of your definitions, or report an issue."
+  in
+  log#serror err;
+  (* If we fail hard on errors, raise an exception *)
+  if !Config.fail_hard then raise (Failure err)
 
-          Also note that the opaque ids don't contain the ids of the assumed
-          definitions. In practice, assumed definitions are opaque_defs. However, they
-          are not grouped in the opaque module, meaning we never need to
-          prefix them (with, say, "opaque_defs."): we thus consider them as non-opaque
-          with regards to the names map.
-       *)
-}
+let names_map_get_id_from_name (name : string) (nm : names_map) : id option =
+  StringMap.find_opt name nm.name_to_id
 
-let names_map_add (id_to_string : id -> string) (is_opaque : bool) (id : id)
-    (name : string) (nm : names_map) : names_map =
-  (* Check if there is a clash *)
-  (match StringMap.find_opt name nm.name_to_id with
+let names_map_check_collision (id_to_string : id -> string) (id : id)
+    (name : string) (nm : names_map) : unit =
+  match names_map_get_id_from_name name nm with
   | None -> () (* Ok *)
   | Some clash ->
       (* There is a clash: print a nice debugging message for the user *)
-      let id1 = "\n- " ^ id_to_string clash in
-      let id2 = "\n- " ^ id_to_string id in
-      let err =
-        "Name clash detected: the following identifiers are bound to the same \
-         name \"" ^ name ^ "\":" ^ id1 ^ id2
-      in
-      log#serror err;
-      raise (Failure err));
-  (* Sanity check *)
-  assert (not (StringSet.mem name nm.names_set));
+      report_name_collision id_to_string clash id name
+
+(** Insert bindings in a names map without checking for collisions *)
+let names_map_add_unchecked (id : id) (name : string) (nm : names_map) :
+    names_map =
   (* Insert *)
   let id_to_name = IdMap.add id name nm.id_to_name in
   let name_to_id = StringMap.add name id nm.name_to_id in
   let names_set = StringSet.add name nm.names_set in
-  let opaque_ids =
-    if is_opaque then IdSet.add id nm.opaque_ids else nm.opaque_ids
-  in
-  { id_to_name; name_to_id; names_set; opaque_ids }
-
-let names_map_add_assumed_type (id_to_string : id -> string) (id : assumed_ty)
-    (name : string) (nm : names_map) : names_map =
-  let is_opaque = false in
-  names_map_add id_to_string is_opaque (TypeId (Assumed id)) name nm
-
-let names_map_add_assumed_struct (id_to_string : id -> string) (id : assumed_ty)
-    (name : string) (nm : names_map) : names_map =
-  let is_opaque = false in
-  names_map_add id_to_string is_opaque (StructId (Assumed id)) name nm
+  { id_to_name; name_to_id; names_set }
 
-let names_map_add_assumed_variant (id_to_string : id -> string)
-    (id : assumed_ty) (variant_id : VariantId.id) (name : string)
+let names_map_add (id_to_string : id -> string) (id : id) (name : string)
     (nm : names_map) : names_map =
-  let is_opaque = false in
-  names_map_add id_to_string is_opaque
-    (VariantId (Assumed id, variant_id))
-    name nm
-
-let names_map_add_function (id_to_string : id -> string) (is_opaque : bool)
-    (fid : fun_id) (name : string) (nm : names_map) : names_map =
-  names_map_add id_to_string is_opaque (FunId fid) name nm
+  (* Check if there is a clash *)
+  names_map_check_collision id_to_string id name nm;
+  (* Sanity check *)
+  if StringSet.mem name nm.names_set then (
+    let err =
+      "Error when registering the name for id: " ^ id_to_string id
+      ^ ":\nThe chosen name is already in the names set: " ^ name
+    in
+    log#serror err;
+    (* If we fail hard on errors, raise an exception *)
+    if !Config.fail_hard then raise (Failure err));
+  (* Insert *)
+  names_map_add_unchecked id name nm
 
 (** The unsafe names map stores mappings from identifiers to names which might
     collide. For some backends and some names, it might be acceptable to have
@@ -503,6 +538,8 @@ let names_map_add_function (id_to_string : id -> string) (is_opaque : bool)
   *)
 type unsafe_names_map = { id_to_name : string IdMap.t }
 
+let empty_unsafe_names_map = { id_to_name = IdMap.empty }
+
 let unsafe_names_map_add (id : id) (name : string) (nm : unsafe_names_map) :
     unsafe_names_map =
   { id_to_name = IdMap.add id name nm.id_to_name }
@@ -541,6 +578,24 @@ let basename_to_unique (names_set : StringSet.t)
 
 type fun_name_info = { keep_fwd : bool; num_backs : int }
 
+type names_maps = {
+  names_map : names_map;
+      (** The map for id to names, where we forbid name collisions
+          (ex.: we always forbid function name collisions). *)
+  unsafe_names_map : unsafe_names_map;
+      (** The map for id to names, where we allow name collisions
+          (ex.: we might allow record field name collisions). *)
+  strict_names_map : names_map;
+      (** This map is a sub-map of [names_map]. For the ids in this map we also
+          forbid collisions with names in the [unsafe_names_map].
+
+          We do so for keywords for instance, but also for types (in a dependently
+          typed language, we might have an issue if the field of a record has, say,
+          the name "u32", and another field of the same record refers to "u32"
+          (for instance in its type).
+       *)
+}
+
 (** Extraction context.
 
     Note that the extraction context contains information coming from the
@@ -549,24 +604,12 @@ type fun_name_info = { keep_fwd : bool; num_backs : int }
     functions, etc.
  *)
 type extraction_ctx = {
+  crate : A.crate;
   trans_ctx : trans_ctx;
-  names_map : names_map;
-      (** The map for id to names, where we forbid name collisions
-          (ex.: we always forbid function name collisions). *)
-  unsafe_names_map : unsafe_names_map;
-      (** The map for id to names, where we allow name collisions
-          (ex.: we might allow record field name collisions). *)
+  names_maps : names_maps;
   fmt : formatter;
   indent_incr : int;
       (** The indent increment we insert whenever we need to indent more *)
-  use_opaque_pre : bool;
-      (** Do we use the "opaque_defs." prefix for the opaque definitions?
-
-          Opaque function definitions might refer opaque types: if we are in the
-          opaque module, we musn't use the "opaque_defs." prefix, otherwise we
-          use it.
-          Also see {!names_map.opaque_ids}.
-       *)
   use_dep_ite : bool;
       (** For Lean: do we use dependent-if then else expressions?
 
@@ -586,6 +629,29 @@ type extraction_ctx = {
           in case a Rust function only has one backward translation
           and we filter the forward function because it returns unit.
         *)
+  trait_decl_id : trait_decl_id option;
+      (** If we are extracting a trait declaration, identifies it *)
+  is_provided_method : bool;
+  trans_types : Pure.type_decl Pure.TypeDeclId.Map.t;
+  trans_funs : pure_fun_translation A.FunDeclId.Map.t;
+  functions_with_decreases_clause : PureUtils.FunLoopIdSet.t;
+  trans_trait_decls : Pure.trait_decl Pure.TraitDeclId.Map.t;
+  trans_trait_impls : Pure.trait_impl Pure.TraitImplId.Map.t;
+  types_filter_type_args_map : bool list TypeDeclId.Map.t;
+      (** The map to filter the type arguments for the builtin type
+          definitions.
+
+          We need this for type `Vec`, for instance, which takes a useless
+          (in the context of the type translation) type argument for the
+          allocator which is used, and which we want to remove.
+
+          TODO: it would be cleaner to filter those types in a micro-pass,
+          rather than at code generation time.
+        *)
+  funs_filter_type_args_map : bool list FunDeclId.Map.t;
+      (** Same as {!types_filter_type_args_map}, but for functions *)
+  trait_impls_filter_type_args_map : bool list TraitImplId.Map.t;
+      (** Same as {!types_filter_type_args_map}, but for trait implementations *)
 }
 
 (** Debugging function, used when communicating name collisions to the user,
@@ -593,9 +659,16 @@ type extraction_ctx = {
     instance).
  *)
 let id_to_string (id : id) (ctx : extraction_ctx) : string =
-  let global_decls = ctx.trans_ctx.global_context.global_decls in
-  let fun_decls = ctx.trans_ctx.fun_context.fun_decls in
-  let type_decls = ctx.trans_ctx.type_context.type_decls in
+  let global_decls = ctx.trans_ctx.global_ctx.global_decls in
+  let fun_decls = ctx.trans_ctx.fun_ctx.fun_decls in
+  let type_decls = ctx.trans_ctx.type_ctx.type_decls in
+  let trait_decls = ctx.trans_ctx.trait_decls_ctx.trait_decls in
+  let trait_decl_id_to_string (id : A.TraitDeclId.id) : string =
+    let trait_name =
+      Print.fun_name_to_string (A.TraitDeclId.Map.find id trait_decls).name
+    in
+    "trait_decl: " ^ trait_name ^ " (id: " ^ A.TraitDeclId.to_string id ^ ")"
+  in
   (* TODO: factorize the pretty-printing with what is in PrintPure *)
   let get_type_name (id : type_id) : string =
     match id with
@@ -614,10 +687,17 @@ let id_to_string (id : id) (ctx : extraction_ctx) : string =
       | FromLlbc (fid, lp_id, rg_id) ->
           let fun_name =
             match fid with
-            | Regular fid ->
+            | FunId (Regular fid) ->
                 Print.fun_name_to_string
                   (A.FunDeclId.Map.find fid fun_decls).name
-            | Assumed aid -> A.show_assumed_fun_id aid
+            | FunId (Assumed aid) -> A.show_assumed_fun_id aid
+            | TraitMethod (trait_ref, method_name, _) ->
+                (* Shouldn't happen *)
+                if !Config.fail_hard then raise (Failure "Unexpected")
+                else
+                  "Trait method: decl: "
+                  ^ TraitDeclId.to_string trait_ref.trait_decl_ref.trait_decl_id
+                  ^ ", method_name: " ^ method_name
           in
 
           let lp_kind =
@@ -673,12 +753,16 @@ let id_to_string (id : id) (ctx : extraction_ctx) : string =
             if variant_id = error_failure_id then "@error::Failure"
             else if variant_id = error_out_of_fuel_id then "@error::OutOfFuel"
             else raise (Failure "Unreachable")
-        | Assumed Option ->
-            if variant_id = option_some_id then "@option::Some"
-            else if variant_id = option_none_id then "@option::None"
+        | Assumed Fuel ->
+            if variant_id = fuel_zero_id then "@fuel::0"
+            else if variant_id = fuel_succ_id then "@fuel::Succ"
             else raise (Failure "Unreachable")
-        | Assumed (State | Vec | Fuel | Array | Slice | Str | Range) ->
-            raise (Failure "Unreachable")
+        | Assumed (State | Array | Slice | Str | RawPtr _) ->
+            raise
+              (Failure
+                 ("Unreachable: variant id ("
+                 ^ VariantId.to_string variant_id
+                 ^ ") for " ^ show_type_id id))
         | AdtId id -> (
             let def = TypeDeclId.Map.find id type_decls in
             match def.kind with
@@ -693,8 +777,7 @@ let id_to_string (id : id) (ctx : extraction_ctx) : string =
         match id with
         | Tuple -> raise (Failure "Unreachable")
         | Assumed
-            ( State | Result | Error | Fuel | Option | Vec | Array | Slice | Str
-            | Range ) ->
+            (State | Result | Error | Fuel | Array | Slice | Str | RawPtr _) ->
             (* We can't directly have access to the fields of those types *)
             raise (Failure "Unreachable")
         | AdtId id -> (
@@ -716,134 +799,265 @@ let id_to_string (id : id) (ctx : extraction_ctx) : string =
   | ConstGenericVarId id ->
       "const_generic_var_id: " ^ ConstGenericVarId.to_string id
   | VarId id -> "var_id: " ^ VarId.to_string id
+  | TraitDeclId id -> "trait_decl_id: " ^ TraitDeclId.to_string id
+  | TraitImplId id -> "trait_impl_id: " ^ TraitImplId.to_string id
+  | LocalTraitClauseId id ->
+      "local_trait_clause_id: " ^ TraitClauseId.to_string id
+  | TraitDeclConstructorId id ->
+      "trait_decl_constructor: " ^ trait_decl_id_to_string id
+  | TraitParentClauseId (id, clause_id) ->
+      "trait_parent_clause_id: " ^ trait_decl_id_to_string id ^ ", clause_id: "
+      ^ TraitClauseId.to_string clause_id
+  | TraitItemClauseId (id, item_name, clause_id) ->
+      "trait_item_clause_id: " ^ trait_decl_id_to_string id ^ ", item name: "
+      ^ item_name ^ ", clause_id: "
+      ^ TraitClauseId.to_string clause_id
+  | TraitItemId (id, name) ->
+      "trait_item_id: " ^ trait_decl_id_to_string id ^ ", type name: " ^ name
+  | TraitMethodId (trait_decl_id, fun_name, rg_id) ->
+      let fwd_back_kind =
+        match rg_id with
+        | None -> "forward"
+        | Some rg_id -> "backward " ^ RegionGroupId.to_string rg_id
+      in
+      trait_decl_id_to_string trait_decl_id
+      ^ ", method name (" ^ fwd_back_kind ^ "): " ^ fun_name
+  | TraitSelfClauseId -> "trait_self_clause"
+
+(** Return [true] if we are strict on collisions for this id (i.e., we forbid
+    collisions even with the ids in the unsafe names map) *)
+let strict_collisions (id : id) : bool =
+  match id with UnknownId | TypeId _ -> true | _ -> false
 
 (** We might not check for collisions for some specific ids (ex.: field names) *)
 let allow_collisions (id : id) : bool =
   match id with
-  | FieldId (_, _) -> !Config.record_fields_short_names
+  | FieldId _ | TraitItemClauseId _ | TraitParentClauseId _ | TraitItemId _
+  | TraitMethodId _ ->
+      !Config.record_fields_short_names
+  | FunId (Pure _ | FromLlbc (FunId (Assumed _), _, _)) ->
+      (* We map several assumed functions to the same id *)
+      true
   | _ -> false
 
-let ctx_add (is_opaque : bool) (id : id) (name : string) (ctx : extraction_ctx)
-    : extraction_ctx =
-  (* We do not use the same name map if we allow/disallow collisions *)
+(** The [id_to_string] function to print nice debugging messages if there are
+    collisions *)
+let names_maps_add (id_to_string : id -> string) (id : id) (name : string)
+    (nm : names_maps) : names_maps =
+  (* We do not use the same name map if we allow/disallow collisions.
+     We notably use it for field names: some backends like Lean can use the
+     type information to disambiguate field projections.
+
+     Remark: we still need to check that those "unsafe" ids don't collide with
+     the ids that we mark as "strict on collision".
+
+     For instance, we don't allow naming a field "let". We enforce this by
+     not checking collision between ids for which we permit collisions (ex.:
+     between fields), but still checking collisions between those ids and the
+     others (ex.: fields and keywords).
+  *)
   if allow_collisions id then (
-    assert (not is_opaque);
+    (* Check with the ids which are considered to be strict on collisions *)
+    names_map_check_collision id_to_string id name nm.strict_names_map;
     {
-      ctx with
-      unsafe_names_map = unsafe_names_map_add id name ctx.unsafe_names_map;
+      nm with
+      unsafe_names_map = unsafe_names_map_add id name nm.unsafe_names_map;
     })
   else
-    (* The id_to_string function to print nice debugging messages if there are
-     * collisions *)
-    let id_to_string (id : id) : string = id_to_string id ctx in
-    let names_map =
-      names_map_add id_to_string is_opaque id name ctx.names_map
+    (* Remark: if we are strict on collisions:
+       - we add the id to the strict collisions map
+       - we check that the id doesn't collide with the unsafe map
+       TODO: we might not check that:
+       - a user defined function doesn't collide with an assumed function
+       - two trait decl items don't collide with each other
+    *)
+    let strict_names_map =
+      if strict_collisions id then
+        names_map_add id_to_string id name nm.strict_names_map
+      else nm.strict_names_map
     in
-    { ctx with names_map }
+    let names_map = names_map_add id_to_string id name nm.names_map in
+    { nm with strict_names_map; names_map }
+
+let ctx_add (id : id) (name : string) (ctx : extraction_ctx) : extraction_ctx =
+  let id_to_string (id : id) : string = id_to_string id ctx in
+  let names_maps = names_maps_add id_to_string id name ctx.names_maps in
+  { ctx with names_maps }
 
-(** [with_opaque_pre]: if [true] and the definition is opaque, add the opaque prefix *)
-let ctx_get (with_opaque_pre : bool) (id : id) (ctx : extraction_ctx) : string =
+(** The [id_to_string] function to print nice debugging messages if there are
+    collisions *)
+let names_maps_get (id_to_string : id -> string) (id : id) (nm : names_maps) :
+    string =
   (* We do not use the same name map if we allow/disallow collisions *)
-  if allow_collisions id then IdMap.find id ctx.unsafe_names_map.id_to_name
+  let map_to_string (m : string IdMap.t) : string =
+    "[\n"
+    ^ String.concat ","
+        (List.map
+           (fun (id, n) -> "\n  " ^ id_to_string id ^ " -> " ^ n)
+           (IdMap.bindings m))
+    ^ "\n]"
+  in
+  if allow_collisions id then (
+    let m = nm.unsafe_names_map.id_to_name in
+    match IdMap.find_opt id m with
+    | Some s -> s
+    | None ->
+        let err =
+          "Could not find: " ^ id_to_string id ^ "\nNames map:\n"
+          ^ map_to_string m
+        in
+        log#serror err;
+        if !Config.fail_hard then raise (Failure err)
+        else "(%%%ERROR: unknown identifier\": " ^ id_to_string id ^ "\"%%%)")
   else
-    match IdMap.find_opt id ctx.names_map.id_to_name with
-    | Some s ->
-        let is_opaque = IdSet.mem id ctx.names_map.opaque_ids in
-        if with_opaque_pre && is_opaque then ctx.fmt.opaque_pre () ^ s else s
+    let m = nm.names_map.id_to_name in
+    match IdMap.find_opt id m with
+    | Some s -> s
     | None ->
-        log#serror ("Could not find: " ^ id_to_string id ctx);
-        raise Not_found
+        let err =
+          "Could not find: " ^ id_to_string id ^ "\nNames map:\n"
+          ^ map_to_string m
+        in
+        log#serror err;
+        if !Config.fail_hard then raise (Failure err)
+        else "(ERROR: \"" ^ id_to_string id ^ "\")"
+
+let ctx_get (id : id) (ctx : extraction_ctx) : string =
+  let id_to_string (id : id) : string = id_to_string id ctx in
+  names_maps_get id_to_string id ctx.names_maps
+
+let names_maps_add_assumed_type (id_to_string : id -> string) (id : assumed_ty)
+    (name : string) (nm : names_maps) : names_maps =
+  names_maps_add id_to_string (TypeId (Assumed id)) name nm
+
+let names_maps_add_assumed_struct (id_to_string : id -> string)
+    (id : assumed_ty) (name : string) (nm : names_maps) : names_maps =
+  names_maps_add id_to_string (StructId (Assumed id)) name nm
 
-let ctx_get_global (with_opaque_pre : bool) (id : A.GlobalDeclId.id)
+let names_maps_add_assumed_variant (id_to_string : id -> string)
+    (id : assumed_ty) (variant_id : VariantId.id) (name : string)
+    (nm : names_maps) : names_maps =
+  names_maps_add id_to_string (VariantId (Assumed id, variant_id)) name nm
+
+let names_maps_add_function (id_to_string : id -> string) (fid : fun_id)
+    (name : string) (nm : names_maps) : names_maps =
+  names_maps_add id_to_string (FunId fid) name nm
+
+let ctx_get_global (id : A.GlobalDeclId.id) (ctx : extraction_ctx) : string =
+  ctx_get (GlobalId id) ctx
+
+let ctx_get_function (id : fun_id) (ctx : extraction_ctx) : string =
+  ctx_get (FunId id) ctx
+
+let ctx_get_local_function (id : A.FunDeclId.id) (lp : LoopId.id option)
+    (rg : RegionGroupId.id option) (ctx : extraction_ctx) : string =
+  ctx_get_function (FromLlbc (FunId (Regular id), lp, rg)) ctx
+
+let ctx_get_type (id : type_id) (ctx : extraction_ctx) : string =
+  assert (id <> Tuple);
+  ctx_get (TypeId id) ctx
+
+let ctx_get_local_type (id : TypeDeclId.id) (ctx : extraction_ctx) : string =
+  ctx_get_type (AdtId id) ctx
+
+let ctx_get_assumed_type (id : assumed_ty) (ctx : extraction_ctx) : string =
+  ctx_get_type (Assumed id) ctx
+
+let ctx_get_trait_constructor (id : trait_decl_id) (ctx : extraction_ctx) :
+    string =
+  ctx_get (TraitDeclConstructorId id) ctx
+
+let ctx_get_trait_self_clause (ctx : extraction_ctx) : string =
+  ctx_get TraitSelfClauseId ctx
+
+let ctx_get_trait_decl (id : trait_decl_id) (ctx : extraction_ctx) : string =
+  ctx_get (TraitDeclId id) ctx
+
+let ctx_get_trait_impl (id : trait_impl_id) (ctx : extraction_ctx) : string =
+  ctx_get (TraitImplId id) ctx
+
+let ctx_get_trait_item (id : trait_decl_id) (item_name : string)
     (ctx : extraction_ctx) : string =
-  ctx_get with_opaque_pre (GlobalId id) ctx
+  ctx_get (TraitItemId (id, item_name)) ctx
 
-let ctx_get_function (with_opaque_pre : bool) (id : fun_id)
+let ctx_get_trait_const (id : trait_decl_id) (item_name : string)
     (ctx : extraction_ctx) : string =
-  ctx_get with_opaque_pre (FunId id) ctx
+  ctx_get_trait_item id item_name ctx
 
-let ctx_get_local_function (with_opaque_pre : bool) (id : A.FunDeclId.id)
-    (lp : LoopId.id option) (rg : RegionGroupId.id option)
+let ctx_get_trait_type (id : trait_decl_id) (item_name : string)
     (ctx : extraction_ctx) : string =
-  ctx_get_function with_opaque_pre (FromLlbc (Regular id, lp, rg)) ctx
+  ctx_get_trait_item id item_name ctx
 
-let ctx_get_type (with_opaque_pre : bool) (id : type_id) (ctx : extraction_ctx)
-    : string =
-  assert (id <> Tuple);
-  ctx_get with_opaque_pre (TypeId id) ctx
+let ctx_get_trait_method (id : trait_decl_id) (item_name : string)
+    (rg_id : T.RegionGroupId.id option) (ctx : extraction_ctx) : string =
+  ctx_get (TraitMethodId (id, item_name, rg_id)) ctx
 
-let ctx_get_local_type (with_opaque_pre : bool) (id : TypeDeclId.id)
+let ctx_get_trait_parent_clause (id : trait_decl_id) (clause : trait_clause_id)
     (ctx : extraction_ctx) : string =
-  ctx_get_type with_opaque_pre (AdtId id) ctx
+  ctx_get (TraitParentClauseId (id, clause)) ctx
 
-let ctx_get_assumed_type (id : assumed_ty) (ctx : extraction_ctx) : string =
-  (* In practice, the assumed types are opaque. However, assumed types
-     are never grouped in the opaque module, meaning we never need to
-     prefix them: we thus consider them as non-opaque with regards to the
-     names map.
-  *)
-  let is_opaque = false in
-  ctx_get_type is_opaque (Assumed id) ctx
+let ctx_get_trait_item_clause (id : trait_decl_id) (item : string)
+    (clause : trait_clause_id) (ctx : extraction_ctx) : string =
+  ctx_get (TraitItemClauseId (id, item, clause)) ctx
 
 let ctx_get_var (id : VarId.id) (ctx : extraction_ctx) : string =
-  let is_opaque = false in
-  ctx_get is_opaque (VarId id) ctx
+  ctx_get (VarId id) ctx
 
 let ctx_get_type_var (id : TypeVarId.id) (ctx : extraction_ctx) : string =
-  let is_opaque = false in
-  ctx_get is_opaque (TypeVarId id) ctx
+  ctx_get (TypeVarId id) ctx
 
 let ctx_get_const_generic_var (id : ConstGenericVarId.id) (ctx : extraction_ctx)
     : string =
-  let is_opaque = false in
-  ctx_get is_opaque (ConstGenericVarId id) ctx
+  ctx_get (ConstGenericVarId id) ctx
+
+let ctx_get_local_trait_clause (id : TraitClauseId.id) (ctx : extraction_ctx) :
+    string =
+  ctx_get (LocalTraitClauseId id) ctx
 
 let ctx_get_field (type_id : type_id) (field_id : FieldId.id)
     (ctx : extraction_ctx) : string =
-  let is_opaque = false in
-  ctx_get is_opaque (FieldId (type_id, field_id)) ctx
+  ctx_get (FieldId (type_id, field_id)) ctx
 
-let ctx_get_struct (with_opaque_pre : bool) (def_id : type_id)
-    (ctx : extraction_ctx) : string =
-  ctx_get with_opaque_pre (StructId def_id) ctx
+let ctx_get_struct (def_id : type_id) (ctx : extraction_ctx) : string =
+  ctx_get (StructId def_id) ctx
 
 let ctx_get_variant (def_id : type_id) (variant_id : VariantId.id)
     (ctx : extraction_ctx) : string =
-  let is_opaque = false in
-  ctx_get is_opaque (VariantId (def_id, variant_id)) ctx
+  ctx_get (VariantId (def_id, variant_id)) ctx
 
 let ctx_get_decreases_proof (def_id : A.FunDeclId.id)
     (loop_id : LoopId.id option) (ctx : extraction_ctx) : string =
-  let is_opaque = false in
-  ctx_get is_opaque (DecreasesProofId (Regular def_id, loop_id)) ctx
+  ctx_get (DecreasesProofId (Regular def_id, loop_id)) ctx
 
 let ctx_get_termination_measure (def_id : A.FunDeclId.id)
     (loop_id : LoopId.id option) (ctx : extraction_ctx) : string =
-  let is_opaque = false in
-  ctx_get is_opaque (TerminationMeasureId (Regular def_id, loop_id)) ctx
+  ctx_get (TerminationMeasureId (Regular def_id, loop_id)) ctx
 
 (** Generate a unique type variable name and add it to the context *)
 let ctx_add_type_var (basename : string) (id : TypeVarId.id)
     (ctx : extraction_ctx) : extraction_ctx * string =
-  let is_opaque = false in
-  let name = ctx.fmt.type_var_basename ctx.names_map.names_set basename in
   let name =
-    basename_to_unique ctx.names_map.names_set ctx.fmt.append_index name
+    ctx.fmt.type_var_basename ctx.names_maps.names_map.names_set basename
+  in
+  let name =
+    basename_to_unique ctx.names_maps.names_map.names_set ctx.fmt.append_index
+      name
   in
-  let ctx = ctx_add is_opaque (TypeVarId id) name ctx in
+  let ctx = ctx_add (TypeVarId id) name ctx in
   (ctx, name)
 
 (** Generate a unique const generic variable name and add it to the context *)
 let ctx_add_const_generic_var (basename : string) (id : ConstGenericVarId.id)
     (ctx : extraction_ctx) : extraction_ctx * string =
-  let is_opaque = false in
   let name =
-    ctx.fmt.const_generic_var_basename ctx.names_map.names_set basename
+    ctx.fmt.const_generic_var_basename ctx.names_maps.names_map.names_set
+      basename
   in
   let name =
-    basename_to_unique ctx.names_map.names_set ctx.fmt.append_index name
+    basename_to_unique ctx.names_maps.names_map.names_set ctx.fmt.append_index
+      name
   in
-  let ctx = ctx_add is_opaque (ConstGenericVarId id) name ctx in
+  let ctx = ctx_add (ConstGenericVarId id) name ctx in
   (ctx, name)
 
 (** See {!ctx_add_type_var} *)
@@ -856,11 +1070,31 @@ let ctx_add_type_vars (vars : (string * TypeVarId.id) list)
 (** Generate a unique variable name and add it to the context *)
 let ctx_add_var (basename : string) (id : VarId.id) (ctx : extraction_ctx) :
     extraction_ctx * string =
-  let is_opaque = false in
   let name =
-    basename_to_unique ctx.names_map.names_set ctx.fmt.append_index basename
+    basename_to_unique ctx.names_maps.names_map.names_set ctx.fmt.append_index
+      basename
   in
-  let ctx = ctx_add is_opaque (VarId id) name ctx in
+  let ctx = ctx_add (VarId id) name ctx in
+  (ctx, name)
+
+(** Generate a unique variable name for the trait self clause and add it to the context *)
+let ctx_add_trait_self_clause (ctx : extraction_ctx) : extraction_ctx * string =
+  let basename = ctx.fmt.trait_self_clause_basename in
+  let name =
+    basename_to_unique ctx.names_maps.names_map.names_set ctx.fmt.append_index
+      basename
+  in
+  let ctx = ctx_add TraitSelfClauseId name ctx in
+  (ctx, name)
+
+(** Generate a unique trait clause name and add it to the context *)
+let ctx_add_local_trait_clause (basename : string) (id : TraitClauseId.id)
+    (ctx : extraction_ctx) : extraction_ctx * string =
+  let name =
+    basename_to_unique ctx.names_maps.names_map.names_set ctx.fmt.append_index
+      basename
+  in
+  let ctx = ctx_add (LocalTraitClauseId id) name ctx in
   (ctx, name)
 
 (** See {!ctx_add_var} *)
@@ -868,7 +1102,9 @@ let ctx_add_vars (vars : var list) (ctx : extraction_ctx) :
     extraction_ctx * string list =
   List.fold_left_map
     (fun ctx (v : var) ->
-      let name = ctx.fmt.var_basename ctx.names_map.names_set v.basename v.ty in
+      let name =
+        ctx.fmt.var_basename ctx.names_maps.names_map.names_set v.basename v.ty
+      in
       ctx_add_var name v.id ctx)
     ctx vars
 
@@ -885,142 +1121,105 @@ let ctx_add_const_generic_params (vars : const_generic_var list)
       ctx_add_const_generic_var var.name var.index ctx)
     ctx vars
 
-let ctx_add_type_const_generic_params (tvars : type_var list)
-    (cgvars : const_generic_var list) (ctx : extraction_ctx) :
-    extraction_ctx * string list * string list =
-  let ctx, tys = ctx_add_type_params tvars ctx in
-  let ctx, cgs = ctx_add_const_generic_params cgvars ctx in
-  (ctx, tys, cgs)
-
-let ctx_add_type_decl_struct (def : type_decl) (ctx : extraction_ctx) :
-    extraction_ctx * string =
-  assert (match def.kind with Struct _ -> true | _ -> false);
-  let is_opaque = false in
-  let cons_name = ctx.fmt.struct_constructor def.name in
-  let ctx = ctx_add is_opaque (StructId (AdtId def.def_id)) cons_name ctx in
-  (ctx, cons_name)
-
-let ctx_add_type_decl (def : type_decl) (ctx : extraction_ctx) : extraction_ctx
-    =
-  let is_opaque = def.kind = Opaque in
-  let def_name = ctx.fmt.type_name def.name in
-  let ctx = ctx_add is_opaque (TypeId (AdtId def.def_id)) def_name ctx in
-  ctx
-
-let ctx_add_field (def : type_decl) (field_id : FieldId.id) (field : field)
-    (ctx : extraction_ctx) : extraction_ctx * string =
-  let is_opaque = false in
-  let name = ctx.fmt.field_name def.name field_id field.field_name in
-  let ctx = ctx_add is_opaque (FieldId (AdtId def.def_id, field_id)) name ctx in
-  (ctx, name)
-
-let ctx_add_fields (def : type_decl) (fields : (FieldId.id * field) list)
+let ctx_add_local_trait_clauses (clauses : trait_clause list)
     (ctx : extraction_ctx) : extraction_ctx * string list =
   List.fold_left_map
-    (fun ctx (vid, v) -> ctx_add_field def vid v ctx)
-    ctx fields
-
-let ctx_add_variant (def : type_decl) (variant_id : VariantId.id)
-    (variant : variant) (ctx : extraction_ctx) : extraction_ctx * string =
-  let is_opaque = false in
-  let name = ctx.fmt.variant_name def.name variant.variant_name in
-  (* Add the type name prefix for Lean *)
-  let name =
-    if !Config.backend = Lean then
-      let type_name = ctx.fmt.type_name def.name in
-      type_name ^ "." ^ name
-    else name
-  in
-  let ctx =
-    ctx_add is_opaque (VariantId (AdtId def.def_id, variant_id)) name ctx
-  in
-  (ctx, name)
-
-let ctx_add_variants (def : type_decl)
-    (variants : (VariantId.id * variant) list) (ctx : extraction_ctx) :
-    extraction_ctx * string list =
-  List.fold_left_map
-    (fun ctx (vid, v) -> ctx_add_variant def vid v ctx)
-    ctx variants
+    (fun ctx (c : trait_clause) ->
+      let basename =
+        ctx.fmt.trait_clause_basename ctx.names_maps.names_map.names_set c
+      in
+      ctx_add_local_trait_clause basename c.clause_id ctx)
+    ctx clauses
 
-let ctx_add_struct (def : type_decl) (ctx : extraction_ctx) :
-    extraction_ctx * string =
-  assert (match def.kind with Struct _ -> true | _ -> false);
-  let is_opaque = false in
-  let name = ctx.fmt.struct_constructor def.name in
-  let ctx = ctx_add is_opaque (StructId (AdtId def.def_id)) name ctx in
-  (ctx, name)
+(** Returns the lists of names for:
+    - the type variables
+    - the const generic variables
+    - the trait clauses
+  *)
+let ctx_add_generic_params (generics : generic_params) (ctx : extraction_ctx) :
+    extraction_ctx * string list * string list * string list =
+  let { types; const_generics; trait_clauses } = generics in
+  let ctx, tys = ctx_add_type_params types ctx in
+  let ctx, cgs = ctx_add_const_generic_params const_generics ctx in
+  let ctx, tcs = ctx_add_local_trait_clauses trait_clauses ctx in
+  (ctx, tys, cgs, tcs)
 
 let ctx_add_decreases_proof (def : fun_decl) (ctx : extraction_ctx) :
     extraction_ctx =
-  let is_opaque = false in
   let name =
     ctx.fmt.decreases_proof_name def.def_id def.basename def.num_loops
       def.loop_id
   in
-  ctx_add is_opaque
-    (DecreasesProofId (Regular def.def_id, def.loop_id))
-    name ctx
+  ctx_add (DecreasesProofId (Regular def.def_id, def.loop_id)) name ctx
 
 let ctx_add_termination_measure (def : fun_decl) (ctx : extraction_ctx) :
     extraction_ctx =
-  let is_opaque = false in
   let name =
     ctx.fmt.termination_measure_name def.def_id def.basename def.num_loops
       def.loop_id
   in
-  ctx_add is_opaque
-    (TerminationMeasureId (Regular def.def_id, def.loop_id))
-    name ctx
+  ctx_add (TerminationMeasureId (Regular def.def_id, def.loop_id)) name ctx
 
 let ctx_add_global_decl_and_body (def : A.global_decl) (ctx : extraction_ctx) :
     extraction_ctx =
   (* TODO: update once the body id can be an option *)
-  let is_opaque = false in
-  let name = ctx.fmt.global_name def.name in
   let decl = GlobalId def.def_id in
-  let body = FunId (FromLlbc (Regular def.body_id, None, None)) in
-  let ctx = ctx_add is_opaque decl (name ^ "_c") ctx in
-  let ctx = ctx_add is_opaque body (name ^ "_body") ctx in
-  ctx
 
-let ctx_add_fun_decl (trans_group : bool * pure_fun_translation)
-    (def : fun_decl) (ctx : extraction_ctx) : extraction_ctx =
-  (* Sanity check: the function should not be a global body - those are handled
-   * separately *)
-  assert (not def.is_global_decl_body);
+  (* Check if the global corresponds to an assumed global that we should map
+     to a custom definition in our standard library (for instance, happens
+     with "core::num::usize::MAX") *)
+  let sname = name_to_simple_name def.name in
+  match SimpleNameMap.find_opt sname builtin_globals_map with
+  | Some name ->
+      (* Yes: register the custom binding *)
+      ctx_add decl name ctx
+  | None ->
+      (* Not the case: "standard" registration *)
+      let name = ctx.fmt.global_name def.name in
+      let body = FunId (FromLlbc (FunId (Regular def.body_id), None, None)) in
+      let ctx = ctx_add decl (name ^ "_c") ctx in
+      let ctx = ctx_add body (name ^ "_body") ctx in
+      ctx
+
+let ctx_compute_fun_name (trans_group : pure_fun_translation) (def : fun_decl)
+    (ctx : extraction_ctx) : string =
   (* Lookup the LLBC def to compute the region group information *)
   let def_id = def.def_id in
-  let llbc_def =
-    A.FunDeclId.Map.find def_id ctx.trans_ctx.fun_context.fun_decls
-  in
+  let llbc_def = A.FunDeclId.Map.find def_id ctx.trans_ctx.fun_ctx.fun_decls in
   let sg = llbc_def.signature in
   let num_rgs = List.length sg.regions_hierarchy in
-  let keep_fwd, (_, backs) = trans_group in
+  let { keep_fwd; fwd = _; backs } = trans_group in
   let num_backs = List.length backs in
   let rg_info =
     match def.back_id with
     | None -> None
     | Some rg_id ->
         let rg = T.RegionGroupId.nth sg.regions_hierarchy rg_id in
-        let regions =
+        let region_names =
           List.map
-            (fun rid -> T.RegionVarId.nth sg.region_params rid)
+            (fun rid -> (T.RegionVarId.nth sg.generics.regions rid).name)
             rg.regions
         in
-        let region_names =
-          List.map (fun (r : T.region_var) -> r.name) regions
-        in
         Some { id = rg_id; region_names }
   in
-  let is_opaque = def.body = None in
   (* Add the function name *)
-  let def_name =
-    ctx.fmt.fun_name def.basename def.num_loops def.loop_id num_rgs rg_info
-      (keep_fwd, num_backs)
-  in
-  let fun_id = (A.Regular def_id, def.loop_id, def.back_id) in
-  let ctx = ctx_add is_opaque (FunId (FromLlbc fun_id)) def_name ctx in
+  ctx.fmt.fun_name def.basename def.num_loops def.loop_id num_rgs rg_info
+    (keep_fwd, num_backs)
+
+(* TODO: move to Extract *)
+let ctx_add_fun_decl (trans_group : pure_fun_translation) (def : fun_decl)
+    (ctx : extraction_ctx) : extraction_ctx =
+  (* Sanity check: the function should not be a global body - those are handled
+   * separately *)
+  assert (not def.is_global_decl_body);
+  (* Lookup the LLBC def to compute the region group information *)
+  let def_id = def.def_id in
+  let { keep_fwd; fwd = _; backs } = trans_group in
+  let num_backs = List.length backs in
+  (* Add the function name *)
+  let def_name = ctx_compute_fun_name trans_group def ctx in
+  let fun_id = (Pure.FunId (Regular def_id), def.loop_id, def.back_id) in
+  let ctx = ctx_add (FunId (FromLlbc fun_id)) def_name ctx in
   (* Add the name info *)
   {
     ctx with
@@ -1039,9 +1238,10 @@ type names_map_init = {
   assumed_pure_functions : (pure_assumed_fun_id * string) list;
 }
 
-(** Initialize a names map with a proper set of keywords/names coming from the
+(** Initialize names maps with a proper set of keywords/names coming from the
     target language/prover. *)
-let initialize_names_map (fmt : formatter) (init : names_map_init) : names_map =
+let initialize_names_maps (fmt : formatter) (init : names_map_init) : names_maps
+    =
   let int_names = List.map fmt.int_name T.all_int_types in
   let keywords =
     List.concat
@@ -1049,20 +1249,30 @@ let initialize_names_map (fmt : formatter) (init : names_map_init) : names_map =
         [ fmt.bool_name; fmt.char_name; fmt.str_name ]; int_names; init.keywords;
       ]
   in
-  let names_set = StringSet.of_list keywords in
-  let name_to_id =
-    StringMap.of_list (List.map (fun x -> (x, UnknownId)) keywords)
-  in
-  let opaque_ids = IdSet.empty in
+  let names_set = StringSet.empty in
+  let name_to_id = StringMap.empty in
   (* We fist initialize [id_to_name] as empty, because the id of a keyword is [UnknownId].
    * Also note that we don't need this mapping for keywords: we insert keywords only
    * to check collisions. *)
   let id_to_name = IdMap.empty in
-  let nm = { id_to_name; name_to_id; names_set; opaque_ids } in
+  let names_map = { id_to_name; name_to_id; names_set } in
+  let unsafe_names_map = empty_unsafe_names_map in
+  let strict_names_map = empty_names_map in
   (* For debugging - we are creating bindings for assumed types and functions, so
    * it is ok if we simply use the "show" function (those aren't simply identified
    * by numbers) *)
   let id_to_string = show_id in
+  (* Add the keywords as strict collisions *)
+  let strict_names_map =
+    List.fold_left
+      (fun nm name ->
+        (* There is duplication in the keywords so we don't check the collisions
+           while registering them (what is important is that there are no collisions
+           between keywords and user-defined identifiers) *)
+        names_map_add_unchecked UnknownId name nm)
+      strict_names_map keywords
+  in
+  let nm = { names_map; unsafe_names_map; strict_names_map } in
   (* Then we add:
    * - the assumed types
    * - the assumed struct constructors
@@ -1072,37 +1282,31 @@ let initialize_names_map (fmt : formatter) (init : names_map_init) : names_map =
   let nm =
     List.fold_left
       (fun nm (type_id, name) ->
-        names_map_add_assumed_type id_to_string type_id name nm)
+        names_maps_add_assumed_type id_to_string type_id name nm)
       nm init.assumed_adts
   in
   let nm =
     List.fold_left
       (fun nm (type_id, name) ->
-        names_map_add_assumed_struct id_to_string type_id name nm)
+        names_maps_add_assumed_struct id_to_string type_id name nm)
       nm init.assumed_structs
   in
   let nm =
     List.fold_left
       (fun nm (type_id, variant_id, name) ->
-        names_map_add_assumed_variant id_to_string type_id variant_id name nm)
+        names_maps_add_assumed_variant id_to_string type_id variant_id name nm)
       nm init.assumed_variants
   in
   let assumed_functions =
     List.map
-      (fun (fid, rg, name) -> (FromLlbc (A.Assumed fid, None, rg), name))
+      (fun (fid, rg, name) ->
+        (FromLlbc (Pure.FunId (Assumed fid), None, rg), name))
       init.assumed_llbc_functions
     @ List.map (fun (fid, name) -> (Pure fid, name)) init.assumed_pure_functions
   in
   let nm =
-    (* In practice, the assumed function are opaque. However, assumed functions
-       are never grouped in the opaque module, meaning we never need to
-       prefix them: we thus consider them as non-opaque with regards to the
-       names map.
-    *)
-    let is_opaque = false in
     List.fold_left
-      (fun nm (fid, name) ->
-        names_map_add_function id_to_string is_opaque fid name nm)
+      (fun nm (fid, name) -> names_maps_add_function id_to_string fid name nm)
       nm assumed_functions
   in
   (* Return *)
@@ -1150,22 +1354,20 @@ let default_fun_suffix (num_loops : int) (loop_id : LoopId.id option)
   let rg_suff =
     (* TODO: make all the backends match what is done for Lean *)
     match rg with
-    | None -> (
-        match !Config.backend with
-        | FStar | Coq | HOL4 -> "_fwd"
-        | Lean ->
-            (* In order to avoid name conflicts:
-             * - if the forward is eliminated, we add the suffix "_fwd" (it won't be used)
-             * - otherwise, no suffix (because the backward functions will have a suffix)
-             *)
-            if num_backs = 1 && not keep_fwd then "_fwd" else "")
+    | None ->
+        if
+          (* In order to avoid name conflicts:
+           * - if the forward is eliminated, we add the suffix "_fwd" (it won't be used)
+           * - otherwise, no suffix (because the backward functions will have a suffix)
+           *)
+          num_backs = 1 && not keep_fwd
+        then "_fwd"
+        else ""
     | Some rg ->
         assert (num_region_groups > 0 && num_backs > 0);
         if num_backs = 1 then
           (* Exactly one backward function *)
-          match !Config.backend with
-          | FStar | Coq | HOL4 -> if not keep_fwd then "_fwd_back" else "_back"
-          | Lean -> if not keep_fwd then "" else "_back"
+          if not keep_fwd then "" else "_back"
         else if
           (* Several region groups/backward functions:
              - if all the regions in the group have names, we use those names
diff --git a/compiler/ExtractBuiltin.ml b/compiler/ExtractBuiltin.ml
new file mode 100644
index 00000000..a54ab604
--- /dev/null
+++ b/compiler/ExtractBuiltin.ml
@@ -0,0 +1,648 @@
+(** This file declares external identifiers that we catch to map them to
+    definitions coming from the standard libraries in our backends.
+
+    TODO: there misses trait **implementations**
+ *)
+
+open Names
+open Config
+
+type simple_name = string list [@@deriving show, ord]
+
+let name_to_simple_name (s : name) : simple_name =
+  (* We simply ignore the disambiguators *)
+  List.filter_map (function Ident id -> Some id | Disambiguator _ -> None) s
+
+(** Small helper which cuts a string at the occurrences of "::" *)
+let string_to_simple_name (s : string) : simple_name =
+  (* No function to split by using string separator?? *)
+  let name = String.split_on_char ':' s in
+  List.filter (fun s -> s <> "") name
+
+module SimpleNameOrd = struct
+  type t = simple_name
+
+  let compare = compare_simple_name
+  let to_string = show_simple_name
+  let pp_t = pp_simple_name
+  let show_t = show_simple_name
+end
+
+module SimpleNameMap = Collections.MakeMap (SimpleNameOrd)
+module SimpleNameSet = Collections.MakeSet (SimpleNameOrd)
+
+(** Small utility to memoize some computations *)
+let mk_memoized (f : unit -> 'a) : unit -> 'a =
+  let r = ref None in
+  let g () =
+    match !r with
+    | Some x -> x
+    | None ->
+        let x = f () in
+        r := Some x;
+        x
+  in
+  g
+
+(** Switch between two values depending on the target backend.
+
+    We often compute the same value (typically: a name) if the target
+    is F*, Coq or HOL4, and a different value if the target is Lean.
+ *)
+let backend_choice (fstar_coq_hol4 : 'a) (lean : 'a) : 'a =
+  match !backend with Coq | FStar | HOL4 -> fstar_coq_hol4 | Lean -> lean
+
+let builtin_globals : (string * string) list =
+  [
+    (* Min *)
+    ("core::num::usize::MIN", "core_usize_min");
+    ("core::num::u8::MIN", "core_u8_min");
+    ("core::num::u16::MIN", "core_u16_min");
+    ("core::num::u32::MIN", "core_u32_min");
+    ("core::num::u64::MIN", "core_u64_min");
+    ("core::num::u128::MIN", "core_u128_min");
+    ("core::num::isize::MIN", "core_isize_min");
+    ("core::num::i8::MIN", "core_i8_min");
+    ("core::num::i16::MIN", "core_i16_min");
+    ("core::num::i32::MIN", "core_i32_min");
+    ("core::num::i64::MIN", "core_i64_min");
+    ("core::num::i128::MIN", "core_i128_min");
+    (* Max *)
+    ("core::num::usize::MAX", "core_usize_max");
+    ("core::num::u8::MAX", "core_u8_max");
+    ("core::num::u16::MAX", "core_u16_max");
+    ("core::num::u32::MAX", "core_u32_max");
+    ("core::num::u64::MAX", "core_u64_max");
+    ("core::num::u128::MAX", "core_u128_max");
+    ("core::num::isize::MAX", "core_isize_max");
+    ("core::num::i8::MAX", "core_i8_max");
+    ("core::num::i16::MAX", "core_i16_max");
+    ("core::num::i32::MAX", "core_i32_max");
+    ("core::num::i64::MAX", "core_i64_max");
+    ("core::num::i128::MAX", "core_i128_max");
+  ]
+
+let builtin_globals_map : string SimpleNameMap.t =
+  SimpleNameMap.of_list
+    (List.map (fun (x, y) -> (string_to_simple_name x, y)) builtin_globals)
+
+type builtin_variant_info = { fields : (string * string) list }
+[@@deriving show]
+
+type builtin_enum_variant_info = {
+  rust_variant_name : string;
+  extract_variant_name : string;
+  fields : string list option;
+}
+[@@deriving show]
+
+type builtin_type_body_info =
+  | Struct of string * (string * string) list
+    (* The constructor name and the map for the field names *)
+  | Enum of builtin_enum_variant_info list
+(* For every variant, a map for the field names *)
+[@@deriving show]
+
+type builtin_type_info = {
+  rust_name : string list;
+  extract_name : string;
+  keep_params : bool list option;
+      (** We might want to filter some of the type parameters.
+
+          For instance, `Vec` type takes a type parameter for the allocator,
+          which we want to ignore.
+       *)
+  body_info : builtin_type_body_info option;
+}
+[@@deriving show]
+
+type type_variant_kind =
+  | KOpaque
+  | KStruct of (string * string) list
+  (* TODO: handle the tuple case *)
+  | KEnum (* TODO *)
+
+let mk_struct_constructor (type_name : string) : string =
+  let prefix =
+    match !backend with FStar -> "Mk" | Coq | HOL4 -> "mk" | Lean -> ""
+  in
+  let suffix = match !backend with FStar | Coq | HOL4 -> "" | Lean -> ".mk" in
+  prefix ^ type_name ^ suffix
+
+(** The assumed types.
+
+    The optional list of booleans is filtering information for the type
+    parameters. For instance, in the case of the `Vec` functions, there is
+    a type parameter for the allocator to use, which we want to filter.
+ *)
+let builtin_types () : builtin_type_info list =
+  let mk_type (rust_name : string list) ?(keep_params : bool list option = None)
+      ?(kind : type_variant_kind = KOpaque) () : builtin_type_info =
+    let extract_name =
+      let sep = backend_choice "_" "." in
+      String.concat sep rust_name
+    in
+    let body_info : builtin_type_body_info option =
+      match kind with
+      | KOpaque -> None
+      | KStruct fields ->
+          let fields =
+            List.map
+              (fun (rname, name) ->
+                ( rname,
+                  match !backend with
+                  | FStar | Lean -> name
+                  | Coq | HOL4 -> extract_name ^ "_" ^ name ))
+              fields
+          in
+          let constructor = mk_struct_constructor extract_name in
+          Some (Struct (constructor, fields))
+      | KEnum -> raise (Failure "TODO")
+    in
+    { rust_name; extract_name; keep_params; body_info }
+  in
+
+  [
+    (* Alloc *)
+    mk_type [ "alloc"; "alloc"; "Global" ] ();
+    (* Vec *)
+    mk_type [ "alloc"; "vec"; "Vec" ] ~keep_params:(Some [ true; false ]) ();
+    (* Range *)
+    mk_type
+      [ "core"; "ops"; "range"; "Range" ]
+      ~kind:(KStruct [ ("start", "start"); ("end", "end_") ])
+      ();
+    (* Option
+
+       This one is more custom because we use the standard "option" type from
+       the target backend.
+    *)
+    {
+      rust_name = [ "core"; "option"; "Option" ];
+      extract_name =
+        (match !backend with
+        | Lean -> "Option"
+        | Coq | FStar | HOL4 -> "option");
+      keep_params = None;
+      body_info =
+        Some
+          (Enum
+             [
+               {
+                 rust_variant_name = "None";
+                 extract_variant_name =
+                   (match !backend with
+                   | FStar | Coq -> "None"
+                   | Lean -> "none"
+                   | HOL4 -> "NONE");
+                 fields = None;
+               };
+               {
+                 rust_variant_name = "Some";
+                 extract_variant_name =
+                   (match !backend with
+                   | FStar | Coq -> "Some"
+                   | Lean -> "some"
+                   | HOL4 -> "SOME");
+                 fields = None;
+               };
+             ]);
+    };
+  ]
+
+let mk_builtin_types_map () =
+  SimpleNameMap.of_list
+    (List.map (fun info -> (info.rust_name, info)) (builtin_types ()))
+
+let builtin_types_map = mk_memoized mk_builtin_types_map
+
+type builtin_fun_info = {
+  rg : Types.RegionGroupId.id option;
+  extract_name : string;
+}
+[@@deriving show]
+
+(** The assumed functions.
+
+    The optional list of booleans is filtering information for the type
+    parameters. For instance, in the case of the `Vec` functions, there is
+    a type parameter for the allocator to use, which we want to filter.
+ *)
+let builtin_funs () :
+    (string list * bool list option * builtin_fun_info list) list =
+  let rg0 = Some Types.RegionGroupId.zero in
+  (* Small utility *)
+  let mk_fun (name : string list) (extract_name : string list option)
+      (filter : bool list option) (with_back : bool) (back_no_suffix : bool) :
+      string list * bool list option * builtin_fun_info list =
+    let extract_name =
+      match extract_name with None -> name | Some name -> name
+    in
+    let basename =
+      match !backend with
+      | FStar | Coq | HOL4 -> String.concat "_" extract_name
+      | Lean -> String.concat "." extract_name
+    in
+    let fwd_suffix = if with_back && back_no_suffix then "_fwd" else "" in
+    let fwd = [ { rg = None; extract_name = basename ^ fwd_suffix } ] in
+    let back_suffix = if with_back && back_no_suffix then "" else "_back" in
+    let back =
+      if with_back then [ { rg = rg0; extract_name = basename ^ back_suffix } ]
+      else []
+    in
+    (name, filter, fwd @ back)
+  in
+  [
+    mk_fun [ "core"; "mem"; "replace" ] None None true false;
+    mk_fun [ "alloc"; "vec"; "Vec"; "new" ] None None false false;
+    mk_fun
+      [ "alloc"; "vec"; "Vec"; "push" ]
+      None
+      (Some [ true; false ])
+      true true;
+    mk_fun
+      [ "alloc"; "vec"; "Vec"; "insert" ]
+      None
+      (Some [ true; false ])
+      true true;
+    mk_fun
+      [ "alloc"; "vec"; "Vec"; "len" ]
+      None
+      (Some [ true; false ])
+      true false;
+    mk_fun
+      [ "alloc"; "vec"; "Vec"; "index" ]
+      None
+      (Some [ true; true; false ])
+      true false;
+    mk_fun
+      [ "alloc"; "vec"; "Vec"; "index_mut" ]
+      None
+      (Some [ true; true; false ])
+      true false;
+    mk_fun
+      [ "alloc"; "boxed"; "Box"; "deref" ]
+      None
+      (Some [ true; false ])
+      true false;
+    mk_fun
+      [ "alloc"; "boxed"; "Box"; "deref_mut" ]
+      None
+      (Some [ true; false ])
+      true false;
+    (* TODO: fix the same like "[T]" below *)
+    mk_fun
+      [ "core"; "slice"; "index"; "[T]"; "index" ]
+      (Some [ "core"; "slice"; "index"; "Slice"; "index" ])
+      None true false;
+    mk_fun
+      [ "core"; "slice"; "index"; "[T]"; "index_mut" ]
+      (Some [ "core"; "slice"; "index"; "Slice"; "index_mut" ])
+      None true false;
+    mk_fun
+      [ "core"; "array"; "[T; N]"; "index" ]
+      (Some [ "core"; "array"; "Array"; "index" ])
+      None true false;
+    mk_fun
+      [ "core"; "array"; "[T; N]"; "index_mut" ]
+      (Some [ "core"; "array"; "Array"; "index_mut" ])
+      None true false;
+    mk_fun [ "core"; "slice"; "index"; "Range"; "get" ] None None true false;
+    mk_fun [ "core"; "slice"; "index"; "Range"; "get_mut" ] None None true false;
+    mk_fun [ "core"; "slice"; "index"; "Range"; "index" ] None None true false;
+    mk_fun
+      [ "core"; "slice"; "index"; "Range"; "index_mut" ]
+      None None true false;
+    mk_fun
+      [ "core"; "slice"; "index"; "Range"; "get_unchecked" ]
+      None None false false;
+    mk_fun
+      [ "core"; "slice"; "index"; "Range"; "get_unchecked_mut" ]
+      None None false false;
+    mk_fun
+      [ "core"; "slice"; "index"; "usize"; "get" ]
+      (Some [ "core"; "slice"; "index"; "Usize"; "get" ])
+      None true false;
+    mk_fun
+      [ "core"; "slice"; "index"; "usize"; "get_mut" ]
+      (Some [ "core"; "slice"; "index"; "Usize"; "get_mut" ])
+      None true false;
+    mk_fun
+      [ "core"; "slice"; "index"; "usize"; "get_unchecked" ]
+      (Some [ "core"; "slice"; "index"; "Usize"; "get_unchecked" ])
+      None false false;
+    mk_fun
+      [ "core"; "slice"; "index"; "usize"; "get_unchecked_mut" ]
+      (Some [ "core"; "slice"; "index"; "Usize"; "get_unchecked_mut" ])
+      None false false;
+    mk_fun
+      [ "core"; "slice"; "index"; "usize"; "index" ]
+      (Some [ "core"; "slice"; "index"; "Usize"; "index" ])
+      None true false;
+    mk_fun
+      [ "core"; "slice"; "index"; "usize"; "index_mut" ]
+      (Some [ "core"; "slice"; "index"; "Usize"; "index_mut" ])
+      None true false;
+  ]
+
+let mk_builtin_funs_map () =
+  SimpleNameMap.of_list
+    (List.map
+       (fun (name, filter, info) -> (name, (filter, info)))
+       (builtin_funs ()))
+
+let builtin_funs_map = mk_memoized mk_builtin_funs_map
+
+type effect_info = { can_fail : bool; stateful : bool }
+
+let builtin_fun_effects =
+  let int_names =
+    [
+      "usize";
+      "u8";
+      "u16";
+      "u32";
+      "u64";
+      "u128";
+      "isize";
+      "i8";
+      "i16";
+      "i32";
+      "i64";
+      "i128";
+    ]
+  in
+  let int_ops =
+    [ "wrapping_add"; "wrapping_sub"; "rotate_left"; "rotate_right" ]
+  in
+  let int_funs =
+    List.map
+      (fun int_name ->
+        List.map (fun op -> "core::num::" ^ int_name ^ "::" ^ op) int_ops)
+      int_names
+  in
+  let int_funs = List.concat int_funs in
+  let no_fail_no_state_funs =
+    [
+      (* TODO: redundancy with the funs information below *)
+      "alloc::vec::Vec::new";
+      "alloc::vec::Vec::len";
+      "alloc::boxed::Box::deref";
+      "alloc::boxed::Box::deref_mut";
+      "core::mem::replace";
+      "core::mem::take";
+    ]
+    @ int_funs
+  in
+  let no_fail_no_state_funs =
+    List.map
+      (fun n -> (n, { can_fail = false; stateful = false }))
+      no_fail_no_state_funs
+  in
+  let no_state_funs =
+    [
+      (* TODO: redundancy with the funs information below *)
+      "alloc::vec::Vec::push";
+      "alloc::vec::Vec::index";
+      "alloc::vec::Vec::index_mut";
+      "alloc::vec::Vec::index_mut_back";
+    ]
+  in
+  let no_state_funs =
+    List.map (fun n -> (n, { can_fail = true; stateful = false })) no_state_funs
+  in
+  no_fail_no_state_funs @ no_state_funs
+
+let builtin_fun_effects_map =
+  SimpleNameMap.of_list
+    (List.map (fun (n, x) -> (string_to_simple_name n, x)) builtin_fun_effects)
+
+type builtin_trait_decl_info = {
+  rust_name : string;
+  extract_name : string;
+  constructor : string;
+  parent_clauses : string list;
+  consts : (string * string) list;
+  types : (string * (string * string list)) list;
+      (** Every type has:
+          - a Rust name
+          - an extraction name
+          - a list of clauses *)
+  methods : (string * builtin_fun_info list) list;
+}
+[@@deriving show]
+
+let builtin_trait_decls_info () =
+  let rg0 = Some Types.RegionGroupId.zero in
+  let mk_trait (rust_name : string list) ?(extract_name : string option = None)
+      ?(parent_clauses : string list = []) ?(types : string list = [])
+      ?(methods : (string * bool) list = []) () : builtin_trait_decl_info =
+    let extract_name =
+      match extract_name with
+      | Some n -> n
+      | None -> (
+          match !backend with
+          | Coq | FStar | HOL4 -> String.concat "_" rust_name
+          | Lean -> String.concat "." rust_name)
+    in
+    let constructor = mk_struct_constructor extract_name in
+    let consts = [] in
+    let types =
+      let mk_type item_name =
+        let type_name =
+          match !backend with
+          | Coq | FStar | HOL4 -> extract_name ^ "_" ^ item_name
+          | Lean -> item_name
+        in
+        let clauses = [] in
+        (item_name, (type_name, clauses))
+      in
+      List.map mk_type types
+    in
+    let methods =
+      let mk_method (item_name, with_back) =
+        (* TODO: factor out with builtin_funs_info *)
+        let basename =
+          match !backend with
+          | Coq | FStar | HOL4 -> extract_name ^ "_" ^ item_name
+          | Lean -> item_name
+        in
+        let back_no_suffix = false in
+        let fwd_suffix = if with_back && back_no_suffix then "_fwd" else "" in
+        let fwd = [ { rg = None; extract_name = basename ^ fwd_suffix } ] in
+        let back_suffix = if with_back && back_no_suffix then "" else "_back" in
+        let back =
+          if with_back then
+            [ { rg = rg0; extract_name = basename ^ back_suffix } ]
+          else []
+        in
+        (item_name, fwd @ back)
+      in
+      List.map mk_method methods
+    in
+    let rust_name = String.concat "::" rust_name in
+    {
+      rust_name;
+      extract_name;
+      constructor;
+      parent_clauses;
+      consts;
+      types;
+      methods;
+    }
+  in
+  [
+    (* Deref *)
+    mk_trait
+      [ "core"; "ops"; "deref"; "Deref" ]
+      ~types:[ "Target" ]
+      ~methods:[ ("deref", true) ]
+      ();
+    (* DerefMut *)
+    mk_trait
+      [ "core"; "ops"; "deref"; "DerefMut" ]
+      ~parent_clauses:[ backend_choice "deref_inst" "derefInst" ]
+      ~methods:[ ("deref_mut", true) ]
+      ();
+    (* Index *)
+    mk_trait
+      [ "core"; "ops"; "index"; "Index" ]
+      ~types:[ "Output" ]
+      ~methods:[ ("index", true) ]
+      ();
+    (* IndexMut *)
+    mk_trait
+      [ "core"; "ops"; "index"; "IndexMut" ]
+      ~parent_clauses:[ backend_choice "index_inst" "indexInst" ]
+      ~methods:[ ("index_mut", true) ]
+      ();
+    (* Sealed *)
+    mk_trait [ "core"; "slice"; "index"; "private_slice_index"; "Sealed" ] ();
+    (* SliceIndex *)
+    mk_trait
+      [ "core"; "slice"; "index"; "SliceIndex" ]
+      ~parent_clauses:[ backend_choice "sealed_inst" "sealedInst" ]
+      ~types:[ "Output" ]
+      ~methods:
+        [
+          ("get", true);
+          ("get_mut", true);
+          ("get_unchecked", false);
+          ("get_unchecked_mut", false);
+          ("index", true);
+          ("index_mut", true);
+        ]
+      ();
+  ]
+
+let mk_builtin_trait_decls_map () =
+  SimpleNameMap.of_list
+    (List.map
+       (fun info -> (string_to_simple_name info.rust_name, info))
+       (builtin_trait_decls_info ()))
+
+let builtin_trait_decls_map = mk_memoized mk_builtin_trait_decls_map
+
+(* TODO: generalize this.
+
+   For now, the key is:
+   - name of the impl (ex.: "alloc.boxed.Boxed")
+   - name of the implemented trait (ex.: "core.ops.deref.Deref"
+*)
+type simple_name_pair = simple_name * simple_name [@@deriving show, ord]
+
+module SimpleNamePairOrd = struct
+  type t = simple_name_pair
+
+  let compare = compare_simple_name_pair
+  let to_string = show_simple_name_pair
+  let pp_t = pp_simple_name_pair
+  let show_t = show_simple_name_pair
+end
+
+module SimpleNamePairMap = Collections.MakeMap (SimpleNamePairOrd)
+
+let builtin_trait_impls_info () :
+    ((string list * string list) * (bool list option * string)) list =
+  let fmt (type_name : string list)
+      ?(extract_type_name : string list option = None)
+      (trait_name : string list) ?(filter : bool list option = None) () :
+      (string list * string list) * (bool list option * string) =
+    let name =
+      let trait_name = String.concat "" trait_name ^ "Inst" in
+      let sep = backend_choice "_" "." in
+      let type_name =
+        match extract_type_name with
+        | Some type_name -> type_name
+        | None -> type_name
+      in
+      String.concat sep type_name ^ sep ^ trait_name
+    in
+    ((type_name, trait_name), (filter, name))
+  in
+  (* TODO: fix the names like "[T]" below *)
+  [
+    (* core::ops::Deref<alloc::boxed::Box<T>> *)
+    fmt [ "alloc"; "boxed"; "Box" ] [ "core"; "ops"; "deref"; "Deref" ] ();
+    (* core::ops::DerefMut<alloc::boxed::Box<T>> *)
+    fmt [ "alloc"; "boxed"; "Box" ] [ "core"; "ops"; "deref"; "DerefMut" ] ();
+    (* core::ops::index::Index<[T], I> *)
+    fmt
+      [ "core"; "slice"; "index"; "[T]" ]
+      ~extract_type_name:(Some [ "core"; "slice"; "index"; "Slice" ])
+      [ "core"; "ops"; "index"; "Index" ]
+      ();
+    (* core::ops::index::IndexMut<[T], I> *)
+    fmt
+      [ "core"; "slice"; "index"; "[T]" ]
+      ~extract_type_name:(Some [ "core"; "slice"; "index"; "Slice" ])
+      [ "core"; "ops"; "index"; "IndexMut" ]
+      ();
+    (* core::slice::index::private_slice_index::Sealed<Range<usize>> *)
+    fmt
+      [ "core"; "slice"; "index"; "private_slice_index"; "Range" ]
+      [ "core"; "slice"; "index"; "private_slice_index"; "Sealed" ]
+      ();
+    (* core::slice::index::SliceIndex<Range<usize>, [T]> *)
+    fmt
+      [ "core"; "slice"; "index"; "Range" ]
+      [ "core"; "slice"; "index"; "SliceIndex" ]
+      ();
+    (* core::ops::index::Index<[T; N], I> *)
+    fmt
+      [ "core"; "array"; "[T; N]" ]
+      ~extract_type_name:(Some [ "core"; "array"; "Array" ])
+      [ "core"; "ops"; "index"; "Index" ]
+      ();
+    (* core::ops::index::IndexMut<[T; N], I> *)
+    fmt
+      [ "core"; "array"; "[T; N]" ]
+      ~extract_type_name:(Some [ "core"; "array"; "Array" ])
+      [ "core"; "ops"; "index"; "IndexMut" ]
+      ();
+    (* core::slice::index::private_slice_index::Sealed<usize> *)
+    fmt
+      [ "core"; "slice"; "index"; "private_slice_index"; "usize" ]
+      [ "core"; "slice"; "index"; "private_slice_index"; "Sealed" ]
+      ();
+    (* core::slice::index::SliceIndex<usize, [T]> *)
+    fmt
+      [ "core"; "slice"; "index"; "usize" ]
+      [ "core"; "slice"; "index"; "SliceIndex" ]
+      ();
+    (* core::ops::index::Index<Vec<T>, T> *)
+    fmt [ "alloc"; "vec"; "Vec" ]
+      [ "core"; "ops"; "index"; "Index" ]
+      ~filter:(Some [ true; true; false ])
+      ();
+    (* core::ops::index::IndexMut<Vec<T>, T> *)
+    fmt [ "alloc"; "vec"; "Vec" ]
+      [ "core"; "ops"; "index"; "IndexMut" ]
+      ~filter:(Some [ true; true; false ])
+      ();
+  ]
+
+let mk_builtin_trait_impls_map () =
+  SimpleNamePairMap.of_list (builtin_trait_impls_info ())
+
+let builtin_trait_impls_map = mk_memoized mk_builtin_trait_impls_map
diff --git a/compiler/ExtractTypes.ml b/compiler/ExtractTypes.ml
new file mode 100644
index 00000000..77f76bb4
--- /dev/null
+++ b/compiler/ExtractTypes.ml
@@ -0,0 +1,2477 @@
+(** The generic extraction *)
+(* Turn the whole module into a functor: it is very annoying to carry the
+   the formatter everywhere...
+*)
+
+open Pure
+open PureUtils
+open TranslateCore
+open ExtractBase
+open StringUtils
+open Config
+module F = Format
+
+(** Small helper to compute the name of an int type *)
+let int_name (int_ty : integer_type) =
+  let isize, usize, i_format, u_format =
+    match !backend with
+    | FStar | Coq | HOL4 ->
+        ("isize", "usize", format_of_string "i%d", format_of_string "u%d")
+    | Lean -> ("Isize", "Usize", format_of_string "I%d", format_of_string "U%d")
+  in
+  match int_ty with
+  | Isize -> isize
+  | I8 -> Printf.sprintf i_format 8
+  | I16 -> Printf.sprintf i_format 16
+  | I32 -> Printf.sprintf i_format 32
+  | I64 -> Printf.sprintf i_format 64
+  | I128 -> Printf.sprintf i_format 128
+  | Usize -> usize
+  | U8 -> Printf.sprintf u_format 8
+  | U16 -> Printf.sprintf u_format 16
+  | U32 -> Printf.sprintf u_format 32
+  | U64 -> Printf.sprintf u_format 64
+  | U128 -> Printf.sprintf u_format 128
+
+(** Small helper to compute the name of a unary operation *)
+let unop_name (unop : unop) : string =
+  match unop with
+  | Not -> (
+      match !backend with FStar | Lean -> "not" | Coq -> "negb" | HOL4 -> "~")
+  | Neg (int_ty : integer_type) -> (
+      match !backend with Lean -> "-" | _ -> int_name int_ty ^ "_neg")
+  | Cast _ ->
+      (* We never directly use the unop name in this case *)
+      raise (Failure "Unsupported")
+
+(** Small helper to compute the name of a binary operation (note that many
+    binary operations like "less than" are extracted to primitive operations,
+    like [<]).
+ *)
+let named_binop_name (binop : E.binop) (int_ty : integer_type) : string =
+  let binop =
+    match binop with
+    | Div -> "div"
+    | Rem -> "rem"
+    | Add -> "add"
+    | Sub -> "sub"
+    | Mul -> "mul"
+    | Lt -> "lt"
+    | Le -> "le"
+    | Ge -> "ge"
+    | Gt -> "gt"
+    | BitXor -> "xor"
+    | BitAnd -> "and"
+    | BitOr -> "or"
+    | Shl -> "lsl"
+    | Shr ->
+        "asr"
+        (* NOTE: make sure arithmetic shift right is implemented, i.e. OCaml's asr operator, not lsr *)
+    | _ -> raise (Failure "Unreachable")
+  in
+  (* Remark: the Lean case is actually not used *)
+  match !backend with
+  | Lean -> int_name int_ty ^ "." ^ binop
+  | FStar | Coq | HOL4 -> int_name int_ty ^ "_" ^ binop
+
+(** A list of keywords/identifiers used by the backend and with which we
+    want to check collision.
+
+    Remark: this is useful mostly to look for collisions when generating
+    names for *variables*.
+ *)
+let keywords () =
+  let named_unops =
+    unop_name Not
+    :: List.map (fun it -> unop_name (Neg it)) T.all_signed_int_types
+  in
+  let named_binops = [ E.Div; Rem; Add; Sub; Mul ] in
+  let named_binops =
+    List.concat_map
+      (fun bn -> List.map (fun it -> named_binop_name bn it) T.all_int_types)
+      named_binops
+  in
+  let misc =
+    match !backend with
+    | FStar ->
+        [
+          "assert";
+          "assert_norm";
+          "assume";
+          "else";
+          "fun";
+          "fn";
+          "FStar";
+          "FStar.Mul";
+          "if";
+          "in";
+          "include";
+          "int";
+          "let";
+          "list";
+          "match";
+          "open";
+          "rec";
+          "scalar_cast";
+          "then";
+          "type";
+          "Type0";
+          "Type";
+          "unit";
+          "val";
+          "with";
+        ]
+    | Coq ->
+        [
+          "assert";
+          "Arguments";
+          "Axiom";
+          "char_of_byte";
+          "Check";
+          "Declare";
+          "Definition";
+          "else";
+          "End";
+          "fun";
+          "Fixpoint";
+          "if";
+          "in";
+          "int";
+          "Inductive";
+          "Import";
+          "let";
+          "Lemma";
+          "match";
+          "Module";
+          "not";
+          "Notation";
+          "Proof";
+          "Qed";
+          "rec";
+          "Record";
+          "Require";
+          "Scope";
+          "Search";
+          "SearchPattern";
+          "Set";
+          "then";
+          (* [tt] is unit *)
+          "tt";
+          "type";
+          "Type";
+          "unit";
+          "with";
+        ]
+    | Lean ->
+        [
+          "by";
+          "class";
+          "decreasing_by";
+          "def";
+          "deriving";
+          "do";
+          "else";
+          "end";
+          "for";
+          "have";
+          "if";
+          "inductive";
+          "instance";
+          "import";
+          "let";
+          "macro";
+          "match";
+          "namespace";
+          "opaque";
+          "open";
+          "run_cmd";
+          "set_option";
+          "simp";
+          "structure";
+          "syntax";
+          "termination_by";
+          "then";
+          "Type";
+          "unsafe";
+          "where";
+          "with";
+          "opaque_defs";
+        ]
+    | HOL4 ->
+        [
+          "Axiom";
+          "case";
+          "Definition";
+          "else";
+          "End";
+          "fix";
+          "fix_exec";
+          "fn";
+          "fun";
+          "if";
+          "in";
+          "int";
+          "Inductive";
+          "let";
+          "of";
+          "Proof";
+          "QED";
+          "then";
+          "Theorem";
+        ]
+  in
+  List.concat [ named_unops; named_binops; misc ]
+
+let assumed_adts () : (assumed_ty * string) list =
+  match !backend with
+  | Lean ->
+      [
+        (State, "State");
+        (Result, "Result");
+        (Error, "Error");
+        (Fuel, "Nat");
+        (Array, "Array");
+        (Slice, "Slice");
+        (Str, "Str");
+        (RawPtr Mut, "MutRawPtr");
+        (RawPtr Const, "ConstRawPtr");
+      ]
+  | Coq | FStar | HOL4 ->
+      [
+        (State, "state");
+        (Result, "result");
+        (Error, "error");
+        (Fuel, if !backend = HOL4 then "num" else "nat");
+        (Array, "array");
+        (Slice, "slice");
+        (Str, "str");
+        (RawPtr Mut, "mut_raw_ptr");
+        (RawPtr Const, "const_raw_ptr");
+      ]
+
+let assumed_struct_constructors () : (assumed_ty * string) list =
+  match !backend with
+  | Lean -> [ (Array, "Array.make") ]
+  | Coq -> [ (Array, "mk_array") ]
+  | FStar -> [ (Array, "mk_array") ]
+  | HOL4 -> [ (Array, "mk_array") ]
+
+let assumed_variants () : (assumed_ty * VariantId.id * string) list =
+  match !backend with
+  | FStar ->
+      [
+        (Result, result_return_id, "Return");
+        (Result, result_fail_id, "Fail");
+        (Error, error_failure_id, "Failure");
+        (Error, error_out_of_fuel_id, "OutOfFuel");
+        (* No Fuel::Zero on purpose *)
+        (* No Fuel::Succ on purpose *)
+      ]
+  | Coq ->
+      [
+        (Result, result_return_id, "Return");
+        (Result, result_fail_id, "Fail_");
+        (Error, error_failure_id, "Failure");
+        (Error, error_out_of_fuel_id, "OutOfFuel");
+        (Fuel, fuel_zero_id, "O");
+        (Fuel, fuel_succ_id, "S");
+      ]
+  | Lean ->
+      [
+        (Result, result_return_id, "ret");
+        (Result, result_fail_id, "fail");
+        (Error, error_failure_id, "panic");
+        (* No Fuel::Zero on purpose *)
+        (* No Fuel::Succ on purpose *)
+      ]
+  | HOL4 ->
+      [
+        (Result, result_return_id, "Return");
+        (Result, result_fail_id, "Fail");
+        (Error, error_failure_id, "Failure");
+        (* No Fuel::Zero on purpose *)
+        (* No Fuel::Succ on purpose *)
+      ]
+
+let assumed_llbc_functions () :
+    (A.assumed_fun_id * T.RegionGroupId.id option * string) list =
+  let rg0 = Some T.RegionGroupId.zero in
+  match !backend with
+  | FStar | Coq | HOL4 ->
+      [
+        (ArrayIndexShared, None, "array_index_usize");
+        (ArrayIndexMut, None, "array_index_usize");
+        (ArrayIndexMut, rg0, "array_update_usize");
+        (ArrayToSliceShared, None, "array_to_slice");
+        (ArrayToSliceMut, None, "array_to_slice");
+        (ArrayToSliceMut, rg0, "array_from_slice");
+        (ArrayRepeat, None, "array_repeat");
+        (SliceIndexShared, None, "slice_index_usize");
+        (SliceIndexMut, None, "slice_index_usize");
+        (SliceIndexMut, rg0, "slice_update_usize");
+        (SliceLen, None, "slice_len");
+      ]
+  | Lean ->
+      [
+        (ArrayIndexShared, None, "Array.index_usize");
+        (ArrayIndexMut, None, "Array.index_usize");
+        (ArrayIndexMut, rg0, "Array.update_usize");
+        (ArrayToSliceShared, None, "Array.to_slice");
+        (ArrayToSliceMut, None, "Array.to_slice");
+        (ArrayToSliceMut, rg0, "Array.from_slice");
+        (ArrayRepeat, None, "Array.repeat");
+        (SliceIndexShared, None, "Slice.index_usize");
+        (SliceIndexMut, None, "Slice.index_usize");
+        (SliceIndexMut, rg0, "Slice.update_usize");
+        (SliceLen, None, "Slice.len");
+      ]
+
+let assumed_pure_functions () : (pure_assumed_fun_id * string) list =
+  match !backend with
+  | FStar ->
+      [
+        (Return, "return");
+        (Fail, "fail");
+        (Assert, "massert");
+        (FuelDecrease, "decrease");
+        (FuelEqZero, "is_zero");
+      ]
+  | Coq ->
+      (* We don't provide [FuelDecrease] and [FuelEqZero] on purpose *)
+      [ (Return, "return_"); (Fail, "fail_"); (Assert, "massert") ]
+  | Lean ->
+      (* We don't provide [FuelDecrease] and [FuelEqZero] on purpose *)
+      [ (Return, "return"); (Fail, "fail_"); (Assert, "massert") ]
+  | HOL4 ->
+      (* We don't provide [FuelDecrease] and [FuelEqZero] on purpose *)
+      [ (Return, "return"); (Fail, "fail"); (Assert, "massert") ]
+
+let names_map_init () : names_map_init =
+  {
+    keywords = keywords ();
+    assumed_adts = assumed_adts ();
+    assumed_structs = assumed_struct_constructors ();
+    assumed_variants = assumed_variants ();
+    assumed_llbc_functions = assumed_llbc_functions ();
+    assumed_pure_functions = assumed_pure_functions ();
+  }
+
+let extract_unop (extract_expr : bool -> texpression -> unit)
+    (fmt : F.formatter) (inside : bool) (unop : unop) (arg : texpression) : unit
+    =
+  match unop with
+  | Not | Neg _ ->
+      let unop = unop_name unop in
+      if inside then F.pp_print_string fmt "(";
+      F.pp_print_string fmt unop;
+      F.pp_print_space fmt ();
+      extract_expr true arg;
+      if inside then F.pp_print_string fmt ")"
+  | Cast (src, tgt) -> (
+      (* HOL4 has a special treatment: because it doesn't support dependent
+         types, we don't have a specific operator for the cast *)
+      match !backend with
+      | HOL4 ->
+          (* Casting, say, an u32 to an i32 would be done as follows:
+             {[
+               mk_i32 (u32_to_int x)
+             ]}
+          *)
+          if inside then F.pp_print_string fmt "(";
+          F.pp_print_string fmt ("mk_" ^ int_name tgt);
+          F.pp_print_space fmt ();
+          F.pp_print_string fmt "(";
+          F.pp_print_string fmt (int_name src ^ "_to_int");
+          F.pp_print_space fmt ();
+          extract_expr true arg;
+          F.pp_print_string fmt ")";
+          if inside then F.pp_print_string fmt ")"
+      | FStar | Coq | Lean ->
+          (* Rem.: the source type is an implicit parameter *)
+          if inside then F.pp_print_string fmt "(";
+          let cast_str =
+            match !backend with
+            | Coq | FStar -> "scalar_cast"
+            | Lean -> (* TODO: I8.cast, I16.cast, etc.*) "Scalar.cast"
+            | HOL4 -> raise (Failure "Unreachable")
+          in
+          F.pp_print_string fmt cast_str;
+          F.pp_print_space fmt ();
+          if !backend <> Lean then (
+            F.pp_print_string fmt
+              (StringUtils.capitalize_first_letter
+                 (PrintPure.integer_type_to_string src));
+            F.pp_print_space fmt ());
+          if !backend = Lean then F.pp_print_string fmt ("." ^ int_name tgt)
+          else
+            F.pp_print_string fmt
+              (StringUtils.capitalize_first_letter
+                 (PrintPure.integer_type_to_string tgt));
+          F.pp_print_space fmt ();
+          extract_expr true arg;
+          if inside then F.pp_print_string fmt ")")
+
+(** [extract_expr] : the boolean argument is [inside] *)
+let extract_binop (extract_expr : bool -> texpression -> unit)
+    (fmt : F.formatter) (inside : bool) (binop : E.binop)
+    (int_ty : integer_type) (arg0 : texpression) (arg1 : texpression) : unit =
+  if inside then F.pp_print_string fmt "(";
+  (* Some binary operations have a special notation depending on the backend *)
+  (match (!backend, binop) with
+  | HOL4, (Eq | Ne)
+  | (FStar | Coq | Lean), (Eq | Lt | Le | Ne | Ge | Gt)
+  | Lean, (Div | Rem | Add | Sub | Mul) ->
+      let binop =
+        match binop with
+        | Eq -> "="
+        | Lt -> "<"
+        | Le -> "<="
+        | Ne -> if !backend = Lean then "!=" else "<>"
+        | Ge -> ">="
+        | Gt -> ">"
+        | Div -> "/"
+        | Rem -> "%"
+        | Add -> "+"
+        | Sub -> "-"
+        | Mul -> "*"
+        | _ -> raise (Failure "Unreachable")
+      in
+      let binop =
+        match !backend with FStar | Lean | HOL4 -> binop | Coq -> "s" ^ binop
+      in
+      extract_expr false arg0;
+      F.pp_print_space fmt ();
+      F.pp_print_string fmt binop;
+      F.pp_print_space fmt ();
+      extract_expr false arg1
+  | _ ->
+      let binop = named_binop_name binop int_ty in
+      F.pp_print_string fmt binop;
+      F.pp_print_space fmt ();
+      extract_expr true arg0;
+      F.pp_print_space fmt ();
+      extract_expr true arg1);
+  if inside then F.pp_print_string fmt ")"
+
+let type_decl_kind_to_qualif (kind : decl_kind)
+    (type_kind : type_decl_kind option) : string option =
+  match !backend with
+  | FStar -> (
+      match kind with
+      | SingleNonRec -> Some "type"
+      | SingleRec -> Some "type"
+      | MutRecFirst -> Some "type"
+      | MutRecInner -> Some "and"
+      | MutRecLast -> Some "and"
+      | Assumed -> Some "assume type"
+      | Declared -> Some "val")
+  | Coq -> (
+      match (kind, type_kind) with
+      | SingleNonRec, Some Enum -> Some "Inductive"
+      | SingleNonRec, Some Struct -> Some "Record"
+      | (SingleRec | MutRecFirst), Some _ -> Some "Inductive"
+      | (MutRecInner | MutRecLast), Some _ ->
+          (* Coq doesn't support groups of mutually recursive definitions which mix
+           * records and inducties: we convert everything to records if this happens
+           *)
+          Some "with"
+      | (Assumed | Declared), None -> Some "Axiom"
+      | SingleNonRec, None ->
+          (* This is for traits *)
+          Some "Record"
+      | _ ->
+          raise
+            (Failure
+               ("Unexpected: (" ^ show_decl_kind kind ^ ", "
+               ^ Print.option_to_string show_type_decl_kind type_kind
+               ^ ")")))
+  | Lean -> (
+      match kind with
+      | SingleNonRec ->
+          if type_kind = Some Struct then Some "structure" else Some "inductive"
+      | SingleRec -> Some "inductive"
+      | MutRecFirst -> Some "inductive"
+      | MutRecInner -> Some "inductive"
+      | MutRecLast -> Some "inductive"
+      | Assumed -> Some "axiom"
+      | Declared -> Some "axiom")
+  | HOL4 -> None
+
+let fun_decl_kind_to_qualif (kind : decl_kind) : string option =
+  match !backend with
+  | FStar -> (
+      match kind with
+      | SingleNonRec -> Some "let"
+      | SingleRec -> Some "let rec"
+      | MutRecFirst -> Some "let rec"
+      | MutRecInner -> Some "and"
+      | MutRecLast -> Some "and"
+      | Assumed -> Some "assume val"
+      | Declared -> Some "val")
+  | Coq -> (
+      match kind with
+      | SingleNonRec -> Some "Definition"
+      | SingleRec -> Some "Fixpoint"
+      | MutRecFirst -> Some "Fixpoint"
+      | MutRecInner -> Some "with"
+      | MutRecLast -> Some "with"
+      | Assumed -> Some "Axiom"
+      | Declared -> Some "Axiom")
+  | Lean -> (
+      match kind with
+      | SingleNonRec -> Some "def"
+      | SingleRec -> Some "divergent def"
+      | MutRecFirst -> Some "mutual divergent def"
+      | MutRecInner -> Some "divergent def"
+      | MutRecLast -> Some "divergent def"
+      | Assumed -> Some "axiom"
+      | Declared -> Some "axiom")
+  | HOL4 -> None
+
+(** The type of types.
+
+    TODO: move inside the formatter?
+ *)
+let type_keyword () =
+  match !backend with
+  | FStar -> "Type0"
+  | Coq | Lean -> "Type"
+  | HOL4 -> raise (Failure "Unexpected")
+
+(**
+   [ctx]: we use the context to lookup type definitions, to retrieve type names.
+   This is used to compute variable names, when they have no basenames: in this
+   case we use the first letter of the type name.
+
+   [variant_concatenate_type_name]: if true, add the type name as a prefix
+   to the variant names.
+   Ex.:
+   In Rust:
+     {[
+       enum List = {
+         Cons(u32, Box<List>),x
+         Nil,
+       }
+     ]}
+
+   F*, if option activated:
+     {[
+       type list =
+       | ListCons : u32 -> list -> list
+       | ListNil : list
+     ]}
+
+   F*, if option not activated:
+     {[
+       type list =
+       | Cons : u32 -> list -> list
+       | Nil : list
+     ]}
+
+   Rk.: this should be true by default, because in Rust all the variant names
+   are actively uniquely identifier by the type name [List::Cons(...)], while
+   in other languages it is not necessarily the case, and thus clashes can mess
+   up type checking. Note that some languages actually forbids the name clashes
+   (it is the case of F* ).
+ *)
+let mk_formatter (ctx : trans_ctx) (crate_name : string)
+    (variant_concatenate_type_name : bool) : formatter =
+  let int_name = int_name in
+
+  (* Prepare a name.
+   * The first id elem is always the crate: if it is the local crate,
+   * we remove it.
+   * We also remove all the disambiguators, then convert everything to strings.
+   * **Rmk:** because we remove the disambiguators, there may be name collisions
+   * (which is ok, because we check for name collisions and fail if there is any).
+   *)
+  let get_name (name : name) : string list =
+    (* Rmk.: initially we only filtered the disambiguators equal to 0 *)
+    let name = Names.filter_disambiguators name in
+    match name with
+    | Ident crate :: name ->
+        let name = if crate = crate_name then name else Ident crate :: name in
+        let name =
+          List.map
+            (function
+              | Names.Ident s -> s
+              | Disambiguator d -> Names.Disambiguator.to_string d)
+            name
+        in
+        name
+    | _ ->
+        raise (Failure ("Unexpected name shape: " ^ Print.name_to_string name))
+  in
+  let flatten_name (name : string list) : string =
+    match !backend with
+    | FStar | Coq | HOL4 -> String.concat "_" name
+    | Lean -> String.concat "." name
+  in
+  let get_type_name = get_name in
+  let get_type_name_no_suffix name =
+    match !backend with
+    | FStar | Coq | HOL4 -> String.concat "_" (get_type_name name)
+    | Lean -> String.concat "." (get_type_name name)
+  in
+  let type_name name =
+    match !backend with
+    | FStar ->
+        StringUtils.lowercase_first_letter (get_type_name_no_suffix name ^ "_t")
+    | Coq | HOL4 -> get_type_name_no_suffix name ^ "_t"
+    | Lean -> get_type_name_no_suffix name
+  in
+  let field_name (def_name : name) (field_id : FieldId.id)
+      (field_name : string option) : string =
+    let field_name_s =
+      match field_name with
+      | Some field_name -> field_name
+      | None ->
+          (* TODO: extract structs with no field names to tuples *)
+          FieldId.to_string field_id
+    in
+    if !Config.record_fields_short_names then
+      if field_name = None then (* TODO: this is a bit ugly *)
+        "_" ^ field_name_s
+      else field_name_s
+    else
+      let def_name = get_type_name_no_suffix def_name ^ "_" ^ field_name_s in
+      match !backend with
+      | Lean | HOL4 -> def_name
+      | Coq | FStar -> StringUtils.lowercase_first_letter def_name
+  in
+  let variant_name (def_name : name) (variant : string) : string =
+    match !backend with
+    | FStar | Coq | HOL4 ->
+        let variant = to_camel_case variant in
+        if variant_concatenate_type_name then
+          StringUtils.capitalize_first_letter
+            (get_type_name_no_suffix def_name ^ "_" ^ variant)
+        else variant
+    | Lean -> variant
+  in
+  let struct_constructor (basename : name) : string =
+    let tname = type_name basename in
+    ExtractBuiltin.mk_struct_constructor tname
+  in
+  let get_fun_name fname =
+    let fname = get_name fname in
+    (* TODO: don't convert to snake case for Coq, HOL4, F* *)
+    let fname = flatten_name fname in
+    match !backend with
+    | FStar | Coq | HOL4 -> StringUtils.lowercase_first_letter fname
+    | Lean -> fname
+  in
+  let global_name (name : global_name) : string =
+    (* Converting to snake case also lowercases the letters (in Rust, global
+     * names are written in capital letters). *)
+    let parts = List.map to_snake_case (get_name name) in
+    String.concat "_" parts
+  in
+  let fun_name (fname : fun_name) (num_loops : int) (loop_id : LoopId.id option)
+      (num_rgs : int) (rg : region_group_info option) (filter_info : bool * int)
+      : string =
+    let fname = get_fun_name fname in
+    (* Compute the suffix *)
+    let suffix = default_fun_suffix num_loops loop_id num_rgs rg filter_info in
+    (* Concatenate *)
+    fname ^ suffix
+  in
+
+  let trait_decl_name (trait_decl : trait_decl) : string =
+    type_name trait_decl.name
+  in
+
+  let trait_impl_name (trait_decl : trait_decl) (trait_impl : trait_impl) :
+      string =
+    (* TODO: provisional: we concatenate the trait impl name (which is its type)
+       with the trait decl name *)
+    let trait_decl =
+      let name = trait_decl.name in
+      let name = get_type_name_no_suffix name ^ "Inst" in
+      (* Remove the occurrences of '.' *)
+      String.concat "" (String.split_on_char '.' name)
+    in
+    let name = flatten_name (get_type_name trait_impl.name @ [ trait_decl ]) in
+    match !backend with
+    | FStar -> StringUtils.lowercase_first_letter name
+    | Coq | HOL4 | Lean -> name
+  in
+
+  let trait_decl_constructor (trait_decl : trait_decl) : string =
+    let name = trait_decl_name trait_decl in
+    ExtractBuiltin.mk_struct_constructor name
+  in
+
+  let trait_parent_clause_name (trait_decl : trait_decl) (clause : trait_clause)
+      : string =
+    (* TODO: improve - it would be better to not use indices *)
+    let clause = "parent_clause_" ^ TraitClauseId.to_string clause.clause_id in
+    if !Config.record_fields_short_names then clause
+    else trait_decl_name trait_decl ^ "_" ^ clause
+  in
+  let trait_type_name (trait_decl : trait_decl) (item : string) : string =
+    let name =
+      if !Config.record_fields_short_names then item
+      else trait_decl_name trait_decl ^ "_" ^ item
+    in
+    (* Constants are usually all capital letters.
+       Some backends do not support field names starting with a capital letter,
+       and it may be weird to lowercase everything (especially as it may lead
+       to more name collisions): we add a prefix when necessary.
+       For instance, it gives: "U" -> "tU"
+       Note that for some backends we prepend the type name (because those backends
+       can't disambiguate fields coming from different ADTs if they have the same
+       names), and thus don't need to add a prefix starting with a lowercase.
+    *)
+    match !backend with FStar -> "t" ^ name | Coq | Lean | HOL4 -> name
+  in
+  let trait_const_name (trait_decl : trait_decl) (item : string) : string =
+    let name =
+      if !Config.record_fields_short_names then item
+      else trait_decl_name trait_decl ^ "_" ^ item
+    in
+    (* See [trait_type_name] *)
+    match !backend with FStar -> "c" ^ name | Coq | Lean | HOL4 -> name
+  in
+  let trait_method_name (trait_decl : trait_decl) (item : string) : string =
+    if !Config.record_fields_short_names then item
+    else trait_decl_name trait_decl ^ "_" ^ item
+  in
+  let trait_type_clause_name (trait_decl : trait_decl) (item : string)
+      (clause : trait_clause) : string =
+    (* TODO: improve - it would be better to not use indices *)
+    trait_type_name trait_decl item
+    ^ "_clause_"
+    ^ TraitClauseId.to_string clause.clause_id
+  in
+
+  let termination_measure_name (_fid : A.FunDeclId.id) (fname : fun_name)
+      (num_loops : int) (loop_id : LoopId.id option) : string =
+    let fname = get_fun_name fname in
+    let lp_suffix = default_fun_loop_suffix num_loops loop_id in
+    (* Compute the suffix *)
+    let suffix =
+      match !Config.backend with
+      | FStar -> "_decreases"
+      | Lean -> "_terminates"
+      | Coq | HOL4 -> raise (Failure "Unexpected")
+    in
+    (* Concatenate *)
+    fname ^ lp_suffix ^ suffix
+  in
+
+  let decreases_proof_name (_fid : A.FunDeclId.id) (fname : fun_name)
+      (num_loops : int) (loop_id : LoopId.id option) : string =
+    let fname = get_fun_name fname in
+    let lp_suffix = default_fun_loop_suffix num_loops loop_id in
+    (* Compute the suffix *)
+    let suffix =
+      match !Config.backend with
+      | Lean -> "_decreases"
+      | FStar | Coq | HOL4 -> raise (Failure "Unexpected")
+    in
+    (* Concatenate *)
+    fname ^ lp_suffix ^ suffix
+  in
+
+  let var_basename (_varset : StringSet.t) (basename : string option) (ty : ty)
+      : string =
+    (* Small helper to derive var names from ADT type names.
+
+       We do the following:
+       - convert the type name to snake case
+       - take the first letter of every "letter group"
+       Ex.: "HashMap" -> "hash_map" -> "hm"
+    *)
+    let name_from_type_ident (name : string) : string =
+      let cl = to_snake_case name in
+      let cl = String.split_on_char '_' cl in
+      let cl = List.filter (fun s -> String.length s > 0) cl in
+      assert (List.length cl > 0);
+      let cl = List.map (fun s -> s.[0]) cl in
+      StringUtils.string_of_chars cl
+    in
+    (* If there is a basename, we use it *)
+    match basename with
+    | Some basename ->
+        (* This should be a no-op *)
+        to_snake_case basename
+    | None -> (
+        (* No basename: we use the first letter of the type *)
+        match ty with
+        | Adt (type_id, generics) -> (
+            match type_id with
+            | Tuple ->
+                (* The "pair" case is frequent enough to have its special treatment *)
+                if List.length generics.types = 2 then "p" else "t"
+            | Assumed Result -> "r"
+            | Assumed Error -> ConstStrings.error_basename
+            | Assumed Fuel -> ConstStrings.fuel_basename
+            | Assumed Array -> "a"
+            | Assumed Slice -> "s"
+            | Assumed Str -> "s"
+            | Assumed State -> ConstStrings.state_basename
+            | Assumed (RawPtr _) -> "p"
+            | AdtId adt_id ->
+                let def = TypeDeclId.Map.find adt_id ctx.type_ctx.type_decls in
+                (* Derive the var name from the last ident of the type name
+                 * Ex.: ["hashmap"; "HashMap"] ~~> "HashMap" -> "hash_map" -> "hm"
+                 *)
+                (* The name shouldn't be empty, and its last element should
+                 * be an ident *)
+                let cl = List.nth def.name (List.length def.name - 1) in
+                name_from_type_ident (Names.as_ident cl))
+        | TypeVar _ -> (
+            (* TODO: use "t" also for F* *)
+            match !backend with
+            | FStar -> "x" (* lacking inspiration here... *)
+            | Coq | Lean | HOL4 -> "t" (* lacking inspiration here... *))
+        | Literal lty -> (
+            match lty with Bool -> "b" | Char -> "c" | Integer _ -> "i")
+        | Arrow _ -> "f"
+        | TraitType (_, _, name) -> name_from_type_ident name)
+  in
+  let type_var_basename (_varset : StringSet.t) (basename : string) : string =
+    (* Rust type variables are snake-case and start with a capital letter *)
+    match !backend with
+    | FStar ->
+        (* This is *not* a no-op: this removes the capital letter *)
+        to_snake_case basename
+    | HOL4 ->
+        (* In HOL4, type variable names must start with "'" *)
+        "'" ^ to_snake_case basename
+    | Coq | Lean -> basename
+  in
+  let const_generic_var_basename (_varset : StringSet.t) (basename : string) :
+      string =
+    (* Rust type variables are snake-case and start with a capital letter *)
+    match !backend with
+    | FStar | HOL4 ->
+        (* This is *not* a no-op: this removes the capital letter *)
+        to_snake_case basename
+    | Coq | Lean -> basename
+  in
+  let trait_clause_basename (_varset : StringSet.t) (_clause : trait_clause) :
+      string =
+    (* TODO: actually use the clause to derive the name *)
+    "inst"
+  in
+  let trait_self_clause_basename = "self_clause" in
+  let append_index (basename : string) (i : int) : string =
+    basename ^ string_of_int i
+  in
+
+  let extract_literal (fmt : F.formatter) (inside : bool) (cv : literal) : unit
+      =
+    match cv with
+    | Scalar sv -> (
+        match !backend with
+        | FStar -> F.pp_print_string fmt (Z.to_string sv.PV.value)
+        | Coq | HOL4 | Lean ->
+            let print_brackets = inside && !backend = HOL4 in
+            if print_brackets then F.pp_print_string fmt "(";
+            (match !backend with
+            | Coq | Lean -> ()
+            | HOL4 ->
+                F.pp_print_string fmt ("int_to_" ^ int_name sv.PV.int_ty);
+                F.pp_print_space fmt ()
+            | _ -> raise (Failure "Unreachable"));
+            (* We need to add parentheses if the value is negative *)
+            if sv.PV.value >= Z.of_int 0 then
+              F.pp_print_string fmt (Z.to_string sv.PV.value)
+            else if !backend = Lean then
+              (* TODO: parsing issues with Lean because there are ambiguous
+                 interpretations between int values and nat values *)
+              F.pp_print_string fmt
+                ("(-(" ^ Z.to_string (Z.neg sv.PV.value) ^ ":Int))")
+            else F.pp_print_string fmt ("(" ^ Z.to_string sv.PV.value ^ ")");
+            (match !backend with
+            | Coq ->
+                let iname = int_name sv.PV.int_ty in
+                F.pp_print_string fmt ("%" ^ iname)
+            | Lean ->
+                let iname = String.lowercase_ascii (int_name sv.PV.int_ty) in
+                F.pp_print_string fmt ("#" ^ iname)
+            | HOL4 -> ()
+            | _ -> raise (Failure "Unreachable"));
+            if print_brackets then F.pp_print_string fmt ")")
+    | Bool b ->
+        let b =
+          match !backend with
+          | HOL4 -> if b then "T" else "F"
+          | Coq | FStar | Lean -> if b then "true" else "false"
+        in
+        F.pp_print_string fmt b
+    | Char c -> (
+        match !backend with
+        | HOL4 ->
+            (* [#"a"] is a notation for [CHR 97] (97 is the ASCII code for 'a') *)
+            F.pp_print_string fmt ("#\"" ^ String.make 1 c ^ "\"")
+        | FStar | Lean -> F.pp_print_string fmt ("'" ^ String.make 1 c ^ "'")
+        | Coq ->
+            if inside then F.pp_print_string fmt "(";
+            F.pp_print_string fmt "char_of_byte";
+            F.pp_print_space fmt ();
+            (* Convert the the char to ascii *)
+            let c =
+              let i = Char.code c in
+              let x0 = i / 16 in
+              let x1 = i mod 16 in
+              "Coq.Init.Byte.x" ^ string_of_int x0 ^ string_of_int x1
+            in
+            F.pp_print_string fmt c;
+            if inside then F.pp_print_string fmt ")")
+  in
+  let bool_name = if !backend = Lean then "Bool" else "bool" in
+  let char_name = if !backend = Lean then "Char" else "char" in
+  let str_name = if !backend = Lean then "String" else "string" in
+  {
+    bool_name;
+    char_name;
+    int_name;
+    str_name;
+    type_decl_kind_to_qualif;
+    fun_decl_kind_to_qualif;
+    field_name;
+    variant_name;
+    struct_constructor;
+    type_name;
+    global_name;
+    fun_name;
+    termination_measure_name;
+    decreases_proof_name;
+    trait_decl_name;
+    trait_impl_name;
+    trait_decl_constructor;
+    trait_parent_clause_name;
+    trait_const_name;
+    trait_type_name;
+    trait_method_name;
+    trait_type_clause_name;
+    var_basename;
+    type_var_basename;
+    const_generic_var_basename;
+    trait_self_clause_basename;
+    trait_clause_basename;
+    append_index;
+    extract_literal;
+    extract_unop;
+    extract_binop;
+  }
+
+let mk_formatter_and_names_maps (ctx : trans_ctx) (crate_name : string)
+    (variant_concatenate_type_name : bool) : formatter * names_maps =
+  let fmt = mk_formatter ctx crate_name variant_concatenate_type_name in
+  let names_maps = initialize_names_maps fmt (names_map_init ()) in
+  (fmt, names_maps)
+
+let is_single_opaque_fun_decl_group (dg : Pure.fun_decl list) : bool =
+  match dg with [ d ] -> d.body = None | _ -> false
+
+let is_single_opaque_type_decl_group (dg : Pure.type_decl list) : bool =
+  match dg with [ d ] -> d.kind = Opaque | _ -> false
+
+let is_empty_record_type_decl (d : Pure.type_decl) : bool = d.kind = Struct []
+
+let is_empty_record_type_decl_group (dg : Pure.type_decl list) : bool =
+  match dg with [ d ] -> is_empty_record_type_decl d | _ -> false
+
+(** In some provers, groups of definitions must be delimited.
+
+    - in Coq, *every* group (including singletons) must end with "."
+    - in Lean, groups of mutually recursive definitions must end with "end"
+    - in HOL4 (in most situations) the whole group must be within a `Define` command
+
+    Calls to {!extract_fun_decl} should be inserted between calls to
+    {!start_fun_decl_group} and {!end_fun_decl_group}.
+
+    TODO: maybe those [{start/end}_decl_group] functions are not that much a good
+    idea and we should merge them with the corresponding [extract_decl] functions.
+ *)
+let start_fun_decl_group (ctx : extraction_ctx) (fmt : F.formatter)
+    (is_rec : bool) (dg : Pure.fun_decl list) =
+  match !backend with
+  | FStar | Coq | Lean -> ()
+  | HOL4 ->
+      (* In HOL4, opaque functions have a special treatment *)
+      if is_single_opaque_fun_decl_group dg then ()
+      else
+        let compute_fun_def_name (def : Pure.fun_decl) : string =
+          ctx_get_local_function def.def_id def.loop_id def.back_id ctx ^ "_def"
+        in
+        let names = List.map compute_fun_def_name dg in
+        (* Add a break before *)
+        F.pp_print_break fmt 0 0;
+        (* Open the box for the delimiters *)
+        F.pp_open_vbox fmt 0;
+        (* Open the box for the definitions themselves *)
+        F.pp_open_vbox fmt ctx.indent_incr;
+        (* Print the delimiters *)
+        if is_rec then
+          F.pp_print_string fmt
+            ("val [" ^ String.concat ", " names ^ "] = DefineDiv ‘")
+        else (
+          assert (List.length names = 1);
+          let name = List.hd names in
+          F.pp_print_string fmt ("val " ^ name ^ " = Define ‘"));
+        F.pp_print_cut fmt ()
+
+(** See {!start_fun_decl_group}. *)
+let end_fun_decl_group (fmt : F.formatter) (is_rec : bool)
+    (dg : Pure.fun_decl list) =
+  match !backend with
+  | FStar -> ()
+  | Coq ->
+      (* For aesthetic reasons, we print the Coq end group delimiter directly
+         in {!extract_fun_decl}. *)
+      ()
+  | Lean ->
+      (* We must add the "end" keyword to groups of mutually recursive functions *)
+      if is_rec && List.length dg > 1 then (
+        F.pp_print_cut fmt ();
+        F.pp_print_string fmt "end";
+        (* Add breaks to insert new lines between definitions *)
+        F.pp_print_break fmt 0 0)
+      else ()
+  | HOL4 ->
+      (* In HOL4, opaque functions have a special treatment *)
+      if is_single_opaque_fun_decl_group dg then ()
+      else (
+        (* Close the box for the definitions *)
+        F.pp_close_box fmt ();
+        (* Print the end delimiter *)
+        F.pp_print_cut fmt ();
+        F.pp_print_string fmt "’";
+        (* Close the box for the delimiters *)
+        F.pp_close_box fmt ();
+        (* Add breaks to insert new lines between definitions *)
+        F.pp_print_break fmt 0 0)
+
+(** See {!start_fun_decl_group}: similar usage, but for the type declarations. *)
+let start_type_decl_group (ctx : extraction_ctx) (fmt : F.formatter)
+    (is_rec : bool) (dg : Pure.type_decl list) =
+  match !backend with
+  | FStar | Coq -> ()
+  | Lean ->
+      if is_rec && List.length dg > 1 then (
+        F.pp_print_space fmt ();
+        F.pp_print_string fmt "mutual";
+        F.pp_print_space fmt ())
+  | HOL4 ->
+      (* In HOL4, opaque types and empty records have a special treatment *)
+      if
+        is_single_opaque_type_decl_group dg
+        || is_empty_record_type_decl_group dg
+      then ()
+      else (
+        (* Add a break before *)
+        F.pp_print_break fmt 0 0;
+        (* Open the box for the delimiters *)
+        F.pp_open_vbox fmt 0;
+        (* Open the box for the definitions themselves *)
+        F.pp_open_vbox fmt ctx.indent_incr;
+        (* Print the delimiters *)
+        F.pp_print_string fmt "Datatype:";
+        F.pp_print_cut fmt ())
+
+(** See {!start_fun_decl_group}. *)
+let end_type_decl_group (fmt : F.formatter) (is_rec : bool)
+    (dg : Pure.type_decl list) =
+  match !backend with
+  | FStar -> ()
+  | Coq ->
+      (* For aesthetic reasons, we print the Coq end group delimiter directly
+         in {!extract_fun_decl}. *)
+      ()
+  | Lean ->
+      (* We must add the "end" keyword to groups of mutually recursive functions *)
+      if is_rec && List.length dg > 1 then (
+        F.pp_print_cut fmt ();
+        F.pp_print_string fmt "end";
+        (* Add breaks to insert new lines between definitions *)
+        F.pp_print_break fmt 0 0)
+      else ()
+  | HOL4 ->
+      (* In HOL4, opaque types and empty records have a special treatment *)
+      if
+        is_single_opaque_type_decl_group dg
+        || is_empty_record_type_decl_group dg
+      then ()
+      else (
+        (* Close the box for the definitions *)
+        F.pp_close_box fmt ();
+        (* Print the end delimiter *)
+        F.pp_print_cut fmt ();
+        F.pp_print_string fmt "End";
+        (* Close the box for the delimiters *)
+        F.pp_close_box fmt ();
+        (* Add breaks to insert new lines between definitions *)
+        F.pp_print_break fmt 0 0)
+
+let unit_name () =
+  match !backend with Lean -> "Unit" | Coq | FStar | HOL4 -> "unit"
+
+(** Small helper *)
+let extract_arrow (fmt : F.formatter) () : unit =
+  if !Config.backend = Lean then F.pp_print_string fmt "→"
+  else F.pp_print_string fmt "->"
+
+let extract_const_generic (ctx : extraction_ctx) (fmt : F.formatter)
+    (inside : bool) (cg : const_generic) : unit =
+  match cg with
+  | ConstGenericGlobal id ->
+      let s = ctx_get_global id ctx in
+      F.pp_print_string fmt s
+  | ConstGenericValue v -> ctx.fmt.extract_literal fmt inside v
+  | ConstGenericVar id ->
+      let s = ctx_get_const_generic_var id ctx in
+      F.pp_print_string fmt s
+
+let extract_literal_type (ctx : extraction_ctx) (fmt : F.formatter)
+    (ty : literal_type) : unit =
+  match ty with
+  | Bool -> F.pp_print_string fmt ctx.fmt.bool_name
+  | Char -> F.pp_print_string fmt ctx.fmt.char_name
+  | Integer int_ty -> F.pp_print_string fmt (ctx.fmt.int_name int_ty)
+
+(** [inside] constrols whether we should add parentheses or not around type
+    applications (if [true] we add parentheses).
+
+    [no_params_tys]: for all the types inside this set, do not print the type parameters.
+    This is used for HOL4. As polymorphism is uniform in HOL4, printing the
+    type parameters in the recursive definitions is useless (and actually
+    forbidden).
+
+    For instance, where in F* we would write:
+    {[
+      type list a = | Nil : list a | Cons : a -> list a -> list a
+    ]}
+
+    In HOL4 we would simply write:
+    {[
+      Datatype:
+        list = Nil 'a | Cons 'a list
+      End
+    ]}
+ *)
+let rec extract_ty (ctx : extraction_ctx) (fmt : F.formatter)
+    (no_params_tys : TypeDeclId.Set.t) (inside : bool) (ty : ty) : unit =
+  let extract_rec = extract_ty ctx fmt no_params_tys in
+  match ty with
+  | Adt (type_id, generics) -> (
+      let has_params = generics <> empty_generic_args in
+      match type_id with
+      | Tuple ->
+          (* This is a bit annoying, but in F*/Coq/HOL4 [()] is not the unit type:
+           * we have to write [unit]... *)
+          if generics.types = [] then F.pp_print_string fmt (unit_name ())
+          else (
+            F.pp_print_string fmt "(";
+            Collections.List.iter_link
+              (fun () ->
+                F.pp_print_space fmt ();
+                let product =
+                  match !backend with
+                  | FStar -> "&"
+                  | Coq -> "*"
+                  | Lean -> "×"
+                  | HOL4 -> "#"
+                in
+                F.pp_print_string fmt product;
+                F.pp_print_space fmt ())
+              (extract_rec true) generics.types;
+            F.pp_print_string fmt ")")
+      | AdtId _ | Assumed _ -> (
+          (* HOL4 behaves differently. Where in Coq/FStar/Lean we would write:
+             `tree a b`
+
+             In HOL4 we would write:
+             `('a, 'b) tree`
+          *)
+          match !backend with
+          | FStar | Coq | Lean ->
+              let print_paren = inside && has_params in
+              if print_paren then F.pp_print_string fmt "(";
+              (* TODO: for now, only the opaque *functions* are extracted in the
+                 opaque module. The opaque *types* are assumed. *)
+              F.pp_print_string fmt (ctx_get_type type_id ctx);
+              (* We might need to filter the type arguments, if the type
+                 is builtin (for instance, we filter the global allocator type
+                 argument for `Vec`). *)
+              let generics =
+                match type_id with
+                | AdtId id -> (
+                    match
+                      TypeDeclId.Map.find_opt id ctx.types_filter_type_args_map
+                    with
+                    | None -> generics
+                    | Some filter ->
+                        let types = List.combine filter generics.types in
+                        let types =
+                          List.filter_map
+                            (fun (b, ty) -> if b then Some ty else None)
+                            types
+                        in
+                        { generics with types })
+                | _ -> generics
+              in
+              extract_generic_args ctx fmt no_params_tys generics;
+              if print_paren then F.pp_print_string fmt ")"
+          | HOL4 ->
+              let { types; const_generics; trait_refs } = generics in
+              (* Const generics are not supported in HOL4 *)
+              assert (const_generics = []);
+              let print_tys =
+                match type_id with
+                | AdtId id -> not (TypeDeclId.Set.mem id no_params_tys)
+                | Assumed _ -> true
+                | _ -> raise (Failure "Unreachable")
+              in
+              if types <> [] && print_tys then (
+                let print_paren = List.length types > 1 in
+                if print_paren then F.pp_print_string fmt "(";
+                Collections.List.iter_link
+                  (fun () ->
+                    F.pp_print_string fmt ",";
+                    F.pp_print_space fmt ())
+                  (extract_rec true) types;
+                if print_paren then F.pp_print_string fmt ")";
+                F.pp_print_space fmt ());
+              F.pp_print_string fmt (ctx_get_type type_id ctx);
+              if trait_refs <> [] then (
+                F.pp_print_space fmt ();
+                Collections.List.iter_link (F.pp_print_space fmt)
+                  (extract_trait_ref ctx fmt no_params_tys true)
+                  trait_refs)))
+  | TypeVar vid -> F.pp_print_string fmt (ctx_get_type_var vid ctx)
+  | Literal lty -> extract_literal_type ctx fmt lty
+  | Arrow (arg_ty, ret_ty) ->
+      if inside then F.pp_print_string fmt "(";
+      extract_rec false arg_ty;
+      F.pp_print_space fmt ();
+      extract_arrow fmt ();
+      F.pp_print_space fmt ();
+      extract_rec false ret_ty;
+      if inside then F.pp_print_string fmt ")"
+  | TraitType (trait_ref, generics, type_name) -> (
+      if !parameterize_trait_types then raise (Failure "Unimplemented")
+      else
+        let type_name =
+          ctx_get_trait_type trait_ref.trait_decl_ref.trait_decl_id type_name
+            ctx
+        in
+        let add_brackets (s : string) =
+          if !backend = Coq then "(" ^ s ^ ")" else s
+        in
+        (* There may be a special treatment depending on the instance id.
+           See the comments for {!extract_trait_instance_id_with_dot}.
+           TODO: there should be a cleaner way to do. The annoying thing
+           here is that if we project directly over the self clause, then
+           we have to be careful (we may not have to print the "Self.").
+           Otherwise, we can directly call {!extract_trait_ref}.
+        *)
+        match trait_ref.trait_id with
+        | Self ->
+            assert (generics = empty_generic_args);
+            assert (trait_ref.generics = empty_generic_args);
+            extract_trait_instance_id_with_dot ctx fmt no_params_tys false
+              trait_ref.trait_id;
+            F.pp_print_string fmt type_name
+        | _ ->
+            (* HOL4 doesn't have 1st class types *)
+            assert (!backend <> HOL4);
+            let use_brackets = generics <> empty_generic_args in
+            if use_brackets then F.pp_print_string fmt "(";
+            extract_trait_ref ctx fmt no_params_tys false trait_ref;
+            extract_generic_args ctx fmt no_params_tys generics;
+            if use_brackets then F.pp_print_string fmt ")";
+            F.pp_print_string fmt ("." ^ add_brackets type_name))
+
+and extract_trait_ref (ctx : extraction_ctx) (fmt : F.formatter)
+    (no_params_tys : TypeDeclId.Set.t) (inside : bool) (tr : trait_ref) : unit =
+  let use_brackets = tr.generics <> empty_generic_args && inside in
+  if use_brackets then F.pp_print_string fmt "(";
+  (* We may need to filter the parameters if the trait is builtin *)
+  let generics =
+    match tr.trait_id with
+    | TraitImpl id -> (
+        match
+          TraitImplId.Map.find_opt id ctx.trait_impls_filter_type_args_map
+        with
+        | None -> tr.generics
+        | Some filter ->
+            let types =
+              List.filter_map
+                (fun (b, x) -> if b then Some x else None)
+                (List.combine filter tr.generics.types)
+            in
+            { tr.generics with types })
+    | _ -> tr.generics
+  in
+  extract_trait_instance_id ctx fmt no_params_tys inside tr.trait_id;
+  extract_generic_args ctx fmt no_params_tys generics;
+  if use_brackets then F.pp_print_string fmt ")"
+
+and extract_trait_decl_ref (ctx : extraction_ctx) (fmt : F.formatter)
+    (no_params_tys : TypeDeclId.Set.t) (inside : bool) (tr : trait_decl_ref) :
+    unit =
+  let use_brackets = tr.decl_generics <> empty_generic_args && inside in
+  let name = ctx_get_trait_decl tr.trait_decl_id ctx in
+  if use_brackets then F.pp_print_string fmt "(";
+  F.pp_print_string fmt name;
+  (* There is something subtle here: the trait obligations for the implemented
+     trait are put inside the parent clauses, so we must ignore them here *)
+  let generics = { tr.decl_generics with trait_refs = [] } in
+  extract_generic_args ctx fmt no_params_tys generics;
+  if use_brackets then F.pp_print_string fmt ")"
+
+and extract_generic_args (ctx : extraction_ctx) (fmt : F.formatter)
+    (no_params_tys : TypeDeclId.Set.t) (generics : generic_args) : unit =
+  let { types; const_generics; trait_refs } = generics in
+  if !backend <> HOL4 then (
+    if types <> [] then (
+      F.pp_print_space fmt ();
+      Collections.List.iter_link (F.pp_print_space fmt)
+        (extract_ty ctx fmt no_params_tys true)
+        types);
+    if const_generics <> [] then (
+      assert (!backend <> HOL4);
+      F.pp_print_space fmt ();
+      Collections.List.iter_link (F.pp_print_space fmt)
+        (extract_const_generic ctx fmt true)
+        const_generics));
+  if trait_refs <> [] then (
+    F.pp_print_space fmt ();
+    Collections.List.iter_link (F.pp_print_space fmt)
+      (extract_trait_ref ctx fmt no_params_tys true)
+      trait_refs)
+
+(** We sometimes need to ignore references to `Self` when generating the
+    code, espcially when we project associated items. For this reason we
+    have a special function for the cases where we project from an instance
+    id (e.g., `<Self as Foo>::foo` - note that in the extracted code, the
+    projections are often written with a dot '.').
+ *)
+and extract_trait_instance_id_with_dot (ctx : extraction_ctx)
+    (fmt : F.formatter) (no_params_tys : TypeDeclId.Set.t) (inside : bool)
+    (id : trait_instance_id) : unit =
+  match id with
+  | Self ->
+      (* There are two situations:
+         - we are extracting a declared item and need to refer to another
+           item (for instance, we are extracting a method signature and
+           need to refer to an associated type).
+           We directly refer to the other item (we extract trait declarations
+           as structures, so we can refer to their fields)
+         - we are extracting a provided method for a trait declaration. We
+           refer to the item in the self trait clause (see {!SelfTraitClauseId}).
+
+         Remark: we can't get there for trait *implementations* because then the
+         types should have been normalized.
+      *)
+      if ctx.is_provided_method then
+        (* Provided method: use the trait self clause *)
+        let self_clause = ctx_get_trait_self_clause ctx in
+        F.pp_print_string fmt (self_clause ^ ".")
+      else
+        (* Declaration: nothing to print, we will directly refer to
+           the item. *)
+        ()
+  | _ ->
+      (* Other cases *)
+      extract_trait_instance_id ctx fmt no_params_tys inside id;
+      F.pp_print_string fmt "."
+
+and extract_trait_instance_id (ctx : extraction_ctx) (fmt : F.formatter)
+    (no_params_tys : TypeDeclId.Set.t) (inside : bool) (id : trait_instance_id)
+    : unit =
+  let add_brackets (s : string) = if !backend = Coq then "(" ^ s ^ ")" else s in
+  match id with
+  | Self ->
+      (* This has a specific treatment depending on the item we're extracting
+         (associated type, etc.). We should have caught this elsewhere. *)
+      if !Config.fail_hard then
+        raise (Failure "Unexpected occurrence of `Self`")
+      else F.pp_print_string fmt "ERROR(\"Unexpected Self\")"
+  | TraitImpl id ->
+      let name = ctx_get_trait_impl id ctx in
+      F.pp_print_string fmt name
+  | Clause id ->
+      let name = ctx_get_local_trait_clause id ctx in
+      F.pp_print_string fmt name
+  | ParentClause (inst_id, decl_id, clause_id) ->
+      (* Use the trait decl id to lookup the name *)
+      let name = ctx_get_trait_parent_clause decl_id clause_id ctx in
+      extract_trait_instance_id_with_dot ctx fmt no_params_tys true inst_id;
+      F.pp_print_string fmt (add_brackets name)
+  | ItemClause (inst_id, decl_id, item_name, clause_id) ->
+      (* Use the trait decl id to lookup the name *)
+      let name = ctx_get_trait_item_clause decl_id item_name clause_id ctx in
+      extract_trait_instance_id_with_dot ctx fmt no_params_tys true inst_id;
+      F.pp_print_string fmt (add_brackets name)
+  | TraitRef trait_ref ->
+      extract_trait_ref ctx fmt no_params_tys inside trait_ref
+  | UnknownTrait _ ->
+      (* This is an error case *)
+      raise (Failure "Unexpected")
+
+(** Compute the names for all the top-level identifiers used in a type
+    definition (type name, variant names, field names, etc. but not type
+    parameters).
+
+    We need to do this preemptively, beforce extracting any definition,
+    because of recursive definitions.
+ *)
+let extract_type_decl_register_names (ctx : extraction_ctx) (def : type_decl) :
+    extraction_ctx =
+  (* Lookup the builtin information, if there is *)
+  let open ExtractBuiltin in
+  let sname = name_to_simple_name def.name in
+  let info = SimpleNameMap.find_opt sname (builtin_types_map ()) in
+  (* Register the filtering information, if there is *)
+  let ctx =
+    match info with
+    | Some { keep_params = Some keep; _ } ->
+        {
+          ctx with
+          types_filter_type_args_map =
+            TypeDeclId.Map.add def.def_id keep ctx.types_filter_type_args_map;
+        }
+    | _ -> ctx
+  in
+  (* Compute and register the type def name *)
+  let def_name =
+    match info with
+    | None -> ctx.fmt.type_name def.name
+    | Some info -> info.extract_name
+  in
+  let ctx = ctx_add (TypeId (AdtId def.def_id)) def_name ctx in
+  (* Compute and register:
+   * - the variant names, if this is an enumeration
+   * - the field names, if this is a structure
+   *)
+  let ctx =
+    match def.kind with
+    | Struct fields ->
+        (* Compute the names *)
+        let field_names, cons_name =
+          match info with
+          | None | Some { body_info = None; _ } ->
+              let field_names =
+                FieldId.mapi
+                  (fun fid (field : field) ->
+                    (fid, ctx.fmt.field_name def.name fid field.field_name))
+                  fields
+              in
+              let cons_name = ctx.fmt.struct_constructor def.name in
+              (field_names, cons_name)
+          | Some { body_info = Some (Struct (cons_name, field_names)); _ } ->
+              let field_names =
+                FieldId.mapi
+                  (fun fid (field : field) ->
+                    let rust_name = Option.get field.field_name in
+                    let name =
+                      snd (List.find (fun (n, _) -> n = rust_name) field_names)
+                    in
+                    (fid, name))
+                  fields
+              in
+              (field_names, cons_name)
+          | Some info ->
+              raise
+                (Failure
+                   ("Invalid builtin information: "
+                   ^ show_builtin_type_info info))
+        in
+        (* Add the fields *)
+        let ctx =
+          List.fold_left
+            (fun ctx (fid, name) ->
+              ctx_add (FieldId (AdtId def.def_id, fid)) name ctx)
+            ctx field_names
+        in
+        (* Add the constructor name *)
+        ctx_add (StructId (AdtId def.def_id)) cons_name ctx
+    | Enum variants ->
+        let variant_names =
+          match info with
+          | None ->
+              VariantId.mapi
+                (fun variant_id (variant : variant) ->
+                  let name =
+                    ctx.fmt.variant_name def.name variant.variant_name
+                  in
+                  (* Add the type name prefix for Lean *)
+                  let name =
+                    if !Config.backend = Lean then
+                      let type_name = ctx.fmt.type_name def.name in
+                      type_name ^ "." ^ name
+                    else name
+                  in
+                  (variant_id, name))
+                variants
+          | Some { body_info = Some (Enum variant_infos); _ } ->
+              (* We need to compute the map from variant to variant *)
+              let variant_map =
+                StringMap.of_list
+                  (List.map
+                     (fun (info : builtin_enum_variant_info) ->
+                       (info.rust_variant_name, info.extract_variant_name))
+                     variant_infos)
+              in
+              VariantId.mapi
+                (fun variant_id (variant : variant) ->
+                  (variant_id, StringMap.find variant.variant_name variant_map))
+                variants
+          | _ -> raise (Failure "Invalid builtin information")
+        in
+        List.fold_left
+          (fun ctx (vid, vname) ->
+            ctx_add (VariantId (AdtId def.def_id, vid)) vname ctx)
+          ctx variant_names
+    | Opaque ->
+        (* Nothing to do *)
+        ctx
+  in
+  (* Return *)
+  ctx
+
+(** Print the variants *)
+let extract_type_decl_variant (ctx : extraction_ctx) (fmt : F.formatter)
+    (type_decl_group : TypeDeclId.Set.t) (type_name : string)
+    (type_params : string list) (cg_params : string list) (cons_name : string)
+    (fields : field list) : unit =
+  F.pp_print_space fmt ();
+  (* variant box *)
+  F.pp_open_hvbox fmt ctx.indent_incr;
+  (* [| Cons :]
+   * Note that we really don't want any break above so we print everything
+   * at once. *)
+  let opt_colon = if !backend <> HOL4 then " :" else "" in
+  F.pp_print_string fmt ("| " ^ cons_name ^ opt_colon);
+  let print_field (fid : FieldId.id) (f : field) (ctx : extraction_ctx) :
+      extraction_ctx =
+    F.pp_print_space fmt ();
+    (* Open the field box *)
+    F.pp_open_box fmt ctx.indent_incr;
+    (* Print the field names, if the backend accepts it.
+     * [  x :]
+     * Note that when printing fields, we register the field names as
+     * *variables*: they don't need to be unique at the top level. *)
+    let ctx =
+      match !backend with
+      | FStar -> (
+          match f.field_name with
+          | None -> ctx
+          | Some field_name ->
+              let var_id = VarId.of_int (FieldId.to_int fid) in
+              let field_name =
+                ctx.fmt.var_basename ctx.names_maps.names_map.names_set
+                  (Some field_name) f.field_ty
+              in
+              let ctx, field_name = ctx_add_var field_name var_id ctx in
+              F.pp_print_string fmt (field_name ^ " :");
+              F.pp_print_space fmt ();
+              ctx)
+      | Coq | Lean | HOL4 -> ctx
+    in
+    (* Print the field type *)
+    let inside = !backend = HOL4 in
+    extract_ty ctx fmt type_decl_group inside f.field_ty;
+    (* Print the arrow [->] *)
+    if !backend <> HOL4 then (
+      F.pp_print_space fmt ();
+      extract_arrow fmt ());
+    (* Close the field box *)
+    F.pp_close_box fmt ();
+    (* Return *)
+    ctx
+  in
+  (* Print the fields *)
+  let fields = FieldId.mapi (fun fid f -> (fid, f)) fields in
+  let _ =
+    List.fold_left (fun ctx (fid, f) -> print_field fid f ctx) ctx fields
+  in
+  (* Sanity check: HOL4 doesn't support const generics *)
+  assert (cg_params = [] || !backend <> HOL4);
+  (* Print the final type *)
+  if !backend <> HOL4 then (
+    F.pp_print_space fmt ();
+    F.pp_open_hovbox fmt 0;
+    F.pp_print_string fmt type_name;
+    List.iter
+      (fun p ->
+        F.pp_print_space fmt ();
+        F.pp_print_string fmt p)
+      (List.append type_params cg_params);
+    F.pp_close_box fmt ());
+  (* Close the variant box *)
+  F.pp_close_box fmt ()
+
+(* TODO: we don' need the [def_name] paramter: it can be retrieved from the context *)
+let extract_type_decl_enum_body (ctx : extraction_ctx) (fmt : F.formatter)
+    (type_decl_group : TypeDeclId.Set.t) (def : type_decl) (def_name : string)
+    (type_params : string list) (cg_params : string list)
+    (variants : variant list) : unit =
+  (* We want to generate a definition which looks like this (taking F* as example):
+     {[
+       type list a = | Cons : a -> list a -> list a | Nil : list a
+     ]}
+
+     If there isn't enough space on one line:
+     {[
+       type s =
+       | Cons : a -> list a -> list a
+       | Nil : list a
+     ]}
+
+     And if we need to write the type of a variant on several lines:
+     {[
+       type s =
+       | Cons :
+         a ->
+         list a ->
+         list a
+       | Nil : list a
+     ]}
+
+     Finally, it is possible to give names to the variant fields in Rust.
+     In this situation, we generate a definition like this:
+     {[
+       type s =
+       | Cons : hd:a -> tl:list a -> list a
+       | Nil : list a
+     ]}
+
+     Note that we already printed: [type s =]
+  *)
+  let print_variant _variant_id (v : variant) =
+    (* We don't lookup the name, because it may have a prefix for the type
+       id (in the case of Lean) *)
+    let cons_name = ctx.fmt.variant_name def.name v.variant_name in
+    let fields = v.fields in
+    extract_type_decl_variant ctx fmt type_decl_group def_name type_params
+      cg_params cons_name fields
+  in
+  (* Print the variants *)
+  let variants = VariantId.mapi (fun vid v -> (vid, v)) variants in
+  List.iter (fun (vid, v) -> print_variant vid v) variants
+
+let extract_type_decl_struct_body (ctx : extraction_ctx) (fmt : F.formatter)
+    (type_decl_group : TypeDeclId.Set.t) (kind : decl_kind) (def : type_decl)
+    (type_params : string list) (cg_params : string list) (fields : field list)
+    : unit =
+  (* We want to generate a definition which looks like this (taking F* as example):
+     {[
+       type t = { x : int; y : bool; }
+     ]}
+
+     If there isn't enough space on one line:
+     {[
+       type t =
+       {
+         x : int; y : bool;
+       }
+     ]}
+
+     And if there is even less space:
+     {[
+       type t =
+       {
+         x : int;
+         y : bool;
+       }
+     ]}
+
+     Also, in case there are no fields, we need to define the type as [unit]
+     ([type t = {}] doesn't work in F* ).
+
+     Coq:
+     ====
+     We need to define the constructor name upon defining the struct (record, in Coq).
+     The syntex is:
+     {[
+       Record Foo = mkFoo { x : int; y : bool; }.
+     }]
+
+     Also, Coq doesn't support groups of mutually recursive inductives and records.
+     This is fine, because we can then define records as inductives, and leverage
+     the fact that when record fields are accessed, the records are symbolically
+     expanded which introduces let bindings of the form: [let RecordCons ... = x in ...].
+     As a consequence, we never use the record projectors (unless we reconstruct
+     them in the micro passes of course).
+
+     HOL4:
+     =====
+     Type definitions are written as follows:
+     {[
+       Datatype:
+         tree =
+           TLeaf 'a
+         | TNode node ;
+
+         node =
+           Node (tree list)
+       End
+     ]}
+  *)
+  (* Note that we already printed: [type t =] *)
+  let is_rec = decl_is_from_rec_group kind in
+  let _ =
+    if !backend = FStar && fields = [] then (
+      F.pp_print_space fmt ();
+      F.pp_print_string fmt (unit_name ()))
+    else if !backend = Lean && fields = [] then ()
+      (* If the definition is recursive, we may need to extract it as an inductive
+         (instead of a record). We start with the "normal" case: we extract it
+         as a record. *)
+    else if (not is_rec) || (!backend <> Coq && !backend <> Lean) then (
+      if !backend <> Lean then F.pp_print_space fmt ();
+      (* If Coq: print the constructor name *)
+      (* TODO: remove superfluous test not is_rec below *)
+      if !backend = Coq && not is_rec then (
+        F.pp_print_string fmt (ctx_get_struct (AdtId def.def_id) ctx);
+        F.pp_print_string fmt " ");
+      (match !backend with
+      | Lean -> ()
+      | FStar | Coq -> F.pp_print_string fmt "{"
+      | HOL4 -> F.pp_print_string fmt "<|");
+      F.pp_print_break fmt 1 ctx.indent_incr;
+      (* The body itself *)
+      (* Open a box for the body *)
+      (match !backend with
+      | Coq | FStar | HOL4 -> F.pp_open_hvbox fmt 0
+      | Lean -> F.pp_open_vbox fmt 0);
+      (* Print the fields *)
+      let print_field (field_id : FieldId.id) (f : field) : unit =
+        let field_name = ctx_get_field (AdtId def.def_id) field_id ctx in
+        (* Open a box for the field *)
+        F.pp_open_box fmt ctx.indent_incr;
+        F.pp_print_string fmt field_name;
+        F.pp_print_space fmt ();
+        F.pp_print_string fmt ":";
+        F.pp_print_space fmt ();
+        extract_ty ctx fmt type_decl_group false f.field_ty;
+        if !backend <> Lean then F.pp_print_string fmt ";";
+        (* Close the box for the field *)
+        F.pp_close_box fmt ()
+      in
+      let fields = FieldId.mapi (fun fid f -> (fid, f)) fields in
+      Collections.List.iter_link (F.pp_print_space fmt)
+        (fun (fid, f) -> print_field fid f)
+        fields;
+      (* Close the box for the body *)
+      F.pp_close_box fmt ();
+      match !backend with
+      | Lean -> ()
+      | FStar | Coq ->
+          F.pp_print_space fmt ();
+          F.pp_print_string fmt "}"
+      | HOL4 ->
+          F.pp_print_space fmt ();
+          F.pp_print_string fmt "|>")
+    else (
+      (* We extract for Coq or Lean, and we have a recursive record, or a record in
+         a group of mutually recursive types: we extract it as an inductive type *)
+      assert (is_rec && (!backend = Coq || !backend = Lean));
+      (* Small trick: in Lean we use namespaces, meaning we don't need to prefix
+         the constructor name with the name of the type at definition site,
+         i.e., instead of generating `inductive Foo := | MkFoo ...` like in Coq
+         we generate `inductive Foo := | mk ... *)
+      let cons_name =
+        if !backend = Lean then "mk" else ctx_get_struct (AdtId def.def_id) ctx
+      in
+      let def_name = ctx_get_local_type def.def_id ctx in
+      extract_type_decl_variant ctx fmt type_decl_group def_name type_params
+        cg_params cons_name fields)
+  in
+  ()
+
+(** Extract a nestable, muti-line comment *)
+let extract_comment (fmt : F.formatter) (sl : string list) : unit =
+  (* Delimiters, space after we break a line *)
+  let ld, space, rd =
+    match !backend with
+    | Coq | FStar | HOL4 -> ("(** ", 4, " *)")
+    | Lean -> ("/- ", 3, " -/")
+  in
+  F.pp_open_vbox fmt space;
+  F.pp_print_string fmt ld;
+  (match sl with
+  | [] -> ()
+  | s :: sl ->
+      F.pp_print_string fmt s;
+      List.iter
+        (fun s ->
+          F.pp_print_space fmt ();
+          F.pp_print_string fmt s)
+        sl);
+  F.pp_print_string fmt rd;
+  F.pp_close_box fmt ()
+
+let extract_trait_clause_type (ctx : extraction_ctx) (fmt : F.formatter)
+    (no_params_tys : TypeDeclId.Set.t) (clause : trait_clause) : unit =
+  let trait_name = ctx_get_trait_decl clause.trait_id ctx in
+  F.pp_print_string fmt trait_name;
+  extract_generic_args ctx fmt no_params_tys clause.generics
+
+(** Insert a space, if necessary *)
+let insert_req_space (fmt : F.formatter) (space : bool ref) : unit =
+  if !space then space := false else F.pp_print_space fmt ()
+
+(** Extract the trait self clause.
+
+    We add the trait self clause for provided methods (see {!TraitSelfClauseId}).
+ *)
+let extract_trait_self_clause (insert_req_space : unit -> unit)
+    (ctx : extraction_ctx) (fmt : F.formatter) (trait_decl : trait_decl)
+    (params : string list) : unit =
+  insert_req_space ();
+  F.pp_print_string fmt "(";
+  let self_clause = ctx_get_trait_self_clause ctx in
+  F.pp_print_string fmt self_clause;
+  F.pp_print_space fmt ();
+  F.pp_print_string fmt ":";
+  F.pp_print_space fmt ();
+  let trait_id = ctx_get_trait_decl trait_decl.def_id ctx in
+  F.pp_print_string fmt trait_id;
+  List.iter
+    (fun p ->
+      F.pp_print_space fmt ();
+      F.pp_print_string fmt p)
+    params;
+  F.pp_print_string fmt ")"
+
+(**
+ - [trait_decl]: if [Some], it means we are extracting the generics for a provided
+   method and need to insert a trait self clause (see {!TraitSelfClauseId}).
+ *)
+let extract_generic_params (ctx : extraction_ctx) (fmt : F.formatter)
+    (no_params_tys : TypeDeclId.Set.t) ?(use_forall = false)
+    ?(use_forall_use_sep = true) ?(use_arrows = false)
+    ?(as_implicits : bool = false) ?(space : bool ref option = None)
+    ?(trait_decl : trait_decl option = None) (generics : generic_params)
+    (type_params : string list) (cg_params : string list)
+    (trait_clauses : string list) : unit =
+  let all_params = List.concat [ type_params; cg_params; trait_clauses ] in
+  (* HOL4 doesn't support const generics *)
+  assert (cg_params = [] || !backend <> HOL4);
+  let left_bracket (implicit : bool) =
+    if implicit && !backend <> FStar then F.pp_print_string fmt "{"
+    else F.pp_print_string fmt "("
+  in
+  let right_bracket (implicit : bool) =
+    if implicit && !backend <> FStar then F.pp_print_string fmt "}"
+    else F.pp_print_string fmt ")"
+  in
+  let print_implicit_symbol (implicit : bool) =
+    if implicit && !backend = FStar then F.pp_print_string fmt "#" else ()
+  in
+  let insert_req_space () =
+    match space with
+    | None -> F.pp_print_space fmt ()
+    | Some space -> insert_req_space fmt space
+  in
+  (* Print the type/const generic parameters *)
+  if all_params <> [] then (
+    if use_forall then (
+      if use_forall_use_sep then (
+        insert_req_space ();
+        F.pp_print_string fmt ":");
+      insert_req_space ();
+      F.pp_print_string fmt "forall");
+    (* Small helper - we may need to split the parameters *)
+    let print_generics (as_implicits : bool) (type_params : string list)
+        (const_generics : const_generic_var list)
+        (trait_clauses : trait_clause list) : unit =
+      (* Note that in HOL4 we don't print the type parameters. *)
+      if !backend <> HOL4 then (
+        (* Print the type parameters *)
+        if type_params <> [] then (
+          insert_req_space ();
+          (* ( *)
+          left_bracket as_implicits;
+          List.iter
+            (fun s ->
+              print_implicit_symbol as_implicits;
+              F.pp_print_string fmt s;
+              F.pp_print_space fmt ())
+            type_params;
+          F.pp_print_string fmt ":";
+          F.pp_print_space fmt ();
+          F.pp_print_string fmt (type_keyword ());
+          (* ) *)
+          right_bracket as_implicits;
+          if use_arrows then (
+            F.pp_print_space fmt ();
+            F.pp_print_string fmt "->"));
+        (* Print the const generic parameters *)
+        List.iter
+          (fun (var : const_generic_var) ->
+            insert_req_space ();
+            (* ( *)
+            left_bracket as_implicits;
+            let n = ctx_get_const_generic_var var.index ctx in
+            print_implicit_symbol as_implicits;
+            F.pp_print_string fmt n;
+            F.pp_print_space fmt ();
+            F.pp_print_string fmt ":";
+            F.pp_print_space fmt ();
+            extract_literal_type ctx fmt var.ty;
+            (* ) *)
+            right_bracket as_implicits;
+            if use_arrows then (
+              F.pp_print_space fmt ();
+              F.pp_print_string fmt "->"))
+          const_generics);
+      (* Print the trait clauses *)
+      List.iter
+        (fun (clause : trait_clause) ->
+          insert_req_space ();
+          (* ( *)
+          left_bracket as_implicits;
+          let n = ctx_get_local_trait_clause clause.clause_id ctx in
+          print_implicit_symbol as_implicits;
+          F.pp_print_string fmt n;
+          F.pp_print_space fmt ();
+          F.pp_print_string fmt ":";
+          F.pp_print_space fmt ();
+          extract_trait_clause_type ctx fmt no_params_tys clause;
+          (* ) *)
+          right_bracket as_implicits;
+          if use_arrows then (
+            F.pp_print_space fmt ();
+            F.pp_print_string fmt "->"))
+        trait_clauses
+    in
+    (* If we extract the generics for a provided method for a trait declaration
+       (indicated by the trait decl given as input), we need to split the generics:
+       - we print the generics for the trait decl
+       - we print the trait self clause
+       - we print the generics for the trait method
+    *)
+    match trait_decl with
+    | None ->
+        print_generics as_implicits type_params generics.const_generics
+          generics.trait_clauses
+    | Some trait_decl ->
+        (* Split the generics between the generics specific to the trait decl
+           and those specific to the trait method *)
+        let open Collections.List in
+        let dtype_params, mtype_params =
+          split_at type_params (length trait_decl.generics.types)
+        in
+        let dcgs, mcgs =
+          split_at generics.const_generics
+            (length trait_decl.generics.const_generics)
+        in
+        let dtrait_clauses, mtrait_clauses =
+          split_at generics.trait_clauses
+            (length trait_decl.generics.trait_clauses)
+        in
+        (* Extract the trait decl generics - note that we can always deduce
+           those parameters from the trait self clause: for this reason
+           they are always implicit *)
+        print_generics true dtype_params dcgs dtrait_clauses;
+        (* Extract the trait self clause *)
+        let params =
+          concat
+            [
+              dtype_params;
+              map
+                (fun (cg : const_generic_var) ->
+                  ctx_get_const_generic_var cg.index ctx)
+                dcgs;
+              map
+                (fun c -> ctx_get_local_trait_clause c.clause_id ctx)
+                dtrait_clauses;
+            ]
+        in
+        extract_trait_self_clause insert_req_space ctx fmt trait_decl params;
+        (* Extract the method generics *)
+        print_generics as_implicits mtype_params mcgs mtrait_clauses)
+
+(** Extract a type declaration.
+
+    This function is for all type declarations and all backends **at the exception**
+    of opaque (assumed/declared) types format4 HOL4.
+
+    See {!extract_type_decl}.
+ *)
+let extract_type_decl_gen (ctx : extraction_ctx) (fmt : F.formatter)
+    (type_decl_group : TypeDeclId.Set.t) (kind : decl_kind) (def : type_decl)
+    (extract_body : bool) : unit =
+  (* Sanity check *)
+  assert (extract_body || !backend <> HOL4);
+  let type_kind =
+    if extract_body then
+      match def.kind with
+      | Struct _ -> Some Struct
+      | Enum _ -> Some Enum
+      | Opaque -> None
+    else None
+  in
+  (* If in Coq and the declaration is opaque, it must have the shape:
+     [Axiom Ident : forall (T0 ... Tn : Type) (N0 : ...) ... (Nn : ...), ... -> ... -> ...].
+
+     The boolean [is_opaque_coq] is used to detect this case.
+  *)
+  let is_opaque = type_kind = None in
+  let is_opaque_coq = !backend = Coq && is_opaque in
+  let use_forall = is_opaque_coq && def.generics <> empty_generic_params in
+  (* Retrieve the definition name *)
+  let def_name = ctx_get_local_type def.def_id ctx in
+  (* Add the type and const generic params - note that we need those bindings only for the
+   * body translation (they are not top-level) *)
+  let ctx_body, type_params, cg_params, trait_clauses =
+    ctx_add_generic_params def.generics ctx
+  in
+  (* Add a break before *)
+  if !backend <> HOL4 || not (decl_is_first_from_group kind) then
+    F.pp_print_break fmt 0 0;
+  (* Print a comment to link the extracted type to its original rust definition *)
+  extract_comment fmt [ "[" ^ Print.name_to_string def.name ^ "]" ];
+  F.pp_print_break fmt 0 0;
+  (* Open a box for the definition, so that whenever possible it gets printed on
+   * one line. Note however that in the case of Lean line breaks are important
+   * for parsing: we thus use a hovbox. *)
+  (match !backend with
+  | Coq | FStar | HOL4 -> F.pp_open_hvbox fmt 0
+  | Lean -> F.pp_open_vbox fmt 0);
+  (* Open a box for "type TYPE_NAME (TYPE_PARAMS CONST_GEN_PARAMS) =" *)
+  F.pp_open_hovbox fmt ctx.indent_incr;
+  (* > "type TYPE_NAME" *)
+  let qualif = ctx.fmt.type_decl_kind_to_qualif kind type_kind in
+  (match qualif with
+  | Some qualif -> F.pp_print_string fmt (qualif ^ " " ^ def_name)
+  | None -> F.pp_print_string fmt def_name);
+  (* HOL4 doesn't support const generics, and type definitions in HOL4 don't
+     support trait clauses *)
+  assert ((cg_params = [] && trait_clauses = []) || !backend <> HOL4);
+  (* Print the generic parameters *)
+  extract_generic_params ctx_body fmt type_decl_group ~use_forall def.generics
+    type_params cg_params trait_clauses;
+  (* Print the "=" if we extract the body*)
+  if extract_body then (
+    F.pp_print_space fmt ();
+    let eq =
+      match !backend with
+      | FStar -> "="
+      | Coq -> ":="
+      | Lean ->
+          if type_kind = Some Struct && kind = SingleNonRec then "where"
+          else ":="
+      | HOL4 -> "="
+    in
+    F.pp_print_string fmt eq)
+  else (
+    (* Otherwise print ": Type", unless it is the HOL4 backend (in
+       which case we declare the type with `new_type`) *)
+    if use_forall then F.pp_print_string fmt ","
+    else (
+      F.pp_print_space fmt ();
+      F.pp_print_string fmt ":");
+    F.pp_print_space fmt ();
+    F.pp_print_string fmt (type_keyword ()));
+  (* Close the box for "type TYPE_NAME (TYPE_PARAMS) =" *)
+  F.pp_close_box fmt ();
+  (if extract_body then
+     match def.kind with
+     | Struct fields ->
+         extract_type_decl_struct_body ctx_body fmt type_decl_group kind def
+           type_params cg_params fields
+     | Enum variants ->
+         extract_type_decl_enum_body ctx_body fmt type_decl_group def def_name
+           type_params cg_params variants
+     | Opaque -> raise (Failure "Unreachable"));
+  (* Add the definition end delimiter *)
+  if !backend = HOL4 && decl_is_not_last_from_group kind then (
+    F.pp_print_space fmt ();
+    F.pp_print_string fmt ";")
+  else if !backend = Coq && decl_is_last_from_group kind then (
+    (* This is actually an end of group delimiter. For aesthetic reasons
+       we print it here instead of in {!end_type_decl_group}. *)
+    F.pp_print_cut fmt ();
+    F.pp_print_string fmt ".");
+  (* Close the box for the definition *)
+  F.pp_close_box fmt ();
+  (* Add breaks to insert new lines between definitions *)
+  if !backend <> HOL4 || decl_is_not_last_from_group kind then
+    F.pp_print_break fmt 0 0
+
+(** Extract an opaque type declaration to HOL4.
+
+    Remark (SH): having to treat this specific case separately is very annoying,
+    but I could not find a better way.
+ *)
+let extract_type_decl_hol4_opaque (ctx : extraction_ctx) (fmt : F.formatter)
+    (def : type_decl) : unit =
+  (* Retrieve the definition name *)
+  let def_name = ctx_get_local_type def.def_id ctx in
+  (* Generic parameters are unsupported *)
+  assert (def.generics.const_generics = []);
+  (* Trait clauses on type definitions are unsupported *)
+  assert (def.generics.trait_clauses = []);
+  (* Types  *)
+  (* Count the number of parameters *)
+  let num_params = List.length def.generics.types in
+  (* Generate the declaration *)
+  F.pp_print_space fmt ();
+  F.pp_print_string fmt
+    ("val _ = new_type (\"" ^ def_name ^ "\", " ^ string_of_int num_params ^ ")");
+  F.pp_print_space fmt ()
+
+(** Extract an empty record type declaration to HOL4.
+
+    Empty records are not supported in HOL4, so we extract them as type
+    abbreviations to the unit type.
+
+    Remark (SH): having to treat this specific case separately is very annoying,
+    but I could not find a better way.
+ *)
+let extract_type_decl_hol4_empty_record (ctx : extraction_ctx)
+    (fmt : F.formatter) (def : type_decl) : unit =
+  (* Retrieve the definition name *)
+  let def_name = ctx_get_local_type def.def_id ctx in
+  (* Sanity check *)
+  assert (def.generics = empty_generic_params);
+  (* Generate the declaration *)
+  F.pp_print_space fmt ();
+  F.pp_print_string fmt ("Type " ^ def_name ^ " = “: unit”");
+  F.pp_print_space fmt ()
+
+(** Extract a type declaration.
+
+    Note that all the names used for extraction should already have been
+    registered.
+
+    This function should be inserted between calls to {!start_type_decl_group}
+    and {!end_type_decl_group}.
+ *)
+let extract_type_decl (ctx : extraction_ctx) (fmt : F.formatter)
+    (type_decl_group : TypeDeclId.Set.t) (kind : decl_kind) (def : type_decl) :
+    unit =
+  let extract_body =
+    match kind with
+    | SingleNonRec | SingleRec | MutRecFirst | MutRecInner | MutRecLast -> true
+    | Assumed | Declared -> false
+  in
+  if extract_body then
+    if !backend = HOL4 && is_empty_record_type_decl def then
+      extract_type_decl_hol4_empty_record ctx fmt def
+    else extract_type_decl_gen ctx fmt type_decl_group kind def extract_body
+  else
+    match !backend with
+    | FStar | Coq | Lean ->
+        extract_type_decl_gen ctx fmt type_decl_group kind def extract_body
+    | HOL4 -> extract_type_decl_hol4_opaque ctx fmt def
+
+(** Generate a [Argument] instruction in Coq to allow omitting implicit
+    arguments for variants, fields, etc..
+
+    For instance, provided we have this definition:
+    {[
+      Inductive result A :=
+      | Return : A -> result A
+      | Fail_ : error -> result A.
+    ]}
+
+    We may want to generate those instructions:
+    {[
+      Arguments Return {_} a.
+      Arguments Fail_ {_}.
+    ]}
+ *)
+let extract_coq_arguments_instruction (ctx : extraction_ctx) (fmt : F.formatter)
+    (cons_name : string) (num_implicit_params : int) : unit =
+  (* Add a break before *)
+  F.pp_print_break fmt 0 0;
+  (* Open a box *)
+  F.pp_open_hovbox fmt ctx.indent_incr;
+  F.pp_print_break fmt 0 0;
+  F.pp_print_string fmt "Arguments";
+  F.pp_print_space fmt ();
+  F.pp_print_string fmt cons_name;
+  (* Print the type/const params and the trait clauses (`{T}`) *)
+  F.pp_print_space fmt ();
+  F.pp_print_string fmt "{";
+  Collections.List.iter_times num_implicit_params (fun () ->
+      F.pp_print_space fmt ();
+      F.pp_print_string fmt "_");
+  F.pp_print_space fmt ();
+  F.pp_print_string fmt "}.";
+
+  (* Close the box *)
+  F.pp_close_box fmt ()
+
+(** Auxiliary function.
+
+    Generate [Arguments] instructions in Coq for type definitions.
+ *)
+let extract_type_decl_coq_arguments (ctx : extraction_ctx) (fmt : F.formatter)
+    (kind : decl_kind) (decl : type_decl) : unit =
+  assert (!backend = Coq);
+  (* Generating the [Arguments] instructions is useful only if there are parameters *)
+  let num_params =
+    List.length decl.generics.types
+    + List.length decl.generics.const_generics
+    + List.length decl.generics.trait_clauses
+  in
+  if num_params = 0 then ()
+  else
+    (* Generate the [Arguments] instruction *)
+    match decl.kind with
+    | Opaque -> ()
+    | Struct fields ->
+        let adt_id = AdtId decl.def_id in
+        (* Generate the instruction for the record constructor *)
+        let cons_name = ctx_get_struct adt_id ctx in
+        extract_coq_arguments_instruction ctx fmt cons_name num_params;
+        (* Generate the instruction for the record projectors, if there are *)
+        let is_rec = decl_is_from_rec_group kind in
+        if not is_rec then
+          FieldId.iteri
+            (fun fid _ ->
+              let cons_name = ctx_get_field adt_id fid ctx in
+              extract_coq_arguments_instruction ctx fmt cons_name num_params)
+            fields;
+        (* Add breaks to insert new lines between definitions *)
+        F.pp_print_break fmt 0 0
+    | Enum variants ->
+        (* Generate the instructions *)
+        VariantId.iteri
+          (fun vid (_ : variant) ->
+            let cons_name = ctx_get_variant (AdtId decl.def_id) vid ctx in
+            extract_coq_arguments_instruction ctx fmt cons_name num_params)
+          variants;
+        (* Add breaks to insert new lines between definitions *)
+        F.pp_print_break fmt 0 0
+
+(** Auxiliary function.
+
+    Generate field projectors in Coq.
+
+    Sometimes we extract records as inductives in Coq: when this happens we
+    have to define the field projectors afterwards.
+ *)
+let extract_type_decl_record_field_projectors (ctx : extraction_ctx)
+    (fmt : F.formatter) (kind : decl_kind) (decl : type_decl) : unit =
+  assert (!backend = Coq);
+  match decl.kind with
+  | Opaque | Enum _ -> ()
+  | Struct fields ->
+      (* Records are extracted as inductives only if they are recursive *)
+      let is_rec = decl_is_from_rec_group kind in
+      if is_rec then
+        (* Add the type params *)
+        let ctx, type_params, cg_params, trait_clauses =
+          ctx_add_generic_params decl.generics ctx
+        in
+        let ctx, record_var = ctx_add_var "x" (VarId.of_int 0) ctx in
+        let ctx, field_var = ctx_add_var "x" (VarId.of_int 1) ctx in
+        let def_name = ctx_get_local_type decl.def_id ctx in
+        let cons_name = ctx_get_struct (AdtId decl.def_id) ctx in
+        let extract_field_proj (field_id : FieldId.id) (_ : field) : unit =
+          F.pp_print_space fmt ();
+          (* Outer box for the projector definition *)
+          F.pp_open_hvbox fmt 0;
+          (* Inner box for the projector definition *)
+          F.pp_open_hvbox fmt ctx.indent_incr;
+          (* Open a box for the [Definition PROJ ... :=] *)
+          F.pp_open_hovbox fmt ctx.indent_incr;
+          F.pp_print_string fmt "Definition";
+          F.pp_print_space fmt ();
+          let field_name = ctx_get_field (AdtId decl.def_id) field_id ctx in
+          F.pp_print_string fmt field_name;
+          (* Print the generics *)
+          let as_implicits = true in
+          extract_generic_params ctx fmt TypeDeclId.Set.empty ~as_implicits
+            decl.generics type_params cg_params trait_clauses;
+          (* Print the record parameter *)
+          F.pp_print_space fmt ();
+          F.pp_print_string fmt "(";
+          F.pp_print_string fmt record_var;
+          F.pp_print_space fmt ();
+          F.pp_print_string fmt ":";
+          F.pp_print_space fmt ();
+          F.pp_print_string fmt def_name;
+          List.iter
+            (fun p ->
+              F.pp_print_space fmt ();
+              F.pp_print_string fmt p)
+            type_params;
+          F.pp_print_string fmt ")";
+          (* *)
+          F.pp_print_space fmt ();
+          F.pp_print_string fmt ":=";
+          (* Close the box for the [Definition PROJ ... :=] *)
+          F.pp_close_box fmt ();
+          F.pp_print_space fmt ();
+          (* Open a box for the whole match *)
+          F.pp_open_hvbox fmt 0;
+          (* Open a box for the [match ... with] *)
+          F.pp_open_hovbox fmt ctx.indent_incr;
+          F.pp_print_string fmt "match";
+          F.pp_print_space fmt ();
+          F.pp_print_string fmt record_var;
+          F.pp_print_space fmt ();
+          F.pp_print_string fmt "with";
+          (* Close the box for the [match ... with] *)
+          F.pp_close_box fmt ();
+
+          (* Open a box for the branch *)
+          F.pp_open_hovbox fmt ctx.indent_incr;
+          (* Print the match branch *)
+          F.pp_print_space fmt ();
+          F.pp_print_string fmt "|";
+          F.pp_print_space fmt ();
+          F.pp_print_string fmt cons_name;
+          FieldId.iteri
+            (fun id _ ->
+              F.pp_print_space fmt ();
+              if field_id = id then F.pp_print_string fmt field_var
+              else F.pp_print_string fmt "_")
+            fields;
+          F.pp_print_space fmt ();
+          F.pp_print_string fmt "=>";
+          F.pp_print_space fmt ();
+          F.pp_print_string fmt field_var;
+          (* Close the box for the branch *)
+          F.pp_close_box fmt ();
+          (* Print the [end] *)
+          F.pp_print_space fmt ();
+          F.pp_print_string fmt "end";
+          (* Close the box for the whole match *)
+          F.pp_close_box fmt ();
+          (* Close the inner box projector *)
+          F.pp_close_box fmt ();
+          (* If Coq: end the definition with a "." *)
+          if !backend = Coq then (
+            F.pp_print_cut fmt ();
+            F.pp_print_string fmt ".");
+          (* Close the outer box projector  *)
+          F.pp_close_box fmt ();
+          (* Add breaks to insert new lines between definitions *)
+          F.pp_print_break fmt 0 0
+        in
+
+        let extract_proj_notation (field_id : FieldId.id) (_ : field) : unit =
+          F.pp_print_space fmt ();
+          (* Outer box for the projector definition *)
+          F.pp_open_hvbox fmt 0;
+          (* Inner box for the projector definition *)
+          F.pp_open_hovbox fmt ctx.indent_incr;
+          let ctx, record_var = ctx_add_var "x" (VarId.of_int 0) ctx in
+          F.pp_print_string fmt "Notation";
+          F.pp_print_space fmt ();
+          let field_name = ctx_get_field (AdtId decl.def_id) field_id ctx in
+          F.pp_print_string fmt ("\"" ^ record_var ^ " .(" ^ field_name ^ ")\"");
+          F.pp_print_space fmt ();
+          F.pp_print_string fmt ":=";
+          F.pp_print_space fmt ();
+          F.pp_print_string fmt "(";
+          F.pp_print_string fmt field_name;
+          F.pp_print_space fmt ();
+          F.pp_print_string fmt record_var;
+          F.pp_print_string fmt ")";
+          F.pp_print_space fmt ();
+          F.pp_print_string fmt "(at level 9)";
+          (* Close the inner box projector *)
+          F.pp_close_box fmt ();
+          (* If Coq: end the definition with a "." *)
+          if !backend = Coq then (
+            F.pp_print_cut fmt ();
+            F.pp_print_string fmt ".");
+          (* Close the outer box projector  *)
+          F.pp_close_box fmt ();
+          (* Add breaks to insert new lines between definitions *)
+          F.pp_print_break fmt 0 0
+        in
+
+        let extract_field_proj_and_notation (field_id : FieldId.id)
+            (field : field) : unit =
+          extract_field_proj field_id field;
+          extract_proj_notation field_id field
+        in
+
+        FieldId.iteri extract_field_proj_and_notation fields
+
+(** Extract extra information for a type (e.g., [Arguments] instructions in Coq).
+
+    Note that all the names used for extraction should already have been
+    registered.
+ *)
+let extract_type_decl_extra_info (ctx : extraction_ctx) (fmt : F.formatter)
+    (kind : decl_kind) (decl : type_decl) : unit =
+  match !backend with
+  | FStar | Lean | HOL4 -> ()
+  | Coq ->
+      extract_type_decl_coq_arguments ctx fmt kind decl;
+      extract_type_decl_record_field_projectors ctx fmt kind decl
+
+(** Extract the state type declaration. *)
+let extract_state_type (fmt : F.formatter) (ctx : extraction_ctx)
+    (kind : decl_kind) : unit =
+  (* Add a break before *)
+  F.pp_print_break fmt 0 0;
+  (* Print a comment  *)
+  extract_comment fmt [ "The state type used in the state-error monad" ];
+  F.pp_print_break fmt 0 0;
+  (* Open a box for the definition, so that whenever possible it gets printed on
+   * one line *)
+  F.pp_open_hvbox fmt 0;
+  (* Retrieve the name *)
+  let state_name = ctx_get_assumed_type State ctx in
+  (* The syntax for Lean and Coq is almost identical. *)
+  let print_axiom () =
+    let axiom =
+      match !backend with
+      | Coq -> "Axiom"
+      | Lean -> "axiom"
+      | FStar | HOL4 -> raise (Failure "Unexpected")
+    in
+    F.pp_print_string fmt axiom;
+    F.pp_print_space fmt ();
+    F.pp_print_string fmt state_name;
+    F.pp_print_space fmt ();
+    F.pp_print_string fmt ":";
+    F.pp_print_space fmt ();
+    F.pp_print_string fmt "Type";
+    if !backend = Coq then F.pp_print_string fmt "."
+  in
+  (* The kind should be [Assumed] or [Declared] *)
+  (match kind with
+  | SingleNonRec | SingleRec | MutRecFirst | MutRecInner | MutRecLast ->
+      raise (Failure "Unexpected")
+  | Assumed -> (
+      match !backend with
+      | FStar ->
+          F.pp_print_string fmt "assume";
+          F.pp_print_space fmt ();
+          F.pp_print_string fmt "type";
+          F.pp_print_space fmt ();
+          F.pp_print_string fmt state_name;
+          F.pp_print_space fmt ();
+          F.pp_print_string fmt ":";
+          F.pp_print_space fmt ();
+          F.pp_print_string fmt "Type0"
+      | HOL4 ->
+          F.pp_print_string fmt ("val _ = new_type (\"" ^ state_name ^ "\", 0)")
+      | Coq | Lean -> print_axiom ())
+  | Declared -> (
+      match !backend with
+      | FStar ->
+          F.pp_print_string fmt "val";
+          F.pp_print_space fmt ();
+          F.pp_print_string fmt state_name;
+          F.pp_print_space fmt ();
+          F.pp_print_string fmt ":";
+          F.pp_print_space fmt ();
+          F.pp_print_string fmt "Type0"
+      | HOL4 ->
+          F.pp_print_string fmt ("val _ = new_type (\"" ^ state_name ^ "\", 0)")
+      | Coq | Lean -> print_axiom ()));
+  (* Close the box for the definition *)
+  F.pp_close_box fmt ();
+  (* Add breaks to insert new lines between definitions *)
+  F.pp_print_break fmt 0 0
diff --git a/compiler/FunsAnalysis.ml b/compiler/FunsAnalysis.ml
index b72fa078..e17ea16f 100644
--- a/compiler/FunsAnalysis.ml
+++ b/compiler/FunsAnalysis.ml
@@ -57,12 +57,26 @@ let analyze_module (m : crate) (funs_map : fun_decl FunDeclId.Map.t)
     let stateful = ref false in
     let can_diverge = ref false in
     let is_rec = ref false in
+    let group_has_builtin_info = ref false in
+
+    (* We have some specialized knowledge of some library functions; we don't
+       have any more custom treatment than this, and these functions can be modeled
+       suitably in Primitives.fst, rather than special-casing for them all the
+       way. *)
+    let get_builtin_info (f : fun_decl) : ExtractBuiltin.effect_info option =
+      let open ExtractBuiltin in
+      let name = name_to_simple_name f.name in
+      SimpleNameMap.find_opt name builtin_fun_effects_map
+    in
 
+    (* JP: Why not use a reduce visitor here with a tuple of the values to be
+       computed? *)
     let visit_fun (f : fun_decl) : unit =
       let obj =
         object (self)
           inherit [_] iter_statement as super
           method may_fail b = can_fail := !can_fail || b
+          method maybe_stateful b = stateful := !stateful || b
 
           method! visit_Assert env a =
             self#may_fail true;
@@ -70,14 +84,14 @@ let analyze_module (m : crate) (funs_map : fun_decl FunDeclId.Map.t)
 
           method! visit_rvalue _env rv =
             match rv with
-            | Use _ | Ref _ | Global _ | Discriminant _ | Aggregate _ -> ()
+            | Use _ | RvRef _ | Global _ | Discriminant _ | Aggregate _ -> ()
             | UnaryOp (uop, _) -> can_fail := EU.unop_can_fail uop || !can_fail
             | BinaryOp (bop, _, _) ->
                 can_fail := EU.binop_can_fail bop || !can_fail
 
           method! visit_Call env call =
-            (match call.func with
-            | Regular id ->
+            (match call.func.func with
+            | FunId (Regular id) ->
                 if FunDeclId.Set.mem id fun_ids then (
                   can_diverge := true;
                   is_rec := true)
@@ -86,9 +100,14 @@ let analyze_module (m : crate) (funs_map : fun_decl FunDeclId.Map.t)
                   self#may_fail info.can_fail;
                   stateful := !stateful || info.stateful;
                   can_diverge := !can_diverge || info.can_diverge
-            | Assumed id ->
+            | FunId (Assumed id) ->
                 (* None of the assumed functions can diverge nor are considered stateful *)
-                can_fail := !can_fail || Assumed.assumed_can_fail id);
+                can_fail := !can_fail || Assumed.assumed_fun_can_fail id
+            | TraitMethod _ ->
+                (* We consider trait functions can fail, but can not diverge and are not stateful.
+                   TODO: this may cause issues if we use use a fuel parameter.
+                *)
+                can_fail := true);
             super#visit_Call env call
 
           method! visit_Panic env =
@@ -102,11 +121,21 @@ let analyze_module (m : crate) (funs_map : fun_decl FunDeclId.Map.t)
       in
       (* Sanity check: global bodies don't contain stateful calls *)
       assert ((not f.is_global_decl_body) || not !stateful);
+      let builtin_info = get_builtin_info f in
+      let has_builtin_info = builtin_info <> None in
+      group_has_builtin_info := !group_has_builtin_info || has_builtin_info;
       match f.body with
       | None ->
-          (* Opaque function: we consider they fail by default *)
-          obj#may_fail true;
-          stateful := (not f.is_global_decl_body) && use_state
+          let info_can_fail, info_stateful =
+            match builtin_info with
+            | None -> (true, use_state)
+            | Some { can_fail; stateful } -> (can_fail, stateful)
+          in
+          obj#may_fail info_can_fail;
+          obj#maybe_stateful
+            (if f.is_global_decl_body then false
+             else if not use_state then false
+             else info_stateful)
       | Some body -> obj#visit_statement () body.body
     in
     List.iter visit_fun d;
@@ -114,12 +143,17 @@ let analyze_module (m : crate) (funs_map : fun_decl FunDeclId.Map.t)
      * groups containing globals contain exactly one declaration *)
     let is_global_decl_body = List.exists (fun f -> f.is_global_decl_body) d in
     assert ((not is_global_decl_body) || List.length d = 1);
+    assert ((not !group_has_builtin_info) || List.length d = 1);
     (* We ignore on purpose functions that cannot fail and consider they *can*
      * fail: the result of the analysis is not used yet to adjust the translation
      * so that the functions which syntactically can't fail don't use an error monad.
-     * However, we do keep the result of the analysis for global bodies.
+     * However, we do keep the result of the analysis for global bodies and for
+     * builtin functions which are marked as non-fallible.
      * *)
-    can_fail := (not is_global_decl_body) || !can_fail;
+    can_fail :=
+      if is_global_decl_body then !can_fail
+      else if !group_has_builtin_info then !can_fail
+      else true;
     {
       can_fail = !can_fail;
       stateful = !stateful;
@@ -141,7 +175,8 @@ let analyze_module (m : crate) (funs_map : fun_decl FunDeclId.Map.t)
   let rec analyze_decl_groups (decls : declaration_group list) : unit =
     match decls with
     | [] -> ()
-    | Type _ :: decls' -> analyze_decl_groups decls'
+    | (Type _ | TraitDecl _ | TraitImpl _) :: decls' ->
+        analyze_decl_groups decls'
     | Fun decl :: decls' ->
         analyze_fun_decl_group decl;
         analyze_decl_groups decls'
diff --git a/compiler/Interpreter.ml b/compiler/Interpreter.ml
index 154c5a21..24ff4808 100644
--- a/compiler/Interpreter.ml
+++ b/compiler/Interpreter.ml
@@ -12,55 +12,165 @@ module SA = SymbolicAst
 (** The local logger *)
 let log = L.interpreter_log
 
-let compute_type_fun_global_contexts (m : A.crate) :
-    C.type_context * C.fun_context * C.global_context =
-  let type_decls_list, _, _ = split_declarations m.declarations in
+let compute_contexts (m : A.crate) : C.decls_ctx =
+  let type_decls_list, _, _, _, _ = split_declarations m.declarations in
   let type_decls = m.types in
   let fun_decls = m.functions in
   let global_decls = m.globals in
-  let type_decls_groups, _funs_defs_groups, _globals_defs_groups =
+  let trait_decls = m.trait_decls in
+  let trait_impls = m.trait_impls in
+  let type_decls_groups, _, _, _, _ =
     split_declarations_to_group_maps m.declarations
   in
   let type_infos =
     TypesAnalysis.analyze_type_declarations type_decls type_decls_list
   in
-  let type_context = { C.type_decls_groups; type_decls; type_infos } in
-  let fun_context = { C.fun_decls } in
-  let global_context = { C.global_decls } in
-  (type_context, fun_context, global_context)
-
-let initialize_eval_context (type_context : C.type_context)
-    (fun_context : C.fun_context) (global_context : C.global_context)
-    (region_groups : T.RegionGroupId.id list) (type_vars : T.type_var list)
-    (const_generic_vars : T.const_generic_var list) : C.eval_ctx =
-  C.reset_global_counters ();
-  {
-    C.type_context;
-    C.fun_context;
-    C.global_context;
-    C.region_groups;
-    C.type_vars;
-    C.const_generic_vars;
-    C.env = [ C.Frame ];
-    C.ended_regions = T.RegionId.Set.empty;
-  }
+  let type_ctx = { C.type_decls_groups; type_decls; type_infos } in
+  let fun_infos =
+    FunsAnalysis.analyze_module m fun_decls global_decls !Config.use_state
+  in
+  let fun_ctx = { C.fun_decls; fun_infos } in
+  let global_ctx = { C.global_decls } in
+  let trait_decls_ctx = { C.trait_decls } in
+  let trait_impls_ctx = { C.trait_impls } in
+  { C.type_ctx; fun_ctx; global_ctx; trait_decls_ctx; trait_impls_ctx }
+
+(** Small helper.
+
+    Normalize an instantiated function signature provided we used this signature
+    to compute a normalization map (for the associated types) and that we added
+    it in the context.
+ *)
+let normalize_inst_fun_sig (ctx : C.eval_ctx) (sg : A.inst_fun_sig) :
+    A.inst_fun_sig =
+  let { A.regions_hierarchy = _; trait_type_constraints = _; inputs; output } =
+    sg
+  in
+  let norm = AssociatedTypes.ctx_normalize_rty ctx in
+  let inputs = List.map norm inputs in
+  let output = norm output in
+  { sg with A.inputs; output }
+
+(** Instantiate a function signature for a symbolic execution.
+
+    We return a new context because we compute and add the type normalization
+    map in the same step.
+
+    **WARNING**: this doesn't normalize the types. This step has to be done
+    separately. Remark: we need to normalize essentially because of the where
+    clauses (we are not considering a function call, so we don't need to
+    normalize because a trait clause was instantiated with a specific trait ref).
+ *)
+let symbolic_instantiate_fun_sig (ctx : C.eval_ctx) (sg : A.fun_sig)
+    (kind : A.fun_kind) : C.eval_ctx * A.inst_fun_sig =
+  let tr_self =
+    match kind with
+    | RegularKind | TraitMethodImpl _ -> T.UnknownTrait __FUNCTION__
+    | TraitMethodDecl _ | TraitMethodProvided _ -> T.Self
+  in
+  let generics =
+    let { T.regions; types; const_generics; trait_clauses } = sg.generics in
+    let regions = List.map (fun _ -> T.Erased) regions in
+    let types = List.map (fun (v : T.type_var) -> T.TypeVar v.T.index) types in
+    let const_generics =
+      List.map
+        (fun (v : T.const_generic_var) -> T.ConstGenericVar v.T.index)
+        const_generics
+    in
+    (* Annoying that we have to generate this substitution here *)
+    let r_subst _ = raise (Failure "Unexpected region") in
+    let ty_subst = Subst.make_type_subst_from_vars sg.generics.types types in
+    let cg_subst =
+      Subst.make_const_generic_subst_from_vars sg.generics.const_generics
+        const_generics
+    in
+    (* TODO: some clauses may use the types of other clauses, so we may have to
+       reorder them.
+
+       Example:
+       If in Rust we write:
+       {[
+         pub fn use_get<'a, T: Get>(x: &'a mut T) -> u32
+         where
+             T::Item: ToU32,
+         {
+             x.get().to_u32()
+         }
+       ]}
+
+       In LLBC we get:
+       {[
+         fn demo::use_get<'a, T>(@1: &'a mut (T)) -> u32
+         where
+             [@TraitClause0]: demo::Get<T>,
+             [@TraitClause1]: demo::ToU32<@TraitClause0::Item>, // HERE
+         {
+             ... // Omitted
+         }
+       ]}
+    *)
+    (* We will need to update the trait refs map while we perform the instantiations *)
+    let mk_tr_subst
+        (tr_map : T.erased_region T.trait_instance_id T.TraitClauseId.Map.t)
+        clause_id : T.erased_region T.trait_instance_id =
+      match T.TraitClauseId.Map.find_opt clause_id tr_map with
+      | Some tr -> tr
+      | None -> raise (Failure "Local trait clause not found")
+    in
+    let mk_subst tr_map =
+      let tr_subst = mk_tr_subst tr_map in
+      { Subst.r_subst; ty_subst; cg_subst; tr_subst; tr_self }
+    in
+    let _, trait_refs =
+      List.fold_left_map
+        (fun tr_map (c : T.trait_clause) ->
+          let subst = mk_subst tr_map in
+          let { T.trait_id = trait_decl_id; generics; _ } = c in
+          let generics = Subst.generic_args_substitute subst generics in
+          let trait_decl_ref = { T.trait_decl_id; decl_generics = generics } in
+          (* Note that because we directly refer to the clause, we give it
+             empty generics *)
+          let trait_id = T.Clause c.clause_id in
+          let trait_ref =
+            {
+              T.trait_id;
+              generics = TypesUtils.mk_empty_generic_args;
+              trait_decl_ref;
+            }
+          in
+          (* Update the traits map *)
+          let tr_map = T.TraitClauseId.Map.add c.T.clause_id trait_id tr_map in
+          (tr_map, trait_ref))
+        T.TraitClauseId.Map.empty trait_clauses
+    in
+    { T.regions; types; const_generics; trait_refs }
+  in
+  let inst_sg = instantiate_fun_sig ctx generics tr_self sg in
+  (* Compute the normalization maps *)
+  let ctx =
+    AssociatedTypes.ctx_add_norm_trait_types_from_preds ctx
+      inst_sg.trait_type_constraints
+  in
+  (* Normalize the signature *)
+  let inst_sg = normalize_inst_fun_sig ctx inst_sg in
+  (* Return *)
+  (ctx, inst_sg)
 
 (** Initialize an evaluation context to execute a function.
 
-      Introduces local variables initialized in the following manner:
-      - input arguments are initialized as symbolic values
-      - the remaining locals are initialized as [⊥]
-      Abstractions are introduced for the regions present in the function
-      signature.
-      
-      We return:
-      - the initialized evaluation context
-      - the list of symbolic values introduced for the input values
-      - the instantiated function signature
+    Introduces local variables initialized in the following manner:
+    - input arguments are initialized as symbolic values
+    - the remaining locals are initialized as [⊥]
+    Abstractions are introduced for the regions present in the function
+    signature.
+
+    We return:
+    - the initialized evaluation context
+    - the list of symbolic values introduced for the input values
+    - the instantiated function signature
  *)
-let initialize_symbolic_context_for_fun (type_context : C.type_context)
-    (fun_context : C.fun_context) (global_context : C.global_context)
-    (fdef : A.fun_decl) : C.eval_ctx * V.symbolic_value list * A.inst_fun_sig =
+let initialize_symbolic_context_for_fun (ctx : C.decls_ctx) (fdef : A.fun_decl)
+    : C.eval_ctx * V.symbolic_value list * A.inst_fun_sig =
   (* The abstractions are not initialized the same way as for function
    * calls: they contain *loan* projectors, because they "provide" us
    * with the input values (which behave as if they had been returned
@@ -78,19 +188,15 @@ let initialize_symbolic_context_for_fun (type_context : C.type_context)
     List.map (fun (g : T.region_var_group) -> g.id) sg.regions_hierarchy
   in
   let ctx =
-    initialize_eval_context type_context fun_context global_context
-      region_groups sg.type_params sg.const_generic_params
+    initialize_eval_context ctx region_groups sg.generics.types
+      sg.generics.const_generics
   in
-  (* Instantiate the signature *)
-  let type_params =
-    List.map (fun (v : T.type_var) -> T.TypeVar v.T.index) sg.type_params
+  (* Instantiate the signature. This updates the context because we compute
+     at the same time the normalization map for the associated types.
+  *)
+  let ctx, inst_sg =
+    symbolic_instantiate_fun_sig ctx fdef.signature fdef.kind
   in
-  let cg_params =
-    List.map
-      (fun (v : T.const_generic_var) -> T.ConstGenericVar v.T.index)
-      sg.const_generic_params
-  in
-  let inst_sg = instantiate_fun_sig type_params cg_params sg in
   (* Create fresh symbolic values for the inputs *)
   let input_svs =
     List.map (fun ty -> mk_fresh_symbolic_value V.SynthInput ty) inst_sg.inputs
@@ -165,15 +271,9 @@ let evaluate_function_symbolic_synthesize_backward_from_return
    * an instantiation of the signature, so that we use fresh
    * region ids for the return abstractions. *)
   let sg = fdef.signature in
-  let type_params =
-    List.map (fun (v : T.type_var) -> T.TypeVar v.T.index) sg.type_params
-  in
-  let cg_params =
-    List.map
-      (fun (v : T.const_generic_var) -> T.ConstGenericVar v.T.index)
-      sg.const_generic_params
+  let _, ret_inst_sg =
+    symbolic_instantiate_fun_sig ctx fdef.signature fdef.kind
   in
-  let ret_inst_sg = instantiate_fun_sig type_params cg_params sg in
   let ret_rty = ret_inst_sg.output in
   (* Move the return value out of the return variable *)
   let pop_return_value = is_regular_return in
@@ -347,19 +447,14 @@ let evaluate_function_symbolic_synthesize_backward_from_return
       for the synthesis)
     - the symbolic AST generated by the symbolic execution
  *)
-let evaluate_function_symbolic (synthesize : bool)
-    (type_context : C.type_context) (fun_context : C.fun_context)
-    (global_context : C.global_context) (fdef : A.fun_decl) :
-    V.symbolic_value list * SA.expression option =
+let evaluate_function_symbolic (synthesize : bool) (ctx : C.decls_ctx)
+    (fdef : A.fun_decl) : V.symbolic_value list * SA.expression option =
   (* Debug *)
   let name_to_string () = Print.fun_name_to_string fdef.A.name in
   log#ldebug (lazy ("evaluate_function_symbolic: " ^ name_to_string ()));
 
   (* Create the evaluation context *)
-  let ctx, input_svs, inst_sg =
-    initialize_symbolic_context_for_fun type_context fun_context global_context
-      fdef
-  in
+  let ctx, input_svs, inst_sg = initialize_symbolic_context_for_fun ctx fdef in
 
   (* Create the continuation to finish the evaluation *)
   let config = C.mk_config C.SymbolicMode in
@@ -488,7 +583,8 @@ module Test = struct
   (** Test a unit function (taking no arguments) by evaluating it in an empty
       environment.
    *)
-  let test_unit_function (crate : A.crate) (fid : A.FunDeclId.id) : unit =
+  let test_unit_function (crate : A.crate) (decls_ctx : C.decls_ctx)
+      (fid : A.FunDeclId.id) : unit =
     (* Retrieve the function declaration *)
     let fdef = A.FunDeclId.Map.find fid crate.functions in
     let body = Option.get fdef.body in
@@ -498,17 +594,11 @@ module Test = struct
       (lazy ("test_unit_function: " ^ Print.fun_name_to_string fdef.A.name));
 
     (* Sanity check - *)
-    assert (List.length fdef.A.signature.region_params = 0);
-    assert (List.length fdef.A.signature.type_params = 0);
+    assert (fdef.A.signature.generics = TypesUtils.mk_empty_generic_params);
     assert (body.A.arg_count = 0);
 
     (* Create the evaluation context *)
-    let type_context, fun_context, global_context =
-      compute_type_fun_global_contexts crate
-    in
-    let ctx =
-      initialize_eval_context type_context fun_context global_context [] [] []
-    in
+    let ctx = initialize_eval_context decls_ctx [] [] [] in
 
     (* Insert the (uninitialized) local variables *)
     let ctx = C.ctx_push_uninitialized_vars ctx body.A.locals in
@@ -536,9 +626,7 @@ module Test = struct
       (no parameters, no arguments) - TODO: move *)
   let fun_decl_is_transparent_unit (def : A.fun_decl) : bool =
     Option.is_some def.body
-    && def.A.signature.region_params = []
-    && def.A.signature.type_params = []
-    && def.A.signature.const_generic_params = []
+    && def.A.signature.generics = TypesUtils.mk_empty_generic_params
     && def.A.signature.inputs = []
 
   (** Test all the unit functions in a list of function definitions *)
@@ -548,24 +636,9 @@ module Test = struct
         (fun _ -> fun_decl_is_transparent_unit)
         crate.functions
     in
+    let decls_ctx = compute_contexts crate in
     let test_unit_fun _ (def : A.fun_decl) : unit =
-      test_unit_function crate def.A.def_id
+      test_unit_function crate decls_ctx def.A.def_id
     in
     A.FunDeclId.Map.iter test_unit_fun unit_funs
-
-  (** Execute the symbolic interpreter on a function. *)
-  let test_function_symbolic (synthesize : bool) (type_context : C.type_context)
-      (fun_context : C.fun_context) (global_context : C.global_context)
-      (fdef : A.fun_decl) : unit =
-    (* Debug *)
-    log#ldebug
-      (lazy ("test_function_symbolic: " ^ Print.fun_name_to_string fdef.A.name));
-
-    (* Evaluate *)
-    let _ =
-      evaluate_function_symbolic synthesize type_context fun_context
-        global_context fdef
-    in
-
-    ()
 end
diff --git a/compiler/InterpreterBorrows.ml b/compiler/InterpreterBorrows.ml
index 4d67a4e4..e97795a1 100644
--- a/compiler/InterpreterBorrows.ml
+++ b/compiler/InterpreterBorrows.ml
@@ -452,7 +452,8 @@ let give_back_symbolic_value (_config : C.config)
   | V.SynthInputGivenBack | SynthRetGivenBack | FunCallGivenBack | LoopGivenBack
     ->
       ()
-  | FunCallRet | SynthInput | Global | LoopOutput | LoopJoin | Aggregate ->
+  | FunCallRet | SynthInput | Global | LoopOutput | LoopJoin | Aggregate
+  | ConstGeneric | TraitConst ->
       raise (Failure "Unreachable"));
   (* Store the given-back value as a meta-value for synthesis purposes *)
   let mv = nsv in
diff --git a/compiler/InterpreterBorrowsCore.ml b/compiler/InterpreterBorrowsCore.ml
index bf083aa4..e7da045c 100644
--- a/compiler/InterpreterBorrowsCore.ml
+++ b/compiler/InterpreterBorrowsCore.ml
@@ -100,15 +100,18 @@ let rec compare_rtys (default : bool) (combine : bool -> bool -> bool)
     (compare_regions : T.RegionId.id T.region -> T.RegionId.id T.region -> bool)
     (ty1 : T.rty) (ty2 : T.rty) : bool =
   let compare = compare_rtys default combine compare_regions in
+  (* Normalize the associated types *)
   match (ty1, ty2) with
   | T.Literal lit1, T.Literal lit2 ->
       assert (lit1 = lit2);
       default
-  | T.Adt (id1, regions1, tys1, cgs1), T.Adt (id2, regions2, tys2, cgs2) ->
+  | T.Adt (id1, generics1), T.Adt (id2, generics2) ->
       assert (id1 = id2);
       (* There are no regions in the const generics, so we ignore them,
          but we still check they are the same, for sanity *)
-      assert (cgs1 = cgs2);
+      assert (generics1.const_generics = generics2.const_generics);
+
+      (* We also ignore the trait refs *)
 
       (* The check for the ADTs is very crude: we simply compare the arguments
        * two by two.
@@ -123,14 +126,14 @@ let rec compare_rtys (default : bool) (combine : bool -> bool -> bool)
        * this check would still be a reasonable conservative approximation. *)
 
       (* Check the region parameters *)
-      let regions = List.combine regions1 regions2 in
+      let regions = List.combine generics1.regions generics2.regions in
       let params_b =
         List.fold_left
           (fun b (r1, r2) -> combine b (compare_regions r1 r2))
           default regions
       in
       (* Check the type parameters *)
-      let tys = List.combine tys1 tys2 in
+      let tys = List.combine generics1.types generics2.types in
       let tys_b =
         List.fold_left
           (fun b (ty1, ty2) -> combine b (compare ty1 ty2))
@@ -150,6 +153,11 @@ let rec compare_rtys (default : bool) (combine : bool -> bool -> bool)
   | T.TypeVar id1, T.TypeVar id2 ->
       assert (id1 = id2);
       default
+  | T.TraitType _, T.TraitType _ ->
+      (* The types should have been normalized. If after normalization we
+         get trait types, we can consider them as variables *)
+      assert (ty1 = ty2);
+      default
   | _ ->
       log#lerror
         (lazy
diff --git a/compiler/InterpreterExpansion.ml b/compiler/InterpreterExpansion.ml
index 81e73e3e..b267bb51 100644
--- a/compiler/InterpreterExpansion.ml
+++ b/compiler/InterpreterExpansion.ml
@@ -9,6 +9,7 @@ module V = Values
 module E = Expressions
 module C = Contexts
 module Subst = Substitute
+module Assoc = AssociatedTypes
 module L = Logging
 open TypesUtils
 module Inv = Invariants
@@ -204,7 +205,7 @@ let apply_symbolic_expansion_non_borrow (config : C.config)
   apply_symbolic_expansion_to_avalues config allow_reborrows original_sv
     expansion ctx
 
-(** Compute the expansion of a non-assumed (i.e.: not [Option], [Box], etc.)
+(** Compute the expansion of a non-assumed (i.e.: not [Box], etc.)
     adt value.
 
     The function might return a list of values if the symbolic value to expand
@@ -214,18 +215,15 @@ let apply_symbolic_expansion_non_borrow (config : C.config)
     doesn't allow the expansion of enumerations *containing several variants*.
  *)
 let compute_expanded_symbolic_non_assumed_adt_value (expand_enumerations : bool)
-    (kind : V.sv_kind) (def_id : T.TypeDeclId.id)
-    (regions : T.RegionId.id T.region list) (types : T.rty list)
-    (cgs : T.const_generic list) (ctx : C.eval_ctx) : V.symbolic_expansion list
-    =
+    (kind : V.sv_kind) (def_id : T.TypeDeclId.id) (generics : T.rgeneric_args)
+    (ctx : C.eval_ctx) : V.symbolic_expansion list =
   (* Lookup the definition and check if it is an enumeration with several
    * variants *)
   let def = C.ctx_lookup_type_decl ctx def_id in
-  assert (List.length regions = List.length def.T.region_params);
+  assert (List.length generics.regions = List.length def.T.generics.regions);
   (* Retrieve, for every variant, the list of its instantiated field types *)
   let variants_fields_types =
-    Subst.type_decl_get_instantiated_variants_fields_rtypes def regions types
-      cgs
+    Assoc.type_decl_get_inst_norm_variants_fields_rtypes ctx def generics
   in
   (* Check if there is strictly more than one variant *)
   if List.length variants_fields_types > 1 && not expand_enumerations then
@@ -243,17 +241,6 @@ let compute_expanded_symbolic_non_assumed_adt_value (expand_enumerations : bool)
   (* Initialize all the expanded values of all the variants *)
   List.map initialize variants_fields_types
 
-(** Compute the expansion of an Option value.
- *)
-let compute_expanded_symbolic_option_value (expand_enumerations : bool)
-    (kind : V.sv_kind) (ty : T.rty) : V.symbolic_expansion list =
-  assert expand_enumerations;
-  let some_se =
-    V.SeAdt (Some T.option_some_id, [ mk_fresh_symbolic_value kind ty ])
-  in
-  let none_se = V.SeAdt (Some T.option_none_id, []) in
-  [ none_se; some_se ]
-
 let compute_expanded_symbolic_tuple_value (kind : V.sv_kind)
     (field_types : T.rty list) : V.symbolic_expansion =
   (* Generate the field values *)
@@ -280,17 +267,14 @@ let compute_expanded_symbolic_box_value (kind : V.sv_kind) (boxed_ty : T.rty) :
     doesn't allow the expansion of enumerations *containing several variants*.
  *)
 let compute_expanded_symbolic_adt_value (expand_enumerations : bool)
-    (kind : V.sv_kind) (adt_id : T.type_id)
-    (regions : T.RegionId.id T.region list) (types : T.rty list)
-    (cgs : T.const_generic list) (ctx : C.eval_ctx) : V.symbolic_expansion list
-    =
-  match (adt_id, regions, types) with
+    (kind : V.sv_kind) (adt_id : T.type_id) (generics : T.rgeneric_args)
+    (ctx : C.eval_ctx) : V.symbolic_expansion list =
+  match (adt_id, generics.regions, generics.types) with
   | T.AdtId def_id, _, _ ->
       compute_expanded_symbolic_non_assumed_adt_value expand_enumerations kind
-        def_id regions types cgs ctx
-  | T.Tuple, [], _ -> [ compute_expanded_symbolic_tuple_value kind types ]
-  | T.Assumed T.Option, [], [ ty ] ->
-      compute_expanded_symbolic_option_value expand_enumerations kind ty
+        def_id generics ctx
+  | T.Tuple, [], _ ->
+      [ compute_expanded_symbolic_tuple_value kind generics.types ]
   | T.Assumed T.Box, [], [ boxed_ty ] ->
       [ compute_expanded_symbolic_box_value kind boxed_ty ]
   | _ ->
@@ -543,12 +527,12 @@ let expand_symbolic_value_no_branching (config : C.config)
    fun cf ctx ->
     match rty with
     (* ADTs *)
-    | T.Adt (adt_id, regions, types, cgs) ->
+    | T.Adt (adt_id, generics) ->
         (* Compute the expanded value *)
         let allow_branching = false in
         let seel =
           compute_expanded_symbolic_adt_value allow_branching sv.sv_kind adt_id
-            regions types cgs ctx
+            generics ctx
         in
         (* There should be exacly one branch *)
         let see = Collections.List.to_cons_nil seel in
@@ -600,12 +584,12 @@ let expand_symbolic_adt (config : C.config) (sv : V.symbolic_value)
   (* Execute *)
   match rty with
   (* ADTs *)
-  | T.Adt (adt_id, regions, types, cgs) ->
+  | T.Adt (adt_id, generics) ->
       let allow_branching = true in
       (* Compute the expanded value *)
       let seel =
         compute_expanded_symbolic_adt_value allow_branching sv.sv_kind adt_id
-          regions types cgs ctx
+          generics ctx
       in
       (* Apply *)
       let seel = List.map (fun see -> (Some see, cf_branches)) seel in
@@ -679,7 +663,7 @@ let greedy_expand_symbolics_with_borrows (config : C.config) : cm_fun =
           ^ symbolic_value_to_string ctx sv));
       let cc : cm_fun =
         match sv.V.sv_ty with
-        | T.Adt (AdtId def_id, _, _, _) ->
+        | T.Adt (AdtId def_id, _) ->
             (* {!expand_symbolic_value_no_branching} checks if there are branchings,
              * but we prefer to also check it here - this leads to cleaner messages
              * and debugging *)
@@ -704,16 +688,17 @@ let greedy_expand_symbolics_with_borrows (config : C.config) : cm_fun =
                      [config]): "
                    ^ Print.name_to_string def.name))
             else expand_symbolic_value_no_branching config sv None
-        | T.Adt ((Tuple | Assumed Box), _, _, _) | T.Ref (_, _, _) ->
+        | T.Adt ((Tuple | Assumed Box), _) | T.Ref (_, _, _) ->
             (* Ok *)
             expand_symbolic_value_no_branching config sv None
-        | T.Adt (Assumed (Vec | Option | Array | Slice | Str | Range), _, _, _)
-          ->
+        | T.Adt (Assumed (Array | Slice | Str), _) ->
             (* We can't expand those *)
             raise
               (Failure
                  "Attempted to greedily expand an ADT which can't be expanded ")
-        | T.TypeVar _ | T.Literal _ | Never -> raise (Failure "Unreachable")
+        | T.TypeVar _ | T.Literal _ | Never | T.TraitType _ | T.Arrow _
+        | T.RawPtr _ ->
+            raise (Failure "Unreachable")
       in
       (* Compose and continue *)
       comp cc expand cf ctx
diff --git a/compiler/InterpreterExpressions.ml b/compiler/InterpreterExpressions.ml
index 8b2070c6..245f3b77 100644
--- a/compiler/InterpreterExpressions.ml
+++ b/compiler/InterpreterExpressions.ml
@@ -7,6 +7,7 @@ module E = Expressions
 open Utils
 module C = Contexts
 module Subst = Substitute
+module Assoc = AssociatedTypes
 module L = Logging
 open TypesUtils
 open ValuesUtils
@@ -141,11 +142,19 @@ let rec copy_value (allow_adt_copy : bool) (config : C.config)
   | V.Adt av ->
       (* Sanity check *)
       (match v.V.ty with
-      | T.Adt (T.Assumed (T.Box | Vec), _, _, _) ->
+      | T.Adt (T.Assumed T.Box, _) ->
           raise (Failure "Can't copy an assumed value other than Option")
-      | T.Adt (T.AdtId _, _, _, _) -> assert allow_adt_copy
-      | T.Adt ((T.Assumed Option | T.Tuple), _, _, _) -> () (* Ok *)
-      | T.Adt (T.Assumed (Slice | T.Array), [], [ ty ], []) ->
+      | T.Adt (T.AdtId _, _) as ty ->
+          assert (allow_adt_copy || ty_is_primitively_copyable ty)
+      | T.Adt (T.Tuple, _) -> () (* Ok *)
+      | T.Adt
+          ( T.Assumed (Slice | T.Array),
+            {
+              regions = [];
+              types = [ ty ];
+              const_generics = [];
+              trait_refs = [];
+            } ) ->
           assert (ty_is_primitively_copyable ty)
       | _ -> raise (Failure "Unreachable"));
       let ctx, fields =
@@ -230,17 +239,16 @@ let prepare_eval_operand_reorganize (config : C.config) (op : E.operand) :
   let prepare : cm_fun =
    fun cf ctx ->
     match op with
-    | Expressions.Constant (ty, cv) ->
+    | E.Constant _ ->
         (* No need to reorganize the context *)
-        literal_to_typed_value (TypesUtils.ty_as_literal ty) cv |> ignore;
         cf ctx
-    | Expressions.Copy p ->
+    | E.Copy p ->
         (* Access the value *)
         let access = Read in
         (* Expand the symbolic values, if necessary *)
         let expand_prim_copy = true in
         access_rplace_reorganize config expand_prim_copy access p cf ctx
-    | Expressions.Move p ->
+    | E.Move p ->
         (* Access the value *)
         let access = Move in
         let expand_prim_copy = false in
@@ -260,9 +268,71 @@ let eval_operand_no_reorganize (config : C.config) (op : E.operand)
      ^ "\n- ctx:\n" ^ eval_ctx_to_string ctx ^ "\n"));
   (* Evaluate *)
   match op with
-  | Expressions.Constant (ty, cv) ->
-      cf (literal_to_typed_value (TypesUtils.ty_as_literal ty) cv) ctx
-  | Expressions.Copy p ->
+  | E.Constant cv -> (
+      match cv.value with
+      | E.CLiteral lit ->
+          cf (literal_to_typed_value (TypesUtils.ty_as_literal cv.ty) lit) ctx
+      | E.CTraitConst (trait_ref, generics, const_name) -> (
+          assert (generics = TypesUtils.mk_empty_generic_args);
+          match trait_ref.trait_id with
+          | T.TraitImpl _ ->
+              (* This shouldn't happen: if we refer to a concrete implementation, we
+                 should directly refer to the top-level constant *)
+              raise (Failure "Unreachable")
+          | _ -> (
+              (* We refer to a constant defined in a local clause: simply
+                 introduce a fresh symbolic value *)
+              let ctx0 = ctx in
+              (* Lookup the trait declaration to retrieve the type of the symbolic value *)
+              let trait_decl =
+                C.ctx_lookup_trait_decl ctx
+                  trait_ref.trait_decl_ref.trait_decl_id
+              in
+              let _, (ty, _) =
+                List.find (fun (name, _) -> name = const_name) trait_decl.consts
+              in
+              (* Introduce a fresh symbolic value *)
+              let v = mk_fresh_symbolic_typed_value_from_ety V.TraitConst ty in
+              (* Continue the evaluation *)
+              let e = cf v ctx in
+              (* We have to wrap the generated expression *)
+              match e with
+              | None -> None
+              | Some e ->
+                  Some
+                    (SymbolicAst.IntroSymbolic
+                       ( ctx0,
+                         None,
+                         value_as_symbolic v.value,
+                         SymbolicAst.TraitConstValue
+                           (trait_ref, generics, const_name),
+                         e ))))
+      | E.CVar vid -> (
+          let ctx0 = ctx in
+          (* Lookup the const generic value *)
+          let cv = C.ctx_lookup_const_generic_value ctx vid in
+          (* Copy the value *)
+          let allow_adt_copy = false in
+          let ctx, v = copy_value allow_adt_copy config ctx cv in
+          (* Continue *)
+          let e = cf v ctx in
+          (* We have to wrap the generated expression *)
+          match e with
+          | None -> None
+          | Some e ->
+              (* If we are synthesizing a symbolic AST, it means that we are in symbolic
+                 mode: the value of the const generic is necessarily symbolic. *)
+              assert (is_symbolic cv.V.value);
+              (* *)
+              Some
+                (SymbolicAst.IntroSymbolic
+                   ( ctx0,
+                     None,
+                     value_as_symbolic v.value,
+                     SymbolicAst.ConstGenericValue vid,
+                     e )))
+      | E.CFnPtr _ -> raise (Failure "TODO"))
+  | E.Copy p ->
       (* Access the value *)
       let access = Read in
       let cc = read_place access p in
@@ -283,7 +353,7 @@ let eval_operand_no_reorganize (config : C.config) (op : E.operand)
       in
       (* Compose and apply *)
       comp cc copy cf ctx
-  | Expressions.Move p ->
+  | E.Move p ->
       (* Access the value *)
       let access = Move in
       let cc = read_place access p in
@@ -358,7 +428,7 @@ let eval_unary_op_concrete (config : C.config) (unop : E.unop) (op : E.operand)
         match mk_scalar sv.int_ty i with
         | Error _ -> cf (Error EPanic)
         | Ok sv -> cf (Ok { v with V.value = V.Literal (PV.Scalar sv) }))
-    | E.Cast (src_ty, tgt_ty), V.Literal (PV.Scalar sv) -> (
+    | E.Cast (E.CastInteger (src_ty, tgt_ty)), V.Literal (PV.Scalar sv) -> (
         assert (src_ty = sv.int_ty);
         let i = sv.PV.value in
         match mk_scalar tgt_ty i with
@@ -384,7 +454,7 @@ let eval_unary_op_symbolic (config : C.config) (unop : E.unop) (op : E.operand)
       match (unop, v.V.ty) with
       | E.Not, (T.Literal Bool as lty) -> lty
       | E.Neg, (T.Literal (Integer _) as lty) -> lty
-      | E.Cast (_, tgt_ty), _ -> T.Literal (Integer tgt_ty)
+      | E.Cast (E.CastInteger (_, tgt_ty)), _ -> T.Literal (Integer tgt_ty)
       | _ -> raise (Failure "Invalid input for unop")
     in
     let res_sv =
@@ -653,73 +723,46 @@ let eval_rvalue_aggregate (config : C.config)
    fun ctx ->
     (* Match on the aggregate kind *)
     match aggregate_kind with
-    | E.AggregatedTuple ->
-        let tys = List.map (fun (v : V.typed_value) -> v.V.ty) values in
-        let v = V.Adt { variant_id = None; field_values = values } in
-        let ty = T.Adt (T.Tuple, [], tys, []) in
-        let aggregated : V.typed_value = { V.value = v; ty } in
-        (* Call the continuation *)
-        cf aggregated ctx
-    | E.AggregatedOption (variant_id, ty) ->
-        (* Sanity check *)
-        if variant_id = T.option_none_id then assert (values = [])
-        else if variant_id = T.option_some_id then
-          assert (List.length values = 1)
-        else raise (Failure "Unreachable");
-        (* Construt the value *)
-        let aty = T.Adt (T.Assumed T.Option, [], [ ty ], []) in
-        let av : V.adt_value =
-          { V.variant_id = Some variant_id; V.field_values = values }
-        in
-        let aggregated : V.typed_value = { V.value = Adt av; ty = aty } in
-        (* Call the continuation *)
-        cf aggregated ctx
-    | E.AggregatedAdt (def_id, opt_variant_id, regions, types, cgs) ->
-        (* Sanity checks *)
-        let type_decl = C.ctx_lookup_type_decl ctx def_id in
-        assert (List.length type_decl.region_params = List.length regions);
-        let expected_field_types =
-          Subst.ctx_adt_get_instantiated_field_etypes ctx def_id opt_variant_id
-            types cgs
-        in
-        assert (
-          expected_field_types
-          = List.map (fun (v : V.typed_value) -> v.V.ty) values);
-        (* Construct the value *)
-        let av : V.adt_value =
-          { V.variant_id = opt_variant_id; V.field_values = values }
-        in
-        let aty = T.Adt (T.AdtId def_id, regions, types, cgs) in
-        let aggregated : V.typed_value = { V.value = Adt av; ty = aty } in
-        (* Call the continuation *)
-        cf aggregated ctx
-    | E.AggregatedRange ety ->
-        (* There should be two fields exactly *)
-        let v0, v1 =
-          match values with
-          | [ v0; v1 ] -> (v0, v1)
-          | _ -> raise (Failure "Unreachable")
-        in
-        (* Ranges are parametric over the type of indices. For now we only
-           support scalars, which can be of any type *)
-        assert (literal_type_is_integer (ty_as_literal ety));
-        assert (v0.ty = ety);
-        assert (v1.ty = ety);
-        (* Construct the value *)
-        let av : V.adt_value =
-          { V.variant_id = None; V.field_values = values }
-        in
-        let aty = T.Adt (T.Assumed T.Range, [], [ ety ], []) in
-        let aggregated : V.typed_value = { V.value = Adt av; ty = aty } in
-        (* Call the continuation *)
-        cf aggregated ctx
+    | E.AggregatedAdt (type_id, opt_variant_id, generics) -> (
+        match type_id with
+        | Tuple ->
+            let tys = List.map (fun (v : V.typed_value) -> v.V.ty) values in
+            let v = V.Adt { variant_id = None; field_values = values } in
+            let generics = TypesUtils.mk_generic_args [] tys [] [] in
+            let ty = T.Adt (T.Tuple, generics) in
+            let aggregated : V.typed_value = { V.value = v; ty } in
+            (* Call the continuation *)
+            cf aggregated ctx
+        | AdtId def_id ->
+            (* Sanity checks *)
+            let type_decl = C.ctx_lookup_type_decl ctx def_id in
+            assert (
+              List.length type_decl.generics.regions
+              = List.length generics.regions);
+            let expected_field_types =
+              Assoc.ctx_adt_get_inst_norm_field_etypes ctx def_id opt_variant_id
+                generics
+            in
+            assert (
+              expected_field_types
+              = List.map (fun (v : V.typed_value) -> v.V.ty) values);
+            (* Construct the value *)
+            let av : V.adt_value =
+              { V.variant_id = opt_variant_id; V.field_values = values }
+            in
+            let aty = T.Adt (T.AdtId def_id, generics) in
+            let aggregated : V.typed_value = { V.value = Adt av; ty = aty } in
+            (* Call the continuation *)
+            cf aggregated ctx
+        | Assumed _ -> raise (Failure "Unreachable"))
     | E.AggregatedArray (ety, cg) -> (
         (* Sanity check: all the values have the proper type *)
         assert (List.for_all (fun (v : V.typed_value) -> v.V.ty = ety) values);
         (* Sanity check: the number of values is consistent with the length *)
         let len = (literal_as_scalar (const_generic_as_literal cg)).value in
         assert (len = Z.of_int (List.length values));
-        let ty = T.Adt (T.Assumed T.Array, [], [ ety ], [ cg ]) in
+        let generics = TypesUtils.mk_generic_args [] [ ety ] [ cg ] [] in
+        let ty = T.Adt (T.Assumed T.Array, generics) in
         (* In order to generate a better AST, we introduce a symbolic
            value equal to the array. The reason is that otherwise, the
            array we introduce here might be duplicated in the generated
@@ -752,7 +795,7 @@ let eval_rvalue_not_global (config : C.config) (rvalue : E.rvalue)
   (* Delegate to the proper auxiliary function *)
   match rvalue with
   | E.Use op -> comp_wrap (eval_operand config op) ctx
-  | E.Ref (p, bkind) -> comp_wrap (eval_rvalue_ref config p bkind) ctx
+  | E.RvRef (p, bkind) -> comp_wrap (eval_rvalue_ref config p bkind) ctx
   | E.UnaryOp (unop, op) -> eval_unary_op config unop op cf ctx
   | E.BinaryOp (binop, op1, op2) -> eval_binary_op config binop op1 op2 cf ctx
   | E.Aggregate (aggregate_kind, ops) ->
diff --git a/compiler/InterpreterLoopsJoinCtxs.ml b/compiler/InterpreterLoopsJoinCtxs.ml
index bf88e055..6d3ecb18 100644
--- a/compiler/InterpreterLoopsJoinCtxs.ml
+++ b/compiler/InterpreterLoopsJoinCtxs.ml
@@ -554,9 +554,15 @@ let join_ctxs (loop_id : V.LoopId.id) (fixed_ids : ids_sets) (ctx0 : C.eval_ctx)
       C.type_context;
       fun_context;
       global_context;
+      trait_decls_context;
+      trait_impls_context;
       region_groups;
       type_vars;
       const_generic_vars;
+      const_generic_vars_map;
+      norm_trait_etypes;
+      norm_trait_rtypes;
+      norm_trait_stypes;
       env = _;
       ended_regions = ended_regions0;
     } =
@@ -566,9 +572,15 @@ let join_ctxs (loop_id : V.LoopId.id) (fixed_ids : ids_sets) (ctx0 : C.eval_ctx)
       C.type_context = _;
       fun_context = _;
       global_context = _;
+      trait_decls_context = _;
+      trait_impls_context = _;
       region_groups = _;
       type_vars = _;
       const_generic_vars = _;
+      const_generic_vars_map = _;
+      norm_trait_etypes = _;
+      norm_trait_rtypes = _;
+      norm_trait_stypes = _;
       env = _;
       ended_regions = ended_regions1;
     } =
@@ -580,9 +592,15 @@ let join_ctxs (loop_id : V.LoopId.id) (fixed_ids : ids_sets) (ctx0 : C.eval_ctx)
         C.type_context;
         fun_context;
         global_context;
+        trait_decls_context;
+        trait_impls_context;
         region_groups;
         type_vars;
         const_generic_vars;
+        const_generic_vars_map;
+        norm_trait_etypes;
+        norm_trait_rtypes;
+        norm_trait_stypes;
         env;
         ended_regions;
       }
diff --git a/compiler/InterpreterLoopsMatchCtxs.ml b/compiler/InterpreterLoopsMatchCtxs.ml
index 9248e513..8cab546e 100644
--- a/compiler/InterpreterLoopsMatchCtxs.ml
+++ b/compiler/InterpreterLoopsMatchCtxs.ml
@@ -149,20 +149,25 @@ let rec match_types (match_distinct_types : 'r T.ty -> 'r T.ty -> 'r T.ty)
     (match_regions : 'r -> 'r -> 'r) (ty0 : 'r T.ty) (ty1 : 'r T.ty) : 'r T.ty =
   let match_rec = match_types match_distinct_types match_regions in
   match (ty0, ty1) with
-  | Adt (id0, regions0, tys0, cgs0), Adt (id1, regions1, tys1, cgs1) ->
+  | Adt (id0, generics0), Adt (id1, generics1) ->
       assert (id0 = id1);
-      assert (cgs0 = cgs1);
+      assert (generics0.const_generics = generics1.const_generics);
+      assert (generics0.trait_refs = generics1.trait_refs);
       let id = id0 in
-      let cgs = cgs1 in
+      let const_generics = generics1.const_generics in
+      let trait_refs = generics1.trait_refs in
       let regions =
         List.map
           (fun (id0, id1) -> match_regions id0 id1)
-          (List.combine regions0 regions1)
+          (List.combine generics0.regions generics1.regions)
       in
-      let tys =
-        List.map (fun (ty0, ty1) -> match_rec ty0 ty1) (List.combine tys0 tys1)
+      let types =
+        List.map
+          (fun (ty0, ty1) -> match_rec ty0 ty1)
+          (List.combine generics0.types generics1.types)
       in
-      Adt (id, regions, tys, cgs)
+      let generics = { T.regions; types; const_generics; trait_refs } in
+      Adt (id, generics)
   | TypeVar vid0, TypeVar vid1 ->
       assert (vid0 = vid1);
       let vid = vid0 in
diff --git a/compiler/InterpreterPaths.ml b/compiler/InterpreterPaths.ml
index 04dc8892..2a277c91 100644
--- a/compiler/InterpreterPaths.ml
+++ b/compiler/InterpreterPaths.ml
@@ -3,6 +3,7 @@ module V = Values
 module E = Expressions
 module C = Contexts
 module Subst = Substitute
+module Assoc = AssociatedTypes
 module L = Logging
 open Cps
 open ValuesUtils
@@ -95,16 +96,14 @@ let rec access_projection (access : projection_access) (ctx : C.eval_ctx)
   | pe :: p' -> (
       (* Match on the projection element and the value *)
       match (pe, v.V.value, v.V.ty) with
-      | ( Field (((ProjAdt (_, _) | ProjOption _) as proj_kind), field_id),
+      | ( Field ((ProjAdt (_, _) as proj_kind), field_id),
           V.Adt adt,
-          T.Adt (type_id, _, _, _) ) -> (
+          T.Adt (type_id, _) ) -> (
           (* Check consistency *)
           (match (proj_kind, type_id) with
           | ProjAdt (def_id, opt_variant_id), T.AdtId def_id' ->
               assert (def_id = def_id');
               assert (opt_variant_id = adt.variant_id)
-          | ProjOption variant_id, T.Assumed T.Option ->
-              assert (Some variant_id = adt.variant_id)
           | _ -> raise (Failure "Unreachable"));
           (* Actually project *)
           let fv = T.FieldId.nth adt.field_values field_id in
@@ -119,8 +118,7 @@ let rec access_projection (access : projection_access) (ctx : C.eval_ctx)
               let updated = { v with value = nadt } in
               Ok (ctx, { res with updated }))
       (* Tuples *)
-      | Field (ProjTuple arity, field_id), V.Adt adt, T.Adt (T.Tuple, _, _, _)
-        -> (
+      | Field (ProjTuple arity, field_id), V.Adt adt, T.Adt (T.Tuple, _) -> (
           assert (arity = List.length adt.field_values);
           let fv = T.FieldId.nth adt.field_values field_id in
           (* Project *)
@@ -136,7 +134,7 @@ let rec access_projection (access : projection_access) (ctx : C.eval_ctx)
               Ok (ctx, { res with updated })
           (* If we reach Bottom, it may mean we need to expand an uninitialized
            * enumeration value *))
-      | Field ((ProjAdt (_, _) | ProjTuple _ | ProjOption _), _), V.Bottom, _ ->
+      | Field ((ProjAdt (_, _) | ProjTuple _), _), V.Bottom, _ ->
           Error (FailBottom (1 + List.length p', pe, v.ty))
       (* Symbolic value: needs to be expanded *)
       | _, Symbolic sp, _ ->
@@ -145,9 +143,9 @@ let rec access_projection (access : projection_access) (ctx : C.eval_ctx)
       (* Box dereferencement *)
       | ( DerefBox,
           Adt { variant_id = None; field_values = [ bv ] },
-          T.Adt (T.Assumed T.Box, _, _, _) ) -> (
-          (* We allow moving inside of boxes. In practice, this kind of
-           * manipulations should happen only inside unsage code, so
+          T.Adt (T.Assumed T.Box, _) ) -> (
+          (* We allow moving outside of boxes. In practice, this kind of
+           * manipulations should happen only inside unsafe code, so
            * it shouldn't happen due to user code, and we leverage it
            * when implementing box dereferencement for the concrete
            * interpreter *)
@@ -357,45 +355,32 @@ let write_place (access : access_kind) (p : E.place) (nv : V.typed_value)
   | Error e -> raise (Failure ("Unreachable: " ^ show_path_fail_kind e))
   | Ok ctx -> ctx
 
-let compute_expanded_bottom_adt_value (tyctx : T.type_decl T.TypeDeclId.Map.t)
+let compute_expanded_bottom_adt_value (ctx : C.eval_ctx)
     (def_id : T.TypeDeclId.id) (opt_variant_id : T.VariantId.id option)
-    (regions : T.erased_region list) (types : T.ety list)
-    (cgs : T.const_generic list) : V.typed_value =
+    (generics : T.egeneric_args) : V.typed_value =
   (* Lookup the definition and check if it is an enumeration - it
      should be an enumeration if and only if the projection element
      is a field projection with *some* variant id. Retrieve the list
      of fields at the same time. *)
-  let def = T.TypeDeclId.Map.find def_id tyctx in
-  assert (List.length regions = List.length def.T.region_params);
+  let def = C.ctx_lookup_type_decl ctx def_id in
+  assert (List.length generics.regions = List.length def.T.generics.regions);
   (* Compute the field types *)
   let field_types =
-    Subst.type_decl_get_instantiated_field_etypes def opt_variant_id types cgs
+    Assoc.type_decl_get_inst_norm_field_etypes ctx def opt_variant_id generics
   in
   (* Initialize the expanded value *)
   let fields = List.map mk_bottom field_types in
   let av = V.Adt { variant_id = opt_variant_id; field_values = fields } in
-  let ty = T.Adt (T.AdtId def_id, regions, types, cgs) in
+  let ty = T.Adt (T.AdtId def_id, generics) in
   { V.value = av; V.ty }
 
-let compute_expanded_bottom_option_value (variant_id : T.VariantId.id)
-    (param_ty : T.ety) : V.typed_value =
-  (* Note that the variant can be [Some] or [None]: we expand bottom values
-   * when writing to fields or setting discriminants *)
-  let field_values =
-    if variant_id = T.option_some_id then [ mk_bottom param_ty ]
-    else if variant_id = T.option_none_id then []
-    else raise (Failure "Unreachable")
-  in
-  let av = V.Adt { variant_id = Some variant_id; field_values } in
-  let ty = T.Adt (T.Assumed T.Option, [], [ param_ty ], []) in
-  { V.value = av; ty }
-
 let compute_expanded_bottom_tuple_value (field_types : T.ety list) :
     V.typed_value =
   (* Generate the field values *)
   let fields = List.map mk_bottom field_types in
   let v = V.Adt { variant_id = None; field_values = fields } in
-  let ty = T.Adt (T.Tuple, [], field_types, []) in
+  let generics = TypesUtils.mk_generic_args [] field_types [] [] in
+  let ty = T.Adt (T.Tuple, generics) in
   { V.value = v; V.ty }
 
 (** Auxiliary helper to expand {!V.Bottom} values.
@@ -447,19 +432,18 @@ let expand_bottom_value_from_projection (access : access_kind) (p : E.place)
     match (pe, ty) with
     (* "Regular" ADTs *)
     | ( Field (ProjAdt (def_id, opt_variant_id), _),
-        T.Adt (T.AdtId def_id', regions, types, cgs) ) ->
+        T.Adt (T.AdtId def_id', generics) ) ->
         assert (def_id = def_id');
-        compute_expanded_bottom_adt_value ctx.type_context.type_decls def_id
-          opt_variant_id regions types cgs
-    (* Option *)
-    | ( Field (ProjOption variant_id, _),
-        T.Adt (T.Assumed T.Option, [], [ ty ], []) ) ->
-        compute_expanded_bottom_option_value variant_id ty
+        compute_expanded_bottom_adt_value ctx def_id opt_variant_id generics
     (* Tuples *)
-    | Field (ProjTuple arity, _), T.Adt (T.Tuple, [], tys, []) ->
-        assert (arity = List.length tys);
+    | ( Field (ProjTuple arity, _),
+        T.Adt
+          ( T.Tuple,
+            { T.regions = []; types; const_generics = []; trait_refs = [] } ) )
+      ->
+        assert (arity = List.length types);
         (* Generate the field values *)
-        compute_expanded_bottom_tuple_value tys
+        compute_expanded_bottom_tuple_value types
     | _ ->
         raise
           (Failure
diff --git a/compiler/InterpreterPaths.mli b/compiler/InterpreterPaths.mli
index 4a9f3b41..0ff8063f 100644
--- a/compiler/InterpreterPaths.mli
+++ b/compiler/InterpreterPaths.mli
@@ -3,6 +3,7 @@ module V = Values
 module E = Expressions
 module C = Contexts
 module Subst = Substitute
+module Assoc = AssociatedTypes
 module L = Logging
 open Cps
 open InterpreterExpansion
@@ -56,18 +57,12 @@ val compute_expanded_bottom_tuple_value : T.ety list -> V.typed_value
 
 (** Compute an expanded ADT ⊥ value *)
 val compute_expanded_bottom_adt_value :
-  T.type_decl T.TypeDeclId.Map.t ->
+  C.eval_ctx ->
   T.TypeDeclId.id ->
   T.VariantId.id option ->
-  T.erased_region list ->
-  T.ety list ->
-  T.const_generic list ->
+  T.egeneric_args ->
   V.typed_value
 
-(** Compute an expanded [Option] ⊥ value *)
-val compute_expanded_bottom_option_value :
-  T.VariantId.id -> T.ety -> V.typed_value
-
 (** Drop (end) outer loans at a given place, which should be seen as an l-value
     (we will write to it later, but need to drop the loans before writing).
 
diff --git a/compiler/InterpreterProjectors.ml b/compiler/InterpreterProjectors.ml
index faed066b..9e0c2b75 100644
--- a/compiler/InterpreterProjectors.ml
+++ b/compiler/InterpreterProjectors.ml
@@ -3,6 +3,7 @@ module V = Values
 module E = Expressions
 module C = Contexts
 module Subst = Substitute
+module Assoc = AssociatedTypes
 module L = Logging
 open TypesUtils
 open InterpreterUtils
@@ -24,12 +25,12 @@ let rec apply_proj_borrows_on_shared_borrow (ctx : C.eval_ctx)
   else
     match (v.V.value, ty) with
     | V.Literal _, T.Literal _ -> []
-    | V.Adt adt, T.Adt (id, region_params, tys, cgs) ->
+    | V.Adt adt, T.Adt (id, generics) ->
         (* Retrieve the types of the fields *)
         let field_types =
-          Subst.ctx_adt_value_get_instantiated_field_rtypes ctx adt id
-            region_params tys cgs
+          Assoc.ctx_adt_value_get_inst_norm_field_rtypes ctx adt id generics
         in
+
         (* Project over the field values *)
         let fields_types = List.combine adt.V.field_values field_types in
         let proj_fields =
@@ -103,11 +104,10 @@ let rec apply_proj_borrows (check_symbolic_no_ended : bool) (ctx : C.eval_ctx)
     let value : V.avalue =
       match (v.V.value, ty) with
       | V.Literal _, T.Literal _ -> V.AIgnored
-      | V.Adt adt, T.Adt (id, region_params, tys, cgs) ->
+      | V.Adt adt, T.Adt (id, generics) ->
           (* Retrieve the types of the fields *)
           let field_types =
-            Subst.ctx_adt_value_get_instantiated_field_rtypes ctx adt id
-              region_params tys cgs
+            Assoc.ctx_adt_value_get_inst_norm_field_rtypes ctx adt id generics
           in
           (* Project over the field values *)
           let fields_types = List.combine adt.V.field_values field_types in
@@ -268,8 +268,7 @@ let apply_proj_loans_on_symbolic_expansion (regions : T.RegionId.Set.t)
   let (value, ty) : V.avalue * T.rty =
     match (see, original_sv_ty) with
     | SeLiteral _, T.Literal _ -> (V.AIgnored, original_sv_ty)
-    | SeAdt (variant_id, field_values), T.Adt (_id, _region_params, _tys, _cgs)
-      ->
+    | SeAdt (variant_id, field_values), T.Adt (_id, _generics) ->
         (* Project over the field values *)
         let field_values =
           List.map
diff --git a/compiler/InterpreterStatements.ml b/compiler/InterpreterStatements.ml
index 045c4484..e0c4703b 100644
--- a/compiler/InterpreterStatements.ml
+++ b/compiler/InterpreterStatements.ml
@@ -10,13 +10,13 @@ open TypesUtils
 open ValuesUtils
 module Inv = Invariants
 module S = SynthesizeSymbolic
-open Utils
 open Cps
 open InterpreterUtils
 open InterpreterProjectors
 open InterpreterExpansion
 open InterpreterPaths
 open InterpreterExpressions
+module PCtx = Print.EvalCtxLlbcAst
 
 (** The local logger *)
 let log = L.statements_log
@@ -232,9 +232,7 @@ let set_discriminant (config : C.config) (p : E.place)
   let update_value cf (v : V.typed_value) : m_fun =
    fun ctx ->
     match (v.V.ty, v.V.value) with
-    | ( T.Adt
-          (((T.AdtId _ | T.Assumed T.Option) as type_id), regions, types, cgs),
-        V.Adt av ) -> (
+    | T.Adt ((T.AdtId _ as type_id), generics), V.Adt av -> (
         (* There are two situations:
            - either the discriminant is already the proper one (in which case we
              don't do anything)
@@ -251,28 +249,17 @@ let set_discriminant (config : C.config) (p : E.place)
               let bottom_v =
                 match type_id with
                 | T.AdtId def_id ->
-                    compute_expanded_bottom_adt_value
-                      ctx.type_context.type_decls def_id (Some variant_id)
-                      regions types cgs
-                | T.Assumed T.Option ->
-                    assert (regions = []);
-                    compute_expanded_bottom_option_value variant_id
-                      (Collections.List.to_cons_nil types)
+                    compute_expanded_bottom_adt_value ctx def_id
+                      (Some variant_id) generics
                 | _ -> raise (Failure "Unreachable")
               in
               assign_to_place config bottom_v p (cf Unit) ctx)
-    | ( T.Adt
-          (((T.AdtId _ | T.Assumed T.Option) as type_id), regions, types, cgs),
-        V.Bottom ) ->
+    | T.Adt ((T.AdtId _ as type_id), generics), V.Bottom ->
         let bottom_v =
           match type_id with
           | T.AdtId def_id ->
-              compute_expanded_bottom_adt_value ctx.type_context.type_decls
-                def_id (Some variant_id) regions types cgs
-          | T.Assumed T.Option ->
-              assert (regions = []);
-              compute_expanded_bottom_option_value variant_id
-                (Collections.List.to_cons_nil types)
+              compute_expanded_bottom_adt_value ctx def_id (Some variant_id)
+                generics
           | _ -> raise (Failure "Unreachable")
         in
         assign_to_place config bottom_v p (cf Unit) ctx
@@ -301,24 +288,34 @@ let ctx_push_frame (ctx : C.eval_ctx) : C.eval_ctx =
 let push_frame : cm_fun = fun cf ctx -> cf (ctx_push_frame ctx)
 
 (** Small helper: compute the type of the return value for a specific
-    instantiation of a non-local function.
+    instantiation of an assumed function.
  *)
-let get_non_local_function_return_type (fid : A.assumed_fun_id)
-    (region_params : T.erased_region list) (type_params : T.ety list)
-    (const_generic_params : T.const_generic list) : T.ety =
+let get_assumed_function_return_type (ctx : C.eval_ctx) (fid : A.assumed_fun_id)
+    (generics : T.egeneric_args) : T.ety =
+  assert (generics.trait_refs = []);
   (* [Box::free] has a special treatment *)
-  match (fid, region_params, type_params, const_generic_params) with
-  | A.BoxFree, [], [ _ ], [] -> mk_unit_ty
+  match fid with
+  | BoxFree ->
+      assert (generics.regions = []);
+      assert (List.length generics.types = 1);
+      assert (generics.const_generics = []);
+      mk_unit_ty
   | _ ->
       (* Retrieve the function's signature *)
-      let sg = Assumed.get_assumed_sig fid in
+      let sg = Assumed.get_assumed_fun_sig fid in
       (* Instantiate the return type  *)
-      let tsubst = Subst.make_type_subst_from_vars sg.type_params type_params in
-      let cgsubst =
-        Subst.make_const_generic_subst_from_vars sg.const_generic_params
-          const_generic_params
+      (* There shouldn't be any reference to Self *)
+      let tr_self : T.erased_region T.trait_instance_id =
+        T.UnknownTrait __FUNCTION__
+      in
+      let { Subst.r_subst = _; ty_subst; cg_subst; tr_subst; tr_self } =
+        Subst.make_esubst_from_generics sg.generics generics tr_self
+      in
+      let ty =
+        Subst.erase_regions_substitute_types ty_subst cg_subst tr_subst tr_self
+          sg.output
       in
-      Subst.erase_regions_substitute_types tsubst cgsubst sg.output
+      Assoc.ctx_normalize_ety ctx ty
 
 let move_return_value (config : C.config) (pop_return_value : bool)
     (cf : V.typed_value option -> m_fun) : m_fun =
@@ -418,19 +415,14 @@ let pop_frame_assign (config : C.config) (dest : E.place) : cm_fun =
   in
   comp cf_pop cf_assign
 
-(** Auxiliary function - see {!eval_non_local_function_call} *)
-let eval_replace_concrete (_config : C.config)
-    (_region_params : T.erased_region list) (_type_params : T.ety list)
-    (_cg_params : T.const_generic list) : cm_fun =
- fun _cf _ctx -> raise Unimplemented
-
-(** Auxiliary function - see {!eval_non_local_function_call} *)
-let eval_box_new_concrete (config : C.config)
-    (region_params : T.erased_region list) (type_params : T.ety list)
-    (cg_params : T.const_generic list) : cm_fun =
+(** Auxiliary function - see {!eval_assumed_function_call} *)
+let eval_box_new_concrete (config : C.config) (generics : T.egeneric_args) :
+    cm_fun =
  fun cf ctx ->
   (* Check and retrieve the arguments *)
-  match (region_params, type_params, cg_params, ctx.env) with
+  match
+    (generics.regions, generics.types, generics.const_generics, ctx.env)
+  with
   | ( [],
       [ boxed_ty ],
       [],
@@ -448,7 +440,8 @@ let eval_box_new_concrete (config : C.config)
       (* Create the new box *)
       let cf_create cf (moved_input_value : V.typed_value) : m_fun =
         (* Create the box value *)
-        let box_ty = T.Adt (T.Assumed T.Box, [], [ boxed_ty ], []) in
+        let generics = TypesUtils.mk_generic_args_from_types [ boxed_ty ] in
+        let box_ty = T.Adt (T.Assumed T.Box, generics) in
         let box_v =
           V.Adt { variant_id = None; field_values = [ moved_input_value ] }
         in
@@ -466,71 +459,7 @@ let eval_box_new_concrete (config : C.config)
       comp cf_move cf_create cf ctx
   | _ -> raise (Failure "Inconsistent state")
 
-(** Auxiliary function which factorizes code to evaluate [std::Deref::deref]
-    and [std::DerefMut::deref_mut] - see {!eval_non_local_function_call} *)
-let eval_box_deref_mut_or_shared_concrete (config : C.config)
-    (region_params : T.erased_region list) (type_params : T.ety list)
-    (cg_params : T.const_generic list) (is_mut : bool) : cm_fun =
- fun cf ctx ->
-  (* Check the arguments *)
-  match (region_params, type_params, cg_params, ctx.env) with
-  | ( [],
-      [ boxed_ty ],
-      [],
-      Var (VarBinder input_var, input_value)
-      :: Var (_ret_var, _)
-      :: C.Frame :: _ ) ->
-      (* Required type checking. We must have:
-         - input_value.ty = & (mut) Box<ty>
-         - boxed_ty = ty
-         for some ty
-      *)
-      (let _, input_ty, ref_kind = ty_get_ref input_value.V.ty in
-       assert (match ref_kind with T.Shared -> not is_mut | T.Mut -> is_mut);
-       let input_ty = ty_get_box input_ty in
-       assert (input_ty = boxed_ty));
-
-      (* Borrow the boxed value *)
-      let p =
-        { E.var_id = input_var.C.index; projection = [ E.Deref; E.DerefBox ] }
-      in
-      let borrow_kind = if is_mut then E.Mut else E.Shared in
-      let rv = E.Ref (p, borrow_kind) in
-      let cf_borrow = eval_rvalue_not_global config rv in
-
-      (* Move the borrow to its destination *)
-      let cf_move cf res : m_fun =
-        match res with
-        | Error EPanic ->
-            (* We can't get there by borrowing a value *)
-            raise (Failure "Unreachable")
-        | Ok borrowed_value ->
-            (* Move and continue *)
-            let destp = mk_place_from_var_id E.VarId.zero in
-            assign_to_place config borrowed_value destp cf
-      in
-
-      (* Compose and apply *)
-      comp cf_borrow cf_move cf ctx
-  | _ -> raise (Failure "Inconsistent state")
-
-(** Auxiliary function - see {!eval_non_local_function_call} *)
-let eval_box_deref_concrete (config : C.config)
-    (region_params : T.erased_region list) (type_params : T.ety list)
-    (cg_params : T.const_generic list) : cm_fun =
-  let is_mut = false in
-  eval_box_deref_mut_or_shared_concrete config region_params type_params
-    cg_params is_mut
-
-(** Auxiliary function - see {!eval_non_local_function_call} *)
-let eval_box_deref_mut_concrete (config : C.config)
-    (region_params : T.erased_region list) (type_params : T.ety list)
-    (cg_params : T.const_generic list) : cm_fun =
-  let is_mut = true in
-  eval_box_deref_mut_or_shared_concrete config region_params type_params
-    cg_params is_mut
-
-(** Auxiliary function - see {!eval_non_local_function_call}.
+(** Auxiliary function - see {!eval_assumed_function_call}.
 
     [Box::free] is not handled the same way as the other assumed functions:
     - in the regular case, whenever we need to evaluate an assumed function,
@@ -549,11 +478,10 @@ let eval_box_deref_mut_concrete (config : C.config)
     It thus updates the box value (by calling {!drop_value}) and updates
     the destination (by setting it to [()]).
 *)
-let eval_box_free (config : C.config) (region_params : T.erased_region list)
-    (type_params : T.ety list) (cg_params : T.const_generic list)
+let eval_box_free (config : C.config) (generics : T.egeneric_args)
     (args : E.operand list) (dest : E.place) : cm_fun =
  fun cf ctx ->
-  match (region_params, type_params, cg_params, args) with
+  match (generics.regions, generics.types, generics.const_generics, args) with
   | [], [ boxed_ty ], [], [ E.Move input_box_place ] ->
       (* Required type checking *)
       let input_box = InterpreterPaths.read_place Write input_box_place ctx in
@@ -570,26 +498,24 @@ let eval_box_free (config : C.config) (region_params : T.erased_region list)
       cc cf ctx
   | _ -> raise (Failure "Inconsistent state")
 
-(** Auxiliary function - see {!eval_non_local_function_call} *)
-let eval_vec_function_concrete (_config : C.config) (_fid : A.assumed_fun_id)
-    (_region_params : T.erased_region list) (_type_params : T.ety list)
-    (_cg_params : T.const_generic list) : cm_fun =
- fun _cf _ctx -> raise Unimplemented
-
 (** Evaluate a non-local function call in concrete mode *)
-let eval_non_local_function_call_concrete (config : C.config)
-    (fid : A.assumed_fun_id) (region_params : T.erased_region list)
-    (type_params : T.ety list) (cg_params : T.const_generic list)
-    (args : E.operand list) (dest : E.place) : cm_fun =
+let eval_assumed_function_call_concrete (config : C.config)
+    (fid : A.assumed_fun_id) (call : A.call) : cm_fun =
+  let generics = call.func.generics in
+  let args = call.args in
+  let dest = call.dest in
+  (* Sanity check: we don't fully handle the const generic vars environment
+     in concrete mode yet *)
+  assert (generics.const_generics = []);
   (* There are two cases (and this is extremely annoying):
      - the function is not box_free
      - the function is box_free
      See {!eval_box_free}
   *)
   match fid with
-  | A.BoxFree ->
+  | BoxFree ->
       (* Degenerate case: box_free *)
-      eval_box_free config region_params type_params cg_params args dest
+      eval_box_free config generics args dest
   | _ ->
       (* "Normal" case: not box_free *)
       (* Evaluate the operands *)
@@ -604,16 +530,14 @@ let eval_non_local_function_call_concrete (config : C.config)
        * but it made it less clear where the computed values came from,
        * so we reversed the modifications. *)
       let cf_eval_call cf (args_vl : V.typed_value list) : m_fun =
+       fun ctx ->
         (* Push the stack frame: we initialize the frame with the return variable,
            and one variable per input argument *)
         let cc = push_frame in
 
         (* Create and push the return variable *)
         let ret_vid = E.VarId.zero in
-        let ret_ty =
-          get_non_local_function_return_type fid region_params type_params
-            cg_params
-        in
+        let ret_ty = get_assumed_function_return_type ctx fid generics in
         let ret_var = mk_var ret_vid (Some "@return") ret_ty in
         let cc = comp cc (push_uninitialized_var ret_var) in
 
@@ -630,24 +554,12 @@ let eval_non_local_function_call_concrete (config : C.config)
          * access to a body. *)
         let cf_eval_body : cm_fun =
           match fid with
-          | A.Replace ->
-              eval_replace_concrete config region_params type_params cg_params
-          | BoxNew ->
-              eval_box_new_concrete config region_params type_params cg_params
-          | BoxDeref ->
-              eval_box_deref_concrete config region_params type_params cg_params
-          | BoxDerefMut ->
-              eval_box_deref_mut_concrete config region_params type_params
-                cg_params
+          | BoxNew -> eval_box_new_concrete config generics
           | BoxFree ->
               (* Should have been treated above *) raise (Failure "Unreachable")
-          | VecNew | VecPush | VecInsert | VecLen | VecIndex | VecIndexMut ->
-              eval_vec_function_concrete config fid region_params type_params
-                cg_params
           | ArrayIndexShared | ArrayIndexMut | ArrayToSliceShared
-          | ArrayToSliceMut | ArraySubsliceShared | ArraySubsliceMut
-          | SliceIndexShared | SliceIndexMut | SliceSubsliceShared
-          | SliceSubsliceMut | SliceLen ->
+          | ArrayToSliceMut | ArrayRepeat | SliceIndexShared | SliceIndexMut
+          | SliceLen ->
               raise (Failure "Unimplemented")
         in
 
@@ -657,50 +569,11 @@ let eval_non_local_function_call_concrete (config : C.config)
         let cc = comp cc (pop_frame_assign config dest) in
 
         (* Continue *)
-        cc cf
+        cc cf ctx
       in
       (* Compose and apply *)
       comp cf_eval_ops cf_eval_call
 
-let instantiate_fun_sig (type_params : T.ety list)
-    (cg_params : T.const_generic list) (sg : A.fun_sig) : A.inst_fun_sig =
-  (* Generate fresh abstraction ids and create a substitution from region
-   * group ids to abstraction ids *)
-  let rg_abs_ids_bindings =
-    List.map
-      (fun rg ->
-        let abs_id = C.fresh_abstraction_id () in
-        (rg.T.id, abs_id))
-      sg.regions_hierarchy
-  in
-  let asubst_map : V.AbstractionId.id T.RegionGroupId.Map.t =
-    List.fold_left
-      (fun mp (rg_id, abs_id) -> T.RegionGroupId.Map.add rg_id abs_id mp)
-      T.RegionGroupId.Map.empty rg_abs_ids_bindings
-  in
-  let asubst (rg_id : T.RegionGroupId.id) : V.AbstractionId.id =
-    T.RegionGroupId.Map.find rg_id asubst_map
-  in
-  (* Generate fresh regions and their substitutions *)
-  let _, rsubst, _ = Subst.fresh_regions_with_substs sg.region_params in
-  (* Generate the type substitution
-   * Note that we need the substitution to map the type variables to
-   * {!rty} types (not {!ety}). In order to do that, we convert the
-   * type parameters to types with regions. This is possible only
-   * if those types don't contain any regions.
-   * This is a current limitation of the analysis: there is still some
-   * work to do to properly handle full type parametrization.
-   * *)
-  let rtype_params = List.map ety_no_regions_to_rty type_params in
-  let tsubst = Subst.make_type_subst_from_vars sg.type_params rtype_params in
-  let cgsubst =
-    Subst.make_const_generic_subst_from_vars sg.const_generic_params cg_params
-  in
-  (* Substitute the signature *)
-  let inst_sig = Subst.substitute_signature asubst rsubst tsubst cgsubst sg in
-  (* Return *)
-  inst_sig
-
 (** Helper
  
     Create abstractions (with no avalues, which have to be inserted afterwards)
@@ -836,7 +709,7 @@ let rec eval_statement (config : C.config) (st : A.statement) : st_cm_fun =
                   match rvalue with
                   | E.Global _ -> raise (Failure "Unreachable")
                   | E.Use _
-                  | E.Ref (_, (E.Shared | E.Mut | E.TwoPhaseMut | E.Shallow))
+                  | E.RvRef (_, (E.Shared | E.Mut | E.TwoPhaseMut | E.Shallow))
                   | E.UnaryOp _ | E.BinaryOp _ | E.Discriminant _
                   | E.Aggregate _ ->
                       let rp = rvalue_get_place rvalue in
@@ -893,7 +766,15 @@ and eval_global (config : C.config) (dest : E.place) (gid : LA.GlobalDeclId.id)
   match config.mode with
   | ConcreteMode ->
       (* Treat the evaluation of the global as a call to the global body (without arguments) *)
-      (eval_local_function_call_concrete config global.body_id [] [] [] [] dest)
+      let func =
+        {
+          E.func = FunId (Regular global.body_id);
+          generics = TypesUtils.mk_empty_generic_args;
+          trait_and_method_generic_args = None;
+        }
+      in
+      let call = { A.func; args = []; dest } in
+      (eval_transparent_function_call_concrete config global.body_id call)
         cf ctx
   | SymbolicMode ->
       (* Generate a fresh symbolic value. In the translation, this fresh symbolic value will be
@@ -1037,128 +918,374 @@ and eval_switch (config : C.config) (switch : A.switch) : st_cm_fun =
 
 (** Evaluate a function call (auxiliary helper for [eval_statement]) *)
 and eval_function_call (config : C.config) (call : A.call) : st_cm_fun =
-  (* There are two cases:
+  (* There are several cases:
      - this is a local function, in which case we execute its body
-     - this is a non-local function, in which case there is a special treatment
+     - this is an assumed function, in which case there is a special treatment
+     - this is a trait method
   *)
-  match call.func with
-  | A.Regular fid ->
-      eval_local_function_call config fid call.region_args call.type_args
-        call.const_generic_args call.args call.dest
-  | A.Assumed fid ->
-      eval_non_local_function_call config fid call.region_args call.type_args
-        call.const_generic_args call.args call.dest
+  match config.mode with
+  | C.ConcreteMode -> eval_function_call_concrete config call
+  | C.SymbolicMode -> eval_function_call_symbolic config call
 
-(** Evaluate a local (i.e., non-assumed) function call in concrete mode *)
-and eval_local_function_call_concrete (config : C.config) (fid : A.FunDeclId.id)
-    (_region_args : T.erased_region list) (type_args : T.ety list)
-    (cg_args : T.const_generic list) (args : E.operand list) (dest : E.place) :
-    st_cm_fun =
+and eval_function_call_concrete (config : C.config) (call : A.call) : st_cm_fun
+    =
  fun cf ctx ->
-  (* Retrieve the (correctly instantiated) body *)
-  let def = C.ctx_lookup_fun_decl ctx fid in
-  (* We can evaluate the function call only if it is not opaque *)
-  let body =
-    match def.body with
-    | None ->
-        raise
-          (Failure
-             ("Can't evaluate a call to an opaque function: "
-             ^ Print.name_to_string def.name))
-    | Some body -> body
-  in
-  let tsubst =
-    Subst.make_type_subst_from_vars def.A.signature.type_params type_args
-  in
-  let cgsubst =
-    Subst.make_const_generic_subst_from_vars
-      def.A.signature.const_generic_params cg_args
-  in
-  let locals, body_st = Subst.fun_body_substitute_in_body tsubst cgsubst body in
-
-  (* Evaluate the input operands *)
-  assert (List.length args = body.A.arg_count);
-  let cc = eval_operands config args in
-
-  (* Push a frame delimiter - we use {!comp_transmit} to transmit the result
-   * of the operands evaluation from above to the functions afterwards, while
-   * ignoring it in this function *)
-  let cc = comp_transmit cc push_frame in
-
-  (* Compute the initial values for the local variables *)
-  (* 1. Push the return value *)
-  let ret_var, locals =
-    match locals with
-    | ret_ty :: locals -> (ret_ty, locals)
-    | _ -> raise (Failure "Unreachable")
-  in
-  let input_locals, locals =
-    Collections.List.split_at locals body.A.arg_count
-  in
+  match call.func.func with
+  | FunId (Regular fid) ->
+      eval_transparent_function_call_concrete config fid call cf ctx
+  | FunId (Assumed fid) ->
+      (* Continue - note that we do as if the function call has been successful,
+       * by giving {!Unit} to the continuation, because we place us in the case
+       * where we haven't panicked. Of course, the translation needs to take the
+       * panic case into account... *)
+      eval_assumed_function_call_concrete config fid call (cf Unit) ctx
+  | TraitMethod _ -> raise (Failure "Unimplemented")
+
+and eval_function_call_symbolic (config : C.config) (call : A.call) : st_cm_fun
+    =
+  match call.func.func with
+  | FunId (Regular _) | TraitMethod _ ->
+      eval_transparent_function_call_symbolic config call
+  | FunId (Assumed fid) -> eval_assumed_function_call_symbolic config fid call
 
-  let cc = comp_transmit cc (push_var ret_var (mk_bottom ret_var.var_ty)) in
-
-  (* 2. Push the input values *)
-  let cf_push_inputs cf args =
-    let inputs = List.combine input_locals args in
-    (* Note that this function checks that the variables and their values
-     * have the same type (this is important) *)
-    push_vars inputs cf
-  in
-  let cc = comp cc cf_push_inputs in
-
-  (* 3. Push the remaining local variables (initialized as {!Bottom}) *)
-  let cc = comp cc (push_uninitialized_vars locals) in
+(** Evaluate a local (i.e., non-assumed) function call in concrete mode *)
+and eval_transparent_function_call_concrete (config : C.config)
+    (fid : A.FunDeclId.id) (call : A.call) : st_cm_fun =
+  let generics = call.func.generics in
+  let args = call.A.args in
+  let dest = call.A.dest in
+  (* Sanity check: we don't fully handle the const generic vars environment
+     in concrete mode yet *)
+  assert (generics.const_generics = []);
+  fun cf ctx ->
+    (* Retrieve the (correctly instantiated) body *)
+    let def = C.ctx_lookup_fun_decl ctx fid in
+    (* We can evaluate the function call only if it is not opaque *)
+    let body =
+      match def.body with
+      | None ->
+          raise
+            (Failure
+               ("Can't evaluate a call to an opaque function: "
+               ^ Print.name_to_string def.name))
+      | Some body -> body
+    in
+    (* TODO: we need to normalize the types if we want to correctly support traits *)
+    assert (generics.trait_refs = []);
+    (* There shouldn't be any reference to Self *)
+    let tr_self = T.UnknownTrait __FUNCTION__ in
+    let subst =
+      Subst.make_esubst_from_generics def.A.signature.generics generics tr_self
+    in
+    let locals, body_st = Subst.fun_body_substitute_in_body subst body in
+
+    (* Evaluate the input operands *)
+    assert (List.length args = body.A.arg_count);
+    let cc = eval_operands config args in
+
+    (* Push a frame delimiter - we use {!comp_transmit} to transmit the result
+     * of the operands evaluation from above to the functions afterwards, while
+     * ignoring it in this function *)
+    let cc = comp_transmit cc push_frame in
+
+    (* Compute the initial values for the local variables *)
+    (* 1. Push the return value *)
+    let ret_var, locals =
+      match locals with
+      | ret_ty :: locals -> (ret_ty, locals)
+      | _ -> raise (Failure "Unreachable")
+    in
+    let input_locals, locals =
+      Collections.List.split_at locals body.A.arg_count
+    in
 
-  (* Execute the function body *)
-  let cc = comp cc (eval_function_body config body_st) in
+    let cc = comp_transmit cc (push_var ret_var (mk_bottom ret_var.var_ty)) in
 
-  (* Pop the stack frame and move the return value to its destination *)
-  let cf_finish cf res =
-    match res with
-    | Panic -> cf Panic
-    | Return ->
-        (* Pop the stack frame, retrieve the return value, move it to
-         * its destination and continue *)
-        pop_frame_assign config dest (cf Unit)
-    | Break _ | Continue _ | Unit | LoopReturn _ | EndEnterLoop _
-    | EndContinue _ ->
-        raise (Failure "Unreachable")
-  in
-  let cc = comp cc cf_finish in
+    (* 2. Push the input values *)
+    let cf_push_inputs cf args =
+      let inputs = List.combine input_locals args in
+      (* Note that this function checks that the variables and their values
+       * have the same type (this is important) *)
+      push_vars inputs cf
+    in
+    let cc = comp cc cf_push_inputs in
+
+    (* 3. Push the remaining local variables (initialized as {!Bottom}) *)
+    let cc = comp cc (push_uninitialized_vars locals) in
+
+    (* Execute the function body *)
+    let cc = comp cc (eval_function_body config body_st) in
+
+    (* Pop the stack frame and move the return value to its destination *)
+    let cf_finish cf res =
+      match res with
+      | Panic -> cf Panic
+      | Return ->
+          (* Pop the stack frame, retrieve the return value, move it to
+           * its destination and continue *)
+          pop_frame_assign config dest (cf Unit)
+      | Break _ | Continue _ | Unit | LoopReturn _ | EndEnterLoop _
+      | EndContinue _ ->
+          raise (Failure "Unreachable")
+    in
+    let cc = comp cc cf_finish in
 
-  (* Continue *)
-  cc cf ctx
+    (* Continue *)
+    cc cf ctx
 
 (** Evaluate a local (i.e., non-assumed) function call in symbolic mode *)
-and eval_local_function_call_symbolic (config : C.config) (fid : A.FunDeclId.id)
-    (region_args : T.erased_region list) (type_args : T.ety list)
-    (cg_args : T.const_generic list) (args : E.operand list) (dest : E.place) :
-    st_cm_fun =
+and eval_transparent_function_call_symbolic (config : C.config) (call : A.call)
+    : st_cm_fun =
  fun cf ctx ->
-  (* Retrieve the (correctly instantiated) signature *)
-  let def = C.ctx_lookup_fun_decl ctx fid in
-  let sg = def.A.signature in
-  (* Instantiate the signature and introduce fresh abstraction and region ids
-   * while doing so *)
-  let inst_sg = instantiate_fun_sig type_args cg_args sg in
+  (* Instantiate the signature and introduce fresh abstractions and region ids while doing so.
+
+     We perform some manipulations when instantiating the signature.
+
+     # Trait impl calls
+     ==================
+     In particular, we have a special treatment of trait method calls when
+     the trait ref is a known impl.
+
+     For instance:
+     {[
+       trait HasValue {
+         fn has_value(&self) -> bool;
+       }
+
+       impl<T> HasValue for Option<T> {
+         fn has_value(&self) {
+           match self {
+             None => false,
+             Some(_) => true,
+           }
+         }
+       }
+
+       fn option_has_value<T>(x: &Option<T>) -> bool {
+         x.has_value()
+       }
+     ]}
+
+     The generated code looks like this:
+     {[
+       structure HasValue (Self : Type) = {
+         has_value : Self -> result bool
+       }
+
+       let OptionHasValueImpl.has_value (Self : Type) (self : Self) : result bool =
+         match self with
+         | None => false
+         | Some _ => true
+
+       let OptionHasValueInstance (T : Type) : HasValue (Option T) = {
+         has_value = OptionHasValueInstance.has_value
+       }
+     ]}
+
+     In [option_has_value], we don't want to refer to the [has_value] method
+     of the instance of [HasValue] for [Option<T>]. We want to refer directly
+     to the function which implements [has_value] for [Option<T>].
+     That is, instead of generating this:
+     {[
+       let option_has_value (T : Type) (x : Option T) : result bool =
+         (OptionHasValueInstance T).has_value x
+     ]}
+
+     We want to generate this:
+     {[
+       let option_has_value (T : Type) (x : Option T) : result bool =
+         OptionHasValueImpl.has_value T x
+     ]}
+
+     # Provided trait methods
+     ========================
+     Calls to provided trait methods also have a special treatment because
+     for now we forbid overriding provided trait methods in the trait implementations,
+     which means that whenever we call a provided trait method, we do not refer
+     to a trait clause but directly to the method provided in the trait declaration.
+  *)
+  let func, generics, def, inst_sg =
+    match call.func.func with
+    | FunId (Regular fid) ->
+        let def = C.ctx_lookup_fun_decl ctx fid in
+        log#ldebug
+          (lazy
+            ("fun call:\n- call: " ^ call_to_string ctx call
+           ^ "\n- call.generics:\n"
+            ^ egeneric_args_to_string ctx call.func.generics
+            ^ "\n- def.signature:\n"
+            ^ fun_sig_to_string ctx def.A.signature));
+        let tr_self = T.UnknownTrait __FUNCTION__ in
+        let inst_sg =
+          instantiate_fun_sig ctx call.func.generics tr_self def.A.signature
+        in
+        (call.func.func, call.func.generics, def, inst_sg)
+    | FunId (Assumed _) ->
+        (* Unreachable: must be a transparent function *)
+        raise (Failure "Unreachable")
+    | TraitMethod (trait_ref, method_name, _) -> (
+        log#ldebug
+          (lazy
+            ("trait method call:\n- call: " ^ call_to_string ctx call
+           ^ "\n- method name: " ^ method_name ^ "\n- call.generics:\n"
+            ^ egeneric_args_to_string ctx call.func.generics
+            ^ "\n- trait and method generics:\n"
+            ^ egeneric_args_to_string ctx
+                (Option.get call.func.trait_and_method_generic_args)));
+        (* When instantiating, we need to group the generics for the trait ref
+           and the method *)
+        let generics = Option.get call.func.trait_and_method_generic_args in
+        (* Lookup the trait method signature - there are several possibilities
+           depending on whethere we call a top-level trait method impl or the
+           method from a local clause *)
+        match trait_ref.trait_id with
+        | TraitImpl impl_id -> (
+            (* Lookup the trait impl *)
+            let trait_impl = C.ctx_lookup_trait_impl ctx impl_id in
+            log#ldebug
+              (lazy ("trait impl: " ^ trait_impl_to_string ctx trait_impl));
+            (* First look in the required methods *)
+            let method_id =
+              List.find_opt
+                (fun (s, _) -> s = method_name)
+                trait_impl.required_methods
+            in
+            match method_id with
+            | Some (_, id) ->
+                (* This is a required method *)
+                let method_def = C.ctx_lookup_fun_decl ctx id in
+                (* Instantiate *)
+                let tr_self =
+                  T.TraitRef (etrait_ref_no_regions_to_gr_trait_ref trait_ref)
+                in
+                let inst_sg =
+                  instantiate_fun_sig ctx generics tr_self
+                    method_def.A.signature
+                in
+                (* Also update the function identifier: we want to forget
+                   the fact that we called a trait method, and treat it as
+                   a regular function call to the top-level function
+                   which implements the method. In order to do this properly,
+                   we also need to update the generics.
+                *)
+                let func = E.FunId (Regular id) in
+                (func, generics, method_def, inst_sg)
+            | None ->
+                (* If not found, lookup the methods provided by the trait *declaration*
+                   (remember: for now, we forbid overriding provided methods) *)
+                assert (trait_impl.provided_methods = []);
+                let trait_decl =
+                  C.ctx_lookup_trait_decl ctx
+                    trait_ref.trait_decl_ref.trait_decl_id
+                in
+                let _, method_id =
+                  List.find
+                    (fun (s, _) -> s = method_name)
+                    trait_decl.provided_methods
+                in
+                let method_id = Option.get method_id in
+                let method_def = C.ctx_lookup_fun_decl ctx method_id in
+                (* For the instantiation we have to do something peculiar
+                   because the method was defined for the trait declaration.
+                   We have to group:
+                   - the parameters given to the trait decl reference
+                   - the parameters given to the method itself
+                   For instance:
+                   {[
+                     trait Foo<T> {
+                       fn f<U>(...) { ... }
+                     }
+
+                     fn g<G>(x : G) where Clause0: Foo<G, bool>
+                     {
+                       x.f::<u32>(...) // The arguments to f are: <G, bool, u32>
+                     }
+                   ]}
+                *)
+                let all_generics =
+                  TypesUtils.merge_generic_args
+                    trait_ref.trait_decl_ref.decl_generics call.func.generics
+                in
+                log#ldebug
+                  (lazy
+                    ("provided method call:" ^ "\n- method name: " ^ method_name
+                   ^ "\n- all_generics:\n"
+                    ^ egeneric_args_to_string ctx all_generics
+                    ^ "\n- parent params info: "
+                    ^ Print.option_to_string A.show_params_info
+                        method_def.signature.parent_params_info));
+                let tr_self =
+                  T.TraitRef (etrait_ref_no_regions_to_gr_trait_ref trait_ref)
+                in
+                let inst_sg =
+                  instantiate_fun_sig ctx all_generics tr_self
+                    method_def.A.signature
+                in
+                (call.func.func, call.func.generics, method_def, inst_sg))
+        | _ ->
+            (* We are using a local clause - we lookup the trait decl *)
+            let trait_decl =
+              C.ctx_lookup_trait_decl ctx trait_ref.trait_decl_ref.trait_decl_id
+            in
+            (* Lookup the method decl in the required *and* the provided methods *)
+            let _, method_id =
+              let provided =
+                List.filter_map
+                  (fun (id, f) ->
+                    match f with None -> None | Some f -> Some (id, f))
+                  trait_decl.provided_methods
+              in
+              List.find
+                (fun (s, _) -> s = method_name)
+                (List.append trait_decl.required_methods provided)
+            in
+            let method_def = C.ctx_lookup_fun_decl ctx method_id in
+            log#ldebug (lazy ("method:\n" ^ fun_decl_to_string ctx method_def));
+            (* Instantiate *)
+            let tr_self = T.TraitRef trait_ref in
+            let tr_self =
+              TypesUtils.etrait_instance_id_no_regions_to_gr_trait_instance_id
+                tr_self
+            in
+            let inst_sg =
+              instantiate_fun_sig ctx generics tr_self method_def.A.signature
+            in
+            (call.func.func, call.func.generics, method_def, inst_sg))
+  in
   (* Sanity check *)
-  assert (List.length args = List.length def.A.signature.inputs);
+  assert (List.length call.args = List.length def.A.signature.inputs);
   (* Evaluate the function call *)
-  eval_function_call_symbolic_from_inst_sig config (A.Regular fid) inst_sg
-    region_args type_args cg_args args dest cf ctx
+  eval_function_call_symbolic_from_inst_sig config func inst_sg generics
+    call.args call.dest cf ctx
 
 (** Evaluate a function call in symbolic mode by using the function signature.
 
     This allows us to factorize the evaluation of local and non-local function
     calls in symbolic mode: only their signatures matter.
+
+    The [self_trait_ref] trait ref refers to [Self]. We use it when calling
+    a provided trait method, because those methods have a special treatment:
+    we dot not group them with the required trait methods, and forbid (for now)
+    overriding them. We treat them as regular method, which take an additional
+    trait ref as input.
  *)
 and eval_function_call_symbolic_from_inst_sig (config : C.config)
-    (fid : A.fun_id) (inst_sg : A.inst_fun_sig)
-    (_region_args : T.erased_region list) (type_args : T.ety list)
-    (cg_args : T.const_generic list) (args : E.operand list) (dest : E.place) :
+    (fid : A.fun_id_or_trait_method_ref) (inst_sg : A.inst_fun_sig)
+    (generics : T.egeneric_args) (args : E.operand list) (dest : E.place) :
     st_cm_fun =
  fun cf ctx ->
+  log#ldebug
+    (lazy
+      ("eval_function_call_symbolic_from_inst_sig:\n- fid: "
+      ^ fun_id_or_trait_method_ref_to_string ctx fid
+      ^ "\n- inst_sg:\n"
+      ^ inst_fun_sig_to_string ctx inst_sg
+      ^ "\n- call.generics:\n"
+      ^ egeneric_args_to_string ctx generics
+      ^ "\n- args:\n"
+      ^ String.concat ", " (List.map (operand_to_string ctx) args)
+      ^ "\n- dest:\n" ^ place_to_string ctx dest));
+
   (* Generate a fresh symbolic value for the return value *)
   let ret_sv_ty = inst_sg.A.output in
   let ret_spc = mk_fresh_symbolic_value V.FunCallRet ret_sv_ty in
@@ -1224,8 +1351,8 @@ and eval_function_call_symbolic_from_inst_sig (config : C.config)
     let expr = cf ctx in
 
     (* Synthesize the symbolic AST *)
-    S.synthesize_regular_function_call fid call_id ctx abs_ids type_args cg_args
-      args args_places ret_spc dest_place expr
+    S.synthesize_regular_function_call fid call_id ctx abs_ids generics args
+      args_places ret_spc dest_place expr
   in
   let cc = comp cc cf_call in
 
@@ -1286,17 +1413,18 @@ and eval_function_call_symbolic_from_inst_sig (config : C.config)
   cc (cf Unit) ctx
 
 (** Evaluate a non-local function call in symbolic mode *)
-and eval_non_local_function_call_symbolic (config : C.config)
-    (fid : A.assumed_fun_id) (region_args : T.erased_region list)
-    (type_args : T.ety list) (cg_args : T.const_generic list)
-    (args : E.operand list) (dest : E.place) : st_cm_fun =
+and eval_assumed_function_call_symbolic (config : C.config)
+    (fid : A.assumed_fun_id) (call : A.call) : st_cm_fun =
  fun cf ctx ->
+  let generics = call.func.generics in
+  let args = call.args in
+  let dest = call.dest in
   (* Sanity check: make sure the type parameters don't contain regions -
    * this is a current limitation of our synthesis *)
   assert (
     List.for_all
       (fun ty -> not (ty_has_borrows ctx.type_context.type_infos ty))
-      type_args);
+      generics.types);
 
   (* There are two cases (and this is extremely annoying):
      - the function is not box_free
@@ -1304,10 +1432,10 @@ and eval_non_local_function_call_symbolic (config : C.config)
        See {!eval_box_free}
   *)
   match fid with
-  | A.BoxFree ->
+  | BoxFree ->
       (* Degenerate case: box_free - note that this is not really a function
        * call: no need to call a "synthesize_..." function *)
-      eval_box_free config region_args type_args cg_args args dest (cf Unit) ctx
+      eval_box_free config generics args dest (cf Unit) ctx
   | _ ->
       (* "Normal" case: not box_free *)
       (* In symbolic mode, the behaviour of a function call is completely defined
@@ -1315,59 +1443,19 @@ and eval_non_local_function_call_symbolic (config : C.config)
        * instantiated signatures, and delegate the work to an auxiliary function *)
       let inst_sig =
         match fid with
-        | A.BoxFree ->
+        | BoxFree ->
             (* should have been treated above *)
             raise (Failure "Unreachable")
         | _ ->
-            instantiate_fun_sig type_args cg_args (Assumed.get_assumed_sig fid)
+            (* There shouldn't be any reference to Self *)
+            let tr_self = T.UnknownTrait __FUNCTION__ in
+            instantiate_fun_sig ctx generics tr_self
+              (Assumed.get_assumed_fun_sig fid)
       in
 
       (* Evaluate the function call *)
-      eval_function_call_symbolic_from_inst_sig config (A.Assumed fid) inst_sig
-        region_args type_args cg_args args dest cf ctx
-
-(** Evaluate a non-local (i.e, assumed) function call such as [Box::deref]
-    (auxiliary helper for [eval_statement]) *)
-and eval_non_local_function_call (config : C.config) (fid : A.assumed_fun_id)
-    (region_args : T.erased_region list) (type_args : T.ety list)
-    (cg_args : T.const_generic list) (args : E.operand list) (dest : E.place) :
-    st_cm_fun =
- fun cf ctx ->
-  (* Debug *)
-  log#ldebug
-    (lazy
-      (let type_args =
-         "[" ^ String.concat ", " (List.map (ety_to_string ctx) type_args) ^ "]"
-       in
-       let args =
-         "[" ^ String.concat ", " (List.map (operand_to_string ctx) args) ^ "]"
-       in
-       let dest = place_to_string ctx dest in
-       "eval_non_local_function_call:\n- fid:" ^ A.show_assumed_fun_id fid
-       ^ "\n- type_args: " ^ type_args ^ "\n- args: " ^ args ^ "\n- dest: "
-       ^ dest));
-
-  match config.mode with
-  | C.ConcreteMode ->
-      eval_non_local_function_call_concrete config fid region_args type_args
-        cg_args args dest (cf Unit) ctx
-  | C.SymbolicMode ->
-      eval_non_local_function_call_symbolic config fid region_args type_args
-        cg_args args dest cf ctx
-
-(** Evaluate a local (i.e, not assumed) function call (auxiliary helper for
-    [eval_statement]) *)
-and eval_local_function_call (config : C.config) (fid : A.FunDeclId.id)
-    (region_args : T.erased_region list) (type_args : T.ety list)
-    (cg_args : T.const_generic list) (args : E.operand list) (dest : E.place) :
-    st_cm_fun =
-  match config.mode with
-  | ConcreteMode ->
-      eval_local_function_call_concrete config fid region_args type_args cg_args
-        args dest
-  | SymbolicMode ->
-      eval_local_function_call_symbolic config fid region_args type_args cg_args
-        args dest
+      eval_function_call_symbolic_from_inst_sig config (FunId (Assumed fid))
+        inst_sig generics args dest cf ctx
 
 (** Evaluate a statement seen as a function body *)
 and eval_function_body (config : C.config) (body : A.statement) : st_cm_fun =
diff --git a/compiler/InterpreterStatements.mli b/compiler/InterpreterStatements.mli
index 814bc964..e65758ae 100644
--- a/compiler/InterpreterStatements.mli
+++ b/compiler/InterpreterStatements.mli
@@ -25,15 +25,6 @@ open InterpreterExpressions
  *)
 val pop_frame : C.config -> bool -> (V.typed_value option -> m_fun) -> m_fun
 
-(** Instantiate a function signature, introducing **fresh** abstraction ids and
-    region ids. This is mostly used in preparation of function calls, when
-    evaluating in symbolic mode of course.
-
-    Note: there are no region parameters, because they should be erased.
- *)
-val instantiate_fun_sig :
-  T.ety list -> T.const_generic list -> LA.fun_sig -> LA.inst_fun_sig
-
 (** Helper.
 
     Create a list of abstractions from a list of regions groups, and insert
diff --git a/compiler/InterpreterUtils.ml b/compiler/InterpreterUtils.ml
index 7bd37550..6e08e553 100644
--- a/compiler/InterpreterUtils.ml
+++ b/compiler/InterpreterUtils.ml
@@ -10,6 +10,11 @@ open TypesUtils
 module PA = Print.EvalCtxLlbcAst
 open Cps
 
+(* TODO: we should probably rename the file to ContextsUtils *)
+
+(** The local logger *)
+let log = L.interpreter_log
+
 (** Some utilities *)
 
 (** Auxiliary function - call a function which requires a continuation,
@@ -38,6 +43,20 @@ let typed_value_to_string = PA.typed_value_to_string
 let typed_avalue_to_string = PA.typed_avalue_to_string
 let place_to_string = PA.place_to_string
 let operand_to_string = PA.operand_to_string
+let egeneric_args_to_string = PA.egeneric_args_to_string
+let rtrait_instance_id_to_string = PA.rtrait_instance_id_to_string
+let fun_sig_to_string = PA.fun_sig_to_string
+let inst_fun_sig_to_string = PA.inst_fun_sig_to_string
+
+let fun_id_or_trait_method_ref_to_string =
+  PA.fun_id_or_trait_method_ref_to_string
+
+let fun_decl_to_string = PA.fun_decl_to_string
+let call_to_string = PA.call_to_string
+
+let trait_impl_to_string ctx =
+  PA.trait_impl_to_string { ctx with type_vars = []; const_generic_vars = [] }
+
 let statement_to_string ctx = PA.statement_to_string ctx "" "  "
 let statement_to_string_with_tab ctx = PA.statement_to_string ctx "  " "  "
 let env_elem_to_string ctx = PA.env_elem_to_string ctx "" "  "
@@ -255,7 +274,8 @@ let value_has_ret_symbolic_value_with_borrow_under_mut (ctx : C.eval_ctx)
               raise Found
             else ()
         | V.SynthInput | V.SynthInputGivenBack | V.FunCallGivenBack
-        | V.SynthRetGivenBack | V.Global | V.LoopGivenBack | V.Aggregate ->
+        | V.SynthRetGivenBack | V.Global | V.LoopGivenBack | V.Aggregate
+        | V.ConstGeneric | V.TraitConst ->
             ()
     end
   in
@@ -272,7 +292,7 @@ let rvalue_get_place (rv : E.rvalue) : E.place option =
   match rv with
   | Use (Copy p | Move p) -> Some p
   | Use (Constant _) -> None
-  | Ref (p, _) -> Some p
+  | RvRef (p, _) -> Some p
   | UnaryOp _ | BinaryOp _ | Global _ | Discriminant _ | Aggregate _ -> None
 
 (** See {!ValuesUtils.symbolic_value_has_borrows} *)
@@ -403,3 +423,103 @@ let compute_contexts_ids (ctxl : C.eval_ctx list) : ids_sets * ids_to_values =
 (** Compute the sets of ids found in a context. *)
 let compute_context_ids (ctx : C.eval_ctx) : ids_sets * ids_to_values =
   compute_contexts_ids [ ctx ]
+
+(** **WARNING**: this function doesn't compute the normalized types
+    (for the trait type aliases). This should be computed afterwards.
+ *)
+let initialize_eval_context (ctx : C.decls_ctx)
+    (region_groups : T.RegionGroupId.id list) (type_vars : T.type_var list)
+    (const_generic_vars : T.const_generic_var list) : C.eval_ctx =
+  C.reset_global_counters ();
+  let const_generic_vars_map =
+    T.ConstGenericVarId.Map.of_list
+      (List.map
+         (fun (cg : T.const_generic_var) ->
+           let ty = TypesUtils.ety_no_regions_to_rty (T.Literal cg.ty) in
+           let cv = mk_fresh_symbolic_typed_value V.ConstGeneric ty in
+           (cg.index, cv))
+         const_generic_vars)
+  in
+  {
+    C.type_context = ctx.type_ctx;
+    C.fun_context = ctx.fun_ctx;
+    C.global_context = ctx.global_ctx;
+    C.trait_decls_context = ctx.trait_decls_ctx;
+    C.trait_impls_context = ctx.trait_impls_ctx;
+    C.region_groups;
+    C.type_vars;
+    C.const_generic_vars;
+    C.const_generic_vars_map;
+    C.norm_trait_etypes = C.ETraitTypeRefMap.empty (* Empty for now *);
+    C.norm_trait_rtypes = C.RTraitTypeRefMap.empty (* Empty for now *);
+    C.norm_trait_stypes = C.STraitTypeRefMap.empty (* Empty for now *);
+    C.env = [ C.Frame ];
+    C.ended_regions = T.RegionId.Set.empty;
+  }
+
+(** Instantiate a function signature, introducing **fresh** abstraction ids and
+    region ids. This is mostly used in preparation of function calls (when
+    evaluating in symbolic mode).
+
+    Note: there are no region parameters, because they should be erased.
+ *)
+let instantiate_fun_sig (ctx : C.eval_ctx) (generics : T.egeneric_args)
+    (tr_self : T.rtrait_instance_id) (sg : A.fun_sig) : A.inst_fun_sig =
+  log#ldebug
+    (lazy
+      ("instantiate_fun_sig:" ^ "\n- generics: "
+      ^ egeneric_args_to_string ctx generics
+      ^ "\n- tr_self: "
+      ^ rtrait_instance_id_to_string ctx tr_self
+      ^ "\n- sg: " ^ fun_sig_to_string ctx sg));
+  (* Generate fresh abstraction ids and create a substitution from region
+   * group ids to abstraction ids *)
+  let rg_abs_ids_bindings =
+    List.map
+      (fun rg ->
+        let abs_id = C.fresh_abstraction_id () in
+        (rg.T.id, abs_id))
+      sg.regions_hierarchy
+  in
+  let asubst_map : V.AbstractionId.id T.RegionGroupId.Map.t =
+    List.fold_left
+      (fun mp (rg_id, abs_id) -> T.RegionGroupId.Map.add rg_id abs_id mp)
+      T.RegionGroupId.Map.empty rg_abs_ids_bindings
+  in
+  let asubst (rg_id : T.RegionGroupId.id) : V.AbstractionId.id =
+    T.RegionGroupId.Map.find rg_id asubst_map
+  in
+  (* Generate fresh regions and their substitutions *)
+  let _, rsubst, _ = Subst.fresh_regions_with_substs sg.generics.regions in
+  (* Generate the type substitution
+   * Note that we need the substitution to map the type variables to
+   * {!rty} types (not {!ety}). In order to do that, we convert the
+   * type parameters to types with regions. This is possible only
+   * if those types don't contain any regions.
+   * This is a current limitation of the analysis: there is still some
+   * work to do to properly handle full type parametrization.
+   * *)
+  let rtype_params = List.map ety_no_regions_to_rty generics.types in
+  let tsubst = Subst.make_type_subst_from_vars sg.generics.types rtype_params in
+  let cgsubst =
+    Subst.make_const_generic_subst_from_vars sg.generics.const_generics
+      generics.const_generics
+  in
+  (* TODO: something annoying with the trait ref subst: we need to use region
+     types, but the arguments use erased regions. For now we use the fact
+     that no regions should appear inside. In the future: we should merge
+     ety and rty. *)
+  let trait_refs =
+    List.map TypesUtils.etrait_ref_no_regions_to_gr_trait_ref
+      generics.trait_refs
+  in
+  let tr_subst =
+    Subst.make_trait_subst_from_clauses sg.generics.trait_clauses trait_refs
+  in
+  (* Substitute the signature *)
+  let inst_sig =
+    AssociatedTypes.ctx_subst_norm_signature ctx asubst rsubst tsubst cgsubst
+      tr_subst tr_self sg
+  in
+  (* Return *)
+  inst_sig
diff --git a/compiler/Invariants.ml b/compiler/Invariants.ml
index f29c7f88..5c8ec7af 100644
--- a/compiler/Invariants.ml
+++ b/compiler/Invariants.ml
@@ -7,6 +7,7 @@ module V = Values
 module E = Expressions
 module C = Contexts
 module Subst = Substitute
+module Assoc = AssociatedTypes
 module A = LlbcAst
 module L = Logging
 open Cps
@@ -406,13 +407,14 @@ let check_typing_invariant (ctx : C.eval_ctx) : unit =
         (match (tv.V.value, tv.V.ty) with
         | V.Literal cv, T.Literal ty -> check_literal_type cv ty
         (* ADT case *)
-        | V.Adt av, T.Adt (T.AdtId def_id, regions, tys, cgs) ->
+        | V.Adt av, T.Adt (T.AdtId def_id, generics) ->
             (* Retrieve the definition to check the variant id, the number of
              * parameters, etc. *)
             let def = C.ctx_lookup_type_decl ctx def_id in
             (* Check the number of parameters *)
-            assert (List.length regions = List.length def.region_params);
-            assert (List.length tys = List.length def.type_params);
+            assert (
+              List.length generics.regions = List.length def.generics.regions);
+            assert (List.length generics.types = List.length def.generics.types);
             (* Check that the variant id is consistent *)
             (match (av.V.variant_id, def.T.kind) with
             | Some variant_id, T.Enum variants ->
@@ -421,8 +423,8 @@ let check_typing_invariant (ctx : C.eval_ctx) : unit =
             | _ -> raise (Failure "Erroneous typing"));
             (* Check that the field types are correct *)
             let field_types =
-              Subst.type_decl_get_instantiated_field_etypes def av.V.variant_id
-                tys cgs
+              Assoc.type_decl_get_inst_norm_field_etypes ctx def av.V.variant_id
+                generics
             in
             let fields_with_types =
               List.combine av.V.field_values field_types
@@ -431,34 +433,31 @@ let check_typing_invariant (ctx : C.eval_ctx) : unit =
               (fun ((v, ty) : V.typed_value * T.ety) -> assert (v.V.ty = ty))
               fields_with_types
         (* Tuple case *)
-        | V.Adt av, T.Adt (T.Tuple, regions, tys, cgs) ->
-            assert (regions = []);
-            assert (cgs = []);
+        | V.Adt av, T.Adt (T.Tuple, generics) ->
+            assert (generics.regions = []);
+            assert (generics.const_generics = []);
             assert (av.V.variant_id = None);
             (* Check that the fields have the proper values - and check that there
              * are as many fields as field types at the same time *)
-            let fields_with_types = List.combine av.V.field_values tys in
+            let fields_with_types =
+              List.combine av.V.field_values generics.types
+            in
             List.iter
               (fun ((v, ty) : V.typed_value * T.ety) -> assert (v.V.ty = ty))
               fields_with_types
         (* Assumed type case *)
-        | V.Adt av, T.Adt (T.Assumed aty_id, regions, tys, cgs) -> (
-            assert (av.V.variant_id = None || aty_id = T.Option);
-            match (aty_id, av.V.field_values, regions, tys, cgs) with
+        | V.Adt av, T.Adt (T.Assumed aty_id, generics) -> (
+            assert (av.V.variant_id = None);
+            match
+              ( aty_id,
+                av.V.field_values,
+                generics.regions,
+                generics.types,
+                generics.const_generics )
+            with
             (* Box *)
-            | T.Box, [ inner_value ], [], [ inner_ty ], []
-            | T.Option, [ inner_value ], [], [ inner_ty ], [] ->
+            | T.Box, [ inner_value ], [], [ inner_ty ], [] ->
                 assert (inner_value.V.ty = inner_ty)
-            | T.Option, _, [], [ _ ], [] ->
-                (* Option::None: nothing to check *)
-                ()
-            | T.Vec, fvs, [], [ vec_ty ], [] ->
-                List.iter
-                  (fun (v : V.typed_value) -> assert (v.ty = vec_ty))
-                  fvs
-            | T.Range, [ v0; v1 ], [], [ inner_ty ], [] ->
-                assert (v0.V.ty = inner_ty);
-                assert (v1.V.ty = inner_ty)
             | T.Array, inner_values, _, [ inner_ty ], [ cg ] ->
                 (* *)
                 assert (
@@ -520,14 +519,17 @@ let check_typing_invariant (ctx : C.eval_ctx) : unit =
         (* Check the current pair (value, type) *)
         (match (atv.V.value, atv.V.ty) with
         (* ADT case *)
-        | V.AAdt av, T.Adt (T.AdtId def_id, regions, tys, cgs) ->
+        | V.AAdt av, T.Adt (T.AdtId def_id, generics) ->
             (* Retrieve the definition to check the variant id, the number of
              * parameters, etc. *)
             let def = C.ctx_lookup_type_decl ctx def_id in
             (* Check the number of parameters *)
-            assert (List.length regions = List.length def.region_params);
-            assert (List.length tys = List.length def.type_params);
-            assert (List.length cgs = List.length def.const_generic_params);
+            assert (
+              List.length generics.regions = List.length def.generics.regions);
+            assert (List.length generics.types = List.length def.generics.types);
+            assert (
+              List.length generics.const_generics
+              = List.length def.generics.const_generics);
             (* Check that the variant id is consistent *)
             (match (av.V.variant_id, def.T.kind) with
             | Some variant_id, T.Enum variants ->
@@ -536,8 +538,8 @@ let check_typing_invariant (ctx : C.eval_ctx) : unit =
             | _ -> raise (Failure "Erroneous typing"));
             (* Check that the field types are correct *)
             let field_types =
-              Subst.type_decl_get_instantiated_field_rtypes def av.V.variant_id
-                regions tys cgs
+              Assoc.type_decl_get_inst_norm_field_rtypes ctx def av.V.variant_id
+                generics
             in
             let fields_with_types =
               List.combine av.V.field_values field_types
@@ -546,20 +548,28 @@ let check_typing_invariant (ctx : C.eval_ctx) : unit =
               (fun ((v, ty) : V.typed_avalue * T.rty) -> assert (v.V.ty = ty))
               fields_with_types
         (* Tuple case *)
-        | V.AAdt av, T.Adt (T.Tuple, regions, tys, cgs) ->
-            assert (regions = []);
-            assert (cgs = []);
+        | V.AAdt av, T.Adt (T.Tuple, generics) ->
+            assert (generics.regions = []);
+            assert (generics.const_generics = []);
             assert (av.V.variant_id = None);
             (* Check that the fields have the proper values - and check that there
              * are as many fields as field types at the same time *)
-            let fields_with_types = List.combine av.V.field_values tys in
+            let fields_with_types =
+              List.combine av.V.field_values generics.types
+            in
             List.iter
               (fun ((v, ty) : V.typed_avalue * T.rty) -> assert (v.V.ty = ty))
               fields_with_types
         (* Assumed type case *)
-        | V.AAdt av, T.Adt (T.Assumed aty_id, regions, tys, cgs) -> (
+        | V.AAdt av, T.Adt (T.Assumed aty_id, generics) -> (
             assert (av.V.variant_id = None);
-            match (aty_id, av.V.field_values, regions, tys, cgs) with
+            match
+              ( aty_id,
+                av.V.field_values,
+                generics.regions,
+                generics.types,
+                generics.const_generics )
+            with
             (* Box *)
             | T.Box, [ boxed_value ], [], [ boxed_ty ], [] ->
                 assert (boxed_value.V.ty = boxed_ty)
diff --git a/compiler/LlbcAst.ml b/compiler/LlbcAst.ml
index f4d26e18..2db859b2 100644
--- a/compiler/LlbcAst.ml
+++ b/compiler/LlbcAst.ml
@@ -11,6 +11,7 @@ type abs_region_groups = (AbstractionId.id, RegionId.id) g_region_groups
 (** A function signature, after instantiation *)
 type inst_fun_sig = {
   regions_hierarchy : abs_region_groups;
+  trait_type_constraints : rtrait_type_constraint list;
   inputs : rty list;
   output : rty;
 }
diff --git a/compiler/LlbcAstUtils.ml b/compiler/LlbcAstUtils.ml
index 1111c297..0ab4ed94 100644
--- a/compiler/LlbcAstUtils.ml
+++ b/compiler/LlbcAstUtils.ml
@@ -5,10 +5,46 @@ let lookup_fun_sig (fun_id : fun_id) (fun_decls : fun_decl FunDeclId.Map.t) :
     fun_sig =
   match fun_id with
   | Regular id -> (FunDeclId.Map.find id fun_decls).signature
-  | Assumed aid -> Assumed.get_assumed_sig aid
+  | Assumed aid -> Assumed.get_assumed_fun_sig aid
 
 let lookup_fun_name (fun_id : fun_id) (fun_decls : fun_decl FunDeclId.Map.t) :
     Names.fun_name =
   match fun_id with
   | Regular id -> (FunDeclId.Map.find id fun_decls).name
-  | Assumed aid -> Assumed.get_assumed_name aid
+  | Assumed aid -> Assumed.get_assumed_fun_name aid
+
+(** Return the opaque declarations found in the crate, which are also *not builtin*.
+
+    [filter_assumed]: if [true], do not consider as opaque the external definitions
+    that we will map to definitions from the standard library.
+
+    Remark: the list of functions also contains the list of opaque global bodies.
+ *)
+let crate_get_opaque_non_builtin_decls (k : crate) (filter_assumed : bool) :
+    T.type_decl list * fun_decl list =
+  let open ExtractBuiltin in
+  let is_opaque_fun (d : fun_decl) : bool =
+    let sname = name_to_simple_name d.name in
+    d.body = None
+    (* Something to pay attention to: we must ignore trait method *declarations*
+       (which don't have a body but must not be considered as opaque) *)
+    && (match d.kind with TraitMethodDecl _ -> false | _ -> true)
+    && ((not filter_assumed)
+       || (not (SimpleNameMap.mem sname builtin_globals_map))
+          && not (SimpleNameMap.mem sname (builtin_funs_map ())))
+  in
+  let is_opaque_type (d : T.type_decl) : bool =
+    let sname = name_to_simple_name d.name in
+    d.kind = T.Opaque
+    && ((not filter_assumed)
+       || not (SimpleNameMap.mem sname (builtin_types_map ())))
+  in
+  (* Note that by checking the function bodies we also the globals *)
+  ( List.filter is_opaque_type (T.TypeDeclId.Map.values k.types),
+    List.filter is_opaque_fun (FunDeclId.Map.values k.functions) )
+
+(** Return true if the crate contains opaque declarations, ignoring the assumed
+    definitions. *)
+let crate_has_opaque_non_builtin_decls (k : crate) (filter_assumed : bool) :
+    bool =
+  crate_get_opaque_non_builtin_decls k filter_assumed <> ([], [])
diff --git a/compiler/Logging.ml b/compiler/Logging.ml
index 9dc1f5e3..721655b8 100644
--- a/compiler/Logging.ml
+++ b/compiler/Logging.ml
@@ -9,6 +9,9 @@ let pre_passes_log = L.get_logger "MainLogger.PrePasses"
 (** Logger for Translate *)
 let translate_log = L.get_logger "MainLogger.Translate"
 
+(** Logger for Contexts *)
+let contexts_log = L.get_logger "MainLogger.Contexts"
+
 (** Logger for PureUtils *)
 let pure_utils_log = L.get_logger "MainLogger.PureUtils"
 
@@ -19,7 +22,7 @@ let symbolic_to_pure_log = L.get_logger "MainLogger.SymbolicToPure"
 let pure_micro_passes_log = L.get_logger "MainLogger.PureMicroPasses"
 
 (** Logger for ExtractBase *)
-let pure_to_extract_log = L.get_logger "MainLogger.ExtractBase"
+let extract_log = L.get_logger "MainLogger.ExtractBase"
 
 (** Logger for Interpreter *)
 let interpreter_log = L.get_logger "MainLogger.Interpreter"
@@ -57,6 +60,9 @@ let borrows_log = L.get_logger "MainLogger.Interpreter.Borrows"
 (** Logger for Invariants *)
 let invariants_log = L.get_logger "MainLogger.Interpreter.Invariants"
 
+(** Logger for AssociatedTypes *)
+let associated_types_log = L.get_logger "MainLogger.AssociatedTypes"
+
 (** Logger for SCC *)
 let scc_log = L.get_logger "MainLogger.Graph.SCC"
 
diff --git a/compiler/PrePasses.ml b/compiler/PrePasses.ml
index b348ba1d..ee06fa07 100644
--- a/compiler/PrePasses.ml
+++ b/compiler/PrePasses.ml
@@ -107,8 +107,8 @@ let remove_useless_cf_merges (crate : A.crate) (f : A.fun_decl) : A.fun_decl =
         false
     | Assign (_, rv) -> (
         match rv with
-        | Use _ | Ref _ -> not must_end_with_exit
-        | Aggregate (AggregatedTuple, []) -> not must_end_with_exit
+        | Use _ | RvRef _ -> not must_end_with_exit
+        | Aggregate (AggregatedAdt (Tuple, _, _), []) -> not must_end_with_exit
         | _ -> false)
     | FakeRead _ | Drop _ | Nop -> not must_end_with_exit
     | Panic | Return -> true
@@ -376,7 +376,7 @@ let remove_shallow_borrows (crate : A.crate) (f : A.fun_decl) : A.fun_decl =
 
         method! visit_Assign env p rv =
           match (p.projection, rv) with
-          | [], E.Ref (_, E.Shallow) ->
+          | [], E.RvRef (_, E.Shallow) ->
               (* Filter *)
               filtered := E.VarId.Set.add p.var_id !filtered;
               Nop
diff --git a/compiler/Print.ml b/compiler/Print.ml
index 9aa73d7c..7f0d95ff 100644
--- a/compiler/Print.ml
+++ b/compiler/Print.ml
@@ -21,6 +21,9 @@ module Values = struct
     type_decl_id_to_string : T.TypeDeclId.id -> string;
     const_generic_var_id_to_string : T.ConstGenericVarId.id -> string;
     global_decl_id_to_string : T.GlobalDeclId.id -> string;
+    trait_decl_id_to_string : T.TraitDeclId.id -> string;
+    trait_impl_id_to_string : T.TraitImplId.id -> string;
+    trait_clause_id_to_string : T.TraitClauseId.id -> string;
     adt_variant_to_string : T.TypeDeclId.id -> T.VariantId.id -> string;
     var_id_to_string : E.VarId.id -> string;
     adt_field_names :
@@ -34,6 +37,9 @@ module Values = struct
       PT.type_decl_id_to_string = fmt.type_decl_id_to_string;
       PT.const_generic_var_id_to_string = fmt.const_generic_var_id_to_string;
       PT.global_decl_id_to_string = fmt.global_decl_id_to_string;
+      PT.trait_decl_id_to_string = fmt.trait_decl_id_to_string;
+      PT.trait_impl_id_to_string = fmt.trait_impl_id_to_string;
+      PT.trait_clause_id_to_string = fmt.trait_clause_id_to_string;
     }
 
   let value_to_rtype_formatter (fmt : value_formatter) : PT.rtype_formatter =
@@ -43,6 +49,9 @@ module Values = struct
       PT.type_decl_id_to_string = fmt.type_decl_id_to_string;
       PT.const_generic_var_id_to_string = fmt.const_generic_var_id_to_string;
       PT.global_decl_id_to_string = fmt.global_decl_id_to_string;
+      PT.trait_decl_id_to_string = fmt.trait_decl_id_to_string;
+      PT.trait_impl_id_to_string = fmt.trait_impl_id_to_string;
+      PT.trait_clause_id_to_string = fmt.trait_clause_id_to_string;
     }
 
   let value_to_stype_formatter (fmt : value_formatter) : PT.stype_formatter =
@@ -52,6 +61,9 @@ module Values = struct
       PT.type_decl_id_to_string = fmt.type_decl_id_to_string;
       PT.const_generic_var_id_to_string = fmt.const_generic_var_id_to_string;
       PT.global_decl_id_to_string = fmt.global_decl_id_to_string;
+      PT.trait_decl_id_to_string = fmt.trait_decl_id_to_string;
+      PT.trait_impl_id_to_string = fmt.trait_impl_id_to_string;
+      PT.trait_clause_id_to_string = fmt.trait_clause_id_to_string;
     }
 
   let var_id_to_string (id : E.VarId.id) : string =
@@ -86,10 +98,10 @@ module Values = struct
           List.map (typed_value_to_string fmt) av.field_values
         in
         match v.ty with
-        | T.Adt (T.Tuple, _, _, _) ->
+        | T.Adt (T.Tuple, _) ->
             (* Tuple *)
             "(" ^ String.concat ", " field_values ^ ")"
-        | T.Adt (T.AdtId def_id, _, _, _) ->
+        | T.Adt (T.AdtId def_id, _) ->
             (* "Regular" ADT *)
             let adt_ident =
               match av.variant_id with
@@ -111,21 +123,10 @@ module Values = struct
                   let field_values = String.concat " " field_values in
                   adt_ident ^ " { " ^ field_values ^ " }"
             else adt_ident
-        | T.Adt (T.Assumed aty, _, _, _) -> (
+        | T.Adt (T.Assumed aty, _) -> (
             (* Assumed type *)
             match (aty, field_values) with
             | Box, [ bv ] -> "@Box(" ^ bv ^ ")"
-            | Option, _ ->
-                if av.variant_id = Some T.option_some_id then
-                  "@Option::Some("
-                  ^ Collections.List.to_cons_nil field_values
-                  ^ ")"
-                else if av.variant_id = Some T.option_none_id then (
-                  assert (field_values = []);
-                  "@Option::None")
-                else raise (Failure "Unreachable")
-            | Range, _ -> "@Range{ " ^ String.concat ", " field_values ^ "}"
-            | Vec, _ -> "@Vec[" ^ String.concat ", " field_values ^ "]"
             | Array, _ ->
                 (* Happens when we aggregate values *)
                 "@Array[" ^ String.concat ", " field_values ^ "]"
@@ -201,10 +202,10 @@ module Values = struct
           List.map (typed_avalue_to_string fmt) av.field_values
         in
         match v.ty with
-        | T.Adt (T.Tuple, _, _, _) ->
+        | T.Adt (T.Tuple, _) ->
             (* Tuple *)
             "(" ^ String.concat ", " field_values ^ ")"
-        | T.Adt (T.AdtId def_id, _, _, _) ->
+        | T.Adt (T.AdtId def_id, _) ->
             (* "Regular" ADT *)
             let adt_ident =
               match av.variant_id with
@@ -226,7 +227,7 @@ module Values = struct
                   let field_values = String.concat " " field_values in
                   adt_ident ^ " { " ^ field_values ^ " }"
             else adt_ident
-        | T.Adt (T.Assumed aty, _, _, _) -> (
+        | T.Adt (T.Assumed aty, _) -> (
             (* Assumed type *)
             match (aty, field_values) with
             | Box, [ bv ] -> "@Box(" ^ bv ^ ")"
@@ -347,6 +348,18 @@ module Values = struct
     ^ "}" ^ "{regions="
     ^ T.RegionId.Set.to_string None abs.regions
     ^ "}" ^ " {\n" ^ avs ^ "\n" ^ indent ^ "}"
+
+  let inst_fun_sig_to_string (fmt : value_formatter) (sg : LlbcAst.inst_fun_sig)
+      : string =
+    (* TODO: print the trait type constraints? *)
+    let ty_fmt = value_to_rtype_formatter fmt in
+    let ty_to_string = PT.ty_to_string ty_fmt in
+
+    let inputs =
+      "(" ^ String.concat ", " (List.map ty_to_string sg.inputs) ^ ")"
+    in
+    let output = ty_to_string sg.output in
+    inputs ^ " -> " ^ output
 end
 
 module PV = Values (* local module *)
@@ -452,6 +465,9 @@ module Contexts = struct
       PV.adt_variant_to_string = fmt.adt_variant_to_string;
       PV.var_id_to_string = fmt.var_id_to_string;
       PV.adt_field_names = fmt.adt_field_names;
+      PV.trait_decl_id_to_string = fmt.trait_decl_id_to_string;
+      PV.trait_impl_id_to_string = fmt.trait_impl_id_to_string;
+      PV.trait_clause_id_to_string = fmt.trait_clause_id_to_string;
     }
 
   let ast_to_value_formatter (fmt : PA.ast_formatter) : PV.value_formatter =
@@ -463,20 +479,27 @@ module Contexts = struct
   let ctx_to_rtype_formatter (fmt : ctx_formatter) : PT.rtype_formatter =
     PV.value_to_rtype_formatter fmt
 
+  let ctx_to_stype_formatter (fmt : ctx_formatter) : PT.stype_formatter =
+    PV.value_to_stype_formatter fmt
+
   let eval_ctx_to_ctx_formatter (ctx : C.eval_ctx) : ctx_formatter =
-    (* We shouldn't use rvar_to_string *)
-    let rvar_to_string _r =
-      raise (Failure "Unexpected use of rvar_to_string")
+    let rvar_to_string r =
+      (* In theory we shouldn't use rvar_to_string, but it can happen
+         when printing definitions for instance... *)
+      T.RegionVarId.to_string r
     in
     let r_to_string r = PT.region_id_to_string r in
 
     let type_var_id_to_string vid =
-      let v = C.lookup_type_var ctx vid in
-      v.name
+      (* The context may be invalid *)
+      match C.lookup_type_var_opt ctx vid with
+      | None -> T.TypeVarId.to_string vid
+      | Some v -> v.name
     in
     let const_generic_var_id_to_string vid =
-      let v = C.lookup_const_generic_var ctx vid in
-      v.name
+      match C.lookup_const_generic_var_opt ctx vid with
+      | None -> T.ConstGenericVarId.to_string vid
+      | Some v -> v.name
     in
     let type_decl_id_to_string def_id =
       let def = C.ctx_lookup_type_decl ctx def_id in
@@ -486,6 +509,15 @@ module Contexts = struct
       let def = C.ctx_lookup_global_decl ctx def_id in
       name_to_string def.name
     in
+    let trait_decl_id_to_string def_id =
+      let def = C.ctx_lookup_trait_decl ctx def_id in
+      name_to_string def.name
+    in
+    let trait_impl_id_to_string def_id =
+      let def = C.ctx_lookup_trait_impl ctx def_id in
+      name_to_string def.name
+    in
+    let trait_clause_id_to_string id = PT.trait_clause_id_to_pretty_string id in
     let adt_variant_to_string =
       PT.type_ctx_to_adt_variant_to_string_fun ctx.type_context.type_decls
     in
@@ -506,6 +538,9 @@ module Contexts = struct
       adt_variant_to_string;
       var_id_to_string;
       adt_field_names;
+      trait_decl_id_to_string;
+      trait_impl_id_to_string;
+      trait_clause_id_to_string;
     }
 
   let eval_ctx_to_ast_formatter (ctx : C.eval_ctx) : PA.ast_formatter =
@@ -521,6 +556,15 @@ module Contexts = struct
       let def = C.ctx_lookup_global_decl ctx def_id in
       global_name_to_string def.name
     in
+    let trait_decl_id_to_string def_id =
+      let def = C.ctx_lookup_trait_decl ctx def_id in
+      name_to_string def.name
+    in
+    let trait_impl_id_to_string def_id =
+      let def = C.ctx_lookup_trait_impl ctx def_id in
+      name_to_string def.name
+    in
+    let trait_clause_id_to_string id = PT.trait_clause_id_to_pretty_string id in
     {
       rvar_to_string = ctx_fmt.PV.rvar_to_string;
       r_to_string = ctx_fmt.PV.r_to_string;
@@ -533,6 +577,9 @@ module Contexts = struct
       adt_field_to_string;
       fun_decl_id_to_string;
       global_decl_id_to_string;
+      trait_decl_id_to_string;
+      trait_impl_id_to_string;
+      trait_clause_id_to_string;
     }
 
   (** Split an [env] at every occurrence of [Frame], eliminating those elements.
@@ -608,6 +655,68 @@ module EvalCtxLlbcAst = struct
     let fmt = PC.ctx_to_rtype_formatter fmt in
     PT.rty_to_string fmt t
 
+  let sty_to_string (ctx : C.eval_ctx) (t : T.sty) : string =
+    let fmt = PC.eval_ctx_to_ctx_formatter ctx in
+    let fmt = PC.ctx_to_stype_formatter fmt in
+    PT.sty_to_string fmt t
+
+  let generic_params_to_strings (ctx : C.eval_ctx) (x : T.generic_params) :
+      string list * string list =
+    let fmt = PC.eval_ctx_to_ctx_formatter ctx in
+    let fmt = PC.ctx_to_stype_formatter fmt in
+    PT.generic_params_to_strings fmt x
+
+  let egeneric_args_to_string (ctx : C.eval_ctx) (x : T.egeneric_args) : string
+      =
+    let fmt = PC.eval_ctx_to_ctx_formatter ctx in
+    let fmt = PC.ctx_to_etype_formatter fmt in
+    PT.egeneric_args_to_string fmt x
+
+  let rgeneric_args_to_string (ctx : C.eval_ctx) (x : T.rgeneric_args) : string
+      =
+    let fmt = PC.eval_ctx_to_ctx_formatter ctx in
+    let fmt = PC.ctx_to_rtype_formatter fmt in
+    PT.rgeneric_args_to_string fmt x
+
+  let sgeneric_args_to_string (ctx : C.eval_ctx) (x : T.sgeneric_args) : string
+      =
+    let fmt = PC.eval_ctx_to_ctx_formatter ctx in
+    let fmt = PC.ctx_to_stype_formatter fmt in
+    PT.sgeneric_args_to_string fmt x
+
+  let etrait_ref_to_string (ctx : C.eval_ctx) (x : T.etrait_ref) : string =
+    let fmt = PC.eval_ctx_to_ctx_formatter ctx in
+    let fmt = PC.ctx_to_etype_formatter fmt in
+    PT.etrait_ref_to_string fmt x
+
+  let rtrait_ref_to_string (ctx : C.eval_ctx) (x : T.rtrait_ref) : string =
+    let fmt = PC.eval_ctx_to_ctx_formatter ctx in
+    let fmt = PC.ctx_to_rtype_formatter fmt in
+    PT.rtrait_ref_to_string fmt x
+
+  let strait_ref_to_string (ctx : C.eval_ctx) (x : T.strait_ref) : string =
+    let fmt = PC.eval_ctx_to_ctx_formatter ctx in
+    let fmt = PC.ctx_to_stype_formatter fmt in
+    PT.strait_ref_to_string fmt x
+
+  let etrait_instance_id_to_string (ctx : C.eval_ctx) (x : T.etrait_instance_id)
+      : string =
+    let fmt = PC.eval_ctx_to_ctx_formatter ctx in
+    let fmt = PC.ctx_to_etype_formatter fmt in
+    PT.etrait_instance_id_to_string fmt x
+
+  let rtrait_instance_id_to_string (ctx : C.eval_ctx) (x : T.rtrait_instance_id)
+      : string =
+    let fmt = PC.eval_ctx_to_ctx_formatter ctx in
+    let fmt = PC.ctx_to_rtype_formatter fmt in
+    PT.rtrait_instance_id_to_string fmt x
+
+  let strait_instance_id_to_string (ctx : C.eval_ctx) (x : T.strait_instance_id)
+      : string =
+    let fmt = PC.eval_ctx_to_ctx_formatter ctx in
+    let fmt = PC.ctx_to_stype_formatter fmt in
+    PT.strait_instance_id_to_string fmt x
+
   let borrow_content_to_string (ctx : C.eval_ctx) (bc : V.borrow_content) :
       string =
     let fmt = PC.eval_ctx_to_ctx_formatter ctx in
@@ -653,11 +762,38 @@ module EvalCtxLlbcAst = struct
     let fmt = PC.eval_ctx_to_ast_formatter ctx in
     PE.operand_to_string fmt op
 
+  let call_to_string (ctx : C.eval_ctx) (call : A.call) : string =
+    let fmt = PC.eval_ctx_to_ast_formatter ctx in
+    PA.call_to_string fmt "" call
+
+  let fun_decl_to_string (ctx : C.eval_ctx) (f : A.fun_decl) : string =
+    let fmt = PC.eval_ctx_to_ast_formatter ctx in
+    PA.fun_decl_to_string fmt "" "  " f
+
+  let fun_sig_to_string (ctx : C.eval_ctx) (x : A.fun_sig) : string =
+    let fmt = PC.eval_ctx_to_ast_formatter ctx in
+    PA.fun_sig_to_string fmt "" "  " x
+
+  let inst_fun_sig_to_string (ctx : C.eval_ctx) (x : LlbcAst.inst_fun_sig) :
+      string =
+    let fmt = PC.eval_ctx_to_ast_formatter ctx in
+    let fmt = PC.ast_to_value_formatter fmt in
+    PV.inst_fun_sig_to_string fmt x
+
+  let fun_id_or_trait_method_ref_to_string (ctx : C.eval_ctx)
+      (x : E.fun_id_or_trait_method_ref) : string =
+    let fmt = PC.eval_ctx_to_ast_formatter ctx in
+    PE.fun_id_or_trait_method_ref_to_string fmt x "..."
+
   let statement_to_string (ctx : C.eval_ctx) (indent : string)
       (indent_incr : string) (e : A.statement) : string =
     let fmt = PC.eval_ctx_to_ast_formatter ctx in
     PA.statement_to_string fmt indent indent_incr e
 
+  let trait_impl_to_string (ctx : C.eval_ctx) (timpl : A.trait_impl) : string =
+    let fmt = PC.eval_ctx_to_ast_formatter ctx in
+    PA.trait_impl_to_string fmt "  " "  " timpl
+
   let env_elem_to_string (ctx : C.eval_ctx) (indent : string)
       (indent_incr : string) (ev : C.env_elem) : string =
     let fmt = PC.eval_ctx_to_ctx_formatter ctx in
diff --git a/compiler/PrintPure.ml b/compiler/PrintPure.ml
index cfb63ec2..ec75fcfd 100644
--- a/compiler/PrintPure.ml
+++ b/compiler/PrintPure.ml
@@ -8,6 +8,9 @@ type type_formatter = {
   type_decl_id_to_string : TypeDeclId.id -> string;
   const_generic_var_id_to_string : ConstGenericVarId.id -> string;
   global_decl_id_to_string : GlobalDeclId.id -> string;
+  trait_decl_id_to_string : TraitDeclId.id -> string;
+  trait_impl_id_to_string : TraitImplId.id -> string;
+  trait_clause_id_to_string : TraitClauseId.id -> string;
 }
 
 type value_formatter = {
@@ -18,6 +21,9 @@ type value_formatter = {
   adt_variant_to_string : TypeDeclId.id -> VariantId.id -> string;
   var_id_to_string : VarId.id -> string;
   adt_field_names : TypeDeclId.id -> VariantId.id option -> string list option;
+  trait_decl_id_to_string : TraitDeclId.id -> string;
+  trait_impl_id_to_string : TraitImplId.id -> string;
+  trait_clause_id_to_string : TraitClauseId.id -> string;
 }
 
 let value_to_type_formatter (fmt : value_formatter) : type_formatter =
@@ -26,6 +32,9 @@ let value_to_type_formatter (fmt : value_formatter) : type_formatter =
     type_decl_id_to_string = fmt.type_decl_id_to_string;
     const_generic_var_id_to_string = fmt.const_generic_var_id_to_string;
     global_decl_id_to_string = fmt.global_decl_id_to_string;
+    trait_decl_id_to_string = fmt.trait_decl_id_to_string;
+    trait_impl_id_to_string = fmt.trait_impl_id_to_string;
+    trait_clause_id_to_string = fmt.trait_clause_id_to_string;
   }
 
 (* TODO: we need to store which variables we have encountered so far, and
@@ -42,6 +51,9 @@ type ast_formatter = {
   adt_field_names : TypeDeclId.id -> VariantId.id option -> string list option;
   fun_decl_id_to_string : FunDeclId.id -> string;
   global_decl_id_to_string : GlobalDeclId.id -> string;
+  trait_decl_id_to_string : TraitDeclId.id -> string;
+  trait_impl_id_to_string : TraitImplId.id -> string;
+  trait_clause_id_to_string : TraitClauseId.id -> string;
 }
 
 let ast_to_value_formatter (fmt : ast_formatter) : value_formatter =
@@ -53,6 +65,9 @@ let ast_to_value_formatter (fmt : ast_formatter) : value_formatter =
     adt_variant_to_string = fmt.adt_variant_to_string;
     var_id_to_string = fmt.var_id_to_string;
     adt_field_names = fmt.adt_field_names;
+    trait_decl_id_to_string = fmt.trait_decl_id_to_string;
+    trait_impl_id_to_string = fmt.trait_impl_id_to_string;
+    trait_clause_id_to_string = fmt.trait_clause_id_to_string;
   }
 
 let ast_to_type_formatter (fmt : ast_formatter) : type_formatter =
@@ -70,31 +85,51 @@ let literal_type_to_string = Print.PrimitiveValues.literal_type_to_string
 let scalar_value_to_string = Print.PrimitiveValues.scalar_value_to_string
 let literal_to_string = Print.PrimitiveValues.literal_to_string
 
+(* Remark: not using generic_params on purpose, because we may use parameters
+   which either come from LLBC or from pure, and the [generic_params] type
+   for those ASTs is not the same. Note that it works because we actually don't
+   need to know the trait clauses to print the AST: we can thus ignore them.
+*)
 let mk_type_formatter (type_decls : T.type_decl TypeDeclId.Map.t)
     (global_decls : A.global_decl GlobalDeclId.Map.t)
-    (type_params : type_var list)
+    (trait_decls : A.trait_decl TraitDeclId.Map.t)
+    (trait_impls : A.trait_impl TraitImplId.Map.t) (type_params : type_var list)
     (const_generic_params : const_generic_var list) : type_formatter =
   let type_var_id_to_string vid =
-    let var = T.TypeVarId.nth type_params vid in
+    let var = TypeVarId.nth type_params vid in
     type_var_to_string var
   in
   let const_generic_var_id_to_string vid =
-    let var = T.ConstGenericVarId.nth const_generic_params vid in
+    let var = ConstGenericVarId.nth const_generic_params vid in
     const_generic_var_to_string var
   in
   let type_decl_id_to_string def_id =
-    let def = T.TypeDeclId.Map.find def_id type_decls in
+    let def = TypeDeclId.Map.find def_id type_decls in
     name_to_string def.name
   in
   let global_decl_id_to_string def_id =
-    let def = T.GlobalDeclId.Map.find def_id global_decls in
+    let def = GlobalDeclId.Map.find def_id global_decls in
+    name_to_string def.name
+  in
+  let trait_decl_id_to_string def_id =
+    let def = TraitDeclId.Map.find def_id trait_decls in
+    name_to_string def.name
+  in
+  let trait_impl_id_to_string def_id =
+    let def = TraitImplId.Map.find def_id trait_impls in
     name_to_string def.name
   in
+  let trait_clause_id_to_string id =
+    Print.PT.trait_clause_id_to_pretty_string id
+  in
   {
     type_var_id_to_string;
     type_decl_id_to_string;
     const_generic_var_id_to_string;
     global_decl_id_to_string;
+    trait_decl_id_to_string;
+    trait_impl_id_to_string;
+    trait_clause_id_to_string;
   }
 
 (* TODO: there is a bit of duplication with Print.fun_decl_to_ast_formatter.
@@ -106,19 +141,21 @@ let mk_type_formatter (type_decls : T.type_decl TypeDeclId.Map.t)
 let mk_ast_formatter (type_decls : T.type_decl TypeDeclId.Map.t)
     (fun_decls : A.fun_decl FunDeclId.Map.t)
     (global_decls : A.global_decl GlobalDeclId.Map.t)
-    (type_params : type_var list)
+    (trait_decls : A.trait_decl TraitDeclId.Map.t)
+    (trait_impls : A.trait_impl TraitImplId.Map.t) (type_params : type_var list)
     (const_generic_params : const_generic_var list) : ast_formatter =
-  let type_var_id_to_string vid =
-    let var = T.TypeVarId.nth type_params vid in
-    type_var_to_string var
-  in
-  let const_generic_var_id_to_string vid =
-    let var = T.ConstGenericVarId.nth const_generic_params vid in
-    const_generic_var_to_string var
-  in
-  let type_decl_id_to_string def_id =
-    let def = T.TypeDeclId.Map.find def_id type_decls in
-    name_to_string def.name
+  let ({
+         type_var_id_to_string;
+         type_decl_id_to_string;
+         const_generic_var_id_to_string;
+         global_decl_id_to_string;
+         trait_decl_id_to_string;
+         trait_impl_id_to_string;
+         trait_clause_id_to_string;
+       }
+        : type_formatter) =
+    mk_type_formatter type_decls global_decls trait_decls trait_impls
+      type_params const_generic_params
   in
   let adt_variant_to_string =
     Print.Types.type_ctx_to_adt_variant_to_string_fun type_decls
@@ -137,10 +174,6 @@ let mk_ast_formatter (type_decls : T.type_decl TypeDeclId.Map.t)
     let def = FunDeclId.Map.find def_id fun_decls in
     fun_name_to_string def.name
   in
-  let global_decl_id_to_string def_id =
-    let def = GlobalDeclId.Map.find def_id global_decls in
-    global_name_to_string def.name
-  in
   {
     type_var_id_to_string;
     const_generic_var_id_to_string;
@@ -151,6 +184,9 @@ let mk_ast_formatter (type_decls : T.type_decl TypeDeclId.Map.t)
     adt_field_to_string;
     fun_decl_id_to_string;
     global_decl_id_to_string;
+    trait_decl_id_to_string;
+    trait_impl_id_to_string;
+    trait_clause_id_to_string;
   }
 
 let assumed_ty_to_string (aty : assumed_ty) : string =
@@ -159,12 +195,11 @@ let assumed_ty_to_string (aty : assumed_ty) : string =
   | Result -> "Result"
   | Error -> "Error"
   | Fuel -> "Fuel"
-  | Option -> "Option"
-  | Vec -> "Vec"
   | Array -> "Array"
   | Slice -> "Slice"
   | Str -> "Str"
-  | Range -> "Range"
+  | RawPtr Mut -> "MutRawPtr"
+  | RawPtr Const -> "ConstRawPtr"
 
 let type_id_to_string (fmt : type_formatter) (id : type_id) : string =
   match id with
@@ -182,20 +217,18 @@ let const_generic_to_string (fmt : type_formatter) (cg : T.const_generic) :
 
 let rec ty_to_string (fmt : type_formatter) (inside : bool) (ty : ty) : string =
   match ty with
-  | Adt (id, tys, cgs) -> (
-      let tys = List.map (ty_to_string fmt false) tys in
-      let cgs = List.map (const_generic_to_string fmt) cgs in
-      let params = List.append tys cgs in
+  | Adt (id, generics) -> (
       match id with
       | Tuple ->
-          assert (cgs = []);
-          "(" ^ String.concat " * " tys ^ ")"
+          let generics = generic_args_to_strings fmt false generics in
+          "(" ^ String.concat " * " generics ^ ")"
       | AdtId _ | Assumed _ ->
-          let params_s =
-            if params = [] then "" else " " ^ String.concat " " params
+          let generics = generic_args_to_strings fmt true generics in
+          let generics_s =
+            if generics = [] then "" else " " ^ String.concat " " generics
           in
-          let ty_s = type_id_to_string fmt id ^ params_s in
-          if params <> [] && inside then "(" ^ ty_s ^ ")" else ty_s)
+          let ty_s = type_id_to_string fmt id ^ generics_s in
+          if generics <> [] && inside then "(" ^ ty_s ^ ")" else ty_s)
   | TypeVar tv -> fmt.type_var_id_to_string tv
   | Literal lty -> literal_type_to_string lty
   | Arrow (arg_ty, ret_ty) ->
@@ -203,6 +236,71 @@ let rec ty_to_string (fmt : type_formatter) (inside : bool) (ty : ty) : string =
         ty_to_string fmt true arg_ty ^ " -> " ^ ty_to_string fmt false ret_ty
       in
       if inside then "(" ^ ty ^ ")" else ty
+  | TraitType (trait_ref, generics, type_name) ->
+      let trait_ref = trait_ref_to_string fmt false trait_ref in
+      let s =
+        if generics = empty_generic_args then trait_ref ^ "::" ^ type_name
+        else
+          let generics = generic_args_to_string fmt generics in
+          "(" ^ trait_ref ^ " " ^ generics ^ ")::" ^ type_name
+      in
+      if inside then "(" ^ s ^ ")" else s
+
+and generic_args_to_strings (fmt : type_formatter) (inside : bool)
+    (generics : generic_args) : string list =
+  let tys = List.map (ty_to_string fmt inside) generics.types in
+  let cgs = List.map (const_generic_to_string fmt) generics.const_generics in
+  let trait_refs =
+    List.map (trait_ref_to_string fmt inside) generics.trait_refs
+  in
+  List.concat [ tys; cgs; trait_refs ]
+
+and generic_args_to_string (fmt : type_formatter) (generics : generic_args) :
+    string =
+  String.concat " " (generic_args_to_strings fmt true generics)
+
+and trait_ref_to_string (fmt : type_formatter) (inside : bool) (tr : trait_ref)
+    : string =
+  let trait_id = trait_instance_id_to_string fmt false tr.trait_id in
+  let generics = generic_args_to_string fmt tr.generics in
+  let s = trait_id ^ generics in
+  if tr.generics = empty_generic_args || not inside then s else "(" ^ s ^ ")"
+
+and trait_instance_id_to_string (fmt : type_formatter) (inside : bool)
+    (id : trait_instance_id) : string =
+  match id with
+  | Self -> "Self"
+  | TraitImpl id -> fmt.trait_impl_id_to_string id
+  | Clause id -> fmt.trait_clause_id_to_string id
+  | ParentClause (inst_id, _decl_id, clause_id) ->
+      let inst_id = trait_instance_id_to_string fmt false inst_id in
+      let clause_id = fmt.trait_clause_id_to_string clause_id in
+      "parent(" ^ inst_id ^ ")::" ^ clause_id
+  | ItemClause (inst_id, _decl_id, item_name, clause_id) ->
+      let inst_id = trait_instance_id_to_string fmt false inst_id in
+      let clause_id = fmt.trait_clause_id_to_string clause_id in
+      "(" ^ inst_id ^ ")::" ^ item_name ^ "::[" ^ clause_id ^ "]"
+  | TraitRef tr -> trait_ref_to_string fmt inside tr
+  | UnknownTrait msg -> "UNKNOWN(" ^ msg ^ ")"
+
+let trait_clause_to_string (fmt : type_formatter) (clause : trait_clause) :
+    string =
+  let clause_id = fmt.trait_clause_id_to_string clause.clause_id in
+  let trait_id = fmt.trait_decl_id_to_string clause.trait_id in
+  let generics = generic_args_to_strings fmt true clause.generics in
+  let generics =
+    if generics = [] then "" else " " ^ String.concat " " generics
+  in
+  "[" ^ clause_id ^ "]: " ^ trait_id ^ generics
+
+let generic_params_to_strings (fmt : type_formatter) (generics : generic_params)
+    : string list =
+  let tys = List.map type_var_to_string generics.types in
+  let cgs = List.map const_generic_var_to_string generics.const_generics in
+  let trait_clauses =
+    List.map (trait_clause_to_string fmt) generics.trait_clauses
+  in
+  List.concat [ tys; cgs; trait_clauses ]
 
 let field_to_string fmt inside (f : field) : string =
   match f.field_name with
@@ -217,11 +315,10 @@ let variant_to_string fmt (v : variant) : string =
   ^ ")"
 
 let type_decl_to_string (fmt : type_formatter) (def : type_decl) : string =
-  let types = def.type_params in
   let name = name_to_string def.name in
   let params =
-    if types = [] then ""
-    else " " ^ String.concat " " (List.map type_var_to_string types)
+    if def.generics = empty_generic_params then ""
+    else " " ^ String.concat " " (generic_params_to_strings fmt def.generics)
   in
   match def.kind with
   | Struct fields ->
@@ -256,10 +353,6 @@ let rec mprojection_to_string (fmt : ast_formatter) (inside : string)
   | pe :: p' -> (
       let s = mprojection_to_string fmt inside p' in
       match pe.pkind with
-      | E.ProjOption variant_id ->
-          assert (variant_id = T.option_some_id);
-          assert (pe.field_id = T.FieldId.zero);
-          "(" ^ s ^ "as Option::Some)." ^ T.FieldId.to_string pe.field_id
       | E.ProjTuple _ -> "(" ^ s ^ ")." ^ T.FieldId.to_string pe.field_id
       | E.ProjAdt (adt_id, opt_variant_id) -> (
           let field_name =
@@ -294,11 +387,9 @@ let adt_variant_to_string (fmt : value_formatter) (adt_id : type_id)
   | Assumed aty -> (
       (* Assumed type *)
       match aty with
-      | State | Array | Slice | Str ->
+      | State | Array | Slice | Str | RawPtr _ ->
           (* Those types are opaque: we can't get there *)
           raise (Failure "Unreachable")
-      | Vec -> "@Vec"
-      | Range -> "@Range"
       | Result ->
           let variant_id = Option.get variant_id in
           if variant_id = result_return_id then "@Result::Return"
@@ -314,13 +405,7 @@ let adt_variant_to_string (fmt : value_formatter) (adt_id : type_id)
           let variant_id = Option.get variant_id in
           if variant_id = fuel_zero_id then "@Fuel::Zero"
           else if variant_id = fuel_succ_id then "@Fuel::Succ"
-          else raise (Failure "Unreachable: improper variant id for fuel type")
-      | Option ->
-          let variant_id = Option.get variant_id in
-          if variant_id = option_some_id then "@Option::Some "
-          else if variant_id = option_none_id then "@Option::None"
-          else
-            raise (Failure "Unreachable: improper variant id for result type"))
+          else raise (Failure "Unreachable: improper variant id for fuel type"))
 
 let adt_field_to_string (fmt : value_formatter) (adt_id : type_id)
     (field_id : FieldId.id) : string =
@@ -337,11 +422,10 @@ let adt_field_to_string (fmt : value_formatter) (adt_id : type_id)
   | Assumed aty -> (
       (* Assumed type *)
       match aty with
-      | Range -> FieldId.to_string field_id
-      | State | Fuel | Vec | Array | Slice | Str ->
+      | State | Fuel | Array | Slice | Str ->
           (* Opaque types: we can't get there *)
           raise (Failure "Unreachable")
-      | Result | Error | Option ->
+      | Result | Error | RawPtr _ ->
           (* Enumerations: we can't get there *)
           raise (Failure "Unreachable"))
 
@@ -353,10 +437,10 @@ let adt_g_value_to_string (fmt : value_formatter)
     (field_values : 'v list) (ty : ty) : string =
   let field_values = List.map value_to_string field_values in
   match ty with
-  | Adt (Tuple, _, _) ->
+  | Adt (Tuple, _) ->
       (* Tuple *)
       "(" ^ String.concat ", " field_values ^ ")"
-  | Adt (AdtId def_id, _, _) ->
+  | Adt (AdtId def_id, _) ->
       (* "Regular" ADT *)
       let adt_ident =
         match variant_id with
@@ -378,10 +462,10 @@ let adt_g_value_to_string (fmt : value_formatter)
             let field_values = String.concat " " field_values in
             adt_ident ^ " { " ^ field_values ^ " }"
       else adt_ident
-  | Adt (Assumed aty, _, _) -> (
+  | Adt (Assumed aty, _) -> (
       (* Assumed type *)
       match aty with
-      | State ->
+      | State | RawPtr _ ->
           (* This type is opaque: we can't get there *)
           raise (Failure "Unreachable")
       | Result ->
@@ -412,31 +496,13 @@ let adt_g_value_to_string (fmt : value_formatter)
             | [ v ] -> "@Fuel::Succ " ^ v
             | _ -> raise (Failure "@Fuel::Succ takes exactly one value")
           else raise (Failure "Unreachable: improper variant id for fuel type")
-      | Option ->
-          let variant_id = Option.get variant_id in
-          if variant_id = option_some_id then
-            match field_values with
-            | [ v ] -> "@Option::Some " ^ v
-            | _ -> raise (Failure "Option::Some takes exactly one value")
-          else if variant_id = option_none_id then (
-            assert (field_values = []);
-            "@Option::None")
-          else
-            raise (Failure "Unreachable: improper variant id for result type")
-      | Vec | Array | Slice | Str ->
+      | Array | Slice | Str ->
           assert (variant_id = None);
           let field_values =
             List.mapi (fun i v -> string_of_int i ^ " -> " ^ v) field_values
           in
           let id = assumed_ty_to_string aty in
-          id ^ " [" ^ String.concat "; " field_values ^ "]"
-      | Range ->
-          assert (variant_id = None);
-          let field_values =
-            List.mapi (fun i v -> string_of_int i ^ " -> " ^ v) field_values
-          in
-          let id = assumed_ty_to_string aty in
-          id ^ " {" ^ String.concat "; " field_values ^ "}")
+          id ^ " [" ^ String.concat "; " field_values ^ "]")
   | _ ->
       let fmt = value_to_type_formatter fmt in
       raise
@@ -464,10 +530,10 @@ let rec typed_pattern_to_string (fmt : ast_formatter) (v : typed_pattern) :
 
 let fun_sig_to_string (fmt : ast_formatter) (sg : fun_sig) : string =
   let ty_fmt = ast_to_type_formatter fmt in
-  let type_params = List.map type_var_to_string sg.type_params in
+  let generics = generic_params_to_strings ty_fmt sg.generics in
   let inputs = List.map (ty_to_string ty_fmt false) sg.inputs in
   let output = ty_to_string ty_fmt false sg.output in
-  let all_types = List.concat [ type_params; inputs; [ output ] ] in
+  let all_types = List.concat [ generics; inputs; [ output ] ] in
   String.concat " -> " all_types
 
 let inst_fun_sig_to_string (fmt : ast_formatter) (sg : inst_fun_sig) : string =
@@ -495,28 +561,16 @@ let fun_suffix (lp_id : LoopId.id option) (rg_id : T.RegionGroupId.id option) :
 
 let llbc_assumed_fun_id_to_string (fid : A.assumed_fun_id) : string =
   match fid with
-  | A.Replace -> "core::mem::replace"
-  | A.BoxNew -> "alloc::boxed::Box::new"
-  | A.BoxDeref -> "core::ops::deref::Deref::deref"
-  | A.BoxDerefMut -> "core::ops::deref::DerefMut::deref_mut"
-  | A.BoxFree -> "alloc::alloc::box_free"
-  | A.VecNew -> "alloc::vec::Vec::new"
-  | A.VecPush -> "alloc::vec::Vec::push"
-  | A.VecInsert -> "alloc::vec::Vec::insert"
-  | A.VecLen -> "alloc::vec::Vec::len"
-  | A.VecIndex -> "core::ops::index::Index<alloc::vec::Vec>::index"
-  | A.VecIndexMut -> "core::ops::index::IndexMut<alloc::vec::Vec>::index_mut"
+  | BoxNew -> "alloc::boxed::Box::new"
+  | BoxFree -> "alloc::alloc::box_free"
   | ArrayIndexShared -> "@ArrayIndexShared"
   | ArrayIndexMut -> "@ArrayIndexMut"
   | ArrayToSliceShared -> "@ArrayToSliceShared"
   | ArrayToSliceMut -> "@ArrayToSliceMut"
-  | ArraySubsliceShared -> "@ArraySubsliceShared"
-  | ArraySubsliceMut -> "@ArraySubsliceMut"
+  | ArrayRepeat -> "@ArrayRepeat"
   | SliceLen -> "@SliceLen"
   | SliceIndexShared -> "@SliceIndexShared"
   | SliceIndexMut -> "@SliceIndexMut"
-  | SliceSubsliceShared -> "@SliceSubsliceShared"
-  | SliceSubsliceMut -> "@SliceSubsliceMut"
 
 let pure_assumed_fun_id_to_string (fid : pure_assumed_fun_id) : string =
   match fid with
@@ -531,8 +585,11 @@ let regular_fun_id_to_string (fmt : ast_formatter) (fun_id : fun_id) : string =
   | FromLlbc (fid, lp_id, rg_id) ->
       let f =
         match fid with
-        | Regular fid -> fmt.fun_decl_id_to_string fid
-        | Assumed fid -> llbc_assumed_fun_id_to_string fid
+        | FunId (Regular fid) -> fmt.fun_decl_id_to_string fid
+        | FunId (Assumed fid) -> llbc_assumed_fun_id_to_string fid
+        | TraitMethod (trait_ref, method_name, _) ->
+            let fmt = ast_to_type_formatter fmt in
+            trait_ref_to_string fmt true trait_ref ^ "." ^ method_name
       in
       f ^ fun_suffix lp_id rg_id
   | Pure fid -> pure_assumed_fun_id_to_string fid
@@ -559,9 +616,8 @@ let fun_or_op_id_to_string (fmt : ast_formatter) (fun_id : fun_or_op_id) :
 let rec texpression_to_string (fmt : ast_formatter) (inside : bool)
     (indent : string) (indent_incr : string) (e : texpression) : string =
   match e.e with
-  | Var var_id ->
-      let s = fmt.var_id_to_string var_id in
-      if inside then "(" ^ s ^ ")" else s
+  | Var var_id -> fmt.var_id_to_string var_id
+  | CVar cg_id -> fmt.const_generic_var_id_to_string cg_id
   | Const cv -> literal_to_string cv
   | App _ ->
       (* Recursively destruct the app, to have a pair (app, arguments list) *)
@@ -632,10 +688,11 @@ and app_to_string (fmt : ast_formatter) (inside : bool) (indent : string)
   (* There are two possibilities: either the [app] is an instantiated,
    * top-level qualifier (function, ADT constructore...), or it is a "regular"
    * expression *)
-  let app, tys =
+  let app, generics =
     match app.e with
     | Qualif qualif ->
         (* Qualifier case *)
+        let ty_fmt = ast_to_type_formatter fmt in
         (* Convert the qualifier identifier *)
         let qualif_s =
           match qualif.id with
@@ -654,12 +711,17 @@ and app_to_string (fmt : ast_formatter) (inside : bool) (indent : string)
               let field_s = adt_field_to_string value_fmt adt_id field_id in
               (* Adopting an F*-like syntax *)
               ConstStrings.constructor_prefix ^ adt_s ^ "?." ^ field_s
+          | TraitConst (trait_ref, generics, const_name) ->
+              let trait_ref = trait_ref_to_string ty_fmt true trait_ref in
+              let generics_s = generic_args_to_string ty_fmt generics in
+              if generics <> empty_generic_args then
+                "(" ^ trait_ref ^ generics_s ^ ")." ^ const_name
+              else trait_ref ^ "." ^ const_name
         in
         (* Convert the type instantiation *)
-        let ty_fmt = ast_to_type_formatter fmt in
-        let tys = List.map (ty_to_string ty_fmt true) qualif.type_args in
+        let generics = generic_args_to_strings ty_fmt true qualif.generics in
         (* *)
-        (qualif_s, tys)
+        (qualif_s, generics)
     | _ ->
         (* "Regular" expression case *)
         let inside = args <> [] || (args = [] && inside) in
@@ -674,7 +736,7 @@ and app_to_string (fmt : ast_formatter) (inside : bool) (indent : string)
     texpression_to_string fmt inside indent1 indent_incr
   in
   let args = List.map arg_to_string args in
-  let all_args = List.append tys args in
+  let all_args = List.append generics args in
   (* Put together *)
   let e =
     if all_args = [] then app else app ^ " " ^ String.concat " " all_args
diff --git a/compiler/Pure.ml b/compiler/Pure.ml
index ac4ca081..e6a3dab5 100644
--- a/compiler/Pure.ml
+++ b/compiler/Pure.ml
@@ -13,6 +13,9 @@ module FieldId = T.FieldId
 module SymbolicValueId = V.SymbolicValueId
 module FunDeclId = A.FunDeclId
 module GlobalDeclId = A.GlobalDeclId
+module TraitDeclId = T.TraitDeclId
+module TraitImplId = T.TraitImplId
+module TraitClauseId = T.TraitClauseId
 
 (** We redefine identifiers for loop: in {!Values}, the identifiers are global
     (they monotonically increase across functions) while in {!module:Pure} we want
@@ -21,8 +24,6 @@ module GlobalDeclId = A.GlobalDeclId
 module LoopId =
 IdGen ()
 
-type loop_id = LoopId.id [@@deriving show, ord]
-
 (** We give an identifier to every phase of the synthesis (forward, backward
     for group of regions 0, etc.) *)
 module SynthPhaseId =
@@ -37,6 +38,16 @@ module ConstGenericVarId = T.ConstGenericVarId
 type integer_type = T.integer_type [@@deriving show, ord]
 type const_generic_var = T.const_generic_var [@@deriving show, ord]
 type const_generic = T.const_generic [@@deriving show, ord]
+type const_generic_var_id = T.const_generic_var_id [@@deriving show, ord]
+type trait_decl_id = T.trait_decl_id [@@deriving show, ord]
+type trait_impl_id = T.trait_impl_id [@@deriving show, ord]
+type trait_clause_id = T.trait_clause_id [@@deriving show, ord]
+type trait_item_name = T.trait_item_name [@@deriving show, ord]
+type global_decl_id = T.global_decl_id [@@deriving show, ord]
+type fun_decl_id = A.fun_decl_id [@@deriving show, ord]
+type loop_id = LoopId.id [@@deriving show, ord]
+type region_group_id = T.region_group_id [@@deriving show, ord]
+type mutability = Mut | Const [@@deriving show, ord]
 
 (** The assumed types for the pure AST.
 
@@ -59,12 +70,17 @@ type assumed_ty =
   | Result
   | Error
   | Fuel
-  | Vec
-  | Option
   | Array
   | Slice
   | Str
-  | Range
+  | RawPtr of mutability
+      (** The bool
+          Raw pointers don't make sense in the pure world, but we don't know
+          how to translate them yet and we have to handle some functions which
+          use raw pointers in their signature (for instance some trait declarations
+          for the slices). For now, we use a dedicated type to "mark" the raw pointers,
+          and make sure that those functions are actually not used in the translation.
+       *)
 [@@deriving show, ord]
 
 (* TODO: we should never directly manipulate [Return] and [Fail], but rather
@@ -176,6 +192,14 @@ class ['self] iter_ty_base =
     inherit! [_] T.iter_const_generic
     inherit! [_] PV.iter_literal_type
     method visit_type_var_id : 'env -> type_var_id -> unit = fun _ _ -> ()
+    method visit_trait_decl_id : 'env -> trait_decl_id -> unit = fun _ _ -> ()
+    method visit_trait_impl_id : 'env -> trait_impl_id -> unit = fun _ _ -> ()
+
+    method visit_trait_clause_id : 'env -> trait_clause_id -> unit =
+      fun _ _ -> ()
+
+    method visit_trait_item_name : 'env -> trait_item_name -> unit =
+      fun _ _ -> ()
   end
 
 (** Ancestor for map visitor for [ty] *)
@@ -185,6 +209,18 @@ class ['self] map_ty_base =
     inherit! [_] T.map_const_generic
     inherit! [_] PV.map_literal_type
     method visit_type_var_id : 'env -> type_var_id -> type_var_id = fun _ x -> x
+
+    method visit_trait_decl_id : 'env -> trait_decl_id -> trait_decl_id =
+      fun _ x -> x
+
+    method visit_trait_impl_id : 'env -> trait_impl_id -> trait_impl_id =
+      fun _ x -> x
+
+    method visit_trait_clause_id : 'env -> trait_clause_id -> trait_clause_id =
+      fun _ x -> x
+
+    method visit_trait_item_name : 'env -> trait_item_name -> trait_item_name =
+      fun _ x -> x
   end
 
 (** Ancestor for reduce visitor for [ty] *)
@@ -194,6 +230,18 @@ class virtual ['self] reduce_ty_base =
     inherit! [_] T.reduce_const_generic
     inherit! [_] PV.reduce_literal_type
     method visit_type_var_id : 'env -> type_var_id -> 'a = fun _ _ -> self#zero
+
+    method visit_trait_decl_id : 'env -> trait_decl_id -> 'a =
+      fun _ _ -> self#zero
+
+    method visit_trait_impl_id : 'env -> trait_impl_id -> 'a =
+      fun _ _ -> self#zero
+
+    method visit_trait_clause_id : 'env -> trait_clause_id -> 'a =
+      fun _ _ -> self#zero
+
+    method visit_trait_item_name : 'env -> trait_item_name -> 'a =
+      fun _ _ -> self#zero
   end
 
 (** Ancestor for mapreduce visitor for [ty] *)
@@ -205,10 +253,24 @@ class virtual ['self] mapreduce_ty_base =
 
     method visit_type_var_id : 'env -> type_var_id -> type_var_id * 'a =
       fun _ x -> (x, self#zero)
+
+    method visit_trait_decl_id : 'env -> trait_decl_id -> trait_decl_id * 'a =
+      fun _ x -> (x, self#zero)
+
+    method visit_trait_impl_id : 'env -> trait_impl_id -> trait_impl_id * 'a =
+      fun _ x -> (x, self#zero)
+
+    method visit_trait_clause_id
+        : 'env -> trait_clause_id -> trait_clause_id * 'a =
+      fun _ x -> (x, self#zero)
+
+    method visit_trait_item_name
+        : 'env -> trait_item_name -> trait_item_name * 'a =
+      fun _ x -> (x, self#zero)
   end
 
 type ty =
-  | Adt of type_id * ty list * const_generic list
+  | Adt of type_id * generic_args
       (** {!Adt} encodes ADTs and tuples and assumed types.
 
           TODO: what about the ended regions? (ADTs may be parameterized
@@ -219,8 +281,38 @@ type ty =
   | TypeVar of type_var_id
   | Literal of literal_type
   | Arrow of ty * ty
+  | TraitType of trait_ref * generic_args * string
+      (** The string is for the name of the associated type *)
+
+and trait_ref = {
+  trait_id : trait_instance_id;
+  generics : generic_args;
+  trait_decl_ref : trait_decl_ref;
+}
+
+and trait_decl_ref = {
+  trait_decl_id : trait_decl_id;
+  decl_generics : generic_args; (* The name: annoying field collisions... *)
+}
+
+and generic_args = {
+  types : ty list;
+  const_generics : const_generic list;
+  trait_refs : trait_ref list;
+}
+
+and trait_instance_id =
+  | Self
+  | TraitImpl of trait_impl_id
+  | Clause of trait_clause_id
+  | ParentClause of trait_instance_id * trait_decl_id * trait_clause_id
+  | ItemClause of
+      trait_instance_id * trait_decl_id * trait_item_name * trait_clause_id
+  | TraitRef of trait_ref
+  | UnknownTrait of string
 [@@deriving
   show,
+    ord,
     visitors
       {
         name = "iter_ty";
@@ -264,12 +356,37 @@ type type_decl_kind = Struct of field list | Enum of variant list | Opaque
 
 type type_var = T.type_var [@@deriving show]
 
+type trait_clause = {
+  clause_id : trait_clause_id;
+  trait_id : trait_decl_id;
+  generics : generic_args;
+}
+[@@deriving show]
+
+type generic_params = {
+  types : type_var list;
+  const_generics : const_generic_var list;
+  trait_clauses : trait_clause list;
+}
+[@@deriving show]
+
+type trait_type_constraint = {
+  trait_ref : trait_ref;
+  generics : generic_args;
+  type_name : trait_item_name;
+  ty : ty;
+}
+[@@deriving show, ord]
+
+type predicates = { trait_type_constraints : trait_type_constraint list }
+[@@deriving show]
+
 type type_decl = {
   def_id : TypeDeclId.id;
   name : name;
-  type_params : type_var list;
-  const_generic_params : const_generic_var list;
+  generics : generic_params;
   kind : type_decl_kind;
+  preds : predicates;
 }
 [@@deriving show]
 
@@ -420,8 +537,15 @@ type pure_assumed_fun_id =
   | FuelEqZero  (** Test if some fuel is equal to 0 - TODO: ugly *)
 [@@deriving show, ord]
 
+type fun_id_or_trait_method_ref =
+  | FunId of A.fun_id
+  | TraitMethod of trait_ref * string * fun_decl_id
+      (** The fun decl id is not really needed and here for convenience purposes *)
+[@@deriving show, ord]
+
 (** A function id for a non-assumed function *)
-type regular_fun_id = A.fun_id * LoopId.id option * T.RegionGroupId.id option
+type regular_fun_id =
+  fun_id_or_trait_method_ref * LoopId.id option * T.RegionGroupId.id option
 [@@deriving show, ord]
 
 (** A function identifier *)
@@ -457,23 +581,20 @@ type projection = { adt_id : type_id; field_id : FieldId.id } [@@deriving show]
 
 type qualif_id =
   | FunOrOp of fun_or_op_id  (** A function or an operation *)
-  | Global of GlobalDeclId.id
+  | Global of global_decl_id
   | AdtCons of adt_cons_id  (** A function or ADT constructor identifier *)
   | Proj of projection  (** Field projector *)
+  | TraitConst of trait_ref * generic_args * string
+      (** A trait associated constant *)
 [@@deriving show]
 
-(** An instantiated qualified.
+(** An instantiated qualifier.
 
     Note that for now we have a clear separation between types and expressions,
-    which explains why we have the [type_params] field: a function or ADT
+    which explains why we have the [generics] field: a function or ADT
     constructor is always fully instantiated.
  *)
-type qualif = {
-  id : qualif_id;
-  type_args : ty list;
-  const_generic_args : const_generic list;
-}
-[@@deriving show]
+type qualif = { id : qualif_id; generics : generic_args } [@@deriving show]
 
 type field_id = FieldId.id [@@deriving show, ord]
 type var_id = VarId.id [@@deriving show, ord]
@@ -536,6 +657,7 @@ class virtual ['self] mapreduce_expression_base =
  *)
 type expression =
   | Var of var_id  (** a variable *)
+  | CVar of const_generic_var_id  (** a const generic var *)
   | Const of literal
   | App of texpression * texpression
       (** Application of a function to an argument.
@@ -787,11 +909,11 @@ type fun_sig_info = {
     - etc.
  *)
 type fun_sig = {
-  type_params : type_var list;
-  const_generic_params : const_generic_var list;
+  generics : generic_params;
       (** TODO: we should analyse the signature to make the type parameters implicit whenever possible *)
+  preds : predicates;
   inputs : ty list;
-      (** The input types.
+      (** The types of the inputs.
 
           Note that those input types take into account the [fuel] parameter,
           if the function uses fuel for termination, and the [state] parameter,
@@ -861,8 +983,11 @@ type fun_body = {
 }
 [@@deriving show]
 
+type fun_kind = A.fun_kind [@@deriving show]
+
 type fun_decl = {
   def_id : FunDeclId.id;
+  kind : fun_kind;
   num_loops : int;
       (** The number of loops in the parent forward function (basically the number
           of loops appearing in the original Rust functions, unless some loops are
@@ -882,3 +1007,30 @@ type fun_decl = {
   body : fun_body option;
 }
 [@@deriving show]
+
+type trait_decl = {
+  def_id : trait_decl_id;
+  name : name;
+  generics : generic_params;
+  preds : predicates;
+  parent_clauses : trait_clause list;
+  consts : (trait_item_name * (ty * global_decl_id option)) list;
+  types : (trait_item_name * (trait_clause list * ty option)) list;
+  required_methods : (trait_item_name * fun_decl_id) list;
+  provided_methods : (trait_item_name * fun_decl_id option) list;
+}
+[@@deriving show]
+
+type trait_impl = {
+  def_id : trait_impl_id;
+  name : name;
+  impl_trait : trait_decl_ref;
+  generics : generic_params;
+  preds : predicates;
+  parent_trait_refs : trait_ref list;
+  consts : (trait_item_name * (ty * global_decl_id)) list;
+  types : (trait_item_name * (trait_ref list * ty)) list;
+  required_methods : (trait_item_name * fun_decl_id) list;
+  provided_methods : (trait_item_name * fun_decl_id) list;
+}
+[@@deriving show]
diff --git a/compiler/PureMicroPasses.ml b/compiler/PureMicroPasses.ml
index b6025df4..f3e6cbe2 100644
--- a/compiler/PureMicroPasses.ml
+++ b/compiler/PureMicroPasses.ml
@@ -376,8 +376,7 @@ let compute_pretty_names (def : fun_decl) : fun_decl =
     let ty = e.ty in
     let ctx, e =
       match e.e with
-      | Var _ -> (* Nothing to do *) (ctx, e.e)
-      | Const _ -> (* Nothing to do *) (ctx, e.e)
+      | Var _ | CVar _ | Const _ -> (* Nothing to do *) (ctx, e.e)
       | App (app, arg) ->
           let ctx, app = update_texpression app ctx in
           let ctx, arg = update_texpression arg ctx in
@@ -584,13 +583,10 @@ let intro_struct_updates (ctx : trans_ctx) (def : fun_decl) : fun_decl =
             | Qualif
                 {
                   id = AdtCons { adt_id = AdtId adt_id; variant_id = None };
-                  type_args = _;
-                  const_generic_args = _;
+                  generics = _;
                 } ->
                 (* Lookup the def *)
-                let decl =
-                  TypeDeclId.Map.find adt_id ctx.type_context.type_decls
-                in
+                let decl = TypeDeclId.Map.find adt_id ctx.type_ctx.type_decls in
                 (* Check that there are as many arguments as there are fields - note
                    that the def should have a body (otherwise we couldn't use the
                    constructor) *)
@@ -599,8 +595,7 @@ let intro_struct_updates (ctx : trans_ctx) (def : fun_decl) : fun_decl =
                   (* Check if the definition is recursive *)
                   let is_rec =
                     match
-                      TypeDeclId.Map.find adt_id
-                        ctx.type_context.type_decls_groups
+                      TypeDeclId.Map.find adt_id ctx.type_ctx.type_decls_groups
                     with
                     | NonRec _ -> false
                     | Rec _ -> true
@@ -682,8 +677,8 @@ let inline_useless_var_reassignments (inline_named : bool) (inline_pure : bool)
               | _ -> false
             in
             (* And either:
-             * 2.1 the right-expression is a variable or a global *)
-            let var_or_global = is_var re || is_global re in
+             * 2.1 the right-expression is a variable, a global or a const generic var *)
+            let var_or_global = is_var re || is_cvar re || is_global re in
             (* Or:
              * 2.2 the right-expression is a constant value, an ADT value,
              *     a projection or a primitive function call *and* the flag
@@ -767,10 +762,10 @@ let inline_useless_var_reassignments (inline_named : bool) (inline_pure : bool)
     In this situation, we can remove the call [f@fwd x].
  *)
 let expression_contains_child_call_in_all_paths (ctx : trans_ctx)
-    (id0 : A.fun_id) (lp_id0 : LoopId.id option)
-    (rg_id0 : T.RegionGroupId.id option) (tys0 : ty list)
+    (id0 : fun_id_or_trait_method_ref) (lp_id0 : LoopId.id option)
+    (rg_id0 : T.RegionGroupId.id option) (generics0 : generic_args)
     (args0 : texpression list) (e : texpression) : bool =
-  let check_call (fun_id1 : fun_or_op_id) (tys1 : ty list)
+  let check_call (fun_id1 : fun_or_op_id) (generics1 : generic_args)
       (args1 : texpression list) : bool =
     (* Check the fun_ids, to see if call1's function is a child of call0's function *)
     match fun_id1 with
@@ -793,7 +788,12 @@ let expression_contains_child_call_in_all_paths (ctx : trans_ctx)
                   (* We need to use the regions hierarchy *)
                   (* First, lookup the signature of the LLBC function *)
                   let sg =
-                    LlbcAstUtils.lookup_fun_sig id0 ctx.fun_context.fun_decls
+                    let id0 =
+                      match id0 with
+                      | FunId fun_id -> fun_id
+                      | TraitMethod (_, _, fun_decl_id) -> Regular fun_decl_id
+                    in
+                    LlbcAstUtils.lookup_fun_sig id0 ctx.fun_ctx.fun_decls
                   in
                   (* Compute the set of ancestors of the function in call1 *)
                   let call1_ancestors =
@@ -817,8 +817,8 @@ let expression_contains_child_call_in_all_paths (ctx : trans_ctx)
             let input_eq (v0, v1) =
               PureUtils.remove_meta v0 = PureUtils.remove_meta v1
             in
-            (* Compare the input types and the prefix of the input arguments *)
-            tys0 = tys1 && List.for_all input_eq args
+            (* Compare the generics and the prefix of the input arguments *)
+            generics0 = generics1 && List.for_all input_eq args
           else (* Not a child *)
             false
         else (* Not the same function *)
@@ -834,7 +834,7 @@ let expression_contains_child_call_in_all_paths (ctx : trans_ctx)
 
       method! visit_texpression env e =
         match e.e with
-        | Var _ | Const _ -> fun _ -> false
+        | Var _ | CVar _ | Const _ -> fun _ -> false
         | StructUpdate _ ->
             (* There shouldn't be monadic calls in structure updates - also
                note that by returning [false] we are conservative: we might
@@ -844,8 +844,8 @@ let expression_contains_child_call_in_all_paths (ctx : trans_ctx)
         | Let (_, _, re, e) -> (
             match opt_destruct_function_call re with
             | None -> fun () -> self#visit_texpression env e ()
-            | Some (func1, tys1, args1) ->
-                let call_is_child = check_call func1 tys1 args1 in
+            | Some (func1, generics1, args1) ->
+                let call_is_child = check_call func1 generics1 args1 in
                 if call_is_child then fun () -> true
                 else fun () -> self#visit_texpression env e ())
         | App _ -> (
@@ -930,7 +930,7 @@ let filter_useless (filter_monadic_calls : bool) (ctx : trans_ctx)
 
       method! visit_expression env e =
         match e with
-        | Var _ | Const _ | App _ | Qualif _
+        | Var _ | CVar _ | Const _ | App _ | Qualif _
         | Switch (_, _)
         | Meta (_, _)
         | StructUpdate _ | Abs _ ->
@@ -1086,13 +1086,12 @@ let simplify_aggregates (ctx : trans_ctx) (def : fun_decl) : fun_decl =
             | Qualif
                 {
                   id = AdtCons { adt_id = AdtId adt_id; variant_id = None };
-                  type_args;
-                  const_generic_args;
+                  generics;
                 } ->
                 (* This is a struct *)
                 (* Retrieve the definiton, to find how many fields there are *)
                 let adt_decl =
-                  TypeDeclId.Map.find adt_id ctx.type_context.type_decls
+                  TypeDeclId.Map.find adt_id ctx.type_ctx.type_decls
                 in
                 let fields =
                   match adt_decl.kind with
@@ -1108,7 +1107,7 @@ let simplify_aggregates (ctx : trans_ctx) (def : fun_decl) : fun_decl =
                    * [x.field] for some variable [x], and where the projection
                    * is for the proper ADT *)
                   let to_var_proj (i : int) (arg : texpression) :
-                      (ty list * const_generic list * var_id) option =
+                      (generic_args * var_id) option =
                     match arg.e with
                     | App (proj, x) -> (
                         match (proj.e, x.e) with
@@ -1116,16 +1115,14 @@ let simplify_aggregates (ctx : trans_ctx) (def : fun_decl) : fun_decl =
                               {
                                 id =
                                   Proj { adt_id = AdtId proj_adt_id; field_id };
-                                type_args = proj_type_args;
-                                const_generic_args = proj_const_generic_args;
+                                generics = proj_generics;
                               },
                             Var v ) ->
                             (* We check that this is the proper ADT, and the proper field *)
                             if
                               proj_adt_id = adt_id
                               && FieldId.to_int field_id = i
-                            then
-                              Some (proj_type_args, proj_const_generic_args, v)
+                            then Some (proj_generics, v)
                             else None
                         | _ -> None)
                     | _ -> None
@@ -1136,14 +1133,13 @@ let simplify_aggregates (ctx : trans_ctx) (def : fun_decl) : fun_decl =
                   if List.length args = num_fields then
                     (* Check that this is the same variable we project from -
                      * note that we checked above that there is at least one field *)
-                    let (_, _, x), end_args = Collections.List.pop args in
-                    if List.for_all (fun (_, _, y) -> y = x) end_args then (
+                    let (_, x), end_args = Collections.List.pop args in
+                    if List.for_all (fun (_, y) -> y = x) end_args then (
                       (* We can substitute *)
                       (* Sanity check: all types correct *)
                       assert (
                         List.for_all
-                          (fun (tys, cgs, _) ->
-                            tys = type_args && cgs = const_generic_args)
+                          (fun (generics1, _) -> generics1 = generics)
                           args);
                       { e with e = Var x })
                     else super#visit_texpression env e
@@ -1162,8 +1158,7 @@ let simplify_aggregates (ctx : trans_ctx) (def : fun_decl) : fun_decl =
                   | ( Qualif
                         {
                           id = Proj { adt_id = AdtId proj_adt_id; field_id };
-                          type_args = _;
-                          const_generic_args = _;
+                          generics = _;
                         },
                       Var v ) ->
                       (* We check that this is the proper ADT, and the proper field *)
@@ -1361,8 +1356,8 @@ let decompose_loops (def : fun_decl) : fun_decl * fun_decl list =
 
             let loop_sig =
               {
-                type_params = fun_sig.type_params;
-                const_generic_params = fun_sig.const_generic_params;
+                generics = fun_sig.generics;
+                preds = fun_sig.preds;
                 inputs = inputs_tys;
                 output;
                 doutputs;
@@ -1427,6 +1422,7 @@ let decompose_loops (def : fun_decl) : fun_decl * fun_decl list =
             let loop_def =
               {
                 def_id = def.def_id;
+                kind = def.kind;
                 num_loops;
                 loop_id = Some loop.loop_id;
                 back_id = def.back_id;
@@ -1466,13 +1462,12 @@ let decompose_loops (def : fun_decl) : fun_decl * fun_decl list =
     In such situation, we can remove the forward function definition
     altogether.
   *)
-let keep_forward (trans : pure_fun_translation) : bool =
-  let (fwd, _), backs = trans in
+let keep_forward (fwd : fun_and_loops) (backs : fun_and_loops list) : bool =
   (* Note that at this point, the output types are no longer seen as tuples:
    * they should be lists of length 1. *)
   if
     !Config.filter_useless_functions
-    && fwd.signature.output = mk_result_ty mk_unit_ty
+    && fwd.f.signature.output = mk_result_ty mk_unit_ty
     && backs <> []
   then false
   else true
@@ -1518,7 +1513,7 @@ let unit_vars_to_unit (def : fun_decl) : fun_decl =
     function calls, and when translating end abstractions. Here, we can do
     something simpler, in one micro-pass.
  *)
-let eliminate_box_functions (_ctx : trans_ctx) (def : fun_decl) : fun_decl =
+let eliminate_box_functions (ctx : trans_ctx) (def : fun_decl) : fun_decl =
   (* The map visitor *)
   let obj =
     object
@@ -1527,30 +1522,44 @@ let eliminate_box_functions (_ctx : trans_ctx) (def : fun_decl) : fun_decl =
       method! visit_texpression env e =
         match opt_destruct_function_call e with
         | Some (fun_id, _tys, args) -> (
+            (* Below, when dealing with the arguments: we consider the very
+             * general case, where functions could be boxed (meaning we
+             * could have: [box_new f x])
+             * *)
             match fun_id with
-            | Fun (FromLlbc (A.Assumed aid, _lp_id, rg_id)) -> (
-                (* Below, when dealing with the arguments: we consider the very
-                 * general case, where functions could be boxed (meaning we
-                 * could have: [box_new f x])
-                 * *)
+            | Fun (FromLlbc (FunId (Assumed aid), _lp_id, rg_id)) -> (
                 match (aid, rg_id) with
-                | A.BoxNew, _ ->
+                | BoxNew, _ ->
                     assert (rg_id = None);
                     let arg, args = Collections.List.pop args in
                     mk_apps arg args
-                | A.BoxDeref, None ->
+                | BoxFree, _ ->
+                    assert (args = []);
+                    mk_unit_rvalue
+                | ( ( SliceIndexShared | SliceIndexMut | ArrayIndexShared
+                    | ArrayIndexMut | ArrayToSliceShared | ArrayToSliceMut
+                    | ArrayRepeat | SliceLen ),
+                    _ ) ->
+                    super#visit_texpression env e)
+            | Fun (FromLlbc (FunId (Regular fid), _lp_id, rg_id)) -> (
+                (* Lookup the function name *)
+                let def = FunDeclId.Map.find fid ctx.fun_ctx.fun_decls in
+                match
+                  (Names.name_no_disambiguators_to_string def.name, rg_id)
+                with
+                | "alloc::boxed::Box::deref", None ->
                     (* [Box::deref] forward is the identity *)
                     let arg, args = Collections.List.pop args in
                     mk_apps arg args
-                | A.BoxDeref, Some _ ->
+                | "alloc::boxed::Box::deref", Some _ ->
                     (* [Box::deref] backward is [()] (doesn't give back anything) *)
                     assert (args = []);
                     mk_unit_rvalue
-                | A.BoxDerefMut, None ->
+                | "alloc::boxed::Box::deref_mut", None ->
                     (* [Box::deref_mut] forward is the identity *)
                     let arg, args = Collections.List.pop args in
                     mk_apps arg args
-                | A.BoxDerefMut, Some _ ->
+                | "alloc::boxed::Box::deref_mut", Some _ ->
                     (* [Box::deref_mut] back is almost the identity:
                      * let box_deref_mut (x_init : t) (x_back : t) : t = x_back
                      * *)
@@ -1560,17 +1569,7 @@ let eliminate_box_functions (_ctx : trans_ctx) (def : fun_decl) : fun_decl =
                       | _ -> raise (Failure "Unreachable")
                     in
                     mk_apps arg args
-                | A.BoxFree, _ ->
-                    assert (args = []);
-                    mk_unit_rvalue
-                | ( ( A.Replace | VecNew | VecPush | VecInsert | VecLen
-                    | VecIndex | VecIndexMut | ArraySubsliceShared
-                    | ArraySubsliceMut | SliceIndexShared | SliceIndexMut
-                    | SliceSubsliceShared | SliceSubsliceMut | ArrayIndexShared
-                    | ArrayIndexMut | ArrayToSliceShared | ArrayToSliceMut
-                    | SliceLen ),
-                    _ ) ->
-                    super#visit_texpression env e)
+                | _ -> super#visit_texpression env e)
             | _ -> super#visit_texpression env e)
         | _ -> super#visit_texpression env e
     end
@@ -1914,7 +1913,7 @@ let apply_end_passes_to_def (ctx : trans_ctx) (def : fun_decl) : fun_decl =
     [ctx]: used only for printing.
  *)
 let apply_passes_to_def (ctx : trans_ctx) (def : fun_decl) :
-    (fun_decl * fun_decl list) option =
+    fun_and_loops option =
   (* Debug *)
   log#ldebug
     (lazy
@@ -1955,9 +1954,9 @@ let apply_passes_to_def (ctx : trans_ctx) (def : fun_decl) :
       let def, loops = decompose_loops def in
 
       (* Apply the remaining passes *)
-      let def = apply_end_passes_to_def ctx def in
+      let f = apply_end_passes_to_def ctx def in
       let loops = List.map (apply_end_passes_to_def ctx) loops in
-      Some (def, loops)
+      Some { f; loops }
 
 (** Small utility for {!filter_loop_inputs} *)
 let filter_prefix (keep : bool list) (ls : 'a list) : 'a list =
@@ -1983,8 +1982,8 @@ end
 module FunLoopIdMap = Collections.MakeMap (FunLoopIdOrderedType)
 
 (** Filter the useless loop input parameters. *)
-let filter_loop_inputs (transl : (bool * pure_fun_translation) list) :
-    (bool * pure_fun_translation) list =
+let filter_loop_inputs (transl : pure_fun_translation list) :
+    pure_fun_translation list =
   (* We need to explore groups of mutually recursive functions. In order
      to compute which parameters are useless, we need to explore the
      functions by groups of mutually recursive definitions.
@@ -2002,10 +2001,11 @@ let filter_loop_inputs (transl : (bool * pure_fun_translation) list) :
       (List.concat
          (List.concat
             (List.map
-               (fun (_, ((fwd, loops_fwd), backs)) ->
-                 [ fwd :: loops_fwd ]
+               (fun { fwd; backs; _ } ->
+                 [ fwd.f :: fwd.loops ]
                  :: List.map
-                      (fun (back, loops_back) -> [ back :: loops_back ])
+                      (fun { f = back; loops = loops_back } ->
+                        [ back :: loops_back ])
                       backs)
                transl)))
   in
@@ -2030,7 +2030,6 @@ let filter_loop_inputs (transl : (bool * pure_fun_translation) list) :
      additional parameters.
   *)
   let used_map = ref FunLoopIdMap.empty in
-  let fun_id_to_fun_loop_id (fid, loop_id, _) = (fid, loop_id) in
 
   (* We start by computing the filtering information, for each function *)
   let compute_one_filter_info (decl : fun_decl) =
@@ -2051,7 +2050,7 @@ let filter_loop_inputs (transl : (bool * pure_fun_translation) list) :
     let inputs_set = VarId.Set.of_list (List.map var_get_id inputs_prefix) in
     assert (Option.is_some decl.loop_id);
 
-    let fun_id = (A.Regular decl.def_id, decl.loop_id) in
+    let fun_id = (E.Regular decl.def_id, decl.loop_id) in
 
     let set_used vid =
       used := List.map (fun (vid', b) -> (vid', b || vid = vid')) !used
@@ -2075,8 +2074,8 @@ let filter_loop_inputs (transl : (bool * pure_fun_translation) list) :
               match e_app.e with
               | Qualif qualif -> (
                   match qualif.id with
-                  | FunOrOp (Fun (FromLlbc fun_id')) ->
-                      if fun_id_to_fun_loop_id fun_id' = fun_id then (
+                  | FunOrOp (Fun (FromLlbc (FunId fun_id', loop_id', _))) ->
+                      if (fun_id', loop_id') = fun_id then (
                         (* For each argument, check if it is exactly the original
                            input parameter. Note that there shouldn't be partial
                            applications of loop functions: the number of arguments
@@ -2135,22 +2134,15 @@ let filter_loop_inputs (transl : (bool * pure_fun_translation) list) :
   (* We then apply the filtering to all the function definitions at once *)
   let filter_in_one (decl : fun_decl) : fun_decl =
     (* Filter the function signature *)
-    let fun_id = (A.Regular decl.def_id, decl.loop_id, decl.back_id) in
+    let fun_id = (E.Regular decl.def_id, decl.loop_id) in
     let decl =
-      match FunLoopIdMap.find_opt (fun_id_to_fun_loop_id fun_id) !used_map with
+      match FunLoopIdMap.find_opt fun_id !used_map with
       | None -> (* Nothing to filter *) decl
       | Some used_info ->
           let num_filtered =
             List.length (List.filter (fun b -> not b) used_info)
           in
-          let {
-            type_params;
-            const_generic_params;
-            inputs;
-            output;
-            doutputs;
-            info;
-          } =
+          let { generics; preds; inputs; output; doutputs; info } =
             decl.signature
           in
           let {
@@ -2178,16 +2170,7 @@ let filter_loop_inputs (transl : (bool * pure_fun_translation) list) :
               effect_info;
             }
           in
-          let signature =
-            {
-              type_params;
-              const_generic_params;
-              inputs;
-              output;
-              doutputs;
-              info;
-            }
-          in
+          let signature = { generics; preds; inputs; output; doutputs; info } in
 
           { decl with signature }
     in
@@ -2201,9 +2184,7 @@ let filter_loop_inputs (transl : (bool * pure_fun_translation) list) :
           let { inputs; inputs_lvs; body } = body in
 
           let inputs, inputs_lvs =
-            match
-              FunLoopIdMap.find_opt (fun_id_to_fun_loop_id fun_id) !used_map
-            with
+            match FunLoopIdMap.find_opt fun_id !used_map with
             | None -> (* Nothing to filter *) (inputs, inputs_lvs)
             | Some used_info ->
                 let inputs = filter_prefix used_info inputs in
@@ -2223,11 +2204,10 @@ let filter_loop_inputs (transl : (bool * pure_fun_translation) list) :
                     match e_app.e with
                     | Qualif qualif -> (
                         match qualif.id with
-                        | FunOrOp (Fun (FromLlbc fun_id)) -> (
+                        | FunOrOp (Fun (FromLlbc (FunId fun_id, loop_id, _)))
+                          -> (
                             match
-                              FunLoopIdMap.find_opt
-                                (fun_id_to_fun_loop_id fun_id)
-                                !used_map
+                              FunLoopIdMap.find_opt (fun_id, loop_id) !used_map
                             with
                             | None -> super#visit_texpression env e
                             | Some used_info ->
@@ -2267,13 +2247,13 @@ let filter_loop_inputs (transl : (bool * pure_fun_translation) list) :
   in
   let transl =
     List.map
-      (fun (b, (fwd, backs)) ->
-        let filter_fun_and_loops (f, fl) =
-          (filter_in_one f, List.map filter_in_one fl)
+      (fun trans ->
+        let filter_fun_and_loops f =
+          { f = filter_in_one f.f; loops = List.map filter_in_one f.loops }
         in
-        let fwd = filter_fun_and_loops fwd in
-        let backs = List.map filter_fun_and_loops backs in
-        (b, (fwd, backs)))
+        let fwd = filter_fun_and_loops trans.fwd in
+        let backs = List.map filter_fun_and_loops trans.backs in
+        { trans with fwd; backs })
       transl
   in
 
@@ -2294,18 +2274,17 @@ let filter_loop_inputs (transl : (bool * pure_fun_translation) list) :
     but convenient.
  *)
 let apply_passes_to_pure_fun_translations (ctx : trans_ctx)
-    (transl : (fun_decl * fun_decl list) list) :
-    (bool * pure_fun_translation) list =
-  let apply_to_one (trans : fun_decl * fun_decl list) :
-      bool * pure_fun_translation =
+    (transl : (fun_decl * fun_decl list) list) : pure_fun_translation list =
+  let apply_to_one (trans : fun_decl * fun_decl list) : pure_fun_translation =
     (* Apply the passes to the individual functions *)
-    let forward, backwards = trans in
-    let forward = Option.get (apply_passes_to_def ctx forward) in
-    let backwards = List.filter_map (apply_passes_to_def ctx) backwards in
-    let trans = (forward, backwards) in
+    let fwd, backs = trans in
+    let fwd = Option.get (apply_passes_to_def ctx fwd) in
+    let backs = List.filter_map (apply_passes_to_def ctx) backs in
     (* Compute whether we need to filter the forward function or not *)
-    (keep_forward trans, trans)
+    let keep_fwd = keep_forward fwd backs in
+    { keep_fwd; fwd; backs }
   in
+
   let transl = List.map apply_to_one transl in
 
   (* Filter the useless inputs in the loop functions *)
diff --git a/compiler/PureTypeCheck.ml b/compiler/PureTypeCheck.ml
index 8d28bb8a..2ad942bb 100644
--- a/compiler/PureTypeCheck.ml
+++ b/compiler/PureTypeCheck.ml
@@ -9,17 +9,19 @@ open PureUtils
     of fields is fixed: it shouldn't be used for arrays, slices, etc.
  *)
 let get_adt_field_types (type_decls : type_decl TypeDeclId.Map.t)
-    (type_id : type_id) (variant_id : VariantId.id option) (tys : ty list)
-    (cgs : const_generic list) : ty list =
+    (type_id : type_id) (variant_id : VariantId.id option)
+    (generics : generic_args) : ty list =
   match type_id with
   | Tuple ->
       (* Tuple *)
+      assert (generics.const_generics = []);
+      assert (generics.trait_refs = []);
       assert (variant_id = None);
-      tys
+      generics.types
   | AdtId def_id ->
       (* "Regular" ADT *)
       let def = TypeDeclId.Map.find def_id type_decls in
-      type_decl_get_instantiated_fields_types def variant_id tys cgs
+      type_decl_get_instantiated_fields_types def variant_id generics
   | Assumed aty -> (
       (* Assumed type *)
       match aty with
@@ -27,14 +29,14 @@ let get_adt_field_types (type_decls : type_decl TypeDeclId.Map.t)
           (* This type is opaque *)
           raise (Failure "Unreachable: opaque type")
       | Result ->
-          let ty = Collections.List.to_cons_nil tys in
+          let ty = Collections.List.to_cons_nil generics.types in
           let variant_id = Option.get variant_id in
           if variant_id = result_return_id then [ ty ]
           else if variant_id = result_fail_id then [ mk_error_ty ]
           else
             raise (Failure "Unreachable: improper variant id for result type")
       | Error ->
-          assert (tys = []);
+          assert (generics = empty_generic_args);
           let variant_id = Option.get variant_id in
           assert (
             variant_id = error_failure_id || variant_id = error_out_of_fuel_id);
@@ -44,18 +46,7 @@ let get_adt_field_types (type_decls : type_decl TypeDeclId.Map.t)
           if variant_id = fuel_zero_id then []
           else if variant_id = fuel_succ_id then [ mk_fuel_ty ]
           else raise (Failure "Unreachable: improper variant id for fuel type")
-      | Option ->
-          let ty = Collections.List.to_cons_nil tys in
-          let variant_id = Option.get variant_id in
-          if variant_id = option_some_id then [ ty ]
-          else if variant_id = option_none_id then []
-          else
-            raise (Failure "Unreachable: improper variant id for option type")
-      | Range ->
-          let ty = Collections.List.to_cons_nil tys in
-          assert (variant_id = None);
-          [ ty; ty ]
-      | Vec | Array | Slice | Str ->
+      | Array | Slice | Str | RawPtr _ ->
           (* Array: when not symbolic values (for instance, because of aggregates),
              the array expressions are introduced as struct updates *)
           raise (Failure "Attempting to access the fields of an opaque type"))
@@ -65,6 +56,9 @@ type tc_ctx = {
   global_decls : A.global_decl A.GlobalDeclId.Map.t;
       (** The global declarations *)
   env : ty VarId.Map.t;  (** Environment from variables to types *)
+  const_generics : ty T.ConstGenericVarId.Map.t;
+      (** The types of the const generics *)
+      (* TODO: add trait type constraints *)
 }
 
 let check_literal (v : literal) (ty : literal_type) : unit =
@@ -86,12 +80,13 @@ let rec check_typed_pattern (ctx : tc_ctx) (v : typed_pattern) : tc_ctx =
       { ctx with env }
   | PatAdt av ->
       (* Compute the field types *)
-      let type_id, tys, cgs = ty_as_adt v.ty in
+      let type_id, generics = ty_as_adt v.ty in
       let field_tys =
-        get_adt_field_types ctx.type_decls type_id av.variant_id tys cgs
+        get_adt_field_types ctx.type_decls type_id av.variant_id generics
       in
       let check_value (ctx : tc_ctx) (ty : ty) (v : typed_pattern) : tc_ctx =
         if ty <> v.ty then (
+          (* TODO: we need to normalize the types *)
           log#serror
             ("check_typed_pattern: not the same types:" ^ "\n- ty: "
            ^ show_ty ty ^ "\n- v.ty: " ^ show_ty v.ty);
@@ -115,6 +110,9 @@ let rec check_texpression (ctx : tc_ctx) (e : texpression) : unit =
       match VarId.Map.find_opt var_id ctx.env with
       | None -> ()
       | Some ty -> assert (ty = e.ty))
+  | CVar cg_id ->
+      let ty = T.ConstGenericVarId.Map.find cg_id ctx.const_generics in
+      assert (ty = e.ty)
   | Const cv -> check_literal cv (ty_as_literal e.ty)
   | App (app, arg) ->
       let input_ty, output_ty = destruct_arrow app.ty in
@@ -133,35 +131,34 @@ let rec check_texpression (ctx : tc_ctx) (e : texpression) : unit =
       match qualif.id with
       | FunOrOp _ -> () (* TODO *)
       | Global _ -> () (* TODO *)
+      | TraitConst _ -> () (* TODO *)
       | Proj { adt_id = proj_adt_id; field_id } ->
           (* Note we can only project fields of structures (not enumerations) *)
           (* Deconstruct the projector type *)
           let adt_ty, field_ty = destruct_arrow e.ty in
-          let adt_id, adt_type_args, adt_cg_args = ty_as_adt adt_ty in
+          let adt_id, adt_generics = ty_as_adt adt_ty in
           (* Check the ADT type *)
           assert (adt_id = proj_adt_id);
-          assert (adt_type_args = qualif.type_args);
-          assert (adt_cg_args = qualif.const_generic_args);
+          assert (adt_generics = qualif.generics);
           (* Retrieve and check the expected field type *)
           let variant_id = None in
           let expected_field_tys =
             get_adt_field_types ctx.type_decls proj_adt_id variant_id
-              qualif.type_args qualif.const_generic_args
+              qualif.generics
           in
           let expected_field_ty = FieldId.nth expected_field_tys field_id in
           assert (expected_field_ty = field_ty)
       | AdtCons id -> (
           let expected_field_tys =
             get_adt_field_types ctx.type_decls id.adt_id id.variant_id
-              qualif.type_args qualif.const_generic_args
+              qualif.generics
           in
           let field_tys, adt_ty = destruct_arrows e.ty in
           assert (expected_field_tys = field_tys);
           match adt_ty with
-          | Adt (type_id, tys, cgs) ->
+          | Adt (type_id, generics) ->
               assert (type_id = id.adt_id);
-              assert (tys = qualif.type_args);
-              assert (cgs = qualif.const_generic_args)
+              assert (generics = qualif.generics)
           | _ -> raise (Failure "Unreachable")))
   | Let (monadic, pat, re, e_next) ->
       let expected_pat_ty = if monadic then destruct_result re.ty else re.ty in
@@ -207,15 +204,14 @@ let rec check_texpression (ctx : tc_ctx) (e : texpression) : unit =
          | Some ty -> assert (ty = e.ty));
       (* Check the fields *)
       (* Retrieve and check the expected field type *)
-      let adt_id, adt_type_args, adt_cg_args = ty_as_adt e.ty in
+      let adt_id, adt_generics = ty_as_adt e.ty in
       assert (adt_id = supd.struct_id);
       (* The id can only be: a custom type decl or an array *)
       match adt_id with
       | AdtId _ ->
           let variant_id = None in
           let expected_field_tys =
-            get_adt_field_types ctx.type_decls adt_id variant_id adt_type_args
-              adt_cg_args
+            get_adt_field_types ctx.type_decls adt_id variant_id adt_generics
           in
           List.iter
             (fun (fid, fe) ->
@@ -224,7 +220,9 @@ let rec check_texpression (ctx : tc_ctx) (e : texpression) : unit =
               check_texpression ctx fe)
             supd.updates
       | Assumed Array ->
-          let expected_field_ty = Collections.List.to_cons_nil adt_type_args in
+          let expected_field_ty =
+            Collections.List.to_cons_nil adt_generics.types
+          in
           List.iter
             (fun (_, fe) ->
               assert (expected_field_ty = fe.ty);
diff --git a/compiler/PureUtils.ml b/compiler/PureUtils.ml
index 1c8d8921..3aeabffe 100644
--- a/compiler/PureUtils.ml
+++ b/compiler/PureUtils.ml
@@ -89,14 +89,31 @@ let mk_mplace (var_id : E.VarId.id) (name : string option)
     (projection : mprojection) : mplace =
   { var_id; name; projection }
 
+let empty_generic_params : generic_params =
+  { types = []; const_generics = []; trait_clauses = [] }
+
+let empty_generic_args : generic_args =
+  { types = []; const_generics = []; trait_refs = [] }
+
+let mk_generic_args_from_types (types : ty list) : generic_args =
+  { types; const_generics = []; trait_refs = [] }
+
+type subst = {
+  ty_subst : TypeVarId.id -> ty;
+  cg_subst : ConstGenericVarId.id -> const_generic;
+  tr_subst : TraitClauseId.id -> trait_instance_id;
+  tr_self : trait_instance_id;
+}
+
 (** Type substitution *)
-let ty_substitute (tsubst : TypeVarId.id -> ty)
-    (cgsubst : ConstGenericVarId.id -> const_generic) (ty : ty) : ty =
+let ty_substitute (subst : subst) (ty : ty) : ty =
   let obj =
     object
       inherit [_] map_ty
-      method! visit_TypeVar _ var_id = tsubst var_id
-      method! visit_ConstGenericVar _ var_id = cgsubst var_id
+      method! visit_TypeVar _ var_id = subst.ty_subst var_id
+      method! visit_ConstGenericVar _ var_id = subst.cg_subst var_id
+      method! visit_Clause _ id = subst.tr_subst id
+      method! visit_Self _ = subst.tr_self
     end
   in
   obj#visit_ty () ty
@@ -115,6 +132,18 @@ let make_const_generic_subst (vars : const_generic_var list)
     (cgs : const_generic list) : ConstGenericVarId.id -> const_generic =
   Substitute.make_const_generic_subst_from_vars vars cgs
 
+let make_trait_subst (clauses : trait_clause list) (refs : trait_ref list) :
+    TraitClauseId.id -> trait_instance_id =
+  let clauses = List.map (fun x -> x.clause_id) clauses in
+  let refs = List.map (fun x -> TraitRef x) refs in
+  let ls = List.combine clauses refs in
+  let mp =
+    List.fold_left
+      (fun mp (k, v) -> TraitClauseId.Map.add k v mp)
+      TraitClauseId.Map.empty ls
+  in
+  fun id -> TraitClauseId.Map.find id mp
+
 (** Retrieve the list of fields for the given variant of a {!type:Aeneas.Pure.type_decl}.
 
     Raises [Invalid_argument] if the arguments are incorrect.
@@ -135,20 +164,27 @@ let type_decl_get_fields (def : type_decl)
              - def: " ^ show_type_decl def ^ "\n- opt_variant_id: "
           ^ opt_variant_id))
 
+let make_subst_from_generics (params : generic_params) (args : generic_args)
+    (tr_self : trait_instance_id) : subst =
+  let ty_subst = make_type_subst params.types args.types in
+  let cg_subst =
+    make_const_generic_subst params.const_generics args.const_generics
+  in
+  let tr_subst = make_trait_subst params.trait_clauses args.trait_refs in
+  { ty_subst; cg_subst; tr_subst; tr_self }
+
 (** Instantiate the type variables for the chosen variant in an ADT definition,
     and return the list of the types of its fields *)
 let type_decl_get_instantiated_fields_types (def : type_decl)
-    (opt_variant_id : VariantId.id option) (types : ty list)
-    (cgs : const_generic list) : ty list =
-  let ty_subst = make_type_subst def.type_params types in
-  let cg_subst = make_const_generic_subst def.const_generic_params cgs in
+    (opt_variant_id : VariantId.id option) (generics : generic_args) : ty list =
+  (* There shouldn't be any reference to Self *)
+  let tr_self = UnknownTrait __FUNCTION__ in
+  let subst = make_subst_from_generics def.generics generics tr_self in
   let fields = type_decl_get_fields def opt_variant_id in
-  List.map (fun f -> ty_substitute ty_subst cg_subst f.field_ty) fields
+  List.map (fun f -> ty_substitute subst f.field_ty) fields
 
-let fun_sig_substitute (tsubst : TypeVarId.id -> ty)
-    (cgsubst : ConstGenericVarId.id -> const_generic) (sg : fun_sig) :
-    inst_fun_sig =
-  let subst = ty_substitute tsubst cgsubst in
+let fun_sig_substitute (subst : subst) (sg : fun_sig) : inst_fun_sig =
+  let subst = ty_substitute subst in
   let inputs = List.map subst sg.inputs in
   let output = subst sg.output in
   let doutputs = List.map subst sg.doutputs in
@@ -164,7 +200,8 @@ let fun_sig_substitute (tsubst : TypeVarId.id -> ty)
  *)
 let rec let_group_requires_parentheses (e : texpression) : bool =
   match e.e with
-  | Var _ | Const _ | App _ | Abs _ | Qualif _ | StructUpdate _ -> false
+  | Var _ | CVar _ | Const _ | App _ | Abs _ | Qualif _ | StructUpdate _ ->
+      false
   | Let (monadic, _, _, next_e) ->
       if monadic then true else let_group_requires_parentheses next_e
   | Switch (_, _) -> false
@@ -184,15 +221,18 @@ let is_var (e : texpression) : bool =
 let as_var (e : texpression) : VarId.id =
   match e.e with Var v -> v | _ -> raise (Failure "Unreachable")
 
+let is_cvar (e : texpression) : bool =
+  match e.e with CVar _ -> true | _ -> false
+
 let is_global (e : texpression) : bool =
   match e.e with Qualif { id = Global _; _ } -> true | _ -> false
 
 let is_const (e : texpression) : bool =
   match e.e with Const _ -> true | _ -> false
 
-let ty_as_adt (ty : ty) : type_id * ty list * const_generic list =
+let ty_as_adt (ty : ty) : type_id * generic_args =
   match ty with
-  | Adt (id, tys, cgs) -> (id, tys, cgs)
+  | Adt (id, generics) -> (id, generics)
   | _ -> raise (Failure "Unreachable")
 
 (** Remove the external occurrences of {!Meta} *)
@@ -290,28 +330,30 @@ let destruct_qualif_app (e : texpression) : qualif * texpression list =
 
 (** Destruct an expression into a function call, if possible *)
 let opt_destruct_function_call (e : texpression) :
-    (fun_or_op_id * ty list * texpression list) option =
+    (fun_or_op_id * generic_args * texpression list) option =
   match opt_destruct_qualif_app e with
   | None -> None
   | Some (qualif, args) -> (
       match qualif.id with
-      | FunOrOp fun_id -> Some (fun_id, qualif.type_args, args)
+      | FunOrOp fun_id -> Some (fun_id, qualif.generics, args)
       | _ -> None)
 
 let opt_destruct_result (ty : ty) : ty option =
   match ty with
-  | Adt (Assumed Result, tys, cgs) ->
-      assert (cgs = []);
-      Some (Collections.List.to_cons_nil tys)
+  | Adt (Assumed Result, generics) ->
+      assert (generics.const_generics = []);
+      assert (generics.trait_refs = []);
+      Some (Collections.List.to_cons_nil generics.types)
   | _ -> None
 
 let destruct_result (ty : ty) : ty = Option.get (opt_destruct_result ty)
 
 let opt_destruct_tuple (ty : ty) : ty list option =
   match ty with
-  | Adt (Tuple, tys, cgs) ->
-      assert (cgs = []);
-      Some tys
+  | Adt (Tuple, generics) ->
+      assert (generics.const_generics = []);
+      assert (generics.trait_refs = []);
+      Some generics.types
   | _ -> None
 
 let mk_abs (x : typed_pattern) (e : texpression) : texpression =
@@ -383,14 +425,16 @@ let mk_switch (scrut : texpression) (sb : switch_body) : texpression =
     - if there is > one type: wrap them in a tuple
  *)
 let mk_simpl_tuple_ty (tys : ty list) : ty =
-  match tys with [ ty ] -> ty | _ -> Adt (Tuple, tys, [])
+  match tys with
+  | [ ty ] -> ty
+  | _ -> Adt (Tuple, mk_generic_args_from_types tys)
 
 let mk_bool_ty : ty = Literal Bool
-let mk_unit_ty : ty = Adt (Tuple, [], [])
+let mk_unit_ty : ty = Adt (Tuple, empty_generic_args)
 
 let mk_unit_rvalue : texpression =
   let id = AdtCons { adt_id = Tuple; variant_id = None } in
-  let qualif = { id; type_args = []; const_generic_args = [] } in
+  let qualif = { id; generics = empty_generic_args } in
   let e = Qualif qualif in
   let ty = mk_unit_ty in
   { e; ty }
@@ -430,7 +474,7 @@ let mk_simpl_tuple_pattern (vl : typed_pattern list) : typed_pattern =
   | [ v ] -> v
   | _ ->
       let tys = List.map (fun (v : typed_pattern) -> v.ty) vl in
-      let ty = Adt (Tuple, tys, []) in
+      let ty = Adt (Tuple, mk_generic_args_from_types tys) in
       let value = PatAdt { variant_id = None; field_values = vl } in
       { value; ty }
 
@@ -441,11 +485,11 @@ let mk_simpl_tuple_texpression (vl : texpression list) : texpression =
   | _ ->
       (* Compute the types of the fields, and the type of the tuple constructor *)
       let tys = List.map (fun (v : texpression) -> v.ty) vl in
-      let ty = Adt (Tuple, tys, []) in
+      let ty = Adt (Tuple, mk_generic_args_from_types tys) in
       let ty = mk_arrows tys ty in
       (* Construct the tuple constructor qualifier *)
       let id = AdtCons { adt_id = Tuple; variant_id = None } in
-      let qualif = { id; type_args = tys; const_generic_args = [] } in
+      let qualif = { id; generics = mk_generic_args_from_types tys } in
       (* Put everything together *)
       let cons = { e = Qualif qualif; ty } in
       mk_apps cons vl
@@ -463,32 +507,36 @@ let ty_as_integer (t : ty) : T.integer_type =
 let ty_as_literal (t : ty) : T.literal_type =
   match t with Literal ty -> ty | _ -> raise (Failure "Unreachable")
 
-let mk_state_ty : ty = Adt (Assumed State, [], [])
-let mk_result_ty (ty : ty) : ty = Adt (Assumed Result, [ ty ], [])
-let mk_error_ty : ty = Adt (Assumed Error, [], [])
-let mk_fuel_ty : ty = Adt (Assumed Fuel, [], [])
+let mk_state_ty : ty = Adt (Assumed State, empty_generic_args)
+
+let mk_result_ty (ty : ty) : ty =
+  Adt (Assumed Result, mk_generic_args_from_types [ ty ])
+
+let mk_error_ty : ty = Adt (Assumed Error, empty_generic_args)
+let mk_fuel_ty : ty = Adt (Assumed Fuel, empty_generic_args)
 
 let mk_error (error : VariantId.id) : texpression =
   let ty = mk_error_ty in
   let id = AdtCons { adt_id = Assumed Error; variant_id = Some error } in
-  let qualif = { id; type_args = []; const_generic_args = [] } in
+  let qualif = { id; generics = empty_generic_args } in
   let e = Qualif qualif in
   { e; ty }
 
 let unwrap_result_ty (ty : ty) : ty =
   match ty with
-  | Adt (Assumed Result, [ ty ], cgs) ->
-      assert (cgs = []);
+  | Adt
+      (Assumed Result, { types = [ ty ]; const_generics = []; trait_refs = [] })
+    ->
       ty
   | _ -> raise (Failure "not a result type")
 
 let mk_result_fail_texpression (error : texpression) (ty : ty) : texpression =
   let type_args = [ ty ] in
-  let ty = Adt (Assumed Result, type_args, []) in
+  let ty = Adt (Assumed Result, mk_generic_args_from_types type_args) in
   let id =
     AdtCons { adt_id = Assumed Result; variant_id = Some result_fail_id }
   in
-  let qualif = { id; type_args; const_generic_args = [] } in
+  let qualif = { id; generics = mk_generic_args_from_types type_args } in
   let cons_e = Qualif qualif in
   let cons_ty = mk_arrow error.ty ty in
   let cons = { e = cons_e; ty = cons_ty } in
@@ -501,11 +549,11 @@ let mk_result_fail_texpression_with_error_id (error : VariantId.id) (ty : ty) :
 
 let mk_result_return_texpression (v : texpression) : texpression =
   let type_args = [ v.ty ] in
-  let ty = Adt (Assumed Result, type_args, []) in
+  let ty = Adt (Assumed Result, mk_generic_args_from_types type_args) in
   let id =
     AdtCons { adt_id = Assumed Result; variant_id = Some result_return_id }
   in
-  let qualif = { id; type_args; const_generic_args = [] } in
+  let qualif = { id; generics = mk_generic_args_from_types type_args } in
   let cons_e = Qualif qualif in
   let cons_ty = mk_arrow v.ty ty in
   let cons = { e = cons_e; ty = cons_ty } in
@@ -514,7 +562,7 @@ let mk_result_return_texpression (v : texpression) : texpression =
 (** Create a [Fail err] pattern which captures the error *)
 let mk_result_fail_pattern (error_pat : pattern) (ty : ty) : typed_pattern =
   let error_pat : typed_pattern = { value = error_pat; ty = mk_error_ty } in
-  let ty = Adt (Assumed Result, [ ty ], []) in
+  let ty = Adt (Assumed Result, mk_generic_args_from_types [ ty ]) in
   let value =
     PatAdt { variant_id = Some result_fail_id; field_values = [ error_pat ] }
   in
@@ -526,7 +574,7 @@ let mk_result_fail_pattern_ignore_error (ty : ty) : typed_pattern =
   mk_result_fail_pattern error_pat ty
 
 let mk_result_return_pattern (v : typed_pattern) : typed_pattern =
-  let ty = Adt (Assumed Result, [ v.ty ], []) in
+  let ty = Adt (Assumed Result, mk_generic_args_from_types [ v.ty ]) in
   let value =
     PatAdt { variant_id = Some result_return_id; field_values = [ v ] }
   in
@@ -561,11 +609,11 @@ let rec typed_pattern_to_texpression (pat : typed_pattern) : texpression option
           let fields_values = List.map (fun e -> Option.get e) fields in
 
           (* Retrieve the type id and the type args from the pat type (simpler this way *)
-          let adt_id, type_args, const_generic_args = ty_as_adt pat.ty in
+          let adt_id, generics = ty_as_adt pat.ty in
 
           (* Create the constructor *)
           let qualif_id = AdtCons { adt_id; variant_id = av.variant_id } in
-          let qualif = { id = qualif_id; type_args; const_generic_args } in
+          let qualif = { id = qualif_id; generics } in
           let cons_e = Qualif qualif in
           let field_tys =
             List.map (fun (v : texpression) -> v.ty) fields_values
@@ -577,3 +625,55 @@ let rec typed_pattern_to_texpression (pat : typed_pattern) : texpression option
           Some (mk_apps cons fields_values).e
   in
   match e_opt with None -> None | Some e -> Some { e; ty = pat.ty }
+
+type trait_decl_method_decl_id = { is_provided : bool; id : fun_decl_id }
+
+let trait_decl_get_method (trait_decl : trait_decl) (method_name : string) :
+    trait_decl_method_decl_id =
+  (* First look in the required methods *)
+  let method_id =
+    List.find_opt (fun (s, _) -> s = method_name) trait_decl.required_methods
+  in
+  match method_id with
+  | Some (_, id) -> { is_provided = false; id }
+  | None ->
+      (* Must be a provided method *)
+      let _, id =
+        List.find (fun (s, _) -> s = method_name) trait_decl.provided_methods
+      in
+      { is_provided = true; id = Option.get id }
+
+let trait_decl_is_empty (trait_decl : trait_decl) : bool =
+  let {
+    def_id = _;
+    name = _;
+    generics = _;
+    preds = _;
+    parent_clauses;
+    consts;
+    types;
+    required_methods;
+    provided_methods;
+  } =
+    trait_decl
+  in
+  parent_clauses = [] && consts = [] && types = [] && required_methods = []
+  && provided_methods = []
+
+let trait_impl_is_empty (trait_impl : trait_impl) : bool =
+  let {
+    def_id = _;
+    name = _;
+    impl_trait = _;
+    generics = _;
+    preds = _;
+    parent_trait_refs;
+    consts;
+    types;
+    required_methods;
+    provided_methods;
+  } =
+    trait_impl
+  in
+  parent_trait_refs = [] && consts = [] && types = [] && required_methods = []
+  && provided_methods = []
diff --git a/compiler/ReorderDecls.ml b/compiler/ReorderDecls.ml
index fc4744bc..10b68da3 100644
--- a/compiler/ReorderDecls.ml
+++ b/compiler/ReorderDecls.ml
@@ -38,14 +38,16 @@ let compute_body_fun_deps (e : texpression) : FunIdSet.t =
 
       method! visit_qualif _ id =
         match id.id with
-        | FunOrOp (Unop _ | Binop _) | Global _ | AdtCons _ | Proj _ -> ()
+        | FunOrOp (Unop _ | Binop _)
+        | Global _ | AdtCons _ | Proj _ | TraitConst _ ->
+            ()
         | FunOrOp (Fun fid) -> (
             match fid with
             | Pure _ -> ()
             | FromLlbc (fid, lp_id, rg_id) -> (
                 match fid with
-                | Assumed _ -> ()
-                | Regular fid ->
+                | FunId (Assumed _) -> ()
+                | TraitMethod (_, _, fid) | FunId (Regular fid) ->
                     let id = { def_id = fid; lp_id; rg_id } in
                     ids := FunIdSet.add id !ids))
     end
diff --git a/compiler/Substitute.ml b/compiler/Substitute.ml
index 38850243..23f618e2 100644
--- a/compiler/Substitute.ml
+++ b/compiler/Substitute.ml
@@ -9,51 +9,70 @@ module E = Expressions
 module A = LlbcAst
 module C = Contexts
 
-(** Substitute types variables and regions in a type. *)
-let ty_substitute (rsubst : 'r1 -> 'r2) (tsubst : T.TypeVarId.id -> 'r2 T.ty)
-    (cgsubst : T.ConstGenericVarId.id -> T.const_generic) (ty : 'r1 T.ty) :
-    'r2 T.ty =
-  let open T in
-  let visitor =
-    object
-      inherit [_] map_ty
-      method visit_'r _ r = rsubst r
-      method! visit_TypeVar _ id = tsubst id
+type ('r1, 'r2) subst = {
+  r_subst : 'r1 -> 'r2;
+  ty_subst : T.TypeVarId.id -> 'r2 T.ty;
+  cg_subst : T.ConstGenericVarId.id -> T.const_generic;
+      (** Substitution from *local* trait clause to trait instance *)
+  tr_subst : T.TraitClauseId.id -> 'r2 T.trait_instance_id;
+      (** Substitution for the [Self] trait instance *)
+  tr_self : 'r2 T.trait_instance_id;
+}
+
+let ty_substitute_visitor (subst : ('r1, 'r2) subst) =
+  object
+    inherit [_] T.map_ty
+    method visit_'r _ r = subst.r_subst r
+    method! visit_TypeVar _ id = subst.ty_subst id
 
-      method! visit_type_var_id _ _ =
-        (* We should never get here because we reimplemented [visit_TypeVar] *)
-        raise (Failure "Unexpected")
+    method! visit_type_var_id _ _ =
+      (* We should never get here because we reimplemented [visit_TypeVar] *)
+      raise (Failure "Unexpected")
 
-      method! visit_ConstGenericVar _ id = cgsubst id
+    method! visit_ConstGenericVar _ id = subst.cg_subst id
 
-      method! visit_const_generic_var_id _ _ =
-        (* We should never get here because we reimplemented [visit_Var] *)
-        raise (Failure "Unexpected")
-    end
-  in
+    method! visit_const_generic_var_id _ _ =
+      (* We should never get here because we reimplemented [visit_Var] *)
+      raise (Failure "Unexpected")
 
-  visitor#visit_ty () ty
+    method! visit_Clause _ id = subst.tr_subst id
+    method! visit_Self _ = subst.tr_self
+  end
 
-let rty_substitute (rsubst : T.RegionId.id -> T.RegionId.id)
-    (tsubst : T.TypeVarId.id -> T.rty)
-    (cgsubst : T.ConstGenericVarId.id -> T.const_generic) (ty : T.rty) : T.rty =
-  let rsubst r =
-    match r with T.Static -> T.Static | T.Var rid -> T.Var (rsubst rid)
-  in
-  ty_substitute rsubst tsubst cgsubst ty
+(** Substitute types variables and regions in a type.
 
-let ety_substitute (tsubst : T.TypeVarId.id -> T.ety)
-    (cgsubst : T.ConstGenericVarId.id -> T.const_generic) (ty : T.ety) : T.ety =
-  let rsubst r = r in
-  ty_substitute rsubst tsubst cgsubst ty
+    **IMPORTANT**: this doesn't normalize the types.
+ *)
+let ty_substitute (subst : ('r1, 'r2) subst) (ty : 'r1 T.ty) : 'r2 T.ty =
+  let visitor = ty_substitute_visitor subst in
+  visitor#visit_ty () ty
+
+(** **IMPORTANT**: this doesn't normalize the types. *)
+let trait_ref_substitute (subst : ('r1, 'r2) subst) (tr : 'r1 T.trait_ref) :
+    'r2 T.trait_ref =
+  let visitor = ty_substitute_visitor subst in
+  visitor#visit_trait_ref () tr
+
+(** **IMPORTANT**: this doesn't normalize the types. *)
+let generic_args_substitute (subst : ('r1, 'r2) subst) (g : 'r1 T.generic_args)
+    : 'r2 T.generic_args =
+  let visitor = ty_substitute_visitor subst in
+  visitor#visit_generic_args () g
+
+let erase_regions_subst : ('r, T.erased_region) subst =
+  {
+    r_subst = (fun _ -> T.Erased);
+    ty_subst = (fun vid -> T.TypeVar vid);
+    cg_subst = (fun id -> T.ConstGenericVar id);
+    tr_subst = (fun id -> T.Clause id);
+    tr_self = T.Self;
+  }
 
 (** Convert an {!T.rty} to an {!T.ety} by erasing the region variables *)
-let erase_regions (ty : T.rty) : T.ety =
-  ty_substitute
-    (fun _ -> T.Erased)
-    (fun vid -> T.TypeVar vid)
-    (fun id -> T.ConstGenericVar id)
-    ty
+let erase_regions (ty : 'r T.ty) : T.ety = ty_substitute erase_regions_subst ty
+
+let trait_ref_erase_regions (tr : 'r T.trait_ref) : T.etrait_ref =
+  trait_ref_substitute erase_regions_subst tr
 
 (** Generate fresh regions for region variables.
 
@@ -78,18 +97,20 @@ let fresh_regions_with_substs (region_vars : T.region_var list) :
   (* Generate the substitution from region var id to region *)
   let rid_subst id = T.RegionVarId.Map.find id rid_map in
   (* Generate the substitution from region to region *)
-  let rsubst r =
+  let r_subst r =
     match r with T.Static -> T.Static | T.Var id -> T.Var (rid_subst id)
   in
   (* Return *)
-  (fresh_region_ids, rid_subst, rsubst)
+  (fresh_region_ids, rid_subst, r_subst)
 
-(** Erase the regions in a type and substitute the type variables *)
-let erase_regions_substitute_types (tsubst : T.TypeVarId.id -> T.ety)
-    (cgsubst : T.ConstGenericVarId.id -> T.const_generic)
-    (ty : 'r T.region T.ty) : T.ety =
-  let rsubst (_ : 'r T.region) : T.erased_region = T.Erased in
-  ty_substitute rsubst tsubst cgsubst ty
+(** Erase the regions in a type and perform a substitution *)
+let erase_regions_substitute_types (ty_subst : T.TypeVarId.id -> T.ety)
+    (cg_subst : T.ConstGenericVarId.id -> T.const_generic)
+    (tr_subst : T.TraitClauseId.id -> T.etrait_instance_id)
+    (tr_self : T.etrait_instance_id) (ty : 'r T.ty) : T.ety =
+  let r_subst (_ : 'r) : T.erased_region = T.Erased in
+  let subst = { r_subst; ty_subst; cg_subst; tr_subst; tr_self } in
+  ty_substitute subst ty
 
 (** Create a region substitution from a list of region variable ids and a list of
     regions (with which to substitute the region variable ids *)
@@ -146,16 +167,81 @@ let make_const_generic_subst_from_vars (vars : T.const_generic_var list)
     (List.map (fun (x : T.const_generic_var) -> x.T.index) vars)
     cgs
 
-(** Instantiate the type variables in an ADT definition, and return, for
-    every variant, the list of the types of its fields *)
-let type_decl_get_instantiated_variants_fields_rtypes (def : T.type_decl)
-    (regions : T.RegionId.id T.region list) (types : T.rty list)
-    (cgs : T.const_generic list) : (T.VariantId.id option * T.rty list) list =
-  let r_subst = make_region_subst_from_vars def.T.region_params regions in
-  let ty_subst = make_type_subst_from_vars def.T.type_params types in
+(** Create a trait substitution from a list of trait clause ids and a list of
+    trait refs *)
+let make_trait_subst (clause_ids : T.TraitClauseId.id list)
+    (trs : 'r T.trait_ref list) : T.TraitClauseId.id -> 'r T.trait_instance_id =
+  let ls = List.combine clause_ids trs in
+  let mp =
+    List.fold_left
+      (fun mp (k, v) -> T.TraitClauseId.Map.add k (T.TraitRef v) mp)
+      T.TraitClauseId.Map.empty ls
+  in
+  fun id -> T.TraitClauseId.Map.find id mp
+
+let make_trait_subst_from_clauses (clauses : T.trait_clause list)
+    (trs : 'r T.trait_ref list) : T.TraitClauseId.id -> 'r T.trait_instance_id =
+  make_trait_subst
+    (List.map (fun (x : T.trait_clause) -> x.T.clause_id) clauses)
+    trs
+
+let make_subst_from_generics (params : T.generic_params)
+    (args : 'r T.region T.generic_args)
+    (tr_self : 'r T.region T.trait_instance_id) :
+    (T.region_var_id T.region, 'r T.region) subst =
+  let r_subst = make_region_subst_from_vars params.T.regions args.T.regions in
+  let ty_subst = make_type_subst_from_vars params.T.types args.T.types in
   let cg_subst =
-    make_const_generic_subst_from_vars def.T.const_generic_params cgs
+    make_const_generic_subst_from_vars params.T.const_generics
+      args.T.const_generics
+  in
+  let tr_subst =
+    make_trait_subst_from_clauses params.T.trait_clauses args.T.trait_refs
+  in
+  { r_subst; ty_subst; cg_subst; tr_subst; tr_self }
+
+let make_subst_from_generics_no_regions :
+      'r.
+      T.generic_params ->
+      'r T.generic_args ->
+      'r T.trait_instance_id ->
+      (T.region_var_id T.region, 'r) subst =
+ fun params args tr_self ->
+  let r_subst _ = raise (Failure "Unexpected region") in
+  let ty_subst = make_type_subst_from_vars params.T.types args.T.types in
+  let cg_subst =
+    make_const_generic_subst_from_vars params.T.const_generics
+      args.T.const_generics
+  in
+  let tr_subst =
+    make_trait_subst_from_clauses params.T.trait_clauses args.T.trait_refs
+  in
+  { r_subst; ty_subst; cg_subst; tr_subst; tr_self }
+
+let make_esubst_from_generics (params : T.generic_params)
+    (generics : T.egeneric_args) (tr_self : T.etrait_instance_id) =
+  let r_subst _ = T.Erased in
+  let ty_subst = make_type_subst_from_vars params.types generics.T.types in
+  let cg_subst =
+    make_const_generic_subst_from_vars params.const_generics
+      generics.T.const_generics
+  in
+  let tr_subst =
+    make_trait_subst_from_clauses params.trait_clauses generics.T.trait_refs
   in
+  { r_subst; ty_subst; cg_subst; tr_subst; tr_self }
+
+(** Instantiate the type variables in an ADT definition, and return, for
+    every variant, the list of the types of its fields.
+
+    **IMPORTANT**: this function doesn't normalize the types, you may want to
+    use the [AssociatedTypes] equivalent instead.
+*)
+let type_decl_get_instantiated_variants_fields_rtypes (def : T.type_decl)
+    (generics : T.rgeneric_args) : (T.VariantId.id option * T.rty list) list =
+  (* There shouldn't be any reference to Self *)
+  let tr_self = T.UnknownTrait __FUNCTION__ in
+  let subst = make_subst_from_generics def.T.generics generics tr_self in
   let (variants_fields : (T.VariantId.id option * T.field list) list) =
     match def.T.kind with
     | T.Enum variants ->
@@ -171,191 +257,220 @@ let type_decl_get_instantiated_variants_fields_rtypes (def : T.type_decl)
   in
   List.map
     (fun (id, fields) ->
-      ( id,
-        List.map
-          (fun f -> ty_substitute r_subst ty_subst cg_subst f.T.field_ty)
-          fields ))
+      (id, List.map (fun f -> ty_substitute subst f.T.field_ty) fields))
     variants_fields
 
 (** Instantiate the type variables in an ADT definition, and return the list
-    of types of the fields for the chosen variant *)
+    of types of the fields for the chosen variant.
+
+    **IMPORTANT**: this function doesn't normalize the types, you may want to
+    use the [AssociatedTypes] equivalent instead.
+*)
 let type_decl_get_instantiated_field_rtypes (def : T.type_decl)
-    (opt_variant_id : T.VariantId.id option)
-    (regions : T.RegionId.id T.region list) (types : T.rty list)
-    (cgs : T.const_generic list) : T.rty list =
-  let r_subst = make_region_subst_from_vars def.T.region_params regions in
-  let ty_subst = make_type_subst_from_vars def.T.type_params types in
-  let cg_subst =
-    make_const_generic_subst_from_vars def.T.const_generic_params cgs
-  in
+    (opt_variant_id : T.VariantId.id option) (generics : T.rgeneric_args) :
+    T.rty list =
+  (* For now, check that there are no clauses - otherwise we might need
+     to normalize the types *)
+  assert (def.generics.trait_clauses = []);
+  (* There shouldn't be any reference to Self *)
+  let tr_self = T.UnknownTrait __FUNCTION__ in
+  let subst = make_subst_from_generics def.T.generics generics tr_self in
   let fields = TU.type_decl_get_fields def opt_variant_id in
-  List.map
-    (fun f -> ty_substitute r_subst ty_subst cg_subst f.T.field_ty)
-    fields
+  List.map (fun f -> ty_substitute subst f.T.field_ty) fields
 
 (** Return the types of the properly instantiated ADT's variant, provided a
-    context *)
+    context.
+
+    **IMPORTANT**: this function doesn't normalize the types, you may want to
+    use the [AssociatedTypes] equivalent instead.
+*)
 let ctx_adt_get_instantiated_field_rtypes (ctx : C.eval_ctx)
     (def_id : T.TypeDeclId.id) (opt_variant_id : T.VariantId.id option)
-    (regions : T.RegionId.id T.region list) (types : T.rty list)
-    (cgs : T.const_generic list) : T.rty list =
+    (generics : T.rgeneric_args) : T.rty list =
   let def = C.ctx_lookup_type_decl ctx def_id in
-  type_decl_get_instantiated_field_rtypes def opt_variant_id regions types cgs
+  type_decl_get_instantiated_field_rtypes def opt_variant_id generics
 
 (** Return the types of the properly instantiated ADT value (note that
-    here, ADT is understood in its broad meaning: ADT, assumed value or tuple) *)
+    here, ADT is understood in its broad meaning: ADT, assumed value or tuple).
+
+    **IMPORTANT**: this function doesn't normalize the types, you may want to
+    use the [AssociatedTypes] equivalent instead.
+ *)
 let ctx_adt_value_get_instantiated_field_rtypes (ctx : C.eval_ctx)
-    (adt : V.adt_value) (id : T.type_id)
-    (region_params : T.RegionId.id T.region list) (type_params : T.rty list)
-    (cg_params : T.const_generic list) : T.rty list =
+    (adt : V.adt_value) (id : T.type_id) (generics : T.rgeneric_args) :
+    T.rty list =
   match id with
   | T.AdtId id ->
       (* Retrieve the types of the fields *)
-      ctx_adt_get_instantiated_field_rtypes ctx id adt.V.variant_id
-        region_params type_params cg_params
+      ctx_adt_get_instantiated_field_rtypes ctx id adt.V.variant_id generics
   | T.Tuple ->
-      assert (List.length region_params = 0);
-      type_params
+      assert (generics.regions = []);
+      generics.types
   | T.Assumed aty -> (
       match aty with
-      | T.Box | T.Vec ->
-          assert (List.length region_params = 0);
-          assert (List.length type_params = 1);
-          assert (List.length cg_params = 0);
-          type_params
-      | T.Option ->
-          assert (List.length region_params = 0);
-          assert (List.length type_params = 1);
-          assert (List.length cg_params = 0);
-          if adt.V.variant_id = Some T.option_some_id then type_params
-          else if adt.V.variant_id = Some T.option_none_id then []
-          else raise (Failure "Unreachable")
-      | T.Range ->
-          assert (List.length region_params = 0);
-          assert (List.length type_params = 1);
-          assert (List.length cg_params = 0);
-          type_params
+      | T.Box ->
+          assert (generics.regions = []);
+          assert (List.length generics.types = 1);
+          assert (generics.const_generics = []);
+          generics.types
       | T.Array | T.Slice | T.Str ->
           (* Those types don't have fields *)
           raise (Failure "Unreachable"))
 
 (** Instantiate the type variables in an ADT definition, and return the list
-    of types of the fields for the chosen variant *)
+    of types of the fields for the chosen variant.
+
+    **IMPORTANT**: this function doesn't normalize the types, you may want to
+    use the [AssociatedTypes] equivalent instead.
+*)
 let type_decl_get_instantiated_field_etypes (def : T.type_decl)
-    (opt_variant_id : T.VariantId.id option) (types : T.ety list)
-    (cgs : T.const_generic list) : T.ety list =
-  let ty_subst = make_type_subst_from_vars def.T.type_params types in
-  let cg_subst =
-    make_const_generic_subst_from_vars def.T.const_generic_params cgs
+    (opt_variant_id : T.VariantId.id option) (generics : T.egeneric_args) :
+    T.ety list =
+  (* For now, check that there are no clauses - otherwise we might need
+     to normalize the types *)
+  assert (def.generics.trait_clauses = []);
+  (* There shouldn't be any reference to Self *)
+  let tr_self : T.erased_region T.trait_instance_id =
+    T.UnknownTrait __FUNCTION__
+  in
+  let { r_subst = _; ty_subst; cg_subst; tr_subst; tr_self } =
+    make_esubst_from_generics def.T.generics generics tr_self
   in
   let fields = TU.type_decl_get_fields def opt_variant_id in
   List.map
-    (fun f -> erase_regions_substitute_types ty_subst cg_subst f.T.field_ty)
+    (fun (f : T.field) ->
+      erase_regions_substitute_types ty_subst cg_subst tr_subst tr_self
+        f.T.field_ty)
     fields
 
 (** Return the types of the properly instantiated ADT's variant, provided a
-    context *)
+    context.
+
+    **IMPORTANT**: this function doesn't normalize the types, you may want to
+    use the [AssociatedTypes] equivalent instead.
+ *)
 let ctx_adt_get_instantiated_field_etypes (ctx : C.eval_ctx)
     (def_id : T.TypeDeclId.id) (opt_variant_id : T.VariantId.id option)
-    (types : T.ety list) (cgs : T.const_generic list) : T.ety list =
+    (generics : T.egeneric_args) : T.ety list =
   let def = C.ctx_lookup_type_decl ctx def_id in
-  type_decl_get_instantiated_field_etypes def opt_variant_id types cgs
+  type_decl_get_instantiated_field_etypes def opt_variant_id generics
 
-let statement_substitute_visitor (tsubst : T.TypeVarId.id -> T.ety)
-    (cgsubst : T.ConstGenericVarId.id -> T.const_generic) =
+let statement_substitute_visitor
+    (subst : (T.erased_region, T.erased_region) subst) =
+  (* Keep in synch with [ty_substitute_visitor] *)
   object
     inherit [_] A.map_statement
-    method! visit_ety _ ty = ety_substitute tsubst cgsubst ty
-    method! visit_ConstGenericVar _ id = cgsubst id
+    method! visit_'r _ r = subst.r_subst r
+    method! visit_TypeVar _ id = subst.ty_subst id
+
+    method! visit_type_var_id _ _ =
+      (* We should never get here because we reimplemented [visit_TypeVar] *)
+      raise (Failure "Unexpected")
+
+    method! visit_ConstGenericVar _ id = subst.cg_subst id
 
     method! visit_const_generic_var_id _ _ =
       (* We should never get here because we reimplemented [visit_Var] *)
       raise (Failure "Unexpected")
+
+    method! visit_Clause _ id = subst.tr_subst id
+    method! visit_Self _ = subst.tr_self
   end
 
 (** Apply a type substitution to a place *)
-let place_substitute (tsubst : T.TypeVarId.id -> T.ety)
-    (cgsubst : T.ConstGenericVarId.id -> T.const_generic) (p : E.place) :
-    E.place =
+let place_substitute (subst : (T.erased_region, T.erased_region) subst)
+    (p : E.place) : E.place =
   (* There is in fact nothing to do *)
-  (statement_substitute_visitor tsubst cgsubst)#visit_place () p
+  (statement_substitute_visitor subst)#visit_place () p
 
 (** Apply a type substitution to an operand *)
-let operand_substitute (tsubst : T.TypeVarId.id -> T.ety)
-    (cgsubst : T.ConstGenericVarId.id -> T.const_generic) (op : E.operand) :
-    E.operand =
-  (statement_substitute_visitor tsubst cgsubst)#visit_operand () op
+let operand_substitute (subst : (T.erased_region, T.erased_region) subst)
+    (op : E.operand) : E.operand =
+  (statement_substitute_visitor subst)#visit_operand () op
 
 (** Apply a type substitution to an rvalue *)
-let rvalue_substitute (tsubst : T.TypeVarId.id -> T.ety)
-    (cgsubst : T.ConstGenericVarId.id -> T.const_generic) (rv : E.rvalue) :
-    E.rvalue =
-  (statement_substitute_visitor tsubst cgsubst)#visit_rvalue () rv
+let rvalue_substitute (subst : (T.erased_region, T.erased_region) subst)
+    (rv : E.rvalue) : E.rvalue =
+  (statement_substitute_visitor subst)#visit_rvalue () rv
 
 (** Apply a type substitution to an assertion *)
-let assertion_substitute (tsubst : T.TypeVarId.id -> T.ety)
-    (cgsubst : T.ConstGenericVarId.id -> T.const_generic) (a : A.assertion) :
-    A.assertion =
-  (statement_substitute_visitor tsubst cgsubst)#visit_assertion () a
+let assertion_substitute (subst : (T.erased_region, T.erased_region) subst)
+    (a : A.assertion) : A.assertion =
+  (statement_substitute_visitor subst)#visit_assertion () a
 
 (** Apply a type substitution to a call *)
-let call_substitute (tsubst : T.TypeVarId.id -> T.ety)
-    (cgsubst : T.ConstGenericVarId.id -> T.const_generic) (call : A.call) :
-    A.call =
-  (statement_substitute_visitor tsubst cgsubst)#visit_call () call
+let call_substitute (subst : (T.erased_region, T.erased_region) subst)
+    (call : A.call) : A.call =
+  (statement_substitute_visitor subst)#visit_call () call
 
 (** Apply a type substitution to a statement *)
-let statement_substitute (tsubst : T.TypeVarId.id -> T.ety)
-    (cgsubst : T.ConstGenericVarId.id -> T.const_generic) (st : A.statement) :
-    A.statement =
-  (statement_substitute_visitor tsubst cgsubst)#visit_statement () st
+let statement_substitute (subst : (T.erased_region, T.erased_region) subst)
+    (st : A.statement) : A.statement =
+  (statement_substitute_visitor subst)#visit_statement () st
 
 (** Apply a type substitution to a function body. Return the local variables
     and the body. *)
-let fun_body_substitute_in_body (tsubst : T.TypeVarId.id -> T.ety)
-    (cgsubst : T.ConstGenericVarId.id -> T.const_generic) (body : A.fun_body) :
+let fun_body_substitute_in_body
+    (subst : (T.erased_region, T.erased_region) subst) (body : A.fun_body) :
     A.var list * A.statement =
-  let rsubst r = r in
   let locals =
     List.map
-      (fun (v : A.var) ->
-        { v with A.var_ty = ty_substitute rsubst tsubst cgsubst v.A.var_ty })
+      (fun (v : A.var) -> { v with A.var_ty = ty_substitute subst v.A.var_ty })
       body.A.locals
   in
-  let body = statement_substitute tsubst cgsubst body.body in
+  let body = statement_substitute subst body.body in
   (locals, body)
 
-(** Substitute a function signature *)
+let trait_type_constraint_substitute (subst : ('r1, 'r2) subst)
+    (ttc : 'r1 T.trait_type_constraint) : 'r2 T.trait_type_constraint =
+  let { T.trait_ref; generics; type_name; ty } = ttc in
+  let visitor = ty_substitute_visitor subst in
+  let trait_ref = visitor#visit_trait_ref () trait_ref in
+  let generics = visitor#visit_generic_args () generics in
+  let ty = visitor#visit_ty () ty in
+  { T.trait_ref; generics; type_name; ty }
+
+(** Substitute a function signature.
+
+    **IMPORTANT:** this function doesn't normalize the types.
+ *)
 let substitute_signature (asubst : T.RegionGroupId.id -> V.AbstractionId.id)
-    (rsubst : T.RegionVarId.id -> T.RegionId.id)
-    (tsubst : T.TypeVarId.id -> T.rty)
-    (cgsubst : T.ConstGenericVarId.id -> T.const_generic) (sg : A.fun_sig) :
-    A.inst_fun_sig =
-  let rsubst' (r : T.RegionVarId.id T.region) : T.RegionId.id T.region =
-    match r with T.Static -> T.Static | T.Var rid -> T.Var (rsubst rid)
+    (r_subst : T.RegionVarId.id -> T.RegionId.id)
+    (ty_subst : T.TypeVarId.id -> T.rty)
+    (cg_subst : T.ConstGenericVarId.id -> T.const_generic)
+    (tr_subst : T.TraitClauseId.id -> T.rtrait_instance_id)
+    (tr_self : T.rtrait_instance_id) (sg : A.fun_sig) : A.inst_fun_sig =
+  let r_subst' (r : T.RegionVarId.id T.region) : T.RegionId.id T.region =
+    match r with T.Static -> T.Static | T.Var rid -> T.Var (r_subst rid)
   in
-  let inputs = List.map (ty_substitute rsubst' tsubst cgsubst) sg.A.inputs in
-  let output = ty_substitute rsubst' tsubst cgsubst sg.A.output in
+  let subst = { r_subst = r_subst'; ty_subst; cg_subst; tr_subst; tr_self } in
+  let inputs = List.map (ty_substitute subst) sg.A.inputs in
+  let output = ty_substitute subst sg.A.output in
   let subst_region_group (rg : T.region_var_group) : A.abs_region_group =
     let id = asubst rg.id in
-    let regions = List.map rsubst rg.regions in
+    let regions = List.map r_subst rg.regions in
     let parents = List.map asubst rg.parents in
     { id; regions; parents }
   in
   let regions_hierarchy = List.map subst_region_group sg.A.regions_hierarchy in
-  { A.regions_hierarchy; inputs; output }
+  let trait_type_constraints =
+    List.map
+      (trait_type_constraint_substitute subst)
+      sg.preds.trait_type_constraints
+  in
+  { A.inputs; output; regions_hierarchy; trait_type_constraints }
 
-(** Substitute type variable identifiers in a type *)
-let ty_substitute_ids (tsubst : T.TypeVarId.id -> T.TypeVarId.id)
-    (cgsubst : T.ConstGenericVarId.id -> T.ConstGenericVarId.id) (ty : 'r T.ty)
+(** Substitute variable identifiers in a type *)
+let ty_substitute_ids (ty_subst : T.TypeVarId.id -> T.TypeVarId.id)
+    (cg_subst : T.ConstGenericVarId.id -> T.ConstGenericVarId.id) (ty : 'r T.ty)
     : 'r T.ty =
   let open T in
   let visitor =
     object
       inherit [_] map_ty
       method visit_'r _ r = r
-      method! visit_type_var_id _ id = tsubst id
-      method! visit_const_generic_var_id _ id = cgsubst id
+      method! visit_type_var_id _ id = ty_subst id
+      method! visit_const_generic_var_id _ id = cg_subst id
     end
   in
 
@@ -371,10 +486,10 @@ let ty_substitute_ids (tsubst : T.TypeVarId.id -> T.TypeVarId.id)
    [visit_'r] if we define a class which visits objects of types [ety] and [rty]
    while inheriting a class which visit [ty]...
 *)
-let subst_ids_visitor (rsubst : T.RegionId.id -> T.RegionId.id)
+let subst_ids_visitor (r_subst : T.RegionId.id -> T.RegionId.id)
     (rvsubst : T.RegionVarId.id -> T.RegionVarId.id)
-    (tsubst : T.TypeVarId.id -> T.TypeVarId.id)
-    (cgsubst : T.ConstGenericVarId.id -> T.ConstGenericVarId.id)
+    (ty_subst : T.TypeVarId.id -> T.TypeVarId.id)
+    (cg_subst : T.ConstGenericVarId.id -> T.ConstGenericVarId.id)
     (ssubst : V.SymbolicValueId.id -> V.SymbolicValueId.id)
     (bsubst : V.BorrowId.id -> V.BorrowId.id)
     (asubst : V.AbstractionId.id -> V.AbstractionId.id) =
@@ -383,10 +498,10 @@ let subst_ids_visitor (rsubst : T.RegionId.id -> T.RegionId.id)
       inherit [_] T.map_ty
 
       method visit_'r _ r =
-        match r with T.Static -> T.Static | T.Var rid -> T.Var (rsubst rid)
+        match r with T.Static -> T.Static | T.Var rid -> T.Var (r_subst rid)
 
-      method! visit_type_var_id _ id = tsubst id
-      method! visit_const_generic_var_id _ id = cgsubst id
+      method! visit_type_var_id _ id = ty_subst id
+      method! visit_const_generic_var_id _ id = cg_subst id
     end
   in
 
@@ -395,7 +510,7 @@ let subst_ids_visitor (rsubst : T.RegionId.id -> T.RegionId.id)
       inherit [_] C.map_env
       method! visit_borrow_id _ bid = bsubst bid
       method! visit_loan_id _ bid = bsubst bid
-      method! visit_ety _ ty = ty_substitute_ids tsubst cgsubst ty
+      method! visit_ety _ ty = ty_substitute_ids ty_subst cg_subst ty
       method! visit_rty env ty = subst_rty#visit_ty env ty
       method! visit_symbolic_value_id _ id = ssubst id
 
@@ -405,7 +520,7 @@ let subst_ids_visitor (rsubst : T.RegionId.id -> T.RegionId.id)
       (** We *do* visit meta-values *)
       method! visit_mvalue env v = self#visit_typed_value env v
 
-      method! visit_region_id _ id = rsubst id
+      method! visit_region_id _ id = r_subst id
       method! visit_region_var_id _ id = rvsubst id
       method! visit_abstraction_id _ id = asubst id
     end
@@ -425,20 +540,20 @@ let subst_ids_visitor (rsubst : T.RegionId.id -> T.RegionId.id)
     method visit_env (env : C.env) : C.env = visitor#visit_env () env
   end
 
-let typed_value_subst_ids (rsubst : T.RegionId.id -> T.RegionId.id)
+let typed_value_subst_ids (r_subst : T.RegionId.id -> T.RegionId.id)
     (rvsubst : T.RegionVarId.id -> T.RegionVarId.id)
-    (tsubst : T.TypeVarId.id -> T.TypeVarId.id)
-    (cgsubst : T.ConstGenericVarId.id -> T.ConstGenericVarId.id)
+    (ty_subst : T.TypeVarId.id -> T.TypeVarId.id)
+    (cg_subst : T.ConstGenericVarId.id -> T.ConstGenericVarId.id)
     (ssubst : V.SymbolicValueId.id -> V.SymbolicValueId.id)
     (bsubst : V.BorrowId.id -> V.BorrowId.id) (v : V.typed_value) :
     V.typed_value =
   let asubst _ = raise (Failure "Unreachable") in
-  (subst_ids_visitor rsubst rvsubst tsubst cgsubst ssubst bsubst asubst)
+  (subst_ids_visitor r_subst rvsubst ty_subst cg_subst ssubst bsubst asubst)
     #visit_typed_value v
 
-let typed_value_subst_rids (rsubst : T.RegionId.id -> T.RegionId.id)
+let typed_value_subst_rids (r_subst : T.RegionId.id -> T.RegionId.id)
     (v : V.typed_value) : V.typed_value =
-  typed_value_subst_ids rsubst
+  typed_value_subst_ids r_subst
     (fun x -> x)
     (fun x -> x)
     (fun x -> x)
@@ -446,41 +561,41 @@ let typed_value_subst_rids (rsubst : T.RegionId.id -> T.RegionId.id)
     (fun x -> x)
     v
 
-let typed_avalue_subst_ids (rsubst : T.RegionId.id -> T.RegionId.id)
+let typed_avalue_subst_ids (r_subst : T.RegionId.id -> T.RegionId.id)
     (rvsubst : T.RegionVarId.id -> T.RegionVarId.id)
-    (tsubst : T.TypeVarId.id -> T.TypeVarId.id)
-    (cgsubst : T.ConstGenericVarId.id -> T.ConstGenericVarId.id)
+    (ty_subst : T.TypeVarId.id -> T.TypeVarId.id)
+    (cg_subst : T.ConstGenericVarId.id -> T.ConstGenericVarId.id)
     (ssubst : V.SymbolicValueId.id -> V.SymbolicValueId.id)
     (bsubst : V.BorrowId.id -> V.BorrowId.id) (v : V.typed_avalue) :
     V.typed_avalue =
   let asubst _ = raise (Failure "Unreachable") in
-  (subst_ids_visitor rsubst rvsubst tsubst cgsubst ssubst bsubst asubst)
+  (subst_ids_visitor r_subst rvsubst ty_subst cg_subst ssubst bsubst asubst)
     #visit_typed_avalue v
 
-let abs_subst_ids (rsubst : T.RegionId.id -> T.RegionId.id)
+let abs_subst_ids (r_subst : T.RegionId.id -> T.RegionId.id)
     (rvsubst : T.RegionVarId.id -> T.RegionVarId.id)
-    (tsubst : T.TypeVarId.id -> T.TypeVarId.id)
-    (cgsubst : T.ConstGenericVarId.id -> T.ConstGenericVarId.id)
+    (ty_subst : T.TypeVarId.id -> T.TypeVarId.id)
+    (cg_subst : T.ConstGenericVarId.id -> T.ConstGenericVarId.id)
     (ssubst : V.SymbolicValueId.id -> V.SymbolicValueId.id)
     (bsubst : V.BorrowId.id -> V.BorrowId.id)
     (asubst : V.AbstractionId.id -> V.AbstractionId.id) (x : V.abs) : V.abs =
-  (subst_ids_visitor rsubst rvsubst tsubst cgsubst ssubst bsubst asubst)
+  (subst_ids_visitor r_subst rvsubst ty_subst cg_subst ssubst bsubst asubst)
     #visit_abs x
 
-let env_subst_ids (rsubst : T.RegionId.id -> T.RegionId.id)
+let env_subst_ids (r_subst : T.RegionId.id -> T.RegionId.id)
     (rvsubst : T.RegionVarId.id -> T.RegionVarId.id)
-    (tsubst : T.TypeVarId.id -> T.TypeVarId.id)
-    (cgsubst : T.ConstGenericVarId.id -> T.ConstGenericVarId.id)
+    (ty_subst : T.TypeVarId.id -> T.TypeVarId.id)
+    (cg_subst : T.ConstGenericVarId.id -> T.ConstGenericVarId.id)
     (ssubst : V.SymbolicValueId.id -> V.SymbolicValueId.id)
     (bsubst : V.BorrowId.id -> V.BorrowId.id)
     (asubst : V.AbstractionId.id -> V.AbstractionId.id) (x : C.env) : C.env =
-  (subst_ids_visitor rsubst rvsubst tsubst cgsubst ssubst bsubst asubst)
+  (subst_ids_visitor r_subst rvsubst ty_subst cg_subst ssubst bsubst asubst)
     #visit_env x
 
-let typed_avalue_subst_rids (rsubst : T.RegionId.id -> T.RegionId.id)
+let typed_avalue_subst_rids (r_subst : T.RegionId.id -> T.RegionId.id)
     (x : V.typed_avalue) : V.typed_avalue =
   let asubst _ = raise (Failure "Unreachable") in
-  (subst_ids_visitor rsubst
+  (subst_ids_visitor r_subst
      (fun x -> x)
      (fun x -> x)
      (fun x -> x)
@@ -490,9 +605,9 @@ let typed_avalue_subst_rids (rsubst : T.RegionId.id -> T.RegionId.id)
     #visit_typed_avalue
     x
 
-let env_subst_rids (rsubst : T.RegionId.id -> T.RegionId.id) (x : C.env) : C.env
-    =
-  (subst_ids_visitor rsubst
+let env_subst_rids (r_subst : T.RegionId.id -> T.RegionId.id) (x : C.env) :
+    C.env =
+  (subst_ids_visitor r_subst
      (fun x -> x)
      (fun x -> x)
      (fun x -> x)
diff --git a/compiler/SymbolicAst.ml b/compiler/SymbolicAst.ml
index 7dc94dcd..4df8fec7 100644
--- a/compiler/SymbolicAst.ml
+++ b/compiler/SymbolicAst.ml
@@ -29,7 +29,7 @@ type mplace = {
 [@@deriving show]
 
 type call_id =
-  | Fun of A.fun_id * V.FunCallId.id
+  | Fun of A.fun_id_or_trait_method_ref * V.FunCallId.id
       (** A "regular" function (i.e., a function which is not a primitive operation) *)
   | Unop of E.unop
   | Binop of E.binop
@@ -43,10 +43,7 @@ type call = {
           borrows (we need to perform lookups).
        *)
   abstractions : V.AbstractionId.id list;
-  (* TODO: rename to "...args" *)
-  type_params : T.ety list;
-  (* TODO: rename to "...args" *)
-  const_generic_params : T.const_generic list;
+  generics : T.egeneric_args;
   args : V.typed_value list;
   args_places : mplace option list;  (** Meta information *)
   dest : V.symbolic_value;
@@ -79,6 +76,9 @@ class ['self] iter_expression_base =
     method visit_loop_id : 'env -> V.loop_id -> unit = fun _ _ -> ()
     method visit_variant_id : 'env -> variant_id -> unit = fun _ _ -> ()
 
+    method visit_const_generic_var_id : 'env -> T.const_generic_var_id -> unit =
+      fun _ _ -> ()
+
     method visit_symbolic_value_id : 'env -> V.symbolic_value_id -> unit =
       fun _ _ -> ()
 
@@ -120,6 +120,9 @@ class ['self] iter_expression_base =
 
     method visit_symbolic_expansion : 'env -> V.symbolic_expansion -> unit =
       fun _ _ -> ()
+
+    method visit_etrait_ref : 'env -> T.etrait_ref -> unit = fun _ _ -> ()
+    method visit_egeneric_args : 'env -> T.egeneric_args -> unit = fun _ _ -> ()
   end
 
 (** **Rem.:** here, {!expression} is not at all equivalent to the expressions
@@ -171,14 +174,15 @@ type expression =
       * expression
       (** We introduce a new symbolic value, equal to some other value.
 
-        This is used for instance when reorganizing the environment to compute
-        fixed points: we duplicate some shared symbolic values to destructure
-        the shared values, in order to make the environment a bit more general
-        (while losing precision of course).
+          This is used for instance when reorganizing the environment to compute
+          fixed points: we duplicate some shared symbolic values to destructure
+          the shared values, in order to make the environment a bit more general
+          (while losing precision of course). We also use it to introduce symbolic
+          values when evaluating constant generics, or trait constants.
 
-        The context is the evaluation context from before introducing the new
-        value. It has the same purpose as for the {!Return} case.
-      *)
+          The context is the evaluation context from before introducing the new
+          value. It has the same purpose as for the {!Return} case.
+       *)
   | ForwardEnd of
       Contexts.eval_ctx
       * V.typed_value symbolic_value_id_map option
@@ -253,6 +257,11 @@ and value_aggregate =
   | SingleValue of V.typed_value  (** Regular case *)
   | Array of V.typed_value list
       (** This is used when introducing array aggregates *)
+  | ConstGenericValue of T.const_generic_var_id
+      (** This is used when evaluating a const generic value: in the interpreter,
+          we introduce a fresh symbolic value. *)
+  | TraitConstValue of T.etrait_ref * T.egeneric_args * string
+      (** A trait constant value *)
 [@@deriving
   show,
     visitors
diff --git a/compiler/SymbolicToPure.ml b/compiler/SymbolicToPure.ml
index 3512270a..2ce8c706 100644
--- a/compiler/SymbolicToPure.ml
+++ b/compiler/SymbolicToPure.ml
@@ -4,6 +4,7 @@ open Pure
 open PureUtils
 module Id = Identifiers
 module C = Contexts
+module A = LlbcAst
 module S = SymbolicAst
 module TA = TypesAnalysis
 module L = Logging
@@ -52,6 +53,9 @@ type fun_context = {
 type global_context = { llbc_global_decls : A.global_decl A.GlobalDeclId.Map.t }
 [@@deriving show]
 
+type trait_decls_context = A.trait_decl A.TraitDeclId.Map.t [@@deriving show]
+type trait_impls_context = A.trait_impl A.TraitImplId.Map.t [@@deriving show]
+
 (** Whenever we translate a function call or an ended abstraction, we
     store the related information (this is useful when translating ended
     children abstractions).
@@ -106,8 +110,7 @@ type loop_info = {
   loop_id : LoopId.id;
   input_vars : var list;
   input_svl : V.symbolic_value list;
-  type_args : ty list;
-  const_generic_args : const_generic list;
+  generics : generic_args;
   forward_inputs : texpression list option;
       (** The forward inputs are initialized at [None] *)
   forward_output_no_state_no_result : var option;
@@ -120,6 +123,8 @@ type bs_ctx = {
   type_context : type_context;
   fun_context : fun_context;
   global_context : global_context;
+  trait_decls_ctx : trait_decls_context;
+  trait_impls_ctx : trait_impls_context;
   fun_decl : A.fun_decl;
   bid : T.RegionGroupId.id option;  (** TODO: rename *)
   sg : fun_sig;
@@ -201,34 +206,11 @@ type bs_ctx = {
 }
 [@@deriving show]
 
-let type_check_pattern (ctx : bs_ctx) (v : typed_pattern) : unit =
-  let env = VarId.Map.empty in
-  let ctx =
-    {
-      PureTypeCheck.type_decls = ctx.type_context.type_decls;
-      global_decls = ctx.global_context.llbc_global_decls;
-      env;
-    }
-  in
-  let _ = PureTypeCheck.check_typed_pattern ctx v in
-  ()
-
-let type_check_texpression (ctx : bs_ctx) (e : texpression) : unit =
-  let env = VarId.Map.empty in
-  let ctx =
-    {
-      PureTypeCheck.type_decls = ctx.type_context.type_decls;
-      global_decls = ctx.global_context.llbc_global_decls;
-      env;
-    }
-  in
-  PureTypeCheck.check_texpression ctx e
-
 (* TODO: move *)
 let bs_ctx_to_ast_formatter (ctx : bs_ctx) : Print.Ast.ast_formatter =
   Print.Ast.decls_and_fun_decl_to_ast_formatter ctx.type_context.llbc_type_decls
     ctx.fun_context.llbc_fun_decls ctx.global_context.llbc_global_decls
-    ctx.fun_decl
+    ctx.trait_decls_ctx ctx.trait_impls_ctx ctx.fun_decl
 
 let bs_ctx_to_ctx_formatter (ctx : bs_ctx) : Print.Contexts.ctx_formatter =
   let rvar_to_string = Print.Types.region_var_id_to_string in
@@ -246,16 +228,25 @@ let bs_ctx_to_ctx_formatter (ctx : bs_ctx) : Print.Contexts.ctx_formatter =
     adt_variant_to_string = ast_fmt.adt_variant_to_string;
     var_id_to_string;
     adt_field_names = ast_fmt.adt_field_names;
+    trait_decl_id_to_string = ast_fmt.trait_decl_id_to_string;
+    trait_impl_id_to_string = ast_fmt.trait_impl_id_to_string;
+    trait_clause_id_to_string = ast_fmt.trait_clause_id_to_string;
   }
 
 let bs_ctx_to_pp_ast_formatter (ctx : bs_ctx) : PrintPure.ast_formatter =
-  let type_params = ctx.fun_decl.signature.type_params in
-  let cg_params = ctx.fun_decl.signature.const_generic_params in
+  let generics = ctx.fun_decl.signature.generics in
   let type_decls = ctx.type_context.llbc_type_decls in
   let fun_decls = ctx.fun_context.llbc_fun_decls in
   let global_decls = ctx.global_context.llbc_global_decls in
-  PrintPure.mk_ast_formatter type_decls fun_decls global_decls type_params
-    cg_params
+  PrintPure.mk_ast_formatter type_decls fun_decls global_decls
+    ctx.trait_decls_ctx ctx.trait_impls_ctx generics.types
+    generics.const_generics
+
+let ctx_egeneric_args_to_string (ctx : bs_ctx) (args : T.egeneric_args) : string
+    =
+  let fmt = bs_ctx_to_ctx_formatter ctx in
+  let fmt = Print.PC.ctx_to_etype_formatter fmt in
+  Print.PT.egeneric_args_to_string fmt args
 
 let symbolic_value_to_string (ctx : bs_ctx) (sv : V.symbolic_value) : string =
   let fmt = bs_ctx_to_ctx_formatter ctx in
@@ -277,12 +268,11 @@ let rty_to_string (ctx : bs_ctx) (ty : T.rty) : string =
   Print.PT.rty_to_string fmt ty
 
 let type_decl_to_string (ctx : bs_ctx) (def : type_decl) : string =
-  let type_params = def.type_params in
-  let cg_params = def.const_generic_params in
   let type_decls = ctx.type_context.llbc_type_decls in
   let global_decls = ctx.global_context.llbc_global_decls in
   let fmt =
-    PrintPure.mk_type_formatter type_decls global_decls type_params cg_params
+    PrintPure.mk_type_formatter type_decls global_decls ctx.trait_decls_ctx
+      ctx.trait_impls_ctx def.generics.types def.generics.const_generics
   in
   PrintPure.type_decl_to_string fmt def
 
@@ -291,26 +281,27 @@ let texpression_to_string (ctx : bs_ctx) (e : texpression) : string =
   PrintPure.texpression_to_string fmt false "" "  " e
 
 let fun_sig_to_string (ctx : bs_ctx) (sg : fun_sig) : string =
-  let type_params = sg.type_params in
-  let cg_params = sg.const_generic_params in
+  let type_params = sg.generics.types in
+  let cg_params = sg.generics.const_generics in
   let type_decls = ctx.type_context.llbc_type_decls in
   let fun_decls = ctx.fun_context.llbc_fun_decls in
   let global_decls = ctx.global_context.llbc_global_decls in
   let fmt =
-    PrintPure.mk_ast_formatter type_decls fun_decls global_decls type_params
-      cg_params
+    PrintPure.mk_ast_formatter type_decls fun_decls global_decls
+      ctx.trait_decls_ctx ctx.trait_impls_ctx type_params cg_params
   in
   PrintPure.fun_sig_to_string fmt sg
 
 let fun_decl_to_string (ctx : bs_ctx) (def : Pure.fun_decl) : string =
-  let type_params = def.signature.type_params in
-  let cg_params = def.signature.const_generic_params in
+  let generics = def.signature.generics in
+  let type_params = generics.types in
+  let cg_params = generics.const_generics in
   let type_decls = ctx.type_context.llbc_type_decls in
   let fun_decls = ctx.fun_context.llbc_fun_decls in
   let global_decls = ctx.global_context.llbc_global_decls in
   let fmt =
-    PrintPure.mk_ast_formatter type_decls fun_decls global_decls type_params
-      cg_params
+    PrintPure.mk_ast_formatter type_decls fun_decls global_decls
+      ctx.trait_decls_ctx ctx.trait_impls_ctx type_params cg_params
   in
   PrintPure.fun_decl_to_string fmt def
 
@@ -328,17 +319,18 @@ let abs_to_string (ctx : bs_ctx) (abs : V.abs) : string =
   Print.Values.abs_to_string fmt verbose indent indent_incr abs
 
 let get_instantiated_fun_sig (fun_id : A.fun_id)
-    (back_id : T.RegionGroupId.id option) (tys : ty list)
-    (cgs : const_generic list) (ctx : bs_ctx) : inst_fun_sig =
+    (back_id : T.RegionGroupId.id option) (generics : generic_args)
+    (ctx : bs_ctx) : inst_fun_sig =
   (* Lookup the non-instantiated function signature *)
   let sg =
     (RegularFunIdNotLoopMap.find (fun_id, back_id) ctx.fun_context.fun_sigs).sg
   in
   (* Create the substitution *)
-  let tsubst = make_type_subst sg.type_params tys in
-  let cgsubst = make_const_generic_subst sg.const_generic_params cgs in
+  (* There shouldn't be any reference to Self *)
+  let tr_self = UnknownTrait __FUNCTION__ in
+  let subst = make_subst_from_generics sg.generics generics tr_self in
   (* Apply *)
-  fun_sig_substitute tsubst cgsubst sg
+  fun_sig_substitute subst sg
 
 let bs_ctx_lookup_llbc_type_decl (id : TypeDeclId.id) (ctx : bs_ctx) :
     T.type_decl =
@@ -351,77 +343,128 @@ let bs_ctx_lookup_llbc_fun_decl (id : A.FunDeclId.id) (ctx : bs_ctx) :
 (* TODO: move *)
 let bs_ctx_lookup_local_function_sig (def_id : A.FunDeclId.id)
     (back_id : T.RegionGroupId.id option) (ctx : bs_ctx) : fun_sig =
-  let id = (A.Regular def_id, back_id) in
+  let id = (E.Regular def_id, back_id) in
   (RegularFunIdNotLoopMap.find id ctx.fun_context.fun_sigs).sg
 
-let bs_ctx_register_forward_call (call_id : V.FunCallId.id) (forward : S.call)
-    (args : texpression list) (ctx : bs_ctx) : bs_ctx =
-  let calls = ctx.calls in
-  assert (not (V.FunCallId.Map.mem call_id calls));
-  let info =
-    { forward; forward_inputs = args; backwards = T.RegionGroupId.Map.empty }
-  in
-  let calls = V.FunCallId.Map.add call_id info calls in
-  { ctx with calls }
-
-(** [back_args]: the *additional* list of inputs received by the backward function *)
-let bs_ctx_register_backward_call (abs : V.abs) (call_id : V.FunCallId.id)
-    (back_id : T.RegionGroupId.id) (back_args : texpression list) (ctx : bs_ctx)
-    : bs_ctx * fun_or_op_id =
-  (* Insert the abstraction in the call informations *)
-  let info = V.FunCallId.Map.find call_id ctx.calls in
-  assert (not (T.RegionGroupId.Map.mem back_id info.backwards));
-  let backwards =
-    T.RegionGroupId.Map.add back_id (abs, back_args) info.backwards
-  in
-  let info = { info with backwards } in
-  let calls = V.FunCallId.Map.add call_id info ctx.calls in
-  (* Insert the abstraction in the abstractions map *)
-  let abstractions = ctx.abstractions in
-  assert (not (V.AbstractionId.Map.mem abs.abs_id abstractions));
-  let abstractions =
-    V.AbstractionId.Map.add abs.abs_id (abs, back_args) abstractions
-  in
-  (* Retrieve the fun_id *)
-  let fun_id =
-    match info.forward.call_id with
-    | S.Fun (fid, _) -> Fun (FromLlbc (fid, None, Some back_id))
-    | S.Unop _ | S.Binop _ -> raise (Failure "Unreachable")
-  in
-  (* Update the context and return *)
-  ({ ctx with calls; abstractions }, fun_id)
+(* Some generic translation functions (we need to translate different "flavours"
+   of types: sty, forward types, backward types, etc.) *)
+let rec translate_generic_args (translate_ty : 'r T.ty -> ty)
+    (generics : 'r T.generic_args) : generic_args =
+  (* We ignore the regions: if they didn't cause trouble for the symbolic execution,
+     then everything's fine *)
+  let types = List.map translate_ty generics.types in
+  let const_generics = generics.const_generics in
+  let trait_refs =
+    List.map (translate_trait_ref translate_ty) generics.trait_refs
+  in
+  { types; const_generics; trait_refs }
+
+and translate_trait_ref (translate_ty : 'r T.ty -> ty) (tr : 'r T.trait_ref) :
+    trait_ref =
+  let trait_id = translate_trait_instance_id translate_ty tr.trait_id in
+  let generics = translate_generic_args translate_ty tr.generics in
+  let trait_decl_ref =
+    translate_trait_decl_ref translate_ty tr.trait_decl_ref
+  in
+  { trait_id; generics; trait_decl_ref }
+
+and translate_trait_decl_ref (translate_ty : 'r T.ty -> ty)
+    (tr : 'r T.trait_decl_ref) : trait_decl_ref =
+  let decl_generics = translate_generic_args translate_ty tr.decl_generics in
+  { trait_decl_id = tr.trait_decl_id; decl_generics }
+
+and translate_trait_instance_id (translate_ty : 'r T.ty -> ty)
+    (id : 'r T.trait_instance_id) : trait_instance_id =
+  let translate_trait_instance_id = translate_trait_instance_id translate_ty in
+  match id with
+  | T.Self -> Self
+  | TraitImpl id -> TraitImpl id
+  | BuiltinOrAuto _ ->
+      (* We should have eliminated those in the prepasses *)
+      raise (Failure "Unreachable")
+  | Clause id -> Clause id
+  | ParentClause (inst_id, decl_id, clause_id) ->
+      let inst_id = translate_trait_instance_id inst_id in
+      ParentClause (inst_id, decl_id, clause_id)
+  | ItemClause (inst_id, decl_id, item_name, clause_id) ->
+      let inst_id = translate_trait_instance_id inst_id in
+      ItemClause (inst_id, decl_id, item_name, clause_id)
+  | TraitRef tr -> TraitRef (translate_trait_ref translate_ty tr)
+  | FnPointer _ -> raise (Failure "TODO")
+  | UnknownTrait s -> raise (Failure ("Unknown trait found: " ^ s))
 
 let rec translate_sty (ty : T.sty) : ty =
   let translate = translate_sty in
   match ty with
-  | T.Adt (type_id, regions, tys, cgs) -> (
-      (* Can't translate types with regions for now *)
-      assert (regions = []);
-      let tys = List.map translate tys in
+  | T.Adt (type_id, generics) -> (
+      let generics = translate_sgeneric_args generics in
       match type_id with
-      | T.AdtId adt_id -> Adt (AdtId adt_id, tys, cgs)
-      | T.Tuple -> mk_simpl_tuple_ty tys
+      | T.AdtId adt_id -> Adt (AdtId adt_id, generics)
+      | T.Tuple ->
+          assert (generics.const_generics = []);
+          mk_simpl_tuple_ty generics.types
       | T.Assumed aty -> (
           match aty with
-          | T.Vec -> Adt (Assumed Vec, tys, cgs)
-          | T.Option -> Adt (Assumed Option, tys, cgs)
           | T.Box -> (
               (* Eliminate the boxes *)
-              match tys with
+              match generics.types with
               | [ ty ] -> ty
               | _ ->
                   raise
                     (Failure
                        "Box/vec/option type with incorrect number of arguments")
               )
-          | T.Array -> Adt (Assumed Array, tys, cgs)
-          | T.Slice -> Adt (Assumed Slice, tys, cgs)
-          | T.Str -> Adt (Assumed Str, tys, cgs)
-          | T.Range -> Adt (Assumed Range, tys, cgs)))
+          | T.Array -> Adt (Assumed Array, generics)
+          | T.Slice -> Adt (Assumed Slice, generics)
+          | T.Str -> Adt (Assumed Str, generics)))
   | TypeVar vid -> TypeVar vid
   | Literal ty -> Literal ty
   | Never -> raise (Failure "Unreachable")
   | Ref (_, rty, _) -> translate rty
+  | RawPtr (ty, rkind) ->
+      let mut = match rkind with Mut -> Mut | Shared -> Const in
+      let ty = translate ty in
+      let generics = { types = [ ty ]; const_generics = []; trait_refs = [] } in
+      Adt (Assumed (RawPtr mut), generics)
+  | TraitType (trait_ref, generics, type_name) ->
+      let trait_ref = translate_strait_ref trait_ref in
+      let generics = translate_sgeneric_args generics in
+      TraitType (trait_ref, generics, type_name)
+  | Arrow _ -> raise (Failure "TODO")
+
+and translate_sgeneric_args (generics : T.sgeneric_args) : generic_args =
+  translate_generic_args translate_sty generics
+
+and translate_strait_ref (tr : T.strait_ref) : trait_ref =
+  translate_trait_ref translate_sty tr
+
+and translate_strait_instance_id (id : T.strait_instance_id) : trait_instance_id
+    =
+  translate_trait_instance_id translate_sty id
+
+let translate_trait_clause (clause : T.trait_clause) : trait_clause =
+  let { T.clause_id; meta = _; trait_id; generics } = clause in
+  let generics = translate_sgeneric_args generics in
+  { clause_id; trait_id; generics }
+
+let translate_strait_type_constraint (ttc : T.strait_type_constraint) :
+    trait_type_constraint =
+  let { T.trait_ref; generics; type_name; ty } = ttc in
+  let trait_ref = translate_strait_ref trait_ref in
+  let generics = translate_sgeneric_args generics in
+  let ty = translate_sty ty in
+  { trait_ref; generics; type_name; ty }
+
+let translate_predicates (preds : T.predicates) : predicates =
+  let trait_type_constraints =
+    List.map translate_strait_type_constraint preds.trait_type_constraints
+  in
+  { trait_type_constraints }
+
+let translate_generic_params (generics : T.generic_params) : generic_params =
+  let { T.regions = _; types; const_generics; trait_clauses } = generics in
+  let trait_clauses = List.map translate_trait_clause trait_clauses in
+  { types; const_generics; trait_clauses }
 
 let translate_field (f : T.field) : field =
   let field_name = f.field_name in
@@ -452,15 +495,16 @@ let translate_type_decl_kind (kind : T.type_decl_kind) : type_decl_kind =
     point of moving this definition for now.
  *)
 let translate_type_decl (def : T.type_decl) : type_decl =
-  (* Translate *)
   let def_id = def.T.def_id in
   let name = def.name in
+  let { T.regions; types; const_generics; trait_clauses } = def.generics in
   (* Can't translate types with regions for now *)
-  assert (def.region_params = []);
-  let type_params = def.type_params in
-  let const_generic_params = def.const_generic_params in
+  assert (regions = []);
+  let trait_clauses = List.map translate_trait_clause trait_clauses in
+  let generics = { types; const_generics; trait_clauses } in
   let kind = translate_type_decl_kind def.T.kind in
-  { def_id; name; type_params; const_generic_params; kind }
+  let preds = translate_predicates def.preds in
+  { def_id; name; generics; kind; preds }
 
 let translate_type_id (id : T.type_id) : type_id =
   match id with
@@ -468,12 +512,9 @@ let translate_type_id (id : T.type_id) : type_id =
   | T.Assumed aty ->
       let aty =
         match aty with
-        | T.Vec -> Vec
-        | T.Option -> Option
         | T.Array -> Array
         | T.Slice -> Slice
         | T.Str -> Str
-        | T.Range -> Range
         | T.Box ->
             (* Boxes have to be eliminated: this type id shouldn't
                be translated *)
@@ -488,28 +529,26 @@ let translate_type_id (id : T.type_id) : type_id =
 let rec translate_fwd_ty (type_infos : TA.type_infos) (ty : 'r T.ty) : ty =
   let translate = translate_fwd_ty type_infos in
   match ty with
-  | T.Adt (type_id, regions, tys, cgs) -> (
-      (* Can't translate types with regions for now *)
-      assert (regions = []);
-      (* Translate the type parameters *)
-      let t_tys = List.map translate tys in
+  | T.Adt (type_id, generics) -> (
+      let t_generics = translate_fwd_generic_args type_infos generics in
       (* Eliminate boxes and simplify tuples *)
       match type_id with
-      | AdtId _
-      | T.Assumed (T.Vec | T.Option | T.Array | T.Slice | T.Str | T.Range) ->
-          (* No general parametricity for now *)
-          assert (not (List.exists (TypesUtils.ty_has_borrows type_infos) tys));
+      | AdtId _ | T.Assumed (T.Array | T.Slice | T.Str) ->
           let type_id = translate_type_id type_id in
-          Adt (type_id, t_tys, cgs)
+          Adt (type_id, t_generics)
       | Tuple ->
           (* Note that if there is exactly one type, [mk_simpl_tuple_ty] is the
              identity *)
-          mk_simpl_tuple_ty t_tys
+          mk_simpl_tuple_ty t_generics.types
       | T.Assumed T.Box -> (
           (* We eliminate boxes *)
           (* No general parametricity for now *)
-          assert (not (List.exists (TypesUtils.ty_has_borrows type_infos) tys));
-          match t_tys with
+          assert (
+            not
+              (List.exists
+                 (TypesUtils.ty_has_borrows type_infos)
+                 generics.types));
+          match t_generics.types with
           | [ bty ] -> bty
           | _ ->
               raise
@@ -520,12 +559,40 @@ let rec translate_fwd_ty (type_infos : TA.type_infos) (ty : 'r T.ty) : ty =
   | Never -> raise (Failure "Unreachable")
   | Literal lty -> Literal lty
   | Ref (_, rty, _) -> translate rty
+  | RawPtr (ty, rkind) ->
+      let mut = match rkind with Mut -> Mut | Shared -> Const in
+      let ty = translate ty in
+      let generics = { types = [ ty ]; const_generics = []; trait_refs = [] } in
+      Adt (Assumed (RawPtr mut), generics)
+  | TraitType (trait_ref, generics, type_name) ->
+      let trait_ref = translate_fwd_trait_ref type_infos trait_ref in
+      let generics = translate_fwd_generic_args type_infos generics in
+      TraitType (trait_ref, generics, type_name)
+  | Arrow _ -> raise (Failure "TODO")
+
+and translate_fwd_generic_args (type_infos : TA.type_infos)
+    (generics : 'r T.generic_args) : generic_args =
+  translate_generic_args (translate_fwd_ty type_infos) generics
+
+and translate_fwd_trait_ref (type_infos : TA.type_infos) (tr : 'r T.trait_ref) :
+    trait_ref =
+  translate_trait_ref (translate_fwd_ty type_infos) tr
+
+and translate_fwd_trait_instance_id (type_infos : TA.type_infos)
+    (id : 'r T.trait_instance_id) : trait_instance_id =
+  translate_trait_instance_id (translate_fwd_ty type_infos) id
 
 (** Simply calls [translate_fwd_ty] *)
 let ctx_translate_fwd_ty (ctx : bs_ctx) (ty : 'r T.ty) : ty =
   let type_infos = ctx.type_context.type_infos in
   translate_fwd_ty type_infos ty
 
+(** Simply calls [translate_fwd_generic_args] *)
+let ctx_translate_fwd_generic_args (ctx : bs_ctx) (generics : 'r T.generic_args)
+    : generic_args =
+  let type_infos = ctx.type_context.type_infos in
+  translate_fwd_generic_args type_infos generics
+
 (** Translate a type, when some regions may have ended.
     
     We return an option, because the translated type may be empty.
@@ -538,30 +605,40 @@ let rec translate_back_ty (type_infos : TA.type_infos)
   (* A small helper for "leave" types *)
   let wrap ty = if inside_mut then Some ty else None in
   match ty with
-  | T.Adt (type_id, _, tys, cgs) -> (
+  | T.Adt (type_id, generics) -> (
       match type_id with
-      | T.AdtId _
-      | Assumed (T.Vec | T.Option | T.Array | T.Slice | T.Str | T.Range) ->
-          (* Don't accept ADTs (which are not tuples) with borrows for now *)
-          assert (not (TypesUtils.ty_has_borrows type_infos ty));
+      | T.AdtId _ | Assumed (T.Array | T.Slice | T.Str) ->
           let type_id = translate_type_id type_id in
           if inside_mut then
-            let tys_t = List.filter_map translate tys in
-            Some (Adt (type_id, tys_t, cgs))
-          else None
+            (* We do not want to filter anything, so we translate the generics
+               as "forward" types *)
+            let generics = translate_fwd_generic_args type_infos generics in
+            Some (Adt (type_id, generics))
+          else
+            (* If not inside a mutable reference: check if at least one
+               of the generics contains a mutable reference (i.e., is not
+               translated to `None`. If yes, keep the whole type, and
+               translate all the generics as "forward" types (the backward
+               function will extract the proper information from the ADT value)
+            *)
+            let types = List.filter_map translate generics.types in
+            if types <> [] then
+              let generics = translate_fwd_generic_args type_infos generics in
+              Some (Adt (type_id, generics))
+            else None
       | Assumed T.Box -> (
           (* Don't accept ADTs (which are not tuples) with borrows for now *)
           assert (not (TypesUtils.ty_has_borrows type_infos ty));
           (* Eliminate the box *)
-          match tys with
+          match generics.types with
           | [ bty ] -> translate bty
           | _ ->
               raise
                 (Failure "Unreachable: boxes receive exactly one type parameter")
           )
       | T.Tuple -> (
-          (* Tuples can contain borrows (which we eliminated) *)
-          let tys_t = List.filter_map translate tys in
+          (* Tuples can contain borrows (which we eliminate) *)
+          let tys_t = List.filter_map translate generics.types in
           match tys_t with
           | [] -> None
           | _ ->
@@ -582,6 +659,17 @@ let rec translate_back_ty (type_infos : TA.type_infos)
           if keep_region r then
             translate_back_ty type_infos keep_region inside_mut rty
           else None)
+  | RawPtr _ ->
+      (* TODO: not sure what to do here *)
+      None
+  | TraitType (trait_ref, generics, type_name) ->
+      assert (generics.regions = []);
+      (* Translate the trait ref and the generics as "forward" generics -
+         we do not want to filter any type *)
+      let trait_ref = translate_fwd_trait_ref type_infos trait_ref in
+      let generics = translate_fwd_generic_args type_infos generics in
+      Some (TraitType (trait_ref, generics, type_name))
+  | Arrow _ -> raise (Failure "TODO")
 
 (** Simply calls [translate_back_ty] *)
 let ctx_translate_back_ty (ctx : bs_ctx) (keep_region : 'r -> bool)
@@ -589,6 +677,80 @@ let ctx_translate_back_ty (ctx : bs_ctx) (keep_region : 'r -> bool)
   let type_infos = ctx.type_context.type_infos in
   translate_back_ty type_infos keep_region inside_mut ty
 
+let mk_type_check_ctx (ctx : bs_ctx) : PureTypeCheck.tc_ctx =
+  let const_generics =
+    T.ConstGenericVarId.Map.of_list
+      (List.map
+         (fun (cg : T.const_generic_var) ->
+           (cg.index, ctx_translate_fwd_ty ctx (T.Literal cg.ty)))
+         ctx.sg.generics.const_generics)
+  in
+  let env = VarId.Map.empty in
+  {
+    PureTypeCheck.type_decls = ctx.type_context.type_decls;
+    global_decls = ctx.global_context.llbc_global_decls;
+    env;
+    const_generics;
+  }
+
+let type_check_pattern (ctx : bs_ctx) (v : typed_pattern) : unit =
+  let ctx = mk_type_check_ctx ctx in
+  let _ = PureTypeCheck.check_typed_pattern ctx v in
+  ()
+
+let type_check_texpression (ctx : bs_ctx) (e : texpression) : unit =
+  if !Config.type_check_pure_code then
+    let ctx = mk_type_check_ctx ctx in
+    PureTypeCheck.check_texpression ctx e
+
+let translate_fun_id_or_trait_method_ref (ctx : bs_ctx)
+    (id : A.fun_id_or_trait_method_ref) : fun_id_or_trait_method_ref =
+  match id with
+  | FunId fun_id -> FunId fun_id
+  | TraitMethod (trait_ref, method_name, fun_decl_id) ->
+      let type_infos = ctx.type_context.type_infos in
+      let trait_ref = translate_fwd_trait_ref type_infos trait_ref in
+      TraitMethod (trait_ref, method_name, fun_decl_id)
+
+let bs_ctx_register_forward_call (call_id : V.FunCallId.id) (forward : S.call)
+    (args : texpression list) (ctx : bs_ctx) : bs_ctx =
+  let calls = ctx.calls in
+  assert (not (V.FunCallId.Map.mem call_id calls));
+  let info =
+    { forward; forward_inputs = args; backwards = T.RegionGroupId.Map.empty }
+  in
+  let calls = V.FunCallId.Map.add call_id info calls in
+  { ctx with calls }
+
+(** [back_args]: the *additional* list of inputs received by the backward function *)
+let bs_ctx_register_backward_call (abs : V.abs) (call_id : V.FunCallId.id)
+    (back_id : T.RegionGroupId.id) (back_args : texpression list) (ctx : bs_ctx)
+    : bs_ctx * fun_or_op_id =
+  (* Insert the abstraction in the call informations *)
+  let info = V.FunCallId.Map.find call_id ctx.calls in
+  assert (not (T.RegionGroupId.Map.mem back_id info.backwards));
+  let backwards =
+    T.RegionGroupId.Map.add back_id (abs, back_args) info.backwards
+  in
+  let info = { info with backwards } in
+  let calls = V.FunCallId.Map.add call_id info ctx.calls in
+  (* Insert the abstraction in the abstractions map *)
+  let abstractions = ctx.abstractions in
+  assert (not (V.AbstractionId.Map.mem abs.abs_id abstractions));
+  let abstractions =
+    V.AbstractionId.Map.add abs.abs_id (abs, back_args) abstractions
+  in
+  (* Retrieve the fun_id *)
+  let fun_id =
+    match info.forward.call_id with
+    | S.Fun (fid, _) ->
+        let fid = translate_fun_id_or_trait_method_ref ctx fid in
+        Fun (FromLlbc (fid, None, Some back_id))
+    | S.Unop _ | S.Binop _ -> raise (Failure "Unreachable")
+  in
+  (* Update the context and return *)
+  ({ ctx with calls; abstractions }, fun_id)
+
 (** List the ancestors of an abstraction *)
 let list_ancestor_abstractions_ids (ctx : bs_ctx) (abs : V.abs)
     (call_id : V.FunCallId.id) : V.AbstractionId.id list =
@@ -642,10 +804,10 @@ let mk_fuel_input_as_list (ctx : bs_ctx) (info : fun_effect_info) :
 
 (** Small utility. *)
 let get_fun_effect_info (fun_infos : FA.fun_info A.FunDeclId.Map.t)
-    (fun_id : A.fun_id) (lid : V.LoopId.id option)
+    (fun_id : A.fun_id_or_trait_method_ref) (lid : V.LoopId.id option)
     (gid : T.RegionGroupId.id option) : fun_effect_info =
   match fun_id with
-  | A.Regular fid ->
+  | TraitMethod (_, _, fid) | FunId (Regular fid) ->
       let info = A.FunDeclId.Map.find fid fun_infos in
       let stateful_group = info.stateful in
       let stateful =
@@ -658,10 +820,10 @@ let get_fun_effect_info (fun_infos : FA.fun_info A.FunDeclId.Map.t)
         can_diverge = info.can_diverge;
         is_rec = info.is_rec || Option.is_some lid;
       }
-  | A.Assumed aid ->
+  | FunId (Assumed aid) ->
       assert (lid = None);
       {
-        can_fail = Assumed.assumed_can_fail aid;
+        can_fail = Assumed.assumed_fun_can_fail aid;
         stateful_group = false;
         stateful = false;
         can_diverge = false;
@@ -673,12 +835,14 @@ let get_fun_effect_info (fun_infos : FA.fun_info A.FunDeclId.Map.t)
     Note that the function also takes a list of names for the inputs, and
     computes, for every output for the backward functions, a corresponding
     name (outputs for backward functions come from borrows in the inputs
-    of the forward function) which we use as hints to generate pretty names.
+    of the forward function) which we use as hints to generate pretty names
+    in the extracted code.
  *)
-let translate_fun_sig (fun_infos : FA.fun_info A.FunDeclId.Map.t)
-    (fun_id : A.fun_id) (type_infos : TA.type_infos) (sg : A.fun_sig)
-    (input_names : string option list) (bid : T.RegionGroupId.id option) :
-    fun_sig_named_outputs =
+let translate_fun_sig (decls_ctx : C.decls_ctx) (fun_id : A.fun_id)
+    (sg : A.fun_sig) (input_names : string option list)
+    (bid : T.RegionGroupId.id option) : fun_sig_named_outputs =
+  let fun_infos = decls_ctx.fun_ctx.fun_infos in
+  let type_infos = decls_ctx.type_ctx.type_infos in
   (* Retrieve the list of parent backward functions *)
   let gid, parents =
     match bid with
@@ -689,7 +853,34 @@ let translate_fun_sig (fun_infos : FA.fun_info A.FunDeclId.Map.t)
   in
   (* Is the function stateful, and can it fail? *)
   let lid = None in
-  let effect_info = get_fun_effect_info fun_infos fun_id lid bid in
+  let effect_info = get_fun_effect_info fun_infos (FunId fun_id) lid bid in
+  (* We need an evaluation context to normalize the types (to normalize the
+     associated types, etc. - for instance it may happen that the types
+     refer to the types associated to a trait ref, but where the trait ref
+     is a known impl). *)
+  (* Create the context *)
+  let ctx =
+    let region_groups =
+      List.map (fun (g : T.region_var_group) -> g.id) sg.regions_hierarchy
+    in
+    let ctx =
+      InterpreterUtils.initialize_eval_context decls_ctx region_groups
+        sg.generics.types sg.generics.const_generics
+    in
+    (* Compute the normalization map for the *sty* types and add it to the context *)
+    AssociatedTypes.ctx_add_norm_trait_stypes_from_preds ctx
+      sg.preds.trait_type_constraints
+  in
+
+  (* Normalize the signature *)
+  let sg =
+    let ({ A.inputs; output; _ } : A.fun_sig) = sg in
+    let norm = AssociatedTypes.ctx_normalize_sty ctx in
+    let inputs = List.map norm inputs in
+    let output = norm output in
+    { sg with A.inputs; output }
+  in
+
   (* List the inputs for:
    * - the fuel
    * - the forward function
@@ -806,9 +997,8 @@ let translate_fun_sig (fun_infos : FA.fun_info A.FunDeclId.Map.t)
     (* Wrap in a result type *)
     if effect_info.can_fail then mk_result_ty output else output
   in
-  (* Type/const generic parameters *)
-  let type_params = sg.type_params in
-  let const_generic_params = sg.const_generic_params in
+  (* Generic parameters *)
+  let generics = translate_generic_params sg.generics in
   (* Return *)
   let has_fuel = fuel <> [] in
   let num_fwd_inputs_no_state = List.length fwd_inputs in
@@ -836,9 +1026,8 @@ let translate_fun_sig (fun_infos : FA.fun_info A.FunDeclId.Map.t)
       effect_info;
     }
   in
-  let sg =
-    { type_params; const_generic_params; inputs; output; doutputs; info }
-  in
+  let preds = translate_predicates sg.A.preds in
+  let sg = { generics; preds; inputs; output; doutputs; info } in
   { sg; output_names }
 
 let bs_ctx_fresh_state_var (ctx : bs_ctx) : bs_ctx * typed_pattern =
@@ -917,7 +1106,7 @@ let lookup_var_for_symbolic_value (sv : V.symbolic_value) (ctx : bs_ctx) : var =
 (** Peel boxes as long as the value is of the form [Box<T>] *)
 let rec unbox_typed_value (v : V.typed_value) : V.typed_value =
   match (v.value, v.ty) with
-  | V.Adt av, T.Adt (T.Assumed T.Box, _, _, _) -> (
+  | V.Adt av, T.Adt (T.Assumed T.Box, _) -> (
       match av.field_values with
       | [ bv ] -> unbox_typed_value bv
       | _ -> raise (Failure "Unreachable"))
@@ -962,16 +1151,16 @@ let rec typed_value_to_texpression (ctx : bs_ctx) (ectx : C.eval_ctx)
         let field_values = List.map translate av.field_values in
         (* Eliminate the tuple wrapper if it is a tuple with exactly one field *)
         match v.ty with
-        | T.Adt (T.Tuple, _, _, _) ->
+        | T.Adt (T.Tuple, _) ->
             assert (variant_id = None);
             mk_simpl_tuple_texpression field_values
         | _ ->
-            (* Retrieve the type, the translated type arguments and the
-             * const generic arguments from the translated type (simpler this way) *)
-            let adt_id, type_args, const_generic_args = ty_as_adt ty in
+            (* Retrieve the type and the translated generics from the translated
+               type (simpler this way) *)
+            let adt_id, generics = ty_as_adt ty in
             (* Create the constructor *)
             let qualif_id = AdtCons { adt_id; variant_id = av.variant_id } in
-            let qualif = { id = qualif_id; type_args; const_generic_args } in
+            let qualif = { id = qualif_id; generics } in
             let cons_e = Qualif qualif in
             let field_tys =
               List.map (fun (v : texpression) -> v.ty) field_values
@@ -1038,11 +1227,9 @@ let rec typed_avalue_to_consumed (ctx : bs_ctx) (ectx : C.eval_ctx)
         (* Translate the field values *)
         let field_values = List.filter_map translate adt_v.field_values in
         (* For now, only tuples can contain borrows *)
-        let adt_id, _, _, _ = TypesUtils.ty_as_adt av.ty in
+        let adt_id, _ = TypesUtils.ty_as_adt av.ty in
         match adt_id with
-        | T.AdtId _
-        | T.Assumed
-            (T.Box | T.Vec | T.Option | T.Array | T.Slice | T.Str | T.Range) ->
+        | T.AdtId _ | T.Assumed (T.Box | T.Array | T.Slice | T.Str) ->
             assert (field_values = []);
             None
         | T.Tuple ->
@@ -1185,11 +1372,9 @@ let rec typed_avalue_to_given_back (mp : mplace option) (av : V.typed_avalue)
         (* For now, only tuples can contain borrows - note that if we gave
          * something like a [&mut Vec] to a function, we give back the
          * vector value upon visiting the "abstraction borrow" node *)
-        let adt_id, _, _, _ = TypesUtils.ty_as_adt av.ty in
+        let adt_id, _ = TypesUtils.ty_as_adt av.ty in
         match adt_id with
-        | T.AdtId _
-        | T.Assumed
-            (T.Box | T.Vec | T.Option | T.Array | T.Slice | T.Str | T.Range) ->
+        | T.AdtId _ | T.Assumed (T.Box | T.Array | T.Slice | T.Str) ->
             assert (field_values = []);
             (ctx, None)
         | T.Tuple ->
@@ -1457,9 +1642,12 @@ and translate_return_with_loop (loop_id : V.LoopId.id) (is_continue : bool)
 
 and translate_function_call (call : S.call) (e : S.expression) (ctx : bs_ctx) :
     texpression =
+  log#ldebug
+    (lazy
+      ("translate_function_call:\n"
+      ^ ctx_egeneric_args_to_string ctx call.generics));
   (* Translate the function call *)
-  let type_args = List.map (ctx_translate_fwd_ty ctx) call.type_params in
-  let const_generic_args = call.const_generic_params in
+  let generics = ctx_translate_fwd_generic_args ctx call.generics in
   let args =
     let args = List.map (typed_value_to_texpression ctx call.ctx) call.args in
     let args_mplaces = List.map translate_opt_mplace call.args_places in
@@ -1475,7 +1663,8 @@ and translate_function_call (call : S.call) (e : S.expression) (ctx : bs_ctx) :
     match call.call_id with
     | S.Fun (fid, call_id) ->
         (* Regular function call *)
-        let func = Fun (FromLlbc (fid, None, None)) in
+        let fid_t = translate_fun_id_or_trait_method_ref ctx fid in
+        let func = Fun (FromLlbc (fid_t, None, None)) in
         (* Retrieve the effect information about this function (can fail,
          * takes a state as input, etc.) *)
         let effect_info =
@@ -1525,18 +1714,20 @@ and translate_function_call (call : S.call) (e : S.expression) (ctx : bs_ctx) :
             in
             (ctx, Unop (Neg int_ty), effect_info, args, None)
         | _ -> raise (Failure "Unreachable"))
-    | S.Unop (E.Cast (src_ty, tgt_ty)) ->
-        (* Note that cast can fail *)
-        let effect_info =
-          {
-            can_fail = true;
-            stateful_group = false;
-            stateful = false;
-            can_diverge = false;
-            is_rec = false;
-          }
-        in
-        (ctx, Unop (Cast (src_ty, tgt_ty)), effect_info, args, None)
+    | S.Unop (E.Cast cast_kind) -> (
+        match cast_kind with
+        | CastInteger (src_ty, tgt_ty) ->
+            (* Note that cast can fail *)
+            let effect_info =
+              {
+                can_fail = true;
+                stateful_group = false;
+                stateful = false;
+                can_diverge = false;
+                is_rec = false;
+              }
+            in
+            (ctx, Unop (Cast (src_ty, tgt_ty)), effect_info, args, None))
     | S.Binop binop -> (
         match args with
         | [ arg0; arg1 ] ->
@@ -1561,7 +1752,7 @@ and translate_function_call (call : S.call) (e : S.expression) (ctx : bs_ctx) :
     | None -> dest
     | Some out_state -> mk_simpl_tuple_pattern [ out_state; dest ]
   in
-  let func = { id = FunOrOp fun_id; type_args; const_generic_args } in
+  let func = { id = FunOrOp fun_id; generics } in
   let input_tys = (List.map (fun (x : texpression) -> x.ty)) args in
   let ret_ty =
     if effect_info.can_fail then mk_result_ty dest_v.ty else dest_v.ty
@@ -1665,9 +1856,11 @@ and translate_end_abstraction_synth_input (ectx : C.eval_ctx) (abs : V.abs)
   (* Group the two lists *)
   let variables_values = List.combine given_back_variables consumed_values in
   (* Sanity check: the two lists match (same types) *)
-  List.iter
-    (fun (var, v) -> assert ((var : var).ty = (v : texpression).ty))
-    variables_values;
+  (* TODO: normalize the types *)
+  if !Config.type_check_pure_code then
+    List.iter
+      (fun (var, v) -> assert ((var : var).ty = (v : texpression).ty))
+      variables_values;
   (* Translate the next expression *)
   let next_e = translate_expression e ctx in
   (* Generate the assignemnts *)
@@ -1692,8 +1885,7 @@ and translate_end_abstraction_fun_call (ectx : C.eval_ctx) (abs : V.abs)
   let effect_info =
     get_fun_effect_info ctx.fun_context.fun_infos fun_id None (Some rg_id)
   in
-  let type_args = List.map (ctx_translate_fwd_ty ctx) call.type_params in
-  let const_generic_args = call.const_generic_params in
+  let generics = ctx_translate_fwd_generic_args ctx call.generics in
   (* Retrieve the original call and the parent abstractions *)
   let _forward, backwards = get_abs_ancestors ctx abs call_id in
   (* Retrieve the values consumed when we called the forward function and
@@ -1741,34 +1933,35 @@ and translate_end_abstraction_fun_call (ectx : C.eval_ctx) (abs : V.abs)
     | Some nstate -> mk_simpl_tuple_pattern [ nstate; output ]
   in
   (* Sanity check: there is the proper number of inputs and outputs, and they have the proper type *)
-  let _ =
-    let inst_sg =
-      get_instantiated_fun_sig fun_id (Some rg_id) type_args const_generic_args
-        ctx
-    in
-    log#ldebug
-      (lazy
-        ("\n- fun_id: " ^ A.show_fun_id fun_id ^ "\n- inputs ("
-        ^ string_of_int (List.length inputs)
-        ^ "): "
-        ^ String.concat ", " (List.map (texpression_to_string ctx) inputs)
-        ^ "\n- inst_sg.inputs ("
-        ^ string_of_int (List.length inst_sg.inputs)
-        ^ "): "
-        ^ String.concat ", " (List.map (ty_to_string ctx) inst_sg.inputs)));
-    List.iter
-      (fun (x, ty) -> assert ((x : texpression).ty = ty))
-      (List.combine inputs inst_sg.inputs);
-    log#ldebug
-      (lazy
-        ("\n- outputs: "
-        ^ string_of_int (List.length outputs)
-        ^ "\n- expected outputs: "
-        ^ string_of_int (List.length inst_sg.doutputs)));
-    List.iter
-      (fun (x, ty) -> assert ((x : typed_pattern).ty = ty))
-      (List.combine outputs inst_sg.doutputs)
-  in
+  (if (* TODO: normalize the types *) !Config.type_check_pure_code then
+     match fun_id with
+     | FunId fun_id ->
+         let inst_sg =
+           get_instantiated_fun_sig fun_id (Some rg_id) generics ctx
+         in
+         log#ldebug
+           (lazy
+             ("\n- fun_id: " ^ A.show_fun_id fun_id ^ "\n- inputs ("
+             ^ string_of_int (List.length inputs)
+             ^ "): "
+             ^ String.concat ", " (List.map (texpression_to_string ctx) inputs)
+             ^ "\n- inst_sg.inputs ("
+             ^ string_of_int (List.length inst_sg.inputs)
+             ^ "): "
+             ^ String.concat ", " (List.map (ty_to_string ctx) inst_sg.inputs)));
+         List.iter
+           (fun (x, ty) -> assert ((x : texpression).ty = ty))
+           (List.combine inputs inst_sg.inputs);
+         log#ldebug
+           (lazy
+             ("\n- outputs: "
+             ^ string_of_int (List.length outputs)
+             ^ "\n- expected outputs: "
+             ^ string_of_int (List.length inst_sg.doutputs)));
+         List.iter
+           (fun (x, ty) -> assert ((x : typed_pattern).ty = ty))
+           (List.combine outputs inst_sg.doutputs)
+     | _ -> (* TODO: trait methods *) ());
   (* Retrieve the function id, and register the function call in the context
    * if necessary *)
   let ctx, func =
@@ -1788,7 +1981,7 @@ and translate_end_abstraction_fun_call (ectx : C.eval_ctx) (abs : V.abs)
     if effect_info.can_fail then mk_result_ty output.ty else output.ty
   in
   let func_ty = mk_arrows input_tys ret_ty in
-  let func = { id = FunOrOp func; type_args; const_generic_args } in
+  let func = { id = FunOrOp func; generics } in
   let func = { e = Qualif func; ty = func_ty } in
   let call = mk_apps func args in
   (* **Optimization**:
@@ -1905,14 +2098,13 @@ and translate_end_abstraction_loop (ectx : C.eval_ctx) (abs : V.abs)
       (* Actually the same case as [SynthInput] *)
       translate_end_abstraction_synth_input ectx abs e ctx rg_id
   | V.LoopCall ->
-      let fun_id = A.Regular ctx.fun_decl.A.def_id in
+      let fun_id = E.Regular ctx.fun_decl.A.def_id in
       let effect_info =
-        get_fun_effect_info ctx.fun_context.fun_infos fun_id (Some vloop_id)
-          (Some rg_id)
+        get_fun_effect_info ctx.fun_context.fun_infos (FunId fun_id)
+          (Some vloop_id) (Some rg_id)
       in
       let loop_info = LoopId.Map.find loop_id ctx.loops in
-      let type_args = loop_info.type_args in
-      let const_generic_args = loop_info.const_generic_args in
+      let generics = loop_info.generics in
       let fwd_inputs = Option.get loop_info.forward_inputs in
       (* Retrieve the additional backward inputs. Note that those are actually
          the backward inputs of the function we are synthesizing (and that we
@@ -1960,8 +2152,8 @@ and translate_end_abstraction_loop (ectx : C.eval_ctx) (abs : V.abs)
         if effect_info.can_fail then mk_result_ty output.ty else output.ty
       in
       let func_ty = mk_arrows input_tys ret_ty in
-      let func = Fun (FromLlbc (fun_id, Some loop_id, Some rg_id)) in
-      let func = { id = FunOrOp func; type_args; const_generic_args } in
+      let func = Fun (FromLlbc (FunId fun_id, Some loop_id, Some rg_id)) in
+      let func = { id = FunOrOp func; generics } in
       let func = { e = Qualif func; ty = func_ty } in
       let call = mk_apps func args in
       (* **Optimization**:
@@ -2021,9 +2213,7 @@ and translate_global_eval (gid : A.GlobalDeclId.id) (sval : V.symbolic_value)
     (e : S.expression) (ctx : bs_ctx) : texpression =
   let ctx, var = fresh_var_for_symbolic_value sval ctx in
   let decl = A.GlobalDeclId.Map.find gid ctx.global_context.llbc_global_decls in
-  let global_expr =
-    { id = Global gid; type_args = []; const_generic_args = [] }
-  in
+  let global_expr = { id = Global gid; generics = empty_generic_args } in
   (* We use translate_fwd_ty to translate the global type *)
   let ty = ctx_translate_fwd_ty ctx decl.ty in
   let gval = { e = Qualif global_expr; ty } in
@@ -2037,11 +2227,7 @@ and translate_assertion (ectx : C.eval_ctx) (v : V.typed_value)
   let v = typed_value_to_texpression ctx ectx v in
   let args = [ v ] in
   let func =
-    {
-      id = FunOrOp (Fun (Pure Assert));
-      type_args = [];
-      const_generic_args = [];
-    }
+    { id = FunOrOp (Fun (Pure Assert)); generics = empty_generic_args }
   in
   let func_ty = mk_arrow (Literal Bool) mk_unit_ty in
   let func = { e = Qualif func; ty = func_ty } in
@@ -2189,7 +2375,7 @@ and translate_ExpandAdt_one_branch (sv : V.symbolic_value)
     (branch : S.expression) (ctx : bs_ctx) : texpression =
   (* TODO: always introduce a match, and use micro-passes to turn the
      the match into a let? *)
-  let type_id, _, _, _ = TypesUtils.ty_as_adt sv.V.sv_ty in
+  let type_id, _ = TypesUtils.ty_as_adt sv.V.sv_ty in
   let ctx, vars = fresh_vars_for_symbolic_values svl ctx in
   let branch = translate_expression branch ctx in
   match type_id with
@@ -2224,10 +2410,10 @@ and translate_ExpandAdt_one_branch (sv : V.symbolic_value)
          * field.
          * We use the [dest] variable in order not to have to recompute
          * the type of the result of the projection... *)
-        let adt_id, type_args, const_generic_args = ty_as_adt scrutinee.ty in
+        let adt_id, generics = ty_as_adt scrutinee.ty in
         let gen_field_proj (field_id : FieldId.id) (dest : var) : texpression =
           let proj_kind = { adt_id; field_id } in
-          let qualif = { id = Proj proj_kind; type_args; const_generic_args } in
+          let qualif = { id = Proj proj_kind; generics } in
           let proj_e = Qualif qualif in
           let proj_ty = mk_arrow scrutinee.ty dest.ty in
           let proj = { e = proj_e; ty = proj_ty } in
@@ -2259,17 +2445,12 @@ and translate_ExpandAdt_one_branch (sv : V.symbolic_value)
         (mk_typed_pattern_from_var var None)
         (mk_opt_mplace_texpression scrutinee_mplace scrutinee)
         branch
-  | T.Assumed (T.Vec | T.Array | T.Slice | T.Str) ->
+  | T.Assumed (T.Array | T.Slice | T.Str) ->
       (* We can't expand those values: we can access the fields only
        * through the functions provided by the API (note that we don't
        * know how to expand values like vectors or arrays, because they have a variable number
        * of fields!) *)
       raise (Failure "Attempt to expand a non-expandable value")
-  | T.Assumed Range -> raise (Failure "Unimplemented")
-  | T.Assumed T.Option ->
-      (* We shouldn't get there in the "one-branch" case: options have
-       * two variants *)
-      raise (Failure "Unreachable")
 
 and translate_intro_symbolic (ectx : C.eval_ctx) (p : S.mplace option)
     (sv : V.symbolic_value) (v : S.value_aggregate) (e : S.expression)
@@ -2282,8 +2463,9 @@ and translate_intro_symbolic (ectx : C.eval_ctx) (p : S.mplace option)
   (* Translate the next expression *)
   let next_e = translate_expression e ctx in
 
-  (* Translate the value: there are two cases, depending on whether this
-     is a "regular" let-binding or an array aggregate.
+  (* Translate the value: there are several cases, depending on whether this
+     is a "regular" let-binding, an array aggregate, a const generic or
+     a trait associated constant.
   *)
   let v =
     match v with
@@ -2298,6 +2480,14 @@ and translate_intro_symbolic (ectx : C.eval_ctx) (p : S.mplace option)
           { struct_id = Assumed Array; init = None; updates = values }
         in
         { e = StructUpdate su; ty = var.ty }
+    | ConstGenericValue cg_id -> { e = CVar cg_id; ty = var.ty }
+    | TraitConstValue (trait_ref, generics, const_name) ->
+        let type_infos = ctx.type_context.type_infos in
+        let trait_ref = translate_fwd_trait_ref type_infos trait_ref in
+        let generics = translate_fwd_generic_args type_infos generics in
+        let qualif_id = TraitConst (trait_ref, generics, const_name) in
+        let qualif = { id = qualif_id; generics = empty_generic_args } in
+        { e = Qualif qualif; ty = var.ty }
   in
 
   (* Make the let-binding *)
@@ -2368,9 +2558,9 @@ and translate_forward_end (ectx : C.eval_ctx)
       let org_args = args in
 
       (* Lookup the effect info for the loop function *)
-      let fid = A.Regular ctx.fun_decl.A.def_id in
+      let fid = E.Regular ctx.fun_decl.A.def_id in
       let effect_info =
-        get_fun_effect_info ctx.fun_context.fun_infos fid None ctx.bid
+        get_fun_effect_info ctx.fun_context.fun_infos (FunId fid) None ctx.bid
       in
 
       (* Introduce a fresh output value for the forward function *)
@@ -2415,14 +2605,8 @@ and translate_forward_end (ectx : C.eval_ctx)
       let out_pat = mk_simpl_tuple_pattern out_pats in
 
       let loop_call =
-        let fun_id = Fun (FromLlbc (fid, Some loop_id, None)) in
-        let func =
-          {
-            id = FunOrOp fun_id;
-            type_args = loop_info.type_args;
-            const_generic_args = loop_info.const_generic_args;
-          }
-        in
+        let fun_id = Fun (FromLlbc (FunId fid, Some loop_id, None)) in
+        let func = { id = FunOrOp fun_id; generics = loop_info.generics } in
         let input_tys = (List.map (fun (x : texpression) -> x.ty)) args in
         let ret_ty =
           if effect_info.can_fail then mk_result_ty out_pat.ty else out_pat.ty
@@ -2541,14 +2725,31 @@ and translate_loop (loop : S.loop) (ctx : bs_ctx) : texpression =
 
     (* Note that we will retrieve the input values later in the [ForwardEnd]
        (and will introduce the outputs at that moment, together with the actual
-       call to the loop forward function *)
-    let type_args =
-      List.map (fun (ty : T.type_var) -> TypeVar ty.T.index) ctx.sg.type_params
-    in
-    let const_generic_args =
-      List.map
-        (fun (cg : T.const_generic_var) -> T.ConstGenericVar cg.T.index)
-        ctx.sg.const_generic_params
+       call to the loop forward function) *)
+    let generics =
+      let { types; const_generics; trait_clauses } = ctx.sg.generics in
+      let types =
+        List.map (fun (ty : T.type_var) -> TypeVar ty.T.index) types
+      in
+      let const_generics =
+        List.map
+          (fun (cg : T.const_generic_var) -> T.ConstGenericVar cg.T.index)
+          const_generics
+      in
+      let trait_refs =
+        List.map
+          (fun (c : trait_clause) ->
+            let trait_decl_ref =
+              { trait_decl_id = c.trait_id; decl_generics = empty_generic_args }
+            in
+            {
+              trait_id = Clause c.clause_id;
+              generics = empty_generic_args;
+              trait_decl_ref;
+            })
+          trait_clauses
+      in
+      { types; const_generics; trait_refs }
     in
 
     let loop_info =
@@ -2556,8 +2757,7 @@ and translate_loop (loop : S.loop) (ctx : bs_ctx) : texpression =
         loop_id;
         input_vars = inputs;
         input_svl = loop.input_svalues;
-        type_args;
-        const_generic_args;
+        generics;
         forward_inputs = None;
         forward_output_no_state_no_result = None;
       }
@@ -2648,8 +2848,7 @@ let wrap_in_match_fuel (fuel0 : VarId.id) (fuel : VarId.id) (body : texpression)
         let func =
           {
             id = FunOrOp (Fun (Pure FuelEqZero));
-            type_args = [];
-            const_generic_args = [];
+            generics = empty_generic_args;
           }
         in
         let func_ty = mk_arrow mk_fuel_ty mk_bool_ty in
@@ -2661,8 +2860,7 @@ let wrap_in_match_fuel (fuel0 : VarId.id) (fuel : VarId.id) (body : texpression)
         let func =
           {
             id = FunOrOp (Fun (Pure FuelDecrease));
-            type_args = [];
-            const_generic_args = [];
+            generics = empty_generic_args;
           }
         in
         let func_ty = mk_arrow mk_fuel_ty mk_fuel_ty in
@@ -2727,8 +2925,8 @@ let translate_fun_decl (ctx : bs_ctx) (body : S.expression option) : fun_decl =
     | None -> None
     | Some body ->
         let effect_info =
-          get_fun_effect_info ctx.fun_context.fun_infos (Regular def_id) None
-            bid
+          get_fun_effect_info ctx.fun_context.fun_infos (FunId (Regular def_id))
+            None bid
         in
         let body = translate_expression body ctx in
         (* Add a match over the fuel, if necessary *)
@@ -2803,10 +3001,12 @@ let translate_fun_decl (ctx : bs_ctx) (body : S.expression option) : fun_decl =
             ^ "\n- signature.inputs: "
             ^ String.concat ", " (List.map (ty_to_string ctx) signature.inputs)
             ));
-        assert (
-          List.for_all
-            (fun (var, ty) -> (var : var).ty = ty)
-            (List.combine inputs signature.inputs));
+        (* TODO: we need to normalize the types *)
+        if !Config.type_check_pure_code then
+          assert (
+            List.for_all
+              (fun (var, ty) -> (var : var).ty = ty)
+              (List.combine inputs signature.inputs));
         Some { inputs; inputs_lvs; body }
   in
 
@@ -2821,6 +3021,7 @@ let translate_fun_decl (ctx : bs_ctx) (body : S.expression option) : fun_decl =
   let def =
     {
       def_id;
+      kind = def.kind;
       num_loops;
       loop_id;
       back_id = bid;
@@ -2853,8 +3054,7 @@ let translate_type_decls (type_decls : T.type_decl list) : type_decl list =
     - optional names for the outputs values (we derive them for the backward
       functions)
  *)
-let translate_fun_signatures (fun_infos : FA.fun_info A.FunDeclId.Map.t)
-    (type_infos : TA.type_infos)
+let translate_fun_signatures (decls_ctx : C.decls_ctx)
     (functions : (A.fun_id * string option list * A.fun_sig) list) :
     fun_sig_named_outputs RegularFunIdNotLoopMap.t =
   (* For every function, translate the signatures of:
@@ -2865,17 +3065,14 @@ let translate_fun_signatures (fun_infos : FA.fun_info A.FunDeclId.Map.t)
       (sg : A.fun_sig) : (regular_fun_id_not_loop * fun_sig_named_outputs) list
       =
     (* The forward function *)
-    let fwd_sg =
-      translate_fun_sig fun_infos fun_id type_infos sg input_names None
-    in
+    let fwd_sg = translate_fun_sig decls_ctx fun_id sg input_names None in
     let fwd_id = (fun_id, None) in
     (* The backward functions *)
     let back_sgs =
       List.map
         (fun (rg : T.region_var_group) ->
           let tsg =
-            translate_fun_sig fun_infos fun_id type_infos sg input_names
-              (Some rg.id)
+            translate_fun_sig decls_ctx fun_id sg input_names (Some rg.id)
           in
           let id = (fun_id, Some rg.id) in
           (id, tsg))
@@ -2891,3 +3088,94 @@ let translate_fun_signatures (fun_infos : FA.fun_info A.FunDeclId.Map.t)
   List.fold_left
     (fun m (id, sg) -> RegularFunIdNotLoopMap.add id sg m)
     RegularFunIdNotLoopMap.empty translated
+
+let translate_trait_decl (type_infos : TA.type_infos)
+    (trait_decl : A.trait_decl) : trait_decl =
+  let {
+    def_id;
+    name;
+    generics;
+    preds;
+    parent_clauses;
+    consts;
+    types;
+    required_methods;
+    provided_methods;
+  } : A.trait_decl =
+    trait_decl
+  in
+  let generics = translate_generic_params generics in
+  let preds = translate_predicates preds in
+  let parent_clauses = List.map translate_trait_clause parent_clauses in
+  let consts =
+    List.map
+      (fun (name, (ty, id)) -> (name, (translate_fwd_ty type_infos ty, id)))
+      consts
+  in
+  let types =
+    List.map
+      (fun (name, (trait_clauses, ty)) ->
+        ( name,
+          ( List.map translate_trait_clause trait_clauses,
+            Option.map (translate_fwd_ty type_infos) ty ) ))
+      types
+  in
+  {
+    def_id;
+    name;
+    generics;
+    preds;
+    parent_clauses;
+    consts;
+    types;
+    required_methods;
+    provided_methods;
+  }
+
+let translate_trait_impl (type_infos : TA.type_infos)
+    (trait_impl : A.trait_impl) : trait_impl =
+  let {
+    A.def_id;
+    name;
+    impl_trait;
+    generics;
+    preds;
+    parent_trait_refs;
+    consts;
+    types;
+    required_methods;
+    provided_methods;
+  } =
+    trait_impl
+  in
+  let impl_trait =
+    translate_trait_decl_ref (translate_fwd_ty type_infos) impl_trait
+  in
+  let generics = translate_generic_params generics in
+  let preds = translate_predicates preds in
+  let parent_trait_refs = List.map translate_strait_ref parent_trait_refs in
+  let consts =
+    List.map
+      (fun (name, (ty, id)) -> (name, (translate_fwd_ty type_infos ty, id)))
+      consts
+  in
+  let types =
+    List.map
+      (fun (name, (trait_refs, ty)) ->
+        ( name,
+          ( List.map (translate_fwd_trait_ref type_infos) trait_refs,
+            translate_fwd_ty type_infos ty ) ))
+      types
+  in
+  {
+    def_id;
+    name;
+    impl_trait;
+    generics;
+    preds;
+    parent_trait_refs;
+    consts;
+    types;
+    required_methods;
+    provided_methods;
+  }
diff --git a/compiler/SynthesizeSymbolic.ml b/compiler/SynthesizeSymbolic.ml
index 857fea97..9dd65c84 100644
--- a/compiler/SynthesizeSymbolic.ml
+++ b/compiler/SynthesizeSymbolic.ml
@@ -64,7 +64,7 @@ let synthesize_symbolic_expansion (sv : V.symbolic_value)
             assert (otherwise_see = None);
             (* Return *)
             ExpandInt (int_ty, branches, otherwise)
-        | T.Adt (_, _, _, _) ->
+        | T.Adt (_, _) ->
             (* Branching: it is necessarily an enumeration expansion *)
             let get_variant (see : V.symbolic_expansion option) :
                 T.VariantId.id option * V.symbolic_value list =
@@ -85,7 +85,9 @@ let synthesize_symbolic_expansion (sv : V.symbolic_value)
             match ls with
             | [ (Some see, exp) ] -> ExpandNoBranch (see, exp)
             | _ -> raise (Failure "Ill-formed borrow expansion"))
-        | T.TypeVar _ | T.Literal Char | Never ->
+        | T.TypeVar _
+        | T.Literal Char
+        | Never | T.TraitType _ | T.Arrow _ | T.RawPtr _ ->
             raise (Failure "Ill-formed symbolic expansion")
       in
       Some (Expansion (place, sv, expansion))
@@ -97,10 +99,10 @@ let synthesize_symbolic_expansion_no_branching (sv : V.symbolic_value)
   synthesize_symbolic_expansion sv place [ Some see ] el
 
 let synthesize_function_call (call_id : call_id) (ctx : Contexts.eval_ctx)
-    (abstractions : V.AbstractionId.id list) (type_params : T.ety list)
-    (const_generic_params : T.const_generic list) (args : V.typed_value list)
-    (args_places : mplace option list) (dest : V.symbolic_value)
-    (dest_place : mplace option) (e : expression option) : expression option =
+    (abstractions : V.AbstractionId.id list) (generics : T.egeneric_args)
+    (args : V.typed_value list) (args_places : mplace option list)
+    (dest : V.symbolic_value) (dest_place : mplace option)
+    (e : expression option) : expression option =
   Option.map
     (fun e ->
       let call =
@@ -108,8 +110,7 @@ let synthesize_function_call (call_id : call_id) (ctx : Contexts.eval_ctx)
           call_id;
           ctx;
           abstractions;
-          type_params;
-          const_generic_params;
+          generics;
           args;
           dest;
           args_places;
@@ -123,28 +124,29 @@ let synthesize_global_eval (gid : A.GlobalDeclId.id) (dest : V.symbolic_value)
     (e : expression option) : expression option =
   Option.map (fun e -> EvalGlobal (gid, dest, e)) e
 
-let synthesize_regular_function_call (fun_id : A.fun_id)
+let synthesize_regular_function_call (fun_id : A.fun_id_or_trait_method_ref)
     (call_id : V.FunCallId.id) (ctx : Contexts.eval_ctx)
-    (abstractions : V.AbstractionId.id list) (type_params : T.ety list)
-    (const_generic_params : T.const_generic list) (args : V.typed_value list)
-    (args_places : mplace option list) (dest : V.symbolic_value)
-    (dest_place : mplace option) (e : expression option) : expression option =
+    (abstractions : V.AbstractionId.id list) (generics : T.egeneric_args)
+    (args : V.typed_value list) (args_places : mplace option list)
+    (dest : V.symbolic_value) (dest_place : mplace option)
+    (e : expression option) : expression option =
   synthesize_function_call
     (Fun (fun_id, call_id))
-    ctx abstractions type_params const_generic_params args args_places dest
-    dest_place e
+    ctx abstractions generics args args_places dest dest_place e
 
 let synthesize_unary_op (ctx : Contexts.eval_ctx) (unop : E.unop)
     (arg : V.typed_value) (arg_place : mplace option) (dest : V.symbolic_value)
     (dest_place : mplace option) (e : expression option) : expression option =
-  synthesize_function_call (Unop unop) ctx [] [] [] [ arg ] [ arg_place ] dest
-    dest_place e
+  let generics = TypesUtils.mk_empty_generic_args in
+  synthesize_function_call (Unop unop) ctx [] generics [ arg ] [ arg_place ]
+    dest dest_place e
 
 let synthesize_binary_op (ctx : Contexts.eval_ctx) (binop : E.binop)
     (arg0 : V.typed_value) (arg0_place : mplace option) (arg1 : V.typed_value)
     (arg1_place : mplace option) (dest : V.symbolic_value)
     (dest_place : mplace option) (e : expression option) : expression option =
-  synthesize_function_call (Binop binop) ctx [] [] [] [ arg0; arg1 ]
+  let generics = TypesUtils.mk_empty_generic_args in
+  synthesize_function_call (Binop binop) ctx [] generics [ arg0; arg1 ]
     [ arg0_place; arg1_place ] dest dest_place e
 
 let synthesize_end_abstraction (ctx : Contexts.eval_ctx) (abs : V.abs)
diff --git a/compiler/Translate.ml b/compiler/Translate.ml
index 70ef5e3d..a3d96023 100644
--- a/compiler/Translate.ml
+++ b/compiler/Translate.ml
@@ -5,6 +5,7 @@ module T = Types
 module A = LlbcAst
 module SA = SymbolicAst
 module Micro = PureMicroPasses
+module C = Contexts
 open PureUtils
 open TranslateCore
 
@@ -28,18 +29,12 @@ let translate_function_to_symbolics (trans_ctx : trans_ctx) (fdef : A.fun_decl)
       ("translate_function_to_symbolics: "
       ^ Print.fun_name_to_string fdef.A.name));
 
-  let { type_context; fun_context; global_context } = trans_ctx in
-  let fun_context = { C.fun_decls = fun_context.fun_decls } in
-
   match fdef.body with
   | None -> None
   | Some _ ->
       (* Evaluate *)
       let synthesize = true in
-      let inputs, symb =
-        evaluate_function_symbolic synthesize type_context fun_context
-          global_context fdef
-      in
+      let inputs, symb = evaluate_function_symbolic synthesize trans_ctx fdef in
       Some (inputs, Option.get symb)
 
 (** Translate a function, by generating its forward and backward translations.
@@ -57,7 +52,6 @@ let translate_function_to_pure (trans_ctx : trans_ctx)
     (lazy
       ("translate_function_to_pure: " ^ Print.fun_name_to_string fdef.A.name));
 
-  let { type_context; fun_context; global_context } = trans_ctx in
   let def_id = fdef.def_id in
 
   (* Compute the symbolic ASTs, if the function is transparent *)
@@ -67,7 +61,7 @@ let translate_function_to_pure (trans_ctx : trans_ctx)
 
   (* Initialize the context *)
   let forward_sig =
-    RegularFunIdNotLoopMap.find (A.Regular def_id, None) fun_sigs
+    RegularFunIdNotLoopMap.find (E.Regular def_id, None) fun_sigs
   in
   let sv_to_var = V.SymbolicValueId.Map.empty in
   let var_counter = Pure.VarId.generator_zero in
@@ -82,25 +76,25 @@ let translate_function_to_pure (trans_ctx : trans_ctx)
       (List.filter_map
          (fun (tid, g) ->
            match g with Charon.GAst.NonRec _ -> None | Rec _ -> Some tid)
-         (T.TypeDeclId.Map.bindings trans_ctx.type_context.type_decls_groups))
+         (T.TypeDeclId.Map.bindings trans_ctx.type_ctx.type_decls_groups))
   in
   let type_context =
     {
-      SymbolicToPure.type_infos = type_context.type_infos;
-      llbc_type_decls = type_context.type_decls;
+      SymbolicToPure.type_infos = trans_ctx.type_ctx.type_infos;
+      llbc_type_decls = trans_ctx.type_ctx.type_decls;
       type_decls = pure_type_decls;
       recursive_decls = recursive_type_decls;
     }
   in
   let fun_context =
     {
-      SymbolicToPure.llbc_fun_decls = fun_context.fun_decls;
+      SymbolicToPure.llbc_fun_decls = trans_ctx.fun_ctx.fun_decls;
       fun_sigs;
-      fun_infos = fun_context.fun_infos;
+      fun_infos = trans_ctx.fun_ctx.fun_infos;
     }
   in
   let global_context =
-    { SymbolicToPure.llbc_global_decls = global_context.global_decls }
+    { SymbolicToPure.llbc_global_decls = trans_ctx.global_ctx.global_decls }
   in
 
   (* Compute the set of loops, and find better ids for them (starting at 0).
@@ -148,6 +142,8 @@ let translate_function_to_pure (trans_ctx : trans_ctx)
       type_context;
       fun_context;
       global_context;
+      trait_decls_ctx = trans_ctx.trait_decls_ctx.trait_decls;
+      trait_impls_ctx = trans_ctx.trait_impls_ctx.trait_impls;
       fun_decl = fdef;
       forward_inputs = [];
       (* Empty for now *)
@@ -204,7 +200,7 @@ let translate_function_to_pure (trans_ctx : trans_ctx)
         (* Initialize the context - note that the ret_ty is not really
          * useful as we don't translate a body *)
         let backward_sg =
-          RegularFunIdNotLoopMap.find (A.Regular def_id, Some back_id) fun_sigs
+          RegularFunIdNotLoopMap.find (Regular def_id, Some back_id) fun_sigs
         in
         let ctx = { ctx with bid = Some back_id; sg = backward_sg.sg } in
 
@@ -215,7 +211,7 @@ let translate_function_to_pure (trans_ctx : trans_ctx)
            variables required by the backward function.
         *)
         let backward_sg =
-          RegularFunIdNotLoopMap.find (A.Regular def_id, Some back_id) fun_sigs
+          RegularFunIdNotLoopMap.find (Regular def_id, Some back_id) fun_sigs
         in
         (* We need to ignore the forward inputs, and the state input (if there is) *)
         let backward_inputs =
@@ -274,21 +270,18 @@ let translate_function_to_pure (trans_ctx : trans_ctx)
   (* Return *)
   (pure_forward, pure_backwards)
 
+(* TODO: factor out the return type *)
 let translate_crate_to_pure (crate : A.crate) :
-    trans_ctx * Pure.type_decl list * (bool * pure_fun_translation) list =
+    trans_ctx
+    * Pure.type_decl list
+    * pure_fun_translation list
+    * Pure.trait_decl list
+    * Pure.trait_impl list =
   (* Debug *)
   log#ldebug (lazy "translate_crate_to_pure");
 
-  (* Compute the type and function contexts *)
-  let type_context, fun_context, global_context =
-    compute_type_fun_global_contexts crate
-  in
-  let fun_infos =
-    FA.analyze_module crate fun_context.C.fun_decls
-      global_context.C.global_decls !Config.use_state
-  in
-  let fun_context = { fun_decls = fun_context.fun_decls; fun_infos } in
-  let trans_ctx = { type_context; fun_context; global_context } in
+  (* Compute the translation context *)
+  let trans_ctx = compute_contexts crate in
 
   (* Translate all the type definitions *)
   let type_decls =
@@ -304,9 +297,11 @@ let translate_crate_to_pure (crate : A.crate) :
   (* Translate all the function *signatures* *)
   let assumed_sigs =
     List.map
-      (fun (id, sg, _, _) ->
-        (A.Assumed id, List.map (fun _ -> None) (sg : A.fun_sig).inputs, sg))
-      Assumed.assumed_infos
+      (fun (info : Assumed.assumed_fun_info) ->
+        ( E.Assumed info.fun_id,
+          List.map (fun _ -> None) info.fun_sig.inputs,
+          info.fun_sig ))
+      Assumed.assumed_fun_infos
   in
   let local_sigs =
     List.map
@@ -319,14 +314,11 @@ let translate_crate_to_pure (crate : A.crate) :
                 (fun (v : A.var) -> v.name)
                 (LlbcAstUtils.fun_body_get_input_vars body)
         in
-        (A.Regular fdef.def_id, input_names, fdef.signature))
+        (E.Regular fdef.def_id, input_names, fdef.signature))
       (A.FunDeclId.Map.values crate.functions)
   in
   let sigs = List.append assumed_sigs local_sigs in
-  let fun_sigs =
-    SymbolicToPure.translate_fun_signatures fun_context.fun_infos
-      type_context.type_infos sigs
-  in
+  let fun_sigs = SymbolicToPure.translate_fun_signatures trans_ctx sigs in
 
   (* Translate all the *transparent* functions *)
   let pure_translations =
@@ -335,28 +327,38 @@ let translate_crate_to_pure (crate : A.crate) :
       (A.FunDeclId.Map.values crate.functions)
   in
 
+  (* Translate the trait declarations *)
+  let type_infos = trans_ctx.type_ctx.type_infos in
+  let trait_decls =
+    List.map
+      (SymbolicToPure.translate_trait_decl type_infos)
+      (T.TraitDeclId.Map.values trans_ctx.trait_decls_ctx.trait_decls)
+  in
+
+  (* Translate the trait implementations *)
+  let trait_impls =
+    List.map
+      (SymbolicToPure.translate_trait_impl type_infos)
+      (T.TraitImplId.Map.values trans_ctx.trait_impls_ctx.trait_impls)
+  in
+
   (* Apply the micro-passes *)
   let pure_translations =
     Micro.apply_passes_to_pure_fun_translations trans_ctx pure_translations
   in
 
   (* Return *)
-  (trans_ctx, type_decls, pure_translations)
-
-(** Extraction context *)
-type gen_ctx = {
-  crate : A.crate;
-  extract_ctx : ExtractBase.extraction_ctx;
-  trans_types : Pure.type_decl Pure.TypeDeclId.Map.t;
-  trans_funs : (bool * pure_fun_translation) A.FunDeclId.Map.t;
-  functions_with_decreases_clause : PureUtils.FunLoopIdSet.t;
-}
+  (trans_ctx, type_decls, pure_translations, trait_decls, trait_impls)
+
+type gen_ctx = ExtractBase.extraction_ctx
 
 type gen_config = {
   extract_types : bool;
   extract_decreases_clauses : bool;
   extract_template_decreases_clauses : bool;
   extract_fun_decls : bool;
+  extract_trait_decls : bool;
+  extract_trait_impls : bool;
   extract_transparent : bool;
       (** If [true], extract the transparent declarations, otherwise ignore. *)
   extract_opaque : bool;
@@ -383,21 +385,23 @@ type gen_config = {
   test_trans_unit_functions : bool;
 }
 
-(** Returns the pair: (has opaque type decls, has opaque fun decls) *)
-let module_has_opaque_decls (ctx : gen_ctx) : bool * bool =
-  let has_opaque_types =
-    Pure.TypeDeclId.Map.exists
-      (fun _ (d : Pure.type_decl) ->
-        match d.kind with Opaque -> true | _ -> false)
-      ctx.trans_types
-  in
-  let has_opaque_funs =
-    A.FunDeclId.Map.exists
-      (fun _ ((_, ((t_fwd, _), _)) : bool * pure_fun_translation) ->
-        Option.is_none t_fwd.body)
-      ctx.trans_funs
+(** Returns the pair: (has opaque type decls, has opaque fun decls).
+
+    [filter_assumed]: if [true], do not consider as opaque the external definitions
+    that we will map to definitions from the standard library.
+ *)
+let crate_has_opaque_non_builtin_decls (ctx : gen_ctx) (filter_assumed : bool) :
+    bool * bool =
+  let types, funs =
+    LlbcAstUtils.crate_get_opaque_non_builtin_decls ctx.crate filter_assumed
   in
-  (has_opaque_types, has_opaque_funs)
+  log#ldebug
+    (lazy
+      ("Opaque decls:" ^ "\n- types:\n"
+      ^ String.concat ",\n" (List.map T.show_type_decl types)
+      ^ "\n- functions:\n"
+      ^ String.concat ",\n" (List.map A.show_fun_decl funs)));
+  (types <> [], funs <> [])
 
 (** Export a type declaration.
 
@@ -423,15 +427,19 @@ let export_type (fmt : Format.formatter) (config : gen_config) (ctx : gen_ctx)
         (true, kind)
   in
   (* Extract, if the config instructs to do so (depending on whether the type
-   * is opaque or not) *)
-  if
+     is opaque or not). Remark: we don't check if the definitions are builtin
+     here but in the function [export_types_group]: the reason is that if one
+     definition in the group is builtin, then we must check that all the
+     definitions are marked builtin *)
+  let extract =
     (is_opaque && config.extract_opaque)
     || ((not is_opaque) && config.extract_transparent)
-  then (
+  in
+  if extract then (
     if extract_decl then
-      Extract.extract_type_decl ctx.extract_ctx fmt type_decl_group kind def;
+      Extract.extract_type_decl ctx fmt type_decl_group kind def;
     if extract_extra_info then
-      Extract.extract_type_decl_extra_info ctx.extract_ctx fmt kind def)
+      Extract.extract_type_decl_extra_info ctx fmt kind def)
 
 (** Export a group of types.
 
@@ -462,41 +470,58 @@ let export_types_group (fmt : Format.formatter) (config : gen_config)
     List.map (fun id -> Pure.TypeDeclId.Map.find id ctx.trans_types) ids
   in
 
-  (* Extract the type declarations.
-
-     Because some declaration groups are delimited, we wrap the declarations
-     between [{start,end}_type_decl_group].
+  (* Check if the definition are builtin - if yes they must be ignored.
+     Note that if one definition in the group is builtin, then all the
+     definitions must be builtin *)
+  let builtin =
+    let open ExtractBuiltin in
+    let types_map = builtin_types_map () in
+    List.map
+      (fun (def : Pure.type_decl) ->
+        let sname = name_to_simple_name def.name in
+        SimpleNameMap.find_opt sname types_map <> None)
+      defs
+  in
 
-     Ex.:
-     ====
-     When targeting HOL4, the calls to [{start,end}_type_decl_group] would generate
-     the [Datatype] and [End] delimiters in the snippet of code below:
+  if List.exists (fun b -> b) builtin then
+    (* Sanity check *)
+    assert (List.for_all (fun b -> b) builtin)
+  else (
+    (* Extract the type declarations.
+
+       Because some declaration groups are delimited, we wrap the declarations
+       between [{start,end}_type_decl_group].
+
+       Ex.:
+       ====
+       When targeting HOL4, the calls to [{start,end}_type_decl_group] would generate
+       the [Datatype] and [End] delimiters in the snippet of code below:
+
+       {[
+         Datatype:
+           tree =
+             TLeaf 'a
+           | TNode node ;
+
+           node =
+             Node (tree list)
+         End
+       ]}
+    *)
+    Extract.start_type_decl_group ctx fmt is_rec defs;
+    List.iteri
+      (fun i def ->
+        let kind = kind_from_index i in
+        export_type_decl kind def)
+      defs;
+    Extract.end_type_decl_group fmt is_rec defs;
 
-     {[
-       Datatype:
-         tree =
-           TLeaf 'a
-         | TNode node ;
-
-         node =
-           Node (tree list)
-       End
-     ]}
-  *)
-  Extract.start_type_decl_group ctx.extract_ctx fmt is_rec defs;
-  List.iteri
-    (fun i def ->
-      let kind = kind_from_index i in
-      export_type_decl kind def)
-    defs;
-  Extract.end_type_decl_group fmt is_rec defs;
-
-  (* Export the extra information (ex.: [Arguments] instructions in Coq) *)
-  List.iteri
-    (fun i def ->
-      let kind = kind_from_index i in
-      export_type_extra_info kind def)
-    defs
+    (* Export the extra information (ex.: [Arguments] instructions in Coq) *)
+    List.iteri
+      (fun i def ->
+        let kind = kind_from_index i in
+        export_type_extra_info kind def)
+      defs)
 
 (** Export a global declaration.
 
@@ -504,26 +529,34 @@ let export_types_group (fmt : Format.formatter) (config : gen_config)
  *)
 let export_global (fmt : Format.formatter) (config : gen_config) (ctx : gen_ctx)
     (id : A.GlobalDeclId.id) : unit =
-  let global_decls = ctx.extract_ctx.trans_ctx.global_context.global_decls in
+  let global_decls = ctx.trans_ctx.global_ctx.global_decls in
   let global = A.GlobalDeclId.Map.find id global_decls in
-  let _, ((body, loop_fwds), body_backs) =
-    A.FunDeclId.Map.find global.body_id ctx.trans_funs
-  in
-  assert (body_backs = []);
-  assert (loop_fwds = []);
+  let trans = A.FunDeclId.Map.find global.body_id ctx.trans_funs in
+  assert (trans.fwd.loops = []);
+  assert (trans.backs = []);
+  let body = trans.fwd.f in
 
   let is_opaque = Option.is_none body.Pure.body in
-  if
+  (* Check if we extract the global *)
+  let extract =
     config.extract_globals
     && (((not is_opaque) && config.extract_transparent)
        || (is_opaque && config.extract_opaque))
-  then
+  in
+  (* Check if it is a builtin global - if yes, we ignore it because we
+     map the definition to one in the standard library *)
+  let open ExtractBuiltin in
+  let sname = name_to_simple_name global.name in
+  let extract =
+    extract && SimpleNameMap.find_opt sname builtin_globals_map = None
+  in
+  if extract then
     (* We don't wrap global declaration groups between calls to functions
        [{start, end}_global_decl_group] (which don't exist): global declaration
        groups are always singletons, so the [extract_global_decl] function
        takes care of generating the delimiters.
     *)
-    Extract.extract_global_decl ctx.extract_ctx fmt global body config.interface
+    Extract.extract_global_decl ctx fmt global body config.interface
 
 (** Utility.
 
@@ -604,14 +637,13 @@ let export_functions_group_scc (fmt : Format.formatter) (config : gen_config)
         then
           Some
             (fun () ->
-              Extract.extract_fun_decl ctx.extract_ctx fmt kind has_decr_clause
-                def)
+              Extract.extract_fun_decl ctx fmt kind has_decr_clause def)
         else None)
       decls
   in
   let extract_defs = List.filter_map (fun x -> x) extract_defs in
   if extract_defs <> [] then (
-    Extract.start_fun_decl_group ctx.extract_ctx fmt is_rec decls;
+    Extract.start_fun_decl_group ctx fmt is_rec decls;
     List.iter (fun f -> f ()) extract_defs;
     Extract.end_fun_decl_group fmt is_rec decls)
 
@@ -621,82 +653,137 @@ let export_functions_group_scc (fmt : Format.formatter) (config : gen_config)
     check if the forward and backward functions are mutually recursive.
  *)
 let export_functions_group (fmt : Format.formatter) (config : gen_config)
-    (ctx : gen_ctx) (pure_ls : (bool * pure_fun_translation) list) : unit =
-  (* Utility to check a function has a decrease clause *)
-  let has_decreases_clause (def : Pure.fun_decl) : bool =
-    PureUtils.FunLoopIdSet.mem (def.def_id, def.loop_id)
-      ctx.functions_with_decreases_clause
+    (ctx : gen_ctx) (pure_ls : pure_fun_translation list) : unit =
+  (* Check if the definition are builtin - if yes they must be ignored.
+     Note that if one definition in the group is builtin, then all the
+     definitions must be builtin *)
+  let builtin =
+    let open ExtractBuiltin in
+    let funs_map = builtin_funs_map () in
+    List.map
+      (fun (trans : pure_fun_translation) ->
+        let sname = name_to_simple_name trans.fwd.f.basename in
+        SimpleNameMap.find_opt sname funs_map <> None)
+      pure_ls
   in
 
-  (* Extract the decrease clauses template bodies *)
-  if config.extract_template_decreases_clauses then
-    List.iter
-      (fun (_, ((fwd, loop_fwds), _)) ->
-        (* We only generate decreases clauses for the forward functions, because
-           the termination argument should only depend on the forward inputs.
-           The backward functions thus use the same decreases clauses as the
-           forward function.
-
-           Rem.: we might filter backward functions in {!PureMicroPasses}, but
-           we don't remove forward functions. Instead, we remember if we should
-           filter those functions at extraction time with a boolean (see the
-           type of the [pure_ls] input parameter).
-        *)
-        let extract_decrease decl =
-          let has_decr_clause = has_decreases_clause decl in
-          if has_decr_clause then
-            match !Config.backend with
-            | Lean ->
-                Extract.extract_template_lean_termination_and_decreasing
-                  ctx.extract_ctx fmt decl
-            | FStar ->
-                Extract.extract_template_fstar_decreases_clause ctx.extract_ctx
-                  fmt decl
-            | Coq ->
-                raise (Failure "Coq doesn't have decreases/termination clauses")
-            | HOL4 ->
-                raise
-                  (Failure "HOL4 doesn't have decreases/termination clauses")
-        in
-        extract_decrease fwd;
-        List.iter extract_decrease loop_fwds)
-      pure_ls;
-
-  (* Concatenate the function definitions, filtering the useless forward
-   * functions. *)
-  let decls =
-    List.concat
-      (List.map
-         (fun (keep_fwd, ((fwd, fwd_loops), (back_ls : fun_and_loops list))) ->
-           let fwd = if keep_fwd then List.append fwd_loops [ fwd ] else [] in
-           let back : Pure.fun_decl list =
-             List.concat
-               (List.map
-                  (fun (back, loop_backs) -> List.append loop_backs [ back ])
-                  back_ls)
-           in
-           List.append fwd back)
-         pure_ls)
-  in
+  if List.exists (fun b -> b) builtin then
+    (* Sanity check *)
+    assert (List.for_all (fun b -> b) builtin)
+  else
+    (* Utility to check a function has a decrease clause *)
+    let has_decreases_clause (def : Pure.fun_decl) : bool =
+      PureUtils.FunLoopIdSet.mem (def.def_id, def.loop_id)
+        ctx.functions_with_decreases_clause
+    in
 
-  (* Extract the function definitions *)
-  (if config.extract_fun_decls then
-     (* Group the mutually recursive definitions *)
-     let subgroups = ReorderDecls.group_reorder_fun_decls decls in
+    (* Extract the decrease clauses template bodies *)
+    if config.extract_template_decreases_clauses then
+      List.iter
+        (fun { fwd; _ } ->
+          (* We only generate decreases clauses for the forward functions, because
+             the termination argument should only depend on the forward inputs.
+             The backward functions thus use the same decreases clauses as the
+             forward function.
+
+             Rem.: we might filter backward functions in {!PureMicroPasses}, but
+             we don't remove forward functions. Instead, we remember if we should
+             filter those functions at extraction time with a boolean (see the
+             type of the [pure_ls] input parameter).
+          *)
+          let extract_decrease decl =
+            let has_decr_clause = has_decreases_clause decl in
+            if has_decr_clause then
+              match !Config.backend with
+              | Lean ->
+                  Extract.extract_template_lean_termination_and_decreasing ctx
+                    fmt decl
+              | FStar ->
+                  Extract.extract_template_fstar_decreases_clause ctx fmt decl
+              | Coq ->
+                  raise
+                    (Failure "Coq doesn't have decreases/termination clauses")
+              | HOL4 ->
+                  raise
+                    (Failure "HOL4 doesn't have decreases/termination clauses")
+          in
+          extract_decrease fwd.f;
+          List.iter extract_decrease fwd.loops)
+        pure_ls;
+
+    (* Concatenate the function definitions, filtering the useless forward
+     * functions. *)
+    let decls =
+      List.concat
+        (List.map
+           (fun { keep_fwd; fwd; backs } ->
+             let fwd =
+               if keep_fwd then List.append fwd.loops [ fwd.f ] else []
+             in
+             let backs : Pure.fun_decl list =
+               List.concat
+                 (List.map
+                    (fun back -> List.append back.loops [ back.f ])
+                    backs)
+             in
+             List.append fwd backs)
+           pure_ls)
+    in
 
-     (* Extract the subgroups *)
-     let export_subgroup (is_rec : bool) (decls : Pure.fun_decl list) : unit =
-       export_functions_group_scc fmt config ctx is_rec decls
-     in
-     List.iter (fun (is_rec, decls) -> export_subgroup is_rec decls) subgroups);
-
-  (* Insert unit tests if necessary *)
-  if config.test_trans_unit_functions then
-    List.iter
-      (fun (keep_fwd, ((fwd, _), _)) ->
-        if keep_fwd then
-          Extract.extract_unit_test_if_unit_fun ctx.extract_ctx fmt fwd)
-      pure_ls
+    (* Extract the function definitions *)
+    (if config.extract_fun_decls then
+       (* Group the mutually recursive definitions *)
+       let subgroups = ReorderDecls.group_reorder_fun_decls decls in
+
+       (* Extract the subgroups *)
+       let export_subgroup (is_rec : bool) (decls : Pure.fun_decl list) : unit =
+         export_functions_group_scc fmt config ctx is_rec decls
+       in
+       List.iter (fun (is_rec, decls) -> export_subgroup is_rec decls) subgroups);
+
+    (* Insert unit tests if necessary *)
+    if config.test_trans_unit_functions then
+      List.iter
+        (fun trans ->
+          if trans.keep_fwd then
+            Extract.extract_unit_test_if_unit_fun ctx fmt trans.fwd.f)
+        pure_ls
+
+(** Export a trait declaration. *)
+let export_trait_decl (fmt : Format.formatter) (_config : gen_config)
+    (ctx : gen_ctx) (trait_decl_id : Pure.trait_decl_id) (extract_decl : bool)
+    (extract_extra_info : bool) : unit =
+  let trait_decl = T.TraitDeclId.Map.find trait_decl_id ctx.trans_trait_decls in
+  (* Check if the trait declaration is builtin, in which case we ignore it *)
+  let open ExtractBuiltin in
+  let sname = name_to_simple_name trait_decl.name in
+  if SimpleNameMap.find_opt sname (builtin_trait_decls_map ()) = None then (
+    let ctx = { ctx with trait_decl_id = Some trait_decl.def_id } in
+    if extract_decl then Extract.extract_trait_decl ctx fmt trait_decl;
+    if extract_extra_info then
+      Extract.extract_trait_decl_extra_info ctx fmt trait_decl)
+  else ()
+
+(** Export a trait implementation. *)
+let export_trait_impl (fmt : Format.formatter) (_config : gen_config)
+    (ctx : gen_ctx) (trait_impl_id : Pure.trait_impl_id) : unit =
+  (* Lookup the definition *)
+  let trait_impl = T.TraitImplId.Map.find trait_impl_id ctx.trans_trait_impls in
+  let trait_decl =
+    Pure.TraitDeclId.Map.find trait_impl.impl_trait.trait_decl_id
+      ctx.trans_trait_decls
+  in
+  (* Check if the trait implementation is builtin *)
+  let builtin_info =
+    let open ExtractBuiltin in
+    let type_sname = name_to_simple_name trait_impl.name in
+    let trait_sname = name_to_simple_name trait_decl.name in
+    SimpleNamePairMap.find_opt (type_sname, trait_sname)
+      (builtin_trait_impls_map ())
+  in
+  match builtin_info with
+  | None -> Extract.extract_trait_impl ctx fmt trait_impl
+  | Some _ -> ()
 
 (** A generic utility to generate the extracted definitions: as we may want to
     split the definitions between different files (or not), we can control
@@ -712,12 +799,19 @@ let extract_definitions (fmt : Format.formatter) (config : gen_config)
   let export_functions_group = export_functions_group fmt config ctx in
   let export_global = export_global fmt config ctx in
   let export_types_group = export_types_group fmt config ctx in
+  let export_trait_decl_group id =
+    export_trait_decl fmt config ctx id true false
+  in
+  let export_trait_decl_group_extra_info id =
+    export_trait_decl fmt config ctx id false true
+  in
+  let export_trait_impl = export_trait_impl fmt config ctx in
 
   let export_state_type () : unit =
     let kind =
       if config.interface then ExtractBase.Declared else ExtractBase.Assumed
     in
-    Extract.extract_state_type fmt ctx.extract_ctx kind
+    Extract.extract_state_type fmt ctx kind
   in
 
   let export_decl_group (dg : A.declaration_group) : unit =
@@ -725,11 +819,18 @@ let extract_definitions (fmt : Format.formatter) (config : gen_config)
     | Type (NonRec id) ->
         if config.extract_types then export_types_group false [ id ]
     | Type (Rec ids) -> if config.extract_types then export_types_group true ids
-    | Fun (NonRec id) ->
+    | Fun (NonRec id) -> (
         (* Lookup *)
         let pure_fun = A.FunDeclId.Map.find id ctx.trans_funs in
-        (* Translate *)
-        export_functions_group [ pure_fun ]
+        (* Special case: we skip trait method *declarations* (we will
+           extract their type directly in the records we generate for
+           the trait declarations themselves, there is no point in having
+           separate type definitions) *)
+        match pure_fun.fwd.f.Pure.kind with
+        | TraitMethodDecl _ -> ()
+        | _ ->
+            (* Translate *)
+            export_functions_group [ pure_fun ])
     | Fun (Rec ids) ->
         (* General case of mutually recursive functions *)
         (* Lookup *)
@@ -739,11 +840,19 @@ let extract_definitions (fmt : Format.formatter) (config : gen_config)
         (* Translate *)
         export_functions_group pure_funs
     | Global id -> export_global id
+    | TraitDecl id ->
+        (* TODO: update to extract groups *)
+        if config.extract_trait_decls && config.extract_transparent then (
+          export_trait_decl_group id;
+          export_trait_decl_group_extra_info id)
+    | TraitImpl id ->
+        if config.extract_trait_impls && config.extract_transparent then
+          export_trait_impl id
   in
 
   (* If we need to export the state type: we try to export it after we defined
    * the type definitions, because if the user wants to define a model for the
-   * type, he might want to reuse those in the state type.
+   * type, they might want to reuse those in the state type.
    * More specifically: if we extract functions in the same file as the type,
    * we have no choice but to define the state type before the functions,
    * because they may reuse this state type: in this case, we define/declare
@@ -752,37 +861,10 @@ let extract_definitions (fmt : Format.formatter) (config : gen_config)
   if config.extract_state_type && config.extract_fun_decls then
     export_state_type ();
 
-  (* Obsolete: (TODO: remove) For Lean we parameterize the entire development by a section
-     variable called opaque_defs, of type OpaqueDefs. The code below emits the type
-     definition for OpaqueDefs, which is a structure, in which each field is one of the
-     functions marked as Opaque. We emit the `structure ...` bit here, then rely on
-     `extract_fun_decl` to be aware of this, and skip the keyword (e.g. "axiom" or "val")
-     so as to generate valid syntax for records.
-
-     We also generate such a structure only if there actually are opaque definitions. *)
-  let wrap_in_sig =
-    config.extract_opaque && config.extract_fun_decls
-    && !Config.wrap_opaque_in_sig
-    &&
-    let _, opaque_funs = module_has_opaque_decls ctx in
-    opaque_funs
-  in
-  if wrap_in_sig then (
-    (* We change the name of the structure depending on whether we *only*
-       extract opaque definitions, or if we extract all definitions *)
-    let struct_name =
-      if config.extract_transparent then "Definitions" else "OpaqueDefs"
-    in
-    Format.pp_print_break fmt 0 0;
-    Format.pp_open_vbox fmt ctx.extract_ctx.indent_incr;
-    Format.pp_print_string fmt ("structure " ^ struct_name ^ " where");
-    Format.pp_print_break fmt 0 0);
   List.iter export_decl_group ctx.crate.declarations;
 
   if config.extract_state_type && not config.extract_fun_decls then
-    export_state_type ();
-
-  if wrap_in_sig then Format.pp_close_box fmt ()
+    export_state_type ()
 
 type extract_file_info = {
   filename : string;
@@ -904,7 +986,9 @@ let extract_file (config : gen_config) (ctx : gen_ctx) (fi : extract_file_info)
 let translate_crate (filename : string) (dest_dir : string) (crate : A.crate) :
     unit =
   (* Translate the module to the pure AST *)
-  let trans_ctx, trans_types, trans_funs = translate_crate_to_pure crate in
+  let trans_ctx, trans_types, trans_funs, trans_trait_decls, trans_trait_impls =
+    translate_crate_to_pure crate
+  in
 
   (* Initialize the extraction context - for now we extract only to F*.
    * We initialize the names map by registering the keywords used in the
@@ -916,41 +1000,27 @@ let translate_crate (filename : string) (dest_dir : string) (crate : A.crate) :
   in
   (* Initialize the names map (we insert the names of the "primitives"
      declarations, and insert the names of the local declarations later) *)
-  let mk_formatter_and_names_map = Extract.mk_formatter_and_names_map in
-  let fmt, names_map =
-    mk_formatter_and_names_map trans_ctx crate.name
+  let fmt, names_maps =
+    Extract.mk_formatter_and_names_maps trans_ctx crate.name
       variant_concatenate_type_name
   in
-  (* Put everything in the context *)
-  let ctx =
-    {
-      ExtractBase.trans_ctx;
-      names_map;
-      unsafe_names_map = { id_to_name = ExtractBase.IdMap.empty };
-      fmt;
-      indent_incr = 2;
-      use_opaque_pre = !Config.split_files;
-      use_dep_ite = !Config.backend = Lean && !Config.extract_decreases_clauses;
-      fun_name_info = PureUtils.RegularFunIdMap.empty;
-    }
-  in
 
   (* We need to compute which functions are recursive, in order to know
    * whether we should generate a decrease clause or not. *)
   let rec_functions =
     List.map
-      (fun (_, ((fwd, loop_fwds), _)) ->
-        let fwd =
-          if fwd.Pure.signature.info.effect_info.is_rec then
-            [ (fwd.def_id, None) ]
+      (fun { fwd; _ } ->
+        let fwd_f =
+          if fwd.f.Pure.signature.info.effect_info.is_rec then
+            [ (fwd.f.def_id, None) ]
           else []
         in
         let loop_fwds =
           List.map
             (fun (def : Pure.fun_decl) -> [ (def.def_id, def.loop_id) ])
-            loop_fwds
+            fwd.loops
         in
-        fwd :: loop_fwds)
+        fwd_f :: loop_fwds)
       trans_funs
   in
   let rec_functions : PureUtils.fun_loop_id list =
@@ -958,22 +1028,70 @@ let translate_crate (filename : string) (dest_dir : string) (crate : A.crate) :
   in
   let rec_functions = PureUtils.FunLoopIdSet.of_list rec_functions in
 
-  (* Register unique names for all the top-level types, globals and functions.
+  (* Put the translated definitions in maps *)
+  let trans_types =
+    Pure.TypeDeclId.Map.of_list
+      (List.map (fun (d : Pure.type_decl) -> (d.def_id, d)) trans_types)
+  in
+  let trans_funs : pure_fun_translation A.FunDeclId.Map.t =
+    A.FunDeclId.Map.of_list
+      (List.map
+         (fun (trans : pure_fun_translation) -> (trans.fwd.f.def_id, trans))
+         trans_funs)
+  in
+
+  (* Put everything in the context *)
+  let ctx =
+    let trans_trait_decls =
+      T.TraitDeclId.Map.of_list
+        (List.map
+           (fun (d : Pure.trait_decl) -> (d.def_id, d))
+           trans_trait_decls)
+    in
+    let trans_trait_impls =
+      T.TraitImplId.Map.of_list
+        (List.map
+           (fun (d : Pure.trait_impl) -> (d.def_id, d))
+           trans_trait_impls)
+    in
+    {
+      ExtractBase.crate;
+      trans_ctx;
+      names_maps;
+      fmt;
+      indent_incr = 2;
+      use_dep_ite = !Config.backend = Lean && !Config.extract_decreases_clauses;
+      fun_name_info = PureUtils.RegularFunIdMap.empty;
+      trait_decl_id = None (* None by default *);
+      is_provided_method = false (* false by default *);
+      trans_trait_decls;
+      trans_trait_impls;
+      trans_types;
+      trans_funs;
+      functions_with_decreases_clause = rec_functions;
+      types_filter_type_args_map = Pure.TypeDeclId.Map.empty;
+      funs_filter_type_args_map = Pure.FunDeclId.Map.empty;
+      trait_impls_filter_type_args_map = Pure.TraitImplId.Map.empty;
+    }
+  in
+
+  (* Register unique names for all the top-level types, globals, functions...
    * Note that the order in which we generate the names doesn't matter:
    * we just need to generate a mapping from identifier to name, and make
    * sure there are no name clashes. *)
   let ctx =
     List.fold_left
       (fun ctx def -> Extract.extract_type_decl_register_names ctx def)
-      ctx trans_types
+      ctx
+      (Pure.TypeDeclId.Map.values trans_types)
   in
 
   let ctx =
     List.fold_left
-      (fun ctx (keep_fwd, defs) ->
+      (fun ctx (trans : pure_fun_translation) ->
         (* If requested by the user, register termination measures and decreases
            proofs for all the recursive functions *)
-        let fwd_def = fst (fst defs) in
+        let fwd_def = trans.fwd.f in
         let gen_decr_clause (def : Pure.fun_decl) =
           !Config.extract_decreases_clauses
           && PureUtils.FunLoopIdSet.mem
@@ -984,10 +1102,9 @@ let translate_crate (filename : string) (dest_dir : string) (crate : A.crate) :
          * those are handled later *)
         let is_global = fwd_def.Pure.is_global_decl_body in
         if is_global then ctx
-        else
-          Extract.extract_fun_decl_register_names ctx keep_fwd gen_decr_clause
-            defs)
-      ctx trans_funs
+        else Extract.extract_fun_decl_register_names ctx gen_decr_clause trans)
+      ctx
+      (A.FunDeclId.Map.values trans_funs)
   in
 
   let ctx =
@@ -995,6 +1112,16 @@ let translate_crate (filename : string) (dest_dir : string) (crate : A.crate) :
       (A.GlobalDeclId.Map.values crate.globals)
   in
 
+  let ctx =
+    List.fold_left Extract.extract_trait_decl_register_names ctx
+      trans_trait_decls
+  in
+
+  let ctx =
+    List.fold_left Extract.extract_trait_impl_register_names ctx
+      trans_trait_impls
+  in
+
   (* Open the output file *)
   (* First compute the filename by replacing the extension and converting the
    * case (rust module names are snake case) *)
@@ -1023,19 +1150,6 @@ let translate_crate (filename : string) (dest_dir : string) (crate : A.crate) :
         (namespace, crate_name, Filename.concat dest_dir crate_name)
   in
 
-  (* Put the translated definitions in maps *)
-  let trans_types =
-    Pure.TypeDeclId.Map.of_list
-      (List.map (fun (d : Pure.type_decl) -> (d.def_id, d)) trans_types)
-  in
-  let trans_funs =
-    A.FunDeclId.Map.of_list
-      (List.map
-         (fun ((keep_fwd, (fd, bdl)) : bool * pure_fun_translation) ->
-           ((fst fd).def_id, (keep_fwd, (fd, bdl))))
-         trans_funs)
-  in
-
   let mkdir_if dest_dir =
     if not (Sys.file_exists dest_dir) then (
       log#linfo (lazy ("Creating missing directory: " ^ dest_dir));
@@ -1091,16 +1205,6 @@ let translate_crate (filename : string) (dest_dir : string) (crate : A.crate) :
   in
 
   (* Extract the file(s) *)
-  let gen_ctx =
-    {
-      crate;
-      extract_ctx = ctx;
-      trans_types;
-      trans_funs;
-      functions_with_decreases_clause = rec_functions;
-    }
-  in
-
   let module_delimiter =
     match !Config.backend with
     | FStar -> "."
@@ -1136,6 +1240,8 @@ let translate_crate (filename : string) (dest_dir : string) (crate : A.crate) :
          extract_decreases_clauses = !Config.extract_decreases_clauses;
          extract_template_decreases_clauses = false;
          extract_fun_decls = false;
+         extract_trait_decls = false;
+         extract_trait_impls = false;
          extract_transparent = true;
          extract_opaque = false;
          extract_state_type = false;
@@ -1147,7 +1253,9 @@ let translate_crate (filename : string) (dest_dir : string) (crate : A.crate) :
 
      (* Check if there are opaque types and functions - in which case we need
       * to split *)
-     let has_opaque_types, has_opaque_funs = module_has_opaque_decls gen_ctx in
+     let has_opaque_types, has_opaque_funs =
+       crate_has_opaque_non_builtin_decls ctx true
+     in
      let has_opaque_types = has_opaque_types || !Config.use_state in
 
      (* Extract the types *)
@@ -1168,6 +1276,7 @@ let translate_crate (filename : string) (dest_dir : string) (crate : A.crate) :
        {
          base_gen_config with
          extract_types = true;
+         extract_trait_decls = true;
          extract_opaque = true;
          extract_state_type = !Config.use_state;
          interface = has_opaque_types;
@@ -1186,7 +1295,7 @@ let translate_crate (filename : string) (dest_dir : string) (crate : A.crate) :
          custom_includes = [];
        }
      in
-     extract_file types_config gen_ctx file_info;
+     extract_file types_config ctx file_info;
 
      (* Extract the template clauses *)
      (if needs_clauses_module && !Config.extract_template_decreases_clauses then
@@ -1214,9 +1323,9 @@ let translate_crate (filename : string) (dest_dir : string) (crate : A.crate) :
             custom_includes = [];
           }
         in
-        extract_file template_clauses_config gen_ctx file_info);
+        extract_file template_clauses_config ctx file_info);
 
-     (* Extract the opaque functions, if needed *)
+     (* Extract the opaque declarations, if needed *)
      let opaque_funs_module =
        if has_opaque_funs then (
          (* In the case of Lean we generate a template file *)
@@ -1244,17 +1353,13 @@ let translate_crate (filename : string) (dest_dir : string) (crate : A.crate) :
            {
              base_gen_config with
              extract_fun_decls = true;
+             extract_trait_impls = true;
+             extract_globals = true;
              extract_transparent = false;
              extract_opaque = true;
              interface = true;
            }
          in
-         let gen_ctx =
-           {
-             gen_ctx with
-             extract_ctx = { gen_ctx.extract_ctx with use_opaque_pre = false };
-           }
-         in
          let file_info =
            {
              filename = opaque_filename;
@@ -1268,7 +1373,7 @@ let translate_crate (filename : string) (dest_dir : string) (crate : A.crate) :
              custom_includes = [ types_module ];
            }
          in
-         extract_file opaque_config gen_ctx file_info;
+         extract_file opaque_config ctx file_info;
          (* Return the additional dependencies *)
          [ opaque_imported_module ])
        else []
@@ -1281,6 +1386,7 @@ let translate_crate (filename : string) (dest_dir : string) (crate : A.crate) :
        {
          base_gen_config with
          extract_fun_decls = true;
+         extract_trait_impls = true;
          extract_globals = true;
          test_trans_unit_functions = !Config.test_trans_unit_functions;
        }
@@ -1307,7 +1413,7 @@ let translate_crate (filename : string) (dest_dir : string) (crate : A.crate) :
            [ types_module ] @ opaque_funs_module @ clauses_module;
        }
      in
-     extract_file fun_config gen_ctx file_info)
+     extract_file fun_config ctx file_info)
    else
      let gen_config =
        {
@@ -1316,6 +1422,8 @@ let translate_crate (filename : string) (dest_dir : string) (crate : A.crate) :
          extract_template_decreases_clauses =
            !Config.extract_template_decreases_clauses;
          extract_fun_decls = true;
+         extract_trait_decls = true;
+         extract_trait_impls = true;
          extract_transparent = true;
          extract_opaque = true;
          extract_state_type = !Config.use_state;
@@ -1337,7 +1445,7 @@ let translate_crate (filename : string) (dest_dir : string) (crate : A.crate) :
          custom_includes = [];
        }
      in
-     extract_file gen_config gen_ctx file_info);
+     extract_file gen_config ctx file_info);
 
   (* Generate the build file *)
   match !Config.backend with
diff --git a/compiler/TranslateCore.ml b/compiler/TranslateCore.ml
index ba5e237b..3427fd43 100644
--- a/compiler/TranslateCore.ml
+++ b/compiler/TranslateCore.ml
@@ -10,64 +10,69 @@ module FA = FunsAnalysis
 (** The local logger *)
 let log = L.translate_log
 
-type type_context = C.type_context [@@deriving show]
-
-type fun_context = {
-  fun_decls : A.fun_decl A.FunDeclId.Map.t;
-  fun_infos : FA.fun_info A.FunDeclId.Map.t;
-}
-[@@deriving show]
+type trans_ctx = C.decls_ctx [@@deriving show]
+type fun_and_loops = { f : Pure.fun_decl; loops : Pure.fun_decl list }
+type pure_fun_translation_no_loops = Pure.fun_decl * Pure.fun_decl list
 
-type global_context = C.global_context [@@deriving show]
+type pure_fun_translation = {
+  keep_fwd : bool;
+      (** Should we extract the forward function?
 
-type trans_ctx = {
-  type_context : type_context;
-  fun_context : fun_context;
-  global_context : global_context;
+          If the forward function returns `()` and there is exactly one
+          backward function, we may merge the forward into the backward
+          function and thus don't extract the forward function)?
+       *)
+  fwd : fun_and_loops;
+  backs : fun_and_loops list;
 }
 
-type fun_and_loops = Pure.fun_decl * Pure.fun_decl list
-type pure_fun_translation_no_loops = Pure.fun_decl * Pure.fun_decl list
-type pure_fun_translation = fun_and_loops * fun_and_loops list
+let trans_ctx_to_type_formatter (ctx : trans_ctx)
+    (type_params : Pure.type_var list)
+    (const_generic_params : Pure.const_generic_var list) :
+    PrintPure.type_formatter =
+  let type_decls = ctx.type_ctx.type_decls in
+  let global_decls = ctx.global_ctx.global_decls in
+  let trait_decls = ctx.trait_decls_ctx.trait_decls in
+  let trait_impls = ctx.trait_impls_ctx.trait_impls in
+  PrintPure.mk_type_formatter type_decls global_decls trait_decls trait_impls
+    type_params const_generic_params
 
 let type_decl_to_string (ctx : trans_ctx) (def : Pure.type_decl) : string =
-  let type_params = def.type_params in
-  let cg_params = def.const_generic_params in
-  let type_decls = ctx.type_context.type_decls in
-  let global_decls = ctx.global_context.global_decls in
+  let generics = def.generics in
   let fmt =
-    PrintPure.mk_type_formatter type_decls global_decls type_params cg_params
+    trans_ctx_to_type_formatter ctx generics.types generics.const_generics
   in
   PrintPure.type_decl_to_string fmt def
 
 let type_id_to_string (ctx : trans_ctx) (id : Pure.TypeDeclId.id) : string =
   Print.fun_name_to_string
-    (Pure.TypeDeclId.Map.find id ctx.type_context.type_decls).name
+    (Pure.TypeDeclId.Map.find id ctx.type_ctx.type_decls).name
+
+let trans_ctx_to_ast_formatter (ctx : trans_ctx)
+    (type_params : Pure.type_var list)
+    (const_generic_params : Pure.const_generic_var list) :
+    PrintPure.ast_formatter =
+  let type_decls = ctx.type_ctx.type_decls in
+  let fun_decls = ctx.fun_ctx.fun_decls in
+  let global_decls = ctx.global_ctx.global_decls in
+  let trait_decls = ctx.trait_decls_ctx.trait_decls in
+  let trait_impls = ctx.trait_impls_ctx.trait_impls in
+  PrintPure.mk_ast_formatter type_decls fun_decls global_decls trait_decls
+    trait_impls type_params const_generic_params
 
 let fun_sig_to_string (ctx : trans_ctx) (sg : Pure.fun_sig) : string =
-  let type_params = sg.type_params in
-  let cg_params = sg.const_generic_params in
-  let type_decls = ctx.type_context.type_decls in
-  let fun_decls = ctx.fun_context.fun_decls in
-  let global_decls = ctx.global_context.global_decls in
+  let generics = sg.generics in
   let fmt =
-    PrintPure.mk_ast_formatter type_decls fun_decls global_decls type_params
-      cg_params
+    trans_ctx_to_ast_formatter ctx generics.types generics.const_generics
   in
   PrintPure.fun_sig_to_string fmt sg
 
 let fun_decl_to_string (ctx : trans_ctx) (def : Pure.fun_decl) : string =
-  let type_params = def.signature.type_params in
-  let cg_params = def.signature.const_generic_params in
-  let type_decls = ctx.type_context.type_decls in
-  let fun_decls = ctx.fun_context.fun_decls in
-  let global_decls = ctx.global_context.global_decls in
+  let generics = def.signature.generics in
   let fmt =
-    PrintPure.mk_ast_formatter type_decls fun_decls global_decls type_params
-      cg_params
+    trans_ctx_to_ast_formatter ctx generics.types generics.const_generics
   in
   PrintPure.fun_decl_to_string fmt def
 
 let fun_decl_id_to_string (ctx : trans_ctx) (id : A.FunDeclId.id) : string =
-  Print.fun_name_to_string
-    (A.FunDeclId.Map.find id ctx.fun_context.fun_decls).name
+  Print.fun_name_to_string (A.FunDeclId.Map.find id ctx.fun_ctx.fun_decls).name
diff --git a/compiler/TypesAnalysis.ml b/compiler/TypesAnalysis.ml
index 925f6d39..38d350b1 100644
--- a/compiler/TypesAnalysis.ml
+++ b/compiler/TypesAnalysis.ml
@@ -14,11 +14,10 @@ type expl_info = subtype_info [@@deriving show]
 
 type type_borrows_info = {
   contains_static : bool;
-      (** Does the type (transitively) contains a static borrow? *)
-  contains_borrow : bool;
-      (** Does the type (transitively) contains a borrow? *)
+      (** Does the type (transitively) contain a static borrow? *)
+  contains_borrow : bool;  (** Does the type (transitively) contain a borrow? *)
   contains_nested_borrows : bool;
-      (** Does the type (transitively) contains nested borrows? *)
+      (** Does the type (transitively) contain nested borrows? *)
   contains_borrow_under_mut : bool;
 }
 [@@deriving show]
@@ -61,7 +60,7 @@ let initialize_g_type_info (param_infos : 'p) : 'p g_type_info =
 
 let initialize_type_decl_info (def : type_decl) : type_decl_info =
   let param_info = { under_borrow = false; under_mut_borrow = false } in
-  let param_infos = List.map (fun _ -> param_info) def.type_params in
+  let param_infos = List.map (fun _ -> param_info) def.generics.types in
   initialize_g_type_info param_infos
 
 let type_decl_info_to_partial_type_info (info : type_decl_info) :
@@ -122,7 +121,7 @@ let analyze_full_ty (r_is_static : 'r -> bool) (updated : bool ref)
   let rec analyze (expl_info : expl_info) (ty_info : partial_type_info)
       (ty : 'r ty) : partial_type_info =
     match ty with
-    | Literal _ | Never -> ty_info
+    | Literal _ | Never | TraitType _ -> ty_info
     | TypeVar var_id -> (
         (* Update the information for the proper parameter, if necessary *)
         match ty_info.param_infos with
@@ -169,22 +168,21 @@ let analyze_full_ty (r_is_static : 'r -> bool) (updated : bool ref)
         in
         (* Continue exploring *)
         analyze expl_info ty_info rty
-    | Adt
-        ( (Tuple | Assumed (Box | Vec | Option | Slice | Array | Str | Range)),
-          _,
-          tys,
-          _ ) ->
+    | RawPtr (rty, _) ->
+        (* TODO: not sure what to do here *)
+        analyze expl_info ty_info rty
+    | Adt ((Tuple | Assumed (Box | Slice | Array | Str)), generics) ->
         (* Nothing to update: just explore the type parameters *)
         List.fold_left
           (fun ty_info ty -> analyze expl_info ty_info ty)
-          ty_info tys
-    | Adt (AdtId adt_id, regions, tys, _cgs) ->
+          ty_info generics.types
+    | Adt (AdtId adt_id, generics) ->
         (* Lookup the information for this type definition *)
         let adt_info = TypeDeclId.Map.find adt_id infos in
         (* Update the type info with the information from the adt *)
         let ty_info = update_ty_info ty_info adt_info.borrows_info in
         (* Check if 'static appears in the region parameters *)
-        let found_static = List.exists r_is_static regions in
+        let found_static = List.exists r_is_static generics.regions in
         let borrows_info = ty_info.borrows_info in
         let borrows_info =
           {
@@ -196,7 +194,7 @@ let analyze_full_ty (r_is_static : 'r -> bool) (updated : bool ref)
         let ty_info = { ty_info with borrows_info } in
         (* For every instantiated type parameter: update the exploration info
          * then explore the type *)
-        let params_tys = List.combine adt_info.param_infos tys in
+        let params_tys = List.combine adt_info.param_infos generics.types in
         let ty_info =
           List.fold_left
             (fun ty_info (param_info, ty) ->
@@ -235,6 +233,14 @@ let analyze_full_ty (r_is_static : 'r -> bool) (updated : bool ref)
         in
         (* Return *)
         ty_info
+    | Arrow (inputs, output) ->
+        (* Just dive into the arrow *)
+        let ty_info =
+          List.fold_left
+            (fun ty_info ty -> analyze expl_info ty_info ty)
+            ty_info inputs
+        in
+        analyze expl_info ty_info output
   in
   (* Explore *)
   analyze expl_info_init ty_info ty
diff --git a/compiler/Values.ml b/compiler/Values.ml
index d884c319..de27e7a9 100644
--- a/compiler/Values.ml
+++ b/compiler/Values.ml
@@ -52,6 +52,10 @@ type sv_kind =
       (** The result of a loop join (when computing loop fixed points) *)
   | Aggregate
       (** A symbolic value we introduce in place of an aggregate value *)
+  | ConstGeneric
+      (** A symbolic value we introduce when using a const generic as a value *)
+  | TraitConst
+      (** A symbolic value we introduce when evaluating a trait associated constant *)
 [@@deriving show, ord]
 
 (** Ancestor for {!symbolic_value} iter visitor *)
diff --git a/compiler/dune b/compiler/dune
index 6785cad4..648c7325 100644
--- a/compiler/dune
+++ b/compiler/dune
@@ -12,6 +12,7 @@
   (pps ppx_deriving.show ppx_deriving.ord visitors.ppx))
  (libraries charon core_unix unionFind ocamlgraph)
  (modules
+  AssociatedTypes
   Assumed
   Collections
   Config
@@ -22,6 +23,8 @@
   ExpressionsUtils
   Extract
   ExtractBase
+  ExtractBuiltin
+  ExtractTypes
   FunsAnalysis
   Identifiers
   InterpreterBorrowsCore
@@ -90,4 +93,4 @@
    -g
    ;-dsource
    -warn-error
-   -5-8-9-11-14-33-20-21-26-27-39)))
+   -5@8-9-11-14-33-20-21-26-27-39)))
diff --git a/flake.lock b/flake.lock
index 9258bf18..e637bc27 100644
--- a/flake.lock
+++ b/flake.lock
@@ -5,14 +5,14 @@
         "crane": "crane",
         "flake-utils": "flake-utils",
         "nixpkgs": "nixpkgs",
-        "rust-overlay": "rust-overlay_2"
+        "rust-overlay": "rust-overlay"
       },
       "locked": {
-        "lastModified": 1691568898,
-        "narHash": "sha256-BqKlmpX+tV2VYDZXhIhPbO1v9fbNy1/pzd8AooOXvxE=",
+        "lastModified": 1699619324,
+        "narHash": "sha256-QscTkSBWlmKhODEOavw29MIxOhue9oHdoDXkOmCOgnk=",
         "owner": "aeneasverif",
         "repo": "charon",
-        "rev": "5a81a41bafe18101d368e9ab4af440d7fefeee25",
+        "rev": "7de1d1e7131f20e56b37ce50adbeb7c947f72f44",
         "type": "github"
       },
       "original": {
@@ -23,23 +23,17 @@
     },
     "crane": {
       "inputs": {
-        "flake-compat": "flake-compat",
-        "flake-utils": [
-          "charon",
-          "flake-utils"
-        ],
         "nixpkgs": [
           "charon",
           "nixpkgs"
-        ],
-        "rust-overlay": "rust-overlay"
+        ]
       },
       "locked": {
-        "lastModified": 1691423162,
-        "narHash": "sha256-cReUZCo83YEEmFcHX8CcOVTZYUrcWgHQO34zxQzy7WI=",
+        "lastModified": 1699548976,
+        "narHash": "sha256-xnpxms0koM8mQpxIup9JnT0F7GrKdvv0QvtxvRuOYR4=",
         "owner": "ipetkov",
         "repo": "crane",
-        "rev": "b5d9d42ea3fa8fea1805d9af1416fe207d0dd1dc",
+        "rev": "6849911446e18e520970cc6b7a691e64ee90d649",
         "type": "github"
       },
       "original": {
@@ -48,32 +42,16 @@
         "type": "github"
       }
     },
-    "flake-compat": {
-      "flake": false,
-      "locked": {
-        "lastModified": 1673956053,
-        "narHash": "sha256-4gtG9iQuiKITOjNQQeQIpoIB6b16fm+504Ch3sNKLd8=",
-        "owner": "edolstra",
-        "repo": "flake-compat",
-        "rev": "35bb57c0c8d8b62bbfd284272c928ceb64ddbde9",
-        "type": "github"
-      },
-      "original": {
-        "owner": "edolstra",
-        "repo": "flake-compat",
-        "type": "github"
-      }
-    },
     "flake-utils": {
       "inputs": {
         "systems": "systems"
       },
       "locked": {
-        "lastModified": 1689068808,
-        "narHash": "sha256-6ixXo3wt24N/melDWjq70UuHQLxGV8jZvooRanIHXw0=",
+        "lastModified": 1694529238,
+        "narHash": "sha256-zsNZZGTGnMOf9YpHKJqMSsa0dXbfmxeoJ7xHlrt+xmY=",
         "owner": "numtide",
         "repo": "flake-utils",
-        "rev": "919d646de7be200f3bf08cb76ae1f09402b6f9b4",
+        "rev": "ff7b65b44d01cf9ba6a71320833626af21126384",
         "type": "github"
       },
       "original": {
@@ -87,11 +65,11 @@
         "systems": "systems_2"
       },
       "locked": {
-        "lastModified": 1681202837,
-        "narHash": "sha256-H+Rh19JDwRtpVPAWp64F+rlEtxUWBAQW28eAi3SRSzg=",
+        "lastModified": 1692799911,
+        "narHash": "sha256-3eihraek4qL744EvQXsK1Ha6C3CR7nnT8X2qWap4RNk=",
         "owner": "numtide",
         "repo": "flake-utils",
-        "rev": "cfacdce06f30d2b68473a46042957675eebb3401",
+        "rev": "f9e7cf818399d17d347f847525c5a5a8032e4e44",
         "type": "github"
       },
       "original": {
@@ -104,11 +82,11 @@
         "systems": "systems_3"
       },
       "locked": {
-        "lastModified": 1689068808,
-        "narHash": "sha256-6ixXo3wt24N/melDWjq70UuHQLxGV8jZvooRanIHXw0=",
+        "lastModified": 1694529238,
+        "narHash": "sha256-zsNZZGTGnMOf9YpHKJqMSsa0dXbfmxeoJ7xHlrt+xmY=",
         "owner": "numtide",
         "repo": "flake-utils",
-        "rev": "919d646de7be200f3bf08cb76ae1f09402b6f9b4",
+        "rev": "ff7b65b44d01cf9ba6a71320833626af21126384",
         "type": "github"
       },
       "original": {
@@ -153,11 +131,11 @@
         "nixpkgs": "nixpkgs_2"
       },
       "locked": {
-        "lastModified": 1690839655,
-        "narHash": "sha256-285hRt/qzVSMPf34OS187WH4q4edPtb86UJrdZAPtfY=",
+        "lastModified": 1699558636,
+        "narHash": "sha256-N4fyP0An2JBC3PRI0/zSeAapDG4gOYH2D40eHXCOemQ=",
         "owner": "fstarlang",
         "repo": "fstar",
-        "rev": "8f812f3adb7e35810edca22a02016f269c0d1d2a",
+        "rev": "9b60a5b758581edb32488a13e11039db199f89e1",
         "type": "github"
       },
       "original": {
@@ -186,11 +164,11 @@
         ]
       },
       "locked": {
-        "lastModified": 1688938536,
-        "narHash": "sha256-P+uk/ZbY9+StXs5SivB5lT5qUiPWnz5gSozJ3isezWs=",
+        "lastModified": 1699550761,
+        "narHash": "sha256-BNjPd2DuxNCZBeRwcIJH3SZ9/q7+Ny3j8gZDmOvuENs=",
         "owner": "hacl-star",
         "repo": "hacl-star",
-        "rev": "d2f087304c0b59c0486e25ff2f1daec78d92f69b",
+        "rev": "e1a785f7e88bb6668c9beabd4dc292a03c68bb2e",
         "type": "github"
       },
       "original": {
@@ -216,11 +194,11 @@
         ]
       },
       "locked": {
-        "lastModified": 1690853873,
-        "narHash": "sha256-RWmZC/Qp8+l/HsbYk982Jqp+zxqYzzsbP60NEhZktwY=",
+        "lastModified": 1699578804,
+        "narHash": "sha256-ss+mguIO6C1DBiKkw/5C5M2N3TiNirBagQ0CUZxlt1I=",
         "owner": "hacl-star",
         "repo": "hacl-nix",
-        "rev": "11df45d92e34f23a86bde4134114b023ce0cd6a9",
+        "rev": "19d0224fffa227ca6374d173f5dfeb7c2b61cf4a",
         "type": "github"
       },
       "original": {
@@ -245,11 +223,11 @@
         ]
       },
       "locked": {
-        "lastModified": 1690242065,
-        "narHash": "sha256-YCHBlXiQqO5A27f+2p/NdtKKP0GNqNEUTH2tMwtFDkQ=",
+        "lastModified": 1698968585,
+        "narHash": "sha256-x3ZaGrmuKF5+7xaWHu0yDikl4mrawkY5tQnfovgyPh8=",
         "owner": "fstarlang",
         "repo": "karamel",
-        "rev": "ed0c7e432715f95c6b9f4268eb1082eb636356a1",
+        "rev": "a7be2a7c43eca637ceb57fe8f3ffd16fc6627ebd",
         "type": "github"
       },
       "original": {
@@ -287,11 +265,11 @@
         "nixpkgs": "nixpkgs_4"
       },
       "locked": {
-        "lastModified": 1691545327,
-        "narHash": "sha256-9oAUBNRvZxK8dBuxzH5GGhET5lyolecOHmbwywgyk4s=",
+        "lastModified": 1699614992,
+        "narHash": "sha256-eSxx1UA47oBzpZGc4tIp6YP2qti1Hrc36Yo77XFnXH0=",
         "owner": "leanprover",
         "repo": "lean4",
-        "rev": "e7a1512da8d6f9339766f3a269de56e546757fde",
+        "rev": "5189578a488572b39d102b2e8825bf2a1d2c2b76",
         "type": "github"
       },
       "original": {
@@ -340,11 +318,11 @@
         "nixpkgs": "nixpkgs_7"
       },
       "locked": {
-        "lastModified": 1691545327,
-        "narHash": "sha256-9oAUBNRvZxK8dBuxzH5GGhET5lyolecOHmbwywgyk4s=",
+        "lastModified": 1699614992,
+        "narHash": "sha256-eSxx1UA47oBzpZGc4tIp6YP2qti1Hrc36Yo77XFnXH0=",
         "owner": "leanprover",
         "repo": "lean4",
-        "rev": "e7a1512da8d6f9339766f3a269de56e546757fde",
+        "rev": "5189578a488572b39d102b2e8825bf2a1d2c2b76",
         "type": "github"
       },
       "original": {
@@ -427,11 +405,11 @@
     },
     "nixpkgs": {
       "locked": {
-        "lastModified": 1691472822,
-        "narHash": "sha256-XVfYZ2oB3lNPVq6sHCY9WkdQ8lHoIDzzbpg8bB6oBxA=",
+        "lastModified": 1699099776,
+        "narHash": "sha256-X09iKJ27mGsGambGfkKzqvw5esP1L/Rf8H3u3fCqIiU=",
         "owner": "NixOS",
         "repo": "nixpkgs",
-        "rev": "41c7605718399dcfa53dd7083793b6ae3bc969ff",
+        "rev": "85f1ba3e51676fa8cc604a3d863d729026a6b8eb",
         "type": "github"
       },
       "original": {
@@ -474,11 +452,11 @@
     },
     "nixpkgs_2": {
       "locked": {
-        "lastModified": 1684385584,
-        "narHash": "sha256-O7y0gK8OLIDqz+LaHJJyeu09IGiXlZIS3+JgEzGmmJA=",
+        "lastModified": 1693158576,
+        "narHash": "sha256-aRTTXkYvhXosGx535iAFUaoFboUrZSYb1Ooih/auGp0=",
         "owner": "NixOS",
         "repo": "nixpkgs",
-        "rev": "48a0fb7aab511df92a17cf239c37f2bd2ec9ae3a",
+        "rev": "a999c1cc0c9eb2095729d5aa03e0d8f7ed256780",
         "type": "github"
       },
       "original": {
@@ -587,33 +565,6 @@
       "inputs": {
         "flake-utils": [
           "charon",
-          "crane",
-          "flake-utils"
-        ],
-        "nixpkgs": [
-          "charon",
-          "crane",
-          "nixpkgs"
-        ]
-      },
-      "locked": {
-        "lastModified": 1691029059,
-        "narHash": "sha256-QwVeE9YTgH3LmL7yw2V/hgswL6yorIvYSp4YGI8lZYM=",
-        "owner": "oxalica",
-        "repo": "rust-overlay",
-        "rev": "99df4908445be37ddb2d332580365fce512a7dcf",
-        "type": "github"
-      },
-      "original": {
-        "owner": "oxalica",
-        "repo": "rust-overlay",
-        "type": "github"
-      }
-    },
-    "rust-overlay_2": {
-      "inputs": {
-        "flake-utils": [
-          "charon",
           "flake-utils"
         ],
         "nixpkgs": [
@@ -622,11 +573,11 @@
         ]
       },
       "locked": {
-        "lastModified": 1691547503,
-        "narHash": "sha256-l0AIKJucygbDFc2vuAkxmFMjNNJImDd7jYahA88/E+o=",
+        "lastModified": 1699582387,
+        "narHash": "sha256-sPmUXPDl+cEi+zFtM5lnAs7dWOdRn0ptZ4a/qHwvNDk=",
         "owner": "oxalica",
         "repo": "rust-overlay",
-        "rev": "3380f16b39457b49c8186d5e20e7a68ccf4fc96e",
+        "rev": "41f7b0618052430d3a050e8f937030d00a2fcced",
         "type": "github"
       },
       "original": {
diff --git a/flake.nix b/flake.nix
index ebe1e90d..e2b7a796 100644
--- a/flake.nix
+++ b/flake.nix
@@ -92,11 +92,28 @@
             cp ${aeneas}/bin/aeneas_driver aeneas.exe
             export AENEAS_EXE=./aeneas.exe
 
-            # Run the tests
+            # Copy the tests
+            mkdir tests-copy
+            cp -r tests tests-copy
+
+            # TODO: remove the test files to make sure we regenerate exactly
+            # the files which are checked out (we have to be careful about
+            # files like lakefile.lean, and the user hand-written files)
+
+            # Run the tests - remark: we could remove the file
             make tests -j $NIX_BUILD_CORES
+
+            # Check that there are no differences between the generated tests
+            # and the original tests
+            if [[ $(diff -rq tests tests-copy) ]]; then
+              echo "Ok: the regenerated test files are the same as the checked out files"
+            else
+              echo "Error: the regenerated test files differ from the checked out files"
+              exit 1
+            fi
           '';
           # Tests don't generate anything new as the generated files are
-          # versionned, but the installation phase still needs to prodocue
+          # versionned, but the installation phase still needs to produce
           # something, otherwise Nix will consider the build has failed.
           installPhase = "touch $out";
         };
diff --git a/tests/coq/array/Array.v b/tests/coq/array/Array.v
new file mode 100644
index 00000000..825f73e0
--- /dev/null
+++ b/tests/coq/array/Array.v
@@ -0,0 +1,470 @@
+(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
+(** [array] *)
+Require Import Primitives.
+Import Primitives.
+Require Import Coq.ZArith.ZArith.
+Require Import List.
+Import ListNotations.
+Local Open Scope Primitives_scope.
+Module Array.
+
+(** [array::AB] *)
+Inductive AB_t := | AB_A : AB_t | AB_B : AB_t.
+
+(** [array::incr]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ()) *)
+Definition incr (x : u32) : result u32 :=
+  u32_add x 1%u32.
+
+(** [array::array_to_shared_slice_]: forward function *)
+Definition array_to_shared_slice_
+  (T : Type) (s : array T 32%usize) : result (slice T) :=
+  array_to_slice T 32%usize s
+.
+
+(** [array::array_to_mut_slice_]: forward function *)
+Definition array_to_mut_slice_
+  (T : Type) (s : array T 32%usize) : result (slice T) :=
+  array_to_slice T 32%usize s
+.
+
+(** [array::array_to_mut_slice_]: backward function 0 *)
+Definition array_to_mut_slice__back
+  (T : Type) (s : array T 32%usize) (ret : slice T) :
+  result (array T 32%usize)
+  :=
+  array_from_slice T 32%usize s ret
+.
+
+(** [array::array_len]: forward function *)
+Definition array_len (T : Type) (s : array T 32%usize) : result usize :=
+  s0 <- array_to_slice T 32%usize s; let i := slice_len T s0 in Return i
+.
+
+(** [array::shared_array_len]: forward function *)
+Definition shared_array_len (T : Type) (s : array T 32%usize) : result usize :=
+  s0 <- array_to_slice T 32%usize s; let i := slice_len T s0 in Return i
+.
+
+(** [array::shared_slice_len]: forward function *)
+Definition shared_slice_len (T : Type) (s : slice T) : result usize :=
+  let i := slice_len T s in Return i
+.
+
+(** [array::index_array_shared]: forward function *)
+Definition index_array_shared
+  (T : Type) (s : array T 32%usize) (i : usize) : result T :=
+  array_index_usize T 32%usize s i
+.
+
+(** [array::index_array_u32]: forward function *)
+Definition index_array_u32 (s : array u32 32%usize) (i : usize) : result u32 :=
+  array_index_usize u32 32%usize s i
+.
+
+(** [array::index_array_copy]: forward function *)
+Definition index_array_copy (x : array u32 32%usize) : result u32 :=
+  array_index_usize u32 32%usize x 0%usize
+.
+
+(** [array::index_mut_array]: forward function *)
+Definition index_mut_array
+  (T : Type) (s : array T 32%usize) (i : usize) : result T :=
+  array_index_usize T 32%usize s i
+.
+
+(** [array::index_mut_array]: backward function 0 *)
+Definition index_mut_array_back
+  (T : Type) (s : array T 32%usize) (i : usize) (ret : T) :
+  result (array T 32%usize)
+  :=
+  array_update_usize T 32%usize s i ret
+.
+
+(** [array::index_slice]: forward function *)
+Definition index_slice (T : Type) (s : slice T) (i : usize) : result T :=
+  slice_index_usize T s i
+.
+
+(** [array::index_mut_slice]: forward function *)
+Definition index_mut_slice (T : Type) (s : slice T) (i : usize) : result T :=
+  slice_index_usize T s i
+.
+
+(** [array::index_mut_slice]: backward function 0 *)
+Definition index_mut_slice_back
+  (T : Type) (s : slice T) (i : usize) (ret : T) : result (slice T) :=
+  slice_update_usize T s i ret
+.
+
+(** [array::slice_subslice_shared_]: forward function *)
+Definition slice_subslice_shared_
+  (x : slice u32) (y : usize) (z : usize) : result (slice u32) :=
+  core_slice_index_Slice_index u32 (core_ops_range_Range usize)
+    (core_slice_index_Range_coresliceindexSliceIndexInst u32) x
+    {| core_ops_range_Range_start := y; core_ops_range_Range_end_ := z |}
+.
+
+(** [array::slice_subslice_mut_]: forward function *)
+Definition slice_subslice_mut_
+  (x : slice u32) (y : usize) (z : usize) : result (slice u32) :=
+  core_slice_index_Slice_index_mut u32 (core_ops_range_Range usize)
+    (core_slice_index_Range_coresliceindexSliceIndexInst u32) x
+    {| core_ops_range_Range_start := y; core_ops_range_Range_end_ := z |}
+.
+
+(** [array::slice_subslice_mut_]: backward function 0 *)
+Definition slice_subslice_mut__back
+  (x : slice u32) (y : usize) (z : usize) (ret : slice u32) :
+  result (slice u32)
+  :=
+  core_slice_index_Slice_index_mut_back u32 (core_ops_range_Range usize)
+    (core_slice_index_Range_coresliceindexSliceIndexInst u32) x
+    {| core_ops_range_Range_start := y; core_ops_range_Range_end_ := z |} ret
+.
+
+(** [array::array_to_slice_shared_]: forward function *)
+Definition array_to_slice_shared_
+  (x : array u32 32%usize) : result (slice u32) :=
+  array_to_slice u32 32%usize x
+.
+
+(** [array::array_to_slice_mut_]: forward function *)
+Definition array_to_slice_mut_ (x : array u32 32%usize) : result (slice u32) :=
+  array_to_slice u32 32%usize x
+.
+
+(** [array::array_to_slice_mut_]: backward function 0 *)
+Definition array_to_slice_mut__back
+  (x : array u32 32%usize) (ret : slice u32) : result (array u32 32%usize) :=
+  array_from_slice u32 32%usize x ret
+.
+
+(** [array::array_subslice_shared_]: forward function *)
+Definition array_subslice_shared_
+  (x : array u32 32%usize) (y : usize) (z : usize) : result (slice u32) :=
+  core_array_Array_index u32 (core_ops_range_Range usize) 32%usize
+    (core_slice_index_Slice_coreopsindexIndexInst u32 (core_ops_range_Range
+    usize) (core_slice_index_Range_coresliceindexSliceIndexInst u32)) x
+    {| core_ops_range_Range_start := y; core_ops_range_Range_end_ := z |}
+.
+
+(** [array::array_subslice_mut_]: forward function *)
+Definition array_subslice_mut_
+  (x : array u32 32%usize) (y : usize) (z : usize) : result (slice u32) :=
+  core_array_Array_index_mut u32 (core_ops_range_Range usize) 32%usize
+    (core_slice_index_Slice_coreopsindexIndexMutInst u32 (core_ops_range_Range
+    usize) (core_slice_index_Range_coresliceindexSliceIndexInst u32)) x
+    {| core_ops_range_Range_start := y; core_ops_range_Range_end_ := z |}
+.
+
+(** [array::array_subslice_mut_]: backward function 0 *)
+Definition array_subslice_mut__back
+  (x : array u32 32%usize) (y : usize) (z : usize) (ret : slice u32) :
+  result (array u32 32%usize)
+  :=
+  core_array_Array_index_mut_back u32 (core_ops_range_Range usize) 32%usize
+    (core_slice_index_Slice_coreopsindexIndexMutInst u32 (core_ops_range_Range
+    usize) (core_slice_index_Range_coresliceindexSliceIndexInst u32)) x
+    {| core_ops_range_Range_start := y; core_ops_range_Range_end_ := z |} ret
+.
+
+(** [array::index_slice_0]: forward function *)
+Definition index_slice_0 (T : Type) (s : slice T) : result T :=
+  slice_index_usize T s 0%usize
+.
+
+(** [array::index_array_0]: forward function *)
+Definition index_array_0 (T : Type) (s : array T 32%usize) : result T :=
+  array_index_usize T 32%usize s 0%usize
+.
+
+(** [array::index_index_array]: forward function *)
+Definition index_index_array
+  (s : array (array u32 32%usize) 32%usize) (i : usize) (j : usize) :
+  result u32
+  :=
+  a <- array_index_usize (array u32 32%usize) 32%usize s i;
+  array_index_usize u32 32%usize a j
+.
+
+(** [array::update_update_array]: forward function *)
+Definition update_update_array
+  (s : array (array u32 32%usize) 32%usize) (i : usize) (j : usize) :
+  result unit
+  :=
+  a <- array_index_usize (array u32 32%usize) 32%usize s i;
+  a0 <- array_update_usize u32 32%usize a j 0%u32;
+  _ <- array_update_usize (array u32 32%usize) 32%usize s i a0;
+  Return tt
+.
+
+(** [array::array_local_deep_copy]: forward function *)
+Definition array_local_deep_copy (x : array u32 32%usize) : result unit :=
+  Return tt
+.
+
+(** [array::take_array]: forward function *)
+Definition take_array (a : array u32 2%usize) : result unit :=
+  Return tt.
+
+(** [array::take_array_borrow]: forward function *)
+Definition take_array_borrow (a : array u32 2%usize) : result unit :=
+  Return tt
+.
+
+(** [array::take_slice]: forward function *)
+Definition take_slice (s : slice u32) : result unit :=
+  Return tt.
+
+(** [array::take_mut_slice]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ()) *)
+Definition take_mut_slice (s : slice u32) : result (slice u32) :=
+  Return s.
+
+(** [array::take_all]: forward function *)
+Definition take_all : result unit :=
+  _ <- take_array (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
+  _ <- take_array_borrow (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
+  s <- array_to_slice u32 2%usize (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
+  _ <- take_slice s;
+  s0 <- array_to_slice u32 2%usize (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
+  s1 <- take_mut_slice s0;
+  _ <- array_from_slice u32 2%usize (mk_array u32 2%usize [ 0%u32; 0%u32 ]) s1;
+  Return tt
+.
+
+(** [array::index_array]: forward function *)
+Definition index_array (x : array u32 2%usize) : result u32 :=
+  array_index_usize u32 2%usize x 0%usize
+.
+
+(** [array::index_array_borrow]: forward function *)
+Definition index_array_borrow (x : array u32 2%usize) : result u32 :=
+  array_index_usize u32 2%usize x 0%usize
+.
+
+(** [array::index_slice_u32_0]: forward function *)
+Definition index_slice_u32_0 (x : slice u32) : result u32 :=
+  slice_index_usize u32 x 0%usize
+.
+
+(** [array::index_mut_slice_u32_0]: forward function *)
+Definition index_mut_slice_u32_0 (x : slice u32) : result u32 :=
+  slice_index_usize u32 x 0%usize
+.
+
+(** [array::index_mut_slice_u32_0]: backward function 0 *)
+Definition index_mut_slice_u32_0_back (x : slice u32) : result (slice u32) :=
+  _ <- slice_index_usize u32 x 0%usize; Return x
+.
+
+(** [array::index_all]: forward function *)
+Definition index_all : result u32 :=
+  i <- index_array (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
+  i0 <- index_array (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
+  i1 <- u32_add i i0;
+  i2 <- index_array_borrow (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
+  i3 <- u32_add i1 i2;
+  s <- array_to_slice u32 2%usize (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
+  i4 <- index_slice_u32_0 s;
+  i5 <- u32_add i3 i4;
+  s0 <- array_to_slice u32 2%usize (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
+  i6 <- index_mut_slice_u32_0 s0;
+  i7 <- u32_add i5 i6;
+  s1 <- index_mut_slice_u32_0_back s0;
+  _ <- array_from_slice u32 2%usize (mk_array u32 2%usize [ 0%u32; 0%u32 ]) s1;
+  Return i7
+.
+
+(** [array::update_array]: forward function *)
+Definition update_array (x : array u32 2%usize) : result unit :=
+  _ <- array_update_usize u32 2%usize x 0%usize 1%u32; Return tt
+.
+
+(** [array::update_array_mut_borrow]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ()) *)
+Definition update_array_mut_borrow
+  (x : array u32 2%usize) : result (array u32 2%usize) :=
+  array_update_usize u32 2%usize x 0%usize 1%u32
+.
+
+(** [array::update_mut_slice]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ()) *)
+Definition update_mut_slice (x : slice u32) : result (slice u32) :=
+  slice_update_usize u32 x 0%usize 1%u32
+.
+
+(** [array::update_all]: forward function *)
+Definition update_all : result unit :=
+  _ <- update_array (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
+  x <- update_array_mut_borrow (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
+  s <- array_to_slice u32 2%usize x;
+  s0 <- update_mut_slice s;
+  _ <- array_from_slice u32 2%usize x s0;
+  Return tt
+.
+
+(** [array::range_all]: forward function *)
+Definition range_all : result unit :=
+  s <-
+    core_array_Array_index_mut u32 (core_ops_range_Range usize) 4%usize
+      (core_slice_index_Slice_coreopsindexIndexMutInst u32
+      (core_ops_range_Range usize)
+      (core_slice_index_Range_coresliceindexSliceIndexInst u32))
+      (mk_array u32 4%usize [ 0%u32; 0%u32; 0%u32; 0%u32 ])
+      {|
+        core_ops_range_Range_start := 1%usize;
+        core_ops_range_Range_end_ := 3%usize
+      |};
+  s0 <- update_mut_slice s;
+  _ <-
+    core_array_Array_index_mut_back u32 (core_ops_range_Range usize) 4%usize
+      (core_slice_index_Slice_coreopsindexIndexMutInst u32
+      (core_ops_range_Range usize)
+      (core_slice_index_Range_coresliceindexSliceIndexInst u32))
+      (mk_array u32 4%usize [ 0%u32; 0%u32; 0%u32; 0%u32 ])
+      {|
+        core_ops_range_Range_start := 1%usize;
+        core_ops_range_Range_end_ := 3%usize
+      |} s0;
+  Return tt
+.
+
+(** [array::deref_array_borrow]: forward function *)
+Definition deref_array_borrow (x : array u32 2%usize) : result u32 :=
+  array_index_usize u32 2%usize x 0%usize
+.
+
+(** [array::deref_array_mut_borrow]: forward function *)
+Definition deref_array_mut_borrow (x : array u32 2%usize) : result u32 :=
+  array_index_usize u32 2%usize x 0%usize
+.
+
+(** [array::deref_array_mut_borrow]: backward function 0 *)
+Definition deref_array_mut_borrow_back
+  (x : array u32 2%usize) : result (array u32 2%usize) :=
+  _ <- array_index_usize u32 2%usize x 0%usize; Return x
+.
+
+(** [array::take_array_t]: forward function *)
+Definition take_array_t (a : array AB_t 2%usize) : result unit :=
+  Return tt.
+
+(** [array::non_copyable_array]: forward function *)
+Definition non_copyable_array : result unit :=
+  _ <- take_array_t (mk_array AB_t 2%usize [ AB_A; AB_B ]); Return tt
+.
+
+(** [array::sum]: loop 0: forward function *)
+Fixpoint sum_loop
+  (n : nat) (s : slice u32) (sum0 : u32) (i : usize) : result u32 :=
+  match n with
+  | O => Fail_ OutOfFuel
+  | S n0 =>
+    let i0 := slice_len u32 s in
+    if i s< i0
+    then (
+      i1 <- slice_index_usize u32 s i;
+      sum1 <- u32_add sum0 i1;
+      i2 <- usize_add i 1%usize;
+      sum_loop n0 s sum1 i2)
+    else Return sum0
+  end
+.
+
+(** [array::sum]: forward function *)
+Definition sum (n : nat) (s : slice u32) : result u32 :=
+  sum_loop n s 0%u32 0%usize
+.
+
+(** [array::sum2]: loop 0: forward function *)
+Fixpoint sum2_loop
+  (n : nat) (s : slice u32) (s2 : slice u32) (sum0 : u32) (i : usize) :
+  result u32
+  :=
+  match n with
+  | O => Fail_ OutOfFuel
+  | S n0 =>
+    let i0 := slice_len u32 s in
+    if i s< i0
+    then (
+      i1 <- slice_index_usize u32 s i;
+      i2 <- slice_index_usize u32 s2 i;
+      i3 <- u32_add i1 i2;
+      sum1 <- u32_add sum0 i3;
+      i4 <- usize_add i 1%usize;
+      sum2_loop n0 s s2 sum1 i4)
+    else Return sum0
+  end
+.
+
+(** [array::sum2]: forward function *)
+Definition sum2 (n : nat) (s : slice u32) (s2 : slice u32) : result u32 :=
+  let i := slice_len u32 s in
+  let i0 := slice_len u32 s2 in
+  if negb (i s= i0) then Fail_ Failure else sum2_loop n s s2 0%u32 0%usize
+.
+
+(** [array::f0]: forward function *)
+Definition f0 : result unit :=
+  s <- array_to_slice u32 2%usize (mk_array u32 2%usize [ 1%u32; 2%u32 ]);
+  s0 <- slice_update_usize u32 s 0%usize 1%u32;
+  _ <- array_from_slice u32 2%usize (mk_array u32 2%usize [ 1%u32; 2%u32 ]) s0;
+  Return tt
+.
+
+(** [array::f1]: forward function *)
+Definition f1 : result unit :=
+  _ <-
+    array_update_usize u32 2%usize (mk_array u32 2%usize [ 1%u32; 2%u32 ])
+      0%usize 1%u32;
+  Return tt
+.
+
+(** [array::f2]: forward function *)
+Definition f2 (i : u32) : result unit :=
+  Return tt.
+
+(** [array::f4]: forward function *)
+Definition f4
+  (x : array u32 32%usize) (y : usize) (z : usize) : result (slice u32) :=
+  core_array_Array_index u32 (core_ops_range_Range usize) 32%usize
+    (core_slice_index_Slice_coreopsindexIndexInst u32 (core_ops_range_Range
+    usize) (core_slice_index_Range_coresliceindexSliceIndexInst u32)) x
+    {| core_ops_range_Range_start := y; core_ops_range_Range_end_ := z |}
+.
+
+(** [array::f3]: forward function *)
+Definition f3 (n : nat) : result u32 :=
+  i <-
+    array_index_usize u32 2%usize (mk_array u32 2%usize [ 1%u32; 2%u32 ])
+      0%usize;
+  _ <- f2 i;
+  let b := array_repeat u32 32%usize 0%u32 in
+  s <- array_to_slice u32 2%usize (mk_array u32 2%usize [ 1%u32; 2%u32 ]);
+  s0 <- f4 b 16%usize 18%usize;
+  sum2 n s s0
+.
+
+(** [array::SZ] *)
+Definition sz_body : result usize := Return 32%usize.
+Definition sz_c : usize := sz_body%global.
+
+(** [array::f5]: forward function *)
+Definition f5 (x : array u32 32%usize) : result u32 :=
+  array_index_usize u32 32%usize x 0%usize
+.
+
+(** [array::ite]: forward function *)
+Definition ite : result unit :=
+  s <- array_to_slice u32 2%usize (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
+  s0 <- array_to_slice u32 2%usize (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
+  s1 <- index_mut_slice_u32_0_back s0;
+  _ <- array_from_slice u32 2%usize (mk_array u32 2%usize [ 0%u32; 0%u32 ]) s1;
+  s2 <- index_mut_slice_u32_0_back s;
+  _ <- array_from_slice u32 2%usize (mk_array u32 2%usize [ 0%u32; 0%u32 ]) s2;
+  Return tt
+.
+
+End Array .
diff --git a/tests/coq/array/Array_Funs.v b/tests/coq/array/Array_Funs.v
deleted file mode 100644
index 6d791873..00000000
--- a/tests/coq/array/Array_Funs.v
+++ /dev/null
@@ -1,467 +0,0 @@
-(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
-(** [array]: function definitions *)
-Require Import Primitives.
-Import Primitives.
-Require Import Coq.ZArith.ZArith.
-Require Import List.
-Import ListNotations.
-Local Open Scope Primitives_scope.
-Require Export Array_Types.
-Import Array_Types.
-Module Array_Funs.
-
-(** [array::array_to_shared_slice_]: forward function *)
-Definition array_to_shared_slice__fwd
-  (T : Type) (s : array T 32%usize) : result (slice T) :=
-  array_to_slice_shared T 32%usize s
-.
-
-(** [array::array_to_mut_slice_]: forward function *)
-Definition array_to_mut_slice__fwd
-  (T : Type) (s : array T 32%usize) : result (slice T) :=
-  array_to_slice_mut_fwd T 32%usize s
-.
-
-(** [array::array_to_mut_slice_]: backward function 0 *)
-Definition array_to_mut_slice__back
-  (T : Type) (s : array T 32%usize) (ret : slice T) :
-  result (array T 32%usize)
-  :=
-  array_to_slice_mut_back T 32%usize s ret
-.
-
-(** [array::array_len]: forward function *)
-Definition array_len_fwd (T : Type) (s : array T 32%usize) : result usize :=
-  s0 <- array_to_slice_shared T 32%usize s; let i := slice_len T s0 in Return i
-.
-
-(** [array::shared_array_len]: forward function *)
-Definition shared_array_len_fwd
-  (T : Type) (s : array T 32%usize) : result usize :=
-  s0 <- array_to_slice_shared T 32%usize s; let i := slice_len T s0 in Return i
-.
-
-(** [array::shared_slice_len]: forward function *)
-Definition shared_slice_len_fwd (T : Type) (s : slice T) : result usize :=
-  let i := slice_len T s in Return i
-.
-
-(** [array::index_array_shared]: forward function *)
-Definition index_array_shared_fwd
-  (T : Type) (s : array T 32%usize) (i : usize) : result T :=
-  array_index_shared T 32%usize s i
-.
-
-(** [array::index_array_u32]: forward function *)
-Definition index_array_u32_fwd
-  (s : array u32 32%usize) (i : usize) : result u32 :=
-  array_index_shared u32 32%usize s i
-.
-
-(** [array::index_array_generic]: forward function *)
-Definition index_array_generic_fwd
-  (N : usize) (s : array u32 N) (i : usize) : result u32 :=
-  array_index_shared u32 N s i
-.
-
-(** [array::index_array_generic_call]: forward function *)
-Definition index_array_generic_call_fwd
-  (N : usize) (s : array u32 N) (i : usize) : result u32 :=
-  index_array_generic_fwd N s i
-.
-
-(** [array::index_array_copy]: forward function *)
-Definition index_array_copy_fwd (x : array u32 32%usize) : result u32 :=
-  array_index_shared u32 32%usize x 0%usize
-.
-
-(** [array::index_mut_array]: forward function *)
-Definition index_mut_array_fwd
-  (T : Type) (s : array T 32%usize) (i : usize) : result T :=
-  array_index_mut_fwd T 32%usize s i
-.
-
-(** [array::index_mut_array]: backward function 0 *)
-Definition index_mut_array_back
-  (T : Type) (s : array T 32%usize) (i : usize) (ret : T) :
-  result (array T 32%usize)
-  :=
-  array_index_mut_back T 32%usize s i ret
-.
-
-(** [array::index_slice]: forward function *)
-Definition index_slice_fwd (T : Type) (s : slice T) (i : usize) : result T :=
-  slice_index_shared T s i
-.
-
-(** [array::index_mut_slice]: forward function *)
-Definition index_mut_slice_fwd
-  (T : Type) (s : slice T) (i : usize) : result T :=
-  slice_index_mut_fwd T s i
-.
-
-(** [array::index_mut_slice]: backward function 0 *)
-Definition index_mut_slice_back
-  (T : Type) (s : slice T) (i : usize) (ret : T) : result (slice T) :=
-  slice_index_mut_back T s i ret
-.
-
-(** [array::slice_subslice_shared_]: forward function *)
-Definition slice_subslice_shared__fwd
-  (x : slice u32) (y : usize) (z : usize) : result (slice u32) :=
-  slice_subslice_shared u32 x (mk_range y z)
-.
-
-(** [array::slice_subslice_mut_]: forward function *)
-Definition slice_subslice_mut__fwd
-  (x : slice u32) (y : usize) (z : usize) : result (slice u32) :=
-  slice_subslice_mut_fwd u32 x (mk_range y z)
-.
-
-(** [array::slice_subslice_mut_]: backward function 0 *)
-Definition slice_subslice_mut__back
-  (x : slice u32) (y : usize) (z : usize) (ret : slice u32) :
-  result (slice u32)
-  :=
-  slice_subslice_mut_back u32 x (mk_range y z) ret
-.
-
-(** [array::array_to_slice_shared_]: forward function *)
-Definition array_to_slice_shared__fwd
-  (x : array u32 32%usize) : result (slice u32) :=
-  array_to_slice_shared u32 32%usize x
-.
-
-(** [array::array_to_slice_mut_]: forward function *)
-Definition array_to_slice_mut__fwd
-  (x : array u32 32%usize) : result (slice u32) :=
-  array_to_slice_mut_fwd u32 32%usize x
-.
-
-(** [array::array_to_slice_mut_]: backward function 0 *)
-Definition array_to_slice_mut__back
-  (x : array u32 32%usize) (ret : slice u32) : result (array u32 32%usize) :=
-  array_to_slice_mut_back u32 32%usize x ret
-.
-
-(** [array::array_subslice_shared_]: forward function *)
-Definition array_subslice_shared__fwd
-  (x : array u32 32%usize) (y : usize) (z : usize) : result (slice u32) :=
-  array_subslice_shared u32 32%usize x (mk_range y z)
-.
-
-(** [array::array_subslice_mut_]: forward function *)
-Definition array_subslice_mut__fwd
-  (x : array u32 32%usize) (y : usize) (z : usize) : result (slice u32) :=
-  array_subslice_mut_fwd u32 32%usize x (mk_range y z)
-.
-
-(** [array::array_subslice_mut_]: backward function 0 *)
-Definition array_subslice_mut__back
-  (x : array u32 32%usize) (y : usize) (z : usize) (ret : slice u32) :
-  result (array u32 32%usize)
-  :=
-  array_subslice_mut_back u32 32%usize x (mk_range y z) ret
-.
-
-(** [array::index_slice_0]: forward function *)
-Definition index_slice_0_fwd (T : Type) (s : slice T) : result T :=
-  slice_index_shared T s 0%usize
-.
-
-(** [array::index_array_0]: forward function *)
-Definition index_array_0_fwd (T : Type) (s : array T 32%usize) : result T :=
-  array_index_shared T 32%usize s 0%usize
-.
-
-(** [array::index_index_array]: forward function *)
-Definition index_index_array_fwd
-  (s : array (array u32 32%usize) 32%usize) (i : usize) (j : usize) :
-  result u32
-  :=
-  a <- array_index_shared (array u32 32%usize) 32%usize s i;
-  array_index_shared u32 32%usize a j
-.
-
-(** [array::update_update_array]: forward function *)
-Definition update_update_array_fwd
-  (s : array (array u32 32%usize) 32%usize) (i : usize) (j : usize) :
-  result unit
-  :=
-  a <- array_index_mut_fwd (array u32 32%usize) 32%usize s i;
-  a0 <- array_index_mut_back u32 32%usize a j 0%u32;
-  _ <- array_index_mut_back (array u32 32%usize) 32%usize s i a0;
-  Return tt
-.
-
-(** [array::array_local_deep_copy]: forward function *)
-Definition array_local_deep_copy_fwd (x : array u32 32%usize) : result unit :=
-  Return tt
-.
-
-(** [array::take_array]: forward function *)
-Definition take_array_fwd (a : array u32 2%usize) : result unit :=
-  Return tt.
-
-(** [array::take_array_borrow]: forward function *)
-Definition take_array_borrow_fwd (a : array u32 2%usize) : result unit :=
-  Return tt
-.
-
-(** [array::take_slice]: forward function *)
-Definition take_slice_fwd (s : slice u32) : result unit :=
-  Return tt.
-
-(** [array::take_mut_slice]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ()) *)
-Definition take_mut_slice_fwd_back (s : slice u32) : result (slice u32) :=
-  Return s
-.
-
-(** [array::take_all]: forward function *)
-Definition take_all_fwd : result unit :=
-  _ <- take_array_fwd (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
-  _ <- take_array_borrow_fwd (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
-  s <-
-    array_to_slice_shared u32 2%usize (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
-  _ <- take_slice_fwd s;
-  s0 <-
-    array_to_slice_mut_fwd u32 2%usize (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
-  s1 <- take_mut_slice_fwd_back s0;
-  _ <-
-    array_to_slice_mut_back u32 2%usize (mk_array u32 2%usize [ 0%u32; 0%u32 ])
-      s1;
-  Return tt
-.
-
-(** [array::index_array]: forward function *)
-Definition index_array_fwd (x : array u32 2%usize) : result u32 :=
-  array_index_shared u32 2%usize x 0%usize
-.
-
-(** [array::index_array_borrow]: forward function *)
-Definition index_array_borrow_fwd (x : array u32 2%usize) : result u32 :=
-  array_index_shared u32 2%usize x 0%usize
-.
-
-(** [array::index_slice_u32_0]: forward function *)
-Definition index_slice_u32_0_fwd (x : slice u32) : result u32 :=
-  slice_index_shared u32 x 0%usize
-.
-
-(** [array::index_mut_slice_u32_0]: forward function *)
-Definition index_mut_slice_u32_0_fwd (x : slice u32) : result u32 :=
-  slice_index_shared u32 x 0%usize
-.
-
-(** [array::index_mut_slice_u32_0]: backward function 0 *)
-Definition index_mut_slice_u32_0_back (x : slice u32) : result (slice u32) :=
-  _ <- slice_index_shared u32 x 0%usize; Return x
-.
-
-(** [array::index_all]: forward function *)
-Definition index_all_fwd : result u32 :=
-  i <- index_array_fwd (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
-  i0 <- index_array_fwd (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
-  i1 <- u32_add i i0;
-  i2 <- index_array_borrow_fwd (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
-  i3 <- u32_add i1 i2;
-  s <-
-    array_to_slice_shared u32 2%usize (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
-  i4 <- index_slice_u32_0_fwd s;
-  i5 <- u32_add i3 i4;
-  s0 <-
-    array_to_slice_mut_fwd u32 2%usize (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
-  i6 <- index_mut_slice_u32_0_fwd s0;
-  i7 <- u32_add i5 i6;
-  s1 <- index_mut_slice_u32_0_back s0;
-  _ <-
-    array_to_slice_mut_back u32 2%usize (mk_array u32 2%usize [ 0%u32; 0%u32 ])
-      s1;
-  Return i7
-.
-
-(** [array::update_array]: forward function *)
-Definition update_array_fwd (x : array u32 2%usize) : result unit :=
-  _ <- array_index_mut_back u32 2%usize x 0%usize 1%u32; Return tt
-.
-
-(** [array::update_array_mut_borrow]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ()) *)
-Definition update_array_mut_borrow_fwd_back
-  (x : array u32 2%usize) : result (array u32 2%usize) :=
-  array_index_mut_back u32 2%usize x 0%usize 1%u32
-.
-
-(** [array::update_mut_slice]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ()) *)
-Definition update_mut_slice_fwd_back (x : slice u32) : result (slice u32) :=
-  slice_index_mut_back u32 x 0%usize 1%u32
-.
-
-(** [array::update_all]: forward function *)
-Definition update_all_fwd : result unit :=
-  _ <- update_array_fwd (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
-  x <-
-    update_array_mut_borrow_fwd_back (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
-  s <- array_to_slice_mut_fwd u32 2%usize x;
-  s0 <- update_mut_slice_fwd_back s;
-  _ <- array_to_slice_mut_back u32 2%usize x s0;
-  Return tt
-.
-
-(** [array::range_all]: forward function *)
-Definition range_all_fwd : result unit :=
-  s <-
-    array_subslice_mut_fwd u32 4%usize
-      (mk_array u32 4%usize [ 0%u32; 0%u32; 0%u32; 0%u32 ]) (mk_range 1%usize
-      3%usize);
-  s0 <- update_mut_slice_fwd_back s;
-  _ <-
-    array_subslice_mut_back u32 4%usize
-      (mk_array u32 4%usize [ 0%u32; 0%u32; 0%u32; 0%u32 ]) (mk_range 1%usize
-      3%usize) s0;
-  Return tt
-.
-
-(** [array::deref_array_borrow]: forward function *)
-Definition deref_array_borrow_fwd (x : array u32 2%usize) : result u32 :=
-  array_index_shared u32 2%usize x 0%usize
-.
-
-(** [array::deref_array_mut_borrow]: forward function *)
-Definition deref_array_mut_borrow_fwd (x : array u32 2%usize) : result u32 :=
-  array_index_shared u32 2%usize x 0%usize
-.
-
-(** [array::deref_array_mut_borrow]: backward function 0 *)
-Definition deref_array_mut_borrow_back
-  (x : array u32 2%usize) : result (array u32 2%usize) :=
-  _ <- array_index_shared u32 2%usize x 0%usize; Return x
-.
-
-(** [array::take_array_t]: forward function *)
-Definition take_array_t_fwd (a : array T_t 2%usize) : result unit :=
-  Return tt.
-
-(** [array::non_copyable_array]: forward function *)
-Definition non_copyable_array_fwd : result unit :=
-  _ <- take_array_t_fwd (mk_array T_t 2%usize [ TA; TB ]); Return tt
-.
-
-(** [array::sum]: loop 0: forward function *)
-Fixpoint sum_loop_fwd
-  (n : nat) (s : slice u32) (sum : u32) (i : usize) : result u32 :=
-  match n with
-  | O => Fail_ OutOfFuel
-  | S n0 =>
-    let i0 := slice_len u32 s in
-    if i s< i0
-    then (
-      i1 <- slice_index_shared u32 s i;
-      sum0 <- u32_add sum i1;
-      i2 <- usize_add i 1%usize;
-      sum_loop_fwd n0 s sum0 i2)
-    else Return sum
-  end
-.
-
-(** [array::sum]: forward function *)
-Definition sum_fwd (n : nat) (s : slice u32) : result u32 :=
-  sum_loop_fwd n s 0%u32 0%usize
-.
-
-(** [array::sum2]: loop 0: forward function *)
-Fixpoint sum2_loop_fwd
-  (n : nat) (s : slice u32) (s2 : slice u32) (sum : u32) (i : usize) :
-  result u32
-  :=
-  match n with
-  | O => Fail_ OutOfFuel
-  | S n0 =>
-    let i0 := slice_len u32 s in
-    if i s< i0
-    then (
-      i1 <- slice_index_shared u32 s i;
-      i2 <- slice_index_shared u32 s2 i;
-      i3 <- u32_add i1 i2;
-      sum0 <- u32_add sum i3;
-      i4 <- usize_add i 1%usize;
-      sum2_loop_fwd n0 s s2 sum0 i4)
-    else Return sum
-  end
-.
-
-(** [array::sum2]: forward function *)
-Definition sum2_fwd (n : nat) (s : slice u32) (s2 : slice u32) : result u32 :=
-  let i := slice_len u32 s in
-  let i0 := slice_len u32 s2 in
-  if negb (i s= i0) then Fail_ Failure else sum2_loop_fwd n s s2 0%u32 0%usize
-.
-
-(** [array::f0]: forward function *)
-Definition f0_fwd : result unit :=
-  s <-
-    array_to_slice_mut_fwd u32 2%usize (mk_array u32 2%usize [ 1%u32; 2%u32 ]);
-  s0 <- slice_index_mut_back u32 s 0%usize 1%u32;
-  _ <-
-    array_to_slice_mut_back u32 2%usize (mk_array u32 2%usize [ 1%u32; 2%u32 ])
-      s0;
-  Return tt
-.
-
-(** [array::f1]: forward function *)
-Definition f1_fwd : result unit :=
-  _ <-
-    array_index_mut_back u32 2%usize (mk_array u32 2%usize [ 1%u32; 2%u32 ])
-      0%usize 1%u32;
-  Return tt
-.
-
-(** [array::f2]: forward function *)
-Definition f2_fwd (i : u32) : result unit :=
-  Return tt.
-
-(** [array::f4]: forward function *)
-Definition f4_fwd
-  (x : array u32 32%usize) (y : usize) (z : usize) : result (slice u32) :=
-  array_subslice_shared u32 32%usize x (mk_range y z)
-.
-
-(** [array::f3]: forward function *)
-Definition f3_fwd (n : nat) : result u32 :=
-  i <-
-    array_index_shared u32 2%usize (mk_array u32 2%usize [ 1%u32; 2%u32 ])
-      0%usize;
-  _ <- f2_fwd i;
-  s <-
-    array_to_slice_shared u32 2%usize (mk_array u32 2%usize [ 1%u32; 2%u32 ]);
-  s0 <-
-    f4_fwd
-      (mk_array u32 32%usize [
-        0%u32; 0%u32; 0%u32; 0%u32; 0%u32; 0%u32; 0%u32; 0%u32; 0%u32; 0%u32;
-        0%u32; 0%u32; 0%u32; 0%u32; 0%u32; 0%u32; 0%u32; 0%u32; 0%u32; 0%u32;
-        0%u32; 0%u32; 0%u32; 0%u32; 0%u32; 0%u32; 0%u32; 0%u32; 0%u32; 0%u32;
-        0%u32; 0%u32
-        ]) 16%usize 18%usize;
-  sum2_fwd n s s0
-.
-
-(** [array::ite]: forward function *)
-Definition ite_fwd : result unit :=
-  s <-
-    array_to_slice_mut_fwd u32 2%usize (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
-  s0 <-
-    array_to_slice_mut_fwd u32 2%usize (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
-  s1 <- index_mut_slice_u32_0_back s0;
-  _ <-
-    array_to_slice_mut_back u32 2%usize (mk_array u32 2%usize [ 0%u32; 0%u32 ])
-      s1;
-  s2 <- index_mut_slice_u32_0_back s;
-  _ <-
-    array_to_slice_mut_back u32 2%usize (mk_array u32 2%usize [ 0%u32; 0%u32 ])
-      s2;
-  Return tt
-.
-
-End Array_Funs .
diff --git a/tests/coq/array/Array_Types.v b/tests/coq/array/Array_Types.v
deleted file mode 100644
index 7be6dc9b..00000000
--- a/tests/coq/array/Array_Types.v
+++ /dev/null
@@ -1,14 +0,0 @@
-(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
-(** [array]: type definitions *)
-Require Import Primitives.
-Import Primitives.
-Require Import Coq.ZArith.ZArith.
-Require Import List.
-Import ListNotations.
-Local Open Scope Primitives_scope.
-Module Array_Types.
-
-(** [array::T] *)
-Inductive T_t := | TA : T_t | TB : T_t.
-
-End Array_Types .
diff --git a/tests/coq/array/Primitives.v b/tests/coq/array/Primitives.v
index 71a2d9c3..85e38f01 100644
--- a/tests/coq/array/Primitives.v
+++ b/tests/coq/array/Primitives.v
@@ -63,13 +63,15 @@ Check (if true then Return (1 + 2) else Fail_ Failure)%global = 3.
 
 (*** Misc *)
 
-
 Definition string := Coq.Strings.String.string.
 Definition char := Coq.Strings.Ascii.ascii.
 Definition char_of_byte := Coq.Strings.Ascii.ascii_of_byte.
 
-Definition mem_replace_fwd (a : Type) (x : a) (y : a) : a := x .
-Definition mem_replace_back (a : Type) (x : a) (y : a) : a := y .
+Definition core_mem_replace (a : Type) (x : a) (y : a) : a := x .
+Definition core_mem_replace_back (a : Type) (x : a) (y : a) : a := y .
+
+Record mut_raw_ptr (T : Type) := { mut_raw_ptr_v : T }.
+Record const_raw_ptr (T : Type) := { const_raw_ptr_v : T }.
 
 (*** Scalars *)
 
@@ -394,12 +396,89 @@ Notation "x s< y" := (scalar_ltb x y)  (at level 80) : Primitives_scope.
 Notation "x s>= y" := (scalar_geb x y)  (at level 80) : Primitives_scope.
 Notation "x s> y" := (scalar_gtb x y)  (at level 80) : Primitives_scope.
 
-(*** Range *)
-Record range (T : Type) := mk_range {
-  start: T;
-  end_: T;
+(** Constants *)
+Definition core_u8_max    := u8_max %u32.
+Definition core_u16_max   := u16_max %u32.
+Definition core_u32_max   := u32_max %u32.
+Definition core_u64_max   := u64_max %u64.
+Definition core_u128_max  := u64_max %u128.
+Axiom core_usize_max : usize. (** TODO *)
+Definition core_i8_max    := i8_max %i32.
+Definition core_i16_max   := i16_max %i32.
+Definition core_i32_max   := i32_max %i32.
+Definition core_i64_max   := i64_max %i64.
+Definition core_i128_max  := i64_max %i128.
+Axiom core_isize_max : isize. (** TODO *)
+
+(*** core::ops *)
+
+(* Trait declaration: [core::ops::index::Index] *)
+Record core_ops_index_Index (Self Idx : Type) := mk_core_ops_index_Index {
+  core_ops_index_Index_Output : Type;
+  core_ops_index_Index_index : Self -> Idx -> result core_ops_index_Index_Output;
+}.
+Arguments mk_core_ops_index_Index {_ _}.
+Arguments core_ops_index_Index_Output {_ _}.
+Arguments core_ops_index_Index_index {_ _}.
+
+(* Trait declaration: [core::ops::index::IndexMut] *)
+Record core_ops_index_IndexMut (Self Idx : Type) := mk_core_ops_index_IndexMut {
+  core_ops_index_IndexMut_indexInst : core_ops_index_Index Self Idx;
+  core_ops_index_IndexMut_index_mut : Self -> Idx -> result core_ops_index_IndexMut_indexInst.(core_ops_index_Index_Output);
+  core_ops_index_IndexMut_index_mut_back : Self -> Idx -> core_ops_index_IndexMut_indexInst.(core_ops_index_Index_Output) -> result Self;
+}.
+Arguments mk_core_ops_index_IndexMut {_ _}.
+Arguments core_ops_index_IndexMut_indexInst {_ _}.
+Arguments core_ops_index_IndexMut_index_mut {_ _}.
+Arguments core_ops_index_IndexMut_index_mut_back {_ _}.
+
+(* Trait declaration [core::ops::deref::Deref] *)
+Record core_ops_deref_Deref (Self : Type) := mk_core_ops_deref_Deref {
+  core_ops_deref_Deref_target : Type;
+  core_ops_deref_Deref_deref : Self -> result core_ops_deref_Deref_target;
+}.
+Arguments mk_core_ops_deref_Deref {_}.
+Arguments core_ops_deref_Deref_target {_}.
+Arguments core_ops_deref_Deref_deref {_}.
+
+(* Trait declaration [core::ops::deref::DerefMut] *)
+Record core_ops_deref_DerefMut (Self : Type) := mk_core_ops_deref_DerefMut {
+  core_ops_deref_DerefMut_derefInst : core_ops_deref_Deref Self;
+  core_ops_deref_DerefMut_deref_mut : Self -> result core_ops_deref_DerefMut_derefInst.(core_ops_deref_Deref_target);
+  core_ops_deref_DerefMut_deref_mut_back : Self -> core_ops_deref_DerefMut_derefInst.(core_ops_deref_Deref_target) -> result Self;
 }.
-Arguments mk_range {_}.
+Arguments mk_core_ops_deref_DerefMut {_}.
+Arguments core_ops_deref_DerefMut_derefInst {_}.
+Arguments core_ops_deref_DerefMut_deref_mut {_}.
+Arguments core_ops_deref_DerefMut_deref_mut_back {_}.
+
+Record core_ops_range_Range (T : Type) := mk_core_ops_range_Range {
+  core_ops_range_Range_start : T;
+  core_ops_range_Range_end_ : T;
+}.
+Arguments mk_core_ops_range_Range {_}.
+Arguments core_ops_range_Range_start {_}.
+Arguments core_ops_range_Range_end_ {_}.
+
+(*** [alloc] *)
+
+Definition alloc_boxed_Box_deref (T : Type) (x : T) : result T := Return x.
+Definition alloc_boxed_Box_deref_mut (T : Type) (x : T) : result T := Return x.
+Definition alloc_boxed_Box_deref_mut_back (T : Type) (_ : T) (x : T) : result T := Return x.
+
+(* Trait instance *)
+Definition alloc_boxed_Box_coreOpsDerefInst (Self : Type) : core_ops_deref_Deref Self := {|
+  core_ops_deref_Deref_target := Self;
+  core_ops_deref_Deref_deref := alloc_boxed_Box_deref Self;
+|}.
+
+(* Trait instance *)
+Definition alloc_boxed_Box_coreOpsDerefMutInst (Self : Type) : core_ops_deref_DerefMut Self := {|
+  core_ops_deref_DerefMut_derefInst := alloc_boxed_Box_coreOpsDerefInst Self;
+  core_ops_deref_DerefMut_deref_mut := alloc_boxed_Box_deref_mut Self;
+  core_ops_deref_DerefMut_deref_mut_back := alloc_boxed_Box_deref_mut_back Self;
+|}.
+
 
 (*** Arrays *)
 Definition array T (n : usize) := { l: list T | Z.of_nat (length l) = to_Z n}.
@@ -419,51 +498,50 @@ Qed.
 (* TODO: finish the definitions *)
 Axiom mk_array : forall (T : Type) (n : usize) (l : list T), array T n.
 
-Axiom array_index_shared : forall (T : Type) (n : usize) (x : array T n) (i : usize), result T.
-Axiom array_index_mut_fwd : forall (T : Type) (n : usize) (x : array T n) (i : usize), result T.
-Axiom array_index_mut_back : forall (T : Type) (n : usize) (x : array T n) (i : usize) (nx : T), result (array T n).
+(* For initialization *)
+Axiom array_repeat : forall (T : Type) (n : usize) (x : T), array T n.
+
+Axiom array_index_usize : forall (T : Type) (n : usize) (x : array T n) (i : usize), result T.
+Axiom array_update_usize : forall (T : Type) (n : usize) (x : array T n) (i : usize) (nx : T), result (array T n).
 
 (*** Slice *)
 Definition slice T := { l: list T | Z.of_nat (length l) <= usize_max}.
 
 Axiom slice_len : forall (T : Type) (s : slice T), usize.
-Axiom slice_index_shared : forall (T : Type) (x : slice T) (i : usize), result T.
-Axiom slice_index_mut_fwd : forall (T : Type) (x : slice T) (i : usize), result T.
-Axiom slice_index_mut_back : forall (T : Type) (x : slice T) (i : usize) (nx : T), result (slice T).
+Axiom slice_index_usize : forall (T : Type) (x : slice T) (i : usize), result T.
+Axiom slice_update_usize : forall (T : Type) (x : slice T) (i : usize) (nx : T), result (slice T).
 
 (*** Subslices *)
 
-Axiom array_to_slice_shared : forall (T : Type) (n : usize) (x : array T n), result (slice T).
-Axiom array_to_slice_mut_fwd : forall (T : Type) (n : usize) (x : array T n), result (slice T).
-Axiom array_to_slice_mut_back : forall (T : Type) (n : usize) (x : array T n) (s : slice T), result (array T n).
+Axiom array_to_slice : forall (T : Type) (n : usize) (x : array T n), result (slice T).
+Axiom array_from_slice : forall (T : Type) (n : usize) (x : array T n) (s : slice T), result (array T n).
+
+Axiom array_subslice: forall (T : Type) (n : usize) (x : array T n) (r : core_ops_range_Range usize), result (slice T).
+Axiom array_update_subslice: forall (T : Type) (n : usize) (x : array T n) (r : core_ops_range_Range usize) (ns : slice T), result (array T n).
 
-Axiom array_subslice_shared: forall (T : Type) (n : usize) (x : array T n) (r : range usize), result (slice T).
-Axiom array_subslice_mut_fwd: forall (T : Type) (n : usize) (x : array T n) (r : range usize), result (slice T).
-Axiom array_subslice_mut_back: forall (T : Type) (n : usize) (x : array T n) (r : range usize) (ns : slice T), result (array T n).
-Axiom slice_subslice_shared: forall (T : Type) (x : slice T) (r : range usize), result (slice T).
-Axiom slice_subslice_mut_fwd: forall (T : Type) (x : slice T) (r : range usize), result (slice T).
-Axiom slice_subslice_mut_back: forall (T : Type) (x : slice T) (r : range usize) (ns : slice T), result (slice T).
+Axiom slice_subslice: forall (T : Type) (x : slice T) (r : core_ops_range_Range usize), result (slice T).
+Axiom slice_update_subslice: forall (T : Type) (x : slice T) (r : core_ops_range_Range usize) (ns : slice T), result (slice T).
 
 (*** Vectors *)
 
-Definition vec T := { l: list T | Z.of_nat (length l) <= usize_max }.
+Definition alloc_vec_Vec T := { l: list T | Z.of_nat (length l) <= usize_max }.
 
-Definition vec_to_list {T: Type} (v: vec T) : list T := proj1_sig v.
+Definition alloc_vec_Vec_to_list {T: Type} (v: alloc_vec_Vec T) : list T := proj1_sig v.
 
-Definition vec_length {T: Type} (v: vec T) : Z := Z.of_nat (length (vec_to_list v)).
+Definition alloc_vec_Vec_length {T: Type} (v: alloc_vec_Vec T) : Z := Z.of_nat (length (alloc_vec_Vec_to_list v)).
 
-Definition vec_new (T: Type) : vec T := (exist _ [] le_0_usize_max).
+Definition alloc_vec_Vec_new (T: Type) : alloc_vec_Vec T := (exist _ [] le_0_usize_max).
 
-Lemma vec_len_in_usize {T} (v: vec T) : usize_min <= vec_length v <= usize_max.
+Lemma alloc_vec_Vec_len_in_usize {T} (v: alloc_vec_Vec T) : usize_min <= alloc_vec_Vec_length v <= usize_max.
 Proof.
-  unfold vec_length, usize_min.
+  unfold alloc_vec_Vec_length, usize_min.
   split.
   - lia.
   - apply (proj2_sig v).
 Qed.
 
-Definition vec_len (T: Type) (v: vec T) : usize :=
-  exist _ (vec_length v) (vec_len_in_usize v).
+Definition alloc_vec_Vec_len (T: Type) (v: alloc_vec_Vec T) : usize :=
+  exist _ (alloc_vec_Vec_length v) (alloc_vec_Vec_len_in_usize v).
 
 Fixpoint list_update {A} (l: list A) (n: nat) (a: A)
   : list A :=
@@ -474,50 +552,271 @@ Fixpoint list_update {A} (l: list A) (n: nat) (a: A)
     | S m => x :: (list_update t m a)
 end end.
 
-Definition vec_bind {A B} (v: vec A) (f: list A -> result (list B)) : result (vec B) :=
-  l <- f (vec_to_list v) ;
+Definition alloc_vec_Vec_bind {A B} (v: alloc_vec_Vec A) (f: list A -> result (list B)) : result (alloc_vec_Vec B) :=
+  l <- f (alloc_vec_Vec_to_list v) ;
   match sumbool_of_bool (scalar_le_max Usize (Z.of_nat (length l))) with
   | left H => Return (exist _ l (scalar_le_max_valid _ _ H))
   | right _ => Fail_ Failure
   end.
 
 (* The **forward** function shouldn't be used *)
-Definition vec_push_fwd (T: Type) (v: vec T) (x: T) : unit := tt.
+Definition alloc_vec_Vec_push_fwd (T: Type) (v: alloc_vec_Vec T) (x: T) : unit := tt.
 
-Definition vec_push_back (T: Type) (v: vec T) (x: T) : result (vec T) :=
-  vec_bind v (fun l => Return (l ++ [x])).
+Definition alloc_vec_Vec_push (T: Type) (v: alloc_vec_Vec T) (x: T) : result (alloc_vec_Vec T) :=
+  alloc_vec_Vec_bind v (fun l => Return (l ++ [x])).
 
 (* The **forward** function shouldn't be used *)
-Definition vec_insert_fwd (T: Type) (v: vec T) (i: usize) (x: T) : result unit :=
-  if to_Z i <? vec_length v then Return tt else Fail_ Failure.
+Definition alloc_vec_Vec_insert_fwd (T: Type) (v: alloc_vec_Vec T) (i: usize) (x: T) : result unit :=
+  if to_Z i <? alloc_vec_Vec_length v then Return tt else Fail_ Failure.
 
-Definition vec_insert_back (T: Type) (v: vec T) (i: usize) (x: T) : result (vec T) :=
-  vec_bind v (fun l =>
+Definition alloc_vec_Vec_insert (T: Type) (v: alloc_vec_Vec T) (i: usize) (x: T) : result (alloc_vec_Vec T) :=
+  alloc_vec_Vec_bind v (fun l =>
     if to_Z i <? Z.of_nat (length l)
     then Return (list_update l (usize_to_nat i) x)
     else Fail_ Failure).
 
-(* The **backward** function shouldn't be used *)
-Definition vec_index_fwd (T: Type) (v: vec T) (i: usize) : result T :=
-  match nth_error (vec_to_list v) (usize_to_nat i) with
-  | Some n => Return n
-  | None   => Fail_ Failure
-  end.
-
-Definition vec_index_back (T: Type) (v: vec T) (i: usize) (x: T) : result unit :=
-  if to_Z i <? vec_length v then Return tt else Fail_ Failure.
-
-(* The **backward** function shouldn't be used *)
-Definition vec_index_mut_fwd (T: Type) (v: vec T) (i: usize) : result T :=
-  match nth_error (vec_to_list v) (usize_to_nat i) with
-  | Some n => Return n
-  | None   => Fail_ Failure
+(* Helper *)
+Axiom alloc_vec_Vec_index_usize : forall {T : Type} (v : alloc_vec_Vec T) (i : usize) (x : T), result T.
+
+(* Helper *)
+Axiom alloc_vec_Vec_update_usize : forall {T : Type} (v : alloc_vec_Vec T) (i : usize) (x : T), result (alloc_vec_Vec T).
+
+(* Trait declaration: [core::slice::index::private_slice_index::Sealed] *)
+Definition core_slice_index_private_slice_index_Sealed (self : Type) := unit.
+
+(* Trait declaration: [core::slice::index::SliceIndex] *)
+Record core_slice_index_SliceIndex (Self T : Type) := mk_core_slice_index_SliceIndex {
+  core_slice_index_SliceIndex_sealedInst : core_slice_index_private_slice_index_Sealed Self;
+  core_slice_index_SliceIndex_Output : Type;
+  core_slice_index_SliceIndex_get : Self -> T -> result (option core_slice_index_SliceIndex_Output);
+  core_slice_index_SliceIndex_get_mut : Self -> T -> result (option core_slice_index_SliceIndex_Output);
+  core_slice_index_SliceIndex_get_mut_back : Self -> T -> option core_slice_index_SliceIndex_Output -> result T;
+  core_slice_index_SliceIndex_get_unchecked : Self -> const_raw_ptr T -> result (const_raw_ptr core_slice_index_SliceIndex_Output);
+  core_slice_index_SliceIndex_get_unchecked_mut : Self -> mut_raw_ptr T -> result (mut_raw_ptr core_slice_index_SliceIndex_Output);
+  core_slice_index_SliceIndex_index : Self -> T -> result core_slice_index_SliceIndex_Output;
+  core_slice_index_SliceIndex_index_mut : Self -> T -> result core_slice_index_SliceIndex_Output;
+  core_slice_index_SliceIndex_index_mut_back : Self -> T -> core_slice_index_SliceIndex_Output -> result T;
+}.
+Arguments mk_core_slice_index_SliceIndex {_ _}.
+Arguments core_slice_index_SliceIndex_sealedInst {_ _}.
+Arguments core_slice_index_SliceIndex_Output {_ _}.
+Arguments core_slice_index_SliceIndex_get {_ _}.
+Arguments core_slice_index_SliceIndex_get_mut {_ _}.
+Arguments core_slice_index_SliceIndex_get_mut_back {_ _}.
+Arguments core_slice_index_SliceIndex_get_unchecked {_ _}.
+Arguments core_slice_index_SliceIndex_get_unchecked_mut {_ _}.
+Arguments core_slice_index_SliceIndex_index {_ _}.
+Arguments core_slice_index_SliceIndex_index_mut {_ _}.
+Arguments core_slice_index_SliceIndex_index_mut_back {_ _}.
+
+(* [core::slice::index::[T]::index]: forward function *)
+Definition core_slice_index_Slice_index
+  (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T))
+  (s : slice T) (i : Idx) : result inst.(core_slice_index_SliceIndex_Output) :=
+  x <- inst.(core_slice_index_SliceIndex_get) i s;
+  match x with
+  | None => Fail_ Failure
+  | Some x => Return x
   end.
 
-Definition vec_index_mut_back (T: Type) (v: vec T) (i: usize) (x: T) : result (vec T) :=
-  vec_bind v (fun l =>
-    if to_Z i <? Z.of_nat (length l)
-    then Return (list_update l (usize_to_nat i) x)
-    else Fail_ Failure).
+(* [core::slice::index::Range:::get]: forward function *)
+Axiom core_slice_index_Range_get : forall (T : Type) (i : core_ops_range_Range usize) (s : slice T), result (option (slice T)).
+
+(* [core::slice::index::Range::get_mut]: forward function *)
+Axiom core_slice_index_Range_get_mut :
+  forall (T : Type), core_ops_range_Range usize -> slice T -> result (option (slice T)).
+
+(* [core::slice::index::Range::get_mut]: backward function 0 *)
+Axiom core_slice_index_Range_get_mut_back :
+  forall (T : Type), core_ops_range_Range usize -> slice T -> option (slice T) -> result (slice T).
+
+(* [core::slice::index::Range::get_unchecked]: forward function *)
+Definition core_slice_index_Range_get_unchecked
+  (T : Type) :
+  core_ops_range_Range usize -> const_raw_ptr (slice T) -> result (const_raw_ptr (slice T)) :=
+  (* Don't know what the model should be - for now we always fail to make
+     sure code which uses it fails *)
+  fun _ _ => Fail_ Failure.
+
+(* [core::slice::index::Range::get_unchecked_mut]: forward function *)
+Definition core_slice_index_Range_get_unchecked_mut
+  (T : Type) :
+  core_ops_range_Range usize -> mut_raw_ptr (slice T) -> result (mut_raw_ptr (slice T)) :=
+  (* Don't know what the model should be - for now we always fail to make
+    sure code which uses it fails *)
+  fun _ _ => Fail_ Failure.
+
+(* [core::slice::index::Range::index]: forward function *)
+Axiom core_slice_index_Range_index :
+  forall (T : Type), core_ops_range_Range usize -> slice T -> result (slice T).
+
+(* [core::slice::index::Range::index_mut]: forward function *)
+Axiom core_slice_index_Range_index_mut :
+  forall (T : Type), core_ops_range_Range usize -> slice T -> result (slice T).
+
+(* [core::slice::index::Range::index_mut]: backward function 0 *)
+Axiom core_slice_index_Range_index_mut_back :
+  forall (T : Type), core_ops_range_Range usize -> slice T -> slice T -> result (slice T).
+
+(* [core::slice::index::[T]::index_mut]: forward function *)
+Axiom core_slice_index_Slice_index_mut :
+  forall (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T)),
+  slice T -> Idx -> result inst.(core_slice_index_SliceIndex_Output).
+
+(* [core::slice::index::[T]::index_mut]: backward function 0 *)
+Axiom core_slice_index_Slice_index_mut_back :
+  forall (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T)),
+  slice T -> Idx -> inst.(core_slice_index_SliceIndex_Output) -> result (slice T).
+
+(* [core::array::[T; N]::index]: forward function *)
+Axiom core_array_Array_index :
+  forall (T Idx : Type) (N : usize) (inst : core_ops_index_Index (slice T) Idx)
+  (a : array T N) (i : Idx), result inst.(core_ops_index_Index_Output).
+
+(* [core::array::[T; N]::index_mut]: forward function *)
+Axiom core_array_Array_index_mut :
+  forall (T Idx : Type) (N : usize) (inst : core_ops_index_IndexMut (slice T) Idx)
+  (a : array T N) (i : Idx), result inst.(core_ops_index_IndexMut_indexInst).(core_ops_index_Index_Output).
+
+(* [core::array::[T; N]::index_mut]: backward function 0 *)
+Axiom core_array_Array_index_mut_back :
+  forall (T Idx : Type) (N : usize) (inst : core_ops_index_IndexMut (slice T) Idx)
+  (a : array T N) (i : Idx) (x : inst.(core_ops_index_IndexMut_indexInst).(core_ops_index_Index_Output)), result (array T N).
+
+(* Trait implementation: [core::slice::index::[T]] *)
+Definition core_slice_index_Slice_coreopsindexIndexInst (T Idx : Type)
+  (inst : core_slice_index_SliceIndex Idx (slice T)) :
+  core_ops_index_Index (slice T) Idx := {|
+  core_ops_index_Index_Output := inst.(core_slice_index_SliceIndex_Output);
+  core_ops_index_Index_index := core_slice_index_Slice_index T Idx inst;
+|}.
+
+(* Trait implementation: [core::slice::index::private_slice_index::Range] *)
+Definition core_slice_index_private_slice_index_Range_coresliceindexprivate_slice_indexSealedInst
+  : core_slice_index_private_slice_index_Sealed (core_ops_range_Range usize) := tt.
+
+(* Trait implementation: [core::slice::index::Range] *)
+Definition core_slice_index_Range_coresliceindexSliceIndexInst (T : Type) :
+  core_slice_index_SliceIndex (core_ops_range_Range usize) (slice T) := {|
+  core_slice_index_SliceIndex_sealedInst := core_slice_index_private_slice_index_Range_coresliceindexprivate_slice_indexSealedInst;
+  core_slice_index_SliceIndex_Output := slice T;
+  core_slice_index_SliceIndex_get := core_slice_index_Range_get T;
+  core_slice_index_SliceIndex_get_mut := core_slice_index_Range_get_mut T;
+  core_slice_index_SliceIndex_get_mut_back := core_slice_index_Range_get_mut_back T;
+  core_slice_index_SliceIndex_get_unchecked := core_slice_index_Range_get_unchecked T;
+  core_slice_index_SliceIndex_get_unchecked_mut := core_slice_index_Range_get_unchecked_mut T;
+  core_slice_index_SliceIndex_index := core_slice_index_Range_index T;
+  core_slice_index_SliceIndex_index_mut := core_slice_index_Range_index_mut T;
+  core_slice_index_SliceIndex_index_mut_back := core_slice_index_Range_index_mut_back T;
+|}.
+
+(* Trait implementation: [core::slice::index::[T]] *)
+Definition core_slice_index_Slice_coreopsindexIndexMutInst (T Idx : Type)
+  (inst : core_slice_index_SliceIndex Idx (slice T)) :
+  core_ops_index_IndexMut (slice T) Idx := {|
+  core_ops_index_IndexMut_indexInst := core_slice_index_Slice_coreopsindexIndexInst T Idx inst;
+  core_ops_index_IndexMut_index_mut := core_slice_index_Slice_index_mut T Idx inst;
+  core_ops_index_IndexMut_index_mut_back := core_slice_index_Slice_index_mut_back T Idx inst;
+|}.
+
+(* Trait implementation: [core::array::[T; N]] *)
+Definition core_array_Array_coreopsindexIndexInst (T Idx : Type) (N : usize)
+  (inst : core_ops_index_Index (slice T) Idx) :
+  core_ops_index_Index (array T N) Idx := {|
+  core_ops_index_Index_Output := inst.(core_ops_index_Index_Output);
+  core_ops_index_Index_index := core_array_Array_index T Idx N inst;
+|}.
+
+(* Trait implementation: [core::array::[T; N]] *)
+Definition core_array_Array_coreopsindexIndexMutInst (T Idx : Type) (N : usize)
+  (inst : core_ops_index_IndexMut (slice T) Idx) :
+  core_ops_index_IndexMut (array T N) Idx := {|
+  core_ops_index_IndexMut_indexInst := core_array_Array_coreopsindexIndexInst T Idx N inst.(core_ops_index_IndexMut_indexInst);
+  core_ops_index_IndexMut_index_mut := core_array_Array_index_mut T Idx N inst;
+  core_ops_index_IndexMut_index_mut_back := core_array_Array_index_mut_back T Idx N inst;
+|}.
+
+(* [core::slice::index::usize::get]: forward function *)
+Axiom core_slice_index_usize_get : forall (T : Type), usize -> slice T -> result (option T).
+
+(* [core::slice::index::usize::get_mut]: forward function *)
+Axiom core_slice_index_usize_get_mut : forall (T : Type), usize -> slice T -> result (option T).
+
+(* [core::slice::index::usize::get_mut]: backward function 0 *)
+Axiom core_slice_index_usize_get_mut_back :
+  forall (T : Type), usize -> slice T -> option T -> result (slice T).
+
+(* [core::slice::index::usize::get_unchecked]: forward function *)
+Axiom core_slice_index_usize_get_unchecked :
+  forall (T : Type), usize -> const_raw_ptr (slice T) -> result (const_raw_ptr T).
+
+(* [core::slice::index::usize::get_unchecked_mut]: forward function *)
+Axiom core_slice_index_usize_get_unchecked_mut :
+  forall (T : Type), usize -> mut_raw_ptr (slice T) -> result (mut_raw_ptr T).
+
+(* [core::slice::index::usize::index]: forward function *)
+Axiom core_slice_index_usize_index : forall (T : Type), usize -> slice T -> result T.
+
+(* [core::slice::index::usize::index_mut]: forward function *)
+Axiom core_slice_index_usize_index_mut : forall (T : Type), usize -> slice T -> result T.
+
+(* [core::slice::index::usize::index_mut]: backward function 0 *)
+Axiom core_slice_index_usize_index_mut_back :
+  forall (T : Type), usize -> slice T -> T -> result (slice T).
+
+(* Trait implementation: [core::slice::index::private_slice_index::usize] *)
+Definition core_slice_index_private_slice_index_usize_coresliceindexprivate_slice_indexSealedInst
+  : core_slice_index_private_slice_index_Sealed usize := tt.
+
+(* Trait implementation: [core::slice::index::usize] *)
+Definition core_slice_index_usize_coresliceindexSliceIndexInst (T : Type) :
+  core_slice_index_SliceIndex usize (slice T) := {|
+  core_slice_index_SliceIndex_sealedInst := core_slice_index_private_slice_index_usize_coresliceindexprivate_slice_indexSealedInst;
+  core_slice_index_SliceIndex_Output := T;
+  core_slice_index_SliceIndex_get := core_slice_index_usize_get T;
+  core_slice_index_SliceIndex_get_mut := core_slice_index_usize_get_mut T;
+  core_slice_index_SliceIndex_get_mut_back := core_slice_index_usize_get_mut_back T;
+  core_slice_index_SliceIndex_get_unchecked := core_slice_index_usize_get_unchecked T;
+  core_slice_index_SliceIndex_get_unchecked_mut := core_slice_index_usize_get_unchecked_mut T;
+  core_slice_index_SliceIndex_index := core_slice_index_usize_index T;
+  core_slice_index_SliceIndex_index_mut := core_slice_index_usize_index_mut T;
+  core_slice_index_SliceIndex_index_mut_back := core_slice_index_usize_index_mut_back T;
+|}.
+
+(* [alloc::vec::Vec::index]: forward function *)
+Axiom alloc_vec_Vec_index : forall (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T))
+  (Self : alloc_vec_Vec T) (i : Idx), result inst.(core_slice_index_SliceIndex_Output).
+
+(* [alloc::vec::Vec::index_mut]: forward function *)
+Axiom alloc_vec_Vec_index_mut : forall (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T))
+  (Self : alloc_vec_Vec T) (i : Idx), result inst.(core_slice_index_SliceIndex_Output).
+
+(* [alloc::vec::Vec::index_mut]: backward function 0 *)
+Axiom alloc_vec_Vec_index_mut_back :
+  forall (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T))
+  (Self : alloc_vec_Vec T) (i : Idx) (x : inst.(core_slice_index_SliceIndex_Output)), result (alloc_vec_Vec T).
+
+(* Trait implementation: [alloc::vec::Vec] *)
+Definition alloc_vec_Vec_coreopsindexIndexInst (T Idx : Type)
+  (inst : core_slice_index_SliceIndex Idx (slice T)) :
+  core_ops_index_Index (alloc_vec_Vec T) Idx := {|
+  core_ops_index_Index_Output := inst.(core_slice_index_SliceIndex_Output);
+  core_ops_index_Index_index := alloc_vec_Vec_index T Idx inst;
+|}.
+
+(* Trait implementation: [alloc::vec::Vec] *)
+Definition alloc_vec_Vec_coreopsindexIndexMutInst (T Idx : Type)
+  (inst : core_slice_index_SliceIndex Idx (slice T)) :
+  core_ops_index_IndexMut (alloc_vec_Vec T) Idx := {|
+  core_ops_index_IndexMut_indexInst := alloc_vec_Vec_coreopsindexIndexInst T Idx inst;
+  core_ops_index_IndexMut_index_mut := alloc_vec_Vec_index_mut T Idx inst;
+  core_ops_index_IndexMut_index_mut_back := alloc_vec_Vec_index_mut_back T Idx inst;
+|}.
+
+(*** Theorems *)
+
+Axiom alloc_vec_Vec_index_mut_back_eq : forall {a : Type} (v : alloc_vec_Vec a) (i : usize) (x : a),
+  alloc_vec_Vec_index_mut_back a usize (core_slice_index_usize_coresliceindexSliceIndexInst a) v i x =
+    alloc_vec_Vec_update_usize v i x.
 
 End Primitives.
diff --git a/tests/coq/array/_CoqProject b/tests/coq/array/_CoqProject
index f33cefe6..87d8fc3d 100644
--- a/tests/coq/array/_CoqProject
+++ b/tests/coq/array/_CoqProject
@@ -3,6 +3,5 @@
 -arg -w
 -arg all
 
-Array_Funs.v
 Primitives.v
-Array_Types.v
+Array.v
diff --git a/tests/coq/betree/BetreeMain_Funs.v b/tests/coq/betree/BetreeMain_Funs.v
index 1e457433..261e8270 100644
--- a/tests/coq/betree/BetreeMain_Funs.v
+++ b/tests/coq/betree/BetreeMain_Funs.v
@@ -13,41 +13,41 @@ Import BetreeMain_Opaque.
 Module BetreeMain_Funs.
 
 (** [betree_main::betree::load_internal_node]: forward function *)
-Definition betree_load_internal_node_fwd
+Definition betree_load_internal_node
   (id : u64) (st : state) :
-  result (state * (Betree_list_t (u64 * Betree_message_t)))
+  result (state * (betree_List_t (u64 * betree_Message_t)))
   :=
-  betree_utils_load_internal_node_fwd id st
+  betree_utils_load_internal_node id st
 .
 
 (** [betree_main::betree::store_internal_node]: forward function *)
-Definition betree_store_internal_node_fwd
-  (id : u64) (content : Betree_list_t (u64 * Betree_message_t)) (st : state) :
+Definition betree_store_internal_node
+  (id : u64) (content : betree_List_t (u64 * betree_Message_t)) (st : state) :
   result (state * unit)
   :=
-  p <- betree_utils_store_internal_node_fwd id content st;
+  p <- betree_utils_store_internal_node id content st;
   let (st0, _) := p in
   Return (st0, tt)
 .
 
 (** [betree_main::betree::load_leaf_node]: forward function *)
-Definition betree_load_leaf_node_fwd
-  (id : u64) (st : state) : result (state * (Betree_list_t (u64 * u64))) :=
-  betree_utils_load_leaf_node_fwd id st
+Definition betree_load_leaf_node
+  (id : u64) (st : state) : result (state * (betree_List_t (u64 * u64))) :=
+  betree_utils_load_leaf_node id st
 .
 
 (** [betree_main::betree::store_leaf_node]: forward function *)
-Definition betree_store_leaf_node_fwd
-  (id : u64) (content : Betree_list_t (u64 * u64)) (st : state) :
+Definition betree_store_leaf_node
+  (id : u64) (content : betree_List_t (u64 * u64)) (st : state) :
   result (state * unit)
   :=
-  p <- betree_utils_store_leaf_node_fwd id content st;
+  p <- betree_utils_store_leaf_node id content st;
   let (st0, _) := p in
   Return (st0, tt)
 .
 
 (** [betree_main::betree::fresh_node_id]: forward function *)
-Definition betree_fresh_node_id_fwd (counter : u64) : result u64 :=
+Definition betree_fresh_node_id (counter : u64) : result u64 :=
   _ <- u64_add counter 1%u64; Return counter
 .
 
@@ -57,1142 +57,1121 @@ Definition betree_fresh_node_id_back (counter : u64) : result u64 :=
 .
 
 (** [betree_main::betree::NodeIdCounter::{0}::new]: forward function *)
-Definition betree_node_id_counter_new_fwd : result Betree_node_id_counter_t :=
-  Return {| Betree_node_id_counter_next_node_id := 0%u64 |}
+Definition betree_NodeIdCounter_new : result betree_NodeIdCounter_t :=
+  Return {| betree_NodeIdCounter_next_node_id := 0%u64 |}
 .
 
 (** [betree_main::betree::NodeIdCounter::{0}::fresh_id]: forward function *)
-Definition betree_node_id_counter_fresh_id_fwd
-  (self : Betree_node_id_counter_t) : result u64 :=
-  _ <- u64_add self.(Betree_node_id_counter_next_node_id) 1%u64;
-  Return self.(Betree_node_id_counter_next_node_id)
+Definition betree_NodeIdCounter_fresh_id
+  (self : betree_NodeIdCounter_t) : result u64 :=
+  _ <- u64_add self.(betree_NodeIdCounter_next_node_id) 1%u64;
+  Return self.(betree_NodeIdCounter_next_node_id)
 .
 
 (** [betree_main::betree::NodeIdCounter::{0}::fresh_id]: backward function 0 *)
-Definition betree_node_id_counter_fresh_id_back
-  (self : Betree_node_id_counter_t) : result Betree_node_id_counter_t :=
-  i <- u64_add self.(Betree_node_id_counter_next_node_id) 1%u64;
-  Return {| Betree_node_id_counter_next_node_id := i |}
+Definition betree_NodeIdCounter_fresh_id_back
+  (self : betree_NodeIdCounter_t) : result betree_NodeIdCounter_t :=
+  i <- u64_add self.(betree_NodeIdCounter_next_node_id) 1%u64;
+  Return {| betree_NodeIdCounter_next_node_id := i |}
 .
 
-(** [core::num::u64::{9}::MAX] *)
-Definition core_num_u64_max_body : result u64 :=
-  Return 18446744073709551615%u64
-.
-Definition core_num_u64_max_c : u64 := core_num_u64_max_body%global.
-
 (** [betree_main::betree::upsert_update]: forward function *)
-Definition betree_upsert_update_fwd
-  (prev : option u64) (st : Betree_upsert_fun_state_t) : result u64 :=
+Definition betree_upsert_update
+  (prev : option u64) (st : betree_UpsertFunState_t) : result u64 :=
   match prev with
   | None =>
     match st with
-    | BetreeUpsertFunStateAdd v => Return v
-    | BetreeUpsertFunStateSub i => Return 0%u64
+    | Betree_UpsertFunState_Add v => Return v
+    | Betree_UpsertFunState_Sub i => Return 0%u64
     end
   | Some prev0 =>
     match st with
-    | BetreeUpsertFunStateAdd v =>
-      margin <- u64_sub core_num_u64_max_c prev0;
-      if margin s>= v then u64_add prev0 v else Return core_num_u64_max_c
-    | BetreeUpsertFunStateSub v =>
+    | Betree_UpsertFunState_Add v =>
+      margin <- u64_sub core_u64_max prev0;
+      if margin s>= v then u64_add prev0 v else Return core_u64_max
+    | Betree_UpsertFunState_Sub v =>
       if prev0 s>= v then u64_sub prev0 v else Return 0%u64
     end
   end
 .
 
 (** [betree_main::betree::List::{1}::len]: forward function *)
-Fixpoint betree_list_len_fwd
-  (T : Type) (n : nat) (self : Betree_list_t T) : result u64 :=
+Fixpoint betree_List_len
+  (T : Type) (n : nat) (self : betree_List_t T) : result u64 :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
     match self with
-    | BetreeListCons t tl => i <- betree_list_len_fwd T n0 tl; u64_add 1%u64 i
-    | BetreeListNil => Return 0%u64
+    | Betree_List_Cons t tl => i <- betree_List_len T n0 tl; u64_add 1%u64 i
+    | Betree_List_Nil => Return 0%u64
     end
   end
 .
 
 (** [betree_main::betree::List::{1}::split_at]: forward function *)
-Fixpoint betree_list_split_at_fwd
-  (T : Type) (n : nat) (self : Betree_list_t T) (n0 : u64) :
-  result ((Betree_list_t T) * (Betree_list_t T))
+Fixpoint betree_List_split_at
+  (T : Type) (n : nat) (self : betree_List_t T) (n0 : u64) :
+  result ((betree_List_t T) * (betree_List_t T))
   :=
   match n with
   | O => Fail_ OutOfFuel
   | S n1 =>
     if n0 s= 0%u64
-    then Return (BetreeListNil, self)
+    then Return (Betree_List_Nil, self)
     else
       match self with
-      | BetreeListCons hd tl =>
+      | Betree_List_Cons hd tl =>
         i <- u64_sub n0 1%u64;
-        p <- betree_list_split_at_fwd T n1 tl i;
+        p <- betree_List_split_at T n1 tl i;
         let (ls0, ls1) := p in
         let l := ls0 in
-        Return (BetreeListCons hd l, ls1)
-      | BetreeListNil => Fail_ Failure
+        Return (Betree_List_Cons hd l, ls1)
+      | Betree_List_Nil => Fail_ Failure
       end
   end
 .
 
 (** [betree_main::betree::List::{1}::push_front]: merged forward/backward function
     (there is a single backward function, and the forward function returns ()) *)
-Definition betree_list_push_front_fwd_back
-  (T : Type) (self : Betree_list_t T) (x : T) : result (Betree_list_t T) :=
-  let tl := mem_replace_fwd (Betree_list_t T) self BetreeListNil in
+Definition betree_List_push_front
+  (T : Type) (self : betree_List_t T) (x : T) : result (betree_List_t T) :=
+  let tl := core_mem_replace (betree_List_t T) self Betree_List_Nil in
   let l := tl in
-  Return (BetreeListCons x l)
+  Return (Betree_List_Cons x l)
 .
 
 (** [betree_main::betree::List::{1}::pop_front]: forward function *)
-Definition betree_list_pop_front_fwd
-  (T : Type) (self : Betree_list_t T) : result T :=
-  let ls := mem_replace_fwd (Betree_list_t T) self BetreeListNil in
+Definition betree_List_pop_front
+  (T : Type) (self : betree_List_t T) : result T :=
+  let ls := core_mem_replace (betree_List_t T) self Betree_List_Nil in
   match ls with
-  | BetreeListCons x tl => Return x
-  | BetreeListNil => Fail_ Failure
+  | Betree_List_Cons x tl => Return x
+  | Betree_List_Nil => Fail_ Failure
   end
 .
 
 (** [betree_main::betree::List::{1}::pop_front]: backward function 0 *)
-Definition betree_list_pop_front_back
-  (T : Type) (self : Betree_list_t T) : result (Betree_list_t T) :=
-  let ls := mem_replace_fwd (Betree_list_t T) self BetreeListNil in
+Definition betree_List_pop_front_back
+  (T : Type) (self : betree_List_t T) : result (betree_List_t T) :=
+  let ls := core_mem_replace (betree_List_t T) self Betree_List_Nil in
   match ls with
-  | BetreeListCons x tl => Return tl
-  | BetreeListNil => Fail_ Failure
+  | Betree_List_Cons x tl => Return tl
+  | Betree_List_Nil => Fail_ Failure
   end
 .
 
 (** [betree_main::betree::List::{1}::hd]: forward function *)
-Definition betree_list_hd_fwd (T : Type) (self : Betree_list_t T) : result T :=
+Definition betree_List_hd (T : Type) (self : betree_List_t T) : result T :=
   match self with
-  | BetreeListCons hd l => Return hd
-  | BetreeListNil => Fail_ Failure
+  | Betree_List_Cons hd l => Return hd
+  | Betree_List_Nil => Fail_ Failure
   end
 .
 
 (** [betree_main::betree::List::{2}::head_has_key]: forward function *)
-Definition betree_list_head_has_key_fwd
-  (T : Type) (self : Betree_list_t (u64 * T)) (key : u64) : result bool :=
+Definition betree_List_head_has_key
+  (T : Type) (self : betree_List_t (u64 * T)) (key : u64) : result bool :=
   match self with
-  | BetreeListCons hd l => let (i, _) := hd in Return (i s= key)
-  | BetreeListNil => Return false
+  | Betree_List_Cons hd l => let (i, _) := hd in Return (i s= key)
+  | Betree_List_Nil => Return false
   end
 .
 
 (** [betree_main::betree::List::{2}::partition_at_pivot]: forward function *)
-Fixpoint betree_list_partition_at_pivot_fwd
-  (T : Type) (n : nat) (self : Betree_list_t (u64 * T)) (pivot : u64) :
-  result ((Betree_list_t (u64 * T)) * (Betree_list_t (u64 * T)))
+Fixpoint betree_List_partition_at_pivot
+  (T : Type) (n : nat) (self : betree_List_t (u64 * T)) (pivot : u64) :
+  result ((betree_List_t (u64 * T)) * (betree_List_t (u64 * T)))
   :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
     match self with
-    | BetreeListCons hd tl =>
+    | Betree_List_Cons hd tl =>
       let (i, t) := hd in
       if i s>= pivot
-      then Return (BetreeListNil, BetreeListCons (i, t) tl)
+      then Return (Betree_List_Nil, Betree_List_Cons (i, t) tl)
       else (
-        p <- betree_list_partition_at_pivot_fwd T n0 tl pivot;
+        p <- betree_List_partition_at_pivot T n0 tl pivot;
         let (ls0, ls1) := p in
         let l := ls0 in
-        Return (BetreeListCons (i, t) l, ls1))
-    | BetreeListNil => Return (BetreeListNil, BetreeListNil)
+        Return (Betree_List_Cons (i, t) l, ls1))
+    | Betree_List_Nil => Return (Betree_List_Nil, Betree_List_Nil)
     end
   end
 .
 
 (** [betree_main::betree::Leaf::{3}::split]: forward function *)
-Definition betree_leaf_split_fwd
-  (n : nat) (self : Betree_leaf_t) (content : Betree_list_t (u64 * u64))
-  (params : Betree_params_t) (node_id_cnt : Betree_node_id_counter_t)
+Definition betree_Leaf_split
+  (n : nat) (self : betree_Leaf_t) (content : betree_List_t (u64 * u64))
+  (params : betree_Params_t) (node_id_cnt : betree_NodeIdCounter_t)
   (st : state) :
-  result (state * Betree_internal_t)
+  result (state * betree_Internal_t)
   :=
   p <-
-    betree_list_split_at_fwd (u64 * u64) n content
-      params.(Betree_params_split_size);
+    betree_List_split_at (u64 * u64) n content
+      params.(betree_Params_split_size);
   let (content0, content1) := p in
-  p0 <- betree_list_hd_fwd (u64 * u64) content1;
+  p0 <- betree_List_hd (u64 * u64) content1;
   let (pivot, _) := p0 in
-  id0 <- betree_node_id_counter_fresh_id_fwd node_id_cnt;
-  node_id_cnt0 <- betree_node_id_counter_fresh_id_back node_id_cnt;
-  id1 <- betree_node_id_counter_fresh_id_fwd node_id_cnt0;
-  p1 <- betree_store_leaf_node_fwd id0 content0 st;
+  id0 <- betree_NodeIdCounter_fresh_id node_id_cnt;
+  node_id_cnt0 <- betree_NodeIdCounter_fresh_id_back node_id_cnt;
+  id1 <- betree_NodeIdCounter_fresh_id node_id_cnt0;
+  p1 <- betree_store_leaf_node id0 content0 st;
   let (st0, _) := p1 in
-  p2 <- betree_store_leaf_node_fwd id1 content1 st0;
+  p2 <- betree_store_leaf_node id1 content1 st0;
   let (st1, _) := p2 in
-  let n0 := BetreeNodeLeaf
+  let n0 := Betree_Node_Leaf
     {|
-      Betree_leaf_id := id0;
-      Betree_leaf_size := params.(Betree_params_split_size)
+      betree_Leaf_id := id0;
+      betree_Leaf_size := params.(betree_Params_split_size)
     |} in
-  let n1 := BetreeNodeLeaf
+  let n1 := Betree_Node_Leaf
     {|
-      Betree_leaf_id := id1;
-      Betree_leaf_size := params.(Betree_params_split_size)
+      betree_Leaf_id := id1;
+      betree_Leaf_size := params.(betree_Params_split_size)
     |} in
-  Return (st1, mkBetree_internal_t self.(Betree_leaf_id) pivot n0 n1)
+  Return (st1, mkbetree_Internal_t self.(betree_Leaf_id) pivot n0 n1)
 .
 
 (** [betree_main::betree::Leaf::{3}::split]: backward function 2 *)
-Definition betree_leaf_split_back
-  (n : nat) (self : Betree_leaf_t) (content : Betree_list_t (u64 * u64))
-  (params : Betree_params_t) (node_id_cnt : Betree_node_id_counter_t)
+Definition betree_Leaf_split_back
+  (n : nat) (self : betree_Leaf_t) (content : betree_List_t (u64 * u64))
+  (params : betree_Params_t) (node_id_cnt : betree_NodeIdCounter_t)
   (st : state) :
-  result Betree_node_id_counter_t
+  result betree_NodeIdCounter_t
   :=
   p <-
-    betree_list_split_at_fwd (u64 * u64) n content
-      params.(Betree_params_split_size);
+    betree_List_split_at (u64 * u64) n content
+      params.(betree_Params_split_size);
   let (content0, content1) := p in
-  _ <- betree_list_hd_fwd (u64 * u64) content1;
-  id0 <- betree_node_id_counter_fresh_id_fwd node_id_cnt;
-  node_id_cnt0 <- betree_node_id_counter_fresh_id_back node_id_cnt;
-  id1 <- betree_node_id_counter_fresh_id_fwd node_id_cnt0;
-  p0 <- betree_store_leaf_node_fwd id0 content0 st;
+  _ <- betree_List_hd (u64 * u64) content1;
+  id0 <- betree_NodeIdCounter_fresh_id node_id_cnt;
+  node_id_cnt0 <- betree_NodeIdCounter_fresh_id_back node_id_cnt;
+  id1 <- betree_NodeIdCounter_fresh_id node_id_cnt0;
+  p0 <- betree_store_leaf_node id0 content0 st;
   let (st0, _) := p0 in
-  _ <- betree_store_leaf_node_fwd id1 content1 st0;
-  betree_node_id_counter_fresh_id_back node_id_cnt0
+  _ <- betree_store_leaf_node id1 content1 st0;
+  betree_NodeIdCounter_fresh_id_back node_id_cnt0
 .
 
 (** [betree_main::betree::Node::{5}::lookup_first_message_for_key]: forward function *)
-Fixpoint betree_node_lookup_first_message_for_key_fwd
-  (n : nat) (key : u64) (msgs : Betree_list_t (u64 * Betree_message_t)) :
-  result (Betree_list_t (u64 * Betree_message_t))
+Fixpoint betree_Node_lookup_first_message_for_key
+  (n : nat) (key : u64) (msgs : betree_List_t (u64 * betree_Message_t)) :
+  result (betree_List_t (u64 * betree_Message_t))
   :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
     match msgs with
-    | BetreeListCons x next_msgs =>
+    | Betree_List_Cons x next_msgs =>
       let (i, m) := x in
       if i s>= key
-      then Return (BetreeListCons (i, m) next_msgs)
-      else betree_node_lookup_first_message_for_key_fwd n0 key next_msgs
-    | BetreeListNil => Return BetreeListNil
+      then Return (Betree_List_Cons (i, m) next_msgs)
+      else betree_Node_lookup_first_message_for_key n0 key next_msgs
+    | Betree_List_Nil => Return Betree_List_Nil
     end
   end
 .
 
 (** [betree_main::betree::Node::{5}::lookup_first_message_for_key]: backward function 0 *)
-Fixpoint betree_node_lookup_first_message_for_key_back
-  (n : nat) (key : u64) (msgs : Betree_list_t (u64 * Betree_message_t))
-  (ret : Betree_list_t (u64 * Betree_message_t)) :
-  result (Betree_list_t (u64 * Betree_message_t))
+Fixpoint betree_Node_lookup_first_message_for_key_back
+  (n : nat) (key : u64) (msgs : betree_List_t (u64 * betree_Message_t))
+  (ret : betree_List_t (u64 * betree_Message_t)) :
+  result (betree_List_t (u64 * betree_Message_t))
   :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
     match msgs with
-    | BetreeListCons x next_msgs =>
+    | Betree_List_Cons x next_msgs =>
       let (i, m) := x in
       if i s>= key
       then Return ret
       else (
         next_msgs0 <-
-          betree_node_lookup_first_message_for_key_back n0 key next_msgs ret;
-        Return (BetreeListCons (i, m) next_msgs0))
-    | BetreeListNil => Return ret
+          betree_Node_lookup_first_message_for_key_back n0 key next_msgs ret;
+        Return (Betree_List_Cons (i, m) next_msgs0))
+    | Betree_List_Nil => Return ret
     end
   end
 .
 
 (** [betree_main::betree::Node::{5}::apply_upserts]: forward function *)
-Fixpoint betree_node_apply_upserts_fwd
-  (n : nat) (msgs : Betree_list_t (u64 * Betree_message_t)) (prev : option u64)
+Fixpoint betree_Node_apply_upserts
+  (n : nat) (msgs : betree_List_t (u64 * betree_Message_t)) (prev : option u64)
   (key : u64) (st : state) :
   result (state * u64)
   :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
-    b <- betree_list_head_has_key_fwd Betree_message_t msgs key;
+    b <- betree_List_head_has_key betree_Message_t msgs key;
     if b
     then (
-      msg <- betree_list_pop_front_fwd (u64 * Betree_message_t) msgs;
+      msg <- betree_List_pop_front (u64 * betree_Message_t) msgs;
       let (_, m) := msg in
       match m with
-      | BetreeMessageInsert i => Fail_ Failure
-      | BetreeMessageDelete => Fail_ Failure
-      | BetreeMessageUpsert s =>
-        v <- betree_upsert_update_fwd prev s;
-        msgs0 <- betree_list_pop_front_back (u64 * Betree_message_t) msgs;
-        betree_node_apply_upserts_fwd n0 msgs0 (Some v) key st
+      | Betree_Message_Insert i => Fail_ Failure
+      | Betree_Message_Delete => Fail_ Failure
+      | Betree_Message_Upsert s =>
+        v <- betree_upsert_update prev s;
+        msgs0 <- betree_List_pop_front_back (u64 * betree_Message_t) msgs;
+        betree_Node_apply_upserts n0 msgs0 (Some v) key st
       end)
     else (
-      p <- core_option_option_unwrap_fwd u64 prev st;
+      p <- core_option_Option_unwrap u64 prev st;
       let (st0, v) := p in
       _ <-
-        betree_list_push_front_fwd_back (u64 * Betree_message_t) msgs (key,
-          BetreeMessageInsert v);
+        betree_List_push_front (u64 * betree_Message_t) msgs (key,
+          Betree_Message_Insert v);
       Return (st0, v))
   end
 .
 
 (** [betree_main::betree::Node::{5}::apply_upserts]: backward function 0 *)
-Fixpoint betree_node_apply_upserts_back
-  (n : nat) (msgs : Betree_list_t (u64 * Betree_message_t)) (prev : option u64)
+Fixpoint betree_Node_apply_upserts_back
+  (n : nat) (msgs : betree_List_t (u64 * betree_Message_t)) (prev : option u64)
   (key : u64) (st : state) :
-  result (Betree_list_t (u64 * Betree_message_t))
+  result (betree_List_t (u64 * betree_Message_t))
   :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
-    b <- betree_list_head_has_key_fwd Betree_message_t msgs key;
+    b <- betree_List_head_has_key betree_Message_t msgs key;
     if b
     then (
-      msg <- betree_list_pop_front_fwd (u64 * Betree_message_t) msgs;
+      msg <- betree_List_pop_front (u64 * betree_Message_t) msgs;
       let (_, m) := msg in
       match m with
-      | BetreeMessageInsert i => Fail_ Failure
-      | BetreeMessageDelete => Fail_ Failure
-      | BetreeMessageUpsert s =>
-        v <- betree_upsert_update_fwd prev s;
-        msgs0 <- betree_list_pop_front_back (u64 * Betree_message_t) msgs;
-        betree_node_apply_upserts_back n0 msgs0 (Some v) key st
+      | Betree_Message_Insert i => Fail_ Failure
+      | Betree_Message_Delete => Fail_ Failure
+      | Betree_Message_Upsert s =>
+        v <- betree_upsert_update prev s;
+        msgs0 <- betree_List_pop_front_back (u64 * betree_Message_t) msgs;
+        betree_Node_apply_upserts_back n0 msgs0 (Some v) key st
       end)
     else (
-      p <- core_option_option_unwrap_fwd u64 prev st;
+      p <- core_option_Option_unwrap u64 prev st;
       let (_, v) := p in
-      betree_list_push_front_fwd_back (u64 * Betree_message_t) msgs (key,
-        BetreeMessageInsert v))
+      betree_List_push_front (u64 * betree_Message_t) msgs (key,
+        Betree_Message_Insert v))
   end
 .
 
 (** [betree_main::betree::Node::{5}::lookup_in_bindings]: forward function *)
-Fixpoint betree_node_lookup_in_bindings_fwd
-  (n : nat) (key : u64) (bindings : Betree_list_t (u64 * u64)) :
+Fixpoint betree_Node_lookup_in_bindings
+  (n : nat) (key : u64) (bindings : betree_List_t (u64 * u64)) :
   result (option u64)
   :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
     match bindings with
-    | BetreeListCons hd tl =>
+    | Betree_List_Cons hd tl =>
       let (i, i0) := hd in
       if i s= key
       then Return (Some i0)
       else
         if i s> key
         then Return None
-        else betree_node_lookup_in_bindings_fwd n0 key tl
-    | BetreeListNil => Return None
+        else betree_Node_lookup_in_bindings n0 key tl
+    | Betree_List_Nil => Return None
     end
   end
 .
 
 (** [betree_main::betree::Internal::{4}::lookup_in_children]: forward function *)
-Fixpoint betree_internal_lookup_in_children_fwd
-  (n : nat) (self : Betree_internal_t) (key : u64) (st : state) :
+Fixpoint betree_Internal_lookup_in_children
+  (n : nat) (self : betree_Internal_t) (key : u64) (st : state) :
   result (state * (option u64))
   :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
-    if key s< self.(Betree_internal_pivot)
-    then betree_node_lookup_fwd n0 self.(Betree_internal_left) key st
-    else betree_node_lookup_fwd n0 self.(Betree_internal_right) key st
+    if key s< self.(betree_Internal_pivot)
+    then betree_Node_lookup n0 self.(betree_Internal_left) key st
+    else betree_Node_lookup n0 self.(betree_Internal_right) key st
   end
 
 (** [betree_main::betree::Internal::{4}::lookup_in_children]: backward function 0 *)
-with betree_internal_lookup_in_children_back
-  (n : nat) (self : Betree_internal_t) (key : u64) (st : state) :
-  result Betree_internal_t
+with betree_Internal_lookup_in_children_back
+  (n : nat) (self : betree_Internal_t) (key : u64) (st : state) :
+  result betree_Internal_t
   :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
-    if key s< self.(Betree_internal_pivot)
+    if key s< self.(betree_Internal_pivot)
     then (
-      n1 <- betree_node_lookup_back n0 self.(Betree_internal_left) key st;
-      Return (mkBetree_internal_t self.(Betree_internal_id)
-        self.(Betree_internal_pivot) n1 self.(Betree_internal_right)))
+      n1 <- betree_Node_lookup_back n0 self.(betree_Internal_left) key st;
+      Return (mkbetree_Internal_t self.(betree_Internal_id)
+        self.(betree_Internal_pivot) n1 self.(betree_Internal_right)))
     else (
-      n1 <- betree_node_lookup_back n0 self.(Betree_internal_right) key st;
-      Return (mkBetree_internal_t self.(Betree_internal_id)
-        self.(Betree_internal_pivot) self.(Betree_internal_left) n1))
+      n1 <- betree_Node_lookup_back n0 self.(betree_Internal_right) key st;
+      Return (mkbetree_Internal_t self.(betree_Internal_id)
+        self.(betree_Internal_pivot) self.(betree_Internal_left) n1))
   end
 
 (** [betree_main::betree::Node::{5}::lookup]: forward function *)
-with betree_node_lookup_fwd
-  (n : nat) (self : Betree_node_t) (key : u64) (st : state) :
+with betree_Node_lookup
+  (n : nat) (self : betree_Node_t) (key : u64) (st : state) :
   result (state * (option u64))
   :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
     match self with
-    | BetreeNodeInternal node =>
-      p <- betree_load_internal_node_fwd node.(Betree_internal_id) st;
+    | Betree_Node_Internal node =>
+      p <- betree_load_internal_node node.(betree_Internal_id) st;
       let (st0, msgs) := p in
-      pending <- betree_node_lookup_first_message_for_key_fwd n0 key msgs;
+      pending <- betree_Node_lookup_first_message_for_key n0 key msgs;
       match pending with
-      | BetreeListCons p0 l =>
+      | Betree_List_Cons p0 l =>
         let (k, msg) := p0 in
         if k s<> key
         then (
-          p1 <- betree_internal_lookup_in_children_fwd n0 node key st0;
-          let (st1, opt) := p1 in
+          p1 <- betree_Internal_lookup_in_children n0 node key st0;
+          let (st1, o) := p1 in
           _ <-
-            betree_node_lookup_first_message_for_key_back n0 key msgs
-              (BetreeListCons (k, msg) l);
-          Return (st1, opt))
+            betree_Node_lookup_first_message_for_key_back n0 key msgs
+              (Betree_List_Cons (k, msg) l);
+          Return (st1, o))
         else
           match msg with
-          | BetreeMessageInsert v =>
+          | Betree_Message_Insert v =>
             _ <-
-              betree_node_lookup_first_message_for_key_back n0 key msgs
-                (BetreeListCons (k, BetreeMessageInsert v) l);
+              betree_Node_lookup_first_message_for_key_back n0 key msgs
+                (Betree_List_Cons (k, Betree_Message_Insert v) l);
             Return (st0, Some v)
-          | BetreeMessageDelete =>
+          | Betree_Message_Delete =>
             _ <-
-              betree_node_lookup_first_message_for_key_back n0 key msgs
-                (BetreeListCons (k, BetreeMessageDelete) l);
+              betree_Node_lookup_first_message_for_key_back n0 key msgs
+                (Betree_List_Cons (k, Betree_Message_Delete) l);
             Return (st0, None)
-          | BetreeMessageUpsert ufs =>
-            p1 <- betree_internal_lookup_in_children_fwd n0 node key st0;
+          | Betree_Message_Upsert ufs =>
+            p1 <- betree_Internal_lookup_in_children n0 node key st0;
             let (st1, v) := p1 in
             p2 <-
-              betree_node_apply_upserts_fwd n0 (BetreeListCons (k,
-                BetreeMessageUpsert ufs) l) v key st1;
+              betree_Node_apply_upserts n0 (Betree_List_Cons (k,
+                Betree_Message_Upsert ufs) l) v key st1;
             let (st2, v0) := p2 in
-            node0 <- betree_internal_lookup_in_children_back n0 node key st0;
+            node0 <- betree_Internal_lookup_in_children_back n0 node key st0;
             pending0 <-
-              betree_node_apply_upserts_back n0 (BetreeListCons (k,
-                BetreeMessageUpsert ufs) l) v key st1;
+              betree_Node_apply_upserts_back n0 (Betree_List_Cons (k,
+                Betree_Message_Upsert ufs) l) v key st1;
             msgs0 <-
-              betree_node_lookup_first_message_for_key_back n0 key msgs
+              betree_Node_lookup_first_message_for_key_back n0 key msgs
                 pending0;
             p3 <-
-              betree_store_internal_node_fwd node0.(Betree_internal_id) msgs0
-                st2;
+              betree_store_internal_node node0.(betree_Internal_id) msgs0 st2;
             let (st3, _) := p3 in
             Return (st3, Some v0)
           end
-      | BetreeListNil =>
-        p0 <- betree_internal_lookup_in_children_fwd n0 node key st0;
-        let (st1, opt) := p0 in
+      | Betree_List_Nil =>
+        p0 <- betree_Internal_lookup_in_children n0 node key st0;
+        let (st1, o) := p0 in
         _ <-
-          betree_node_lookup_first_message_for_key_back n0 key msgs
-            BetreeListNil;
-        Return (st1, opt)
+          betree_Node_lookup_first_message_for_key_back n0 key msgs
+            Betree_List_Nil;
+        Return (st1, o)
       end
-    | BetreeNodeLeaf node =>
-      p <- betree_load_leaf_node_fwd node.(Betree_leaf_id) st;
+    | Betree_Node_Leaf node =>
+      p <- betree_load_leaf_node node.(betree_Leaf_id) st;
       let (st0, bindings) := p in
-      opt <- betree_node_lookup_in_bindings_fwd n0 key bindings;
-      Return (st0, opt)
+      o <- betree_Node_lookup_in_bindings n0 key bindings;
+      Return (st0, o)
     end
   end
 
 (** [betree_main::betree::Node::{5}::lookup]: backward function 0 *)
-with betree_node_lookup_back
-  (n : nat) (self : Betree_node_t) (key : u64) (st : state) :
-  result Betree_node_t
+with betree_Node_lookup_back
+  (n : nat) (self : betree_Node_t) (key : u64) (st : state) :
+  result betree_Node_t
   :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
     match self with
-    | BetreeNodeInternal node =>
-      p <- betree_load_internal_node_fwd node.(Betree_internal_id) st;
+    | Betree_Node_Internal node =>
+      p <- betree_load_internal_node node.(betree_Internal_id) st;
       let (st0, msgs) := p in
-      pending <- betree_node_lookup_first_message_for_key_fwd n0 key msgs;
+      pending <- betree_Node_lookup_first_message_for_key n0 key msgs;
       match pending with
-      | BetreeListCons p0 l =>
+      | Betree_List_Cons p0 l =>
         let (k, msg) := p0 in
         if k s<> key
         then (
           _ <-
-            betree_node_lookup_first_message_for_key_back n0 key msgs
-              (BetreeListCons (k, msg) l);
-          node0 <- betree_internal_lookup_in_children_back n0 node key st0;
-          Return (BetreeNodeInternal node0))
+            betree_Node_lookup_first_message_for_key_back n0 key msgs
+              (Betree_List_Cons (k, msg) l);
+          node0 <- betree_Internal_lookup_in_children_back n0 node key st0;
+          Return (Betree_Node_Internal node0))
         else
           match msg with
-          | BetreeMessageInsert v =>
+          | Betree_Message_Insert v =>
             _ <-
-              betree_node_lookup_first_message_for_key_back n0 key msgs
-                (BetreeListCons (k, BetreeMessageInsert v) l);
-            Return (BetreeNodeInternal node)
-          | BetreeMessageDelete =>
+              betree_Node_lookup_first_message_for_key_back n0 key msgs
+                (Betree_List_Cons (k, Betree_Message_Insert v) l);
+            Return (Betree_Node_Internal node)
+          | Betree_Message_Delete =>
             _ <-
-              betree_node_lookup_first_message_for_key_back n0 key msgs
-                (BetreeListCons (k, BetreeMessageDelete) l);
-            Return (BetreeNodeInternal node)
-          | BetreeMessageUpsert ufs =>
-            p1 <- betree_internal_lookup_in_children_fwd n0 node key st0;
+              betree_Node_lookup_first_message_for_key_back n0 key msgs
+                (Betree_List_Cons (k, Betree_Message_Delete) l);
+            Return (Betree_Node_Internal node)
+          | Betree_Message_Upsert ufs =>
+            p1 <- betree_Internal_lookup_in_children n0 node key st0;
             let (st1, v) := p1 in
             p2 <-
-              betree_node_apply_upserts_fwd n0 (BetreeListCons (k,
-                BetreeMessageUpsert ufs) l) v key st1;
+              betree_Node_apply_upserts n0 (Betree_List_Cons (k,
+                Betree_Message_Upsert ufs) l) v key st1;
             let (st2, _) := p2 in
-            node0 <- betree_internal_lookup_in_children_back n0 node key st0;
+            node0 <- betree_Internal_lookup_in_children_back n0 node key st0;
             pending0 <-
-              betree_node_apply_upserts_back n0 (BetreeListCons (k,
-                BetreeMessageUpsert ufs) l) v key st1;
+              betree_Node_apply_upserts_back n0 (Betree_List_Cons (k,
+                Betree_Message_Upsert ufs) l) v key st1;
             msgs0 <-
-              betree_node_lookup_first_message_for_key_back n0 key msgs
+              betree_Node_lookup_first_message_for_key_back n0 key msgs
                 pending0;
             _ <-
-              betree_store_internal_node_fwd node0.(Betree_internal_id) msgs0
-                st2;
-            Return (BetreeNodeInternal node0)
+              betree_store_internal_node node0.(betree_Internal_id) msgs0 st2;
+            Return (Betree_Node_Internal node0)
           end
-      | BetreeListNil =>
+      | Betree_List_Nil =>
         _ <-
-          betree_node_lookup_first_message_for_key_back n0 key msgs
-            BetreeListNil;
-        node0 <- betree_internal_lookup_in_children_back n0 node key st0;
-        Return (BetreeNodeInternal node0)
+          betree_Node_lookup_first_message_for_key_back n0 key msgs
+            Betree_List_Nil;
+        node0 <- betree_Internal_lookup_in_children_back n0 node key st0;
+        Return (Betree_Node_Internal node0)
       end
-    | BetreeNodeLeaf node =>
-      p <- betree_load_leaf_node_fwd node.(Betree_leaf_id) st;
+    | Betree_Node_Leaf node =>
+      p <- betree_load_leaf_node node.(betree_Leaf_id) st;
       let (_, bindings) := p in
-      _ <- betree_node_lookup_in_bindings_fwd n0 key bindings;
-      Return (BetreeNodeLeaf node)
+      _ <- betree_Node_lookup_in_bindings n0 key bindings;
+      Return (Betree_Node_Leaf node)
     end
   end
 .
 
 (** [betree_main::betree::Node::{5}::filter_messages_for_key]: merged forward/backward function
     (there is a single backward function, and the forward function returns ()) *)
-Fixpoint betree_node_filter_messages_for_key_fwd_back
-  (n : nat) (key : u64) (msgs : Betree_list_t (u64 * Betree_message_t)) :
-  result (Betree_list_t (u64 * Betree_message_t))
+Fixpoint betree_Node_filter_messages_for_key
+  (n : nat) (key : u64) (msgs : betree_List_t (u64 * betree_Message_t)) :
+  result (betree_List_t (u64 * betree_Message_t))
   :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
     match msgs with
-    | BetreeListCons p l =>
+    | Betree_List_Cons p l =>
       let (k, m) := p in
       if k s= key
       then (
         msgs0 <-
-          betree_list_pop_front_back (u64 * Betree_message_t) (BetreeListCons
+          betree_List_pop_front_back (u64 * betree_Message_t) (Betree_List_Cons
             (k, m) l);
-        betree_node_filter_messages_for_key_fwd_back n0 key msgs0)
-      else Return (BetreeListCons (k, m) l)
-    | BetreeListNil => Return BetreeListNil
+        betree_Node_filter_messages_for_key n0 key msgs0)
+      else Return (Betree_List_Cons (k, m) l)
+    | Betree_List_Nil => Return Betree_List_Nil
     end
   end
 .
 
 (** [betree_main::betree::Node::{5}::lookup_first_message_after_key]: forward function *)
-Fixpoint betree_node_lookup_first_message_after_key_fwd
-  (n : nat) (key : u64) (msgs : Betree_list_t (u64 * Betree_message_t)) :
-  result (Betree_list_t (u64 * Betree_message_t))
+Fixpoint betree_Node_lookup_first_message_after_key
+  (n : nat) (key : u64) (msgs : betree_List_t (u64 * betree_Message_t)) :
+  result (betree_List_t (u64 * betree_Message_t))
   :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
     match msgs with
-    | BetreeListCons p next_msgs =>
+    | Betree_List_Cons p next_msgs =>
       let (k, m) := p in
       if k s= key
-      then betree_node_lookup_first_message_after_key_fwd n0 key next_msgs
-      else Return (BetreeListCons (k, m) next_msgs)
-    | BetreeListNil => Return BetreeListNil
+      then betree_Node_lookup_first_message_after_key n0 key next_msgs
+      else Return (Betree_List_Cons (k, m) next_msgs)
+    | Betree_List_Nil => Return Betree_List_Nil
     end
   end
 .
 
 (** [betree_main::betree::Node::{5}::lookup_first_message_after_key]: backward function 0 *)
-Fixpoint betree_node_lookup_first_message_after_key_back
-  (n : nat) (key : u64) (msgs : Betree_list_t (u64 * Betree_message_t))
-  (ret : Betree_list_t (u64 * Betree_message_t)) :
-  result (Betree_list_t (u64 * Betree_message_t))
+Fixpoint betree_Node_lookup_first_message_after_key_back
+  (n : nat) (key : u64) (msgs : betree_List_t (u64 * betree_Message_t))
+  (ret : betree_List_t (u64 * betree_Message_t)) :
+  result (betree_List_t (u64 * betree_Message_t))
   :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
     match msgs with
-    | BetreeListCons p next_msgs =>
+    | Betree_List_Cons p next_msgs =>
       let (k, m) := p in
       if k s= key
       then (
         next_msgs0 <-
-          betree_node_lookup_first_message_after_key_back n0 key next_msgs ret;
-        Return (BetreeListCons (k, m) next_msgs0))
+          betree_Node_lookup_first_message_after_key_back n0 key next_msgs ret;
+        Return (Betree_List_Cons (k, m) next_msgs0))
       else Return ret
-    | BetreeListNil => Return ret
+    | Betree_List_Nil => Return ret
     end
   end
 .
 
 (** [betree_main::betree::Node::{5}::apply_to_internal]: merged forward/backward function
     (there is a single backward function, and the forward function returns ()) *)
-Definition betree_node_apply_to_internal_fwd_back
-  (n : nat) (msgs : Betree_list_t (u64 * Betree_message_t)) (key : u64)
-  (new_msg : Betree_message_t) :
-  result (Betree_list_t (u64 * Betree_message_t))
+Definition betree_Node_apply_to_internal
+  (n : nat) (msgs : betree_List_t (u64 * betree_Message_t)) (key : u64)
+  (new_msg : betree_Message_t) :
+  result (betree_List_t (u64 * betree_Message_t))
   :=
-  msgs0 <- betree_node_lookup_first_message_for_key_fwd n key msgs;
-  b <- betree_list_head_has_key_fwd Betree_message_t msgs0 key;
+  msgs0 <- betree_Node_lookup_first_message_for_key n key msgs;
+  b <- betree_List_head_has_key betree_Message_t msgs0 key;
   if b
   then
     match new_msg with
-    | BetreeMessageInsert i =>
-      msgs1 <- betree_node_filter_messages_for_key_fwd_back n key msgs0;
+    | Betree_Message_Insert i =>
+      msgs1 <- betree_Node_filter_messages_for_key n key msgs0;
       msgs2 <-
-        betree_list_push_front_fwd_back (u64 * Betree_message_t) msgs1 (key,
-          BetreeMessageInsert i);
-      betree_node_lookup_first_message_for_key_back n key msgs msgs2
-    | BetreeMessageDelete =>
-      msgs1 <- betree_node_filter_messages_for_key_fwd_back n key msgs0;
+        betree_List_push_front (u64 * betree_Message_t) msgs1 (key,
+          Betree_Message_Insert i);
+      betree_Node_lookup_first_message_for_key_back n key msgs msgs2
+    | Betree_Message_Delete =>
+      msgs1 <- betree_Node_filter_messages_for_key n key msgs0;
       msgs2 <-
-        betree_list_push_front_fwd_back (u64 * Betree_message_t) msgs1 (key,
-          BetreeMessageDelete);
-      betree_node_lookup_first_message_for_key_back n key msgs msgs2
-    | BetreeMessageUpsert s =>
-      p <- betree_list_hd_fwd (u64 * Betree_message_t) msgs0;
+        betree_List_push_front (u64 * betree_Message_t) msgs1 (key,
+          Betree_Message_Delete);
+      betree_Node_lookup_first_message_for_key_back n key msgs msgs2
+    | Betree_Message_Upsert s =>
+      p <- betree_List_hd (u64 * betree_Message_t) msgs0;
       let (_, m) := p in
       match m with
-      | BetreeMessageInsert prev =>
-        v <- betree_upsert_update_fwd (Some prev) s;
-        msgs1 <- betree_list_pop_front_back (u64 * Betree_message_t) msgs0;
+      | Betree_Message_Insert prev =>
+        v <- betree_upsert_update (Some prev) s;
+        msgs1 <- betree_List_pop_front_back (u64 * betree_Message_t) msgs0;
         msgs2 <-
-          betree_list_push_front_fwd_back (u64 * Betree_message_t) msgs1 (key,
-            BetreeMessageInsert v);
-        betree_node_lookup_first_message_for_key_back n key msgs msgs2
-      | BetreeMessageDelete =>
-        v <- betree_upsert_update_fwd None s;
-        msgs1 <- betree_list_pop_front_back (u64 * Betree_message_t) msgs0;
+          betree_List_push_front (u64 * betree_Message_t) msgs1 (key,
+            Betree_Message_Insert v);
+        betree_Node_lookup_first_message_for_key_back n key msgs msgs2
+      | Betree_Message_Delete =>
+        v <- betree_upsert_update None s;
+        msgs1 <- betree_List_pop_front_back (u64 * betree_Message_t) msgs0;
         msgs2 <-
-          betree_list_push_front_fwd_back (u64 * Betree_message_t) msgs1 (key,
-            BetreeMessageInsert v);
-        betree_node_lookup_first_message_for_key_back n key msgs msgs2
-      | BetreeMessageUpsert ufs =>
-        msgs1 <- betree_node_lookup_first_message_after_key_fwd n key msgs0;
+          betree_List_push_front (u64 * betree_Message_t) msgs1 (key,
+            Betree_Message_Insert v);
+        betree_Node_lookup_first_message_for_key_back n key msgs msgs2
+      | Betree_Message_Upsert ufs =>
+        msgs1 <- betree_Node_lookup_first_message_after_key n key msgs0;
         msgs2 <-
-          betree_list_push_front_fwd_back (u64 * Betree_message_t) msgs1 (key,
-            BetreeMessageUpsert s);
+          betree_List_push_front (u64 * betree_Message_t) msgs1 (key,
+            Betree_Message_Upsert s);
         msgs3 <-
-          betree_node_lookup_first_message_after_key_back n key msgs0 msgs2;
-        betree_node_lookup_first_message_for_key_back n key msgs msgs3
+          betree_Node_lookup_first_message_after_key_back n key msgs0 msgs2;
+        betree_Node_lookup_first_message_for_key_back n key msgs msgs3
       end
     end
   else (
     msgs1 <-
-      betree_list_push_front_fwd_back (u64 * Betree_message_t) msgs0 (key,
-        new_msg);
-    betree_node_lookup_first_message_for_key_back n key msgs msgs1)
+      betree_List_push_front (u64 * betree_Message_t) msgs0 (key, new_msg);
+    betree_Node_lookup_first_message_for_key_back n key msgs msgs1)
 .
 
 (** [betree_main::betree::Node::{5}::apply_messages_to_internal]: merged forward/backward function
     (there is a single backward function, and the forward function returns ()) *)
-Fixpoint betree_node_apply_messages_to_internal_fwd_back
-  (n : nat) (msgs : Betree_list_t (u64 * Betree_message_t))
-  (new_msgs : Betree_list_t (u64 * Betree_message_t)) :
-  result (Betree_list_t (u64 * Betree_message_t))
+Fixpoint betree_Node_apply_messages_to_internal
+  (n : nat) (msgs : betree_List_t (u64 * betree_Message_t))
+  (new_msgs : betree_List_t (u64 * betree_Message_t)) :
+  result (betree_List_t (u64 * betree_Message_t))
   :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
     match new_msgs with
-    | BetreeListCons new_msg new_msgs_tl =>
+    | Betree_List_Cons new_msg new_msgs_tl =>
       let (i, m) := new_msg in
-      msgs0 <- betree_node_apply_to_internal_fwd_back n0 msgs i m;
-      betree_node_apply_messages_to_internal_fwd_back n0 msgs0 new_msgs_tl
-    | BetreeListNil => Return msgs
+      msgs0 <- betree_Node_apply_to_internal n0 msgs i m;
+      betree_Node_apply_messages_to_internal n0 msgs0 new_msgs_tl
+    | Betree_List_Nil => Return msgs
     end
   end
 .
 
 (** [betree_main::betree::Node::{5}::lookup_mut_in_bindings]: forward function *)
-Fixpoint betree_node_lookup_mut_in_bindings_fwd
-  (n : nat) (key : u64) (bindings : Betree_list_t (u64 * u64)) :
-  result (Betree_list_t (u64 * u64))
+Fixpoint betree_Node_lookup_mut_in_bindings
+  (n : nat) (key : u64) (bindings : betree_List_t (u64 * u64)) :
+  result (betree_List_t (u64 * u64))
   :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
     match bindings with
-    | BetreeListCons hd tl =>
+    | Betree_List_Cons hd tl =>
       let (i, i0) := hd in
       if i s>= key
-      then Return (BetreeListCons (i, i0) tl)
-      else betree_node_lookup_mut_in_bindings_fwd n0 key tl
-    | BetreeListNil => Return BetreeListNil
+      then Return (Betree_List_Cons (i, i0) tl)
+      else betree_Node_lookup_mut_in_bindings n0 key tl
+    | Betree_List_Nil => Return Betree_List_Nil
     end
   end
 .
 
 (** [betree_main::betree::Node::{5}::lookup_mut_in_bindings]: backward function 0 *)
-Fixpoint betree_node_lookup_mut_in_bindings_back
-  (n : nat) (key : u64) (bindings : Betree_list_t (u64 * u64))
-  (ret : Betree_list_t (u64 * u64)) :
-  result (Betree_list_t (u64 * u64))
+Fixpoint betree_Node_lookup_mut_in_bindings_back
+  (n : nat) (key : u64) (bindings : betree_List_t (u64 * u64))
+  (ret : betree_List_t (u64 * u64)) :
+  result (betree_List_t (u64 * u64))
   :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
     match bindings with
-    | BetreeListCons hd tl =>
+    | Betree_List_Cons hd tl =>
       let (i, i0) := hd in
       if i s>= key
       then Return ret
       else (
-        tl0 <- betree_node_lookup_mut_in_bindings_back n0 key tl ret;
-        Return (BetreeListCons (i, i0) tl0))
-    | BetreeListNil => Return ret
+        tl0 <- betree_Node_lookup_mut_in_bindings_back n0 key tl ret;
+        Return (Betree_List_Cons (i, i0) tl0))
+    | Betree_List_Nil => Return ret
     end
   end
 .
 
 (** [betree_main::betree::Node::{5}::apply_to_leaf]: merged forward/backward function
     (there is a single backward function, and the forward function returns ()) *)
-Definition betree_node_apply_to_leaf_fwd_back
-  (n : nat) (bindings : Betree_list_t (u64 * u64)) (key : u64)
-  (new_msg : Betree_message_t) :
-  result (Betree_list_t (u64 * u64))
+Definition betree_Node_apply_to_leaf
+  (n : nat) (bindings : betree_List_t (u64 * u64)) (key : u64)
+  (new_msg : betree_Message_t) :
+  result (betree_List_t (u64 * u64))
   :=
-  bindings0 <- betree_node_lookup_mut_in_bindings_fwd n key bindings;
-  b <- betree_list_head_has_key_fwd u64 bindings0 key;
+  bindings0 <- betree_Node_lookup_mut_in_bindings n key bindings;
+  b <- betree_List_head_has_key u64 bindings0 key;
   if b
   then (
-    hd <- betree_list_pop_front_fwd (u64 * u64) bindings0;
+    hd <- betree_List_pop_front (u64 * u64) bindings0;
     match new_msg with
-    | BetreeMessageInsert v =>
-      bindings1 <- betree_list_pop_front_back (u64 * u64) bindings0;
-      bindings2 <-
-        betree_list_push_front_fwd_back (u64 * u64) bindings1 (key, v);
-      betree_node_lookup_mut_in_bindings_back n key bindings bindings2
-    | BetreeMessageDelete =>
-      bindings1 <- betree_list_pop_front_back (u64 * u64) bindings0;
-      betree_node_lookup_mut_in_bindings_back n key bindings bindings1
-    | BetreeMessageUpsert s =>
+    | Betree_Message_Insert v =>
+      bindings1 <- betree_List_pop_front_back (u64 * u64) bindings0;
+      bindings2 <- betree_List_push_front (u64 * u64) bindings1 (key, v);
+      betree_Node_lookup_mut_in_bindings_back n key bindings bindings2
+    | Betree_Message_Delete =>
+      bindings1 <- betree_List_pop_front_back (u64 * u64) bindings0;
+      betree_Node_lookup_mut_in_bindings_back n key bindings bindings1
+    | Betree_Message_Upsert s =>
       let (_, i) := hd in
-      v <- betree_upsert_update_fwd (Some i) s;
-      bindings1 <- betree_list_pop_front_back (u64 * u64) bindings0;
-      bindings2 <-
-        betree_list_push_front_fwd_back (u64 * u64) bindings1 (key, v);
-      betree_node_lookup_mut_in_bindings_back n key bindings bindings2
+      v <- betree_upsert_update (Some i) s;
+      bindings1 <- betree_List_pop_front_back (u64 * u64) bindings0;
+      bindings2 <- betree_List_push_front (u64 * u64) bindings1 (key, v);
+      betree_Node_lookup_mut_in_bindings_back n key bindings bindings2
     end)
   else
     match new_msg with
-    | BetreeMessageInsert v =>
-      bindings1 <-
-        betree_list_push_front_fwd_back (u64 * u64) bindings0 (key, v);
-      betree_node_lookup_mut_in_bindings_back n key bindings bindings1
-    | BetreeMessageDelete =>
-      betree_node_lookup_mut_in_bindings_back n key bindings bindings0
-    | BetreeMessageUpsert s =>
-      v <- betree_upsert_update_fwd None s;
-      bindings1 <-
-        betree_list_push_front_fwd_back (u64 * u64) bindings0 (key, v);
-      betree_node_lookup_mut_in_bindings_back n key bindings bindings1
+    | Betree_Message_Insert v =>
+      bindings1 <- betree_List_push_front (u64 * u64) bindings0 (key, v);
+      betree_Node_lookup_mut_in_bindings_back n key bindings bindings1
+    | Betree_Message_Delete =>
+      betree_Node_lookup_mut_in_bindings_back n key bindings bindings0
+    | Betree_Message_Upsert s =>
+      v <- betree_upsert_update None s;
+      bindings1 <- betree_List_push_front (u64 * u64) bindings0 (key, v);
+      betree_Node_lookup_mut_in_bindings_back n key bindings bindings1
     end
 .
 
 (** [betree_main::betree::Node::{5}::apply_messages_to_leaf]: merged forward/backward function
     (there is a single backward function, and the forward function returns ()) *)
-Fixpoint betree_node_apply_messages_to_leaf_fwd_back
-  (n : nat) (bindings : Betree_list_t (u64 * u64))
-  (new_msgs : Betree_list_t (u64 * Betree_message_t)) :
-  result (Betree_list_t (u64 * u64))
+Fixpoint betree_Node_apply_messages_to_leaf
+  (n : nat) (bindings : betree_List_t (u64 * u64))
+  (new_msgs : betree_List_t (u64 * betree_Message_t)) :
+  result (betree_List_t (u64 * u64))
   :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
     match new_msgs with
-    | BetreeListCons new_msg new_msgs_tl =>
+    | Betree_List_Cons new_msg new_msgs_tl =>
       let (i, m) := new_msg in
-      bindings0 <- betree_node_apply_to_leaf_fwd_back n0 bindings i m;
-      betree_node_apply_messages_to_leaf_fwd_back n0 bindings0 new_msgs_tl
-    | BetreeListNil => Return bindings
+      bindings0 <- betree_Node_apply_to_leaf n0 bindings i m;
+      betree_Node_apply_messages_to_leaf n0 bindings0 new_msgs_tl
+    | Betree_List_Nil => Return bindings
     end
   end
 .
 
 (** [betree_main::betree::Internal::{4}::flush]: forward function *)
-Fixpoint betree_internal_flush_fwd
-  (n : nat) (self : Betree_internal_t) (params : Betree_params_t)
-  (node_id_cnt : Betree_node_id_counter_t)
-  (content : Betree_list_t (u64 * Betree_message_t)) (st : state) :
-  result (state * (Betree_list_t (u64 * Betree_message_t)))
+Fixpoint betree_Internal_flush
+  (n : nat) (self : betree_Internal_t) (params : betree_Params_t)
+  (node_id_cnt : betree_NodeIdCounter_t)
+  (content : betree_List_t (u64 * betree_Message_t)) (st : state) :
+  result (state * (betree_List_t (u64 * betree_Message_t)))
   :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
     p <-
-      betree_list_partition_at_pivot_fwd Betree_message_t n0 content
-        self.(Betree_internal_pivot);
+      betree_List_partition_at_pivot betree_Message_t n0 content
+        self.(betree_Internal_pivot);
     let (msgs_left, msgs_right) := p in
-    len_left <- betree_list_len_fwd (u64 * Betree_message_t) n0 msgs_left;
-    if len_left s>= params.(Betree_params_min_flush_size)
+    len_left <- betree_List_len (u64 * betree_Message_t) n0 msgs_left;
+    if len_left s>= params.(betree_Params_min_flush_size)
     then (
       p0 <-
-        betree_node_apply_messages_fwd n0 self.(Betree_internal_left) params
+        betree_Node_apply_messages n0 self.(betree_Internal_left) params
           node_id_cnt msgs_left st;
       let (st0, _) := p0 in
       p1 <-
-        betree_node_apply_messages_back n0 self.(Betree_internal_left) params
+        betree_Node_apply_messages_back n0 self.(betree_Internal_left) params
           node_id_cnt msgs_left st;
       let (_, node_id_cnt0) := p1 in
-      len_right <- betree_list_len_fwd (u64 * Betree_message_t) n0 msgs_right;
-      if len_right s>= params.(Betree_params_min_flush_size)
+      len_right <- betree_List_len (u64 * betree_Message_t) n0 msgs_right;
+      if len_right s>= params.(betree_Params_min_flush_size)
       then (
         p2 <-
-          betree_node_apply_messages_fwd n0 self.(Betree_internal_right) params
+          betree_Node_apply_messages n0 self.(betree_Internal_right) params
             node_id_cnt0 msgs_right st0;
         let (st1, _) := p2 in
         _ <-
-          betree_node_apply_messages_back n0 self.(Betree_internal_right)
+          betree_Node_apply_messages_back n0 self.(betree_Internal_right)
             params node_id_cnt0 msgs_right st0;
-        Return (st1, BetreeListNil))
+        Return (st1, Betree_List_Nil))
       else Return (st0, msgs_right))
     else (
       p0 <-
-        betree_node_apply_messages_fwd n0 self.(Betree_internal_right) params
+        betree_Node_apply_messages n0 self.(betree_Internal_right) params
           node_id_cnt msgs_right st;
       let (st0, _) := p0 in
       _ <-
-        betree_node_apply_messages_back n0 self.(Betree_internal_right) params
+        betree_Node_apply_messages_back n0 self.(betree_Internal_right) params
           node_id_cnt msgs_right st;
       Return (st0, msgs_left))
   end
 
 (** [betree_main::betree::Internal::{4}::flush]: backward function 0 *)
-with betree_internal_flush_back
-  (n : nat) (self : Betree_internal_t) (params : Betree_params_t)
-  (node_id_cnt : Betree_node_id_counter_t)
-  (content : Betree_list_t (u64 * Betree_message_t)) (st : state) :
-  result (Betree_internal_t * Betree_node_id_counter_t)
+with betree_Internal_flush_back
+  (n : nat) (self : betree_Internal_t) (params : betree_Params_t)
+  (node_id_cnt : betree_NodeIdCounter_t)
+  (content : betree_List_t (u64 * betree_Message_t)) (st : state) :
+  result (betree_Internal_t * betree_NodeIdCounter_t)
   :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
     p <-
-      betree_list_partition_at_pivot_fwd Betree_message_t n0 content
-        self.(Betree_internal_pivot);
+      betree_List_partition_at_pivot betree_Message_t n0 content
+        self.(betree_Internal_pivot);
     let (msgs_left, msgs_right) := p in
-    len_left <- betree_list_len_fwd (u64 * Betree_message_t) n0 msgs_left;
-    if len_left s>= params.(Betree_params_min_flush_size)
+    len_left <- betree_List_len (u64 * betree_Message_t) n0 msgs_left;
+    if len_left s>= params.(betree_Params_min_flush_size)
     then (
       p0 <-
-        betree_node_apply_messages_fwd n0 self.(Betree_internal_left) params
+        betree_Node_apply_messages n0 self.(betree_Internal_left) params
           node_id_cnt msgs_left st;
       let (st0, _) := p0 in
       p1 <-
-        betree_node_apply_messages_back n0 self.(Betree_internal_left) params
+        betree_Node_apply_messages_back n0 self.(betree_Internal_left) params
           node_id_cnt msgs_left st;
       let (n1, node_id_cnt0) := p1 in
-      len_right <- betree_list_len_fwd (u64 * Betree_message_t) n0 msgs_right;
-      if len_right s>= params.(Betree_params_min_flush_size)
+      len_right <- betree_List_len (u64 * betree_Message_t) n0 msgs_right;
+      if len_right s>= params.(betree_Params_min_flush_size)
       then (
         p2 <-
-          betree_node_apply_messages_back n0 self.(Betree_internal_right)
+          betree_Node_apply_messages_back n0 self.(betree_Internal_right)
             params node_id_cnt0 msgs_right st0;
         let (n2, node_id_cnt1) := p2 in
-        Return (mkBetree_internal_t self.(Betree_internal_id)
-          self.(Betree_internal_pivot) n1 n2, node_id_cnt1))
+        Return (mkbetree_Internal_t self.(betree_Internal_id)
+          self.(betree_Internal_pivot) n1 n2, node_id_cnt1))
       else
-        Return (mkBetree_internal_t self.(Betree_internal_id)
-          self.(Betree_internal_pivot) n1 self.(Betree_internal_right),
+        Return (mkbetree_Internal_t self.(betree_Internal_id)
+          self.(betree_Internal_pivot) n1 self.(betree_Internal_right),
           node_id_cnt0))
     else (
       p0 <-
-        betree_node_apply_messages_back n0 self.(Betree_internal_right) params
+        betree_Node_apply_messages_back n0 self.(betree_Internal_right) params
           node_id_cnt msgs_right st;
       let (n1, node_id_cnt0) := p0 in
-      Return (mkBetree_internal_t self.(Betree_internal_id)
-        self.(Betree_internal_pivot) self.(Betree_internal_left) n1,
+      Return (mkbetree_Internal_t self.(betree_Internal_id)
+        self.(betree_Internal_pivot) self.(betree_Internal_left) n1,
         node_id_cnt0))
   end
 
 (** [betree_main::betree::Node::{5}::apply_messages]: forward function *)
-with betree_node_apply_messages_fwd
-  (n : nat) (self : Betree_node_t) (params : Betree_params_t)
-  (node_id_cnt : Betree_node_id_counter_t)
-  (msgs : Betree_list_t (u64 * Betree_message_t)) (st : state) :
+with betree_Node_apply_messages
+  (n : nat) (self : betree_Node_t) (params : betree_Params_t)
+  (node_id_cnt : betree_NodeIdCounter_t)
+  (msgs : betree_List_t (u64 * betree_Message_t)) (st : state) :
   result (state * unit)
   :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
     match self with
-    | BetreeNodeInternal node =>
-      p <- betree_load_internal_node_fwd node.(Betree_internal_id) st;
+    | Betree_Node_Internal node =>
+      p <- betree_load_internal_node node.(betree_Internal_id) st;
       let (st0, content) := p in
-      content0 <-
-        betree_node_apply_messages_to_internal_fwd_back n0 content msgs;
-      num_msgs <- betree_list_len_fwd (u64 * Betree_message_t) n0 content0;
-      if num_msgs s>= params.(Betree_params_min_flush_size)
+      content0 <- betree_Node_apply_messages_to_internal n0 content msgs;
+      num_msgs <- betree_List_len (u64 * betree_Message_t) n0 content0;
+      if num_msgs s>= params.(betree_Params_min_flush_size)
       then (
-        p0 <-
-          betree_internal_flush_fwd n0 node params node_id_cnt content0 st0;
+        p0 <- betree_Internal_flush n0 node params node_id_cnt content0 st0;
         let (st1, content1) := p0 in
         p1 <-
-          betree_internal_flush_back n0 node params node_id_cnt content0 st0;
+          betree_Internal_flush_back n0 node params node_id_cnt content0 st0;
         let (node0, _) := p1 in
         p2 <-
-          betree_store_internal_node_fwd node0.(Betree_internal_id) content1
-            st1;
+          betree_store_internal_node node0.(betree_Internal_id) content1 st1;
         let (st2, _) := p2 in
         Return (st2, tt))
       else (
         p0 <-
-          betree_store_internal_node_fwd node.(Betree_internal_id) content0 st0;
+          betree_store_internal_node node.(betree_Internal_id) content0 st0;
         let (st1, _) := p0 in
         Return (st1, tt))
-    | BetreeNodeLeaf node =>
-      p <- betree_load_leaf_node_fwd node.(Betree_leaf_id) st;
+    | Betree_Node_Leaf node =>
+      p <- betree_load_leaf_node node.(betree_Leaf_id) st;
       let (st0, content) := p in
-      content0 <- betree_node_apply_messages_to_leaf_fwd_back n0 content msgs;
-      len <- betree_list_len_fwd (u64 * u64) n0 content0;
-      i <- u64_mul 2%u64 params.(Betree_params_split_size);
+      content0 <- betree_Node_apply_messages_to_leaf n0 content msgs;
+      len <- betree_List_len (u64 * u64) n0 content0;
+      i <- u64_mul 2%u64 params.(betree_Params_split_size);
       if len s>= i
       then (
-        p0 <- betree_leaf_split_fwd n0 node content0 params node_id_cnt st0;
+        p0 <- betree_Leaf_split n0 node content0 params node_id_cnt st0;
         let (st1, _) := p0 in
-        p1 <-
-          betree_store_leaf_node_fwd node.(Betree_leaf_id) BetreeListNil st1;
+        p1 <- betree_store_leaf_node node.(betree_Leaf_id) Betree_List_Nil st1;
         let (st2, _) := p1 in
         Return (st2, tt))
       else (
-        p0 <- betree_store_leaf_node_fwd node.(Betree_leaf_id) content0 st0;
+        p0 <- betree_store_leaf_node node.(betree_Leaf_id) content0 st0;
         let (st1, _) := p0 in
         Return (st1, tt))
     end
   end
 
 (** [betree_main::betree::Node::{5}::apply_messages]: backward function 0 *)
-with betree_node_apply_messages_back
-  (n : nat) (self : Betree_node_t) (params : Betree_params_t)
-  (node_id_cnt : Betree_node_id_counter_t)
-  (msgs : Betree_list_t (u64 * Betree_message_t)) (st : state) :
-  result (Betree_node_t * Betree_node_id_counter_t)
+with betree_Node_apply_messages_back
+  (n : nat) (self : betree_Node_t) (params : betree_Params_t)
+  (node_id_cnt : betree_NodeIdCounter_t)
+  (msgs : betree_List_t (u64 * betree_Message_t)) (st : state) :
+  result (betree_Node_t * betree_NodeIdCounter_t)
   :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
     match self with
-    | BetreeNodeInternal node =>
-      p <- betree_load_internal_node_fwd node.(Betree_internal_id) st;
+    | Betree_Node_Internal node =>
+      p <- betree_load_internal_node node.(betree_Internal_id) st;
       let (st0, content) := p in
-      content0 <-
-        betree_node_apply_messages_to_internal_fwd_back n0 content msgs;
-      num_msgs <- betree_list_len_fwd (u64 * Betree_message_t) n0 content0;
-      if num_msgs s>= params.(Betree_params_min_flush_size)
+      content0 <- betree_Node_apply_messages_to_internal n0 content msgs;
+      num_msgs <- betree_List_len (u64 * betree_Message_t) n0 content0;
+      if num_msgs s>= params.(betree_Params_min_flush_size)
       then (
-        p0 <-
-          betree_internal_flush_fwd n0 node params node_id_cnt content0 st0;
+        p0 <- betree_Internal_flush n0 node params node_id_cnt content0 st0;
         let (st1, content1) := p0 in
         p1 <-
-          betree_internal_flush_back n0 node params node_id_cnt content0 st0;
+          betree_Internal_flush_back n0 node params node_id_cnt content0 st0;
         let (node0, node_id_cnt0) := p1 in
         _ <-
-          betree_store_internal_node_fwd node0.(Betree_internal_id) content1
-            st1;
-        Return (BetreeNodeInternal node0, node_id_cnt0))
+          betree_store_internal_node node0.(betree_Internal_id) content1 st1;
+        Return (Betree_Node_Internal node0, node_id_cnt0))
       else (
-        _ <-
-          betree_store_internal_node_fwd node.(Betree_internal_id) content0 st0;
-        Return (BetreeNodeInternal node, node_id_cnt))
-    | BetreeNodeLeaf node =>
-      p <- betree_load_leaf_node_fwd node.(Betree_leaf_id) st;
+        _ <- betree_store_internal_node node.(betree_Internal_id) content0 st0;
+        Return (Betree_Node_Internal node, node_id_cnt))
+    | Betree_Node_Leaf node =>
+      p <- betree_load_leaf_node node.(betree_Leaf_id) st;
       let (st0, content) := p in
-      content0 <- betree_node_apply_messages_to_leaf_fwd_back n0 content msgs;
-      len <- betree_list_len_fwd (u64 * u64) n0 content0;
-      i <- u64_mul 2%u64 params.(Betree_params_split_size);
+      content0 <- betree_Node_apply_messages_to_leaf n0 content msgs;
+      len <- betree_List_len (u64 * u64) n0 content0;
+      i <- u64_mul 2%u64 params.(betree_Params_split_size);
       if len s>= i
       then (
-        p0 <- betree_leaf_split_fwd n0 node content0 params node_id_cnt st0;
+        p0 <- betree_Leaf_split n0 node content0 params node_id_cnt st0;
         let (st1, new_node) := p0 in
-        _ <-
-          betree_store_leaf_node_fwd node.(Betree_leaf_id) BetreeListNil st1;
+        _ <- betree_store_leaf_node node.(betree_Leaf_id) Betree_List_Nil st1;
         node_id_cnt0 <-
-          betree_leaf_split_back n0 node content0 params node_id_cnt st0;
-        Return (BetreeNodeInternal new_node, node_id_cnt0))
+          betree_Leaf_split_back n0 node content0 params node_id_cnt st0;
+        Return (Betree_Node_Internal new_node, node_id_cnt0))
       else (
-        _ <- betree_store_leaf_node_fwd node.(Betree_leaf_id) content0 st0;
-        Return (BetreeNodeLeaf
-          {| Betree_leaf_id := node.(Betree_leaf_id); Betree_leaf_size := len
+        _ <- betree_store_leaf_node node.(betree_Leaf_id) content0 st0;
+        Return (Betree_Node_Leaf
+          {| betree_Leaf_id := node.(betree_Leaf_id); betree_Leaf_size := len
           |}, node_id_cnt))
     end
   end
 .
 
 (** [betree_main::betree::Node::{5}::apply]: forward function *)
-Definition betree_node_apply_fwd
-  (n : nat) (self : Betree_node_t) (params : Betree_params_t)
-  (node_id_cnt : Betree_node_id_counter_t) (key : u64)
-  (new_msg : Betree_message_t) (st : state) :
+Definition betree_Node_apply
+  (n : nat) (self : betree_Node_t) (params : betree_Params_t)
+  (node_id_cnt : betree_NodeIdCounter_t) (key : u64)
+  (new_msg : betree_Message_t) (st : state) :
   result (state * unit)
   :=
-  let l := BetreeListNil in
+  let l := Betree_List_Nil in
   p <-
-    betree_node_apply_messages_fwd n self params node_id_cnt (BetreeListCons
+    betree_Node_apply_messages n self params node_id_cnt (Betree_List_Cons
       (key, new_msg) l) st;
   let (st0, _) := p in
   _ <-
-    betree_node_apply_messages_back n self params node_id_cnt (BetreeListCons
+    betree_Node_apply_messages_back n self params node_id_cnt (Betree_List_Cons
       (key, new_msg) l) st;
   Return (st0, tt)
 .
 
 (** [betree_main::betree::Node::{5}::apply]: backward function 0 *)
-Definition betree_node_apply_back
-  (n : nat) (self : Betree_node_t) (params : Betree_params_t)
-  (node_id_cnt : Betree_node_id_counter_t) (key : u64)
-  (new_msg : Betree_message_t) (st : state) :
-  result (Betree_node_t * Betree_node_id_counter_t)
+Definition betree_Node_apply_back
+  (n : nat) (self : betree_Node_t) (params : betree_Params_t)
+  (node_id_cnt : betree_NodeIdCounter_t) (key : u64)
+  (new_msg : betree_Message_t) (st : state) :
+  result (betree_Node_t * betree_NodeIdCounter_t)
   :=
-  let l := BetreeListNil in
-  betree_node_apply_messages_back n self params node_id_cnt (BetreeListCons
+  let l := Betree_List_Nil in
+  betree_Node_apply_messages_back n self params node_id_cnt (Betree_List_Cons
     (key, new_msg) l) st
 .
 
 (** [betree_main::betree::BeTree::{6}::new]: forward function *)
-Definition betree_be_tree_new_fwd
+Definition betree_BeTree_new
   (min_flush_size : u64) (split_size : u64) (st : state) :
-  result (state * Betree_be_tree_t)
+  result (state * betree_BeTree_t)
   :=
-  node_id_cnt <- betree_node_id_counter_new_fwd;
-  id <- betree_node_id_counter_fresh_id_fwd node_id_cnt;
-  p <- betree_store_leaf_node_fwd id BetreeListNil st;
+  node_id_cnt <- betree_NodeIdCounter_new;
+  id <- betree_NodeIdCounter_fresh_id node_id_cnt;
+  p <- betree_store_leaf_node id Betree_List_Nil st;
   let (st0, _) := p in
-  node_id_cnt0 <- betree_node_id_counter_fresh_id_back node_id_cnt;
+  node_id_cnt0 <- betree_NodeIdCounter_fresh_id_back node_id_cnt;
   Return (st0,
     {|
-      Betree_be_tree_params :=
+      betree_BeTree_params :=
         {|
-          Betree_params_min_flush_size := min_flush_size;
-          Betree_params_split_size := split_size
+          betree_Params_min_flush_size := min_flush_size;
+          betree_Params_split_size := split_size
         |};
-      Betree_be_tree_node_id_cnt := node_id_cnt0;
-      Betree_be_tree_root :=
-        (BetreeNodeLeaf {| Betree_leaf_id := id; Betree_leaf_size := 0%u64 |})
+      betree_BeTree_node_id_cnt := node_id_cnt0;
+      betree_BeTree_root :=
+        (Betree_Node_Leaf
+          {| betree_Leaf_id := id; betree_Leaf_size := 0%u64 |})
     |})
 .
 
 (** [betree_main::betree::BeTree::{6}::apply]: forward function *)
-Definition betree_be_tree_apply_fwd
-  (n : nat) (self : Betree_be_tree_t) (key : u64) (msg : Betree_message_t)
+Definition betree_BeTree_apply
+  (n : nat) (self : betree_BeTree_t) (key : u64) (msg : betree_Message_t)
   (st : state) :
   result (state * unit)
   :=
   p <-
-    betree_node_apply_fwd n self.(Betree_be_tree_root)
-      self.(Betree_be_tree_params) self.(Betree_be_tree_node_id_cnt) key msg st;
+    betree_Node_apply n self.(betree_BeTree_root) self.(betree_BeTree_params)
+      self.(betree_BeTree_node_id_cnt) key msg st;
   let (st0, _) := p in
   _ <-
-    betree_node_apply_back n self.(Betree_be_tree_root)
-      self.(Betree_be_tree_params) self.(Betree_be_tree_node_id_cnt) key msg st;
+    betree_Node_apply_back n self.(betree_BeTree_root)
+      self.(betree_BeTree_params) self.(betree_BeTree_node_id_cnt) key msg st;
   Return (st0, tt)
 .
 
 (** [betree_main::betree::BeTree::{6}::apply]: backward function 0 *)
-Definition betree_be_tree_apply_back
-  (n : nat) (self : Betree_be_tree_t) (key : u64) (msg : Betree_message_t)
+Definition betree_BeTree_apply_back
+  (n : nat) (self : betree_BeTree_t) (key : u64) (msg : betree_Message_t)
   (st : state) :
-  result Betree_be_tree_t
+  result betree_BeTree_t
   :=
   p <-
-    betree_node_apply_back n self.(Betree_be_tree_root)
-      self.(Betree_be_tree_params) self.(Betree_be_tree_node_id_cnt) key msg st;
+    betree_Node_apply_back n self.(betree_BeTree_root)
+      self.(betree_BeTree_params) self.(betree_BeTree_node_id_cnt) key msg st;
   let (n0, nic) := p in
   Return
     {|
-      Betree_be_tree_params := self.(Betree_be_tree_params);
-      Betree_be_tree_node_id_cnt := nic;
-      Betree_be_tree_root := n0
+      betree_BeTree_params := self.(betree_BeTree_params);
+      betree_BeTree_node_id_cnt := nic;
+      betree_BeTree_root := n0
     |}
 .
 
 (** [betree_main::betree::BeTree::{6}::insert]: forward function *)
-Definition betree_be_tree_insert_fwd
-  (n : nat) (self : Betree_be_tree_t) (key : u64) (value : u64) (st : state) :
+Definition betree_BeTree_insert
+  (n : nat) (self : betree_BeTree_t) (key : u64) (value : u64) (st : state) :
   result (state * unit)
   :=
-  p <- betree_be_tree_apply_fwd n self key (BetreeMessageInsert value) st;
+  p <- betree_BeTree_apply n self key (Betree_Message_Insert value) st;
   let (st0, _) := p in
-  _ <- betree_be_tree_apply_back n self key (BetreeMessageInsert value) st;
+  _ <- betree_BeTree_apply_back n self key (Betree_Message_Insert value) st;
   Return (st0, tt)
 .
 
 (** [betree_main::betree::BeTree::{6}::insert]: backward function 0 *)
-Definition betree_be_tree_insert_back
-  (n : nat) (self : Betree_be_tree_t) (key : u64) (value : u64) (st : state) :
-  result Betree_be_tree_t
+Definition betree_BeTree_insert_back
+  (n : nat) (self : betree_BeTree_t) (key : u64) (value : u64) (st : state) :
+  result betree_BeTree_t
   :=
-  betree_be_tree_apply_back n self key (BetreeMessageInsert value) st
+  betree_BeTree_apply_back n self key (Betree_Message_Insert value) st
 .
 
 (** [betree_main::betree::BeTree::{6}::delete]: forward function *)
-Definition betree_be_tree_delete_fwd
-  (n : nat) (self : Betree_be_tree_t) (key : u64) (st : state) :
+Definition betree_BeTree_delete
+  (n : nat) (self : betree_BeTree_t) (key : u64) (st : state) :
   result (state * unit)
   :=
-  p <- betree_be_tree_apply_fwd n self key BetreeMessageDelete st;
+  p <- betree_BeTree_apply n self key Betree_Message_Delete st;
   let (st0, _) := p in
-  _ <- betree_be_tree_apply_back n self key BetreeMessageDelete st;
+  _ <- betree_BeTree_apply_back n self key Betree_Message_Delete st;
   Return (st0, tt)
 .
 
 (** [betree_main::betree::BeTree::{6}::delete]: backward function 0 *)
-Definition betree_be_tree_delete_back
-  (n : nat) (self : Betree_be_tree_t) (key : u64) (st : state) :
-  result Betree_be_tree_t
+Definition betree_BeTree_delete_back
+  (n : nat) (self : betree_BeTree_t) (key : u64) (st : state) :
+  result betree_BeTree_t
   :=
-  betree_be_tree_apply_back n self key BetreeMessageDelete st
+  betree_BeTree_apply_back n self key Betree_Message_Delete st
 .
 
 (** [betree_main::betree::BeTree::{6}::upsert]: forward function *)
-Definition betree_be_tree_upsert_fwd
-  (n : nat) (self : Betree_be_tree_t) (key : u64)
-  (upd : Betree_upsert_fun_state_t) (st : state) :
+Definition betree_BeTree_upsert
+  (n : nat) (self : betree_BeTree_t) (key : u64)
+  (upd : betree_UpsertFunState_t) (st : state) :
   result (state * unit)
   :=
-  p <- betree_be_tree_apply_fwd n self key (BetreeMessageUpsert upd) st;
+  p <- betree_BeTree_apply n self key (Betree_Message_Upsert upd) st;
   let (st0, _) := p in
-  _ <- betree_be_tree_apply_back n self key (BetreeMessageUpsert upd) st;
+  _ <- betree_BeTree_apply_back n self key (Betree_Message_Upsert upd) st;
   Return (st0, tt)
 .
 
 (** [betree_main::betree::BeTree::{6}::upsert]: backward function 0 *)
-Definition betree_be_tree_upsert_back
-  (n : nat) (self : Betree_be_tree_t) (key : u64)
-  (upd : Betree_upsert_fun_state_t) (st : state) :
-  result Betree_be_tree_t
+Definition betree_BeTree_upsert_back
+  (n : nat) (self : betree_BeTree_t) (key : u64)
+  (upd : betree_UpsertFunState_t) (st : state) :
+  result betree_BeTree_t
   :=
-  betree_be_tree_apply_back n self key (BetreeMessageUpsert upd) st
+  betree_BeTree_apply_back n self key (Betree_Message_Upsert upd) st
 .
 
 (** [betree_main::betree::BeTree::{6}::lookup]: forward function *)
-Definition betree_be_tree_lookup_fwd
-  (n : nat) (self : Betree_be_tree_t) (key : u64) (st : state) :
+Definition betree_BeTree_lookup
+  (n : nat) (self : betree_BeTree_t) (key : u64) (st : state) :
   result (state * (option u64))
   :=
-  betree_node_lookup_fwd n self.(Betree_be_tree_root) key st
+  betree_Node_lookup n self.(betree_BeTree_root) key st
 .
 
 (** [betree_main::betree::BeTree::{6}::lookup]: backward function 0 *)
-Definition betree_be_tree_lookup_back
-  (n : nat) (self : Betree_be_tree_t) (key : u64) (st : state) :
-  result Betree_be_tree_t
+Definition betree_BeTree_lookup_back
+  (n : nat) (self : betree_BeTree_t) (key : u64) (st : state) :
+  result betree_BeTree_t
   :=
-  n0 <- betree_node_lookup_back n self.(Betree_be_tree_root) key st;
+  n0 <- betree_Node_lookup_back n self.(betree_BeTree_root) key st;
   Return
     {|
-      Betree_be_tree_params := self.(Betree_be_tree_params);
-      Betree_be_tree_node_id_cnt := self.(Betree_be_tree_node_id_cnt);
-      Betree_be_tree_root := n0
+      betree_BeTree_params := self.(betree_BeTree_params);
+      betree_BeTree_node_id_cnt := self.(betree_BeTree_node_id_cnt);
+      betree_BeTree_root := n0
     |}
 .
 
 (** [betree_main::main]: forward function *)
-Definition main_fwd : result unit :=
+Definition main : result unit :=
   Return tt.
 
 (** Unit test for [betree_main::main] *)
-Check (main_fwd )%return.
+Check (main )%return.
 
 End BetreeMain_Funs .
diff --git a/tests/coq/betree/BetreeMain_Opaque.v b/tests/coq/betree/BetreeMain_Opaque.v
index ecd81b9d..eade90de 100644
--- a/tests/coq/betree/BetreeMain_Opaque.v
+++ b/tests/coq/betree/BetreeMain_Opaque.v
@@ -11,29 +11,29 @@ Import BetreeMain_Types.
 Module BetreeMain_Opaque.
 
 (** [betree_main::betree_utils::load_internal_node]: forward function *)
-Axiom betree_utils_load_internal_node_fwd
-  : u64 -> state -> result (state * (Betree_list_t (u64 * Betree_message_t)))
+Axiom betree_utils_load_internal_node
+  : u64 -> state -> result (state * (betree_List_t (u64 * betree_Message_t)))
 .
 
 (** [betree_main::betree_utils::store_internal_node]: forward function *)
-Axiom betree_utils_store_internal_node_fwd
+Axiom betree_utils_store_internal_node
   :
-  u64 -> Betree_list_t (u64 * Betree_message_t) -> state -> result (state *
+  u64 -> betree_List_t (u64 * betree_Message_t) -> state -> result (state *
     unit)
 .
 
 (** [betree_main::betree_utils::load_leaf_node]: forward function *)
-Axiom betree_utils_load_leaf_node_fwd
-  : u64 -> state -> result (state * (Betree_list_t (u64 * u64)))
+Axiom betree_utils_load_leaf_node
+  : u64 -> state -> result (state * (betree_List_t (u64 * u64)))
 .
 
 (** [betree_main::betree_utils::store_leaf_node]: forward function *)
-Axiom betree_utils_store_leaf_node_fwd
-  : u64 -> Betree_list_t (u64 * u64) -> state -> result (state * unit)
+Axiom betree_utils_store_leaf_node
+  : u64 -> betree_List_t (u64 * u64) -> state -> result (state * unit)
 .
 
 (** [core::option::Option::{0}::unwrap]: forward function *)
-Axiom core_option_option_unwrap_fwd :
+Axiom core_option_Option_unwrap :
   forall(T : Type), option T -> state -> result (state * T)
 .
 
diff --git a/tests/coq/betree/BetreeMain_Types.v b/tests/coq/betree/BetreeMain_Types.v
index 4a4e75aa..933a670c 100644
--- a/tests/coq/betree/BetreeMain_Types.v
+++ b/tests/coq/betree/BetreeMain_Types.v
@@ -9,98 +9,98 @@ Local Open Scope Primitives_scope.
 Module BetreeMain_Types.
 
 (** [betree_main::betree::List] *)
-Inductive Betree_list_t (T : Type) :=
-| BetreeListCons : T -> Betree_list_t T -> Betree_list_t T
-| BetreeListNil : Betree_list_t T
+Inductive betree_List_t (T : Type) :=
+| Betree_List_Cons : T -> betree_List_t T -> betree_List_t T
+| Betree_List_Nil : betree_List_t T
 .
 
-Arguments BetreeListCons {T} _ _.
-Arguments BetreeListNil {T}.
+Arguments Betree_List_Cons { _ }.
+Arguments Betree_List_Nil { _ }.
 
 (** [betree_main::betree::UpsertFunState] *)
-Inductive Betree_upsert_fun_state_t :=
-| BetreeUpsertFunStateAdd : u64 -> Betree_upsert_fun_state_t
-| BetreeUpsertFunStateSub : u64 -> Betree_upsert_fun_state_t
+Inductive betree_UpsertFunState_t :=
+| Betree_UpsertFunState_Add : u64 -> betree_UpsertFunState_t
+| Betree_UpsertFunState_Sub : u64 -> betree_UpsertFunState_t
 .
 
 (** [betree_main::betree::Message] *)
-Inductive Betree_message_t :=
-| BetreeMessageInsert : u64 -> Betree_message_t
-| BetreeMessageDelete : Betree_message_t
-| BetreeMessageUpsert : Betree_upsert_fun_state_t -> Betree_message_t
+Inductive betree_Message_t :=
+| Betree_Message_Insert : u64 -> betree_Message_t
+| Betree_Message_Delete : betree_Message_t
+| Betree_Message_Upsert : betree_UpsertFunState_t -> betree_Message_t
 .
 
 (** [betree_main::betree::Leaf] *)
-Record Betree_leaf_t :=
-mkBetree_leaf_t {
-  Betree_leaf_id : u64; Betree_leaf_size : u64;
+Record betree_Leaf_t :=
+mkbetree_Leaf_t {
+  betree_Leaf_id : u64; betree_Leaf_size : u64;
 }
 .
 
 (** [betree_main::betree::Internal] *)
-Inductive Betree_internal_t :=
-| mkBetree_internal_t :
+Inductive betree_Internal_t :=
+| mkbetree_Internal_t :
   u64 ->
   u64 ->
-  Betree_node_t ->
-  Betree_node_t ->
-  Betree_internal_t
+  betree_Node_t ->
+  betree_Node_t ->
+  betree_Internal_t
 
 (** [betree_main::betree::Node] *)
-with Betree_node_t :=
-| BetreeNodeInternal : Betree_internal_t -> Betree_node_t
-| BetreeNodeLeaf : Betree_leaf_t -> Betree_node_t
+with betree_Node_t :=
+| Betree_Node_Internal : betree_Internal_t -> betree_Node_t
+| Betree_Node_Leaf : betree_Leaf_t -> betree_Node_t
 .
 
-Definition Betree_internal_id (x : Betree_internal_t) :=
-  match x with | mkBetree_internal_t x0 _ _ _ => x0 end
+Definition betree_Internal_id (x : betree_Internal_t) :=
+  match x with | mkbetree_Internal_t x0 _ _ _ => x0 end
 .
 
-Notation "x1 .(Betree_internal_id)" := (Betree_internal_id x1) (at level 9).
+Notation "x1 .(betree_Internal_id)" := (betree_Internal_id x1) (at level 9).
 
-Definition Betree_internal_pivot (x : Betree_internal_t) :=
-  match x with | mkBetree_internal_t _ x0 _ _ => x0 end
+Definition betree_Internal_pivot (x : betree_Internal_t) :=
+  match x with | mkbetree_Internal_t _ x0 _ _ => x0 end
 .
 
-Notation "x1 .(Betree_internal_pivot)" := (Betree_internal_pivot x1)
+Notation "x1 .(betree_Internal_pivot)" := (betree_Internal_pivot x1)
   (at level 9)
 .
 
-Definition Betree_internal_left (x : Betree_internal_t) :=
-  match x with | mkBetree_internal_t _ _ x0 _ => x0 end
+Definition betree_Internal_left (x : betree_Internal_t) :=
+  match x with | mkbetree_Internal_t _ _ x0 _ => x0 end
 .
 
-Notation "x1 .(Betree_internal_left)" := (Betree_internal_left x1) (at level 9)
+Notation "x1 .(betree_Internal_left)" := (betree_Internal_left x1) (at level 9)
 .
 
-Definition Betree_internal_right (x : Betree_internal_t) :=
-  match x with | mkBetree_internal_t _ _ _ x0 => x0 end
+Definition betree_Internal_right (x : betree_Internal_t) :=
+  match x with | mkbetree_Internal_t _ _ _ x0 => x0 end
 .
 
-Notation "x1 .(Betree_internal_right)" := (Betree_internal_right x1)
+Notation "x1 .(betree_Internal_right)" := (betree_Internal_right x1)
   (at level 9)
 .
 
 (** [betree_main::betree::Params] *)
-Record Betree_params_t :=
-mkBetree_params_t {
-  Betree_params_min_flush_size : u64; Betree_params_split_size : u64;
+Record betree_Params_t :=
+mkbetree_Params_t {
+  betree_Params_min_flush_size : u64; betree_Params_split_size : u64;
 }
 .
 
 (** [betree_main::betree::NodeIdCounter] *)
-Record Betree_node_id_counter_t :=
-mkBetree_node_id_counter_t {
-  Betree_node_id_counter_next_node_id : u64;
+Record betree_NodeIdCounter_t :=
+mkbetree_NodeIdCounter_t {
+  betree_NodeIdCounter_next_node_id : u64;
 }
 .
 
 (** [betree_main::betree::BeTree] *)
-Record Betree_be_tree_t :=
-mkBetree_be_tree_t {
-  Betree_be_tree_params : Betree_params_t;
-  Betree_be_tree_node_id_cnt : Betree_node_id_counter_t;
-  Betree_be_tree_root : Betree_node_t;
+Record betree_BeTree_t :=
+mkbetree_BeTree_t {
+  betree_BeTree_params : betree_Params_t;
+  betree_BeTree_node_id_cnt : betree_NodeIdCounter_t;
+  betree_BeTree_root : betree_Node_t;
 }
 .
 
diff --git a/tests/coq/betree/Primitives.v b/tests/coq/betree/Primitives.v
index 71a2d9c3..85e38f01 100644
--- a/tests/coq/betree/Primitives.v
+++ b/tests/coq/betree/Primitives.v
@@ -63,13 +63,15 @@ Check (if true then Return (1 + 2) else Fail_ Failure)%global = 3.
 
 (*** Misc *)
 
-
 Definition string := Coq.Strings.String.string.
 Definition char := Coq.Strings.Ascii.ascii.
 Definition char_of_byte := Coq.Strings.Ascii.ascii_of_byte.
 
-Definition mem_replace_fwd (a : Type) (x : a) (y : a) : a := x .
-Definition mem_replace_back (a : Type) (x : a) (y : a) : a := y .
+Definition core_mem_replace (a : Type) (x : a) (y : a) : a := x .
+Definition core_mem_replace_back (a : Type) (x : a) (y : a) : a := y .
+
+Record mut_raw_ptr (T : Type) := { mut_raw_ptr_v : T }.
+Record const_raw_ptr (T : Type) := { const_raw_ptr_v : T }.
 
 (*** Scalars *)
 
@@ -394,12 +396,89 @@ Notation "x s< y" := (scalar_ltb x y)  (at level 80) : Primitives_scope.
 Notation "x s>= y" := (scalar_geb x y)  (at level 80) : Primitives_scope.
 Notation "x s> y" := (scalar_gtb x y)  (at level 80) : Primitives_scope.
 
-(*** Range *)
-Record range (T : Type) := mk_range {
-  start: T;
-  end_: T;
+(** Constants *)
+Definition core_u8_max    := u8_max %u32.
+Definition core_u16_max   := u16_max %u32.
+Definition core_u32_max   := u32_max %u32.
+Definition core_u64_max   := u64_max %u64.
+Definition core_u128_max  := u64_max %u128.
+Axiom core_usize_max : usize. (** TODO *)
+Definition core_i8_max    := i8_max %i32.
+Definition core_i16_max   := i16_max %i32.
+Definition core_i32_max   := i32_max %i32.
+Definition core_i64_max   := i64_max %i64.
+Definition core_i128_max  := i64_max %i128.
+Axiom core_isize_max : isize. (** TODO *)
+
+(*** core::ops *)
+
+(* Trait declaration: [core::ops::index::Index] *)
+Record core_ops_index_Index (Self Idx : Type) := mk_core_ops_index_Index {
+  core_ops_index_Index_Output : Type;
+  core_ops_index_Index_index : Self -> Idx -> result core_ops_index_Index_Output;
+}.
+Arguments mk_core_ops_index_Index {_ _}.
+Arguments core_ops_index_Index_Output {_ _}.
+Arguments core_ops_index_Index_index {_ _}.
+
+(* Trait declaration: [core::ops::index::IndexMut] *)
+Record core_ops_index_IndexMut (Self Idx : Type) := mk_core_ops_index_IndexMut {
+  core_ops_index_IndexMut_indexInst : core_ops_index_Index Self Idx;
+  core_ops_index_IndexMut_index_mut : Self -> Idx -> result core_ops_index_IndexMut_indexInst.(core_ops_index_Index_Output);
+  core_ops_index_IndexMut_index_mut_back : Self -> Idx -> core_ops_index_IndexMut_indexInst.(core_ops_index_Index_Output) -> result Self;
+}.
+Arguments mk_core_ops_index_IndexMut {_ _}.
+Arguments core_ops_index_IndexMut_indexInst {_ _}.
+Arguments core_ops_index_IndexMut_index_mut {_ _}.
+Arguments core_ops_index_IndexMut_index_mut_back {_ _}.
+
+(* Trait declaration [core::ops::deref::Deref] *)
+Record core_ops_deref_Deref (Self : Type) := mk_core_ops_deref_Deref {
+  core_ops_deref_Deref_target : Type;
+  core_ops_deref_Deref_deref : Self -> result core_ops_deref_Deref_target;
+}.
+Arguments mk_core_ops_deref_Deref {_}.
+Arguments core_ops_deref_Deref_target {_}.
+Arguments core_ops_deref_Deref_deref {_}.
+
+(* Trait declaration [core::ops::deref::DerefMut] *)
+Record core_ops_deref_DerefMut (Self : Type) := mk_core_ops_deref_DerefMut {
+  core_ops_deref_DerefMut_derefInst : core_ops_deref_Deref Self;
+  core_ops_deref_DerefMut_deref_mut : Self -> result core_ops_deref_DerefMut_derefInst.(core_ops_deref_Deref_target);
+  core_ops_deref_DerefMut_deref_mut_back : Self -> core_ops_deref_DerefMut_derefInst.(core_ops_deref_Deref_target) -> result Self;
 }.
-Arguments mk_range {_}.
+Arguments mk_core_ops_deref_DerefMut {_}.
+Arguments core_ops_deref_DerefMut_derefInst {_}.
+Arguments core_ops_deref_DerefMut_deref_mut {_}.
+Arguments core_ops_deref_DerefMut_deref_mut_back {_}.
+
+Record core_ops_range_Range (T : Type) := mk_core_ops_range_Range {
+  core_ops_range_Range_start : T;
+  core_ops_range_Range_end_ : T;
+}.
+Arguments mk_core_ops_range_Range {_}.
+Arguments core_ops_range_Range_start {_}.
+Arguments core_ops_range_Range_end_ {_}.
+
+(*** [alloc] *)
+
+Definition alloc_boxed_Box_deref (T : Type) (x : T) : result T := Return x.
+Definition alloc_boxed_Box_deref_mut (T : Type) (x : T) : result T := Return x.
+Definition alloc_boxed_Box_deref_mut_back (T : Type) (_ : T) (x : T) : result T := Return x.
+
+(* Trait instance *)
+Definition alloc_boxed_Box_coreOpsDerefInst (Self : Type) : core_ops_deref_Deref Self := {|
+  core_ops_deref_Deref_target := Self;
+  core_ops_deref_Deref_deref := alloc_boxed_Box_deref Self;
+|}.
+
+(* Trait instance *)
+Definition alloc_boxed_Box_coreOpsDerefMutInst (Self : Type) : core_ops_deref_DerefMut Self := {|
+  core_ops_deref_DerefMut_derefInst := alloc_boxed_Box_coreOpsDerefInst Self;
+  core_ops_deref_DerefMut_deref_mut := alloc_boxed_Box_deref_mut Self;
+  core_ops_deref_DerefMut_deref_mut_back := alloc_boxed_Box_deref_mut_back Self;
+|}.
+
 
 (*** Arrays *)
 Definition array T (n : usize) := { l: list T | Z.of_nat (length l) = to_Z n}.
@@ -419,51 +498,50 @@ Qed.
 (* TODO: finish the definitions *)
 Axiom mk_array : forall (T : Type) (n : usize) (l : list T), array T n.
 
-Axiom array_index_shared : forall (T : Type) (n : usize) (x : array T n) (i : usize), result T.
-Axiom array_index_mut_fwd : forall (T : Type) (n : usize) (x : array T n) (i : usize), result T.
-Axiom array_index_mut_back : forall (T : Type) (n : usize) (x : array T n) (i : usize) (nx : T), result (array T n).
+(* For initialization *)
+Axiom array_repeat : forall (T : Type) (n : usize) (x : T), array T n.
+
+Axiom array_index_usize : forall (T : Type) (n : usize) (x : array T n) (i : usize), result T.
+Axiom array_update_usize : forall (T : Type) (n : usize) (x : array T n) (i : usize) (nx : T), result (array T n).
 
 (*** Slice *)
 Definition slice T := { l: list T | Z.of_nat (length l) <= usize_max}.
 
 Axiom slice_len : forall (T : Type) (s : slice T), usize.
-Axiom slice_index_shared : forall (T : Type) (x : slice T) (i : usize), result T.
-Axiom slice_index_mut_fwd : forall (T : Type) (x : slice T) (i : usize), result T.
-Axiom slice_index_mut_back : forall (T : Type) (x : slice T) (i : usize) (nx : T), result (slice T).
+Axiom slice_index_usize : forall (T : Type) (x : slice T) (i : usize), result T.
+Axiom slice_update_usize : forall (T : Type) (x : slice T) (i : usize) (nx : T), result (slice T).
 
 (*** Subslices *)
 
-Axiom array_to_slice_shared : forall (T : Type) (n : usize) (x : array T n), result (slice T).
-Axiom array_to_slice_mut_fwd : forall (T : Type) (n : usize) (x : array T n), result (slice T).
-Axiom array_to_slice_mut_back : forall (T : Type) (n : usize) (x : array T n) (s : slice T), result (array T n).
+Axiom array_to_slice : forall (T : Type) (n : usize) (x : array T n), result (slice T).
+Axiom array_from_slice : forall (T : Type) (n : usize) (x : array T n) (s : slice T), result (array T n).
+
+Axiom array_subslice: forall (T : Type) (n : usize) (x : array T n) (r : core_ops_range_Range usize), result (slice T).
+Axiom array_update_subslice: forall (T : Type) (n : usize) (x : array T n) (r : core_ops_range_Range usize) (ns : slice T), result (array T n).
 
-Axiom array_subslice_shared: forall (T : Type) (n : usize) (x : array T n) (r : range usize), result (slice T).
-Axiom array_subslice_mut_fwd: forall (T : Type) (n : usize) (x : array T n) (r : range usize), result (slice T).
-Axiom array_subslice_mut_back: forall (T : Type) (n : usize) (x : array T n) (r : range usize) (ns : slice T), result (array T n).
-Axiom slice_subslice_shared: forall (T : Type) (x : slice T) (r : range usize), result (slice T).
-Axiom slice_subslice_mut_fwd: forall (T : Type) (x : slice T) (r : range usize), result (slice T).
-Axiom slice_subslice_mut_back: forall (T : Type) (x : slice T) (r : range usize) (ns : slice T), result (slice T).
+Axiom slice_subslice: forall (T : Type) (x : slice T) (r : core_ops_range_Range usize), result (slice T).
+Axiom slice_update_subslice: forall (T : Type) (x : slice T) (r : core_ops_range_Range usize) (ns : slice T), result (slice T).
 
 (*** Vectors *)
 
-Definition vec T := { l: list T | Z.of_nat (length l) <= usize_max }.
+Definition alloc_vec_Vec T := { l: list T | Z.of_nat (length l) <= usize_max }.
 
-Definition vec_to_list {T: Type} (v: vec T) : list T := proj1_sig v.
+Definition alloc_vec_Vec_to_list {T: Type} (v: alloc_vec_Vec T) : list T := proj1_sig v.
 
-Definition vec_length {T: Type} (v: vec T) : Z := Z.of_nat (length (vec_to_list v)).
+Definition alloc_vec_Vec_length {T: Type} (v: alloc_vec_Vec T) : Z := Z.of_nat (length (alloc_vec_Vec_to_list v)).
 
-Definition vec_new (T: Type) : vec T := (exist _ [] le_0_usize_max).
+Definition alloc_vec_Vec_new (T: Type) : alloc_vec_Vec T := (exist _ [] le_0_usize_max).
 
-Lemma vec_len_in_usize {T} (v: vec T) : usize_min <= vec_length v <= usize_max.
+Lemma alloc_vec_Vec_len_in_usize {T} (v: alloc_vec_Vec T) : usize_min <= alloc_vec_Vec_length v <= usize_max.
 Proof.
-  unfold vec_length, usize_min.
+  unfold alloc_vec_Vec_length, usize_min.
   split.
   - lia.
   - apply (proj2_sig v).
 Qed.
 
-Definition vec_len (T: Type) (v: vec T) : usize :=
-  exist _ (vec_length v) (vec_len_in_usize v).
+Definition alloc_vec_Vec_len (T: Type) (v: alloc_vec_Vec T) : usize :=
+  exist _ (alloc_vec_Vec_length v) (alloc_vec_Vec_len_in_usize v).
 
 Fixpoint list_update {A} (l: list A) (n: nat) (a: A)
   : list A :=
@@ -474,50 +552,271 @@ Fixpoint list_update {A} (l: list A) (n: nat) (a: A)
     | S m => x :: (list_update t m a)
 end end.
 
-Definition vec_bind {A B} (v: vec A) (f: list A -> result (list B)) : result (vec B) :=
-  l <- f (vec_to_list v) ;
+Definition alloc_vec_Vec_bind {A B} (v: alloc_vec_Vec A) (f: list A -> result (list B)) : result (alloc_vec_Vec B) :=
+  l <- f (alloc_vec_Vec_to_list v) ;
   match sumbool_of_bool (scalar_le_max Usize (Z.of_nat (length l))) with
   | left H => Return (exist _ l (scalar_le_max_valid _ _ H))
   | right _ => Fail_ Failure
   end.
 
 (* The **forward** function shouldn't be used *)
-Definition vec_push_fwd (T: Type) (v: vec T) (x: T) : unit := tt.
+Definition alloc_vec_Vec_push_fwd (T: Type) (v: alloc_vec_Vec T) (x: T) : unit := tt.
 
-Definition vec_push_back (T: Type) (v: vec T) (x: T) : result (vec T) :=
-  vec_bind v (fun l => Return (l ++ [x])).
+Definition alloc_vec_Vec_push (T: Type) (v: alloc_vec_Vec T) (x: T) : result (alloc_vec_Vec T) :=
+  alloc_vec_Vec_bind v (fun l => Return (l ++ [x])).
 
 (* The **forward** function shouldn't be used *)
-Definition vec_insert_fwd (T: Type) (v: vec T) (i: usize) (x: T) : result unit :=
-  if to_Z i <? vec_length v then Return tt else Fail_ Failure.
+Definition alloc_vec_Vec_insert_fwd (T: Type) (v: alloc_vec_Vec T) (i: usize) (x: T) : result unit :=
+  if to_Z i <? alloc_vec_Vec_length v then Return tt else Fail_ Failure.
 
-Definition vec_insert_back (T: Type) (v: vec T) (i: usize) (x: T) : result (vec T) :=
-  vec_bind v (fun l =>
+Definition alloc_vec_Vec_insert (T: Type) (v: alloc_vec_Vec T) (i: usize) (x: T) : result (alloc_vec_Vec T) :=
+  alloc_vec_Vec_bind v (fun l =>
     if to_Z i <? Z.of_nat (length l)
     then Return (list_update l (usize_to_nat i) x)
     else Fail_ Failure).
 
-(* The **backward** function shouldn't be used *)
-Definition vec_index_fwd (T: Type) (v: vec T) (i: usize) : result T :=
-  match nth_error (vec_to_list v) (usize_to_nat i) with
-  | Some n => Return n
-  | None   => Fail_ Failure
-  end.
-
-Definition vec_index_back (T: Type) (v: vec T) (i: usize) (x: T) : result unit :=
-  if to_Z i <? vec_length v then Return tt else Fail_ Failure.
-
-(* The **backward** function shouldn't be used *)
-Definition vec_index_mut_fwd (T: Type) (v: vec T) (i: usize) : result T :=
-  match nth_error (vec_to_list v) (usize_to_nat i) with
-  | Some n => Return n
-  | None   => Fail_ Failure
+(* Helper *)
+Axiom alloc_vec_Vec_index_usize : forall {T : Type} (v : alloc_vec_Vec T) (i : usize) (x : T), result T.
+
+(* Helper *)
+Axiom alloc_vec_Vec_update_usize : forall {T : Type} (v : alloc_vec_Vec T) (i : usize) (x : T), result (alloc_vec_Vec T).
+
+(* Trait declaration: [core::slice::index::private_slice_index::Sealed] *)
+Definition core_slice_index_private_slice_index_Sealed (self : Type) := unit.
+
+(* Trait declaration: [core::slice::index::SliceIndex] *)
+Record core_slice_index_SliceIndex (Self T : Type) := mk_core_slice_index_SliceIndex {
+  core_slice_index_SliceIndex_sealedInst : core_slice_index_private_slice_index_Sealed Self;
+  core_slice_index_SliceIndex_Output : Type;
+  core_slice_index_SliceIndex_get : Self -> T -> result (option core_slice_index_SliceIndex_Output);
+  core_slice_index_SliceIndex_get_mut : Self -> T -> result (option core_slice_index_SliceIndex_Output);
+  core_slice_index_SliceIndex_get_mut_back : Self -> T -> option core_slice_index_SliceIndex_Output -> result T;
+  core_slice_index_SliceIndex_get_unchecked : Self -> const_raw_ptr T -> result (const_raw_ptr core_slice_index_SliceIndex_Output);
+  core_slice_index_SliceIndex_get_unchecked_mut : Self -> mut_raw_ptr T -> result (mut_raw_ptr core_slice_index_SliceIndex_Output);
+  core_slice_index_SliceIndex_index : Self -> T -> result core_slice_index_SliceIndex_Output;
+  core_slice_index_SliceIndex_index_mut : Self -> T -> result core_slice_index_SliceIndex_Output;
+  core_slice_index_SliceIndex_index_mut_back : Self -> T -> core_slice_index_SliceIndex_Output -> result T;
+}.
+Arguments mk_core_slice_index_SliceIndex {_ _}.
+Arguments core_slice_index_SliceIndex_sealedInst {_ _}.
+Arguments core_slice_index_SliceIndex_Output {_ _}.
+Arguments core_slice_index_SliceIndex_get {_ _}.
+Arguments core_slice_index_SliceIndex_get_mut {_ _}.
+Arguments core_slice_index_SliceIndex_get_mut_back {_ _}.
+Arguments core_slice_index_SliceIndex_get_unchecked {_ _}.
+Arguments core_slice_index_SliceIndex_get_unchecked_mut {_ _}.
+Arguments core_slice_index_SliceIndex_index {_ _}.
+Arguments core_slice_index_SliceIndex_index_mut {_ _}.
+Arguments core_slice_index_SliceIndex_index_mut_back {_ _}.
+
+(* [core::slice::index::[T]::index]: forward function *)
+Definition core_slice_index_Slice_index
+  (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T))
+  (s : slice T) (i : Idx) : result inst.(core_slice_index_SliceIndex_Output) :=
+  x <- inst.(core_slice_index_SliceIndex_get) i s;
+  match x with
+  | None => Fail_ Failure
+  | Some x => Return x
   end.
 
-Definition vec_index_mut_back (T: Type) (v: vec T) (i: usize) (x: T) : result (vec T) :=
-  vec_bind v (fun l =>
-    if to_Z i <? Z.of_nat (length l)
-    then Return (list_update l (usize_to_nat i) x)
-    else Fail_ Failure).
+(* [core::slice::index::Range:::get]: forward function *)
+Axiom core_slice_index_Range_get : forall (T : Type) (i : core_ops_range_Range usize) (s : slice T), result (option (slice T)).
+
+(* [core::slice::index::Range::get_mut]: forward function *)
+Axiom core_slice_index_Range_get_mut :
+  forall (T : Type), core_ops_range_Range usize -> slice T -> result (option (slice T)).
+
+(* [core::slice::index::Range::get_mut]: backward function 0 *)
+Axiom core_slice_index_Range_get_mut_back :
+  forall (T : Type), core_ops_range_Range usize -> slice T -> option (slice T) -> result (slice T).
+
+(* [core::slice::index::Range::get_unchecked]: forward function *)
+Definition core_slice_index_Range_get_unchecked
+  (T : Type) :
+  core_ops_range_Range usize -> const_raw_ptr (slice T) -> result (const_raw_ptr (slice T)) :=
+  (* Don't know what the model should be - for now we always fail to make
+     sure code which uses it fails *)
+  fun _ _ => Fail_ Failure.
+
+(* [core::slice::index::Range::get_unchecked_mut]: forward function *)
+Definition core_slice_index_Range_get_unchecked_mut
+  (T : Type) :
+  core_ops_range_Range usize -> mut_raw_ptr (slice T) -> result (mut_raw_ptr (slice T)) :=
+  (* Don't know what the model should be - for now we always fail to make
+    sure code which uses it fails *)
+  fun _ _ => Fail_ Failure.
+
+(* [core::slice::index::Range::index]: forward function *)
+Axiom core_slice_index_Range_index :
+  forall (T : Type), core_ops_range_Range usize -> slice T -> result (slice T).
+
+(* [core::slice::index::Range::index_mut]: forward function *)
+Axiom core_slice_index_Range_index_mut :
+  forall (T : Type), core_ops_range_Range usize -> slice T -> result (slice T).
+
+(* [core::slice::index::Range::index_mut]: backward function 0 *)
+Axiom core_slice_index_Range_index_mut_back :
+  forall (T : Type), core_ops_range_Range usize -> slice T -> slice T -> result (slice T).
+
+(* [core::slice::index::[T]::index_mut]: forward function *)
+Axiom core_slice_index_Slice_index_mut :
+  forall (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T)),
+  slice T -> Idx -> result inst.(core_slice_index_SliceIndex_Output).
+
+(* [core::slice::index::[T]::index_mut]: backward function 0 *)
+Axiom core_slice_index_Slice_index_mut_back :
+  forall (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T)),
+  slice T -> Idx -> inst.(core_slice_index_SliceIndex_Output) -> result (slice T).
+
+(* [core::array::[T; N]::index]: forward function *)
+Axiom core_array_Array_index :
+  forall (T Idx : Type) (N : usize) (inst : core_ops_index_Index (slice T) Idx)
+  (a : array T N) (i : Idx), result inst.(core_ops_index_Index_Output).
+
+(* [core::array::[T; N]::index_mut]: forward function *)
+Axiom core_array_Array_index_mut :
+  forall (T Idx : Type) (N : usize) (inst : core_ops_index_IndexMut (slice T) Idx)
+  (a : array T N) (i : Idx), result inst.(core_ops_index_IndexMut_indexInst).(core_ops_index_Index_Output).
+
+(* [core::array::[T; N]::index_mut]: backward function 0 *)
+Axiom core_array_Array_index_mut_back :
+  forall (T Idx : Type) (N : usize) (inst : core_ops_index_IndexMut (slice T) Idx)
+  (a : array T N) (i : Idx) (x : inst.(core_ops_index_IndexMut_indexInst).(core_ops_index_Index_Output)), result (array T N).
+
+(* Trait implementation: [core::slice::index::[T]] *)
+Definition core_slice_index_Slice_coreopsindexIndexInst (T Idx : Type)
+  (inst : core_slice_index_SliceIndex Idx (slice T)) :
+  core_ops_index_Index (slice T) Idx := {|
+  core_ops_index_Index_Output := inst.(core_slice_index_SliceIndex_Output);
+  core_ops_index_Index_index := core_slice_index_Slice_index T Idx inst;
+|}.
+
+(* Trait implementation: [core::slice::index::private_slice_index::Range] *)
+Definition core_slice_index_private_slice_index_Range_coresliceindexprivate_slice_indexSealedInst
+  : core_slice_index_private_slice_index_Sealed (core_ops_range_Range usize) := tt.
+
+(* Trait implementation: [core::slice::index::Range] *)
+Definition core_slice_index_Range_coresliceindexSliceIndexInst (T : Type) :
+  core_slice_index_SliceIndex (core_ops_range_Range usize) (slice T) := {|
+  core_slice_index_SliceIndex_sealedInst := core_slice_index_private_slice_index_Range_coresliceindexprivate_slice_indexSealedInst;
+  core_slice_index_SliceIndex_Output := slice T;
+  core_slice_index_SliceIndex_get := core_slice_index_Range_get T;
+  core_slice_index_SliceIndex_get_mut := core_slice_index_Range_get_mut T;
+  core_slice_index_SliceIndex_get_mut_back := core_slice_index_Range_get_mut_back T;
+  core_slice_index_SliceIndex_get_unchecked := core_slice_index_Range_get_unchecked T;
+  core_slice_index_SliceIndex_get_unchecked_mut := core_slice_index_Range_get_unchecked_mut T;
+  core_slice_index_SliceIndex_index := core_slice_index_Range_index T;
+  core_slice_index_SliceIndex_index_mut := core_slice_index_Range_index_mut T;
+  core_slice_index_SliceIndex_index_mut_back := core_slice_index_Range_index_mut_back T;
+|}.
+
+(* Trait implementation: [core::slice::index::[T]] *)
+Definition core_slice_index_Slice_coreopsindexIndexMutInst (T Idx : Type)
+  (inst : core_slice_index_SliceIndex Idx (slice T)) :
+  core_ops_index_IndexMut (slice T) Idx := {|
+  core_ops_index_IndexMut_indexInst := core_slice_index_Slice_coreopsindexIndexInst T Idx inst;
+  core_ops_index_IndexMut_index_mut := core_slice_index_Slice_index_mut T Idx inst;
+  core_ops_index_IndexMut_index_mut_back := core_slice_index_Slice_index_mut_back T Idx inst;
+|}.
+
+(* Trait implementation: [core::array::[T; N]] *)
+Definition core_array_Array_coreopsindexIndexInst (T Idx : Type) (N : usize)
+  (inst : core_ops_index_Index (slice T) Idx) :
+  core_ops_index_Index (array T N) Idx := {|
+  core_ops_index_Index_Output := inst.(core_ops_index_Index_Output);
+  core_ops_index_Index_index := core_array_Array_index T Idx N inst;
+|}.
+
+(* Trait implementation: [core::array::[T; N]] *)
+Definition core_array_Array_coreopsindexIndexMutInst (T Idx : Type) (N : usize)
+  (inst : core_ops_index_IndexMut (slice T) Idx) :
+  core_ops_index_IndexMut (array T N) Idx := {|
+  core_ops_index_IndexMut_indexInst := core_array_Array_coreopsindexIndexInst T Idx N inst.(core_ops_index_IndexMut_indexInst);
+  core_ops_index_IndexMut_index_mut := core_array_Array_index_mut T Idx N inst;
+  core_ops_index_IndexMut_index_mut_back := core_array_Array_index_mut_back T Idx N inst;
+|}.
+
+(* [core::slice::index::usize::get]: forward function *)
+Axiom core_slice_index_usize_get : forall (T : Type), usize -> slice T -> result (option T).
+
+(* [core::slice::index::usize::get_mut]: forward function *)
+Axiom core_slice_index_usize_get_mut : forall (T : Type), usize -> slice T -> result (option T).
+
+(* [core::slice::index::usize::get_mut]: backward function 0 *)
+Axiom core_slice_index_usize_get_mut_back :
+  forall (T : Type), usize -> slice T -> option T -> result (slice T).
+
+(* [core::slice::index::usize::get_unchecked]: forward function *)
+Axiom core_slice_index_usize_get_unchecked :
+  forall (T : Type), usize -> const_raw_ptr (slice T) -> result (const_raw_ptr T).
+
+(* [core::slice::index::usize::get_unchecked_mut]: forward function *)
+Axiom core_slice_index_usize_get_unchecked_mut :
+  forall (T : Type), usize -> mut_raw_ptr (slice T) -> result (mut_raw_ptr T).
+
+(* [core::slice::index::usize::index]: forward function *)
+Axiom core_slice_index_usize_index : forall (T : Type), usize -> slice T -> result T.
+
+(* [core::slice::index::usize::index_mut]: forward function *)
+Axiom core_slice_index_usize_index_mut : forall (T : Type), usize -> slice T -> result T.
+
+(* [core::slice::index::usize::index_mut]: backward function 0 *)
+Axiom core_slice_index_usize_index_mut_back :
+  forall (T : Type), usize -> slice T -> T -> result (slice T).
+
+(* Trait implementation: [core::slice::index::private_slice_index::usize] *)
+Definition core_slice_index_private_slice_index_usize_coresliceindexprivate_slice_indexSealedInst
+  : core_slice_index_private_slice_index_Sealed usize := tt.
+
+(* Trait implementation: [core::slice::index::usize] *)
+Definition core_slice_index_usize_coresliceindexSliceIndexInst (T : Type) :
+  core_slice_index_SliceIndex usize (slice T) := {|
+  core_slice_index_SliceIndex_sealedInst := core_slice_index_private_slice_index_usize_coresliceindexprivate_slice_indexSealedInst;
+  core_slice_index_SliceIndex_Output := T;
+  core_slice_index_SliceIndex_get := core_slice_index_usize_get T;
+  core_slice_index_SliceIndex_get_mut := core_slice_index_usize_get_mut T;
+  core_slice_index_SliceIndex_get_mut_back := core_slice_index_usize_get_mut_back T;
+  core_slice_index_SliceIndex_get_unchecked := core_slice_index_usize_get_unchecked T;
+  core_slice_index_SliceIndex_get_unchecked_mut := core_slice_index_usize_get_unchecked_mut T;
+  core_slice_index_SliceIndex_index := core_slice_index_usize_index T;
+  core_slice_index_SliceIndex_index_mut := core_slice_index_usize_index_mut T;
+  core_slice_index_SliceIndex_index_mut_back := core_slice_index_usize_index_mut_back T;
+|}.
+
+(* [alloc::vec::Vec::index]: forward function *)
+Axiom alloc_vec_Vec_index : forall (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T))
+  (Self : alloc_vec_Vec T) (i : Idx), result inst.(core_slice_index_SliceIndex_Output).
+
+(* [alloc::vec::Vec::index_mut]: forward function *)
+Axiom alloc_vec_Vec_index_mut : forall (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T))
+  (Self : alloc_vec_Vec T) (i : Idx), result inst.(core_slice_index_SliceIndex_Output).
+
+(* [alloc::vec::Vec::index_mut]: backward function 0 *)
+Axiom alloc_vec_Vec_index_mut_back :
+  forall (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T))
+  (Self : alloc_vec_Vec T) (i : Idx) (x : inst.(core_slice_index_SliceIndex_Output)), result (alloc_vec_Vec T).
+
+(* Trait implementation: [alloc::vec::Vec] *)
+Definition alloc_vec_Vec_coreopsindexIndexInst (T Idx : Type)
+  (inst : core_slice_index_SliceIndex Idx (slice T)) :
+  core_ops_index_Index (alloc_vec_Vec T) Idx := {|
+  core_ops_index_Index_Output := inst.(core_slice_index_SliceIndex_Output);
+  core_ops_index_Index_index := alloc_vec_Vec_index T Idx inst;
+|}.
+
+(* Trait implementation: [alloc::vec::Vec] *)
+Definition alloc_vec_Vec_coreopsindexIndexMutInst (T Idx : Type)
+  (inst : core_slice_index_SliceIndex Idx (slice T)) :
+  core_ops_index_IndexMut (alloc_vec_Vec T) Idx := {|
+  core_ops_index_IndexMut_indexInst := alloc_vec_Vec_coreopsindexIndexInst T Idx inst;
+  core_ops_index_IndexMut_index_mut := alloc_vec_Vec_index_mut T Idx inst;
+  core_ops_index_IndexMut_index_mut_back := alloc_vec_Vec_index_mut_back T Idx inst;
+|}.
+
+(*** Theorems *)
+
+Axiom alloc_vec_Vec_index_mut_back_eq : forall {a : Type} (v : alloc_vec_Vec a) (i : usize) (x : a),
+  alloc_vec_Vec_index_mut_back a usize (core_slice_index_usize_coresliceindexSliceIndexInst a) v i x =
+    alloc_vec_Vec_update_usize v i x.
 
 End Primitives.
diff --git a/tests/coq/hashmap/Hashmap_Funs.v b/tests/coq/hashmap/Hashmap_Funs.v
index e950ba0b..3ca52a9f 100644
--- a/tests/coq/hashmap/Hashmap_Funs.v
+++ b/tests/coq/hashmap/Hashmap_Funs.v
@@ -11,98 +11,101 @@ Import Hashmap_Types.
 Module Hashmap_Funs.
 
 (** [hashmap::hash_key]: forward function *)
-Definition hash_key_fwd (k : usize) : result usize :=
+Definition hash_key (k : usize) : result usize :=
   Return k.
 
 (** [hashmap::HashMap::{0}::allocate_slots]: loop 0: forward function *)
-Fixpoint hash_map_allocate_slots_loop_fwd
-  (T : Type) (n : nat) (slots : vec (List_t T)) (n0 : usize) :
-  result (vec (List_t T))
+Fixpoint hashMap_allocate_slots_loop
+  (T : Type) (n : nat) (slots : alloc_vec_Vec (List_t T)) (n0 : usize) :
+  result (alloc_vec_Vec (List_t T))
   :=
   match n with
   | O => Fail_ OutOfFuel
   | S n1 =>
     if n0 s> 0%usize
     then (
-      slots0 <- vec_push_back (List_t T) slots ListNil;
+      slots0 <- alloc_vec_Vec_push (List_t T) slots List_Nil;
       n2 <- usize_sub n0 1%usize;
-      hash_map_allocate_slots_loop_fwd T n1 slots0 n2)
+      hashMap_allocate_slots_loop T n1 slots0 n2)
     else Return slots
   end
 .
 
 (** [hashmap::HashMap::{0}::allocate_slots]: forward function *)
-Definition hash_map_allocate_slots_fwd
-  (T : Type) (n : nat) (slots : vec (List_t T)) (n0 : usize) :
-  result (vec (List_t T))
+Definition hashMap_allocate_slots
+  (T : Type) (n : nat) (slots : alloc_vec_Vec (List_t T)) (n0 : usize) :
+  result (alloc_vec_Vec (List_t T))
   :=
-  hash_map_allocate_slots_loop_fwd T n slots n0
+  hashMap_allocate_slots_loop T n slots n0
 .
 
 (** [hashmap::HashMap::{0}::new_with_capacity]: forward function *)
-Definition hash_map_new_with_capacity_fwd
+Definition hashMap_new_with_capacity
   (T : Type) (n : nat) (capacity : usize) (max_load_dividend : usize)
   (max_load_divisor : usize) :
-  result (Hash_map_t T)
+  result (HashMap_t T)
   :=
-  let v := vec_new (List_t T) in
-  slots <- hash_map_allocate_slots_fwd T n v capacity;
+  let v := alloc_vec_Vec_new (List_t T) in
+  slots <- hashMap_allocate_slots T n v capacity;
   i <- usize_mul capacity max_load_dividend;
   i0 <- usize_div i max_load_divisor;
   Return
     {|
-      Hash_map_num_entries := 0%usize;
-      Hash_map_max_load_factor := (max_load_dividend, max_load_divisor);
-      Hash_map_max_load := i0;
-      Hash_map_slots := slots
+      hashMap_num_entries := 0%usize;
+      hashMap_max_load_factor := (max_load_dividend, max_load_divisor);
+      hashMap_max_load := i0;
+      hashMap_slots := slots
     |}
 .
 
 (** [hashmap::HashMap::{0}::new]: forward function *)
-Definition hash_map_new_fwd (T : Type) (n : nat) : result (Hash_map_t T) :=
-  hash_map_new_with_capacity_fwd T n 32%usize 4%usize 5%usize
+Definition hashMap_new (T : Type) (n : nat) : result (HashMap_t T) :=
+  hashMap_new_with_capacity T n 32%usize 4%usize 5%usize
 .
 
 (** [hashmap::HashMap::{0}::clear]: loop 0: merged forward/backward function
     (there is a single backward function, and the forward function returns ()) *)
-Fixpoint hash_map_clear_loop_fwd_back
-  (T : Type) (n : nat) (slots : vec (List_t T)) (i : usize) :
-  result (vec (List_t T))
+Fixpoint hashMap_clear_loop
+  (T : Type) (n : nat) (slots : alloc_vec_Vec (List_t T)) (i : usize) :
+  result (alloc_vec_Vec (List_t T))
   :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
-    let i0 := vec_len (List_t T) slots in
+    let i0 := alloc_vec_Vec_len (List_t T) slots in
     if i s< i0
     then (
       i1 <- usize_add i 1%usize;
-      slots0 <- vec_index_mut_back (List_t T) slots i ListNil;
-      hash_map_clear_loop_fwd_back T n0 slots0 i1)
+      slots0 <-
+        alloc_vec_Vec_index_mut_back (List_t T) usize
+          (core_slice_index_usize_coresliceindexSliceIndexInst (List_t T))
+          slots i List_Nil;
+      hashMap_clear_loop T n0 slots0 i1)
     else Return slots
   end
 .
 
 (** [hashmap::HashMap::{0}::clear]: merged forward/backward function
     (there is a single backward function, and the forward function returns ()) *)
-Definition hash_map_clear_fwd_back
-  (T : Type) (n : nat) (self : Hash_map_t T) : result (Hash_map_t T) :=
-  v <- hash_map_clear_loop_fwd_back T n self.(Hash_map_slots) 0%usize;
+Definition hashMap_clear
+  (T : Type) (n : nat) (self : HashMap_t T) : result (HashMap_t T) :=
+  v <- hashMap_clear_loop T n self.(hashMap_slots) 0%usize;
   Return
     {|
-      Hash_map_num_entries := 0%usize;
-      Hash_map_max_load_factor := self.(Hash_map_max_load_factor);
-      Hash_map_max_load := self.(Hash_map_max_load);
-      Hash_map_slots := v
+      hashMap_num_entries := 0%usize;
+      hashMap_max_load_factor := self.(hashMap_max_load_factor);
+      hashMap_max_load := self.(hashMap_max_load);
+      hashMap_slots := v
     |}
 .
 
 (** [hashmap::HashMap::{0}::len]: forward function *)
-Definition hash_map_len_fwd (T : Type) (self : Hash_map_t T) : result usize :=
-  Return self.(Hash_map_num_entries)
+Definition hashMap_len (T : Type) (self : HashMap_t T) : result usize :=
+  Return self.(hashMap_num_entries)
 .
 
 (** [hashmap::HashMap::{0}::insert_in_list]: loop 0: forward function *)
-Fixpoint hash_map_insert_in_list_loop_fwd
+Fixpoint hashMap_insert_in_list_loop
   (T : Type) (n : nat) (key : usize) (value : T) (ls : List_t T) :
   result bool
   :=
@@ -110,25 +113,25 @@ Fixpoint hash_map_insert_in_list_loop_fwd
   | O => Fail_ OutOfFuel
   | S n0 =>
     match ls with
-    | ListCons ckey cvalue tl =>
+    | List_Cons ckey cvalue tl =>
       if ckey s= key
       then Return false
-      else hash_map_insert_in_list_loop_fwd T n0 key value tl
-    | ListNil => Return true
+      else hashMap_insert_in_list_loop T n0 key value tl
+    | List_Nil => Return true
     end
   end
 .
 
 (** [hashmap::HashMap::{0}::insert_in_list]: forward function *)
-Definition hash_map_insert_in_list_fwd
+Definition hashMap_insert_in_list
   (T : Type) (n : nat) (key : usize) (value : T) (ls : List_t T) :
   result bool
   :=
-  hash_map_insert_in_list_loop_fwd T n key value ls
+  hashMap_insert_in_list_loop T n key value ls
 .
 
 (** [hashmap::HashMap::{0}::insert_in_list]: loop 0: backward function 0 *)
-Fixpoint hash_map_insert_in_list_loop_back
+Fixpoint hashMap_insert_in_list_loop_back
   (T : Type) (n : nat) (key : usize) (value : T) (ls : List_t T) :
   result (List_t T)
   :=
@@ -136,259 +139,275 @@ Fixpoint hash_map_insert_in_list_loop_back
   | O => Fail_ OutOfFuel
   | S n0 =>
     match ls with
-    | ListCons ckey cvalue tl =>
+    | List_Cons ckey cvalue tl =>
       if ckey s= key
-      then Return (ListCons ckey value tl)
+      then Return (List_Cons ckey value tl)
       else (
-        tl0 <- hash_map_insert_in_list_loop_back T n0 key value tl;
-        Return (ListCons ckey cvalue tl0))
-    | ListNil => let l := ListNil in Return (ListCons key value l)
+        tl0 <- hashMap_insert_in_list_loop_back T n0 key value tl;
+        Return (List_Cons ckey cvalue tl0))
+    | List_Nil => let l := List_Nil in Return (List_Cons key value l)
     end
   end
 .
 
 (** [hashmap::HashMap::{0}::insert_in_list]: backward function 0 *)
-Definition hash_map_insert_in_list_back
+Definition hashMap_insert_in_list_back
   (T : Type) (n : nat) (key : usize) (value : T) (ls : List_t T) :
   result (List_t T)
   :=
-  hash_map_insert_in_list_loop_back T n key value ls
+  hashMap_insert_in_list_loop_back T n key value ls
 .
 
 (** [hashmap::HashMap::{0}::insert_no_resize]: merged forward/backward function
     (there is a single backward function, and the forward function returns ()) *)
-Definition hash_map_insert_no_resize_fwd_back
-  (T : Type) (n : nat) (self : Hash_map_t T) (key : usize) (value : T) :
-  result (Hash_map_t T)
+Definition hashMap_insert_no_resize
+  (T : Type) (n : nat) (self : HashMap_t T) (key : usize) (value : T) :
+  result (HashMap_t T)
   :=
-  hash <- hash_key_fwd key;
-  let i := vec_len (List_t T) self.(Hash_map_slots) in
+  hash <- hash_key key;
+  let i := alloc_vec_Vec_len (List_t T) self.(hashMap_slots) in
   hash_mod <- usize_rem hash i;
-  l <- vec_index_mut_fwd (List_t T) self.(Hash_map_slots) hash_mod;
-  inserted <- hash_map_insert_in_list_fwd T n key value l;
+  l <-
+    alloc_vec_Vec_index_mut (List_t T) usize
+      (core_slice_index_usize_coresliceindexSliceIndexInst (List_t T))
+      self.(hashMap_slots) hash_mod;
+  inserted <- hashMap_insert_in_list T n key value l;
   if inserted
   then (
-    i0 <- usize_add self.(Hash_map_num_entries) 1%usize;
-    l0 <- hash_map_insert_in_list_back T n key value l;
-    v <- vec_index_mut_back (List_t T) self.(Hash_map_slots) hash_mod l0;
+    i0 <- usize_add self.(hashMap_num_entries) 1%usize;
+    l0 <- hashMap_insert_in_list_back T n key value l;
+    v <-
+      alloc_vec_Vec_index_mut_back (List_t T) usize
+        (core_slice_index_usize_coresliceindexSliceIndexInst (List_t T))
+        self.(hashMap_slots) hash_mod l0;
     Return
       {|
-        Hash_map_num_entries := i0;
-        Hash_map_max_load_factor := self.(Hash_map_max_load_factor);
-        Hash_map_max_load := self.(Hash_map_max_load);
-        Hash_map_slots := v
+        hashMap_num_entries := i0;
+        hashMap_max_load_factor := self.(hashMap_max_load_factor);
+        hashMap_max_load := self.(hashMap_max_load);
+        hashMap_slots := v
       |})
   else (
-    l0 <- hash_map_insert_in_list_back T n key value l;
-    v <- vec_index_mut_back (List_t T) self.(Hash_map_slots) hash_mod l0;
+    l0 <- hashMap_insert_in_list_back T n key value l;
+    v <-
+      alloc_vec_Vec_index_mut_back (List_t T) usize
+        (core_slice_index_usize_coresliceindexSliceIndexInst (List_t T))
+        self.(hashMap_slots) hash_mod l0;
     Return
       {|
-        Hash_map_num_entries := self.(Hash_map_num_entries);
-        Hash_map_max_load_factor := self.(Hash_map_max_load_factor);
-        Hash_map_max_load := self.(Hash_map_max_load);
-        Hash_map_slots := v
+        hashMap_num_entries := self.(hashMap_num_entries);
+        hashMap_max_load_factor := self.(hashMap_max_load_factor);
+        hashMap_max_load := self.(hashMap_max_load);
+        hashMap_slots := v
       |})
 .
 
-(** [core::num::u32::{8}::MAX] *)
-Definition core_num_u32_max_body : result u32 := Return 4294967295%u32.
-Definition core_num_u32_max_c : u32 := core_num_u32_max_body%global.
-
 (** [hashmap::HashMap::{0}::move_elements_from_list]: loop 0: merged forward/backward function
     (there is a single backward function, and the forward function returns ()) *)
-Fixpoint hash_map_move_elements_from_list_loop_fwd_back
-  (T : Type) (n : nat) (ntable : Hash_map_t T) (ls : List_t T) :
-  result (Hash_map_t T)
+Fixpoint hashMap_move_elements_from_list_loop
+  (T : Type) (n : nat) (ntable : HashMap_t T) (ls : List_t T) :
+  result (HashMap_t T)
   :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
     match ls with
-    | ListCons k v tl =>
-      ntable0 <- hash_map_insert_no_resize_fwd_back T n0 ntable k v;
-      hash_map_move_elements_from_list_loop_fwd_back T n0 ntable0 tl
-    | ListNil => Return ntable
+    | List_Cons k v tl =>
+      ntable0 <- hashMap_insert_no_resize T n0 ntable k v;
+      hashMap_move_elements_from_list_loop T n0 ntable0 tl
+    | List_Nil => Return ntable
     end
   end
 .
 
 (** [hashmap::HashMap::{0}::move_elements_from_list]: merged forward/backward function
     (there is a single backward function, and the forward function returns ()) *)
-Definition hash_map_move_elements_from_list_fwd_back
-  (T : Type) (n : nat) (ntable : Hash_map_t T) (ls : List_t T) :
-  result (Hash_map_t T)
+Definition hashMap_move_elements_from_list
+  (T : Type) (n : nat) (ntable : HashMap_t T) (ls : List_t T) :
+  result (HashMap_t T)
   :=
-  hash_map_move_elements_from_list_loop_fwd_back T n ntable ls
+  hashMap_move_elements_from_list_loop T n ntable ls
 .
 
 (** [hashmap::HashMap::{0}::move_elements]: loop 0: merged forward/backward function
     (there is a single backward function, and the forward function returns ()) *)
-Fixpoint hash_map_move_elements_loop_fwd_back
-  (T : Type) (n : nat) (ntable : Hash_map_t T) (slots : vec (List_t T))
-  (i : usize) :
-  result ((Hash_map_t T) * (vec (List_t T)))
+Fixpoint hashMap_move_elements_loop
+  (T : Type) (n : nat) (ntable : HashMap_t T)
+  (slots : alloc_vec_Vec (List_t T)) (i : usize) :
+  result ((HashMap_t T) * (alloc_vec_Vec (List_t T)))
   :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
-    let i0 := vec_len (List_t T) slots in
+    let i0 := alloc_vec_Vec_len (List_t T) slots in
     if i s< i0
     then (
-      l <- vec_index_mut_fwd (List_t T) slots i;
-      let ls := mem_replace_fwd (List_t T) l ListNil in
-      ntable0 <- hash_map_move_elements_from_list_fwd_back T n0 ntable ls;
+      l <-
+        alloc_vec_Vec_index_mut (List_t T) usize
+          (core_slice_index_usize_coresliceindexSliceIndexInst (List_t T))
+          slots i;
+      let ls := core_mem_replace (List_t T) l List_Nil in
+      ntable0 <- hashMap_move_elements_from_list T n0 ntable ls;
       i1 <- usize_add i 1%usize;
-      let l0 := mem_replace_back (List_t T) l ListNil in
-      slots0 <- vec_index_mut_back (List_t T) slots i l0;
-      hash_map_move_elements_loop_fwd_back T n0 ntable0 slots0 i1)
+      let l0 := core_mem_replace_back (List_t T) l List_Nil in
+      slots0 <-
+        alloc_vec_Vec_index_mut_back (List_t T) usize
+          (core_slice_index_usize_coresliceindexSliceIndexInst (List_t T))
+          slots i l0;
+      hashMap_move_elements_loop T n0 ntable0 slots0 i1)
     else Return (ntable, slots)
   end
 .
 
 (** [hashmap::HashMap::{0}::move_elements]: merged forward/backward function
     (there is a single backward function, and the forward function returns ()) *)
-Definition hash_map_move_elements_fwd_back
-  (T : Type) (n : nat) (ntable : Hash_map_t T) (slots : vec (List_t T))
-  (i : usize) :
-  result ((Hash_map_t T) * (vec (List_t T)))
+Definition hashMap_move_elements
+  (T : Type) (n : nat) (ntable : HashMap_t T)
+  (slots : alloc_vec_Vec (List_t T)) (i : usize) :
+  result ((HashMap_t T) * (alloc_vec_Vec (List_t T)))
   :=
-  hash_map_move_elements_loop_fwd_back T n ntable slots i
+  hashMap_move_elements_loop T n ntable slots i
 .
 
 (** [hashmap::HashMap::{0}::try_resize]: merged forward/backward function
     (there is a single backward function, and the forward function returns ()) *)
-Definition hash_map_try_resize_fwd_back
-  (T : Type) (n : nat) (self : Hash_map_t T) : result (Hash_map_t T) :=
-  max_usize <- scalar_cast U32 Usize core_num_u32_max_c;
-  let capacity := vec_len (List_t T) self.(Hash_map_slots) in
+Definition hashMap_try_resize
+  (T : Type) (n : nat) (self : HashMap_t T) : result (HashMap_t T) :=
+  max_usize <- scalar_cast U32 Usize core_u32_max;
+  let capacity := alloc_vec_Vec_len (List_t T) self.(hashMap_slots) in
   n1 <- usize_div max_usize 2%usize;
-  let (i, i0) := self.(Hash_map_max_load_factor) in
+  let (i, i0) := self.(hashMap_max_load_factor) in
   i1 <- usize_div n1 i;
   if capacity s<= i1
   then (
     i2 <- usize_mul capacity 2%usize;
-    ntable <- hash_map_new_with_capacity_fwd T n i2 i i0;
-    p <-
-      hash_map_move_elements_fwd_back T n ntable self.(Hash_map_slots) 0%usize;
+    ntable <- hashMap_new_with_capacity T n i2 i i0;
+    p <- hashMap_move_elements T n ntable self.(hashMap_slots) 0%usize;
     let (ntable0, _) := p in
     Return
       {|
-        Hash_map_num_entries := self.(Hash_map_num_entries);
-        Hash_map_max_load_factor := (i, i0);
-        Hash_map_max_load := ntable0.(Hash_map_max_load);
-        Hash_map_slots := ntable0.(Hash_map_slots)
+        hashMap_num_entries := self.(hashMap_num_entries);
+        hashMap_max_load_factor := (i, i0);
+        hashMap_max_load := ntable0.(hashMap_max_load);
+        hashMap_slots := ntable0.(hashMap_slots)
       |})
   else
     Return
       {|
-        Hash_map_num_entries := self.(Hash_map_num_entries);
-        Hash_map_max_load_factor := (i, i0);
-        Hash_map_max_load := self.(Hash_map_max_load);
-        Hash_map_slots := self.(Hash_map_slots)
+        hashMap_num_entries := self.(hashMap_num_entries);
+        hashMap_max_load_factor := (i, i0);
+        hashMap_max_load := self.(hashMap_max_load);
+        hashMap_slots := self.(hashMap_slots)
       |}
 .
 
 (** [hashmap::HashMap::{0}::insert]: merged forward/backward function
     (there is a single backward function, and the forward function returns ()) *)
-Definition hash_map_insert_fwd_back
-  (T : Type) (n : nat) (self : Hash_map_t T) (key : usize) (value : T) :
-  result (Hash_map_t T)
+Definition hashMap_insert
+  (T : Type) (n : nat) (self : HashMap_t T) (key : usize) (value : T) :
+  result (HashMap_t T)
   :=
-  self0 <- hash_map_insert_no_resize_fwd_back T n self key value;
-  i <- hash_map_len_fwd T self0;
-  if i s> self0.(Hash_map_max_load)
-  then hash_map_try_resize_fwd_back T n self0
+  self0 <- hashMap_insert_no_resize T n self key value;
+  i <- hashMap_len T self0;
+  if i s> self0.(hashMap_max_load)
+  then hashMap_try_resize T n self0
   else Return self0
 .
 
 (** [hashmap::HashMap::{0}::contains_key_in_list]: loop 0: forward function *)
-Fixpoint hash_map_contains_key_in_list_loop_fwd
+Fixpoint hashMap_contains_key_in_list_loop
   (T : Type) (n : nat) (key : usize) (ls : List_t T) : result bool :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
     match ls with
-    | ListCons ckey t tl =>
+    | List_Cons ckey t tl =>
       if ckey s= key
       then Return true
-      else hash_map_contains_key_in_list_loop_fwd T n0 key tl
-    | ListNil => Return false
+      else hashMap_contains_key_in_list_loop T n0 key tl
+    | List_Nil => Return false
     end
   end
 .
 
 (** [hashmap::HashMap::{0}::contains_key_in_list]: forward function *)
-Definition hash_map_contains_key_in_list_fwd
+Definition hashMap_contains_key_in_list
   (T : Type) (n : nat) (key : usize) (ls : List_t T) : result bool :=
-  hash_map_contains_key_in_list_loop_fwd T n key ls
+  hashMap_contains_key_in_list_loop T n key ls
 .
 
 (** [hashmap::HashMap::{0}::contains_key]: forward function *)
-Definition hash_map_contains_key_fwd
-  (T : Type) (n : nat) (self : Hash_map_t T) (key : usize) : result bool :=
-  hash <- hash_key_fwd key;
-  let i := vec_len (List_t T) self.(Hash_map_slots) in
+Definition hashMap_contains_key
+  (T : Type) (n : nat) (self : HashMap_t T) (key : usize) : result bool :=
+  hash <- hash_key key;
+  let i := alloc_vec_Vec_len (List_t T) self.(hashMap_slots) in
   hash_mod <- usize_rem hash i;
-  l <- vec_index_fwd (List_t T) self.(Hash_map_slots) hash_mod;
-  hash_map_contains_key_in_list_fwd T n key l
+  l <-
+    alloc_vec_Vec_index (List_t T) usize
+      (core_slice_index_usize_coresliceindexSliceIndexInst (List_t T))
+      self.(hashMap_slots) hash_mod;
+  hashMap_contains_key_in_list T n key l
 .
 
 (** [hashmap::HashMap::{0}::get_in_list]: loop 0: forward function *)
-Fixpoint hash_map_get_in_list_loop_fwd
+Fixpoint hashMap_get_in_list_loop
   (T : Type) (n : nat) (key : usize) (ls : List_t T) : result T :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
     match ls with
-    | ListCons ckey cvalue tl =>
+    | List_Cons ckey cvalue tl =>
       if ckey s= key
       then Return cvalue
-      else hash_map_get_in_list_loop_fwd T n0 key tl
-    | ListNil => Fail_ Failure
+      else hashMap_get_in_list_loop T n0 key tl
+    | List_Nil => Fail_ Failure
     end
   end
 .
 
 (** [hashmap::HashMap::{0}::get_in_list]: forward function *)
-Definition hash_map_get_in_list_fwd
+Definition hashMap_get_in_list
   (T : Type) (n : nat) (key : usize) (ls : List_t T) : result T :=
-  hash_map_get_in_list_loop_fwd T n key ls
+  hashMap_get_in_list_loop T n key ls
 .
 
 (** [hashmap::HashMap::{0}::get]: forward function *)
-Definition hash_map_get_fwd
-  (T : Type) (n : nat) (self : Hash_map_t T) (key : usize) : result T :=
-  hash <- hash_key_fwd key;
-  let i := vec_len (List_t T) self.(Hash_map_slots) in
+Definition hashMap_get
+  (T : Type) (n : nat) (self : HashMap_t T) (key : usize) : result T :=
+  hash <- hash_key key;
+  let i := alloc_vec_Vec_len (List_t T) self.(hashMap_slots) in
   hash_mod <- usize_rem hash i;
-  l <- vec_index_fwd (List_t T) self.(Hash_map_slots) hash_mod;
-  hash_map_get_in_list_fwd T n key l
+  l <-
+    alloc_vec_Vec_index (List_t T) usize
+      (core_slice_index_usize_coresliceindexSliceIndexInst (List_t T))
+      self.(hashMap_slots) hash_mod;
+  hashMap_get_in_list T n key l
 .
 
 (** [hashmap::HashMap::{0}::get_mut_in_list]: loop 0: forward function *)
-Fixpoint hash_map_get_mut_in_list_loop_fwd
+Fixpoint hashMap_get_mut_in_list_loop
   (T : Type) (n : nat) (ls : List_t T) (key : usize) : result T :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
     match ls with
-    | ListCons ckey cvalue tl =>
+    | List_Cons ckey cvalue tl =>
       if ckey s= key
       then Return cvalue
-      else hash_map_get_mut_in_list_loop_fwd T n0 tl key
-    | ListNil => Fail_ Failure
+      else hashMap_get_mut_in_list_loop T n0 tl key
+    | List_Nil => Fail_ Failure
     end
   end
 .
 
 (** [hashmap::HashMap::{0}::get_mut_in_list]: forward function *)
-Definition hash_map_get_mut_in_list_fwd
+Definition hashMap_get_mut_in_list
   (T : Type) (n : nat) (ls : List_t T) (key : usize) : result T :=
-  hash_map_get_mut_in_list_loop_fwd T n ls key
+  hashMap_get_mut_in_list_loop T n ls key
 .
 
 (** [hashmap::HashMap::{0}::get_mut_in_list]: loop 0: backward function 0 *)
-Fixpoint hash_map_get_mut_in_list_loop_back
+Fixpoint hashMap_get_mut_in_list_loop_back
   (T : Type) (n : nat) (ls : List_t T) (key : usize) (ret : T) :
   result (List_t T)
   :=
@@ -396,196 +415,219 @@ Fixpoint hash_map_get_mut_in_list_loop_back
   | O => Fail_ OutOfFuel
   | S n0 =>
     match ls with
-    | ListCons ckey cvalue tl =>
+    | List_Cons ckey cvalue tl =>
       if ckey s= key
-      then Return (ListCons ckey ret tl)
+      then Return (List_Cons ckey ret tl)
       else (
-        tl0 <- hash_map_get_mut_in_list_loop_back T n0 tl key ret;
-        Return (ListCons ckey cvalue tl0))
-    | ListNil => Fail_ Failure
+        tl0 <- hashMap_get_mut_in_list_loop_back T n0 tl key ret;
+        Return (List_Cons ckey cvalue tl0))
+    | List_Nil => Fail_ Failure
     end
   end
 .
 
 (** [hashmap::HashMap::{0}::get_mut_in_list]: backward function 0 *)
-Definition hash_map_get_mut_in_list_back
+Definition hashMap_get_mut_in_list_back
   (T : Type) (n : nat) (ls : List_t T) (key : usize) (ret : T) :
   result (List_t T)
   :=
-  hash_map_get_mut_in_list_loop_back T n ls key ret
+  hashMap_get_mut_in_list_loop_back T n ls key ret
 .
 
 (** [hashmap::HashMap::{0}::get_mut]: forward function *)
-Definition hash_map_get_mut_fwd
-  (T : Type) (n : nat) (self : Hash_map_t T) (key : usize) : result T :=
-  hash <- hash_key_fwd key;
-  let i := vec_len (List_t T) self.(Hash_map_slots) in
+Definition hashMap_get_mut
+  (T : Type) (n : nat) (self : HashMap_t T) (key : usize) : result T :=
+  hash <- hash_key key;
+  let i := alloc_vec_Vec_len (List_t T) self.(hashMap_slots) in
   hash_mod <- usize_rem hash i;
-  l <- vec_index_mut_fwd (List_t T) self.(Hash_map_slots) hash_mod;
-  hash_map_get_mut_in_list_fwd T n l key
+  l <-
+    alloc_vec_Vec_index_mut (List_t T) usize
+      (core_slice_index_usize_coresliceindexSliceIndexInst (List_t T))
+      self.(hashMap_slots) hash_mod;
+  hashMap_get_mut_in_list T n l key
 .
 
 (** [hashmap::HashMap::{0}::get_mut]: backward function 0 *)
-Definition hash_map_get_mut_back
-  (T : Type) (n : nat) (self : Hash_map_t T) (key : usize) (ret : T) :
-  result (Hash_map_t T)
+Definition hashMap_get_mut_back
+  (T : Type) (n : nat) (self : HashMap_t T) (key : usize) (ret : T) :
+  result (HashMap_t T)
   :=
-  hash <- hash_key_fwd key;
-  let i := vec_len (List_t T) self.(Hash_map_slots) in
+  hash <- hash_key key;
+  let i := alloc_vec_Vec_len (List_t T) self.(hashMap_slots) in
   hash_mod <- usize_rem hash i;
-  l <- vec_index_mut_fwd (List_t T) self.(Hash_map_slots) hash_mod;
-  l0 <- hash_map_get_mut_in_list_back T n l key ret;
-  v <- vec_index_mut_back (List_t T) self.(Hash_map_slots) hash_mod l0;
+  l <-
+    alloc_vec_Vec_index_mut (List_t T) usize
+      (core_slice_index_usize_coresliceindexSliceIndexInst (List_t T))
+      self.(hashMap_slots) hash_mod;
+  l0 <- hashMap_get_mut_in_list_back T n l key ret;
+  v <-
+    alloc_vec_Vec_index_mut_back (List_t T) usize
+      (core_slice_index_usize_coresliceindexSliceIndexInst (List_t T))
+      self.(hashMap_slots) hash_mod l0;
   Return
     {|
-      Hash_map_num_entries := self.(Hash_map_num_entries);
-      Hash_map_max_load_factor := self.(Hash_map_max_load_factor);
-      Hash_map_max_load := self.(Hash_map_max_load);
-      Hash_map_slots := v
+      hashMap_num_entries := self.(hashMap_num_entries);
+      hashMap_max_load_factor := self.(hashMap_max_load_factor);
+      hashMap_max_load := self.(hashMap_max_load);
+      hashMap_slots := v
     |}
 .
 
 (** [hashmap::HashMap::{0}::remove_from_list]: loop 0: forward function *)
-Fixpoint hash_map_remove_from_list_loop_fwd
+Fixpoint hashMap_remove_from_list_loop
   (T : Type) (n : nat) (key : usize) (ls : List_t T) : result (option T) :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
     match ls with
-    | ListCons ckey t tl =>
+    | List_Cons ckey t tl =>
       if ckey s= key
       then
-        let mv_ls := mem_replace_fwd (List_t T) (ListCons ckey t tl) ListNil in
+        let mv_ls := core_mem_replace (List_t T) (List_Cons ckey t tl) List_Nil
+          in
         match mv_ls with
-        | ListCons i cvalue tl0 => Return (Some cvalue)
-        | ListNil => Fail_ Failure
+        | List_Cons i cvalue tl0 => Return (Some cvalue)
+        | List_Nil => Fail_ Failure
         end
-      else hash_map_remove_from_list_loop_fwd T n0 key tl
-    | ListNil => Return None
+      else hashMap_remove_from_list_loop T n0 key tl
+    | List_Nil => Return None
     end
   end
 .
 
 (** [hashmap::HashMap::{0}::remove_from_list]: forward function *)
-Definition hash_map_remove_from_list_fwd
+Definition hashMap_remove_from_list
   (T : Type) (n : nat) (key : usize) (ls : List_t T) : result (option T) :=
-  hash_map_remove_from_list_loop_fwd T n key ls
+  hashMap_remove_from_list_loop T n key ls
 .
 
 (** [hashmap::HashMap::{0}::remove_from_list]: loop 0: backward function 1 *)
-Fixpoint hash_map_remove_from_list_loop_back
+Fixpoint hashMap_remove_from_list_loop_back
   (T : Type) (n : nat) (key : usize) (ls : List_t T) : result (List_t T) :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
     match ls with
-    | ListCons ckey t tl =>
+    | List_Cons ckey t tl =>
       if ckey s= key
       then
-        let mv_ls := mem_replace_fwd (List_t T) (ListCons ckey t tl) ListNil in
+        let mv_ls := core_mem_replace (List_t T) (List_Cons ckey t tl) List_Nil
+          in
         match mv_ls with
-        | ListCons i cvalue tl0 => Return tl0
-        | ListNil => Fail_ Failure
+        | List_Cons i cvalue tl0 => Return tl0
+        | List_Nil => Fail_ Failure
         end
       else (
-        tl0 <- hash_map_remove_from_list_loop_back T n0 key tl;
-        Return (ListCons ckey t tl0))
-    | ListNil => Return ListNil
+        tl0 <- hashMap_remove_from_list_loop_back T n0 key tl;
+        Return (List_Cons ckey t tl0))
+    | List_Nil => Return List_Nil
     end
   end
 .
 
 (** [hashmap::HashMap::{0}::remove_from_list]: backward function 1 *)
-Definition hash_map_remove_from_list_back
+Definition hashMap_remove_from_list_back
   (T : Type) (n : nat) (key : usize) (ls : List_t T) : result (List_t T) :=
-  hash_map_remove_from_list_loop_back T n key ls
+  hashMap_remove_from_list_loop_back T n key ls
 .
 
 (** [hashmap::HashMap::{0}::remove]: forward function *)
-Definition hash_map_remove_fwd
-  (T : Type) (n : nat) (self : Hash_map_t T) (key : usize) :
+Definition hashMap_remove
+  (T : Type) (n : nat) (self : HashMap_t T) (key : usize) :
   result (option T)
   :=
-  hash <- hash_key_fwd key;
-  let i := vec_len (List_t T) self.(Hash_map_slots) in
+  hash <- hash_key key;
+  let i := alloc_vec_Vec_len (List_t T) self.(hashMap_slots) in
   hash_mod <- usize_rem hash i;
-  l <- vec_index_mut_fwd (List_t T) self.(Hash_map_slots) hash_mod;
-  x <- hash_map_remove_from_list_fwd T n key l;
+  l <-
+    alloc_vec_Vec_index_mut (List_t T) usize
+      (core_slice_index_usize_coresliceindexSliceIndexInst (List_t T))
+      self.(hashMap_slots) hash_mod;
+  x <- hashMap_remove_from_list T n key l;
   match x with
   | None => Return None
   | Some x0 =>
-    _ <- usize_sub self.(Hash_map_num_entries) 1%usize; Return (Some x0)
+    _ <- usize_sub self.(hashMap_num_entries) 1%usize; Return (Some x0)
   end
 .
 
 (** [hashmap::HashMap::{0}::remove]: backward function 0 *)
-Definition hash_map_remove_back
-  (T : Type) (n : nat) (self : Hash_map_t T) (key : usize) :
-  result (Hash_map_t T)
+Definition hashMap_remove_back
+  (T : Type) (n : nat) (self : HashMap_t T) (key : usize) :
+  result (HashMap_t T)
   :=
-  hash <- hash_key_fwd key;
-  let i := vec_len (List_t T) self.(Hash_map_slots) in
+  hash <- hash_key key;
+  let i := alloc_vec_Vec_len (List_t T) self.(hashMap_slots) in
   hash_mod <- usize_rem hash i;
-  l <- vec_index_mut_fwd (List_t T) self.(Hash_map_slots) hash_mod;
-  x <- hash_map_remove_from_list_fwd T n key l;
+  l <-
+    alloc_vec_Vec_index_mut (List_t T) usize
+      (core_slice_index_usize_coresliceindexSliceIndexInst (List_t T))
+      self.(hashMap_slots) hash_mod;
+  x <- hashMap_remove_from_list T n key l;
   match x with
   | None =>
-    l0 <- hash_map_remove_from_list_back T n key l;
-    v <- vec_index_mut_back (List_t T) self.(Hash_map_slots) hash_mod l0;
+    l0 <- hashMap_remove_from_list_back T n key l;
+    v <-
+      alloc_vec_Vec_index_mut_back (List_t T) usize
+        (core_slice_index_usize_coresliceindexSliceIndexInst (List_t T))
+        self.(hashMap_slots) hash_mod l0;
     Return
       {|
-        Hash_map_num_entries := self.(Hash_map_num_entries);
-        Hash_map_max_load_factor := self.(Hash_map_max_load_factor);
-        Hash_map_max_load := self.(Hash_map_max_load);
-        Hash_map_slots := v
+        hashMap_num_entries := self.(hashMap_num_entries);
+        hashMap_max_load_factor := self.(hashMap_max_load_factor);
+        hashMap_max_load := self.(hashMap_max_load);
+        hashMap_slots := v
       |}
   | Some x0 =>
-    i0 <- usize_sub self.(Hash_map_num_entries) 1%usize;
-    l0 <- hash_map_remove_from_list_back T n key l;
-    v <- vec_index_mut_back (List_t T) self.(Hash_map_slots) hash_mod l0;
+    i0 <- usize_sub self.(hashMap_num_entries) 1%usize;
+    l0 <- hashMap_remove_from_list_back T n key l;
+    v <-
+      alloc_vec_Vec_index_mut_back (List_t T) usize
+        (core_slice_index_usize_coresliceindexSliceIndexInst (List_t T))
+        self.(hashMap_slots) hash_mod l0;
     Return
       {|
-        Hash_map_num_entries := i0;
-        Hash_map_max_load_factor := self.(Hash_map_max_load_factor);
-        Hash_map_max_load := self.(Hash_map_max_load);
-        Hash_map_slots := v
+        hashMap_num_entries := i0;
+        hashMap_max_load_factor := self.(hashMap_max_load_factor);
+        hashMap_max_load := self.(hashMap_max_load);
+        hashMap_slots := v
       |}
   end
 .
 
 (** [hashmap::test1]: forward function *)
-Definition test1_fwd (n : nat) : result unit :=
-  hm <- hash_map_new_fwd u64 n;
-  hm0 <- hash_map_insert_fwd_back u64 n hm 0%usize 42%u64;
-  hm1 <- hash_map_insert_fwd_back u64 n hm0 128%usize 18%u64;
-  hm2 <- hash_map_insert_fwd_back u64 n hm1 1024%usize 138%u64;
-  hm3 <- hash_map_insert_fwd_back u64 n hm2 1056%usize 256%u64;
-  i <- hash_map_get_fwd u64 n hm3 128%usize;
+Definition test1 (n : nat) : result unit :=
+  hm <- hashMap_new u64 n;
+  hm0 <- hashMap_insert u64 n hm 0%usize 42%u64;
+  hm1 <- hashMap_insert u64 n hm0 128%usize 18%u64;
+  hm2 <- hashMap_insert u64 n hm1 1024%usize 138%u64;
+  hm3 <- hashMap_insert u64 n hm2 1056%usize 256%u64;
+  i <- hashMap_get u64 n hm3 128%usize;
   if negb (i s= 18%u64)
   then Fail_ Failure
   else (
-    hm4 <- hash_map_get_mut_back u64 n hm3 1024%usize 56%u64;
-    i0 <- hash_map_get_fwd u64 n hm4 1024%usize;
+    hm4 <- hashMap_get_mut_back u64 n hm3 1024%usize 56%u64;
+    i0 <- hashMap_get u64 n hm4 1024%usize;
     if negb (i0 s= 56%u64)
     then Fail_ Failure
     else (
-      x <- hash_map_remove_fwd u64 n hm4 1024%usize;
+      x <- hashMap_remove u64 n hm4 1024%usize;
       match x with
       | None => Fail_ Failure
       | Some x0 =>
         if negb (x0 s= 56%u64)
         then Fail_ Failure
         else (
-          hm5 <- hash_map_remove_back u64 n hm4 1024%usize;
-          i1 <- hash_map_get_fwd u64 n hm5 0%usize;
+          hm5 <- hashMap_remove_back u64 n hm4 1024%usize;
+          i1 <- hashMap_get u64 n hm5 0%usize;
           if negb (i1 s= 42%u64)
           then Fail_ Failure
           else (
-            i2 <- hash_map_get_fwd u64 n hm5 128%usize;
+            i2 <- hashMap_get u64 n hm5 128%usize;
             if negb (i2 s= 18%u64)
             then Fail_ Failure
             else (
-              i3 <- hash_map_get_fwd u64 n hm5 1056%usize;
+              i3 <- hashMap_get u64 n hm5 1056%usize;
               if negb (i3 s= 256%u64) then Fail_ Failure else Return tt)))
       end))
 .
diff --git a/tests/coq/hashmap/Hashmap_Types.v b/tests/coq/hashmap/Hashmap_Types.v
index dbde6be9..8529803d 100644
--- a/tests/coq/hashmap/Hashmap_Types.v
+++ b/tests/coq/hashmap/Hashmap_Types.v
@@ -10,27 +10,27 @@ Module Hashmap_Types.
 
 (** [hashmap::List] *)
 Inductive List_t (T : Type) :=
-| ListCons : usize -> T -> List_t T -> List_t T
-| ListNil : List_t T
+| List_Cons : usize -> T -> List_t T -> List_t T
+| List_Nil : List_t T
 .
 
-Arguments ListCons {T} _ _ _.
-Arguments ListNil {T}.
+Arguments List_Cons { _ }.
+Arguments List_Nil { _ }.
 
 (** [hashmap::HashMap] *)
-Record Hash_map_t (T : Type) :=
-mkHash_map_t {
-  Hash_map_num_entries : usize;
-  Hash_map_max_load_factor : (usize * usize);
-  Hash_map_max_load : usize;
-  Hash_map_slots : vec (List_t T);
+Record HashMap_t (T : Type) :=
+mkHashMap_t {
+  hashMap_num_entries : usize;
+  hashMap_max_load_factor : (usize * usize);
+  hashMap_max_load : usize;
+  hashMap_slots : alloc_vec_Vec (List_t T);
 }
 .
 
-Arguments mkHash_map_t {T} _ _ _ _.
-Arguments Hash_map_num_entries {T}.
-Arguments Hash_map_max_load_factor {T}.
-Arguments Hash_map_max_load {T}.
-Arguments Hash_map_slots {T}.
+Arguments mkHashMap_t { _ }.
+Arguments hashMap_num_entries { _ }.
+Arguments hashMap_max_load_factor { _ }.
+Arguments hashMap_max_load { _ }.
+Arguments hashMap_slots { _ }.
 
 End Hashmap_Types .
diff --git a/tests/coq/hashmap/Primitives.v b/tests/coq/hashmap/Primitives.v
index 71a2d9c3..85e38f01 100644
--- a/tests/coq/hashmap/Primitives.v
+++ b/tests/coq/hashmap/Primitives.v
@@ -63,13 +63,15 @@ Check (if true then Return (1 + 2) else Fail_ Failure)%global = 3.
 
 (*** Misc *)
 
-
 Definition string := Coq.Strings.String.string.
 Definition char := Coq.Strings.Ascii.ascii.
 Definition char_of_byte := Coq.Strings.Ascii.ascii_of_byte.
 
-Definition mem_replace_fwd (a : Type) (x : a) (y : a) : a := x .
-Definition mem_replace_back (a : Type) (x : a) (y : a) : a := y .
+Definition core_mem_replace (a : Type) (x : a) (y : a) : a := x .
+Definition core_mem_replace_back (a : Type) (x : a) (y : a) : a := y .
+
+Record mut_raw_ptr (T : Type) := { mut_raw_ptr_v : T }.
+Record const_raw_ptr (T : Type) := { const_raw_ptr_v : T }.
 
 (*** Scalars *)
 
@@ -394,12 +396,89 @@ Notation "x s< y" := (scalar_ltb x y)  (at level 80) : Primitives_scope.
 Notation "x s>= y" := (scalar_geb x y)  (at level 80) : Primitives_scope.
 Notation "x s> y" := (scalar_gtb x y)  (at level 80) : Primitives_scope.
 
-(*** Range *)
-Record range (T : Type) := mk_range {
-  start: T;
-  end_: T;
+(** Constants *)
+Definition core_u8_max    := u8_max %u32.
+Definition core_u16_max   := u16_max %u32.
+Definition core_u32_max   := u32_max %u32.
+Definition core_u64_max   := u64_max %u64.
+Definition core_u128_max  := u64_max %u128.
+Axiom core_usize_max : usize. (** TODO *)
+Definition core_i8_max    := i8_max %i32.
+Definition core_i16_max   := i16_max %i32.
+Definition core_i32_max   := i32_max %i32.
+Definition core_i64_max   := i64_max %i64.
+Definition core_i128_max  := i64_max %i128.
+Axiom core_isize_max : isize. (** TODO *)
+
+(*** core::ops *)
+
+(* Trait declaration: [core::ops::index::Index] *)
+Record core_ops_index_Index (Self Idx : Type) := mk_core_ops_index_Index {
+  core_ops_index_Index_Output : Type;
+  core_ops_index_Index_index : Self -> Idx -> result core_ops_index_Index_Output;
+}.
+Arguments mk_core_ops_index_Index {_ _}.
+Arguments core_ops_index_Index_Output {_ _}.
+Arguments core_ops_index_Index_index {_ _}.
+
+(* Trait declaration: [core::ops::index::IndexMut] *)
+Record core_ops_index_IndexMut (Self Idx : Type) := mk_core_ops_index_IndexMut {
+  core_ops_index_IndexMut_indexInst : core_ops_index_Index Self Idx;
+  core_ops_index_IndexMut_index_mut : Self -> Idx -> result core_ops_index_IndexMut_indexInst.(core_ops_index_Index_Output);
+  core_ops_index_IndexMut_index_mut_back : Self -> Idx -> core_ops_index_IndexMut_indexInst.(core_ops_index_Index_Output) -> result Self;
+}.
+Arguments mk_core_ops_index_IndexMut {_ _}.
+Arguments core_ops_index_IndexMut_indexInst {_ _}.
+Arguments core_ops_index_IndexMut_index_mut {_ _}.
+Arguments core_ops_index_IndexMut_index_mut_back {_ _}.
+
+(* Trait declaration [core::ops::deref::Deref] *)
+Record core_ops_deref_Deref (Self : Type) := mk_core_ops_deref_Deref {
+  core_ops_deref_Deref_target : Type;
+  core_ops_deref_Deref_deref : Self -> result core_ops_deref_Deref_target;
+}.
+Arguments mk_core_ops_deref_Deref {_}.
+Arguments core_ops_deref_Deref_target {_}.
+Arguments core_ops_deref_Deref_deref {_}.
+
+(* Trait declaration [core::ops::deref::DerefMut] *)
+Record core_ops_deref_DerefMut (Self : Type) := mk_core_ops_deref_DerefMut {
+  core_ops_deref_DerefMut_derefInst : core_ops_deref_Deref Self;
+  core_ops_deref_DerefMut_deref_mut : Self -> result core_ops_deref_DerefMut_derefInst.(core_ops_deref_Deref_target);
+  core_ops_deref_DerefMut_deref_mut_back : Self -> core_ops_deref_DerefMut_derefInst.(core_ops_deref_Deref_target) -> result Self;
 }.
-Arguments mk_range {_}.
+Arguments mk_core_ops_deref_DerefMut {_}.
+Arguments core_ops_deref_DerefMut_derefInst {_}.
+Arguments core_ops_deref_DerefMut_deref_mut {_}.
+Arguments core_ops_deref_DerefMut_deref_mut_back {_}.
+
+Record core_ops_range_Range (T : Type) := mk_core_ops_range_Range {
+  core_ops_range_Range_start : T;
+  core_ops_range_Range_end_ : T;
+}.
+Arguments mk_core_ops_range_Range {_}.
+Arguments core_ops_range_Range_start {_}.
+Arguments core_ops_range_Range_end_ {_}.
+
+(*** [alloc] *)
+
+Definition alloc_boxed_Box_deref (T : Type) (x : T) : result T := Return x.
+Definition alloc_boxed_Box_deref_mut (T : Type) (x : T) : result T := Return x.
+Definition alloc_boxed_Box_deref_mut_back (T : Type) (_ : T) (x : T) : result T := Return x.
+
+(* Trait instance *)
+Definition alloc_boxed_Box_coreOpsDerefInst (Self : Type) : core_ops_deref_Deref Self := {|
+  core_ops_deref_Deref_target := Self;
+  core_ops_deref_Deref_deref := alloc_boxed_Box_deref Self;
+|}.
+
+(* Trait instance *)
+Definition alloc_boxed_Box_coreOpsDerefMutInst (Self : Type) : core_ops_deref_DerefMut Self := {|
+  core_ops_deref_DerefMut_derefInst := alloc_boxed_Box_coreOpsDerefInst Self;
+  core_ops_deref_DerefMut_deref_mut := alloc_boxed_Box_deref_mut Self;
+  core_ops_deref_DerefMut_deref_mut_back := alloc_boxed_Box_deref_mut_back Self;
+|}.
+
 
 (*** Arrays *)
 Definition array T (n : usize) := { l: list T | Z.of_nat (length l) = to_Z n}.
@@ -419,51 +498,50 @@ Qed.
 (* TODO: finish the definitions *)
 Axiom mk_array : forall (T : Type) (n : usize) (l : list T), array T n.
 
-Axiom array_index_shared : forall (T : Type) (n : usize) (x : array T n) (i : usize), result T.
-Axiom array_index_mut_fwd : forall (T : Type) (n : usize) (x : array T n) (i : usize), result T.
-Axiom array_index_mut_back : forall (T : Type) (n : usize) (x : array T n) (i : usize) (nx : T), result (array T n).
+(* For initialization *)
+Axiom array_repeat : forall (T : Type) (n : usize) (x : T), array T n.
+
+Axiom array_index_usize : forall (T : Type) (n : usize) (x : array T n) (i : usize), result T.
+Axiom array_update_usize : forall (T : Type) (n : usize) (x : array T n) (i : usize) (nx : T), result (array T n).
 
 (*** Slice *)
 Definition slice T := { l: list T | Z.of_nat (length l) <= usize_max}.
 
 Axiom slice_len : forall (T : Type) (s : slice T), usize.
-Axiom slice_index_shared : forall (T : Type) (x : slice T) (i : usize), result T.
-Axiom slice_index_mut_fwd : forall (T : Type) (x : slice T) (i : usize), result T.
-Axiom slice_index_mut_back : forall (T : Type) (x : slice T) (i : usize) (nx : T), result (slice T).
+Axiom slice_index_usize : forall (T : Type) (x : slice T) (i : usize), result T.
+Axiom slice_update_usize : forall (T : Type) (x : slice T) (i : usize) (nx : T), result (slice T).
 
 (*** Subslices *)
 
-Axiom array_to_slice_shared : forall (T : Type) (n : usize) (x : array T n), result (slice T).
-Axiom array_to_slice_mut_fwd : forall (T : Type) (n : usize) (x : array T n), result (slice T).
-Axiom array_to_slice_mut_back : forall (T : Type) (n : usize) (x : array T n) (s : slice T), result (array T n).
+Axiom array_to_slice : forall (T : Type) (n : usize) (x : array T n), result (slice T).
+Axiom array_from_slice : forall (T : Type) (n : usize) (x : array T n) (s : slice T), result (array T n).
+
+Axiom array_subslice: forall (T : Type) (n : usize) (x : array T n) (r : core_ops_range_Range usize), result (slice T).
+Axiom array_update_subslice: forall (T : Type) (n : usize) (x : array T n) (r : core_ops_range_Range usize) (ns : slice T), result (array T n).
 
-Axiom array_subslice_shared: forall (T : Type) (n : usize) (x : array T n) (r : range usize), result (slice T).
-Axiom array_subslice_mut_fwd: forall (T : Type) (n : usize) (x : array T n) (r : range usize), result (slice T).
-Axiom array_subslice_mut_back: forall (T : Type) (n : usize) (x : array T n) (r : range usize) (ns : slice T), result (array T n).
-Axiom slice_subslice_shared: forall (T : Type) (x : slice T) (r : range usize), result (slice T).
-Axiom slice_subslice_mut_fwd: forall (T : Type) (x : slice T) (r : range usize), result (slice T).
-Axiom slice_subslice_mut_back: forall (T : Type) (x : slice T) (r : range usize) (ns : slice T), result (slice T).
+Axiom slice_subslice: forall (T : Type) (x : slice T) (r : core_ops_range_Range usize), result (slice T).
+Axiom slice_update_subslice: forall (T : Type) (x : slice T) (r : core_ops_range_Range usize) (ns : slice T), result (slice T).
 
 (*** Vectors *)
 
-Definition vec T := { l: list T | Z.of_nat (length l) <= usize_max }.
+Definition alloc_vec_Vec T := { l: list T | Z.of_nat (length l) <= usize_max }.
 
-Definition vec_to_list {T: Type} (v: vec T) : list T := proj1_sig v.
+Definition alloc_vec_Vec_to_list {T: Type} (v: alloc_vec_Vec T) : list T := proj1_sig v.
 
-Definition vec_length {T: Type} (v: vec T) : Z := Z.of_nat (length (vec_to_list v)).
+Definition alloc_vec_Vec_length {T: Type} (v: alloc_vec_Vec T) : Z := Z.of_nat (length (alloc_vec_Vec_to_list v)).
 
-Definition vec_new (T: Type) : vec T := (exist _ [] le_0_usize_max).
+Definition alloc_vec_Vec_new (T: Type) : alloc_vec_Vec T := (exist _ [] le_0_usize_max).
 
-Lemma vec_len_in_usize {T} (v: vec T) : usize_min <= vec_length v <= usize_max.
+Lemma alloc_vec_Vec_len_in_usize {T} (v: alloc_vec_Vec T) : usize_min <= alloc_vec_Vec_length v <= usize_max.
 Proof.
-  unfold vec_length, usize_min.
+  unfold alloc_vec_Vec_length, usize_min.
   split.
   - lia.
   - apply (proj2_sig v).
 Qed.
 
-Definition vec_len (T: Type) (v: vec T) : usize :=
-  exist _ (vec_length v) (vec_len_in_usize v).
+Definition alloc_vec_Vec_len (T: Type) (v: alloc_vec_Vec T) : usize :=
+  exist _ (alloc_vec_Vec_length v) (alloc_vec_Vec_len_in_usize v).
 
 Fixpoint list_update {A} (l: list A) (n: nat) (a: A)
   : list A :=
@@ -474,50 +552,271 @@ Fixpoint list_update {A} (l: list A) (n: nat) (a: A)
     | S m => x :: (list_update t m a)
 end end.
 
-Definition vec_bind {A B} (v: vec A) (f: list A -> result (list B)) : result (vec B) :=
-  l <- f (vec_to_list v) ;
+Definition alloc_vec_Vec_bind {A B} (v: alloc_vec_Vec A) (f: list A -> result (list B)) : result (alloc_vec_Vec B) :=
+  l <- f (alloc_vec_Vec_to_list v) ;
   match sumbool_of_bool (scalar_le_max Usize (Z.of_nat (length l))) with
   | left H => Return (exist _ l (scalar_le_max_valid _ _ H))
   | right _ => Fail_ Failure
   end.
 
 (* The **forward** function shouldn't be used *)
-Definition vec_push_fwd (T: Type) (v: vec T) (x: T) : unit := tt.
+Definition alloc_vec_Vec_push_fwd (T: Type) (v: alloc_vec_Vec T) (x: T) : unit := tt.
 
-Definition vec_push_back (T: Type) (v: vec T) (x: T) : result (vec T) :=
-  vec_bind v (fun l => Return (l ++ [x])).
+Definition alloc_vec_Vec_push (T: Type) (v: alloc_vec_Vec T) (x: T) : result (alloc_vec_Vec T) :=
+  alloc_vec_Vec_bind v (fun l => Return (l ++ [x])).
 
 (* The **forward** function shouldn't be used *)
-Definition vec_insert_fwd (T: Type) (v: vec T) (i: usize) (x: T) : result unit :=
-  if to_Z i <? vec_length v then Return tt else Fail_ Failure.
+Definition alloc_vec_Vec_insert_fwd (T: Type) (v: alloc_vec_Vec T) (i: usize) (x: T) : result unit :=
+  if to_Z i <? alloc_vec_Vec_length v then Return tt else Fail_ Failure.
 
-Definition vec_insert_back (T: Type) (v: vec T) (i: usize) (x: T) : result (vec T) :=
-  vec_bind v (fun l =>
+Definition alloc_vec_Vec_insert (T: Type) (v: alloc_vec_Vec T) (i: usize) (x: T) : result (alloc_vec_Vec T) :=
+  alloc_vec_Vec_bind v (fun l =>
     if to_Z i <? Z.of_nat (length l)
     then Return (list_update l (usize_to_nat i) x)
     else Fail_ Failure).
 
-(* The **backward** function shouldn't be used *)
-Definition vec_index_fwd (T: Type) (v: vec T) (i: usize) : result T :=
-  match nth_error (vec_to_list v) (usize_to_nat i) with
-  | Some n => Return n
-  | None   => Fail_ Failure
-  end.
-
-Definition vec_index_back (T: Type) (v: vec T) (i: usize) (x: T) : result unit :=
-  if to_Z i <? vec_length v then Return tt else Fail_ Failure.
-
-(* The **backward** function shouldn't be used *)
-Definition vec_index_mut_fwd (T: Type) (v: vec T) (i: usize) : result T :=
-  match nth_error (vec_to_list v) (usize_to_nat i) with
-  | Some n => Return n
-  | None   => Fail_ Failure
+(* Helper *)
+Axiom alloc_vec_Vec_index_usize : forall {T : Type} (v : alloc_vec_Vec T) (i : usize) (x : T), result T.
+
+(* Helper *)
+Axiom alloc_vec_Vec_update_usize : forall {T : Type} (v : alloc_vec_Vec T) (i : usize) (x : T), result (alloc_vec_Vec T).
+
+(* Trait declaration: [core::slice::index::private_slice_index::Sealed] *)
+Definition core_slice_index_private_slice_index_Sealed (self : Type) := unit.
+
+(* Trait declaration: [core::slice::index::SliceIndex] *)
+Record core_slice_index_SliceIndex (Self T : Type) := mk_core_slice_index_SliceIndex {
+  core_slice_index_SliceIndex_sealedInst : core_slice_index_private_slice_index_Sealed Self;
+  core_slice_index_SliceIndex_Output : Type;
+  core_slice_index_SliceIndex_get : Self -> T -> result (option core_slice_index_SliceIndex_Output);
+  core_slice_index_SliceIndex_get_mut : Self -> T -> result (option core_slice_index_SliceIndex_Output);
+  core_slice_index_SliceIndex_get_mut_back : Self -> T -> option core_slice_index_SliceIndex_Output -> result T;
+  core_slice_index_SliceIndex_get_unchecked : Self -> const_raw_ptr T -> result (const_raw_ptr core_slice_index_SliceIndex_Output);
+  core_slice_index_SliceIndex_get_unchecked_mut : Self -> mut_raw_ptr T -> result (mut_raw_ptr core_slice_index_SliceIndex_Output);
+  core_slice_index_SliceIndex_index : Self -> T -> result core_slice_index_SliceIndex_Output;
+  core_slice_index_SliceIndex_index_mut : Self -> T -> result core_slice_index_SliceIndex_Output;
+  core_slice_index_SliceIndex_index_mut_back : Self -> T -> core_slice_index_SliceIndex_Output -> result T;
+}.
+Arguments mk_core_slice_index_SliceIndex {_ _}.
+Arguments core_slice_index_SliceIndex_sealedInst {_ _}.
+Arguments core_slice_index_SliceIndex_Output {_ _}.
+Arguments core_slice_index_SliceIndex_get {_ _}.
+Arguments core_slice_index_SliceIndex_get_mut {_ _}.
+Arguments core_slice_index_SliceIndex_get_mut_back {_ _}.
+Arguments core_slice_index_SliceIndex_get_unchecked {_ _}.
+Arguments core_slice_index_SliceIndex_get_unchecked_mut {_ _}.
+Arguments core_slice_index_SliceIndex_index {_ _}.
+Arguments core_slice_index_SliceIndex_index_mut {_ _}.
+Arguments core_slice_index_SliceIndex_index_mut_back {_ _}.
+
+(* [core::slice::index::[T]::index]: forward function *)
+Definition core_slice_index_Slice_index
+  (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T))
+  (s : slice T) (i : Idx) : result inst.(core_slice_index_SliceIndex_Output) :=
+  x <- inst.(core_slice_index_SliceIndex_get) i s;
+  match x with
+  | None => Fail_ Failure
+  | Some x => Return x
   end.
 
-Definition vec_index_mut_back (T: Type) (v: vec T) (i: usize) (x: T) : result (vec T) :=
-  vec_bind v (fun l =>
-    if to_Z i <? Z.of_nat (length l)
-    then Return (list_update l (usize_to_nat i) x)
-    else Fail_ Failure).
+(* [core::slice::index::Range:::get]: forward function *)
+Axiom core_slice_index_Range_get : forall (T : Type) (i : core_ops_range_Range usize) (s : slice T), result (option (slice T)).
+
+(* [core::slice::index::Range::get_mut]: forward function *)
+Axiom core_slice_index_Range_get_mut :
+  forall (T : Type), core_ops_range_Range usize -> slice T -> result (option (slice T)).
+
+(* [core::slice::index::Range::get_mut]: backward function 0 *)
+Axiom core_slice_index_Range_get_mut_back :
+  forall (T : Type), core_ops_range_Range usize -> slice T -> option (slice T) -> result (slice T).
+
+(* [core::slice::index::Range::get_unchecked]: forward function *)
+Definition core_slice_index_Range_get_unchecked
+  (T : Type) :
+  core_ops_range_Range usize -> const_raw_ptr (slice T) -> result (const_raw_ptr (slice T)) :=
+  (* Don't know what the model should be - for now we always fail to make
+     sure code which uses it fails *)
+  fun _ _ => Fail_ Failure.
+
+(* [core::slice::index::Range::get_unchecked_mut]: forward function *)
+Definition core_slice_index_Range_get_unchecked_mut
+  (T : Type) :
+  core_ops_range_Range usize -> mut_raw_ptr (slice T) -> result (mut_raw_ptr (slice T)) :=
+  (* Don't know what the model should be - for now we always fail to make
+    sure code which uses it fails *)
+  fun _ _ => Fail_ Failure.
+
+(* [core::slice::index::Range::index]: forward function *)
+Axiom core_slice_index_Range_index :
+  forall (T : Type), core_ops_range_Range usize -> slice T -> result (slice T).
+
+(* [core::slice::index::Range::index_mut]: forward function *)
+Axiom core_slice_index_Range_index_mut :
+  forall (T : Type), core_ops_range_Range usize -> slice T -> result (slice T).
+
+(* [core::slice::index::Range::index_mut]: backward function 0 *)
+Axiom core_slice_index_Range_index_mut_back :
+  forall (T : Type), core_ops_range_Range usize -> slice T -> slice T -> result (slice T).
+
+(* [core::slice::index::[T]::index_mut]: forward function *)
+Axiom core_slice_index_Slice_index_mut :
+  forall (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T)),
+  slice T -> Idx -> result inst.(core_slice_index_SliceIndex_Output).
+
+(* [core::slice::index::[T]::index_mut]: backward function 0 *)
+Axiom core_slice_index_Slice_index_mut_back :
+  forall (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T)),
+  slice T -> Idx -> inst.(core_slice_index_SliceIndex_Output) -> result (slice T).
+
+(* [core::array::[T; N]::index]: forward function *)
+Axiom core_array_Array_index :
+  forall (T Idx : Type) (N : usize) (inst : core_ops_index_Index (slice T) Idx)
+  (a : array T N) (i : Idx), result inst.(core_ops_index_Index_Output).
+
+(* [core::array::[T; N]::index_mut]: forward function *)
+Axiom core_array_Array_index_mut :
+  forall (T Idx : Type) (N : usize) (inst : core_ops_index_IndexMut (slice T) Idx)
+  (a : array T N) (i : Idx), result inst.(core_ops_index_IndexMut_indexInst).(core_ops_index_Index_Output).
+
+(* [core::array::[T; N]::index_mut]: backward function 0 *)
+Axiom core_array_Array_index_mut_back :
+  forall (T Idx : Type) (N : usize) (inst : core_ops_index_IndexMut (slice T) Idx)
+  (a : array T N) (i : Idx) (x : inst.(core_ops_index_IndexMut_indexInst).(core_ops_index_Index_Output)), result (array T N).
+
+(* Trait implementation: [core::slice::index::[T]] *)
+Definition core_slice_index_Slice_coreopsindexIndexInst (T Idx : Type)
+  (inst : core_slice_index_SliceIndex Idx (slice T)) :
+  core_ops_index_Index (slice T) Idx := {|
+  core_ops_index_Index_Output := inst.(core_slice_index_SliceIndex_Output);
+  core_ops_index_Index_index := core_slice_index_Slice_index T Idx inst;
+|}.
+
+(* Trait implementation: [core::slice::index::private_slice_index::Range] *)
+Definition core_slice_index_private_slice_index_Range_coresliceindexprivate_slice_indexSealedInst
+  : core_slice_index_private_slice_index_Sealed (core_ops_range_Range usize) := tt.
+
+(* Trait implementation: [core::slice::index::Range] *)
+Definition core_slice_index_Range_coresliceindexSliceIndexInst (T : Type) :
+  core_slice_index_SliceIndex (core_ops_range_Range usize) (slice T) := {|
+  core_slice_index_SliceIndex_sealedInst := core_slice_index_private_slice_index_Range_coresliceindexprivate_slice_indexSealedInst;
+  core_slice_index_SliceIndex_Output := slice T;
+  core_slice_index_SliceIndex_get := core_slice_index_Range_get T;
+  core_slice_index_SliceIndex_get_mut := core_slice_index_Range_get_mut T;
+  core_slice_index_SliceIndex_get_mut_back := core_slice_index_Range_get_mut_back T;
+  core_slice_index_SliceIndex_get_unchecked := core_slice_index_Range_get_unchecked T;
+  core_slice_index_SliceIndex_get_unchecked_mut := core_slice_index_Range_get_unchecked_mut T;
+  core_slice_index_SliceIndex_index := core_slice_index_Range_index T;
+  core_slice_index_SliceIndex_index_mut := core_slice_index_Range_index_mut T;
+  core_slice_index_SliceIndex_index_mut_back := core_slice_index_Range_index_mut_back T;
+|}.
+
+(* Trait implementation: [core::slice::index::[T]] *)
+Definition core_slice_index_Slice_coreopsindexIndexMutInst (T Idx : Type)
+  (inst : core_slice_index_SliceIndex Idx (slice T)) :
+  core_ops_index_IndexMut (slice T) Idx := {|
+  core_ops_index_IndexMut_indexInst := core_slice_index_Slice_coreopsindexIndexInst T Idx inst;
+  core_ops_index_IndexMut_index_mut := core_slice_index_Slice_index_mut T Idx inst;
+  core_ops_index_IndexMut_index_mut_back := core_slice_index_Slice_index_mut_back T Idx inst;
+|}.
+
+(* Trait implementation: [core::array::[T; N]] *)
+Definition core_array_Array_coreopsindexIndexInst (T Idx : Type) (N : usize)
+  (inst : core_ops_index_Index (slice T) Idx) :
+  core_ops_index_Index (array T N) Idx := {|
+  core_ops_index_Index_Output := inst.(core_ops_index_Index_Output);
+  core_ops_index_Index_index := core_array_Array_index T Idx N inst;
+|}.
+
+(* Trait implementation: [core::array::[T; N]] *)
+Definition core_array_Array_coreopsindexIndexMutInst (T Idx : Type) (N : usize)
+  (inst : core_ops_index_IndexMut (slice T) Idx) :
+  core_ops_index_IndexMut (array T N) Idx := {|
+  core_ops_index_IndexMut_indexInst := core_array_Array_coreopsindexIndexInst T Idx N inst.(core_ops_index_IndexMut_indexInst);
+  core_ops_index_IndexMut_index_mut := core_array_Array_index_mut T Idx N inst;
+  core_ops_index_IndexMut_index_mut_back := core_array_Array_index_mut_back T Idx N inst;
+|}.
+
+(* [core::slice::index::usize::get]: forward function *)
+Axiom core_slice_index_usize_get : forall (T : Type), usize -> slice T -> result (option T).
+
+(* [core::slice::index::usize::get_mut]: forward function *)
+Axiom core_slice_index_usize_get_mut : forall (T : Type), usize -> slice T -> result (option T).
+
+(* [core::slice::index::usize::get_mut]: backward function 0 *)
+Axiom core_slice_index_usize_get_mut_back :
+  forall (T : Type), usize -> slice T -> option T -> result (slice T).
+
+(* [core::slice::index::usize::get_unchecked]: forward function *)
+Axiom core_slice_index_usize_get_unchecked :
+  forall (T : Type), usize -> const_raw_ptr (slice T) -> result (const_raw_ptr T).
+
+(* [core::slice::index::usize::get_unchecked_mut]: forward function *)
+Axiom core_slice_index_usize_get_unchecked_mut :
+  forall (T : Type), usize -> mut_raw_ptr (slice T) -> result (mut_raw_ptr T).
+
+(* [core::slice::index::usize::index]: forward function *)
+Axiom core_slice_index_usize_index : forall (T : Type), usize -> slice T -> result T.
+
+(* [core::slice::index::usize::index_mut]: forward function *)
+Axiom core_slice_index_usize_index_mut : forall (T : Type), usize -> slice T -> result T.
+
+(* [core::slice::index::usize::index_mut]: backward function 0 *)
+Axiom core_slice_index_usize_index_mut_back :
+  forall (T : Type), usize -> slice T -> T -> result (slice T).
+
+(* Trait implementation: [core::slice::index::private_slice_index::usize] *)
+Definition core_slice_index_private_slice_index_usize_coresliceindexprivate_slice_indexSealedInst
+  : core_slice_index_private_slice_index_Sealed usize := tt.
+
+(* Trait implementation: [core::slice::index::usize] *)
+Definition core_slice_index_usize_coresliceindexSliceIndexInst (T : Type) :
+  core_slice_index_SliceIndex usize (slice T) := {|
+  core_slice_index_SliceIndex_sealedInst := core_slice_index_private_slice_index_usize_coresliceindexprivate_slice_indexSealedInst;
+  core_slice_index_SliceIndex_Output := T;
+  core_slice_index_SliceIndex_get := core_slice_index_usize_get T;
+  core_slice_index_SliceIndex_get_mut := core_slice_index_usize_get_mut T;
+  core_slice_index_SliceIndex_get_mut_back := core_slice_index_usize_get_mut_back T;
+  core_slice_index_SliceIndex_get_unchecked := core_slice_index_usize_get_unchecked T;
+  core_slice_index_SliceIndex_get_unchecked_mut := core_slice_index_usize_get_unchecked_mut T;
+  core_slice_index_SliceIndex_index := core_slice_index_usize_index T;
+  core_slice_index_SliceIndex_index_mut := core_slice_index_usize_index_mut T;
+  core_slice_index_SliceIndex_index_mut_back := core_slice_index_usize_index_mut_back T;
+|}.
+
+(* [alloc::vec::Vec::index]: forward function *)
+Axiom alloc_vec_Vec_index : forall (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T))
+  (Self : alloc_vec_Vec T) (i : Idx), result inst.(core_slice_index_SliceIndex_Output).
+
+(* [alloc::vec::Vec::index_mut]: forward function *)
+Axiom alloc_vec_Vec_index_mut : forall (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T))
+  (Self : alloc_vec_Vec T) (i : Idx), result inst.(core_slice_index_SliceIndex_Output).
+
+(* [alloc::vec::Vec::index_mut]: backward function 0 *)
+Axiom alloc_vec_Vec_index_mut_back :
+  forall (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T))
+  (Self : alloc_vec_Vec T) (i : Idx) (x : inst.(core_slice_index_SliceIndex_Output)), result (alloc_vec_Vec T).
+
+(* Trait implementation: [alloc::vec::Vec] *)
+Definition alloc_vec_Vec_coreopsindexIndexInst (T Idx : Type)
+  (inst : core_slice_index_SliceIndex Idx (slice T)) :
+  core_ops_index_Index (alloc_vec_Vec T) Idx := {|
+  core_ops_index_Index_Output := inst.(core_slice_index_SliceIndex_Output);
+  core_ops_index_Index_index := alloc_vec_Vec_index T Idx inst;
+|}.
+
+(* Trait implementation: [alloc::vec::Vec] *)
+Definition alloc_vec_Vec_coreopsindexIndexMutInst (T Idx : Type)
+  (inst : core_slice_index_SliceIndex Idx (slice T)) :
+  core_ops_index_IndexMut (alloc_vec_Vec T) Idx := {|
+  core_ops_index_IndexMut_indexInst := alloc_vec_Vec_coreopsindexIndexInst T Idx inst;
+  core_ops_index_IndexMut_index_mut := alloc_vec_Vec_index_mut T Idx inst;
+  core_ops_index_IndexMut_index_mut_back := alloc_vec_Vec_index_mut_back T Idx inst;
+|}.
+
+(*** Theorems *)
+
+Axiom alloc_vec_Vec_index_mut_back_eq : forall {a : Type} (v : alloc_vec_Vec a) (i : usize) (x : a),
+  alloc_vec_Vec_index_mut_back a usize (core_slice_index_usize_coresliceindexSliceIndexInst a) v i x =
+    alloc_vec_Vec_update_usize v i x.
 
 End Primitives.
diff --git a/tests/coq/hashmap_on_disk/HashmapMain_Funs.v b/tests/coq/hashmap_on_disk/HashmapMain_Funs.v
index 657d5590..eac78186 100644
--- a/tests/coq/hashmap_on_disk/HashmapMain_Funs.v
+++ b/tests/coq/hashmap_on_disk/HashmapMain_Funs.v
@@ -13,656 +13,668 @@ Import HashmapMain_Opaque.
 Module HashmapMain_Funs.
 
 (** [hashmap_main::hashmap::hash_key]: forward function *)
-Definition hashmap_hash_key_fwd (k : usize) : result usize :=
+Definition hashmap_hash_key (k : usize) : result usize :=
   Return k.
 
 (** [hashmap_main::hashmap::HashMap::{0}::allocate_slots]: loop 0: forward function *)
-Fixpoint hashmap_hash_map_allocate_slots_loop_fwd
-  (T : Type) (n : nat) (slots : vec (Hashmap_list_t T)) (n0 : usize) :
-  result (vec (Hashmap_list_t T))
+Fixpoint hashmap_HashMap_allocate_slots_loop
+  (T : Type) (n : nat) (slots : alloc_vec_Vec (hashmap_List_t T)) (n0 : usize)
+  :
+  result (alloc_vec_Vec (hashmap_List_t T))
   :=
   match n with
   | O => Fail_ OutOfFuel
   | S n1 =>
     if n0 s> 0%usize
     then (
-      slots0 <- vec_push_back (Hashmap_list_t T) slots HashmapListNil;
+      slots0 <- alloc_vec_Vec_push (hashmap_List_t T) slots Hashmap_List_Nil;
       n2 <- usize_sub n0 1%usize;
-      hashmap_hash_map_allocate_slots_loop_fwd T n1 slots0 n2)
+      hashmap_HashMap_allocate_slots_loop T n1 slots0 n2)
     else Return slots
   end
 .
 
 (** [hashmap_main::hashmap::HashMap::{0}::allocate_slots]: forward function *)
-Definition hashmap_hash_map_allocate_slots_fwd
-  (T : Type) (n : nat) (slots : vec (Hashmap_list_t T)) (n0 : usize) :
-  result (vec (Hashmap_list_t T))
+Definition hashmap_HashMap_allocate_slots
+  (T : Type) (n : nat) (slots : alloc_vec_Vec (hashmap_List_t T)) (n0 : usize)
+  :
+  result (alloc_vec_Vec (hashmap_List_t T))
   :=
-  hashmap_hash_map_allocate_slots_loop_fwd T n slots n0
+  hashmap_HashMap_allocate_slots_loop T n slots n0
 .
 
 (** [hashmap_main::hashmap::HashMap::{0}::new_with_capacity]: forward function *)
-Definition hashmap_hash_map_new_with_capacity_fwd
+Definition hashmap_HashMap_new_with_capacity
   (T : Type) (n : nat) (capacity : usize) (max_load_dividend : usize)
   (max_load_divisor : usize) :
-  result (Hashmap_hash_map_t T)
+  result (hashmap_HashMap_t T)
   :=
-  let v := vec_new (Hashmap_list_t T) in
-  slots <- hashmap_hash_map_allocate_slots_fwd T n v capacity;
+  let v := alloc_vec_Vec_new (hashmap_List_t T) in
+  slots <- hashmap_HashMap_allocate_slots T n v capacity;
   i <- usize_mul capacity max_load_dividend;
   i0 <- usize_div i max_load_divisor;
   Return
     {|
-      Hashmap_hash_map_num_entries := 0%usize;
-      Hashmap_hash_map_max_load_factor := (max_load_dividend, max_load_divisor);
-      Hashmap_hash_map_max_load := i0;
-      Hashmap_hash_map_slots := slots
+      hashmap_HashMap_num_entries := 0%usize;
+      hashmap_HashMap_max_load_factor := (max_load_dividend, max_load_divisor);
+      hashmap_HashMap_max_load := i0;
+      hashmap_HashMap_slots := slots
     |}
 .
 
 (** [hashmap_main::hashmap::HashMap::{0}::new]: forward function *)
-Definition hashmap_hash_map_new_fwd
-  (T : Type) (n : nat) : result (Hashmap_hash_map_t T) :=
-  hashmap_hash_map_new_with_capacity_fwd T n 32%usize 4%usize 5%usize
+Definition hashmap_HashMap_new
+  (T : Type) (n : nat) : result (hashmap_HashMap_t T) :=
+  hashmap_HashMap_new_with_capacity T n 32%usize 4%usize 5%usize
 .
 
 (** [hashmap_main::hashmap::HashMap::{0}::clear]: loop 0: merged forward/backward function
     (there is a single backward function, and the forward function returns ()) *)
-Fixpoint hashmap_hash_map_clear_loop_fwd_back
-  (T : Type) (n : nat) (slots : vec (Hashmap_list_t T)) (i : usize) :
-  result (vec (Hashmap_list_t T))
+Fixpoint hashmap_HashMap_clear_loop
+  (T : Type) (n : nat) (slots : alloc_vec_Vec (hashmap_List_t T)) (i : usize) :
+  result (alloc_vec_Vec (hashmap_List_t T))
   :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
-    let i0 := vec_len (Hashmap_list_t T) slots in
+    let i0 := alloc_vec_Vec_len (hashmap_List_t T) slots in
     if i s< i0
     then (
       i1 <- usize_add i 1%usize;
-      slots0 <- vec_index_mut_back (Hashmap_list_t T) slots i HashmapListNil;
-      hashmap_hash_map_clear_loop_fwd_back T n0 slots0 i1)
+      slots0 <-
+        alloc_vec_Vec_index_mut_back (hashmap_List_t T) usize
+          (core_slice_index_usize_coresliceindexSliceIndexInst (hashmap_List_t
+          T)) slots i Hashmap_List_Nil;
+      hashmap_HashMap_clear_loop T n0 slots0 i1)
     else Return slots
   end
 .
 
 (** [hashmap_main::hashmap::HashMap::{0}::clear]: merged forward/backward function
     (there is a single backward function, and the forward function returns ()) *)
-Definition hashmap_hash_map_clear_fwd_back
-  (T : Type) (n : nat) (self : Hashmap_hash_map_t T) :
-  result (Hashmap_hash_map_t T)
+Definition hashmap_HashMap_clear
+  (T : Type) (n : nat) (self : hashmap_HashMap_t T) :
+  result (hashmap_HashMap_t T)
   :=
-  v <-
-    hashmap_hash_map_clear_loop_fwd_back T n self.(Hashmap_hash_map_slots)
-      0%usize;
+  v <- hashmap_HashMap_clear_loop T n self.(hashmap_HashMap_slots) 0%usize;
   Return
     {|
-      Hashmap_hash_map_num_entries := 0%usize;
-      Hashmap_hash_map_max_load_factor :=
-        self.(Hashmap_hash_map_max_load_factor);
-      Hashmap_hash_map_max_load := self.(Hashmap_hash_map_max_load);
-      Hashmap_hash_map_slots := v
+      hashmap_HashMap_num_entries := 0%usize;
+      hashmap_HashMap_max_load_factor := self.(hashmap_HashMap_max_load_factor);
+      hashmap_HashMap_max_load := self.(hashmap_HashMap_max_load);
+      hashmap_HashMap_slots := v
     |}
 .
 
 (** [hashmap_main::hashmap::HashMap::{0}::len]: forward function *)
-Definition hashmap_hash_map_len_fwd
-  (T : Type) (self : Hashmap_hash_map_t T) : result usize :=
-  Return self.(Hashmap_hash_map_num_entries)
+Definition hashmap_HashMap_len
+  (T : Type) (self : hashmap_HashMap_t T) : result usize :=
+  Return self.(hashmap_HashMap_num_entries)
 .
 
 (** [hashmap_main::hashmap::HashMap::{0}::insert_in_list]: loop 0: forward function *)
-Fixpoint hashmap_hash_map_insert_in_list_loop_fwd
-  (T : Type) (n : nat) (key : usize) (value : T) (ls : Hashmap_list_t T) :
+Fixpoint hashmap_HashMap_insert_in_list_loop
+  (T : Type) (n : nat) (key : usize) (value : T) (ls : hashmap_List_t T) :
   result bool
   :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
     match ls with
-    | HashmapListCons ckey cvalue tl =>
+    | Hashmap_List_Cons ckey cvalue tl =>
       if ckey s= key
       then Return false
-      else hashmap_hash_map_insert_in_list_loop_fwd T n0 key value tl
-    | HashmapListNil => Return true
+      else hashmap_HashMap_insert_in_list_loop T n0 key value tl
+    | Hashmap_List_Nil => Return true
     end
   end
 .
 
 (** [hashmap_main::hashmap::HashMap::{0}::insert_in_list]: forward function *)
-Definition hashmap_hash_map_insert_in_list_fwd
-  (T : Type) (n : nat) (key : usize) (value : T) (ls : Hashmap_list_t T) :
+Definition hashmap_HashMap_insert_in_list
+  (T : Type) (n : nat) (key : usize) (value : T) (ls : hashmap_List_t T) :
   result bool
   :=
-  hashmap_hash_map_insert_in_list_loop_fwd T n key value ls
+  hashmap_HashMap_insert_in_list_loop T n key value ls
 .
 
 (** [hashmap_main::hashmap::HashMap::{0}::insert_in_list]: loop 0: backward function 0 *)
-Fixpoint hashmap_hash_map_insert_in_list_loop_back
-  (T : Type) (n : nat) (key : usize) (value : T) (ls : Hashmap_list_t T) :
-  result (Hashmap_list_t T)
+Fixpoint hashmap_HashMap_insert_in_list_loop_back
+  (T : Type) (n : nat) (key : usize) (value : T) (ls : hashmap_List_t T) :
+  result (hashmap_List_t T)
   :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
     match ls with
-    | HashmapListCons ckey cvalue tl =>
+    | Hashmap_List_Cons ckey cvalue tl =>
       if ckey s= key
-      then Return (HashmapListCons ckey value tl)
+      then Return (Hashmap_List_Cons ckey value tl)
       else (
-        tl0 <- hashmap_hash_map_insert_in_list_loop_back T n0 key value tl;
-        Return (HashmapListCons ckey cvalue tl0))
-    | HashmapListNil =>
-      let l := HashmapListNil in Return (HashmapListCons key value l)
+        tl0 <- hashmap_HashMap_insert_in_list_loop_back T n0 key value tl;
+        Return (Hashmap_List_Cons ckey cvalue tl0))
+    | Hashmap_List_Nil =>
+      let l := Hashmap_List_Nil in Return (Hashmap_List_Cons key value l)
     end
   end
 .
 
 (** [hashmap_main::hashmap::HashMap::{0}::insert_in_list]: backward function 0 *)
-Definition hashmap_hash_map_insert_in_list_back
-  (T : Type) (n : nat) (key : usize) (value : T) (ls : Hashmap_list_t T) :
-  result (Hashmap_list_t T)
+Definition hashmap_HashMap_insert_in_list_back
+  (T : Type) (n : nat) (key : usize) (value : T) (ls : hashmap_List_t T) :
+  result (hashmap_List_t T)
   :=
-  hashmap_hash_map_insert_in_list_loop_back T n key value ls
+  hashmap_HashMap_insert_in_list_loop_back T n key value ls
 .
 
 (** [hashmap_main::hashmap::HashMap::{0}::insert_no_resize]: merged forward/backward function
     (there is a single backward function, and the forward function returns ()) *)
-Definition hashmap_hash_map_insert_no_resize_fwd_back
-  (T : Type) (n : nat) (self : Hashmap_hash_map_t T) (key : usize) (value : T)
-  :
-  result (Hashmap_hash_map_t T)
+Definition hashmap_HashMap_insert_no_resize
+  (T : Type) (n : nat) (self : hashmap_HashMap_t T) (key : usize) (value : T) :
+  result (hashmap_HashMap_t T)
   :=
-  hash <- hashmap_hash_key_fwd key;
-  let i := vec_len (Hashmap_list_t T) self.(Hashmap_hash_map_slots) in
+  hash <- hashmap_hash_key key;
+  let i := alloc_vec_Vec_len (hashmap_List_t T) self.(hashmap_HashMap_slots) in
   hash_mod <- usize_rem hash i;
   l <-
-    vec_index_mut_fwd (Hashmap_list_t T) self.(Hashmap_hash_map_slots) hash_mod;
-  inserted <- hashmap_hash_map_insert_in_list_fwd T n key value l;
+    alloc_vec_Vec_index_mut (hashmap_List_t T) usize
+      (core_slice_index_usize_coresliceindexSliceIndexInst (hashmap_List_t T))
+      self.(hashmap_HashMap_slots) hash_mod;
+  inserted <- hashmap_HashMap_insert_in_list T n key value l;
   if inserted
   then (
-    i0 <- usize_add self.(Hashmap_hash_map_num_entries) 1%usize;
-    l0 <- hashmap_hash_map_insert_in_list_back T n key value l;
+    i0 <- usize_add self.(hashmap_HashMap_num_entries) 1%usize;
+    l0 <- hashmap_HashMap_insert_in_list_back T n key value l;
     v <-
-      vec_index_mut_back (Hashmap_list_t T) self.(Hashmap_hash_map_slots)
-        hash_mod l0;
+      alloc_vec_Vec_index_mut_back (hashmap_List_t T) usize
+        (core_slice_index_usize_coresliceindexSliceIndexInst (hashmap_List_t
+        T)) self.(hashmap_HashMap_slots) hash_mod l0;
     Return
       {|
-        Hashmap_hash_map_num_entries := i0;
-        Hashmap_hash_map_max_load_factor :=
-          self.(Hashmap_hash_map_max_load_factor);
-        Hashmap_hash_map_max_load := self.(Hashmap_hash_map_max_load);
-        Hashmap_hash_map_slots := v
+        hashmap_HashMap_num_entries := i0;
+        hashmap_HashMap_max_load_factor :=
+          self.(hashmap_HashMap_max_load_factor);
+        hashmap_HashMap_max_load := self.(hashmap_HashMap_max_load);
+        hashmap_HashMap_slots := v
       |})
   else (
-    l0 <- hashmap_hash_map_insert_in_list_back T n key value l;
+    l0 <- hashmap_HashMap_insert_in_list_back T n key value l;
     v <-
-      vec_index_mut_back (Hashmap_list_t T) self.(Hashmap_hash_map_slots)
-        hash_mod l0;
+      alloc_vec_Vec_index_mut_back (hashmap_List_t T) usize
+        (core_slice_index_usize_coresliceindexSliceIndexInst (hashmap_List_t
+        T)) self.(hashmap_HashMap_slots) hash_mod l0;
     Return
       {|
-        Hashmap_hash_map_num_entries := self.(Hashmap_hash_map_num_entries);
-        Hashmap_hash_map_max_load_factor :=
-          self.(Hashmap_hash_map_max_load_factor);
-        Hashmap_hash_map_max_load := self.(Hashmap_hash_map_max_load);
-        Hashmap_hash_map_slots := v
+        hashmap_HashMap_num_entries := self.(hashmap_HashMap_num_entries);
+        hashmap_HashMap_max_load_factor :=
+          self.(hashmap_HashMap_max_load_factor);
+        hashmap_HashMap_max_load := self.(hashmap_HashMap_max_load);
+        hashmap_HashMap_slots := v
       |})
 .
 
-(** [core::num::u32::{8}::MAX] *)
-Definition core_num_u32_max_body : result u32 := Return 4294967295%u32.
-Definition core_num_u32_max_c : u32 := core_num_u32_max_body%global.
-
 (** [hashmap_main::hashmap::HashMap::{0}::move_elements_from_list]: loop 0: merged forward/backward function
     (there is a single backward function, and the forward function returns ()) *)
-Fixpoint hashmap_hash_map_move_elements_from_list_loop_fwd_back
-  (T : Type) (n : nat) (ntable : Hashmap_hash_map_t T) (ls : Hashmap_list_t T)
-  :
-  result (Hashmap_hash_map_t T)
+Fixpoint hashmap_HashMap_move_elements_from_list_loop
+  (T : Type) (n : nat) (ntable : hashmap_HashMap_t T) (ls : hashmap_List_t T) :
+  result (hashmap_HashMap_t T)
   :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
     match ls with
-    | HashmapListCons k v tl =>
-      ntable0 <- hashmap_hash_map_insert_no_resize_fwd_back T n0 ntable k v;
-      hashmap_hash_map_move_elements_from_list_loop_fwd_back T n0 ntable0 tl
-    | HashmapListNil => Return ntable
+    | Hashmap_List_Cons k v tl =>
+      ntable0 <- hashmap_HashMap_insert_no_resize T n0 ntable k v;
+      hashmap_HashMap_move_elements_from_list_loop T n0 ntable0 tl
+    | Hashmap_List_Nil => Return ntable
     end
   end
 .
 
 (** [hashmap_main::hashmap::HashMap::{0}::move_elements_from_list]: merged forward/backward function
     (there is a single backward function, and the forward function returns ()) *)
-Definition hashmap_hash_map_move_elements_from_list_fwd_back
-  (T : Type) (n : nat) (ntable : Hashmap_hash_map_t T) (ls : Hashmap_list_t T)
-  :
-  result (Hashmap_hash_map_t T)
+Definition hashmap_HashMap_move_elements_from_list
+  (T : Type) (n : nat) (ntable : hashmap_HashMap_t T) (ls : hashmap_List_t T) :
+  result (hashmap_HashMap_t T)
   :=
-  hashmap_hash_map_move_elements_from_list_loop_fwd_back T n ntable ls
+  hashmap_HashMap_move_elements_from_list_loop T n ntable ls
 .
 
 (** [hashmap_main::hashmap::HashMap::{0}::move_elements]: loop 0: merged forward/backward function
     (there is a single backward function, and the forward function returns ()) *)
-Fixpoint hashmap_hash_map_move_elements_loop_fwd_back
-  (T : Type) (n : nat) (ntable : Hashmap_hash_map_t T)
-  (slots : vec (Hashmap_list_t T)) (i : usize) :
-  result ((Hashmap_hash_map_t T) * (vec (Hashmap_list_t T)))
+Fixpoint hashmap_HashMap_move_elements_loop
+  (T : Type) (n : nat) (ntable : hashmap_HashMap_t T)
+  (slots : alloc_vec_Vec (hashmap_List_t T)) (i : usize) :
+  result ((hashmap_HashMap_t T) * (alloc_vec_Vec (hashmap_List_t T)))
   :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
-    let i0 := vec_len (Hashmap_list_t T) slots in
+    let i0 := alloc_vec_Vec_len (hashmap_List_t T) slots in
     if i s< i0
     then (
-      l <- vec_index_mut_fwd (Hashmap_list_t T) slots i;
-      let ls := mem_replace_fwd (Hashmap_list_t T) l HashmapListNil in
-      ntable0 <-
-        hashmap_hash_map_move_elements_from_list_fwd_back T n0 ntable ls;
+      l <-
+        alloc_vec_Vec_index_mut (hashmap_List_t T) usize
+          (core_slice_index_usize_coresliceindexSliceIndexInst (hashmap_List_t
+          T)) slots i;
+      let ls := core_mem_replace (hashmap_List_t T) l Hashmap_List_Nil in
+      ntable0 <- hashmap_HashMap_move_elements_from_list T n0 ntable ls;
       i1 <- usize_add i 1%usize;
-      let l0 := mem_replace_back (Hashmap_list_t T) l HashmapListNil in
-      slots0 <- vec_index_mut_back (Hashmap_list_t T) slots i l0;
-      hashmap_hash_map_move_elements_loop_fwd_back T n0 ntable0 slots0 i1)
+      let l0 := core_mem_replace_back (hashmap_List_t T) l Hashmap_List_Nil in
+      slots0 <-
+        alloc_vec_Vec_index_mut_back (hashmap_List_t T) usize
+          (core_slice_index_usize_coresliceindexSliceIndexInst (hashmap_List_t
+          T)) slots i l0;
+      hashmap_HashMap_move_elements_loop T n0 ntable0 slots0 i1)
     else Return (ntable, slots)
   end
 .
 
 (** [hashmap_main::hashmap::HashMap::{0}::move_elements]: merged forward/backward function
     (there is a single backward function, and the forward function returns ()) *)
-Definition hashmap_hash_map_move_elements_fwd_back
-  (T : Type) (n : nat) (ntable : Hashmap_hash_map_t T)
-  (slots : vec (Hashmap_list_t T)) (i : usize) :
-  result ((Hashmap_hash_map_t T) * (vec (Hashmap_list_t T)))
+Definition hashmap_HashMap_move_elements
+  (T : Type) (n : nat) (ntable : hashmap_HashMap_t T)
+  (slots : alloc_vec_Vec (hashmap_List_t T)) (i : usize) :
+  result ((hashmap_HashMap_t T) * (alloc_vec_Vec (hashmap_List_t T)))
   :=
-  hashmap_hash_map_move_elements_loop_fwd_back T n ntable slots i
+  hashmap_HashMap_move_elements_loop T n ntable slots i
 .
 
 (** [hashmap_main::hashmap::HashMap::{0}::try_resize]: merged forward/backward function
     (there is a single backward function, and the forward function returns ()) *)
-Definition hashmap_hash_map_try_resize_fwd_back
-  (T : Type) (n : nat) (self : Hashmap_hash_map_t T) :
-  result (Hashmap_hash_map_t T)
+Definition hashmap_HashMap_try_resize
+  (T : Type) (n : nat) (self : hashmap_HashMap_t T) :
+  result (hashmap_HashMap_t T)
   :=
-  max_usize <- scalar_cast U32 Usize core_num_u32_max_c;
-  let capacity := vec_len (Hashmap_list_t T) self.(Hashmap_hash_map_slots) in
+  max_usize <- scalar_cast U32 Usize core_u32_max;
+  let capacity :=
+    alloc_vec_Vec_len (hashmap_List_t T) self.(hashmap_HashMap_slots) in
   n1 <- usize_div max_usize 2%usize;
-  let (i, i0) := self.(Hashmap_hash_map_max_load_factor) in
+  let (i, i0) := self.(hashmap_HashMap_max_load_factor) in
   i1 <- usize_div n1 i;
   if capacity s<= i1
   then (
     i2 <- usize_mul capacity 2%usize;
-    ntable <- hashmap_hash_map_new_with_capacity_fwd T n i2 i i0;
+    ntable <- hashmap_HashMap_new_with_capacity T n i2 i i0;
     p <-
-      hashmap_hash_map_move_elements_fwd_back T n ntable
-        self.(Hashmap_hash_map_slots) 0%usize;
+      hashmap_HashMap_move_elements T n ntable self.(hashmap_HashMap_slots)
+        0%usize;
     let (ntable0, _) := p in
     Return
       {|
-        Hashmap_hash_map_num_entries := self.(Hashmap_hash_map_num_entries);
-        Hashmap_hash_map_max_load_factor := (i, i0);
-        Hashmap_hash_map_max_load := ntable0.(Hashmap_hash_map_max_load);
-        Hashmap_hash_map_slots := ntable0.(Hashmap_hash_map_slots)
+        hashmap_HashMap_num_entries := self.(hashmap_HashMap_num_entries);
+        hashmap_HashMap_max_load_factor := (i, i0);
+        hashmap_HashMap_max_load := ntable0.(hashmap_HashMap_max_load);
+        hashmap_HashMap_slots := ntable0.(hashmap_HashMap_slots)
       |})
   else
     Return
       {|
-        Hashmap_hash_map_num_entries := self.(Hashmap_hash_map_num_entries);
-        Hashmap_hash_map_max_load_factor := (i, i0);
-        Hashmap_hash_map_max_load := self.(Hashmap_hash_map_max_load);
-        Hashmap_hash_map_slots := self.(Hashmap_hash_map_slots)
+        hashmap_HashMap_num_entries := self.(hashmap_HashMap_num_entries);
+        hashmap_HashMap_max_load_factor := (i, i0);
+        hashmap_HashMap_max_load := self.(hashmap_HashMap_max_load);
+        hashmap_HashMap_slots := self.(hashmap_HashMap_slots)
       |}
 .
 
 (** [hashmap_main::hashmap::HashMap::{0}::insert]: merged forward/backward function
     (there is a single backward function, and the forward function returns ()) *)
-Definition hashmap_hash_map_insert_fwd_back
-  (T : Type) (n : nat) (self : Hashmap_hash_map_t T) (key : usize) (value : T)
-  :
-  result (Hashmap_hash_map_t T)
+Definition hashmap_HashMap_insert
+  (T : Type) (n : nat) (self : hashmap_HashMap_t T) (key : usize) (value : T) :
+  result (hashmap_HashMap_t T)
   :=
-  self0 <- hashmap_hash_map_insert_no_resize_fwd_back T n self key value;
-  i <- hashmap_hash_map_len_fwd T self0;
-  if i s> self0.(Hashmap_hash_map_max_load)
-  then hashmap_hash_map_try_resize_fwd_back T n self0
+  self0 <- hashmap_HashMap_insert_no_resize T n self key value;
+  i <- hashmap_HashMap_len T self0;
+  if i s> self0.(hashmap_HashMap_max_load)
+  then hashmap_HashMap_try_resize T n self0
   else Return self0
 .
 
 (** [hashmap_main::hashmap::HashMap::{0}::contains_key_in_list]: loop 0: forward function *)
-Fixpoint hashmap_hash_map_contains_key_in_list_loop_fwd
-  (T : Type) (n : nat) (key : usize) (ls : Hashmap_list_t T) : result bool :=
+Fixpoint hashmap_HashMap_contains_key_in_list_loop
+  (T : Type) (n : nat) (key : usize) (ls : hashmap_List_t T) : result bool :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
     match ls with
-    | HashmapListCons ckey t tl =>
+    | Hashmap_List_Cons ckey t tl =>
       if ckey s= key
       then Return true
-      else hashmap_hash_map_contains_key_in_list_loop_fwd T n0 key tl
-    | HashmapListNil => Return false
+      else hashmap_HashMap_contains_key_in_list_loop T n0 key tl
+    | Hashmap_List_Nil => Return false
     end
   end
 .
 
 (** [hashmap_main::hashmap::HashMap::{0}::contains_key_in_list]: forward function *)
-Definition hashmap_hash_map_contains_key_in_list_fwd
-  (T : Type) (n : nat) (key : usize) (ls : Hashmap_list_t T) : result bool :=
-  hashmap_hash_map_contains_key_in_list_loop_fwd T n key ls
+Definition hashmap_HashMap_contains_key_in_list
+  (T : Type) (n : nat) (key : usize) (ls : hashmap_List_t T) : result bool :=
+  hashmap_HashMap_contains_key_in_list_loop T n key ls
 .
 
 (** [hashmap_main::hashmap::HashMap::{0}::contains_key]: forward function *)
-Definition hashmap_hash_map_contains_key_fwd
-  (T : Type) (n : nat) (self : Hashmap_hash_map_t T) (key : usize) :
+Definition hashmap_HashMap_contains_key
+  (T : Type) (n : nat) (self : hashmap_HashMap_t T) (key : usize) :
   result bool
   :=
-  hash <- hashmap_hash_key_fwd key;
-  let i := vec_len (Hashmap_list_t T) self.(Hashmap_hash_map_slots) in
+  hash <- hashmap_hash_key key;
+  let i := alloc_vec_Vec_len (hashmap_List_t T) self.(hashmap_HashMap_slots) in
   hash_mod <- usize_rem hash i;
-  l <- vec_index_fwd (Hashmap_list_t T) self.(Hashmap_hash_map_slots) hash_mod;
-  hashmap_hash_map_contains_key_in_list_fwd T n key l
+  l <-
+    alloc_vec_Vec_index (hashmap_List_t T) usize
+      (core_slice_index_usize_coresliceindexSliceIndexInst (hashmap_List_t T))
+      self.(hashmap_HashMap_slots) hash_mod;
+  hashmap_HashMap_contains_key_in_list T n key l
 .
 
 (** [hashmap_main::hashmap::HashMap::{0}::get_in_list]: loop 0: forward function *)
-Fixpoint hashmap_hash_map_get_in_list_loop_fwd
-  (T : Type) (n : nat) (key : usize) (ls : Hashmap_list_t T) : result T :=
+Fixpoint hashmap_HashMap_get_in_list_loop
+  (T : Type) (n : nat) (key : usize) (ls : hashmap_List_t T) : result T :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
     match ls with
-    | HashmapListCons ckey cvalue tl =>
+    | Hashmap_List_Cons ckey cvalue tl =>
       if ckey s= key
       then Return cvalue
-      else hashmap_hash_map_get_in_list_loop_fwd T n0 key tl
-    | HashmapListNil => Fail_ Failure
+      else hashmap_HashMap_get_in_list_loop T n0 key tl
+    | Hashmap_List_Nil => Fail_ Failure
     end
   end
 .
 
 (** [hashmap_main::hashmap::HashMap::{0}::get_in_list]: forward function *)
-Definition hashmap_hash_map_get_in_list_fwd
-  (T : Type) (n : nat) (key : usize) (ls : Hashmap_list_t T) : result T :=
-  hashmap_hash_map_get_in_list_loop_fwd T n key ls
+Definition hashmap_HashMap_get_in_list
+  (T : Type) (n : nat) (key : usize) (ls : hashmap_List_t T) : result T :=
+  hashmap_HashMap_get_in_list_loop T n key ls
 .
 
 (** [hashmap_main::hashmap::HashMap::{0}::get]: forward function *)
-Definition hashmap_hash_map_get_fwd
-  (T : Type) (n : nat) (self : Hashmap_hash_map_t T) (key : usize) :
-  result T
-  :=
-  hash <- hashmap_hash_key_fwd key;
-  let i := vec_len (Hashmap_list_t T) self.(Hashmap_hash_map_slots) in
+Definition hashmap_HashMap_get
+  (T : Type) (n : nat) (self : hashmap_HashMap_t T) (key : usize) : result T :=
+  hash <- hashmap_hash_key key;
+  let i := alloc_vec_Vec_len (hashmap_List_t T) self.(hashmap_HashMap_slots) in
   hash_mod <- usize_rem hash i;
-  l <- vec_index_fwd (Hashmap_list_t T) self.(Hashmap_hash_map_slots) hash_mod;
-  hashmap_hash_map_get_in_list_fwd T n key l
+  l <-
+    alloc_vec_Vec_index (hashmap_List_t T) usize
+      (core_slice_index_usize_coresliceindexSliceIndexInst (hashmap_List_t T))
+      self.(hashmap_HashMap_slots) hash_mod;
+  hashmap_HashMap_get_in_list T n key l
 .
 
 (** [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list]: loop 0: forward function *)
-Fixpoint hashmap_hash_map_get_mut_in_list_loop_fwd
-  (T : Type) (n : nat) (ls : Hashmap_list_t T) (key : usize) : result T :=
+Fixpoint hashmap_HashMap_get_mut_in_list_loop
+  (T : Type) (n : nat) (ls : hashmap_List_t T) (key : usize) : result T :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
     match ls with
-    | HashmapListCons ckey cvalue tl =>
+    | Hashmap_List_Cons ckey cvalue tl =>
       if ckey s= key
       then Return cvalue
-      else hashmap_hash_map_get_mut_in_list_loop_fwd T n0 tl key
-    | HashmapListNil => Fail_ Failure
+      else hashmap_HashMap_get_mut_in_list_loop T n0 tl key
+    | Hashmap_List_Nil => Fail_ Failure
     end
   end
 .
 
 (** [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list]: forward function *)
-Definition hashmap_hash_map_get_mut_in_list_fwd
-  (T : Type) (n : nat) (ls : Hashmap_list_t T) (key : usize) : result T :=
-  hashmap_hash_map_get_mut_in_list_loop_fwd T n ls key
+Definition hashmap_HashMap_get_mut_in_list
+  (T : Type) (n : nat) (ls : hashmap_List_t T) (key : usize) : result T :=
+  hashmap_HashMap_get_mut_in_list_loop T n ls key
 .
 
 (** [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list]: loop 0: backward function 0 *)
-Fixpoint hashmap_hash_map_get_mut_in_list_loop_back
-  (T : Type) (n : nat) (ls : Hashmap_list_t T) (key : usize) (ret : T) :
-  result (Hashmap_list_t T)
+Fixpoint hashmap_HashMap_get_mut_in_list_loop_back
+  (T : Type) (n : nat) (ls : hashmap_List_t T) (key : usize) (ret : T) :
+  result (hashmap_List_t T)
   :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
     match ls with
-    | HashmapListCons ckey cvalue tl =>
+    | Hashmap_List_Cons ckey cvalue tl =>
       if ckey s= key
-      then Return (HashmapListCons ckey ret tl)
+      then Return (Hashmap_List_Cons ckey ret tl)
       else (
-        tl0 <- hashmap_hash_map_get_mut_in_list_loop_back T n0 tl key ret;
-        Return (HashmapListCons ckey cvalue tl0))
-    | HashmapListNil => Fail_ Failure
+        tl0 <- hashmap_HashMap_get_mut_in_list_loop_back T n0 tl key ret;
+        Return (Hashmap_List_Cons ckey cvalue tl0))
+    | Hashmap_List_Nil => Fail_ Failure
     end
   end
 .
 
 (** [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list]: backward function 0 *)
-Definition hashmap_hash_map_get_mut_in_list_back
-  (T : Type) (n : nat) (ls : Hashmap_list_t T) (key : usize) (ret : T) :
-  result (Hashmap_list_t T)
+Definition hashmap_HashMap_get_mut_in_list_back
+  (T : Type) (n : nat) (ls : hashmap_List_t T) (key : usize) (ret : T) :
+  result (hashmap_List_t T)
   :=
-  hashmap_hash_map_get_mut_in_list_loop_back T n ls key ret
+  hashmap_HashMap_get_mut_in_list_loop_back T n ls key ret
 .
 
 (** [hashmap_main::hashmap::HashMap::{0}::get_mut]: forward function *)
-Definition hashmap_hash_map_get_mut_fwd
-  (T : Type) (n : nat) (self : Hashmap_hash_map_t T) (key : usize) :
-  result T
-  :=
-  hash <- hashmap_hash_key_fwd key;
-  let i := vec_len (Hashmap_list_t T) self.(Hashmap_hash_map_slots) in
+Definition hashmap_HashMap_get_mut
+  (T : Type) (n : nat) (self : hashmap_HashMap_t T) (key : usize) : result T :=
+  hash <- hashmap_hash_key key;
+  let i := alloc_vec_Vec_len (hashmap_List_t T) self.(hashmap_HashMap_slots) in
   hash_mod <- usize_rem hash i;
   l <-
-    vec_index_mut_fwd (Hashmap_list_t T) self.(Hashmap_hash_map_slots) hash_mod;
-  hashmap_hash_map_get_mut_in_list_fwd T n l key
+    alloc_vec_Vec_index_mut (hashmap_List_t T) usize
+      (core_slice_index_usize_coresliceindexSliceIndexInst (hashmap_List_t T))
+      self.(hashmap_HashMap_slots) hash_mod;
+  hashmap_HashMap_get_mut_in_list T n l key
 .
 
 (** [hashmap_main::hashmap::HashMap::{0}::get_mut]: backward function 0 *)
-Definition hashmap_hash_map_get_mut_back
-  (T : Type) (n : nat) (self : Hashmap_hash_map_t T) (key : usize) (ret : T) :
-  result (Hashmap_hash_map_t T)
+Definition hashmap_HashMap_get_mut_back
+  (T : Type) (n : nat) (self : hashmap_HashMap_t T) (key : usize) (ret : T) :
+  result (hashmap_HashMap_t T)
   :=
-  hash <- hashmap_hash_key_fwd key;
-  let i := vec_len (Hashmap_list_t T) self.(Hashmap_hash_map_slots) in
+  hash <- hashmap_hash_key key;
+  let i := alloc_vec_Vec_len (hashmap_List_t T) self.(hashmap_HashMap_slots) in
   hash_mod <- usize_rem hash i;
   l <-
-    vec_index_mut_fwd (Hashmap_list_t T) self.(Hashmap_hash_map_slots) hash_mod;
-  l0 <- hashmap_hash_map_get_mut_in_list_back T n l key ret;
+    alloc_vec_Vec_index_mut (hashmap_List_t T) usize
+      (core_slice_index_usize_coresliceindexSliceIndexInst (hashmap_List_t T))
+      self.(hashmap_HashMap_slots) hash_mod;
+  l0 <- hashmap_HashMap_get_mut_in_list_back T n l key ret;
   v <-
-    vec_index_mut_back (Hashmap_list_t T) self.(Hashmap_hash_map_slots)
-      hash_mod l0;
+    alloc_vec_Vec_index_mut_back (hashmap_List_t T) usize
+      (core_slice_index_usize_coresliceindexSliceIndexInst (hashmap_List_t T))
+      self.(hashmap_HashMap_slots) hash_mod l0;
   Return
     {|
-      Hashmap_hash_map_num_entries := self.(Hashmap_hash_map_num_entries);
-      Hashmap_hash_map_max_load_factor :=
-        self.(Hashmap_hash_map_max_load_factor);
-      Hashmap_hash_map_max_load := self.(Hashmap_hash_map_max_load);
-      Hashmap_hash_map_slots := v
+      hashmap_HashMap_num_entries := self.(hashmap_HashMap_num_entries);
+      hashmap_HashMap_max_load_factor := self.(hashmap_HashMap_max_load_factor);
+      hashmap_HashMap_max_load := self.(hashmap_HashMap_max_load);
+      hashmap_HashMap_slots := v
     |}
 .
 
 (** [hashmap_main::hashmap::HashMap::{0}::remove_from_list]: loop 0: forward function *)
-Fixpoint hashmap_hash_map_remove_from_list_loop_fwd
-  (T : Type) (n : nat) (key : usize) (ls : Hashmap_list_t T) :
+Fixpoint hashmap_HashMap_remove_from_list_loop
+  (T : Type) (n : nat) (key : usize) (ls : hashmap_List_t T) :
   result (option T)
   :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
     match ls with
-    | HashmapListCons ckey t tl =>
+    | Hashmap_List_Cons ckey t tl =>
       if ckey s= key
       then
         let mv_ls :=
-          mem_replace_fwd (Hashmap_list_t T) (HashmapListCons ckey t tl)
-            HashmapListNil in
+          core_mem_replace (hashmap_List_t T) (Hashmap_List_Cons ckey t tl)
+            Hashmap_List_Nil in
         match mv_ls with
-        | HashmapListCons i cvalue tl0 => Return (Some cvalue)
-        | HashmapListNil => Fail_ Failure
+        | Hashmap_List_Cons i cvalue tl0 => Return (Some cvalue)
+        | Hashmap_List_Nil => Fail_ Failure
         end
-      else hashmap_hash_map_remove_from_list_loop_fwd T n0 key tl
-    | HashmapListNil => Return None
+      else hashmap_HashMap_remove_from_list_loop T n0 key tl
+    | Hashmap_List_Nil => Return None
     end
   end
 .
 
 (** [hashmap_main::hashmap::HashMap::{0}::remove_from_list]: forward function *)
-Definition hashmap_hash_map_remove_from_list_fwd
-  (T : Type) (n : nat) (key : usize) (ls : Hashmap_list_t T) :
+Definition hashmap_HashMap_remove_from_list
+  (T : Type) (n : nat) (key : usize) (ls : hashmap_List_t T) :
   result (option T)
   :=
-  hashmap_hash_map_remove_from_list_loop_fwd T n key ls
+  hashmap_HashMap_remove_from_list_loop T n key ls
 .
 
 (** [hashmap_main::hashmap::HashMap::{0}::remove_from_list]: loop 0: backward function 1 *)
-Fixpoint hashmap_hash_map_remove_from_list_loop_back
-  (T : Type) (n : nat) (key : usize) (ls : Hashmap_list_t T) :
-  result (Hashmap_list_t T)
+Fixpoint hashmap_HashMap_remove_from_list_loop_back
+  (T : Type) (n : nat) (key : usize) (ls : hashmap_List_t T) :
+  result (hashmap_List_t T)
   :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
     match ls with
-    | HashmapListCons ckey t tl =>
+    | Hashmap_List_Cons ckey t tl =>
       if ckey s= key
       then
         let mv_ls :=
-          mem_replace_fwd (Hashmap_list_t T) (HashmapListCons ckey t tl)
-            HashmapListNil in
+          core_mem_replace (hashmap_List_t T) (Hashmap_List_Cons ckey t tl)
+            Hashmap_List_Nil in
         match mv_ls with
-        | HashmapListCons i cvalue tl0 => Return tl0
-        | HashmapListNil => Fail_ Failure
+        | Hashmap_List_Cons i cvalue tl0 => Return tl0
+        | Hashmap_List_Nil => Fail_ Failure
         end
       else (
-        tl0 <- hashmap_hash_map_remove_from_list_loop_back T n0 key tl;
-        Return (HashmapListCons ckey t tl0))
-    | HashmapListNil => Return HashmapListNil
+        tl0 <- hashmap_HashMap_remove_from_list_loop_back T n0 key tl;
+        Return (Hashmap_List_Cons ckey t tl0))
+    | Hashmap_List_Nil => Return Hashmap_List_Nil
     end
   end
 .
 
 (** [hashmap_main::hashmap::HashMap::{0}::remove_from_list]: backward function 1 *)
-Definition hashmap_hash_map_remove_from_list_back
-  (T : Type) (n : nat) (key : usize) (ls : Hashmap_list_t T) :
-  result (Hashmap_list_t T)
+Definition hashmap_HashMap_remove_from_list_back
+  (T : Type) (n : nat) (key : usize) (ls : hashmap_List_t T) :
+  result (hashmap_List_t T)
   :=
-  hashmap_hash_map_remove_from_list_loop_back T n key ls
+  hashmap_HashMap_remove_from_list_loop_back T n key ls
 .
 
 (** [hashmap_main::hashmap::HashMap::{0}::remove]: forward function *)
-Definition hashmap_hash_map_remove_fwd
-  (T : Type) (n : nat) (self : Hashmap_hash_map_t T) (key : usize) :
+Definition hashmap_HashMap_remove
+  (T : Type) (n : nat) (self : hashmap_HashMap_t T) (key : usize) :
   result (option T)
   :=
-  hash <- hashmap_hash_key_fwd key;
-  let i := vec_len (Hashmap_list_t T) self.(Hashmap_hash_map_slots) in
+  hash <- hashmap_hash_key key;
+  let i := alloc_vec_Vec_len (hashmap_List_t T) self.(hashmap_HashMap_slots) in
   hash_mod <- usize_rem hash i;
   l <-
-    vec_index_mut_fwd (Hashmap_list_t T) self.(Hashmap_hash_map_slots) hash_mod;
-  x <- hashmap_hash_map_remove_from_list_fwd T n key l;
+    alloc_vec_Vec_index_mut (hashmap_List_t T) usize
+      (core_slice_index_usize_coresliceindexSliceIndexInst (hashmap_List_t T))
+      self.(hashmap_HashMap_slots) hash_mod;
+  x <- hashmap_HashMap_remove_from_list T n key l;
   match x with
   | None => Return None
   | Some x0 =>
-    _ <- usize_sub self.(Hashmap_hash_map_num_entries) 1%usize;
-    Return (Some x0)
+    _ <- usize_sub self.(hashmap_HashMap_num_entries) 1%usize; Return (Some x0)
   end
 .
 
 (** [hashmap_main::hashmap::HashMap::{0}::remove]: backward function 0 *)
-Definition hashmap_hash_map_remove_back
-  (T : Type) (n : nat) (self : Hashmap_hash_map_t T) (key : usize) :
-  result (Hashmap_hash_map_t T)
+Definition hashmap_HashMap_remove_back
+  (T : Type) (n : nat) (self : hashmap_HashMap_t T) (key : usize) :
+  result (hashmap_HashMap_t T)
   :=
-  hash <- hashmap_hash_key_fwd key;
-  let i := vec_len (Hashmap_list_t T) self.(Hashmap_hash_map_slots) in
+  hash <- hashmap_hash_key key;
+  let i := alloc_vec_Vec_len (hashmap_List_t T) self.(hashmap_HashMap_slots) in
   hash_mod <- usize_rem hash i;
   l <-
-    vec_index_mut_fwd (Hashmap_list_t T) self.(Hashmap_hash_map_slots) hash_mod;
-  x <- hashmap_hash_map_remove_from_list_fwd T n key l;
+    alloc_vec_Vec_index_mut (hashmap_List_t T) usize
+      (core_slice_index_usize_coresliceindexSliceIndexInst (hashmap_List_t T))
+      self.(hashmap_HashMap_slots) hash_mod;
+  x <- hashmap_HashMap_remove_from_list T n key l;
   match x with
   | None =>
-    l0 <- hashmap_hash_map_remove_from_list_back T n key l;
+    l0 <- hashmap_HashMap_remove_from_list_back T n key l;
     v <-
-      vec_index_mut_back (Hashmap_list_t T) self.(Hashmap_hash_map_slots)
-        hash_mod l0;
+      alloc_vec_Vec_index_mut_back (hashmap_List_t T) usize
+        (core_slice_index_usize_coresliceindexSliceIndexInst (hashmap_List_t
+        T)) self.(hashmap_HashMap_slots) hash_mod l0;
     Return
       {|
-        Hashmap_hash_map_num_entries := self.(Hashmap_hash_map_num_entries);
-        Hashmap_hash_map_max_load_factor :=
-          self.(Hashmap_hash_map_max_load_factor);
-        Hashmap_hash_map_max_load := self.(Hashmap_hash_map_max_load);
-        Hashmap_hash_map_slots := v
+        hashmap_HashMap_num_entries := self.(hashmap_HashMap_num_entries);
+        hashmap_HashMap_max_load_factor :=
+          self.(hashmap_HashMap_max_load_factor);
+        hashmap_HashMap_max_load := self.(hashmap_HashMap_max_load);
+        hashmap_HashMap_slots := v
       |}
   | Some x0 =>
-    i0 <- usize_sub self.(Hashmap_hash_map_num_entries) 1%usize;
-    l0 <- hashmap_hash_map_remove_from_list_back T n key l;
+    i0 <- usize_sub self.(hashmap_HashMap_num_entries) 1%usize;
+    l0 <- hashmap_HashMap_remove_from_list_back T n key l;
     v <-
-      vec_index_mut_back (Hashmap_list_t T) self.(Hashmap_hash_map_slots)
-        hash_mod l0;
+      alloc_vec_Vec_index_mut_back (hashmap_List_t T) usize
+        (core_slice_index_usize_coresliceindexSliceIndexInst (hashmap_List_t
+        T)) self.(hashmap_HashMap_slots) hash_mod l0;
     Return
       {|
-        Hashmap_hash_map_num_entries := i0;
-        Hashmap_hash_map_max_load_factor :=
-          self.(Hashmap_hash_map_max_load_factor);
-        Hashmap_hash_map_max_load := self.(Hashmap_hash_map_max_load);
-        Hashmap_hash_map_slots := v
+        hashmap_HashMap_num_entries := i0;
+        hashmap_HashMap_max_load_factor :=
+          self.(hashmap_HashMap_max_load_factor);
+        hashmap_HashMap_max_load := self.(hashmap_HashMap_max_load);
+        hashmap_HashMap_slots := v
       |}
   end
 .
 
 (** [hashmap_main::hashmap::test1]: forward function *)
-Definition hashmap_test1_fwd (n : nat) : result unit :=
-  hm <- hashmap_hash_map_new_fwd u64 n;
-  hm0 <- hashmap_hash_map_insert_fwd_back u64 n hm 0%usize 42%u64;
-  hm1 <- hashmap_hash_map_insert_fwd_back u64 n hm0 128%usize 18%u64;
-  hm2 <- hashmap_hash_map_insert_fwd_back u64 n hm1 1024%usize 138%u64;
-  hm3 <- hashmap_hash_map_insert_fwd_back u64 n hm2 1056%usize 256%u64;
-  i <- hashmap_hash_map_get_fwd u64 n hm3 128%usize;
+Definition hashmap_test1 (n : nat) : result unit :=
+  hm <- hashmap_HashMap_new u64 n;
+  hm0 <- hashmap_HashMap_insert u64 n hm 0%usize 42%u64;
+  hm1 <- hashmap_HashMap_insert u64 n hm0 128%usize 18%u64;
+  hm2 <- hashmap_HashMap_insert u64 n hm1 1024%usize 138%u64;
+  hm3 <- hashmap_HashMap_insert u64 n hm2 1056%usize 256%u64;
+  i <- hashmap_HashMap_get u64 n hm3 128%usize;
   if negb (i s= 18%u64)
   then Fail_ Failure
   else (
-    hm4 <- hashmap_hash_map_get_mut_back u64 n hm3 1024%usize 56%u64;
-    i0 <- hashmap_hash_map_get_fwd u64 n hm4 1024%usize;
+    hm4 <- hashmap_HashMap_get_mut_back u64 n hm3 1024%usize 56%u64;
+    i0 <- hashmap_HashMap_get u64 n hm4 1024%usize;
     if negb (i0 s= 56%u64)
     then Fail_ Failure
     else (
-      x <- hashmap_hash_map_remove_fwd u64 n hm4 1024%usize;
+      x <- hashmap_HashMap_remove u64 n hm4 1024%usize;
       match x with
       | None => Fail_ Failure
       | Some x0 =>
         if negb (x0 s= 56%u64)
         then Fail_ Failure
         else (
-          hm5 <- hashmap_hash_map_remove_back u64 n hm4 1024%usize;
-          i1 <- hashmap_hash_map_get_fwd u64 n hm5 0%usize;
+          hm5 <- hashmap_HashMap_remove_back u64 n hm4 1024%usize;
+          i1 <- hashmap_HashMap_get u64 n hm5 0%usize;
           if negb (i1 s= 42%u64)
           then Fail_ Failure
           else (
-            i2 <- hashmap_hash_map_get_fwd u64 n hm5 128%usize;
+            i2 <- hashmap_HashMap_get u64 n hm5 128%usize;
             if negb (i2 s= 18%u64)
             then Fail_ Failure
             else (
-              i3 <- hashmap_hash_map_get_fwd u64 n hm5 1056%usize;
+              i3 <- hashmap_HashMap_get u64 n hm5 1056%usize;
               if negb (i3 s= 256%u64) then Fail_ Failure else Return tt)))
       end))
 .
 
 (** [hashmap_main::insert_on_disk]: forward function *)
-Definition insert_on_disk_fwd
+Definition insert_on_disk
   (n : nat) (key : usize) (value : u64) (st : state) : result (state * unit) :=
-  p <- hashmap_utils_deserialize_fwd st;
+  p <- hashmap_utils_deserialize st;
   let (st0, hm) := p in
-  hm0 <- hashmap_hash_map_insert_fwd_back u64 n hm key value;
-  p0 <- hashmap_utils_serialize_fwd hm0 st0;
+  hm0 <- hashmap_HashMap_insert u64 n hm key value;
+  p0 <- hashmap_utils_serialize hm0 st0;
   let (st1, _) := p0 in
   Return (st1, tt)
 .
 
 (** [hashmap_main::main]: forward function *)
-Definition main_fwd : result unit :=
+Definition main : result unit :=
   Return tt.
 
-(** Unit test for [hashmap_main::main] *)
-Check (main_fwd )%return.
-
 End HashmapMain_Funs .
diff --git a/tests/coq/hashmap_on_disk/HashmapMain_Opaque.v b/tests/coq/hashmap_on_disk/HashmapMain_Opaque.v
index 2d17cc29..5e376239 100644
--- a/tests/coq/hashmap_on_disk/HashmapMain_Opaque.v
+++ b/tests/coq/hashmap_on_disk/HashmapMain_Opaque.v
@@ -11,13 +11,13 @@ Import HashmapMain_Types.
 Module HashmapMain_Opaque.
 
 (** [hashmap_main::hashmap_utils::deserialize]: forward function *)
-Axiom hashmap_utils_deserialize_fwd
-  : state -> result (state * (Hashmap_hash_map_t u64))
+Axiom hashmap_utils_deserialize
+  : state -> result (state * (hashmap_HashMap_t u64))
 .
 
 (** [hashmap_main::hashmap_utils::serialize]: forward function *)
-Axiom hashmap_utils_serialize_fwd
-  : Hashmap_hash_map_t u64 -> state -> result (state * unit)
+Axiom hashmap_utils_serialize
+  : hashmap_HashMap_t u64 -> state -> result (state * unit)
 .
 
 End HashmapMain_Opaque .
diff --git a/tests/coq/hashmap_on_disk/HashmapMain_Types.v b/tests/coq/hashmap_on_disk/HashmapMain_Types.v
index 36aaaf25..95e5f35b 100644
--- a/tests/coq/hashmap_on_disk/HashmapMain_Types.v
+++ b/tests/coq/hashmap_on_disk/HashmapMain_Types.v
@@ -9,29 +9,29 @@ Local Open Scope Primitives_scope.
 Module HashmapMain_Types.
 
 (** [hashmap_main::hashmap::List] *)
-Inductive Hashmap_list_t (T : Type) :=
-| HashmapListCons : usize -> T -> Hashmap_list_t T -> Hashmap_list_t T
-| HashmapListNil : Hashmap_list_t T
+Inductive hashmap_List_t (T : Type) :=
+| Hashmap_List_Cons : usize -> T -> hashmap_List_t T -> hashmap_List_t T
+| Hashmap_List_Nil : hashmap_List_t T
 .
 
-Arguments HashmapListCons {T} _ _ _.
-Arguments HashmapListNil {T}.
+Arguments Hashmap_List_Cons { _ }.
+Arguments Hashmap_List_Nil { _ }.
 
 (** [hashmap_main::hashmap::HashMap] *)
-Record Hashmap_hash_map_t (T : Type) :=
-mkHashmap_hash_map_t {
-  Hashmap_hash_map_num_entries : usize;
-  Hashmap_hash_map_max_load_factor : (usize * usize);
-  Hashmap_hash_map_max_load : usize;
-  Hashmap_hash_map_slots : vec (Hashmap_list_t T);
+Record hashmap_HashMap_t (T : Type) :=
+mkhashmap_HashMap_t {
+  hashmap_HashMap_num_entries : usize;
+  hashmap_HashMap_max_load_factor : (usize * usize);
+  hashmap_HashMap_max_load : usize;
+  hashmap_HashMap_slots : alloc_vec_Vec (hashmap_List_t T);
 }
 .
 
-Arguments mkHashmap_hash_map_t {T} _ _ _ _.
-Arguments Hashmap_hash_map_num_entries {T}.
-Arguments Hashmap_hash_map_max_load_factor {T}.
-Arguments Hashmap_hash_map_max_load {T}.
-Arguments Hashmap_hash_map_slots {T}.
+Arguments mkhashmap_HashMap_t { _ }.
+Arguments hashmap_HashMap_num_entries { _ }.
+Arguments hashmap_HashMap_max_load_factor { _ }.
+Arguments hashmap_HashMap_max_load { _ }.
+Arguments hashmap_HashMap_slots { _ }.
 
 (** The state type used in the state-error monad *)
 Axiom state : Type.
diff --git a/tests/coq/hashmap_on_disk/Primitives.v b/tests/coq/hashmap_on_disk/Primitives.v
index 71a2d9c3..85e38f01 100644
--- a/tests/coq/hashmap_on_disk/Primitives.v
+++ b/tests/coq/hashmap_on_disk/Primitives.v
@@ -63,13 +63,15 @@ Check (if true then Return (1 + 2) else Fail_ Failure)%global = 3.
 
 (*** Misc *)
 
-
 Definition string := Coq.Strings.String.string.
 Definition char := Coq.Strings.Ascii.ascii.
 Definition char_of_byte := Coq.Strings.Ascii.ascii_of_byte.
 
-Definition mem_replace_fwd (a : Type) (x : a) (y : a) : a := x .
-Definition mem_replace_back (a : Type) (x : a) (y : a) : a := y .
+Definition core_mem_replace (a : Type) (x : a) (y : a) : a := x .
+Definition core_mem_replace_back (a : Type) (x : a) (y : a) : a := y .
+
+Record mut_raw_ptr (T : Type) := { mut_raw_ptr_v : T }.
+Record const_raw_ptr (T : Type) := { const_raw_ptr_v : T }.
 
 (*** Scalars *)
 
@@ -394,12 +396,89 @@ Notation "x s< y" := (scalar_ltb x y)  (at level 80) : Primitives_scope.
 Notation "x s>= y" := (scalar_geb x y)  (at level 80) : Primitives_scope.
 Notation "x s> y" := (scalar_gtb x y)  (at level 80) : Primitives_scope.
 
-(*** Range *)
-Record range (T : Type) := mk_range {
-  start: T;
-  end_: T;
+(** Constants *)
+Definition core_u8_max    := u8_max %u32.
+Definition core_u16_max   := u16_max %u32.
+Definition core_u32_max   := u32_max %u32.
+Definition core_u64_max   := u64_max %u64.
+Definition core_u128_max  := u64_max %u128.
+Axiom core_usize_max : usize. (** TODO *)
+Definition core_i8_max    := i8_max %i32.
+Definition core_i16_max   := i16_max %i32.
+Definition core_i32_max   := i32_max %i32.
+Definition core_i64_max   := i64_max %i64.
+Definition core_i128_max  := i64_max %i128.
+Axiom core_isize_max : isize. (** TODO *)
+
+(*** core::ops *)
+
+(* Trait declaration: [core::ops::index::Index] *)
+Record core_ops_index_Index (Self Idx : Type) := mk_core_ops_index_Index {
+  core_ops_index_Index_Output : Type;
+  core_ops_index_Index_index : Self -> Idx -> result core_ops_index_Index_Output;
+}.
+Arguments mk_core_ops_index_Index {_ _}.
+Arguments core_ops_index_Index_Output {_ _}.
+Arguments core_ops_index_Index_index {_ _}.
+
+(* Trait declaration: [core::ops::index::IndexMut] *)
+Record core_ops_index_IndexMut (Self Idx : Type) := mk_core_ops_index_IndexMut {
+  core_ops_index_IndexMut_indexInst : core_ops_index_Index Self Idx;
+  core_ops_index_IndexMut_index_mut : Self -> Idx -> result core_ops_index_IndexMut_indexInst.(core_ops_index_Index_Output);
+  core_ops_index_IndexMut_index_mut_back : Self -> Idx -> core_ops_index_IndexMut_indexInst.(core_ops_index_Index_Output) -> result Self;
+}.
+Arguments mk_core_ops_index_IndexMut {_ _}.
+Arguments core_ops_index_IndexMut_indexInst {_ _}.
+Arguments core_ops_index_IndexMut_index_mut {_ _}.
+Arguments core_ops_index_IndexMut_index_mut_back {_ _}.
+
+(* Trait declaration [core::ops::deref::Deref] *)
+Record core_ops_deref_Deref (Self : Type) := mk_core_ops_deref_Deref {
+  core_ops_deref_Deref_target : Type;
+  core_ops_deref_Deref_deref : Self -> result core_ops_deref_Deref_target;
+}.
+Arguments mk_core_ops_deref_Deref {_}.
+Arguments core_ops_deref_Deref_target {_}.
+Arguments core_ops_deref_Deref_deref {_}.
+
+(* Trait declaration [core::ops::deref::DerefMut] *)
+Record core_ops_deref_DerefMut (Self : Type) := mk_core_ops_deref_DerefMut {
+  core_ops_deref_DerefMut_derefInst : core_ops_deref_Deref Self;
+  core_ops_deref_DerefMut_deref_mut : Self -> result core_ops_deref_DerefMut_derefInst.(core_ops_deref_Deref_target);
+  core_ops_deref_DerefMut_deref_mut_back : Self -> core_ops_deref_DerefMut_derefInst.(core_ops_deref_Deref_target) -> result Self;
 }.
-Arguments mk_range {_}.
+Arguments mk_core_ops_deref_DerefMut {_}.
+Arguments core_ops_deref_DerefMut_derefInst {_}.
+Arguments core_ops_deref_DerefMut_deref_mut {_}.
+Arguments core_ops_deref_DerefMut_deref_mut_back {_}.
+
+Record core_ops_range_Range (T : Type) := mk_core_ops_range_Range {
+  core_ops_range_Range_start : T;
+  core_ops_range_Range_end_ : T;
+}.
+Arguments mk_core_ops_range_Range {_}.
+Arguments core_ops_range_Range_start {_}.
+Arguments core_ops_range_Range_end_ {_}.
+
+(*** [alloc] *)
+
+Definition alloc_boxed_Box_deref (T : Type) (x : T) : result T := Return x.
+Definition alloc_boxed_Box_deref_mut (T : Type) (x : T) : result T := Return x.
+Definition alloc_boxed_Box_deref_mut_back (T : Type) (_ : T) (x : T) : result T := Return x.
+
+(* Trait instance *)
+Definition alloc_boxed_Box_coreOpsDerefInst (Self : Type) : core_ops_deref_Deref Self := {|
+  core_ops_deref_Deref_target := Self;
+  core_ops_deref_Deref_deref := alloc_boxed_Box_deref Self;
+|}.
+
+(* Trait instance *)
+Definition alloc_boxed_Box_coreOpsDerefMutInst (Self : Type) : core_ops_deref_DerefMut Self := {|
+  core_ops_deref_DerefMut_derefInst := alloc_boxed_Box_coreOpsDerefInst Self;
+  core_ops_deref_DerefMut_deref_mut := alloc_boxed_Box_deref_mut Self;
+  core_ops_deref_DerefMut_deref_mut_back := alloc_boxed_Box_deref_mut_back Self;
+|}.
+
 
 (*** Arrays *)
 Definition array T (n : usize) := { l: list T | Z.of_nat (length l) = to_Z n}.
@@ -419,51 +498,50 @@ Qed.
 (* TODO: finish the definitions *)
 Axiom mk_array : forall (T : Type) (n : usize) (l : list T), array T n.
 
-Axiom array_index_shared : forall (T : Type) (n : usize) (x : array T n) (i : usize), result T.
-Axiom array_index_mut_fwd : forall (T : Type) (n : usize) (x : array T n) (i : usize), result T.
-Axiom array_index_mut_back : forall (T : Type) (n : usize) (x : array T n) (i : usize) (nx : T), result (array T n).
+(* For initialization *)
+Axiom array_repeat : forall (T : Type) (n : usize) (x : T), array T n.
+
+Axiom array_index_usize : forall (T : Type) (n : usize) (x : array T n) (i : usize), result T.
+Axiom array_update_usize : forall (T : Type) (n : usize) (x : array T n) (i : usize) (nx : T), result (array T n).
 
 (*** Slice *)
 Definition slice T := { l: list T | Z.of_nat (length l) <= usize_max}.
 
 Axiom slice_len : forall (T : Type) (s : slice T), usize.
-Axiom slice_index_shared : forall (T : Type) (x : slice T) (i : usize), result T.
-Axiom slice_index_mut_fwd : forall (T : Type) (x : slice T) (i : usize), result T.
-Axiom slice_index_mut_back : forall (T : Type) (x : slice T) (i : usize) (nx : T), result (slice T).
+Axiom slice_index_usize : forall (T : Type) (x : slice T) (i : usize), result T.
+Axiom slice_update_usize : forall (T : Type) (x : slice T) (i : usize) (nx : T), result (slice T).
 
 (*** Subslices *)
 
-Axiom array_to_slice_shared : forall (T : Type) (n : usize) (x : array T n), result (slice T).
-Axiom array_to_slice_mut_fwd : forall (T : Type) (n : usize) (x : array T n), result (slice T).
-Axiom array_to_slice_mut_back : forall (T : Type) (n : usize) (x : array T n) (s : slice T), result (array T n).
+Axiom array_to_slice : forall (T : Type) (n : usize) (x : array T n), result (slice T).
+Axiom array_from_slice : forall (T : Type) (n : usize) (x : array T n) (s : slice T), result (array T n).
+
+Axiom array_subslice: forall (T : Type) (n : usize) (x : array T n) (r : core_ops_range_Range usize), result (slice T).
+Axiom array_update_subslice: forall (T : Type) (n : usize) (x : array T n) (r : core_ops_range_Range usize) (ns : slice T), result (array T n).
 
-Axiom array_subslice_shared: forall (T : Type) (n : usize) (x : array T n) (r : range usize), result (slice T).
-Axiom array_subslice_mut_fwd: forall (T : Type) (n : usize) (x : array T n) (r : range usize), result (slice T).
-Axiom array_subslice_mut_back: forall (T : Type) (n : usize) (x : array T n) (r : range usize) (ns : slice T), result (array T n).
-Axiom slice_subslice_shared: forall (T : Type) (x : slice T) (r : range usize), result (slice T).
-Axiom slice_subslice_mut_fwd: forall (T : Type) (x : slice T) (r : range usize), result (slice T).
-Axiom slice_subslice_mut_back: forall (T : Type) (x : slice T) (r : range usize) (ns : slice T), result (slice T).
+Axiom slice_subslice: forall (T : Type) (x : slice T) (r : core_ops_range_Range usize), result (slice T).
+Axiom slice_update_subslice: forall (T : Type) (x : slice T) (r : core_ops_range_Range usize) (ns : slice T), result (slice T).
 
 (*** Vectors *)
 
-Definition vec T := { l: list T | Z.of_nat (length l) <= usize_max }.
+Definition alloc_vec_Vec T := { l: list T | Z.of_nat (length l) <= usize_max }.
 
-Definition vec_to_list {T: Type} (v: vec T) : list T := proj1_sig v.
+Definition alloc_vec_Vec_to_list {T: Type} (v: alloc_vec_Vec T) : list T := proj1_sig v.
 
-Definition vec_length {T: Type} (v: vec T) : Z := Z.of_nat (length (vec_to_list v)).
+Definition alloc_vec_Vec_length {T: Type} (v: alloc_vec_Vec T) : Z := Z.of_nat (length (alloc_vec_Vec_to_list v)).
 
-Definition vec_new (T: Type) : vec T := (exist _ [] le_0_usize_max).
+Definition alloc_vec_Vec_new (T: Type) : alloc_vec_Vec T := (exist _ [] le_0_usize_max).
 
-Lemma vec_len_in_usize {T} (v: vec T) : usize_min <= vec_length v <= usize_max.
+Lemma alloc_vec_Vec_len_in_usize {T} (v: alloc_vec_Vec T) : usize_min <= alloc_vec_Vec_length v <= usize_max.
 Proof.
-  unfold vec_length, usize_min.
+  unfold alloc_vec_Vec_length, usize_min.
   split.
   - lia.
   - apply (proj2_sig v).
 Qed.
 
-Definition vec_len (T: Type) (v: vec T) : usize :=
-  exist _ (vec_length v) (vec_len_in_usize v).
+Definition alloc_vec_Vec_len (T: Type) (v: alloc_vec_Vec T) : usize :=
+  exist _ (alloc_vec_Vec_length v) (alloc_vec_Vec_len_in_usize v).
 
 Fixpoint list_update {A} (l: list A) (n: nat) (a: A)
   : list A :=
@@ -474,50 +552,271 @@ Fixpoint list_update {A} (l: list A) (n: nat) (a: A)
     | S m => x :: (list_update t m a)
 end end.
 
-Definition vec_bind {A B} (v: vec A) (f: list A -> result (list B)) : result (vec B) :=
-  l <- f (vec_to_list v) ;
+Definition alloc_vec_Vec_bind {A B} (v: alloc_vec_Vec A) (f: list A -> result (list B)) : result (alloc_vec_Vec B) :=
+  l <- f (alloc_vec_Vec_to_list v) ;
   match sumbool_of_bool (scalar_le_max Usize (Z.of_nat (length l))) with
   | left H => Return (exist _ l (scalar_le_max_valid _ _ H))
   | right _ => Fail_ Failure
   end.
 
 (* The **forward** function shouldn't be used *)
-Definition vec_push_fwd (T: Type) (v: vec T) (x: T) : unit := tt.
+Definition alloc_vec_Vec_push_fwd (T: Type) (v: alloc_vec_Vec T) (x: T) : unit := tt.
 
-Definition vec_push_back (T: Type) (v: vec T) (x: T) : result (vec T) :=
-  vec_bind v (fun l => Return (l ++ [x])).
+Definition alloc_vec_Vec_push (T: Type) (v: alloc_vec_Vec T) (x: T) : result (alloc_vec_Vec T) :=
+  alloc_vec_Vec_bind v (fun l => Return (l ++ [x])).
 
 (* The **forward** function shouldn't be used *)
-Definition vec_insert_fwd (T: Type) (v: vec T) (i: usize) (x: T) : result unit :=
-  if to_Z i <? vec_length v then Return tt else Fail_ Failure.
+Definition alloc_vec_Vec_insert_fwd (T: Type) (v: alloc_vec_Vec T) (i: usize) (x: T) : result unit :=
+  if to_Z i <? alloc_vec_Vec_length v then Return tt else Fail_ Failure.
 
-Definition vec_insert_back (T: Type) (v: vec T) (i: usize) (x: T) : result (vec T) :=
-  vec_bind v (fun l =>
+Definition alloc_vec_Vec_insert (T: Type) (v: alloc_vec_Vec T) (i: usize) (x: T) : result (alloc_vec_Vec T) :=
+  alloc_vec_Vec_bind v (fun l =>
     if to_Z i <? Z.of_nat (length l)
     then Return (list_update l (usize_to_nat i) x)
     else Fail_ Failure).
 
-(* The **backward** function shouldn't be used *)
-Definition vec_index_fwd (T: Type) (v: vec T) (i: usize) : result T :=
-  match nth_error (vec_to_list v) (usize_to_nat i) with
-  | Some n => Return n
-  | None   => Fail_ Failure
-  end.
-
-Definition vec_index_back (T: Type) (v: vec T) (i: usize) (x: T) : result unit :=
-  if to_Z i <? vec_length v then Return tt else Fail_ Failure.
-
-(* The **backward** function shouldn't be used *)
-Definition vec_index_mut_fwd (T: Type) (v: vec T) (i: usize) : result T :=
-  match nth_error (vec_to_list v) (usize_to_nat i) with
-  | Some n => Return n
-  | None   => Fail_ Failure
+(* Helper *)
+Axiom alloc_vec_Vec_index_usize : forall {T : Type} (v : alloc_vec_Vec T) (i : usize) (x : T), result T.
+
+(* Helper *)
+Axiom alloc_vec_Vec_update_usize : forall {T : Type} (v : alloc_vec_Vec T) (i : usize) (x : T), result (alloc_vec_Vec T).
+
+(* Trait declaration: [core::slice::index::private_slice_index::Sealed] *)
+Definition core_slice_index_private_slice_index_Sealed (self : Type) := unit.
+
+(* Trait declaration: [core::slice::index::SliceIndex] *)
+Record core_slice_index_SliceIndex (Self T : Type) := mk_core_slice_index_SliceIndex {
+  core_slice_index_SliceIndex_sealedInst : core_slice_index_private_slice_index_Sealed Self;
+  core_slice_index_SliceIndex_Output : Type;
+  core_slice_index_SliceIndex_get : Self -> T -> result (option core_slice_index_SliceIndex_Output);
+  core_slice_index_SliceIndex_get_mut : Self -> T -> result (option core_slice_index_SliceIndex_Output);
+  core_slice_index_SliceIndex_get_mut_back : Self -> T -> option core_slice_index_SliceIndex_Output -> result T;
+  core_slice_index_SliceIndex_get_unchecked : Self -> const_raw_ptr T -> result (const_raw_ptr core_slice_index_SliceIndex_Output);
+  core_slice_index_SliceIndex_get_unchecked_mut : Self -> mut_raw_ptr T -> result (mut_raw_ptr core_slice_index_SliceIndex_Output);
+  core_slice_index_SliceIndex_index : Self -> T -> result core_slice_index_SliceIndex_Output;
+  core_slice_index_SliceIndex_index_mut : Self -> T -> result core_slice_index_SliceIndex_Output;
+  core_slice_index_SliceIndex_index_mut_back : Self -> T -> core_slice_index_SliceIndex_Output -> result T;
+}.
+Arguments mk_core_slice_index_SliceIndex {_ _}.
+Arguments core_slice_index_SliceIndex_sealedInst {_ _}.
+Arguments core_slice_index_SliceIndex_Output {_ _}.
+Arguments core_slice_index_SliceIndex_get {_ _}.
+Arguments core_slice_index_SliceIndex_get_mut {_ _}.
+Arguments core_slice_index_SliceIndex_get_mut_back {_ _}.
+Arguments core_slice_index_SliceIndex_get_unchecked {_ _}.
+Arguments core_slice_index_SliceIndex_get_unchecked_mut {_ _}.
+Arguments core_slice_index_SliceIndex_index {_ _}.
+Arguments core_slice_index_SliceIndex_index_mut {_ _}.
+Arguments core_slice_index_SliceIndex_index_mut_back {_ _}.
+
+(* [core::slice::index::[T]::index]: forward function *)
+Definition core_slice_index_Slice_index
+  (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T))
+  (s : slice T) (i : Idx) : result inst.(core_slice_index_SliceIndex_Output) :=
+  x <- inst.(core_slice_index_SliceIndex_get) i s;
+  match x with
+  | None => Fail_ Failure
+  | Some x => Return x
   end.
 
-Definition vec_index_mut_back (T: Type) (v: vec T) (i: usize) (x: T) : result (vec T) :=
-  vec_bind v (fun l =>
-    if to_Z i <? Z.of_nat (length l)
-    then Return (list_update l (usize_to_nat i) x)
-    else Fail_ Failure).
+(* [core::slice::index::Range:::get]: forward function *)
+Axiom core_slice_index_Range_get : forall (T : Type) (i : core_ops_range_Range usize) (s : slice T), result (option (slice T)).
+
+(* [core::slice::index::Range::get_mut]: forward function *)
+Axiom core_slice_index_Range_get_mut :
+  forall (T : Type), core_ops_range_Range usize -> slice T -> result (option (slice T)).
+
+(* [core::slice::index::Range::get_mut]: backward function 0 *)
+Axiom core_slice_index_Range_get_mut_back :
+  forall (T : Type), core_ops_range_Range usize -> slice T -> option (slice T) -> result (slice T).
+
+(* [core::slice::index::Range::get_unchecked]: forward function *)
+Definition core_slice_index_Range_get_unchecked
+  (T : Type) :
+  core_ops_range_Range usize -> const_raw_ptr (slice T) -> result (const_raw_ptr (slice T)) :=
+  (* Don't know what the model should be - for now we always fail to make
+     sure code which uses it fails *)
+  fun _ _ => Fail_ Failure.
+
+(* [core::slice::index::Range::get_unchecked_mut]: forward function *)
+Definition core_slice_index_Range_get_unchecked_mut
+  (T : Type) :
+  core_ops_range_Range usize -> mut_raw_ptr (slice T) -> result (mut_raw_ptr (slice T)) :=
+  (* Don't know what the model should be - for now we always fail to make
+    sure code which uses it fails *)
+  fun _ _ => Fail_ Failure.
+
+(* [core::slice::index::Range::index]: forward function *)
+Axiom core_slice_index_Range_index :
+  forall (T : Type), core_ops_range_Range usize -> slice T -> result (slice T).
+
+(* [core::slice::index::Range::index_mut]: forward function *)
+Axiom core_slice_index_Range_index_mut :
+  forall (T : Type), core_ops_range_Range usize -> slice T -> result (slice T).
+
+(* [core::slice::index::Range::index_mut]: backward function 0 *)
+Axiom core_slice_index_Range_index_mut_back :
+  forall (T : Type), core_ops_range_Range usize -> slice T -> slice T -> result (slice T).
+
+(* [core::slice::index::[T]::index_mut]: forward function *)
+Axiom core_slice_index_Slice_index_mut :
+  forall (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T)),
+  slice T -> Idx -> result inst.(core_slice_index_SliceIndex_Output).
+
+(* [core::slice::index::[T]::index_mut]: backward function 0 *)
+Axiom core_slice_index_Slice_index_mut_back :
+  forall (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T)),
+  slice T -> Idx -> inst.(core_slice_index_SliceIndex_Output) -> result (slice T).
+
+(* [core::array::[T; N]::index]: forward function *)
+Axiom core_array_Array_index :
+  forall (T Idx : Type) (N : usize) (inst : core_ops_index_Index (slice T) Idx)
+  (a : array T N) (i : Idx), result inst.(core_ops_index_Index_Output).
+
+(* [core::array::[T; N]::index_mut]: forward function *)
+Axiom core_array_Array_index_mut :
+  forall (T Idx : Type) (N : usize) (inst : core_ops_index_IndexMut (slice T) Idx)
+  (a : array T N) (i : Idx), result inst.(core_ops_index_IndexMut_indexInst).(core_ops_index_Index_Output).
+
+(* [core::array::[T; N]::index_mut]: backward function 0 *)
+Axiom core_array_Array_index_mut_back :
+  forall (T Idx : Type) (N : usize) (inst : core_ops_index_IndexMut (slice T) Idx)
+  (a : array T N) (i : Idx) (x : inst.(core_ops_index_IndexMut_indexInst).(core_ops_index_Index_Output)), result (array T N).
+
+(* Trait implementation: [core::slice::index::[T]] *)
+Definition core_slice_index_Slice_coreopsindexIndexInst (T Idx : Type)
+  (inst : core_slice_index_SliceIndex Idx (slice T)) :
+  core_ops_index_Index (slice T) Idx := {|
+  core_ops_index_Index_Output := inst.(core_slice_index_SliceIndex_Output);
+  core_ops_index_Index_index := core_slice_index_Slice_index T Idx inst;
+|}.
+
+(* Trait implementation: [core::slice::index::private_slice_index::Range] *)
+Definition core_slice_index_private_slice_index_Range_coresliceindexprivate_slice_indexSealedInst
+  : core_slice_index_private_slice_index_Sealed (core_ops_range_Range usize) := tt.
+
+(* Trait implementation: [core::slice::index::Range] *)
+Definition core_slice_index_Range_coresliceindexSliceIndexInst (T : Type) :
+  core_slice_index_SliceIndex (core_ops_range_Range usize) (slice T) := {|
+  core_slice_index_SliceIndex_sealedInst := core_slice_index_private_slice_index_Range_coresliceindexprivate_slice_indexSealedInst;
+  core_slice_index_SliceIndex_Output := slice T;
+  core_slice_index_SliceIndex_get := core_slice_index_Range_get T;
+  core_slice_index_SliceIndex_get_mut := core_slice_index_Range_get_mut T;
+  core_slice_index_SliceIndex_get_mut_back := core_slice_index_Range_get_mut_back T;
+  core_slice_index_SliceIndex_get_unchecked := core_slice_index_Range_get_unchecked T;
+  core_slice_index_SliceIndex_get_unchecked_mut := core_slice_index_Range_get_unchecked_mut T;
+  core_slice_index_SliceIndex_index := core_slice_index_Range_index T;
+  core_slice_index_SliceIndex_index_mut := core_slice_index_Range_index_mut T;
+  core_slice_index_SliceIndex_index_mut_back := core_slice_index_Range_index_mut_back T;
+|}.
+
+(* Trait implementation: [core::slice::index::[T]] *)
+Definition core_slice_index_Slice_coreopsindexIndexMutInst (T Idx : Type)
+  (inst : core_slice_index_SliceIndex Idx (slice T)) :
+  core_ops_index_IndexMut (slice T) Idx := {|
+  core_ops_index_IndexMut_indexInst := core_slice_index_Slice_coreopsindexIndexInst T Idx inst;
+  core_ops_index_IndexMut_index_mut := core_slice_index_Slice_index_mut T Idx inst;
+  core_ops_index_IndexMut_index_mut_back := core_slice_index_Slice_index_mut_back T Idx inst;
+|}.
+
+(* Trait implementation: [core::array::[T; N]] *)
+Definition core_array_Array_coreopsindexIndexInst (T Idx : Type) (N : usize)
+  (inst : core_ops_index_Index (slice T) Idx) :
+  core_ops_index_Index (array T N) Idx := {|
+  core_ops_index_Index_Output := inst.(core_ops_index_Index_Output);
+  core_ops_index_Index_index := core_array_Array_index T Idx N inst;
+|}.
+
+(* Trait implementation: [core::array::[T; N]] *)
+Definition core_array_Array_coreopsindexIndexMutInst (T Idx : Type) (N : usize)
+  (inst : core_ops_index_IndexMut (slice T) Idx) :
+  core_ops_index_IndexMut (array T N) Idx := {|
+  core_ops_index_IndexMut_indexInst := core_array_Array_coreopsindexIndexInst T Idx N inst.(core_ops_index_IndexMut_indexInst);
+  core_ops_index_IndexMut_index_mut := core_array_Array_index_mut T Idx N inst;
+  core_ops_index_IndexMut_index_mut_back := core_array_Array_index_mut_back T Idx N inst;
+|}.
+
+(* [core::slice::index::usize::get]: forward function *)
+Axiom core_slice_index_usize_get : forall (T : Type), usize -> slice T -> result (option T).
+
+(* [core::slice::index::usize::get_mut]: forward function *)
+Axiom core_slice_index_usize_get_mut : forall (T : Type), usize -> slice T -> result (option T).
+
+(* [core::slice::index::usize::get_mut]: backward function 0 *)
+Axiom core_slice_index_usize_get_mut_back :
+  forall (T : Type), usize -> slice T -> option T -> result (slice T).
+
+(* [core::slice::index::usize::get_unchecked]: forward function *)
+Axiom core_slice_index_usize_get_unchecked :
+  forall (T : Type), usize -> const_raw_ptr (slice T) -> result (const_raw_ptr T).
+
+(* [core::slice::index::usize::get_unchecked_mut]: forward function *)
+Axiom core_slice_index_usize_get_unchecked_mut :
+  forall (T : Type), usize -> mut_raw_ptr (slice T) -> result (mut_raw_ptr T).
+
+(* [core::slice::index::usize::index]: forward function *)
+Axiom core_slice_index_usize_index : forall (T : Type), usize -> slice T -> result T.
+
+(* [core::slice::index::usize::index_mut]: forward function *)
+Axiom core_slice_index_usize_index_mut : forall (T : Type), usize -> slice T -> result T.
+
+(* [core::slice::index::usize::index_mut]: backward function 0 *)
+Axiom core_slice_index_usize_index_mut_back :
+  forall (T : Type), usize -> slice T -> T -> result (slice T).
+
+(* Trait implementation: [core::slice::index::private_slice_index::usize] *)
+Definition core_slice_index_private_slice_index_usize_coresliceindexprivate_slice_indexSealedInst
+  : core_slice_index_private_slice_index_Sealed usize := tt.
+
+(* Trait implementation: [core::slice::index::usize] *)
+Definition core_slice_index_usize_coresliceindexSliceIndexInst (T : Type) :
+  core_slice_index_SliceIndex usize (slice T) := {|
+  core_slice_index_SliceIndex_sealedInst := core_slice_index_private_slice_index_usize_coresliceindexprivate_slice_indexSealedInst;
+  core_slice_index_SliceIndex_Output := T;
+  core_slice_index_SliceIndex_get := core_slice_index_usize_get T;
+  core_slice_index_SliceIndex_get_mut := core_slice_index_usize_get_mut T;
+  core_slice_index_SliceIndex_get_mut_back := core_slice_index_usize_get_mut_back T;
+  core_slice_index_SliceIndex_get_unchecked := core_slice_index_usize_get_unchecked T;
+  core_slice_index_SliceIndex_get_unchecked_mut := core_slice_index_usize_get_unchecked_mut T;
+  core_slice_index_SliceIndex_index := core_slice_index_usize_index T;
+  core_slice_index_SliceIndex_index_mut := core_slice_index_usize_index_mut T;
+  core_slice_index_SliceIndex_index_mut_back := core_slice_index_usize_index_mut_back T;
+|}.
+
+(* [alloc::vec::Vec::index]: forward function *)
+Axiom alloc_vec_Vec_index : forall (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T))
+  (Self : alloc_vec_Vec T) (i : Idx), result inst.(core_slice_index_SliceIndex_Output).
+
+(* [alloc::vec::Vec::index_mut]: forward function *)
+Axiom alloc_vec_Vec_index_mut : forall (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T))
+  (Self : alloc_vec_Vec T) (i : Idx), result inst.(core_slice_index_SliceIndex_Output).
+
+(* [alloc::vec::Vec::index_mut]: backward function 0 *)
+Axiom alloc_vec_Vec_index_mut_back :
+  forall (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T))
+  (Self : alloc_vec_Vec T) (i : Idx) (x : inst.(core_slice_index_SliceIndex_Output)), result (alloc_vec_Vec T).
+
+(* Trait implementation: [alloc::vec::Vec] *)
+Definition alloc_vec_Vec_coreopsindexIndexInst (T Idx : Type)
+  (inst : core_slice_index_SliceIndex Idx (slice T)) :
+  core_ops_index_Index (alloc_vec_Vec T) Idx := {|
+  core_ops_index_Index_Output := inst.(core_slice_index_SliceIndex_Output);
+  core_ops_index_Index_index := alloc_vec_Vec_index T Idx inst;
+|}.
+
+(* Trait implementation: [alloc::vec::Vec] *)
+Definition alloc_vec_Vec_coreopsindexIndexMutInst (T Idx : Type)
+  (inst : core_slice_index_SliceIndex Idx (slice T)) :
+  core_ops_index_IndexMut (alloc_vec_Vec T) Idx := {|
+  core_ops_index_IndexMut_indexInst := alloc_vec_Vec_coreopsindexIndexInst T Idx inst;
+  core_ops_index_IndexMut_index_mut := alloc_vec_Vec_index_mut T Idx inst;
+  core_ops_index_IndexMut_index_mut_back := alloc_vec_Vec_index_mut_back T Idx inst;
+|}.
+
+(*** Theorems *)
+
+Axiom alloc_vec_Vec_index_mut_back_eq : forall {a : Type} (v : alloc_vec_Vec a) (i : usize) (x : a),
+  alloc_vec_Vec_index_mut_back a usize (core_slice_index_usize_coresliceindexSliceIndexInst a) v i x =
+    alloc_vec_Vec_update_usize v i x.
 
 End Primitives.
diff --git a/tests/coq/misc/Constants.v b/tests/coq/misc/Constants.v
index f1c32730..03653f69 100644
--- a/tests/coq/misc/Constants.v
+++ b/tests/coq/misc/Constants.v
@@ -12,12 +12,8 @@ Module Constants.
 Definition x0_body : result u32 := Return 0%u32.
 Definition x0_c : u32 := x0_body%global.
 
-(** [core::num::u32::{8}::MAX] *)
-Definition core_num_u32_max_body : result u32 := Return 4294967295%u32.
-Definition core_num_u32_max_c : u32 := core_num_u32_max_body%global.
-
 (** [constants::X1] *)
-Definition x1_body : result u32 := Return core_num_u32_max_c.
+Definition x1_body : result u32 := Return core_u32_max.
 Definition x1_c : u32 := x1_body%global.
 
 (** [constants::X2] *)
@@ -25,36 +21,35 @@ Definition x2_body : result u32 := Return 3%u32.
 Definition x2_c : u32 := x2_body%global.
 
 (** [constants::incr]: forward function *)
-Definition incr_fwd (n : u32) : result u32 :=
+Definition incr (n : u32) : result u32 :=
   u32_add n 1%u32.
 
 (** [constants::X3] *)
-Definition x3_body : result u32 := incr_fwd 32%u32.
+Definition x3_body : result u32 := incr 32%u32.
 Definition x3_c : u32 := x3_body%global.
 
 (** [constants::mk_pair0]: forward function *)
-Definition mk_pair0_fwd (x : u32) (y : u32) : result (u32 * u32) :=
-  Return (x, y)
-.
+Definition mk_pair0 (x : u32) (y : u32) : result (u32 * u32) :=
+  Return (x, y).
 
 (** [constants::Pair] *)
-Record Pair_t (T1 T2 : Type) := mkPair_t { Pair_x : T1; Pair_y : T2; }.
+Record Pair_t (T1 T2 : Type) := mkPair_t { pair_x : T1; pair_y : T2; }.
 
-Arguments mkPair_t {T1} {T2} _ _.
-Arguments Pair_x {T1} {T2}.
-Arguments Pair_y {T1} {T2}.
+Arguments mkPair_t { _ _ }.
+Arguments pair_x { _ _ }.
+Arguments pair_y { _ _ }.
 
 (** [constants::mk_pair1]: forward function *)
-Definition mk_pair1_fwd (x : u32) (y : u32) : result (Pair_t u32 u32) :=
-  Return {| Pair_x := x; Pair_y := y |}
+Definition mk_pair1 (x : u32) (y : u32) : result (Pair_t u32 u32) :=
+  Return {| pair_x := x; pair_y := y |}
 .
 
 (** [constants::P0] *)
-Definition p0_body : result (u32 * u32) := mk_pair0_fwd 0%u32 1%u32.
+Definition p0_body : result (u32 * u32) := mk_pair0 0%u32 1%u32.
 Definition p0_c : (u32 * u32) := p0_body%global.
 
 (** [constants::P1] *)
-Definition p1_body : result (Pair_t u32 u32) := mk_pair1_fwd 0%u32 1%u32.
+Definition p1_body : result (Pair_t u32 u32) := mk_pair1 0%u32 1%u32.
 Definition p1_c : Pair_t u32 u32 := p1_body%global.
 
 (** [constants::P2] *)
@@ -63,31 +58,31 @@ Definition p2_c : (u32 * u32) := p2_body%global.
 
 (** [constants::P3] *)
 Definition p3_body : result (Pair_t u32 u32) :=
-  Return {| Pair_x := 0%u32; Pair_y := 1%u32 |}
+  Return {| pair_x := 0%u32; pair_y := 1%u32 |}
 .
 Definition p3_c : Pair_t u32 u32 := p3_body%global.
 
 (** [constants::Wrap] *)
-Record Wrap_t (T : Type) := mkWrap_t { Wrap_val : T; }.
+Record Wrap_t (T : Type) := mkWrap_t { wrap_value : T; }.
 
-Arguments mkWrap_t {T} _.
-Arguments Wrap_val {T}.
+Arguments mkWrap_t { _ }.
+Arguments wrap_value { _ }.
 
 (** [constants::Wrap::{0}::new]: forward function *)
-Definition wrap_new_fwd (T : Type) (val : T) : result (Wrap_t T) :=
-  Return {| Wrap_val := val |}
+Definition wrap_new (T : Type) (value : T) : result (Wrap_t T) :=
+  Return {| wrap_value := value |}
 .
 
 (** [constants::Y] *)
-Definition y_body : result (Wrap_t i32) := wrap_new_fwd i32 2%i32.
+Definition y_body : result (Wrap_t i32) := wrap_new i32 2%i32.
 Definition y_c : Wrap_t i32 := y_body%global.
 
 (** [constants::unwrap_y]: forward function *)
-Definition unwrap_y_fwd : result i32 :=
-  Return y_c.(Wrap_val).
+Definition unwrap_y : result i32 :=
+  Return y_c.(wrap_value).
 
 (** [constants::YVAL] *)
-Definition yval_body : result i32 := unwrap_y_fwd.
+Definition yval_body : result i32 := unwrap_y.
 Definition yval_c : i32 := yval_body%global.
 
 (** [constants::get_z1::Z1] *)
@@ -95,11 +90,11 @@ Definition get_z1_z1_body : result i32 := Return 3%i32.
 Definition get_z1_z1_c : i32 := get_z1_z1_body%global.
 
 (** [constants::get_z1]: forward function *)
-Definition get_z1_fwd : result i32 :=
+Definition get_z1 : result i32 :=
   Return get_z1_z1_c.
 
 (** [constants::add]: forward function *)
-Definition add_fwd (a : i32) (b : i32) : result i32 :=
+Definition add (a : i32) (b : i32) : result i32 :=
   i32_add a b.
 
 (** [constants::Q1] *)
@@ -111,20 +106,19 @@ Definition q2_body : result i32 := Return q1_c.
 Definition q2_c : i32 := q2_body%global.
 
 (** [constants::Q3] *)
-Definition q3_body : result i32 := add_fwd q2_c 3%i32.
+Definition q3_body : result i32 := add q2_c 3%i32.
 Definition q3_c : i32 := q3_body%global.
 
 (** [constants::get_z2]: forward function *)
-Definition get_z2_fwd : result i32 :=
-  i <- get_z1_fwd; i0 <- add_fwd i q3_c; add_fwd q1_c i0
-.
+Definition get_z2 : result i32 :=
+  i <- get_z1; i0 <- add i q3_c; add q1_c i0.
 
 (** [constants::S1] *)
 Definition s1_body : result u32 := Return 6%u32.
 Definition s1_c : u32 := s1_body%global.
 
 (** [constants::S2] *)
-Definition s2_body : result u32 := incr_fwd s1_c.
+Definition s2_body : result u32 := incr s1_c.
 Definition s2_c : u32 := s2_body%global.
 
 (** [constants::S3] *)
@@ -132,7 +126,7 @@ Definition s3_body : result (Pair_t u32 u32) := Return p3_c.
 Definition s3_c : Pair_t u32 u32 := s3_body%global.
 
 (** [constants::S4] *)
-Definition s4_body : result (Pair_t u32 u32) := mk_pair1_fwd 7%u32 8%u32.
+Definition s4_body : result (Pair_t u32 u32) := mk_pair1 7%u32 8%u32.
 Definition s4_c : Pair_t u32 u32 := s4_body%global.
 
 End Constants .
diff --git a/tests/coq/misc/External_Funs.v b/tests/coq/misc/External_Funs.v
index 28370b2b..018ce13c 100644
--- a/tests/coq/misc/External_Funs.v
+++ b/tests/coq/misc/External_Funs.v
@@ -13,9 +13,9 @@ Import External_Opaque.
 Module External_Funs.
 
 (** [external::swap]: forward function *)
-Definition swap_fwd
+Definition swap
   (T : Type) (x : T) (y : T) (st : state) : result (state * unit) :=
-  p <- core_mem_swap_fwd T x y st;
+  p <- core_mem_swap T x y st;
   let (st0, _) := p in
   p0 <- core_mem_swap_back0 T x y st st0;
   let (st1, _) := p0 in
@@ -29,7 +29,7 @@ Definition swap_back
   (T : Type) (x : T) (y : T) (st : state) (st0 : state) :
   result (state * (T * T))
   :=
-  p <- core_mem_swap_fwd T x y st;
+  p <- core_mem_swap T x y st;
   let (st1, _) := p in
   p0 <- core_mem_swap_back0 T x y st st1;
   let (st2, x0) := p0 in
@@ -39,25 +39,27 @@ Definition swap_back
 .
 
 (** [external::test_new_non_zero_u32]: forward function *)
-Definition test_new_non_zero_u32_fwd
-  (x : u32) (st : state) : result (state * Core_num_nonzero_non_zero_u32_t) :=
-  p <- core_num_nonzero_non_zero_u32_new_fwd x st;
-  let (st0, opt) := p in
-  core_option_option_unwrap_fwd Core_num_nonzero_non_zero_u32_t opt st0
+Definition test_new_non_zero_u32
+  (x : u32) (st : state) : result (state * core_num_nonzero_NonZeroU32_t) :=
+  p <- core_num_nonzero_NonZeroU32_new x st;
+  let (st0, o) := p in
+  core_option_Option_unwrap core_num_nonzero_NonZeroU32_t o st0
 .
 
 (** [external::test_vec]: forward function *)
-Definition test_vec_fwd : result unit :=
-  let v := vec_new u32 in _ <- vec_push_back u32 v 0%u32; Return tt
+Definition test_vec : result unit :=
+  let v := alloc_vec_Vec_new u32 in
+  _ <- alloc_vec_Vec_push u32 v 0%u32;
+  Return tt
 .
 
 (** Unit test for [external::test_vec] *)
-Check (test_vec_fwd )%return.
+Check (test_vec )%return.
 
 (** [external::custom_swap]: forward function *)
-Definition custom_swap_fwd
+Definition custom_swap
   (T : Type) (x : T) (y : T) (st : state) : result (state * T) :=
-  p <- core_mem_swap_fwd T x y st;
+  p <- core_mem_swap T x y st;
   let (st0, _) := p in
   p0 <- core_mem_swap_back0 T x y st st0;
   let (st1, x0) := p0 in
@@ -71,7 +73,7 @@ Definition custom_swap_back
   (T : Type) (x : T) (y : T) (st : state) (ret : T) (st0 : state) :
   result (state * (T * T))
   :=
-  p <- core_mem_swap_fwd T x y st;
+  p <- core_mem_swap T x y st;
   let (st1, _) := p in
   p0 <- core_mem_swap_back0 T x y st st1;
   let (st2, _) := p0 in
@@ -81,9 +83,9 @@ Definition custom_swap_back
 .
 
 (** [external::test_custom_swap]: forward function *)
-Definition test_custom_swap_fwd
+Definition test_custom_swap
   (x : u32) (y : u32) (st : state) : result (state * unit) :=
-  p <- custom_swap_fwd u32 x y st; let (st0, _) := p in Return (st0, tt)
+  p <- custom_swap u32 x y st; let (st0, _) := p in Return (st0, tt)
 .
 
 (** [external::test_custom_swap]: backward function 0 *)
@@ -95,9 +97,8 @@ Definition test_custom_swap_back
 .
 
 (** [external::test_swap_non_zero]: forward function *)
-Definition test_swap_non_zero_fwd
-  (x : u32) (st : state) : result (state * u32) :=
-  p <- swap_fwd u32 x 0%u32 st;
+Definition test_swap_non_zero (x : u32) (st : state) : result (state * u32) :=
+  p <- swap u32 x 0%u32 st;
   let (st0, _) := p in
   p0 <- swap_back u32 x 0%u32 st st0;
   let (st1, p1) := p0 in
diff --git a/tests/coq/misc/External_Opaque.v b/tests/coq/misc/External_Opaque.v
index d2ee42d4..80be37e7 100644
--- a/tests/coq/misc/External_Opaque.v
+++ b/tests/coq/misc/External_Opaque.v
@@ -11,7 +11,7 @@ Import External_Types.
 Module External_Opaque.
 
 (** [core::mem::swap]: forward function *)
-Axiom core_mem_swap_fwd :
+Axiom core_mem_swap :
   forall(T : Type), T -> T -> state -> result (state * unit)
 .
 
@@ -26,12 +26,12 @@ Axiom core_mem_swap_back1 :
 .
 
 (** [core::num::nonzero::NonZeroU32::{14}::new]: forward function *)
-Axiom core_num_nonzero_non_zero_u32_new_fwd
-  : u32 -> state -> result (state * (option Core_num_nonzero_non_zero_u32_t))
+Axiom core_num_nonzero_NonZeroU32_new
+  : u32 -> state -> result (state * (option core_num_nonzero_NonZeroU32_t))
 .
 
 (** [core::option::Option::{0}::unwrap]: forward function *)
-Axiom core_option_option_unwrap_fwd :
+Axiom core_option_Option_unwrap :
   forall(T : Type), option T -> state -> result (state * T)
 .
 
diff --git a/tests/coq/misc/External_Types.v b/tests/coq/misc/External_Types.v
index 1883fa6c..9e49ca41 100644
--- a/tests/coq/misc/External_Types.v
+++ b/tests/coq/misc/External_Types.v
@@ -9,7 +9,7 @@ Local Open Scope Primitives_scope.
 Module External_Types.
 
 (** [core::num::nonzero::NonZeroU32] *)
-Axiom Core_num_nonzero_non_zero_u32_t : Type.
+Axiom core_num_nonzero_NonZeroU32_t : Type.
 
 (** The state type used in the state-error monad *)
 Axiom state : Type.
diff --git a/tests/coq/misc/Loops.v b/tests/coq/misc/Loops.v
index 82e57576..1c0eab17 100644
--- a/tests/coq/misc/Loops.v
+++ b/tests/coq/misc/Loops.v
@@ -9,23 +9,23 @@ Local Open Scope Primitives_scope.
 Module Loops.
 
 (** [loops::sum]: loop 0: forward function *)
-Fixpoint sum_loop_fwd (n : nat) (max : u32) (i : u32) (s : u32) : result u32 :=
+Fixpoint sum_loop (n : nat) (max : u32) (i : u32) (s : u32) : result u32 :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
     if i s< max
-    then (s0 <- u32_add s i; i0 <- u32_add i 1%u32; sum_loop_fwd n0 max i0 s0)
+    then (s0 <- u32_add s i; i0 <- u32_add i 1%u32; sum_loop n0 max i0 s0)
     else u32_mul s 2%u32
   end
 .
 
 (** [loops::sum]: forward function *)
-Definition sum_fwd (n : nat) (max : u32) : result u32 :=
-  sum_loop_fwd n max 0%u32 0%u32
+Definition sum (n : nat) (max : u32) : result u32 :=
+  sum_loop n max 0%u32 0%u32
 .
 
 (** [loops::sum_with_mut_borrows]: loop 0: forward function *)
-Fixpoint sum_with_mut_borrows_loop_fwd
+Fixpoint sum_with_mut_borrows_loop
   (n : nat) (max : u32) (mi : u32) (ms : u32) : result u32 :=
   match n with
   | O => Fail_ OutOfFuel
@@ -34,18 +34,18 @@ Fixpoint sum_with_mut_borrows_loop_fwd
     then (
       ms0 <- u32_add ms mi;
       mi0 <- u32_add mi 1%u32;
-      sum_with_mut_borrows_loop_fwd n0 max mi0 ms0)
+      sum_with_mut_borrows_loop n0 max mi0 ms0)
     else u32_mul ms 2%u32
   end
 .
 
 (** [loops::sum_with_mut_borrows]: forward function *)
-Definition sum_with_mut_borrows_fwd (n : nat) (max : u32) : result u32 :=
-  sum_with_mut_borrows_loop_fwd n max 0%u32 0%u32
+Definition sum_with_mut_borrows (n : nat) (max : u32) : result u32 :=
+  sum_with_mut_borrows_loop n max 0%u32 0%u32
 .
 
 (** [loops::sum_with_shared_borrows]: loop 0: forward function *)
-Fixpoint sum_with_shared_borrows_loop_fwd
+Fixpoint sum_with_shared_borrows_loop
   (n : nat) (max : u32) (i : u32) (s : u32) : result u32 :=
   match n with
   | O => Fail_ OutOfFuel
@@ -54,87 +54,88 @@ Fixpoint sum_with_shared_borrows_loop_fwd
     then (
       i0 <- u32_add i 1%u32;
       s0 <- u32_add s i0;
-      sum_with_shared_borrows_loop_fwd n0 max i0 s0)
+      sum_with_shared_borrows_loop n0 max i0 s0)
     else u32_mul s 2%u32
   end
 .
 
 (** [loops::sum_with_shared_borrows]: forward function *)
-Definition sum_with_shared_borrows_fwd (n : nat) (max : u32) : result u32 :=
-  sum_with_shared_borrows_loop_fwd n max 0%u32 0%u32
+Definition sum_with_shared_borrows (n : nat) (max : u32) : result u32 :=
+  sum_with_shared_borrows_loop n max 0%u32 0%u32
 .
 
 (** [loops::clear]: loop 0: merged forward/backward function
     (there is a single backward function, and the forward function returns ()) *)
-Fixpoint clear_loop_fwd_back
-  (n : nat) (v : vec u32) (i : usize) : result (vec u32) :=
+Fixpoint clear_loop
+  (n : nat) (v : alloc_vec_Vec u32) (i : usize) : result (alloc_vec_Vec u32) :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
-    let i0 := vec_len u32 v in
+    let i0 := alloc_vec_Vec_len u32 v in
     if i s< i0
     then (
       i1 <- usize_add i 1%usize;
-      v0 <- vec_index_mut_back u32 v i 0%u32;
-      clear_loop_fwd_back n0 v0 i1)
+      v0 <-
+        alloc_vec_Vec_index_mut_back u32 usize
+          (core_slice_index_usize_coresliceindexSliceIndexInst u32) v i 0%u32;
+      clear_loop n0 v0 i1)
     else Return v
   end
 .
 
 (** [loops::clear]: merged forward/backward function
     (there is a single backward function, and the forward function returns ()) *)
-Definition clear_fwd_back (n : nat) (v : vec u32) : result (vec u32) :=
-  clear_loop_fwd_back n v 0%usize
+Definition clear
+  (n : nat) (v : alloc_vec_Vec u32) : result (alloc_vec_Vec u32) :=
+  clear_loop n v 0%usize
 .
 
 (** [loops::List] *)
 Inductive List_t (T : Type) :=
-| ListCons : T -> List_t T -> List_t T
-| ListNil : List_t T
+| List_Cons : T -> List_t T -> List_t T
+| List_Nil : List_t T
 .
 
-Arguments ListCons {T} _ _.
-Arguments ListNil {T}.
+Arguments List_Cons { _ }.
+Arguments List_Nil { _ }.
 
 (** [loops::list_mem]: loop 0: forward function *)
-Fixpoint list_mem_loop_fwd
-  (n : nat) (x : u32) (ls : List_t u32) : result bool :=
+Fixpoint list_mem_loop (n : nat) (x : u32) (ls : List_t u32) : result bool :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
     match ls with
-    | ListCons y tl =>
-      if y s= x then Return true else list_mem_loop_fwd n0 x tl
-    | ListNil => Return false
+    | List_Cons y tl => if y s= x then Return true else list_mem_loop n0 x tl
+    | List_Nil => Return false
     end
   end
 .
 
 (** [loops::list_mem]: forward function *)
-Definition list_mem_fwd (n : nat) (x : u32) (ls : List_t u32) : result bool :=
-  list_mem_loop_fwd n x ls
+Definition list_mem (n : nat) (x : u32) (ls : List_t u32) : result bool :=
+  list_mem_loop n x ls
 .
 
 (** [loops::list_nth_mut_loop]: loop 0: forward function *)
-Fixpoint list_nth_mut_loop_loop_fwd
+Fixpoint list_nth_mut_loop_loop
   (T : Type) (n : nat) (ls : List_t T) (i : u32) : result T :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
     match ls with
-    | ListCons x tl =>
+    | List_Cons x tl =>
       if i s= 0%u32
       then Return x
-      else (i0 <- u32_sub i 1%u32; list_nth_mut_loop_loop_fwd T n0 tl i0)
-    | ListNil => Fail_ Failure
+      else (i0 <- u32_sub i 1%u32; list_nth_mut_loop_loop T n0 tl i0)
+    | List_Nil => Fail_ Failure
     end
   end
 .
 
 (** [loops::list_nth_mut_loop]: forward function *)
-Definition list_nth_mut_loop_fwd
+Definition list_nth_mut_loop
   (T : Type) (n : nat) (ls : List_t T) (i : u32) : result T :=
-  list_nth_mut_loop_loop_fwd T n ls i
+  list_nth_mut_loop_loop T n ls i
 .
 
 (** [loops::list_nth_mut_loop]: loop 0: backward function 0 *)
@@ -146,14 +147,14 @@ Fixpoint list_nth_mut_loop_loop_back
   | O => Fail_ OutOfFuel
   | S n0 =>
     match ls with
-    | ListCons x tl =>
+    | List_Cons x tl =>
       if i s= 0%u32
-      then Return (ListCons ret tl)
+      then Return (List_Cons ret tl)
       else (
         i0 <- u32_sub i 1%u32;
         tl0 <- list_nth_mut_loop_loop_back T n0 tl i0 ret;
-        Return (ListCons x tl0))
-    | ListNil => Fail_ Failure
+        Return (List_Cons x tl0))
+    | List_Nil => Fail_ Failure
     end
   end
 .
@@ -167,46 +168,50 @@ Definition list_nth_mut_loop_back
 .
 
 (** [loops::list_nth_shared_loop]: loop 0: forward function *)
-Fixpoint list_nth_shared_loop_loop_fwd
+Fixpoint list_nth_shared_loop_loop
   (T : Type) (n : nat) (ls : List_t T) (i : u32) : result T :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
     match ls with
-    | ListCons x tl =>
+    | List_Cons x tl =>
       if i s= 0%u32
       then Return x
-      else (i0 <- u32_sub i 1%u32; list_nth_shared_loop_loop_fwd T n0 tl i0)
-    | ListNil => Fail_ Failure
+      else (i0 <- u32_sub i 1%u32; list_nth_shared_loop_loop T n0 tl i0)
+    | List_Nil => Fail_ Failure
     end
   end
 .
 
 (** [loops::list_nth_shared_loop]: forward function *)
-Definition list_nth_shared_loop_fwd
+Definition list_nth_shared_loop
   (T : Type) (n : nat) (ls : List_t T) (i : u32) : result T :=
-  list_nth_shared_loop_loop_fwd T n ls i
+  list_nth_shared_loop_loop T n ls i
 .
 
 (** [loops::get_elem_mut]: loop 0: forward function *)
-Fixpoint get_elem_mut_loop_fwd
+Fixpoint get_elem_mut_loop
   (n : nat) (x : usize) (ls : List_t usize) : result usize :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
     match ls with
-    | ListCons y tl =>
-      if y s= x then Return y else get_elem_mut_loop_fwd n0 x tl
-    | ListNil => Fail_ Failure
+    | List_Cons y tl => if y s= x then Return y else get_elem_mut_loop n0 x tl
+    | List_Nil => Fail_ Failure
     end
   end
 .
 
 (** [loops::get_elem_mut]: forward function *)
-Definition get_elem_mut_fwd
-  (n : nat) (slots : vec (List_t usize)) (x : usize) : result usize :=
-  l <- vec_index_mut_fwd (List_t usize) slots 0%usize;
-  get_elem_mut_loop_fwd n x l
+Definition get_elem_mut
+  (n : nat) (slots : alloc_vec_Vec (List_t usize)) (x : usize) :
+  result usize
+  :=
+  l <-
+    alloc_vec_Vec_index_mut (List_t usize) usize
+      (core_slice_index_usize_coresliceindexSliceIndexInst (List_t usize))
+      slots 0%usize;
+  get_elem_mut_loop n x l
 .
 
 (** [loops::get_elem_mut]: loop 0: backward function 0 *)
@@ -218,50 +223,60 @@ Fixpoint get_elem_mut_loop_back
   | O => Fail_ OutOfFuel
   | S n0 =>
     match ls with
-    | ListCons y tl =>
+    | List_Cons y tl =>
       if y s= x
-      then Return (ListCons ret tl)
-      else (tl0 <- get_elem_mut_loop_back n0 x tl ret; Return (ListCons y tl0))
-    | ListNil => Fail_ Failure
+      then Return (List_Cons ret tl)
+      else (
+        tl0 <- get_elem_mut_loop_back n0 x tl ret; Return (List_Cons y tl0))
+    | List_Nil => Fail_ Failure
     end
   end
 .
 
 (** [loops::get_elem_mut]: backward function 0 *)
 Definition get_elem_mut_back
-  (n : nat) (slots : vec (List_t usize)) (x : usize) (ret : usize) :
-  result (vec (List_t usize))
+  (n : nat) (slots : alloc_vec_Vec (List_t usize)) (x : usize) (ret : usize) :
+  result (alloc_vec_Vec (List_t usize))
   :=
-  l <- vec_index_mut_fwd (List_t usize) slots 0%usize;
+  l <-
+    alloc_vec_Vec_index_mut (List_t usize) usize
+      (core_slice_index_usize_coresliceindexSliceIndexInst (List_t usize))
+      slots 0%usize;
   l0 <- get_elem_mut_loop_back n x l ret;
-  vec_index_mut_back (List_t usize) slots 0%usize l0
+  alloc_vec_Vec_index_mut_back (List_t usize) usize
+    (core_slice_index_usize_coresliceindexSliceIndexInst (List_t usize)) slots
+    0%usize l0
 .
 
 (** [loops::get_elem_shared]: loop 0: forward function *)
-Fixpoint get_elem_shared_loop_fwd
+Fixpoint get_elem_shared_loop
   (n : nat) (x : usize) (ls : List_t usize) : result usize :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
     match ls with
-    | ListCons y tl =>
-      if y s= x then Return y else get_elem_shared_loop_fwd n0 x tl
-    | ListNil => Fail_ Failure
+    | List_Cons y tl =>
+      if y s= x then Return y else get_elem_shared_loop n0 x tl
+    | List_Nil => Fail_ Failure
     end
   end
 .
 
 (** [loops::get_elem_shared]: forward function *)
-Definition get_elem_shared_fwd
-  (n : nat) (slots : vec (List_t usize)) (x : usize) : result usize :=
-  l <- vec_index_fwd (List_t usize) slots 0%usize;
-  get_elem_shared_loop_fwd n x l
+Definition get_elem_shared
+  (n : nat) (slots : alloc_vec_Vec (List_t usize)) (x : usize) :
+  result usize
+  :=
+  l <-
+    alloc_vec_Vec_index (List_t usize) usize
+      (core_slice_index_usize_coresliceindexSliceIndexInst (List_t usize))
+      slots 0%usize;
+  get_elem_shared_loop n x l
 .
 
 (** [loops::id_mut]: forward function *)
-Definition id_mut_fwd (T : Type) (ls : List_t T) : result (List_t T) :=
-  Return ls
-.
+Definition id_mut (T : Type) (ls : List_t T) : result (List_t T) :=
+  Return ls.
 
 (** [loops::id_mut]: backward function 0 *)
 Definition id_mut_back
@@ -270,31 +285,30 @@ Definition id_mut_back
 .
 
 (** [loops::id_shared]: forward function *)
-Definition id_shared_fwd (T : Type) (ls : List_t T) : result (List_t T) :=
+Definition id_shared (T : Type) (ls : List_t T) : result (List_t T) :=
   Return ls
 .
 
 (** [loops::list_nth_mut_loop_with_id]: loop 0: forward function *)
-Fixpoint list_nth_mut_loop_with_id_loop_fwd
+Fixpoint list_nth_mut_loop_with_id_loop
   (T : Type) (n : nat) (i : u32) (ls : List_t T) : result T :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
     match ls with
-    | ListCons x tl =>
+    | List_Cons x tl =>
       if i s= 0%u32
       then Return x
-      else (
-        i0 <- u32_sub i 1%u32; list_nth_mut_loop_with_id_loop_fwd T n0 i0 tl)
-    | ListNil => Fail_ Failure
+      else (i0 <- u32_sub i 1%u32; list_nth_mut_loop_with_id_loop T n0 i0 tl)
+    | List_Nil => Fail_ Failure
     end
   end
 .
 
 (** [loops::list_nth_mut_loop_with_id]: forward function *)
-Definition list_nth_mut_loop_with_id_fwd
+Definition list_nth_mut_loop_with_id
   (T : Type) (n : nat) (ls : List_t T) (i : u32) : result T :=
-  ls0 <- id_mut_fwd T ls; list_nth_mut_loop_with_id_loop_fwd T n i ls0
+  ls0 <- id_mut T ls; list_nth_mut_loop_with_id_loop T n i ls0
 .
 
 (** [loops::list_nth_mut_loop_with_id]: loop 0: backward function 0 *)
@@ -306,14 +320,14 @@ Fixpoint list_nth_mut_loop_with_id_loop_back
   | O => Fail_ OutOfFuel
   | S n0 =>
     match ls with
-    | ListCons x tl =>
+    | List_Cons x tl =>
       if i s= 0%u32
-      then Return (ListCons ret tl)
+      then Return (List_Cons ret tl)
       else (
         i0 <- u32_sub i 1%u32;
         tl0 <- list_nth_mut_loop_with_id_loop_back T n0 i0 tl ret;
-        Return (ListCons x tl0))
-    | ListNil => Fail_ Failure
+        Return (List_Cons x tl0))
+    | List_Nil => Fail_ Failure
     end
   end
 .
@@ -323,36 +337,36 @@ Definition list_nth_mut_loop_with_id_back
   (T : Type) (n : nat) (ls : List_t T) (i : u32) (ret : T) :
   result (List_t T)
   :=
-  ls0 <- id_mut_fwd T ls;
+  ls0 <- id_mut T ls;
   l <- list_nth_mut_loop_with_id_loop_back T n i ls0 ret;
   id_mut_back T ls l
 .
 
 (** [loops::list_nth_shared_loop_with_id]: loop 0: forward function *)
-Fixpoint list_nth_shared_loop_with_id_loop_fwd
+Fixpoint list_nth_shared_loop_with_id_loop
   (T : Type) (n : nat) (i : u32) (ls : List_t T) : result T :=
   match n with
   | O => Fail_ OutOfFuel
   | S n0 =>
     match ls with
-    | ListCons x tl =>
+    | List_Cons x tl =>
       if i s= 0%u32
       then Return x
       else (
-        i0 <- u32_sub i 1%u32; list_nth_shared_loop_with_id_loop_fwd T n0 i0 tl)
-    | ListNil => Fail_ Failure
+        i0 <- u32_sub i 1%u32; list_nth_shared_loop_with_id_loop T n0 i0 tl)
+    | List_Nil => Fail_ Failure
     end
   end
 .
 
 (** [loops::list_nth_shared_loop_with_id]: forward function *)
-Definition list_nth_shared_loop_with_id_fwd
+Definition list_nth_shared_loop_with_id
   (T : Type) (n : nat) (ls : List_t T) (i : u32) : result T :=
-  ls0 <- id_shared_fwd T ls; list_nth_shared_loop_with_id_loop_fwd T n i ls0
+  ls0 <- id_shared T ls; list_nth_shared_loop_with_id_loop T n i ls0
 .
 
 (** [loops::list_nth_mut_loop_pair]: loop 0: forward function *)
-Fixpoint list_nth_mut_loop_pair_loop_fwd
+Fixpoint list_nth_mut_loop_pair_loop
   (T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) :
   result (T * T)
   :=
@@ -360,27 +374,26 @@ Fixpoint list_nth_mut_loop_pair_loop_fwd
   | O => Fail_ OutOfFuel
   | S n0 =>
     match ls0 with
-    | ListCons x0 tl0 =>
+    | List_Cons x0 tl0 =>
       match ls1 with
-      | ListCons x1 tl1 =>
+      | List_Cons x1 tl1 =>
         if i s= 0%u32
         then Return (x0, x1)
         else (
-          i0 <- u32_sub i 1%u32;
-          list_nth_mut_loop_pair_loop_fwd T n0 tl0 tl1 i0)
-      | ListNil => Fail_ Failure
+          i0 <- u32_sub i 1%u32; list_nth_mut_loop_pair_loop T n0 tl0 tl1 i0)
+      | List_Nil => Fail_ Failure
       end
-    | ListNil => Fail_ Failure
+    | List_Nil => Fail_ Failure
     end
   end
 .
 
 (** [loops::list_nth_mut_loop_pair]: forward function *)
-Definition list_nth_mut_loop_pair_fwd
+Definition list_nth_mut_loop_pair
   (T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) :
   result (T * T)
   :=
-  list_nth_mut_loop_pair_loop_fwd T n ls0 ls1 i
+  list_nth_mut_loop_pair_loop T n ls0 ls1 i
 .
 
 (** [loops::list_nth_mut_loop_pair]: loop 0: backward function 0 *)
@@ -392,18 +405,18 @@ Fixpoint list_nth_mut_loop_pair_loop_back'a
   | O => Fail_ OutOfFuel
   | S n0 =>
     match ls0 with
-    | ListCons x0 tl0 =>
+    | List_Cons x0 tl0 =>
       match ls1 with
-      | ListCons x1 tl1 =>
+      | List_Cons x1 tl1 =>
         if i s= 0%u32
-        then Return (ListCons ret tl0)
+        then Return (List_Cons ret tl0)
         else (
           i0 <- u32_sub i 1%u32;
           tl00 <- list_nth_mut_loop_pair_loop_back'a T n0 tl0 tl1 i0 ret;
-          Return (ListCons x0 tl00))
-      | ListNil => Fail_ Failure
+          Return (List_Cons x0 tl00))
+      | List_Nil => Fail_ Failure
       end
-    | ListNil => Fail_ Failure
+    | List_Nil => Fail_ Failure
     end
   end
 .
@@ -425,18 +438,18 @@ Fixpoint list_nth_mut_loop_pair_loop_back'b
   | O => Fail_ OutOfFuel
   | S n0 =>
     match ls0 with
-    | ListCons x0 tl0 =>
+    | List_Cons x0 tl0 =>
       match ls1 with
-      | ListCons x1 tl1 =>
+      | List_Cons x1 tl1 =>
         if i s= 0%u32
-        then Return (ListCons ret tl1)
+        then Return (List_Cons ret tl1)
         else (
           i0 <- u32_sub i 1%u32;
           tl10 <- list_nth_mut_loop_pair_loop_back'b T n0 tl0 tl1 i0 ret;
-          Return (ListCons x1 tl10))
-      | ListNil => Fail_ Failure
+          Return (List_Cons x1 tl10))
+      | List_Nil => Fail_ Failure
       end
-    | ListNil => Fail_ Failure
+    | List_Nil => Fail_ Failure
     end
   end
 .
@@ -450,7 +463,7 @@ Definition list_nth_mut_loop_pair_back'b
 .
 
 (** [loops::list_nth_shared_loop_pair]: loop 0: forward function *)
-Fixpoint list_nth_shared_loop_pair_loop_fwd
+Fixpoint list_nth_shared_loop_pair_loop
   (T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) :
   result (T * T)
   :=
@@ -458,31 +471,30 @@ Fixpoint list_nth_shared_loop_pair_loop_fwd
   | O => Fail_ OutOfFuel
   | S n0 =>
     match ls0 with
-    | ListCons x0 tl0 =>
+    | List_Cons x0 tl0 =>
       match ls1 with
-      | ListCons x1 tl1 =>
+      | List_Cons x1 tl1 =>
         if i s= 0%u32
         then Return (x0, x1)
         else (
-          i0 <- u32_sub i 1%u32;
-          list_nth_shared_loop_pair_loop_fwd T n0 tl0 tl1 i0)
-      | ListNil => Fail_ Failure
+          i0 <- u32_sub i 1%u32; list_nth_shared_loop_pair_loop T n0 tl0 tl1 i0)
+      | List_Nil => Fail_ Failure
       end
-    | ListNil => Fail_ Failure
+    | List_Nil => Fail_ Failure
     end
   end
 .
 
 (** [loops::list_nth_shared_loop_pair]: forward function *)
-Definition list_nth_shared_loop_pair_fwd
+Definition list_nth_shared_loop_pair
   (T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) :
   result (T * T)
   :=
-  list_nth_shared_loop_pair_loop_fwd T n ls0 ls1 i
+  list_nth_shared_loop_pair_loop T n ls0 ls1 i
 .
 
 (** [loops::list_nth_mut_loop_pair_merge]: loop 0: forward function *)
-Fixpoint list_nth_mut_loop_pair_merge_loop_fwd
+Fixpoint list_nth_mut_loop_pair_merge_loop
   (T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) :
   result (T * T)
   :=
@@ -490,27 +502,27 @@ Fixpoint list_nth_mut_loop_pair_merge_loop_fwd
   | O => Fail_ OutOfFuel
   | S n0 =>
     match ls0 with
-    | ListCons x0 tl0 =>
+    | List_Cons x0 tl0 =>
       match ls1 with
-      | ListCons x1 tl1 =>
+      | List_Cons x1 tl1 =>
         if i s= 0%u32
         then Return (x0, x1)
         else (
           i0 <- u32_sub i 1%u32;
-          list_nth_mut_loop_pair_merge_loop_fwd T n0 tl0 tl1 i0)
-      | ListNil => Fail_ Failure
+          list_nth_mut_loop_pair_merge_loop T n0 tl0 tl1 i0)
+      | List_Nil => Fail_ Failure
       end
-    | ListNil => Fail_ Failure
+    | List_Nil => Fail_ Failure
     end
   end
 .
 
 (** [loops::list_nth_mut_loop_pair_merge]: forward function *)
-Definition list_nth_mut_loop_pair_merge_fwd
+Definition list_nth_mut_loop_pair_merge
   (T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) :
   result (T * T)
   :=
-  list_nth_mut_loop_pair_merge_loop_fwd T n ls0 ls1 i
+  list_nth_mut_loop_pair_merge_loop T n ls0 ls1 i
 .
 
 (** [loops::list_nth_mut_loop_pair_merge]: loop 0: backward function 0 *)
@@ -523,19 +535,19 @@ Fixpoint list_nth_mut_loop_pair_merge_loop_back
   | O => Fail_ OutOfFuel
   | S n0 =>
     match ls0 with
-    | ListCons x0 tl0 =>
+    | List_Cons x0 tl0 =>
       match ls1 with
-      | ListCons x1 tl1 =>
+      | List_Cons x1 tl1 =>
         if i s= 0%u32
-        then let (t, t0) := ret in Return (ListCons t tl0, ListCons t0 tl1)
+        then let (t, t0) := ret in Return (List_Cons t tl0, List_Cons t0 tl1)
         else (
           i0 <- u32_sub i 1%u32;
           p <- list_nth_mut_loop_pair_merge_loop_back T n0 tl0 tl1 i0 ret;
           let (tl00, tl10) := p in
-          Return (ListCons x0 tl00, ListCons x1 tl10))
-      | ListNil => Fail_ Failure
+          Return (List_Cons x0 tl00, List_Cons x1 tl10))
+      | List_Nil => Fail_ Failure
       end
-    | ListNil => Fail_ Failure
+    | List_Nil => Fail_ Failure
     end
   end
 .
@@ -550,7 +562,7 @@ Definition list_nth_mut_loop_pair_merge_back
 .
 
 (** [loops::list_nth_shared_loop_pair_merge]: loop 0: forward function *)
-Fixpoint list_nth_shared_loop_pair_merge_loop_fwd
+Fixpoint list_nth_shared_loop_pair_merge_loop
   (T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) :
   result (T * T)
   :=
@@ -558,31 +570,31 @@ Fixpoint list_nth_shared_loop_pair_merge_loop_fwd
   | O => Fail_ OutOfFuel
   | S n0 =>
     match ls0 with
-    | ListCons x0 tl0 =>
+    | List_Cons x0 tl0 =>
       match ls1 with
-      | ListCons x1 tl1 =>
+      | List_Cons x1 tl1 =>
         if i s= 0%u32
         then Return (x0, x1)
         else (
           i0 <- u32_sub i 1%u32;
-          list_nth_shared_loop_pair_merge_loop_fwd T n0 tl0 tl1 i0)
-      | ListNil => Fail_ Failure
+          list_nth_shared_loop_pair_merge_loop T n0 tl0 tl1 i0)
+      | List_Nil => Fail_ Failure
       end
-    | ListNil => Fail_ Failure
+    | List_Nil => Fail_ Failure
     end
   end
 .
 
 (** [loops::list_nth_shared_loop_pair_merge]: forward function *)
-Definition list_nth_shared_loop_pair_merge_fwd
+Definition list_nth_shared_loop_pair_merge
   (T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) :
   result (T * T)
   :=
-  list_nth_shared_loop_pair_merge_loop_fwd T n ls0 ls1 i
+  list_nth_shared_loop_pair_merge_loop T n ls0 ls1 i
 .
 
 (** [loops::list_nth_mut_shared_loop_pair]: loop 0: forward function *)
-Fixpoint list_nth_mut_shared_loop_pair_loop_fwd
+Fixpoint list_nth_mut_shared_loop_pair_loop
   (T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) :
   result (T * T)
   :=
@@ -590,27 +602,27 @@ Fixpoint list_nth_mut_shared_loop_pair_loop_fwd
   | O => Fail_ OutOfFuel
   | S n0 =>
     match ls0 with
-    | ListCons x0 tl0 =>
+    | List_Cons x0 tl0 =>
       match ls1 with
-      | ListCons x1 tl1 =>
+      | List_Cons x1 tl1 =>
         if i s= 0%u32
         then Return (x0, x1)
         else (
           i0 <- u32_sub i 1%u32;
-          list_nth_mut_shared_loop_pair_loop_fwd T n0 tl0 tl1 i0)
-      | ListNil => Fail_ Failure
+          list_nth_mut_shared_loop_pair_loop T n0 tl0 tl1 i0)
+      | List_Nil => Fail_ Failure
       end
-    | ListNil => Fail_ Failure
+    | List_Nil => Fail_ Failure
     end
   end
 .
 
 (** [loops::list_nth_mut_shared_loop_pair]: forward function *)
-Definition list_nth_mut_shared_loop_pair_fwd
+Definition list_nth_mut_shared_loop_pair
   (T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) :
   result (T * T)
   :=
-  list_nth_mut_shared_loop_pair_loop_fwd T n ls0 ls1 i
+  list_nth_mut_shared_loop_pair_loop T n ls0 ls1 i
 .
 
 (** [loops::list_nth_mut_shared_loop_pair]: loop 0: backward function 0 *)
@@ -622,18 +634,18 @@ Fixpoint list_nth_mut_shared_loop_pair_loop_back
   | O => Fail_ OutOfFuel
   | S n0 =>
     match ls0 with
-    | ListCons x0 tl0 =>
+    | List_Cons x0 tl0 =>
       match ls1 with
-      | ListCons x1 tl1 =>
+      | List_Cons x1 tl1 =>
         if i s= 0%u32
-        then Return (ListCons ret tl0)
+        then Return (List_Cons ret tl0)
         else (
           i0 <- u32_sub i 1%u32;
           tl00 <- list_nth_mut_shared_loop_pair_loop_back T n0 tl0 tl1 i0 ret;
-          Return (ListCons x0 tl00))
-      | ListNil => Fail_ Failure
+          Return (List_Cons x0 tl00))
+      | List_Nil => Fail_ Failure
       end
-    | ListNil => Fail_ Failure
+    | List_Nil => Fail_ Failure
     end
   end
 .
@@ -647,7 +659,7 @@ Definition list_nth_mut_shared_loop_pair_back
 .
 
 (** [loops::list_nth_mut_shared_loop_pair_merge]: loop 0: forward function *)
-Fixpoint list_nth_mut_shared_loop_pair_merge_loop_fwd
+Fixpoint list_nth_mut_shared_loop_pair_merge_loop
   (T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) :
   result (T * T)
   :=
@@ -655,27 +667,27 @@ Fixpoint list_nth_mut_shared_loop_pair_merge_loop_fwd
   | O => Fail_ OutOfFuel
   | S n0 =>
     match ls0 with
-    | ListCons x0 tl0 =>
+    | List_Cons x0 tl0 =>
       match ls1 with
-      | ListCons x1 tl1 =>
+      | List_Cons x1 tl1 =>
         if i s= 0%u32
         then Return (x0, x1)
         else (
           i0 <- u32_sub i 1%u32;
-          list_nth_mut_shared_loop_pair_merge_loop_fwd T n0 tl0 tl1 i0)
-      | ListNil => Fail_ Failure
+          list_nth_mut_shared_loop_pair_merge_loop T n0 tl0 tl1 i0)
+      | List_Nil => Fail_ Failure
       end
-    | ListNil => Fail_ Failure
+    | List_Nil => Fail_ Failure
     end
   end
 .
 
 (** [loops::list_nth_mut_shared_loop_pair_merge]: forward function *)
-Definition list_nth_mut_shared_loop_pair_merge_fwd
+Definition list_nth_mut_shared_loop_pair_merge
   (T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) :
   result (T * T)
   :=
-  list_nth_mut_shared_loop_pair_merge_loop_fwd T n ls0 ls1 i
+  list_nth_mut_shared_loop_pair_merge_loop T n ls0 ls1 i
 .
 
 (** [loops::list_nth_mut_shared_loop_pair_merge]: loop 0: backward function 0 *)
@@ -687,19 +699,19 @@ Fixpoint list_nth_mut_shared_loop_pair_merge_loop_back
   | O => Fail_ OutOfFuel
   | S n0 =>
     match ls0 with
-    | ListCons x0 tl0 =>
+    | List_Cons x0 tl0 =>
       match ls1 with
-      | ListCons x1 tl1 =>
+      | List_Cons x1 tl1 =>
         if i s= 0%u32
-        then Return (ListCons ret tl0)
+        then Return (List_Cons ret tl0)
         else (
           i0 <- u32_sub i 1%u32;
           tl00 <-
             list_nth_mut_shared_loop_pair_merge_loop_back T n0 tl0 tl1 i0 ret;
-          Return (ListCons x0 tl00))
-      | ListNil => Fail_ Failure
+          Return (List_Cons x0 tl00))
+      | List_Nil => Fail_ Failure
       end
-    | ListNil => Fail_ Failure
+    | List_Nil => Fail_ Failure
     end
   end
 .
@@ -713,7 +725,7 @@ Definition list_nth_mut_shared_loop_pair_merge_back
 .
 
 (** [loops::list_nth_shared_mut_loop_pair]: loop 0: forward function *)
-Fixpoint list_nth_shared_mut_loop_pair_loop_fwd
+Fixpoint list_nth_shared_mut_loop_pair_loop
   (T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) :
   result (T * T)
   :=
@@ -721,27 +733,27 @@ Fixpoint list_nth_shared_mut_loop_pair_loop_fwd
   | O => Fail_ OutOfFuel
   | S n0 =>
     match ls0 with
-    | ListCons x0 tl0 =>
+    | List_Cons x0 tl0 =>
       match ls1 with
-      | ListCons x1 tl1 =>
+      | List_Cons x1 tl1 =>
         if i s= 0%u32
         then Return (x0, x1)
         else (
           i0 <- u32_sub i 1%u32;
-          list_nth_shared_mut_loop_pair_loop_fwd T n0 tl0 tl1 i0)
-      | ListNil => Fail_ Failure
+          list_nth_shared_mut_loop_pair_loop T n0 tl0 tl1 i0)
+      | List_Nil => Fail_ Failure
       end
-    | ListNil => Fail_ Failure
+    | List_Nil => Fail_ Failure
     end
   end
 .
 
 (** [loops::list_nth_shared_mut_loop_pair]: forward function *)
-Definition list_nth_shared_mut_loop_pair_fwd
+Definition list_nth_shared_mut_loop_pair
   (T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) :
   result (T * T)
   :=
-  list_nth_shared_mut_loop_pair_loop_fwd T n ls0 ls1 i
+  list_nth_shared_mut_loop_pair_loop T n ls0 ls1 i
 .
 
 (** [loops::list_nth_shared_mut_loop_pair]: loop 0: backward function 1 *)
@@ -753,18 +765,18 @@ Fixpoint list_nth_shared_mut_loop_pair_loop_back
   | O => Fail_ OutOfFuel
   | S n0 =>
     match ls0 with
-    | ListCons x0 tl0 =>
+    | List_Cons x0 tl0 =>
       match ls1 with
-      | ListCons x1 tl1 =>
+      | List_Cons x1 tl1 =>
         if i s= 0%u32
-        then Return (ListCons ret tl1)
+        then Return (List_Cons ret tl1)
         else (
           i0 <- u32_sub i 1%u32;
           tl10 <- list_nth_shared_mut_loop_pair_loop_back T n0 tl0 tl1 i0 ret;
-          Return (ListCons x1 tl10))
-      | ListNil => Fail_ Failure
+          Return (List_Cons x1 tl10))
+      | List_Nil => Fail_ Failure
       end
-    | ListNil => Fail_ Failure
+    | List_Nil => Fail_ Failure
     end
   end
 .
@@ -778,7 +790,7 @@ Definition list_nth_shared_mut_loop_pair_back
 .
 
 (** [loops::list_nth_shared_mut_loop_pair_merge]: loop 0: forward function *)
-Fixpoint list_nth_shared_mut_loop_pair_merge_loop_fwd
+Fixpoint list_nth_shared_mut_loop_pair_merge_loop
   (T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) :
   result (T * T)
   :=
@@ -786,27 +798,27 @@ Fixpoint list_nth_shared_mut_loop_pair_merge_loop_fwd
   | O => Fail_ OutOfFuel
   | S n0 =>
     match ls0 with
-    | ListCons x0 tl0 =>
+    | List_Cons x0 tl0 =>
       match ls1 with
-      | ListCons x1 tl1 =>
+      | List_Cons x1 tl1 =>
         if i s= 0%u32
         then Return (x0, x1)
         else (
           i0 <- u32_sub i 1%u32;
-          list_nth_shared_mut_loop_pair_merge_loop_fwd T n0 tl0 tl1 i0)
-      | ListNil => Fail_ Failure
+          list_nth_shared_mut_loop_pair_merge_loop T n0 tl0 tl1 i0)
+      | List_Nil => Fail_ Failure
       end
-    | ListNil => Fail_ Failure
+    | List_Nil => Fail_ Failure
     end
   end
 .
 
 (** [loops::list_nth_shared_mut_loop_pair_merge]: forward function *)
-Definition list_nth_shared_mut_loop_pair_merge_fwd
+Definition list_nth_shared_mut_loop_pair_merge
   (T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) :
   result (T * T)
   :=
-  list_nth_shared_mut_loop_pair_merge_loop_fwd T n ls0 ls1 i
+  list_nth_shared_mut_loop_pair_merge_loop T n ls0 ls1 i
 .
 
 (** [loops::list_nth_shared_mut_loop_pair_merge]: loop 0: backward function 0 *)
@@ -818,19 +830,19 @@ Fixpoint list_nth_shared_mut_loop_pair_merge_loop_back
   | O => Fail_ OutOfFuel
   | S n0 =>
     match ls0 with
-    | ListCons x0 tl0 =>
+    | List_Cons x0 tl0 =>
       match ls1 with
-      | ListCons x1 tl1 =>
+      | List_Cons x1 tl1 =>
         if i s= 0%u32
-        then Return (ListCons ret tl1)
+        then Return (List_Cons ret tl1)
         else (
           i0 <- u32_sub i 1%u32;
           tl10 <-
             list_nth_shared_mut_loop_pair_merge_loop_back T n0 tl0 tl1 i0 ret;
-          Return (ListCons x1 tl10))
-      | ListNil => Fail_ Failure
+          Return (List_Cons x1 tl10))
+      | List_Nil => Fail_ Failure
       end
-    | ListNil => Fail_ Failure
+    | List_Nil => Fail_ Failure
     end
   end
 .
diff --git a/tests/coq/misc/NoNestedBorrows.v b/tests/coq/misc/NoNestedBorrows.v
index c1c24e00..c7af496f 100644
--- a/tests/coq/misc/NoNestedBorrows.v
+++ b/tests/coq/misc/NoNestedBorrows.v
@@ -9,113 +9,125 @@ Local Open Scope Primitives_scope.
 Module NoNestedBorrows.
 
 (** [no_nested_borrows::Pair] *)
-Record Pair_t (T1 T2 : Type) := mkPair_t { Pair_x : T1; Pair_y : T2; }.
+Record Pair_t (T1 T2 : Type) := mkPair_t { pair_x : T1; pair_y : T2; }.
 
-Arguments mkPair_t {T1} {T2} _ _.
-Arguments Pair_x {T1} {T2}.
-Arguments Pair_y {T1} {T2}.
+Arguments mkPair_t { _ _ }.
+Arguments pair_x { _ _ }.
+Arguments pair_y { _ _ }.
 
 (** [no_nested_borrows::List] *)
 Inductive List_t (T : Type) :=
-| ListCons : T -> List_t T -> List_t T
-| ListNil : List_t T
+| List_Cons : T -> List_t T -> List_t T
+| List_Nil : List_t T
 .
 
-Arguments ListCons {T} _ _.
-Arguments ListNil {T}.
+Arguments List_Cons { _ }.
+Arguments List_Nil { _ }.
 
 (** [no_nested_borrows::One] *)
-Inductive One_t (T1 : Type) := | OneOne : T1 -> One_t T1.
+Inductive One_t (T1 : Type) := | One_One : T1 -> One_t T1.
 
-Arguments OneOne {T1} _.
+Arguments One_One { _ }.
 
 (** [no_nested_borrows::EmptyEnum] *)
-Inductive Empty_enum_t := | EmptyEnumEmpty : Empty_enum_t.
+Inductive EmptyEnum_t := | EmptyEnum_Empty : EmptyEnum_t.
 
 (** [no_nested_borrows::Enum] *)
-Inductive Enum_t := | EnumVariant1 : Enum_t | EnumVariant2 : Enum_t.
+Inductive Enum_t := | Enum_Variant1 : Enum_t | Enum_Variant2 : Enum_t.
 
 (** [no_nested_borrows::EmptyStruct] *)
-Record Empty_struct_t := mkEmpty_struct_t {  }.
+Record EmptyStruct_t := mkEmptyStruct_t {  }.
 
 (** [no_nested_borrows::Sum] *)
 Inductive Sum_t (T1 T2 : Type) :=
-| SumLeft : T1 -> Sum_t T1 T2
-| SumRight : T2 -> Sum_t T1 T2
+| Sum_Left : T1 -> Sum_t T1 T2
+| Sum_Right : T2 -> Sum_t T1 T2
 .
 
-Arguments SumLeft {T1} {T2} _.
-Arguments SumRight {T1} {T2} _.
+Arguments Sum_Left { _ _ }.
+Arguments Sum_Right { _ _ }.
 
 (** [no_nested_borrows::neg_test]: forward function *)
-Definition neg_test_fwd (x : i32) : result i32 :=
+Definition neg_test (x : i32) : result i32 :=
   i32_neg x.
 
 (** [no_nested_borrows::add_test]: forward function *)
-Definition add_test_fwd (x : u32) (y : u32) : result u32 :=
+Definition add_test (x : u32) (y : u32) : result u32 :=
   u32_add x y.
 
 (** [no_nested_borrows::subs_test]: forward function *)
-Definition subs_test_fwd (x : u32) (y : u32) : result u32 :=
+Definition subs_test (x : u32) (y : u32) : result u32 :=
   u32_sub x y.
 
 (** [no_nested_borrows::div_test]: forward function *)
-Definition div_test_fwd (x : u32) (y : u32) : result u32 :=
+Definition div_test (x : u32) (y : u32) : result u32 :=
   u32_div x y.
 
 (** [no_nested_borrows::div_test1]: forward function *)
-Definition div_test1_fwd (x : u32) : result u32 :=
+Definition div_test1 (x : u32) : result u32 :=
   u32_div x 2%u32.
 
 (** [no_nested_borrows::rem_test]: forward function *)
-Definition rem_test_fwd (x : u32) (y : u32) : result u32 :=
+Definition rem_test (x : u32) (y : u32) : result u32 :=
   u32_rem x y.
 
+(** [no_nested_borrows::mul_test]: forward function *)
+Definition mul_test (x : u32) (y : u32) : result u32 :=
+  u32_mul x y.
+
+(** [no_nested_borrows::CONST0] *)
+Definition const0_body : result usize := usize_add 1%usize 1%usize.
+Definition const0_c : usize := const0_body%global.
+
+(** [no_nested_borrows::CONST1] *)
+Definition const1_body : result usize := usize_mul 2%usize 2%usize.
+Definition const1_c : usize := const1_body%global.
+
 (** [no_nested_borrows::cast_test]: forward function *)
-Definition cast_test_fwd (x : u32) : result i32 :=
+Definition cast_test (x : u32) : result i32 :=
   scalar_cast U32 I32 x.
 
 (** [no_nested_borrows::test2]: forward function *)
-Definition test2_fwd : result unit :=
+Definition test2 : result unit :=
   _ <- u32_add 23%u32 44%u32; Return tt.
 
 (** Unit test for [no_nested_borrows::test2] *)
-Check (test2_fwd )%return.
+Check (test2 )%return.
 
 (** [no_nested_borrows::get_max]: forward function *)
-Definition get_max_fwd (x : u32) (y : u32) : result u32 :=
+Definition get_max (x : u32) (y : u32) : result u32 :=
   if x s>= y then Return x else Return y
 .
 
 (** [no_nested_borrows::test3]: forward function *)
-Definition test3_fwd : result unit :=
-  x <- get_max_fwd 4%u32 3%u32;
-  y <- get_max_fwd 10%u32 11%u32;
+Definition test3 : result unit :=
+  x <- get_max 4%u32 3%u32;
+  y <- get_max 10%u32 11%u32;
   z <- u32_add x y;
   if negb (z s= 15%u32) then Fail_ Failure else Return tt
 .
 
 (** Unit test for [no_nested_borrows::test3] *)
-Check (test3_fwd )%return.
+Check (test3 )%return.
 
 (** [no_nested_borrows::test_neg1]: forward function *)
-Definition test_neg1_fwd : result unit :=
+Definition test_neg1 : result unit :=
   y <- i32_neg 3%i32; if negb (y s= (-3)%i32) then Fail_ Failure else Return tt
 .
 
 (** Unit test for [no_nested_borrows::test_neg1] *)
-Check (test_neg1_fwd )%return.
+Check (test_neg1 )%return.
 
 (** [no_nested_borrows::refs_test1]: forward function *)
-Definition refs_test1_fwd : result unit :=
+Definition refs_test1 : result unit :=
   if negb (1%i32 s= 1%i32) then Fail_ Failure else Return tt
 .
 
 (** Unit test for [no_nested_borrows::refs_test1] *)
-Check (refs_test1_fwd )%return.
+Check (refs_test1 )%return.
 
 (** [no_nested_borrows::refs_test2]: forward function *)
-Definition refs_test2_fwd : result unit :=
+Definition refs_test2 : result unit :=
   if negb (2%i32 s= 2%i32)
   then Fail_ Failure
   else
@@ -128,85 +140,83 @@ Definition refs_test2_fwd : result unit :=
 .
 
 (** Unit test for [no_nested_borrows::refs_test2] *)
-Check (refs_test2_fwd )%return.
+Check (refs_test2 )%return.
 
 (** [no_nested_borrows::test_list1]: forward function *)
-Definition test_list1_fwd : result unit :=
+Definition test_list1 : result unit :=
   Return tt.
 
 (** Unit test for [no_nested_borrows::test_list1] *)
-Check (test_list1_fwd )%return.
+Check (test_list1 )%return.
 
 (** [no_nested_borrows::test_box1]: forward function *)
-Definition test_box1_fwd : result unit :=
+Definition test_box1 : result unit :=
   let b := 1%i32 in
   let x := b in
   if negb (x s= 1%i32) then Fail_ Failure else Return tt
 .
 
 (** Unit test for [no_nested_borrows::test_box1] *)
-Check (test_box1_fwd )%return.
+Check (test_box1 )%return.
 
 (** [no_nested_borrows::copy_int]: forward function *)
-Definition copy_int_fwd (x : i32) : result i32 :=
+Definition copy_int (x : i32) : result i32 :=
   Return x.
 
 (** [no_nested_borrows::test_unreachable]: forward function *)
-Definition test_unreachable_fwd (b : bool) : result unit :=
+Definition test_unreachable (b : bool) : result unit :=
   if b then Fail_ Failure else Return tt
 .
 
 (** [no_nested_borrows::test_panic]: forward function *)
-Definition test_panic_fwd (b : bool) : result unit :=
+Definition test_panic (b : bool) : result unit :=
   if b then Fail_ Failure else Return tt
 .
 
 (** [no_nested_borrows::test_copy_int]: forward function *)
-Definition test_copy_int_fwd : result unit :=
-  y <- copy_int_fwd 0%i32;
-  if negb (0%i32 s= y) then Fail_ Failure else Return tt
+Definition test_copy_int : result unit :=
+  y <- copy_int 0%i32; if negb (0%i32 s= y) then Fail_ Failure else Return tt
 .
 
 (** Unit test for [no_nested_borrows::test_copy_int] *)
-Check (test_copy_int_fwd )%return.
+Check (test_copy_int )%return.
 
 (** [no_nested_borrows::is_cons]: forward function *)
-Definition is_cons_fwd (T : Type) (l : List_t T) : result bool :=
-  match l with | ListCons t l0 => Return true | ListNil => Return false end
+Definition is_cons (T : Type) (l : List_t T) : result bool :=
+  match l with | List_Cons t l0 => Return true | List_Nil => Return false end
 .
 
 (** [no_nested_borrows::test_is_cons]: forward function *)
-Definition test_is_cons_fwd : result unit :=
-  let l := ListNil in
-  b <- is_cons_fwd i32 (ListCons 0%i32 l);
+Definition test_is_cons : result unit :=
+  let l := List_Nil in
+  b <- is_cons i32 (List_Cons 0%i32 l);
   if negb b then Fail_ Failure else Return tt
 .
 
 (** Unit test for [no_nested_borrows::test_is_cons] *)
-Check (test_is_cons_fwd )%return.
+Check (test_is_cons )%return.
 
 (** [no_nested_borrows::split_list]: forward function *)
-Definition split_list_fwd
-  (T : Type) (l : List_t T) : result (T * (List_t T)) :=
+Definition split_list (T : Type) (l : List_t T) : result (T * (List_t T)) :=
   match l with
-  | ListCons hd tl => Return (hd, tl)
-  | ListNil => Fail_ Failure
+  | List_Cons hd tl => Return (hd, tl)
+  | List_Nil => Fail_ Failure
   end
 .
 
 (** [no_nested_borrows::test_split_list]: forward function *)
-Definition test_split_list_fwd : result unit :=
-  let l := ListNil in
-  p <- split_list_fwd i32 (ListCons 0%i32 l);
+Definition test_split_list : result unit :=
+  let l := List_Nil in
+  p <- split_list i32 (List_Cons 0%i32 l);
   let (hd, _) := p in
   if negb (hd s= 0%i32) then Fail_ Failure else Return tt
 .
 
 (** Unit test for [no_nested_borrows::test_split_list] *)
-Check (test_split_list_fwd )%return.
+Check (test_split_list )%return.
 
 (** [no_nested_borrows::choose]: forward function *)
-Definition choose_fwd (T : Type) (b : bool) (x : T) (y : T) : result T :=
+Definition choose (T : Type) (b : bool) (x : T) (y : T) : result T :=
   if b then Return x else Return y
 .
 
@@ -217,8 +227,8 @@ Definition choose_back
 .
 
 (** [no_nested_borrows::choose_test]: forward function *)
-Definition choose_test_fwd : result unit :=
-  z <- choose_fwd i32 true 0%i32 0%i32;
+Definition choose_test : result unit :=
+  z <- choose i32 true 0%i32 0%i32;
   z0 <- i32_add z 1%i32;
   if negb (z0 s= 1%i32)
   then Fail_ Failure
@@ -231,57 +241,56 @@ Definition choose_test_fwd : result unit :=
 .
 
 (** Unit test for [no_nested_borrows::choose_test] *)
-Check (choose_test_fwd )%return.
+Check (choose_test )%return.
 
 (** [no_nested_borrows::test_char]: forward function *)
-Definition test_char_fwd : result char :=
-  Return (char_of_byte Coq.Init.Byte.x61)
-.
+Definition test_char : result char :=
+  Return (char_of_byte Coq.Init.Byte.x61).
 
 (** [no_nested_borrows::Tree] *)
 Inductive Tree_t (T : Type) :=
-| TreeLeaf : T -> Tree_t T
-| TreeNode : T -> Node_elem_t T -> Tree_t T -> Tree_t T
+| Tree_Leaf : T -> Tree_t T
+| Tree_Node : T -> NodeElem_t T -> Tree_t T -> Tree_t T
 
 (** [no_nested_borrows::NodeElem] *)
-with Node_elem_t (T : Type) :=
-| NodeElemCons : Tree_t T -> Node_elem_t T -> Node_elem_t T
-| NodeElemNil : Node_elem_t T
+with NodeElem_t (T : Type) :=
+| NodeElem_Cons : Tree_t T -> NodeElem_t T -> NodeElem_t T
+| NodeElem_Nil : NodeElem_t T
 .
 
-Arguments TreeLeaf {T} _.
-Arguments TreeNode {T} _ _ _.
+Arguments Tree_Leaf { _ }.
+Arguments Tree_Node { _ }.
 
-Arguments NodeElemCons {T} _ _.
-Arguments NodeElemNil {T}.
+Arguments NodeElem_Cons { _ }.
+Arguments NodeElem_Nil { _ }.
 
 (** [no_nested_borrows::list_length]: forward function *)
-Fixpoint list_length_fwd (T : Type) (l : List_t T) : result u32 :=
+Fixpoint list_length (T : Type) (l : List_t T) : result u32 :=
   match l with
-  | ListCons t l1 => i <- list_length_fwd T l1; u32_add 1%u32 i
-  | ListNil => Return 0%u32
+  | List_Cons t l1 => i <- list_length T l1; u32_add 1%u32 i
+  | List_Nil => Return 0%u32
   end
 .
 
 (** [no_nested_borrows::list_nth_shared]: forward function *)
-Fixpoint list_nth_shared_fwd (T : Type) (l : List_t T) (i : u32) : result T :=
+Fixpoint list_nth_shared (T : Type) (l : List_t T) (i : u32) : result T :=
   match l with
-  | ListCons x tl =>
+  | List_Cons x tl =>
     if i s= 0%u32
     then Return x
-    else (i0 <- u32_sub i 1%u32; list_nth_shared_fwd T tl i0)
-  | ListNil => Fail_ Failure
+    else (i0 <- u32_sub i 1%u32; list_nth_shared T tl i0)
+  | List_Nil => Fail_ Failure
   end
 .
 
 (** [no_nested_borrows::list_nth_mut]: forward function *)
-Fixpoint list_nth_mut_fwd (T : Type) (l : List_t T) (i : u32) : result T :=
+Fixpoint list_nth_mut (T : Type) (l : List_t T) (i : u32) : result T :=
   match l with
-  | ListCons x tl =>
+  | List_Cons x tl =>
     if i s= 0%u32
     then Return x
-    else (i0 <- u32_sub i 1%u32; list_nth_mut_fwd T tl i0)
-  | ListNil => Fail_ Failure
+    else (i0 <- u32_sub i 1%u32; list_nth_mut T tl i0)
+  | List_Nil => Fail_ Failure
   end
 .
 
@@ -289,73 +298,72 @@ Fixpoint list_nth_mut_fwd (T : Type) (l : List_t T) (i : u32) : result T :=
 Fixpoint list_nth_mut_back
   (T : Type) (l : List_t T) (i : u32) (ret : T) : result (List_t T) :=
   match l with
-  | ListCons x tl =>
+  | List_Cons x tl =>
     if i s= 0%u32
-    then Return (ListCons ret tl)
+    then Return (List_Cons ret tl)
     else (
       i0 <- u32_sub i 1%u32;
       tl0 <- list_nth_mut_back T tl i0 ret;
-      Return (ListCons x tl0))
-  | ListNil => Fail_ Failure
+      Return (List_Cons x tl0))
+  | List_Nil => Fail_ Failure
   end
 .
 
 (** [no_nested_borrows::list_rev_aux]: forward function *)
-Fixpoint list_rev_aux_fwd
+Fixpoint list_rev_aux
   (T : Type) (li : List_t T) (lo : List_t T) : result (List_t T) :=
   match li with
-  | ListCons hd tl => list_rev_aux_fwd T tl (ListCons hd lo)
-  | ListNil => Return lo
+  | List_Cons hd tl => list_rev_aux T tl (List_Cons hd lo)
+  | List_Nil => Return lo
   end
 .
 
 (** [no_nested_borrows::list_rev]: merged forward/backward function
     (there is a single backward function, and the forward function returns ()) *)
-Definition list_rev_fwd_back (T : Type) (l : List_t T) : result (List_t T) :=
-  let li := mem_replace_fwd (List_t T) l ListNil in
-  list_rev_aux_fwd T li ListNil
+Definition list_rev (T : Type) (l : List_t T) : result (List_t T) :=
+  let li := core_mem_replace (List_t T) l List_Nil in
+  list_rev_aux T li List_Nil
 .
 
 (** [no_nested_borrows::test_list_functions]: forward function *)
-Definition test_list_functions_fwd : result unit :=
-  let l := ListNil in
-  let l0 := ListCons 2%i32 l in
-  let l1 := ListCons 1%i32 l0 in
-  i <- list_length_fwd i32 (ListCons 0%i32 l1);
+Definition test_list_functions : result unit :=
+  let l := List_Nil in
+  let l0 := List_Cons 2%i32 l in
+  let l1 := List_Cons 1%i32 l0 in
+  i <- list_length i32 (List_Cons 0%i32 l1);
   if negb (i s= 3%u32)
   then Fail_ Failure
   else (
-    i0 <- list_nth_shared_fwd i32 (ListCons 0%i32 l1) 0%u32;
+    i0 <- list_nth_shared i32 (List_Cons 0%i32 l1) 0%u32;
     if negb (i0 s= 0%i32)
     then Fail_ Failure
     else (
-      i1 <- list_nth_shared_fwd i32 (ListCons 0%i32 l1) 1%u32;
+      i1 <- list_nth_shared i32 (List_Cons 0%i32 l1) 1%u32;
       if negb (i1 s= 1%i32)
       then Fail_ Failure
       else (
-        i2 <- list_nth_shared_fwd i32 (ListCons 0%i32 l1) 2%u32;
+        i2 <- list_nth_shared i32 (List_Cons 0%i32 l1) 2%u32;
         if negb (i2 s= 2%i32)
         then Fail_ Failure
         else (
-          ls <- list_nth_mut_back i32 (ListCons 0%i32 l1) 1%u32 3%i32;
-          i3 <- list_nth_shared_fwd i32 ls 0%u32;
+          ls <- list_nth_mut_back i32 (List_Cons 0%i32 l1) 1%u32 3%i32;
+          i3 <- list_nth_shared i32 ls 0%u32;
           if negb (i3 s= 0%i32)
           then Fail_ Failure
           else (
-            i4 <- list_nth_shared_fwd i32 ls 1%u32;
+            i4 <- list_nth_shared i32 ls 1%u32;
             if negb (i4 s= 3%i32)
             then Fail_ Failure
             else (
-              i5 <- list_nth_shared_fwd i32 ls 2%u32;
+              i5 <- list_nth_shared i32 ls 2%u32;
               if negb (i5 s= 2%i32) then Fail_ Failure else Return tt))))))
 .
 
 (** Unit test for [no_nested_borrows::test_list_functions] *)
-Check (test_list_functions_fwd )%return.
+Check (test_list_functions )%return.
 
 (** [no_nested_borrows::id_mut_pair1]: forward function *)
-Definition id_mut_pair1_fwd
-  (T1 T2 : Type) (x : T1) (y : T2) : result (T1 * T2) :=
+Definition id_mut_pair1 (T1 T2 : Type) (x : T1) (y : T2) : result (T1 * T2) :=
   Return (x, y)
 .
 
@@ -366,8 +374,7 @@ Definition id_mut_pair1_back
 .
 
 (** [no_nested_borrows::id_mut_pair2]: forward function *)
-Definition id_mut_pair2_fwd
-  (T1 T2 : Type) (p : (T1 * T2)) : result (T1 * T2) :=
+Definition id_mut_pair2 (T1 T2 : Type) (p : (T1 * T2)) : result (T1 * T2) :=
   let (t, t0) := p in Return (t, t0)
 .
 
@@ -378,8 +385,7 @@ Definition id_mut_pair2_back
 .
 
 (** [no_nested_borrows::id_mut_pair3]: forward function *)
-Definition id_mut_pair3_fwd
-  (T1 T2 : Type) (x : T1) (y : T2) : result (T1 * T2) :=
+Definition id_mut_pair3 (T1 T2 : Type) (x : T1) (y : T2) : result (T1 * T2) :=
   Return (x, y)
 .
 
@@ -396,8 +402,7 @@ Definition id_mut_pair3_back'b
 .
 
 (** [no_nested_borrows::id_mut_pair4]: forward function *)
-Definition id_mut_pair4_fwd
-  (T1 T2 : Type) (p : (T1 * T2)) : result (T1 * T2) :=
+Definition id_mut_pair4 (T1 T2 : Type) (p : (T1 * T2)) : result (T1 * T2) :=
   let (t, t0) := p in Return (t, t0)
 .
 
@@ -414,101 +419,101 @@ Definition id_mut_pair4_back'b
 .
 
 (** [no_nested_borrows::StructWithTuple] *)
-Record Struct_with_tuple_t (T1 T2 : Type) :=
-mkStruct_with_tuple_t {
-  Struct_with_tuple_p : (T1 * T2);
+Record StructWithTuple_t (T1 T2 : Type) :=
+mkStructWithTuple_t {
+  structWithTuple_p : (T1 * T2);
 }
 .
 
-Arguments mkStruct_with_tuple_t {T1} {T2} _.
-Arguments Struct_with_tuple_p {T1} {T2}.
+Arguments mkStructWithTuple_t { _ _ }.
+Arguments structWithTuple_p { _ _ }.
 
 (** [no_nested_borrows::new_tuple1]: forward function *)
-Definition new_tuple1_fwd : result (Struct_with_tuple_t u32 u32) :=
-  Return {| Struct_with_tuple_p := (1%u32, 2%u32) |}
+Definition new_tuple1 : result (StructWithTuple_t u32 u32) :=
+  Return {| structWithTuple_p := (1%u32, 2%u32) |}
 .
 
 (** [no_nested_borrows::new_tuple2]: forward function *)
-Definition new_tuple2_fwd : result (Struct_with_tuple_t i16 i16) :=
-  Return {| Struct_with_tuple_p := (1%i16, 2%i16) |}
+Definition new_tuple2 : result (StructWithTuple_t i16 i16) :=
+  Return {| structWithTuple_p := (1%i16, 2%i16) |}
 .
 
 (** [no_nested_borrows::new_tuple3]: forward function *)
-Definition new_tuple3_fwd : result (Struct_with_tuple_t u64 i64) :=
-  Return {| Struct_with_tuple_p := (1%u64, 2%i64) |}
+Definition new_tuple3 : result (StructWithTuple_t u64 i64) :=
+  Return {| structWithTuple_p := (1%u64, 2%i64) |}
 .
 
 (** [no_nested_borrows::StructWithPair] *)
-Record Struct_with_pair_t (T1 T2 : Type) :=
-mkStruct_with_pair_t {
-  Struct_with_pair_p : Pair_t T1 T2;
+Record StructWithPair_t (T1 T2 : Type) :=
+mkStructWithPair_t {
+  structWithPair_p : Pair_t T1 T2;
 }
 .
 
-Arguments mkStruct_with_pair_t {T1} {T2} _.
-Arguments Struct_with_pair_p {T1} {T2}.
+Arguments mkStructWithPair_t { _ _ }.
+Arguments structWithPair_p { _ _ }.
 
 (** [no_nested_borrows::new_pair1]: forward function *)
-Definition new_pair1_fwd : result (Struct_with_pair_t u32 u32) :=
-  Return {| Struct_with_pair_p := {| Pair_x := 1%u32; Pair_y := 2%u32 |} |}
+Definition new_pair1 : result (StructWithPair_t u32 u32) :=
+  Return {| structWithPair_p := {| pair_x := 1%u32; pair_y := 2%u32 |} |}
 .
 
 (** [no_nested_borrows::test_constants]: forward function *)
-Definition test_constants_fwd : result unit :=
-  swt <- new_tuple1_fwd;
-  let (i, _) := swt.(Struct_with_tuple_p) in
+Definition test_constants : result unit :=
+  swt <- new_tuple1;
+  let (i, _) := swt.(structWithTuple_p) in
   if negb (i s= 1%u32)
   then Fail_ Failure
   else (
-    swt0 <- new_tuple2_fwd;
-    let (i0, _) := swt0.(Struct_with_tuple_p) in
+    swt0 <- new_tuple2;
+    let (i0, _) := swt0.(structWithTuple_p) in
     if negb (i0 s= 1%i16)
     then Fail_ Failure
     else (
-      swt1 <- new_tuple3_fwd;
-      let (i1, _) := swt1.(Struct_with_tuple_p) in
+      swt1 <- new_tuple3;
+      let (i1, _) := swt1.(structWithTuple_p) in
       if negb (i1 s= 1%u64)
       then Fail_ Failure
       else (
-        swp <- new_pair1_fwd;
-        if negb (swp.(Struct_with_pair_p).(Pair_x) s= 1%u32)
+        swp <- new_pair1;
+        if negb (swp.(structWithPair_p).(pair_x) s= 1%u32)
         then Fail_ Failure
         else Return tt)))
 .
 
 (** Unit test for [no_nested_borrows::test_constants] *)
-Check (test_constants_fwd )%return.
+Check (test_constants )%return.
 
 (** [no_nested_borrows::test_weird_borrows1]: forward function *)
-Definition test_weird_borrows1_fwd : result unit :=
+Definition test_weird_borrows1 : result unit :=
   Return tt.
 
 (** Unit test for [no_nested_borrows::test_weird_borrows1] *)
-Check (test_weird_borrows1_fwd )%return.
+Check (test_weird_borrows1 )%return.
 
 (** [no_nested_borrows::test_mem_replace]: merged forward/backward function
     (there is a single backward function, and the forward function returns ()) *)
-Definition test_mem_replace_fwd_back (px : u32) : result u32 :=
-  let y := mem_replace_fwd u32 px 1%u32 in
+Definition test_mem_replace (px : u32) : result u32 :=
+  let y := core_mem_replace u32 px 1%u32 in
   if negb (y s= 0%u32) then Fail_ Failure else Return 2%u32
 .
 
 (** [no_nested_borrows::test_shared_borrow_bool1]: forward function *)
-Definition test_shared_borrow_bool1_fwd (b : bool) : result u32 :=
+Definition test_shared_borrow_bool1 (b : bool) : result u32 :=
   if b then Return 0%u32 else Return 1%u32
 .
 
 (** [no_nested_borrows::test_shared_borrow_bool2]: forward function *)
-Definition test_shared_borrow_bool2_fwd : result u32 :=
+Definition test_shared_borrow_bool2 : result u32 :=
   Return 0%u32.
 
 (** [no_nested_borrows::test_shared_borrow_enum1]: forward function *)
-Definition test_shared_borrow_enum1_fwd (l : List_t u32) : result u32 :=
-  match l with | ListCons i l0 => Return 1%u32 | ListNil => Return 0%u32 end
+Definition test_shared_borrow_enum1 (l : List_t u32) : result u32 :=
+  match l with | List_Cons i l0 => Return 1%u32 | List_Nil => Return 0%u32 end
 .
 
 (** [no_nested_borrows::test_shared_borrow_enum2]: forward function *)
-Definition test_shared_borrow_enum2_fwd : result u32 :=
+Definition test_shared_borrow_enum2 : result u32 :=
   Return 0%u32.
 
 End NoNestedBorrows .
diff --git a/tests/coq/misc/Paper.v b/tests/coq/misc/Paper.v
index 175a523d..d3852e6b 100644
--- a/tests/coq/misc/Paper.v
+++ b/tests/coq/misc/Paper.v
@@ -10,20 +10,19 @@ Module Paper.
 
 (** [paper::ref_incr]: merged forward/backward function
     (there is a single backward function, and the forward function returns ()) *)
-Definition ref_incr_fwd_back (x : i32) : result i32 :=
+Definition ref_incr (x : i32) : result i32 :=
   i32_add x 1%i32.
 
 (** [paper::test_incr]: forward function *)
-Definition test_incr_fwd : result unit :=
-  x <- ref_incr_fwd_back 0%i32;
-  if negb (x s= 1%i32) then Fail_ Failure else Return tt
+Definition test_incr : result unit :=
+  x <- ref_incr 0%i32; if negb (x s= 1%i32) then Fail_ Failure else Return tt
 .
 
 (** Unit test for [paper::test_incr] *)
-Check (test_incr_fwd )%return.
+Check (test_incr )%return.
 
 (** [paper::choose]: forward function *)
-Definition choose_fwd (T : Type) (b : bool) (x : T) (y : T) : result T :=
+Definition choose (T : Type) (b : bool) (x : T) (y : T) : result T :=
   if b then Return x else Return y
 .
 
@@ -34,8 +33,8 @@ Definition choose_back
 .
 
 (** [paper::test_choose]: forward function *)
-Definition test_choose_fwd : result unit :=
-  z <- choose_fwd i32 true 0%i32 0%i32;
+Definition test_choose : result unit :=
+  z <- choose i32 true 0%i32 0%i32;
   z0 <- i32_add z 1%i32;
   if negb (z0 s= 1%i32)
   then Fail_ Failure
@@ -48,25 +47,25 @@ Definition test_choose_fwd : result unit :=
 .
 
 (** Unit test for [paper::test_choose] *)
-Check (test_choose_fwd )%return.
+Check (test_choose )%return.
 
 (** [paper::List] *)
 Inductive List_t (T : Type) :=
-| ListCons : T -> List_t T -> List_t T
-| ListNil : List_t T
+| List_Cons : T -> List_t T -> List_t T
+| List_Nil : List_t T
 .
 
-Arguments ListCons {T} _ _.
-Arguments ListNil {T}.
+Arguments List_Cons { _ }.
+Arguments List_Nil { _ }.
 
 (** [paper::list_nth_mut]: forward function *)
-Fixpoint list_nth_mut_fwd (T : Type) (l : List_t T) (i : u32) : result T :=
+Fixpoint list_nth_mut (T : Type) (l : List_t T) (i : u32) : result T :=
   match l with
-  | ListCons x tl =>
+  | List_Cons x tl =>
     if i s= 0%u32
     then Return x
-    else (i0 <- u32_sub i 1%u32; list_nth_mut_fwd T tl i0)
-  | ListNil => Fail_ Failure
+    else (i0 <- u32_sub i 1%u32; list_nth_mut T tl i0)
+  | List_Nil => Fail_ Failure
   end
 .
 
@@ -74,44 +73,44 @@ Fixpoint list_nth_mut_fwd (T : Type) (l : List_t T) (i : u32) : result T :=
 Fixpoint list_nth_mut_back
   (T : Type) (l : List_t T) (i : u32) (ret : T) : result (List_t T) :=
   match l with
-  | ListCons x tl =>
+  | List_Cons x tl =>
     if i s= 0%u32
-    then Return (ListCons ret tl)
+    then Return (List_Cons ret tl)
     else (
       i0 <- u32_sub i 1%u32;
       tl0 <- list_nth_mut_back T tl i0 ret;
-      Return (ListCons x tl0))
-  | ListNil => Fail_ Failure
+      Return (List_Cons x tl0))
+  | List_Nil => Fail_ Failure
   end
 .
 
 (** [paper::sum]: forward function *)
-Fixpoint sum_fwd (l : List_t i32) : result i32 :=
+Fixpoint sum (l : List_t i32) : result i32 :=
   match l with
-  | ListCons x tl => i <- sum_fwd tl; i32_add x i
-  | ListNil => Return 0%i32
+  | List_Cons x tl => i <- sum tl; i32_add x i
+  | List_Nil => Return 0%i32
   end
 .
 
 (** [paper::test_nth]: forward function *)
-Definition test_nth_fwd : result unit :=
-  let l := ListNil in
-  let l0 := ListCons 3%i32 l in
-  let l1 := ListCons 2%i32 l0 in
-  x <- list_nth_mut_fwd i32 (ListCons 1%i32 l1) 2%u32;
+Definition test_nth : result unit :=
+  let l := List_Nil in
+  let l0 := List_Cons 3%i32 l in
+  let l1 := List_Cons 2%i32 l0 in
+  x <- list_nth_mut i32 (List_Cons 1%i32 l1) 2%u32;
   x0 <- i32_add x 1%i32;
-  l2 <- list_nth_mut_back i32 (ListCons 1%i32 l1) 2%u32 x0;
-  i <- sum_fwd l2;
+  l2 <- list_nth_mut_back i32 (List_Cons 1%i32 l1) 2%u32 x0;
+  i <- sum l2;
   if negb (i s= 7%i32) then Fail_ Failure else Return tt
 .
 
 (** Unit test for [paper::test_nth] *)
-Check (test_nth_fwd )%return.
+Check (test_nth )%return.
 
 (** [paper::call_choose]: forward function *)
-Definition call_choose_fwd (p : (u32 * u32)) : result u32 :=
+Definition call_choose (p : (u32 * u32)) : result u32 :=
   let (px, py) := p in
-  pz <- choose_fwd u32 true px py;
+  pz <- choose u32 true px py;
   pz0 <- u32_add pz 1%u32;
   p0 <- choose_back u32 true px py pz0;
   let (px0, _) := p0 in
diff --git a/tests/coq/misc/PoloniusList.v b/tests/coq/misc/PoloniusList.v
index 54021bdf..4848444f 100644
--- a/tests/coq/misc/PoloniusList.v
+++ b/tests/coq/misc/PoloniusList.v
@@ -10,19 +10,19 @@ Module PoloniusList.
 
 (** [polonius_list::List] *)
 Inductive List_t (T : Type) :=
-| ListCons : T -> List_t T -> List_t T
-| ListNil : List_t T
+| List_Cons : T -> List_t T -> List_t T
+| List_Nil : List_t T
 .
 
-Arguments ListCons {T} _ _.
-Arguments ListNil {T}.
+Arguments List_Cons { _ }.
+Arguments List_Nil { _ }.
 
 (** [polonius_list::get_list_at_x]: forward function *)
-Fixpoint get_list_at_x_fwd (ls : List_t u32) (x : u32) : result (List_t u32) :=
+Fixpoint get_list_at_x (ls : List_t u32) (x : u32) : result (List_t u32) :=
   match ls with
-  | ListCons hd tl =>
-    if hd s= x then Return (ListCons hd tl) else get_list_at_x_fwd tl x
-  | ListNil => Return ListNil
+  | List_Cons hd tl =>
+    if hd s= x then Return (List_Cons hd tl) else get_list_at_x tl x
+  | List_Nil => Return List_Nil
   end
 .
 
@@ -30,11 +30,11 @@ Fixpoint get_list_at_x_fwd (ls : List_t u32) (x : u32) : result (List_t u32) :=
 Fixpoint get_list_at_x_back
   (ls : List_t u32) (x : u32) (ret : List_t u32) : result (List_t u32) :=
   match ls with
-  | ListCons hd tl =>
+  | List_Cons hd tl =>
     if hd s= x
     then Return ret
-    else (tl0 <- get_list_at_x_back tl x ret; Return (ListCons hd tl0))
-  | ListNil => Return ret
+    else (tl0 <- get_list_at_x_back tl x ret; Return (List_Cons hd tl0))
+  | List_Nil => Return ret
   end
 .
 
diff --git a/tests/coq/misc/Primitives.v b/tests/coq/misc/Primitives.v
index 71a2d9c3..85e38f01 100644
--- a/tests/coq/misc/Primitives.v
+++ b/tests/coq/misc/Primitives.v
@@ -63,13 +63,15 @@ Check (if true then Return (1 + 2) else Fail_ Failure)%global = 3.
 
 (*** Misc *)
 
-
 Definition string := Coq.Strings.String.string.
 Definition char := Coq.Strings.Ascii.ascii.
 Definition char_of_byte := Coq.Strings.Ascii.ascii_of_byte.
 
-Definition mem_replace_fwd (a : Type) (x : a) (y : a) : a := x .
-Definition mem_replace_back (a : Type) (x : a) (y : a) : a := y .
+Definition core_mem_replace (a : Type) (x : a) (y : a) : a := x .
+Definition core_mem_replace_back (a : Type) (x : a) (y : a) : a := y .
+
+Record mut_raw_ptr (T : Type) := { mut_raw_ptr_v : T }.
+Record const_raw_ptr (T : Type) := { const_raw_ptr_v : T }.
 
 (*** Scalars *)
 
@@ -394,12 +396,89 @@ Notation "x s< y" := (scalar_ltb x y)  (at level 80) : Primitives_scope.
 Notation "x s>= y" := (scalar_geb x y)  (at level 80) : Primitives_scope.
 Notation "x s> y" := (scalar_gtb x y)  (at level 80) : Primitives_scope.
 
-(*** Range *)
-Record range (T : Type) := mk_range {
-  start: T;
-  end_: T;
+(** Constants *)
+Definition core_u8_max    := u8_max %u32.
+Definition core_u16_max   := u16_max %u32.
+Definition core_u32_max   := u32_max %u32.
+Definition core_u64_max   := u64_max %u64.
+Definition core_u128_max  := u64_max %u128.
+Axiom core_usize_max : usize. (** TODO *)
+Definition core_i8_max    := i8_max %i32.
+Definition core_i16_max   := i16_max %i32.
+Definition core_i32_max   := i32_max %i32.
+Definition core_i64_max   := i64_max %i64.
+Definition core_i128_max  := i64_max %i128.
+Axiom core_isize_max : isize. (** TODO *)
+
+(*** core::ops *)
+
+(* Trait declaration: [core::ops::index::Index] *)
+Record core_ops_index_Index (Self Idx : Type) := mk_core_ops_index_Index {
+  core_ops_index_Index_Output : Type;
+  core_ops_index_Index_index : Self -> Idx -> result core_ops_index_Index_Output;
+}.
+Arguments mk_core_ops_index_Index {_ _}.
+Arguments core_ops_index_Index_Output {_ _}.
+Arguments core_ops_index_Index_index {_ _}.
+
+(* Trait declaration: [core::ops::index::IndexMut] *)
+Record core_ops_index_IndexMut (Self Idx : Type) := mk_core_ops_index_IndexMut {
+  core_ops_index_IndexMut_indexInst : core_ops_index_Index Self Idx;
+  core_ops_index_IndexMut_index_mut : Self -> Idx -> result core_ops_index_IndexMut_indexInst.(core_ops_index_Index_Output);
+  core_ops_index_IndexMut_index_mut_back : Self -> Idx -> core_ops_index_IndexMut_indexInst.(core_ops_index_Index_Output) -> result Self;
+}.
+Arguments mk_core_ops_index_IndexMut {_ _}.
+Arguments core_ops_index_IndexMut_indexInst {_ _}.
+Arguments core_ops_index_IndexMut_index_mut {_ _}.
+Arguments core_ops_index_IndexMut_index_mut_back {_ _}.
+
+(* Trait declaration [core::ops::deref::Deref] *)
+Record core_ops_deref_Deref (Self : Type) := mk_core_ops_deref_Deref {
+  core_ops_deref_Deref_target : Type;
+  core_ops_deref_Deref_deref : Self -> result core_ops_deref_Deref_target;
+}.
+Arguments mk_core_ops_deref_Deref {_}.
+Arguments core_ops_deref_Deref_target {_}.
+Arguments core_ops_deref_Deref_deref {_}.
+
+(* Trait declaration [core::ops::deref::DerefMut] *)
+Record core_ops_deref_DerefMut (Self : Type) := mk_core_ops_deref_DerefMut {
+  core_ops_deref_DerefMut_derefInst : core_ops_deref_Deref Self;
+  core_ops_deref_DerefMut_deref_mut : Self -> result core_ops_deref_DerefMut_derefInst.(core_ops_deref_Deref_target);
+  core_ops_deref_DerefMut_deref_mut_back : Self -> core_ops_deref_DerefMut_derefInst.(core_ops_deref_Deref_target) -> result Self;
 }.
-Arguments mk_range {_}.
+Arguments mk_core_ops_deref_DerefMut {_}.
+Arguments core_ops_deref_DerefMut_derefInst {_}.
+Arguments core_ops_deref_DerefMut_deref_mut {_}.
+Arguments core_ops_deref_DerefMut_deref_mut_back {_}.
+
+Record core_ops_range_Range (T : Type) := mk_core_ops_range_Range {
+  core_ops_range_Range_start : T;
+  core_ops_range_Range_end_ : T;
+}.
+Arguments mk_core_ops_range_Range {_}.
+Arguments core_ops_range_Range_start {_}.
+Arguments core_ops_range_Range_end_ {_}.
+
+(*** [alloc] *)
+
+Definition alloc_boxed_Box_deref (T : Type) (x : T) : result T := Return x.
+Definition alloc_boxed_Box_deref_mut (T : Type) (x : T) : result T := Return x.
+Definition alloc_boxed_Box_deref_mut_back (T : Type) (_ : T) (x : T) : result T := Return x.
+
+(* Trait instance *)
+Definition alloc_boxed_Box_coreOpsDerefInst (Self : Type) : core_ops_deref_Deref Self := {|
+  core_ops_deref_Deref_target := Self;
+  core_ops_deref_Deref_deref := alloc_boxed_Box_deref Self;
+|}.
+
+(* Trait instance *)
+Definition alloc_boxed_Box_coreOpsDerefMutInst (Self : Type) : core_ops_deref_DerefMut Self := {|
+  core_ops_deref_DerefMut_derefInst := alloc_boxed_Box_coreOpsDerefInst Self;
+  core_ops_deref_DerefMut_deref_mut := alloc_boxed_Box_deref_mut Self;
+  core_ops_deref_DerefMut_deref_mut_back := alloc_boxed_Box_deref_mut_back Self;
+|}.
+
 
 (*** Arrays *)
 Definition array T (n : usize) := { l: list T | Z.of_nat (length l) = to_Z n}.
@@ -419,51 +498,50 @@ Qed.
 (* TODO: finish the definitions *)
 Axiom mk_array : forall (T : Type) (n : usize) (l : list T), array T n.
 
-Axiom array_index_shared : forall (T : Type) (n : usize) (x : array T n) (i : usize), result T.
-Axiom array_index_mut_fwd : forall (T : Type) (n : usize) (x : array T n) (i : usize), result T.
-Axiom array_index_mut_back : forall (T : Type) (n : usize) (x : array T n) (i : usize) (nx : T), result (array T n).
+(* For initialization *)
+Axiom array_repeat : forall (T : Type) (n : usize) (x : T), array T n.
+
+Axiom array_index_usize : forall (T : Type) (n : usize) (x : array T n) (i : usize), result T.
+Axiom array_update_usize : forall (T : Type) (n : usize) (x : array T n) (i : usize) (nx : T), result (array T n).
 
 (*** Slice *)
 Definition slice T := { l: list T | Z.of_nat (length l) <= usize_max}.
 
 Axiom slice_len : forall (T : Type) (s : slice T), usize.
-Axiom slice_index_shared : forall (T : Type) (x : slice T) (i : usize), result T.
-Axiom slice_index_mut_fwd : forall (T : Type) (x : slice T) (i : usize), result T.
-Axiom slice_index_mut_back : forall (T : Type) (x : slice T) (i : usize) (nx : T), result (slice T).
+Axiom slice_index_usize : forall (T : Type) (x : slice T) (i : usize), result T.
+Axiom slice_update_usize : forall (T : Type) (x : slice T) (i : usize) (nx : T), result (slice T).
 
 (*** Subslices *)
 
-Axiom array_to_slice_shared : forall (T : Type) (n : usize) (x : array T n), result (slice T).
-Axiom array_to_slice_mut_fwd : forall (T : Type) (n : usize) (x : array T n), result (slice T).
-Axiom array_to_slice_mut_back : forall (T : Type) (n : usize) (x : array T n) (s : slice T), result (array T n).
+Axiom array_to_slice : forall (T : Type) (n : usize) (x : array T n), result (slice T).
+Axiom array_from_slice : forall (T : Type) (n : usize) (x : array T n) (s : slice T), result (array T n).
+
+Axiom array_subslice: forall (T : Type) (n : usize) (x : array T n) (r : core_ops_range_Range usize), result (slice T).
+Axiom array_update_subslice: forall (T : Type) (n : usize) (x : array T n) (r : core_ops_range_Range usize) (ns : slice T), result (array T n).
 
-Axiom array_subslice_shared: forall (T : Type) (n : usize) (x : array T n) (r : range usize), result (slice T).
-Axiom array_subslice_mut_fwd: forall (T : Type) (n : usize) (x : array T n) (r : range usize), result (slice T).
-Axiom array_subslice_mut_back: forall (T : Type) (n : usize) (x : array T n) (r : range usize) (ns : slice T), result (array T n).
-Axiom slice_subslice_shared: forall (T : Type) (x : slice T) (r : range usize), result (slice T).
-Axiom slice_subslice_mut_fwd: forall (T : Type) (x : slice T) (r : range usize), result (slice T).
-Axiom slice_subslice_mut_back: forall (T : Type) (x : slice T) (r : range usize) (ns : slice T), result (slice T).
+Axiom slice_subslice: forall (T : Type) (x : slice T) (r : core_ops_range_Range usize), result (slice T).
+Axiom slice_update_subslice: forall (T : Type) (x : slice T) (r : core_ops_range_Range usize) (ns : slice T), result (slice T).
 
 (*** Vectors *)
 
-Definition vec T := { l: list T | Z.of_nat (length l) <= usize_max }.
+Definition alloc_vec_Vec T := { l: list T | Z.of_nat (length l) <= usize_max }.
 
-Definition vec_to_list {T: Type} (v: vec T) : list T := proj1_sig v.
+Definition alloc_vec_Vec_to_list {T: Type} (v: alloc_vec_Vec T) : list T := proj1_sig v.
 
-Definition vec_length {T: Type} (v: vec T) : Z := Z.of_nat (length (vec_to_list v)).
+Definition alloc_vec_Vec_length {T: Type} (v: alloc_vec_Vec T) : Z := Z.of_nat (length (alloc_vec_Vec_to_list v)).
 
-Definition vec_new (T: Type) : vec T := (exist _ [] le_0_usize_max).
+Definition alloc_vec_Vec_new (T: Type) : alloc_vec_Vec T := (exist _ [] le_0_usize_max).
 
-Lemma vec_len_in_usize {T} (v: vec T) : usize_min <= vec_length v <= usize_max.
+Lemma alloc_vec_Vec_len_in_usize {T} (v: alloc_vec_Vec T) : usize_min <= alloc_vec_Vec_length v <= usize_max.
 Proof.
-  unfold vec_length, usize_min.
+  unfold alloc_vec_Vec_length, usize_min.
   split.
   - lia.
   - apply (proj2_sig v).
 Qed.
 
-Definition vec_len (T: Type) (v: vec T) : usize :=
-  exist _ (vec_length v) (vec_len_in_usize v).
+Definition alloc_vec_Vec_len (T: Type) (v: alloc_vec_Vec T) : usize :=
+  exist _ (alloc_vec_Vec_length v) (alloc_vec_Vec_len_in_usize v).
 
 Fixpoint list_update {A} (l: list A) (n: nat) (a: A)
   : list A :=
@@ -474,50 +552,271 @@ Fixpoint list_update {A} (l: list A) (n: nat) (a: A)
     | S m => x :: (list_update t m a)
 end end.
 
-Definition vec_bind {A B} (v: vec A) (f: list A -> result (list B)) : result (vec B) :=
-  l <- f (vec_to_list v) ;
+Definition alloc_vec_Vec_bind {A B} (v: alloc_vec_Vec A) (f: list A -> result (list B)) : result (alloc_vec_Vec B) :=
+  l <- f (alloc_vec_Vec_to_list v) ;
   match sumbool_of_bool (scalar_le_max Usize (Z.of_nat (length l))) with
   | left H => Return (exist _ l (scalar_le_max_valid _ _ H))
   | right _ => Fail_ Failure
   end.
 
 (* The **forward** function shouldn't be used *)
-Definition vec_push_fwd (T: Type) (v: vec T) (x: T) : unit := tt.
+Definition alloc_vec_Vec_push_fwd (T: Type) (v: alloc_vec_Vec T) (x: T) : unit := tt.
 
-Definition vec_push_back (T: Type) (v: vec T) (x: T) : result (vec T) :=
-  vec_bind v (fun l => Return (l ++ [x])).
+Definition alloc_vec_Vec_push (T: Type) (v: alloc_vec_Vec T) (x: T) : result (alloc_vec_Vec T) :=
+  alloc_vec_Vec_bind v (fun l => Return (l ++ [x])).
 
 (* The **forward** function shouldn't be used *)
-Definition vec_insert_fwd (T: Type) (v: vec T) (i: usize) (x: T) : result unit :=
-  if to_Z i <? vec_length v then Return tt else Fail_ Failure.
+Definition alloc_vec_Vec_insert_fwd (T: Type) (v: alloc_vec_Vec T) (i: usize) (x: T) : result unit :=
+  if to_Z i <? alloc_vec_Vec_length v then Return tt else Fail_ Failure.
 
-Definition vec_insert_back (T: Type) (v: vec T) (i: usize) (x: T) : result (vec T) :=
-  vec_bind v (fun l =>
+Definition alloc_vec_Vec_insert (T: Type) (v: alloc_vec_Vec T) (i: usize) (x: T) : result (alloc_vec_Vec T) :=
+  alloc_vec_Vec_bind v (fun l =>
     if to_Z i <? Z.of_nat (length l)
     then Return (list_update l (usize_to_nat i) x)
     else Fail_ Failure).
 
-(* The **backward** function shouldn't be used *)
-Definition vec_index_fwd (T: Type) (v: vec T) (i: usize) : result T :=
-  match nth_error (vec_to_list v) (usize_to_nat i) with
-  | Some n => Return n
-  | None   => Fail_ Failure
-  end.
-
-Definition vec_index_back (T: Type) (v: vec T) (i: usize) (x: T) : result unit :=
-  if to_Z i <? vec_length v then Return tt else Fail_ Failure.
-
-(* The **backward** function shouldn't be used *)
-Definition vec_index_mut_fwd (T: Type) (v: vec T) (i: usize) : result T :=
-  match nth_error (vec_to_list v) (usize_to_nat i) with
-  | Some n => Return n
-  | None   => Fail_ Failure
+(* Helper *)
+Axiom alloc_vec_Vec_index_usize : forall {T : Type} (v : alloc_vec_Vec T) (i : usize) (x : T), result T.
+
+(* Helper *)
+Axiom alloc_vec_Vec_update_usize : forall {T : Type} (v : alloc_vec_Vec T) (i : usize) (x : T), result (alloc_vec_Vec T).
+
+(* Trait declaration: [core::slice::index::private_slice_index::Sealed] *)
+Definition core_slice_index_private_slice_index_Sealed (self : Type) := unit.
+
+(* Trait declaration: [core::slice::index::SliceIndex] *)
+Record core_slice_index_SliceIndex (Self T : Type) := mk_core_slice_index_SliceIndex {
+  core_slice_index_SliceIndex_sealedInst : core_slice_index_private_slice_index_Sealed Self;
+  core_slice_index_SliceIndex_Output : Type;
+  core_slice_index_SliceIndex_get : Self -> T -> result (option core_slice_index_SliceIndex_Output);
+  core_slice_index_SliceIndex_get_mut : Self -> T -> result (option core_slice_index_SliceIndex_Output);
+  core_slice_index_SliceIndex_get_mut_back : Self -> T -> option core_slice_index_SliceIndex_Output -> result T;
+  core_slice_index_SliceIndex_get_unchecked : Self -> const_raw_ptr T -> result (const_raw_ptr core_slice_index_SliceIndex_Output);
+  core_slice_index_SliceIndex_get_unchecked_mut : Self -> mut_raw_ptr T -> result (mut_raw_ptr core_slice_index_SliceIndex_Output);
+  core_slice_index_SliceIndex_index : Self -> T -> result core_slice_index_SliceIndex_Output;
+  core_slice_index_SliceIndex_index_mut : Self -> T -> result core_slice_index_SliceIndex_Output;
+  core_slice_index_SliceIndex_index_mut_back : Self -> T -> core_slice_index_SliceIndex_Output -> result T;
+}.
+Arguments mk_core_slice_index_SliceIndex {_ _}.
+Arguments core_slice_index_SliceIndex_sealedInst {_ _}.
+Arguments core_slice_index_SliceIndex_Output {_ _}.
+Arguments core_slice_index_SliceIndex_get {_ _}.
+Arguments core_slice_index_SliceIndex_get_mut {_ _}.
+Arguments core_slice_index_SliceIndex_get_mut_back {_ _}.
+Arguments core_slice_index_SliceIndex_get_unchecked {_ _}.
+Arguments core_slice_index_SliceIndex_get_unchecked_mut {_ _}.
+Arguments core_slice_index_SliceIndex_index {_ _}.
+Arguments core_slice_index_SliceIndex_index_mut {_ _}.
+Arguments core_slice_index_SliceIndex_index_mut_back {_ _}.
+
+(* [core::slice::index::[T]::index]: forward function *)
+Definition core_slice_index_Slice_index
+  (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T))
+  (s : slice T) (i : Idx) : result inst.(core_slice_index_SliceIndex_Output) :=
+  x <- inst.(core_slice_index_SliceIndex_get) i s;
+  match x with
+  | None => Fail_ Failure
+  | Some x => Return x
   end.
 
-Definition vec_index_mut_back (T: Type) (v: vec T) (i: usize) (x: T) : result (vec T) :=
-  vec_bind v (fun l =>
-    if to_Z i <? Z.of_nat (length l)
-    then Return (list_update l (usize_to_nat i) x)
-    else Fail_ Failure).
+(* [core::slice::index::Range:::get]: forward function *)
+Axiom core_slice_index_Range_get : forall (T : Type) (i : core_ops_range_Range usize) (s : slice T), result (option (slice T)).
+
+(* [core::slice::index::Range::get_mut]: forward function *)
+Axiom core_slice_index_Range_get_mut :
+  forall (T : Type), core_ops_range_Range usize -> slice T -> result (option (slice T)).
+
+(* [core::slice::index::Range::get_mut]: backward function 0 *)
+Axiom core_slice_index_Range_get_mut_back :
+  forall (T : Type), core_ops_range_Range usize -> slice T -> option (slice T) -> result (slice T).
+
+(* [core::slice::index::Range::get_unchecked]: forward function *)
+Definition core_slice_index_Range_get_unchecked
+  (T : Type) :
+  core_ops_range_Range usize -> const_raw_ptr (slice T) -> result (const_raw_ptr (slice T)) :=
+  (* Don't know what the model should be - for now we always fail to make
+     sure code which uses it fails *)
+  fun _ _ => Fail_ Failure.
+
+(* [core::slice::index::Range::get_unchecked_mut]: forward function *)
+Definition core_slice_index_Range_get_unchecked_mut
+  (T : Type) :
+  core_ops_range_Range usize -> mut_raw_ptr (slice T) -> result (mut_raw_ptr (slice T)) :=
+  (* Don't know what the model should be - for now we always fail to make
+    sure code which uses it fails *)
+  fun _ _ => Fail_ Failure.
+
+(* [core::slice::index::Range::index]: forward function *)
+Axiom core_slice_index_Range_index :
+  forall (T : Type), core_ops_range_Range usize -> slice T -> result (slice T).
+
+(* [core::slice::index::Range::index_mut]: forward function *)
+Axiom core_slice_index_Range_index_mut :
+  forall (T : Type), core_ops_range_Range usize -> slice T -> result (slice T).
+
+(* [core::slice::index::Range::index_mut]: backward function 0 *)
+Axiom core_slice_index_Range_index_mut_back :
+  forall (T : Type), core_ops_range_Range usize -> slice T -> slice T -> result (slice T).
+
+(* [core::slice::index::[T]::index_mut]: forward function *)
+Axiom core_slice_index_Slice_index_mut :
+  forall (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T)),
+  slice T -> Idx -> result inst.(core_slice_index_SliceIndex_Output).
+
+(* [core::slice::index::[T]::index_mut]: backward function 0 *)
+Axiom core_slice_index_Slice_index_mut_back :
+  forall (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T)),
+  slice T -> Idx -> inst.(core_slice_index_SliceIndex_Output) -> result (slice T).
+
+(* [core::array::[T; N]::index]: forward function *)
+Axiom core_array_Array_index :
+  forall (T Idx : Type) (N : usize) (inst : core_ops_index_Index (slice T) Idx)
+  (a : array T N) (i : Idx), result inst.(core_ops_index_Index_Output).
+
+(* [core::array::[T; N]::index_mut]: forward function *)
+Axiom core_array_Array_index_mut :
+  forall (T Idx : Type) (N : usize) (inst : core_ops_index_IndexMut (slice T) Idx)
+  (a : array T N) (i : Idx), result inst.(core_ops_index_IndexMut_indexInst).(core_ops_index_Index_Output).
+
+(* [core::array::[T; N]::index_mut]: backward function 0 *)
+Axiom core_array_Array_index_mut_back :
+  forall (T Idx : Type) (N : usize) (inst : core_ops_index_IndexMut (slice T) Idx)
+  (a : array T N) (i : Idx) (x : inst.(core_ops_index_IndexMut_indexInst).(core_ops_index_Index_Output)), result (array T N).
+
+(* Trait implementation: [core::slice::index::[T]] *)
+Definition core_slice_index_Slice_coreopsindexIndexInst (T Idx : Type)
+  (inst : core_slice_index_SliceIndex Idx (slice T)) :
+  core_ops_index_Index (slice T) Idx := {|
+  core_ops_index_Index_Output := inst.(core_slice_index_SliceIndex_Output);
+  core_ops_index_Index_index := core_slice_index_Slice_index T Idx inst;
+|}.
+
+(* Trait implementation: [core::slice::index::private_slice_index::Range] *)
+Definition core_slice_index_private_slice_index_Range_coresliceindexprivate_slice_indexSealedInst
+  : core_slice_index_private_slice_index_Sealed (core_ops_range_Range usize) := tt.
+
+(* Trait implementation: [core::slice::index::Range] *)
+Definition core_slice_index_Range_coresliceindexSliceIndexInst (T : Type) :
+  core_slice_index_SliceIndex (core_ops_range_Range usize) (slice T) := {|
+  core_slice_index_SliceIndex_sealedInst := core_slice_index_private_slice_index_Range_coresliceindexprivate_slice_indexSealedInst;
+  core_slice_index_SliceIndex_Output := slice T;
+  core_slice_index_SliceIndex_get := core_slice_index_Range_get T;
+  core_slice_index_SliceIndex_get_mut := core_slice_index_Range_get_mut T;
+  core_slice_index_SliceIndex_get_mut_back := core_slice_index_Range_get_mut_back T;
+  core_slice_index_SliceIndex_get_unchecked := core_slice_index_Range_get_unchecked T;
+  core_slice_index_SliceIndex_get_unchecked_mut := core_slice_index_Range_get_unchecked_mut T;
+  core_slice_index_SliceIndex_index := core_slice_index_Range_index T;
+  core_slice_index_SliceIndex_index_mut := core_slice_index_Range_index_mut T;
+  core_slice_index_SliceIndex_index_mut_back := core_slice_index_Range_index_mut_back T;
+|}.
+
+(* Trait implementation: [core::slice::index::[T]] *)
+Definition core_slice_index_Slice_coreopsindexIndexMutInst (T Idx : Type)
+  (inst : core_slice_index_SliceIndex Idx (slice T)) :
+  core_ops_index_IndexMut (slice T) Idx := {|
+  core_ops_index_IndexMut_indexInst := core_slice_index_Slice_coreopsindexIndexInst T Idx inst;
+  core_ops_index_IndexMut_index_mut := core_slice_index_Slice_index_mut T Idx inst;
+  core_ops_index_IndexMut_index_mut_back := core_slice_index_Slice_index_mut_back T Idx inst;
+|}.
+
+(* Trait implementation: [core::array::[T; N]] *)
+Definition core_array_Array_coreopsindexIndexInst (T Idx : Type) (N : usize)
+  (inst : core_ops_index_Index (slice T) Idx) :
+  core_ops_index_Index (array T N) Idx := {|
+  core_ops_index_Index_Output := inst.(core_ops_index_Index_Output);
+  core_ops_index_Index_index := core_array_Array_index T Idx N inst;
+|}.
+
+(* Trait implementation: [core::array::[T; N]] *)
+Definition core_array_Array_coreopsindexIndexMutInst (T Idx : Type) (N : usize)
+  (inst : core_ops_index_IndexMut (slice T) Idx) :
+  core_ops_index_IndexMut (array T N) Idx := {|
+  core_ops_index_IndexMut_indexInst := core_array_Array_coreopsindexIndexInst T Idx N inst.(core_ops_index_IndexMut_indexInst);
+  core_ops_index_IndexMut_index_mut := core_array_Array_index_mut T Idx N inst;
+  core_ops_index_IndexMut_index_mut_back := core_array_Array_index_mut_back T Idx N inst;
+|}.
+
+(* [core::slice::index::usize::get]: forward function *)
+Axiom core_slice_index_usize_get : forall (T : Type), usize -> slice T -> result (option T).
+
+(* [core::slice::index::usize::get_mut]: forward function *)
+Axiom core_slice_index_usize_get_mut : forall (T : Type), usize -> slice T -> result (option T).
+
+(* [core::slice::index::usize::get_mut]: backward function 0 *)
+Axiom core_slice_index_usize_get_mut_back :
+  forall (T : Type), usize -> slice T -> option T -> result (slice T).
+
+(* [core::slice::index::usize::get_unchecked]: forward function *)
+Axiom core_slice_index_usize_get_unchecked :
+  forall (T : Type), usize -> const_raw_ptr (slice T) -> result (const_raw_ptr T).
+
+(* [core::slice::index::usize::get_unchecked_mut]: forward function *)
+Axiom core_slice_index_usize_get_unchecked_mut :
+  forall (T : Type), usize -> mut_raw_ptr (slice T) -> result (mut_raw_ptr T).
+
+(* [core::slice::index::usize::index]: forward function *)
+Axiom core_slice_index_usize_index : forall (T : Type), usize -> slice T -> result T.
+
+(* [core::slice::index::usize::index_mut]: forward function *)
+Axiom core_slice_index_usize_index_mut : forall (T : Type), usize -> slice T -> result T.
+
+(* [core::slice::index::usize::index_mut]: backward function 0 *)
+Axiom core_slice_index_usize_index_mut_back :
+  forall (T : Type), usize -> slice T -> T -> result (slice T).
+
+(* Trait implementation: [core::slice::index::private_slice_index::usize] *)
+Definition core_slice_index_private_slice_index_usize_coresliceindexprivate_slice_indexSealedInst
+  : core_slice_index_private_slice_index_Sealed usize := tt.
+
+(* Trait implementation: [core::slice::index::usize] *)
+Definition core_slice_index_usize_coresliceindexSliceIndexInst (T : Type) :
+  core_slice_index_SliceIndex usize (slice T) := {|
+  core_slice_index_SliceIndex_sealedInst := core_slice_index_private_slice_index_usize_coresliceindexprivate_slice_indexSealedInst;
+  core_slice_index_SliceIndex_Output := T;
+  core_slice_index_SliceIndex_get := core_slice_index_usize_get T;
+  core_slice_index_SliceIndex_get_mut := core_slice_index_usize_get_mut T;
+  core_slice_index_SliceIndex_get_mut_back := core_slice_index_usize_get_mut_back T;
+  core_slice_index_SliceIndex_get_unchecked := core_slice_index_usize_get_unchecked T;
+  core_slice_index_SliceIndex_get_unchecked_mut := core_slice_index_usize_get_unchecked_mut T;
+  core_slice_index_SliceIndex_index := core_slice_index_usize_index T;
+  core_slice_index_SliceIndex_index_mut := core_slice_index_usize_index_mut T;
+  core_slice_index_SliceIndex_index_mut_back := core_slice_index_usize_index_mut_back T;
+|}.
+
+(* [alloc::vec::Vec::index]: forward function *)
+Axiom alloc_vec_Vec_index : forall (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T))
+  (Self : alloc_vec_Vec T) (i : Idx), result inst.(core_slice_index_SliceIndex_Output).
+
+(* [alloc::vec::Vec::index_mut]: forward function *)
+Axiom alloc_vec_Vec_index_mut : forall (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T))
+  (Self : alloc_vec_Vec T) (i : Idx), result inst.(core_slice_index_SliceIndex_Output).
+
+(* [alloc::vec::Vec::index_mut]: backward function 0 *)
+Axiom alloc_vec_Vec_index_mut_back :
+  forall (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T))
+  (Self : alloc_vec_Vec T) (i : Idx) (x : inst.(core_slice_index_SliceIndex_Output)), result (alloc_vec_Vec T).
+
+(* Trait implementation: [alloc::vec::Vec] *)
+Definition alloc_vec_Vec_coreopsindexIndexInst (T Idx : Type)
+  (inst : core_slice_index_SliceIndex Idx (slice T)) :
+  core_ops_index_Index (alloc_vec_Vec T) Idx := {|
+  core_ops_index_Index_Output := inst.(core_slice_index_SliceIndex_Output);
+  core_ops_index_Index_index := alloc_vec_Vec_index T Idx inst;
+|}.
+
+(* Trait implementation: [alloc::vec::Vec] *)
+Definition alloc_vec_Vec_coreopsindexIndexMutInst (T Idx : Type)
+  (inst : core_slice_index_SliceIndex Idx (slice T)) :
+  core_ops_index_IndexMut (alloc_vec_Vec T) Idx := {|
+  core_ops_index_IndexMut_indexInst := alloc_vec_Vec_coreopsindexIndexInst T Idx inst;
+  core_ops_index_IndexMut_index_mut := alloc_vec_Vec_index_mut T Idx inst;
+  core_ops_index_IndexMut_index_mut_back := alloc_vec_Vec_index_mut_back T Idx inst;
+|}.
+
+(*** Theorems *)
+
+Axiom alloc_vec_Vec_index_mut_back_eq : forall {a : Type} (v : alloc_vec_Vec a) (i : usize) (x : a),
+  alloc_vec_Vec_index_mut_back a usize (core_slice_index_usize_coresliceindexSliceIndexInst a) v i x =
+    alloc_vec_Vec_update_usize v i x.
 
 End Primitives.
diff --git a/tests/coq/traits/Makefile b/tests/coq/traits/Makefile
new file mode 100644
index 00000000..1a5aee4a
--- /dev/null
+++ b/tests/coq/traits/Makefile
@@ -0,0 +1,23 @@
+# This file was automatically generated - modify ../Makefile.template instead
+# Makefile originally taken from coq-club
+
+%: Makefile.coq phony
+	+make -f Makefile.coq $@
+
+all: Makefile.coq
+	+make -f Makefile.coq all
+
+clean: Makefile.coq
+	+make -f Makefile.coq clean
+	rm -f Makefile.coq
+
+Makefile.coq: _CoqProject Makefile
+	coq_makefile -f _CoqProject | sed 's/$$(COQCHK) $$(COQCHKFLAGS) $$(COQLIBS)/$$(COQCHK) $$(COQCHKFLAGS) $$(subst -Q,-R,$$(COQLIBS))/' > Makefile.coq
+
+_CoqProject: ;
+
+Makefile: ;
+
+phony: ;
+
+.PHONY: all clean phony
diff --git a/tests/coq/traits/Primitives.v b/tests/coq/traits/Primitives.v
new file mode 100644
index 00000000..85e38f01
--- /dev/null
+++ b/tests/coq/traits/Primitives.v
@@ -0,0 +1,822 @@
+Require Import Lia.
+Require Coq.Strings.Ascii.
+Require Coq.Strings.String.
+Require Import Coq.Program.Equality.
+Require Import Coq.ZArith.ZArith.
+Require Import Coq.ZArith.Znat.
+Require Import List.
+Import ListNotations.
+
+Module Primitives.
+
+  (* TODO: use more *)
+Declare Scope Primitives_scope.
+
+(*** Result *)
+
+Inductive error :=
+  | Failure
+  | OutOfFuel.
+
+Inductive result A :=
+  | Return : A -> result A
+  | Fail_ : error -> result A.
+
+Arguments Return {_} a.
+Arguments Fail_ {_}.
+
+Definition bind {A B} (m: result A) (f: A -> result B) : result B :=
+  match m with
+  | Fail_ e => Fail_ e
+  | Return x => f x
+  end.
+
+Definition return_ {A: Type} (x: A) : result A := Return x.
+Definition fail_ {A: Type} (e: error) : result A := Fail_ e.
+
+Notation "x <- c1 ; c2" := (bind c1 (fun x => c2))
+  (at level 61, c1 at next level, right associativity).
+
+(** Monadic assert *)
+Definition massert (b: bool) : result unit :=
+  if b then Return tt else Fail_ Failure.
+
+(** Normalize and unwrap a successful result (used for globals) *)
+Definition eval_result_refl {A} {x} (a: result A) (p: a = Return x) : A :=
+  match a as r return (r = Return x -> A) with
+  | Return a' => fun _  => a'
+  | Fail_ e   => fun p' =>
+      False_rect _ (eq_ind (Fail_ e)
+          (fun e : result A =>
+          match e with
+          | Return _ => False
+          | Fail_ e => True
+          end)
+        I (Return x) p')
+  end p.
+
+Notation "x %global" := (eval_result_refl x eq_refl) (at level 40).
+Notation "x %return" := (eval_result_refl x eq_refl) (at level 40).
+
+(* Sanity check *)
+Check (if true then Return (1 + 2) else Fail_ Failure)%global = 3.
+
+(*** Misc *)
+
+Definition string := Coq.Strings.String.string.
+Definition char := Coq.Strings.Ascii.ascii.
+Definition char_of_byte := Coq.Strings.Ascii.ascii_of_byte.
+
+Definition core_mem_replace (a : Type) (x : a) (y : a) : a := x .
+Definition core_mem_replace_back (a : Type) (x : a) (y : a) : a := y .
+
+Record mut_raw_ptr (T : Type) := { mut_raw_ptr_v : T }.
+Record const_raw_ptr (T : Type) := { const_raw_ptr_v : T }.
+
+(*** Scalars *)
+
+Definition i8_min   : Z := -128%Z.
+Definition i8_max   : Z := 127%Z.
+Definition i16_min  : Z := -32768%Z.
+Definition i16_max  : Z := 32767%Z.
+Definition i32_min  : Z := -2147483648%Z.
+Definition i32_max  : Z := 2147483647%Z.
+Definition i64_min  : Z := -9223372036854775808%Z.
+Definition i64_max  : Z := 9223372036854775807%Z.
+Definition i128_min : Z := -170141183460469231731687303715884105728%Z.
+Definition i128_max : Z := 170141183460469231731687303715884105727%Z.
+Definition u8_min   : Z := 0%Z.
+Definition u8_max   : Z := 255%Z.
+Definition u16_min  : Z := 0%Z.
+Definition u16_max  : Z := 65535%Z.
+Definition u32_min  : Z := 0%Z.
+Definition u32_max  : Z := 4294967295%Z.
+Definition u64_min  : Z := 0%Z.
+Definition u64_max  : Z := 18446744073709551615%Z.
+Definition u128_min : Z := 0%Z.
+Definition u128_max : Z := 340282366920938463463374607431768211455%Z.
+
+(** The bounds of [isize] and [usize] vary with the architecture. *)
+Axiom isize_min : Z.
+Axiom isize_max : Z.
+Definition usize_min : Z := 0%Z.
+Axiom usize_max : Z.
+
+Open Scope Z_scope.
+
+(** We provide those lemmas to reason about the bounds of [isize] and [usize] *)
+Axiom isize_min_bound : isize_min <= i32_min.
+Axiom isize_max_bound : i32_max <= isize_max.
+Axiom usize_max_bound : u32_max <= usize_max.
+
+Inductive scalar_ty :=
+  | Isize
+  | I8
+  | I16
+  | I32
+  | I64
+  | I128
+  | Usize
+  | U8
+  | U16
+  | U32
+  | U64
+  | U128
+.
+
+Definition scalar_min (ty: scalar_ty) : Z :=
+  match ty with
+  | Isize => isize_min
+  | I8 => i8_min
+  | I16 => i16_min
+  | I32 => i32_min
+  | I64 => i64_min
+  | I128 => i128_min
+  | Usize => usize_min
+  | U8 => u8_min
+  | U16 => u16_min
+  | U32 => u32_min
+  | U64 => u64_min
+  | U128 => u128_min
+end.
+
+Definition scalar_max (ty: scalar_ty) : Z :=
+  match ty with
+  | Isize => isize_max
+  | I8 => i8_max
+  | I16 => i16_max
+  | I32 => i32_max
+  | I64 => i64_max
+  | I128 => i128_max
+  | Usize => usize_max
+  | U8 => u8_max
+  | U16 => u16_max
+  | U32 => u32_max
+  | U64 => u64_max
+  | U128 => u128_max
+end.
+
+(** We use the following conservative bounds to make sure we can compute bound
+    checks in most situations *)
+Definition scalar_min_cons (ty: scalar_ty) : Z :=
+  match ty with
+  | Isize => i32_min
+  | Usize => u32_min
+  | _ => scalar_min ty
+end.
+
+Definition scalar_max_cons (ty: scalar_ty) : Z :=
+  match ty with
+  | Isize => i32_max
+  | Usize => u32_max
+  | _ => scalar_max ty
+end.
+
+Lemma scalar_min_cons_valid : forall ty, scalar_min ty <= scalar_min_cons ty .
+Proof.
+  destruct ty; unfold scalar_min_cons, scalar_min; try lia.
+  - pose isize_min_bound; lia.
+  - apply Z.le_refl.
+Qed.
+
+Lemma scalar_max_cons_valid : forall ty, scalar_max ty >= scalar_max_cons ty .
+Proof.
+  destruct ty; unfold scalar_max_cons, scalar_max; try lia.
+  - pose isize_max_bound; lia.
+  - pose usize_max_bound. lia.
+Qed.
+
+Definition scalar (ty: scalar_ty) : Type :=
+ { x: Z | scalar_min ty <= x <= scalar_max ty }.
+
+Definition to_Z {ty} (x: scalar ty) : Z := proj1_sig x.
+
+(** Bounds checks: we start by using the conservative bounds, to make sure we
+    can compute in most situations, then we use the real bounds (for [isize]
+    and [usize]). *)
+Definition scalar_ge_min (ty: scalar_ty) (x: Z) : bool :=
+  Z.leb (scalar_min_cons ty) x || Z.leb (scalar_min ty) x.
+
+Definition scalar_le_max (ty: scalar_ty) (x: Z) : bool :=
+  Z.leb x (scalar_max_cons ty) || Z.leb x (scalar_max ty).
+
+Lemma scalar_ge_min_valid (ty: scalar_ty) (x: Z) :
+  scalar_ge_min ty x = true -> scalar_min ty <= x .
+Proof.
+  unfold scalar_ge_min.
+  pose (scalar_min_cons_valid ty).
+  lia.
+Qed.
+
+Lemma scalar_le_max_valid (ty: scalar_ty) (x: Z) :
+  scalar_le_max ty x = true -> x <= scalar_max ty .
+Proof.
+  unfold scalar_le_max.
+  pose (scalar_max_cons_valid ty).
+  lia.
+Qed.
+
+Definition scalar_in_bounds (ty: scalar_ty) (x: Z) : bool :=
+  scalar_ge_min ty x && scalar_le_max ty x .
+
+Lemma scalar_in_bounds_valid (ty: scalar_ty) (x: Z) :
+  scalar_in_bounds ty x = true -> scalar_min ty <= x <= scalar_max ty .
+Proof.
+  unfold scalar_in_bounds.
+  intros H.
+  destruct (scalar_ge_min ty x) eqn:Hmin.
+  - destruct (scalar_le_max ty x) eqn:Hmax.
+    + pose (scalar_ge_min_valid ty x Hmin).
+      pose (scalar_le_max_valid ty x Hmax).
+      lia.
+    + inversion H.
+  - inversion H.
+Qed.
+
+Import Sumbool.
+
+Definition mk_scalar (ty: scalar_ty) (x: Z) : result (scalar ty) :=
+  match sumbool_of_bool (scalar_in_bounds ty x) with
+  | left H => Return (exist _ x (scalar_in_bounds_valid _ _ H))
+  | right _ => Fail_ Failure
+  end.
+
+Definition scalar_add {ty} (x y: scalar ty) : result (scalar ty) := mk_scalar ty (to_Z x + to_Z y).
+
+Definition scalar_sub {ty} (x y: scalar ty) : result (scalar ty) := mk_scalar ty (to_Z x - to_Z y).
+
+Definition scalar_mul {ty} (x y: scalar ty) : result (scalar ty) := mk_scalar ty (to_Z x * to_Z y).
+
+Definition scalar_div {ty} (x y: scalar ty) : result (scalar ty) :=
+  if to_Z y =? 0 then Fail_ Failure else
+  mk_scalar ty (to_Z x / to_Z y).
+
+Definition scalar_rem {ty} (x y: scalar ty) : result (scalar ty) := mk_scalar ty (Z.rem (to_Z x) (to_Z y)).
+  
+Definition scalar_neg {ty} (x: scalar ty) : result (scalar ty) := mk_scalar ty (-(to_Z x)).
+
+(** Cast an integer from a [src_ty] to a [tgt_ty] *)
+(* TODO: check the semantics of casts in Rust *)
+Definition scalar_cast (src_ty tgt_ty : scalar_ty) (x : scalar src_ty) : result (scalar tgt_ty) :=
+  mk_scalar tgt_ty (to_Z x).
+
+(** Comparisons *)
+Definition scalar_leb {ty : scalar_ty} (x : scalar ty) (y : scalar ty) : bool :=
+  Z.leb (to_Z x) (to_Z y) .
+
+Definition scalar_ltb {ty : scalar_ty} (x : scalar ty) (y : scalar ty) : bool :=
+  Z.ltb (to_Z x) (to_Z y) .
+
+Definition scalar_geb {ty : scalar_ty} (x : scalar ty) (y : scalar ty) : bool :=
+  Z.geb (to_Z x) (to_Z y) .
+
+Definition scalar_gtb {ty : scalar_ty} (x : scalar ty) (y : scalar ty) : bool :=
+  Z.gtb (to_Z x) (to_Z y) .
+
+Definition scalar_eqb {ty : scalar_ty} (x : scalar ty) (y : scalar ty) : bool :=
+  Z.eqb (to_Z x) (to_Z y) .
+
+Definition scalar_neqb {ty : scalar_ty} (x : scalar ty) (y : scalar ty) : bool :=
+  negb (Z.eqb (to_Z x) (to_Z y)) .
+
+
+(** The scalar types *)
+Definition isize := scalar Isize.
+Definition i8    := scalar I8.
+Definition i16   := scalar I16.
+Definition i32   := scalar I32.
+Definition i64   := scalar I64.
+Definition i128  := scalar I128.
+Definition usize := scalar Usize.
+Definition u8    := scalar U8.
+Definition u16   := scalar U16.
+Definition u32   := scalar U32.
+Definition u64   := scalar U64.
+Definition u128  := scalar U128.
+
+(** Negaion *)
+Definition isize_neg := @scalar_neg Isize.
+Definition i8_neg    := @scalar_neg I8.
+Definition i16_neg   := @scalar_neg I16.
+Definition i32_neg   := @scalar_neg I32.
+Definition i64_neg   := @scalar_neg I64.
+Definition i128_neg  := @scalar_neg I128.
+
+(** Division *)
+Definition isize_div := @scalar_div Isize.
+Definition i8_div    := @scalar_div I8.
+Definition i16_div   := @scalar_div I16.
+Definition i32_div   := @scalar_div I32.
+Definition i64_div   := @scalar_div I64.
+Definition i128_div  := @scalar_div I128.
+Definition usize_div := @scalar_div Usize.
+Definition u8_div    := @scalar_div U8.
+Definition u16_div   := @scalar_div U16.
+Definition u32_div   := @scalar_div U32.
+Definition u64_div   := @scalar_div U64.
+Definition u128_div  := @scalar_div U128.
+
+(** Remainder *)
+Definition isize_rem := @scalar_rem Isize.
+Definition i8_rem    := @scalar_rem I8.
+Definition i16_rem   := @scalar_rem I16.
+Definition i32_rem   := @scalar_rem I32.
+Definition i64_rem   := @scalar_rem I64.
+Definition i128_rem  := @scalar_rem I128.
+Definition usize_rem := @scalar_rem Usize.
+Definition u8_rem    := @scalar_rem U8.
+Definition u16_rem   := @scalar_rem U16.
+Definition u32_rem   := @scalar_rem U32.
+Definition u64_rem   := @scalar_rem U64.
+Definition u128_rem  := @scalar_rem U128.
+
+(** Addition *)
+Definition isize_add := @scalar_add Isize.
+Definition i8_add    := @scalar_add I8.
+Definition i16_add   := @scalar_add I16.
+Definition i32_add   := @scalar_add I32.
+Definition i64_add   := @scalar_add I64.
+Definition i128_add  := @scalar_add I128.
+Definition usize_add := @scalar_add Usize.
+Definition u8_add    := @scalar_add U8.
+Definition u16_add   := @scalar_add U16.
+Definition u32_add   := @scalar_add U32.
+Definition u64_add   := @scalar_add U64.
+Definition u128_add  := @scalar_add U128.
+
+(** Substraction *)
+Definition isize_sub := @scalar_sub Isize.
+Definition i8_sub    := @scalar_sub I8.
+Definition i16_sub   := @scalar_sub I16.
+Definition i32_sub   := @scalar_sub I32.
+Definition i64_sub   := @scalar_sub I64.
+Definition i128_sub  := @scalar_sub I128.
+Definition usize_sub := @scalar_sub Usize.
+Definition u8_sub    := @scalar_sub U8.
+Definition u16_sub   := @scalar_sub U16.
+Definition u32_sub   := @scalar_sub U32.
+Definition u64_sub   := @scalar_sub U64.
+Definition u128_sub  := @scalar_sub U128.
+
+(** Multiplication *)
+Definition isize_mul := @scalar_mul Isize.
+Definition i8_mul    := @scalar_mul I8.
+Definition i16_mul   := @scalar_mul I16.
+Definition i32_mul   := @scalar_mul I32.
+Definition i64_mul   := @scalar_mul I64.
+Definition i128_mul  := @scalar_mul I128.
+Definition usize_mul := @scalar_mul Usize.
+Definition u8_mul    := @scalar_mul U8.
+Definition u16_mul   := @scalar_mul U16.
+Definition u32_mul   := @scalar_mul U32.
+Definition u64_mul   := @scalar_mul U64.
+Definition u128_mul  := @scalar_mul U128.
+
+(** Small utility *)
+Definition usize_to_nat (x: usize) : nat := Z.to_nat (to_Z x).
+
+(** Notations *)
+Notation "x %isize" := ((mk_scalar Isize x)%return) (at level 9).
+Notation "x %i8"    := ((mk_scalar I8    x)%return) (at level 9).
+Notation "x %i16"   := ((mk_scalar I16   x)%return) (at level 9).
+Notation "x %i32"   := ((mk_scalar I32   x)%return) (at level 9).
+Notation "x %i64"   := ((mk_scalar I64   x)%return) (at level 9).
+Notation "x %i128"  := ((mk_scalar I128  x)%return) (at level 9).
+Notation "x %usize" := ((mk_scalar Usize x)%return) (at level 9).
+Notation "x %u8"    := ((mk_scalar U8    x)%return) (at level 9).
+Notation "x %u16"   := ((mk_scalar U16   x)%return) (at level 9).
+Notation "x %u32"   := ((mk_scalar U32   x)%return) (at level 9).
+Notation "x %u64"   := ((mk_scalar U64   x)%return) (at level 9).
+Notation "x %u128"  := ((mk_scalar U128  x)%return) (at level 9).
+
+Notation "x s= y" := (scalar_eqb x y)  (at level 80) : Primitives_scope.
+Notation "x s<> y" := (scalar_neqb x y) (at level 80) : Primitives_scope.
+Notation "x s<= y" := (scalar_leb x y)  (at level 80) : Primitives_scope.
+Notation "x s< y" := (scalar_ltb x y)  (at level 80) : Primitives_scope.
+Notation "x s>= y" := (scalar_geb x y)  (at level 80) : Primitives_scope.
+Notation "x s> y" := (scalar_gtb x y)  (at level 80) : Primitives_scope.
+
+(** Constants *)
+Definition core_u8_max    := u8_max %u32.
+Definition core_u16_max   := u16_max %u32.
+Definition core_u32_max   := u32_max %u32.
+Definition core_u64_max   := u64_max %u64.
+Definition core_u128_max  := u64_max %u128.
+Axiom core_usize_max : usize. (** TODO *)
+Definition core_i8_max    := i8_max %i32.
+Definition core_i16_max   := i16_max %i32.
+Definition core_i32_max   := i32_max %i32.
+Definition core_i64_max   := i64_max %i64.
+Definition core_i128_max  := i64_max %i128.
+Axiom core_isize_max : isize. (** TODO *)
+
+(*** core::ops *)
+
+(* Trait declaration: [core::ops::index::Index] *)
+Record core_ops_index_Index (Self Idx : Type) := mk_core_ops_index_Index {
+  core_ops_index_Index_Output : Type;
+  core_ops_index_Index_index : Self -> Idx -> result core_ops_index_Index_Output;
+}.
+Arguments mk_core_ops_index_Index {_ _}.
+Arguments core_ops_index_Index_Output {_ _}.
+Arguments core_ops_index_Index_index {_ _}.
+
+(* Trait declaration: [core::ops::index::IndexMut] *)
+Record core_ops_index_IndexMut (Self Idx : Type) := mk_core_ops_index_IndexMut {
+  core_ops_index_IndexMut_indexInst : core_ops_index_Index Self Idx;
+  core_ops_index_IndexMut_index_mut : Self -> Idx -> result core_ops_index_IndexMut_indexInst.(core_ops_index_Index_Output);
+  core_ops_index_IndexMut_index_mut_back : Self -> Idx -> core_ops_index_IndexMut_indexInst.(core_ops_index_Index_Output) -> result Self;
+}.
+Arguments mk_core_ops_index_IndexMut {_ _}.
+Arguments core_ops_index_IndexMut_indexInst {_ _}.
+Arguments core_ops_index_IndexMut_index_mut {_ _}.
+Arguments core_ops_index_IndexMut_index_mut_back {_ _}.
+
+(* Trait declaration [core::ops::deref::Deref] *)
+Record core_ops_deref_Deref (Self : Type) := mk_core_ops_deref_Deref {
+  core_ops_deref_Deref_target : Type;
+  core_ops_deref_Deref_deref : Self -> result core_ops_deref_Deref_target;
+}.
+Arguments mk_core_ops_deref_Deref {_}.
+Arguments core_ops_deref_Deref_target {_}.
+Arguments core_ops_deref_Deref_deref {_}.
+
+(* Trait declaration [core::ops::deref::DerefMut] *)
+Record core_ops_deref_DerefMut (Self : Type) := mk_core_ops_deref_DerefMut {
+  core_ops_deref_DerefMut_derefInst : core_ops_deref_Deref Self;
+  core_ops_deref_DerefMut_deref_mut : Self -> result core_ops_deref_DerefMut_derefInst.(core_ops_deref_Deref_target);
+  core_ops_deref_DerefMut_deref_mut_back : Self -> core_ops_deref_DerefMut_derefInst.(core_ops_deref_Deref_target) -> result Self;
+}.
+Arguments mk_core_ops_deref_DerefMut {_}.
+Arguments core_ops_deref_DerefMut_derefInst {_}.
+Arguments core_ops_deref_DerefMut_deref_mut {_}.
+Arguments core_ops_deref_DerefMut_deref_mut_back {_}.
+
+Record core_ops_range_Range (T : Type) := mk_core_ops_range_Range {
+  core_ops_range_Range_start : T;
+  core_ops_range_Range_end_ : T;
+}.
+Arguments mk_core_ops_range_Range {_}.
+Arguments core_ops_range_Range_start {_}.
+Arguments core_ops_range_Range_end_ {_}.
+
+(*** [alloc] *)
+
+Definition alloc_boxed_Box_deref (T : Type) (x : T) : result T := Return x.
+Definition alloc_boxed_Box_deref_mut (T : Type) (x : T) : result T := Return x.
+Definition alloc_boxed_Box_deref_mut_back (T : Type) (_ : T) (x : T) : result T := Return x.
+
+(* Trait instance *)
+Definition alloc_boxed_Box_coreOpsDerefInst (Self : Type) : core_ops_deref_Deref Self := {|
+  core_ops_deref_Deref_target := Self;
+  core_ops_deref_Deref_deref := alloc_boxed_Box_deref Self;
+|}.
+
+(* Trait instance *)
+Definition alloc_boxed_Box_coreOpsDerefMutInst (Self : Type) : core_ops_deref_DerefMut Self := {|
+  core_ops_deref_DerefMut_derefInst := alloc_boxed_Box_coreOpsDerefInst Self;
+  core_ops_deref_DerefMut_deref_mut := alloc_boxed_Box_deref_mut Self;
+  core_ops_deref_DerefMut_deref_mut_back := alloc_boxed_Box_deref_mut_back Self;
+|}.
+
+
+(*** Arrays *)
+Definition array T (n : usize) := { l: list T | Z.of_nat (length l) = to_Z n}.
+
+Lemma le_0_usize_max : 0 <= usize_max.
+Proof.
+  pose (H := usize_max_bound).
+  unfold u32_max in H.
+  lia.
+Qed.
+
+Lemma eqb_imp_eq (x y : Z) : Z.eqb x y = true -> x = y.
+Proof.
+  lia.
+Qed.
+
+(* TODO: finish the definitions *)
+Axiom mk_array : forall (T : Type) (n : usize) (l : list T), array T n.
+
+(* For initialization *)
+Axiom array_repeat : forall (T : Type) (n : usize) (x : T), array T n.
+
+Axiom array_index_usize : forall (T : Type) (n : usize) (x : array T n) (i : usize), result T.
+Axiom array_update_usize : forall (T : Type) (n : usize) (x : array T n) (i : usize) (nx : T), result (array T n).
+
+(*** Slice *)
+Definition slice T := { l: list T | Z.of_nat (length l) <= usize_max}.
+
+Axiom slice_len : forall (T : Type) (s : slice T), usize.
+Axiom slice_index_usize : forall (T : Type) (x : slice T) (i : usize), result T.
+Axiom slice_update_usize : forall (T : Type) (x : slice T) (i : usize) (nx : T), result (slice T).
+
+(*** Subslices *)
+
+Axiom array_to_slice : forall (T : Type) (n : usize) (x : array T n), result (slice T).
+Axiom array_from_slice : forall (T : Type) (n : usize) (x : array T n) (s : slice T), result (array T n).
+
+Axiom array_subslice: forall (T : Type) (n : usize) (x : array T n) (r : core_ops_range_Range usize), result (slice T).
+Axiom array_update_subslice: forall (T : Type) (n : usize) (x : array T n) (r : core_ops_range_Range usize) (ns : slice T), result (array T n).
+
+Axiom slice_subslice: forall (T : Type) (x : slice T) (r : core_ops_range_Range usize), result (slice T).
+Axiom slice_update_subslice: forall (T : Type) (x : slice T) (r : core_ops_range_Range usize) (ns : slice T), result (slice T).
+
+(*** Vectors *)
+
+Definition alloc_vec_Vec T := { l: list T | Z.of_nat (length l) <= usize_max }.
+
+Definition alloc_vec_Vec_to_list {T: Type} (v: alloc_vec_Vec T) : list T := proj1_sig v.
+
+Definition alloc_vec_Vec_length {T: Type} (v: alloc_vec_Vec T) : Z := Z.of_nat (length (alloc_vec_Vec_to_list v)).
+
+Definition alloc_vec_Vec_new (T: Type) : alloc_vec_Vec T := (exist _ [] le_0_usize_max).
+
+Lemma alloc_vec_Vec_len_in_usize {T} (v: alloc_vec_Vec T) : usize_min <= alloc_vec_Vec_length v <= usize_max.
+Proof.
+  unfold alloc_vec_Vec_length, usize_min.
+  split.
+  - lia.
+  - apply (proj2_sig v).
+Qed.
+
+Definition alloc_vec_Vec_len (T: Type) (v: alloc_vec_Vec T) : usize :=
+  exist _ (alloc_vec_Vec_length v) (alloc_vec_Vec_len_in_usize v).
+
+Fixpoint list_update {A} (l: list A) (n: nat) (a: A)
+  : list A :=
+  match l with
+  | []     => []
+  | x :: t => match n with
+    | 0%nat => a :: t
+    | S m => x :: (list_update t m a)
+end end.
+
+Definition alloc_vec_Vec_bind {A B} (v: alloc_vec_Vec A) (f: list A -> result (list B)) : result (alloc_vec_Vec B) :=
+  l <- f (alloc_vec_Vec_to_list v) ;
+  match sumbool_of_bool (scalar_le_max Usize (Z.of_nat (length l))) with
+  | left H => Return (exist _ l (scalar_le_max_valid _ _ H))
+  | right _ => Fail_ Failure
+  end.
+
+(* The **forward** function shouldn't be used *)
+Definition alloc_vec_Vec_push_fwd (T: Type) (v: alloc_vec_Vec T) (x: T) : unit := tt.
+
+Definition alloc_vec_Vec_push (T: Type) (v: alloc_vec_Vec T) (x: T) : result (alloc_vec_Vec T) :=
+  alloc_vec_Vec_bind v (fun l => Return (l ++ [x])).
+
+(* The **forward** function shouldn't be used *)
+Definition alloc_vec_Vec_insert_fwd (T: Type) (v: alloc_vec_Vec T) (i: usize) (x: T) : result unit :=
+  if to_Z i <? alloc_vec_Vec_length v then Return tt else Fail_ Failure.
+
+Definition alloc_vec_Vec_insert (T: Type) (v: alloc_vec_Vec T) (i: usize) (x: T) : result (alloc_vec_Vec T) :=
+  alloc_vec_Vec_bind v (fun l =>
+    if to_Z i <? Z.of_nat (length l)
+    then Return (list_update l (usize_to_nat i) x)
+    else Fail_ Failure).
+
+(* Helper *)
+Axiom alloc_vec_Vec_index_usize : forall {T : Type} (v : alloc_vec_Vec T) (i : usize) (x : T), result T.
+
+(* Helper *)
+Axiom alloc_vec_Vec_update_usize : forall {T : Type} (v : alloc_vec_Vec T) (i : usize) (x : T), result (alloc_vec_Vec T).
+
+(* Trait declaration: [core::slice::index::private_slice_index::Sealed] *)
+Definition core_slice_index_private_slice_index_Sealed (self : Type) := unit.
+
+(* Trait declaration: [core::slice::index::SliceIndex] *)
+Record core_slice_index_SliceIndex (Self T : Type) := mk_core_slice_index_SliceIndex {
+  core_slice_index_SliceIndex_sealedInst : core_slice_index_private_slice_index_Sealed Self;
+  core_slice_index_SliceIndex_Output : Type;
+  core_slice_index_SliceIndex_get : Self -> T -> result (option core_slice_index_SliceIndex_Output);
+  core_slice_index_SliceIndex_get_mut : Self -> T -> result (option core_slice_index_SliceIndex_Output);
+  core_slice_index_SliceIndex_get_mut_back : Self -> T -> option core_slice_index_SliceIndex_Output -> result T;
+  core_slice_index_SliceIndex_get_unchecked : Self -> const_raw_ptr T -> result (const_raw_ptr core_slice_index_SliceIndex_Output);
+  core_slice_index_SliceIndex_get_unchecked_mut : Self -> mut_raw_ptr T -> result (mut_raw_ptr core_slice_index_SliceIndex_Output);
+  core_slice_index_SliceIndex_index : Self -> T -> result core_slice_index_SliceIndex_Output;
+  core_slice_index_SliceIndex_index_mut : Self -> T -> result core_slice_index_SliceIndex_Output;
+  core_slice_index_SliceIndex_index_mut_back : Self -> T -> core_slice_index_SliceIndex_Output -> result T;
+}.
+Arguments mk_core_slice_index_SliceIndex {_ _}.
+Arguments core_slice_index_SliceIndex_sealedInst {_ _}.
+Arguments core_slice_index_SliceIndex_Output {_ _}.
+Arguments core_slice_index_SliceIndex_get {_ _}.
+Arguments core_slice_index_SliceIndex_get_mut {_ _}.
+Arguments core_slice_index_SliceIndex_get_mut_back {_ _}.
+Arguments core_slice_index_SliceIndex_get_unchecked {_ _}.
+Arguments core_slice_index_SliceIndex_get_unchecked_mut {_ _}.
+Arguments core_slice_index_SliceIndex_index {_ _}.
+Arguments core_slice_index_SliceIndex_index_mut {_ _}.
+Arguments core_slice_index_SliceIndex_index_mut_back {_ _}.
+
+(* [core::slice::index::[T]::index]: forward function *)
+Definition core_slice_index_Slice_index
+  (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T))
+  (s : slice T) (i : Idx) : result inst.(core_slice_index_SliceIndex_Output) :=
+  x <- inst.(core_slice_index_SliceIndex_get) i s;
+  match x with
+  | None => Fail_ Failure
+  | Some x => Return x
+  end.
+
+(* [core::slice::index::Range:::get]: forward function *)
+Axiom core_slice_index_Range_get : forall (T : Type) (i : core_ops_range_Range usize) (s : slice T), result (option (slice T)).
+
+(* [core::slice::index::Range::get_mut]: forward function *)
+Axiom core_slice_index_Range_get_mut :
+  forall (T : Type), core_ops_range_Range usize -> slice T -> result (option (slice T)).
+
+(* [core::slice::index::Range::get_mut]: backward function 0 *)
+Axiom core_slice_index_Range_get_mut_back :
+  forall (T : Type), core_ops_range_Range usize -> slice T -> option (slice T) -> result (slice T).
+
+(* [core::slice::index::Range::get_unchecked]: forward function *)
+Definition core_slice_index_Range_get_unchecked
+  (T : Type) :
+  core_ops_range_Range usize -> const_raw_ptr (slice T) -> result (const_raw_ptr (slice T)) :=
+  (* Don't know what the model should be - for now we always fail to make
+     sure code which uses it fails *)
+  fun _ _ => Fail_ Failure.
+
+(* [core::slice::index::Range::get_unchecked_mut]: forward function *)
+Definition core_slice_index_Range_get_unchecked_mut
+  (T : Type) :
+  core_ops_range_Range usize -> mut_raw_ptr (slice T) -> result (mut_raw_ptr (slice T)) :=
+  (* Don't know what the model should be - for now we always fail to make
+    sure code which uses it fails *)
+  fun _ _ => Fail_ Failure.
+
+(* [core::slice::index::Range::index]: forward function *)
+Axiom core_slice_index_Range_index :
+  forall (T : Type), core_ops_range_Range usize -> slice T -> result (slice T).
+
+(* [core::slice::index::Range::index_mut]: forward function *)
+Axiom core_slice_index_Range_index_mut :
+  forall (T : Type), core_ops_range_Range usize -> slice T -> result (slice T).
+
+(* [core::slice::index::Range::index_mut]: backward function 0 *)
+Axiom core_slice_index_Range_index_mut_back :
+  forall (T : Type), core_ops_range_Range usize -> slice T -> slice T -> result (slice T).
+
+(* [core::slice::index::[T]::index_mut]: forward function *)
+Axiom core_slice_index_Slice_index_mut :
+  forall (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T)),
+  slice T -> Idx -> result inst.(core_slice_index_SliceIndex_Output).
+
+(* [core::slice::index::[T]::index_mut]: backward function 0 *)
+Axiom core_slice_index_Slice_index_mut_back :
+  forall (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T)),
+  slice T -> Idx -> inst.(core_slice_index_SliceIndex_Output) -> result (slice T).
+
+(* [core::array::[T; N]::index]: forward function *)
+Axiom core_array_Array_index :
+  forall (T Idx : Type) (N : usize) (inst : core_ops_index_Index (slice T) Idx)
+  (a : array T N) (i : Idx), result inst.(core_ops_index_Index_Output).
+
+(* [core::array::[T; N]::index_mut]: forward function *)
+Axiom core_array_Array_index_mut :
+  forall (T Idx : Type) (N : usize) (inst : core_ops_index_IndexMut (slice T) Idx)
+  (a : array T N) (i : Idx), result inst.(core_ops_index_IndexMut_indexInst).(core_ops_index_Index_Output).
+
+(* [core::array::[T; N]::index_mut]: backward function 0 *)
+Axiom core_array_Array_index_mut_back :
+  forall (T Idx : Type) (N : usize) (inst : core_ops_index_IndexMut (slice T) Idx)
+  (a : array T N) (i : Idx) (x : inst.(core_ops_index_IndexMut_indexInst).(core_ops_index_Index_Output)), result (array T N).
+
+(* Trait implementation: [core::slice::index::[T]] *)
+Definition core_slice_index_Slice_coreopsindexIndexInst (T Idx : Type)
+  (inst : core_slice_index_SliceIndex Idx (slice T)) :
+  core_ops_index_Index (slice T) Idx := {|
+  core_ops_index_Index_Output := inst.(core_slice_index_SliceIndex_Output);
+  core_ops_index_Index_index := core_slice_index_Slice_index T Idx inst;
+|}.
+
+(* Trait implementation: [core::slice::index::private_slice_index::Range] *)
+Definition core_slice_index_private_slice_index_Range_coresliceindexprivate_slice_indexSealedInst
+  : core_slice_index_private_slice_index_Sealed (core_ops_range_Range usize) := tt.
+
+(* Trait implementation: [core::slice::index::Range] *)
+Definition core_slice_index_Range_coresliceindexSliceIndexInst (T : Type) :
+  core_slice_index_SliceIndex (core_ops_range_Range usize) (slice T) := {|
+  core_slice_index_SliceIndex_sealedInst := core_slice_index_private_slice_index_Range_coresliceindexprivate_slice_indexSealedInst;
+  core_slice_index_SliceIndex_Output := slice T;
+  core_slice_index_SliceIndex_get := core_slice_index_Range_get T;
+  core_slice_index_SliceIndex_get_mut := core_slice_index_Range_get_mut T;
+  core_slice_index_SliceIndex_get_mut_back := core_slice_index_Range_get_mut_back T;
+  core_slice_index_SliceIndex_get_unchecked := core_slice_index_Range_get_unchecked T;
+  core_slice_index_SliceIndex_get_unchecked_mut := core_slice_index_Range_get_unchecked_mut T;
+  core_slice_index_SliceIndex_index := core_slice_index_Range_index T;
+  core_slice_index_SliceIndex_index_mut := core_slice_index_Range_index_mut T;
+  core_slice_index_SliceIndex_index_mut_back := core_slice_index_Range_index_mut_back T;
+|}.
+
+(* Trait implementation: [core::slice::index::[T]] *)
+Definition core_slice_index_Slice_coreopsindexIndexMutInst (T Idx : Type)
+  (inst : core_slice_index_SliceIndex Idx (slice T)) :
+  core_ops_index_IndexMut (slice T) Idx := {|
+  core_ops_index_IndexMut_indexInst := core_slice_index_Slice_coreopsindexIndexInst T Idx inst;
+  core_ops_index_IndexMut_index_mut := core_slice_index_Slice_index_mut T Idx inst;
+  core_ops_index_IndexMut_index_mut_back := core_slice_index_Slice_index_mut_back T Idx inst;
+|}.
+
+(* Trait implementation: [core::array::[T; N]] *)
+Definition core_array_Array_coreopsindexIndexInst (T Idx : Type) (N : usize)
+  (inst : core_ops_index_Index (slice T) Idx) :
+  core_ops_index_Index (array T N) Idx := {|
+  core_ops_index_Index_Output := inst.(core_ops_index_Index_Output);
+  core_ops_index_Index_index := core_array_Array_index T Idx N inst;
+|}.
+
+(* Trait implementation: [core::array::[T; N]] *)
+Definition core_array_Array_coreopsindexIndexMutInst (T Idx : Type) (N : usize)
+  (inst : core_ops_index_IndexMut (slice T) Idx) :
+  core_ops_index_IndexMut (array T N) Idx := {|
+  core_ops_index_IndexMut_indexInst := core_array_Array_coreopsindexIndexInst T Idx N inst.(core_ops_index_IndexMut_indexInst);
+  core_ops_index_IndexMut_index_mut := core_array_Array_index_mut T Idx N inst;
+  core_ops_index_IndexMut_index_mut_back := core_array_Array_index_mut_back T Idx N inst;
+|}.
+
+(* [core::slice::index::usize::get]: forward function *)
+Axiom core_slice_index_usize_get : forall (T : Type), usize -> slice T -> result (option T).
+
+(* [core::slice::index::usize::get_mut]: forward function *)
+Axiom core_slice_index_usize_get_mut : forall (T : Type), usize -> slice T -> result (option T).
+
+(* [core::slice::index::usize::get_mut]: backward function 0 *)
+Axiom core_slice_index_usize_get_mut_back :
+  forall (T : Type), usize -> slice T -> option T -> result (slice T).
+
+(* [core::slice::index::usize::get_unchecked]: forward function *)
+Axiom core_slice_index_usize_get_unchecked :
+  forall (T : Type), usize -> const_raw_ptr (slice T) -> result (const_raw_ptr T).
+
+(* [core::slice::index::usize::get_unchecked_mut]: forward function *)
+Axiom core_slice_index_usize_get_unchecked_mut :
+  forall (T : Type), usize -> mut_raw_ptr (slice T) -> result (mut_raw_ptr T).
+
+(* [core::slice::index::usize::index]: forward function *)
+Axiom core_slice_index_usize_index : forall (T : Type), usize -> slice T -> result T.
+
+(* [core::slice::index::usize::index_mut]: forward function *)
+Axiom core_slice_index_usize_index_mut : forall (T : Type), usize -> slice T -> result T.
+
+(* [core::slice::index::usize::index_mut]: backward function 0 *)
+Axiom core_slice_index_usize_index_mut_back :
+  forall (T : Type), usize -> slice T -> T -> result (slice T).
+
+(* Trait implementation: [core::slice::index::private_slice_index::usize] *)
+Definition core_slice_index_private_slice_index_usize_coresliceindexprivate_slice_indexSealedInst
+  : core_slice_index_private_slice_index_Sealed usize := tt.
+
+(* Trait implementation: [core::slice::index::usize] *)
+Definition core_slice_index_usize_coresliceindexSliceIndexInst (T : Type) :
+  core_slice_index_SliceIndex usize (slice T) := {|
+  core_slice_index_SliceIndex_sealedInst := core_slice_index_private_slice_index_usize_coresliceindexprivate_slice_indexSealedInst;
+  core_slice_index_SliceIndex_Output := T;
+  core_slice_index_SliceIndex_get := core_slice_index_usize_get T;
+  core_slice_index_SliceIndex_get_mut := core_slice_index_usize_get_mut T;
+  core_slice_index_SliceIndex_get_mut_back := core_slice_index_usize_get_mut_back T;
+  core_slice_index_SliceIndex_get_unchecked := core_slice_index_usize_get_unchecked T;
+  core_slice_index_SliceIndex_get_unchecked_mut := core_slice_index_usize_get_unchecked_mut T;
+  core_slice_index_SliceIndex_index := core_slice_index_usize_index T;
+  core_slice_index_SliceIndex_index_mut := core_slice_index_usize_index_mut T;
+  core_slice_index_SliceIndex_index_mut_back := core_slice_index_usize_index_mut_back T;
+|}.
+
+(* [alloc::vec::Vec::index]: forward function *)
+Axiom alloc_vec_Vec_index : forall (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T))
+  (Self : alloc_vec_Vec T) (i : Idx), result inst.(core_slice_index_SliceIndex_Output).
+
+(* [alloc::vec::Vec::index_mut]: forward function *)
+Axiom alloc_vec_Vec_index_mut : forall (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T))
+  (Self : alloc_vec_Vec T) (i : Idx), result inst.(core_slice_index_SliceIndex_Output).
+
+(* [alloc::vec::Vec::index_mut]: backward function 0 *)
+Axiom alloc_vec_Vec_index_mut_back :
+  forall (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T))
+  (Self : alloc_vec_Vec T) (i : Idx) (x : inst.(core_slice_index_SliceIndex_Output)), result (alloc_vec_Vec T).
+
+(* Trait implementation: [alloc::vec::Vec] *)
+Definition alloc_vec_Vec_coreopsindexIndexInst (T Idx : Type)
+  (inst : core_slice_index_SliceIndex Idx (slice T)) :
+  core_ops_index_Index (alloc_vec_Vec T) Idx := {|
+  core_ops_index_Index_Output := inst.(core_slice_index_SliceIndex_Output);
+  core_ops_index_Index_index := alloc_vec_Vec_index T Idx inst;
+|}.
+
+(* Trait implementation: [alloc::vec::Vec] *)
+Definition alloc_vec_Vec_coreopsindexIndexMutInst (T Idx : Type)
+  (inst : core_slice_index_SliceIndex Idx (slice T)) :
+  core_ops_index_IndexMut (alloc_vec_Vec T) Idx := {|
+  core_ops_index_IndexMut_indexInst := alloc_vec_Vec_coreopsindexIndexInst T Idx inst;
+  core_ops_index_IndexMut_index_mut := alloc_vec_Vec_index_mut T Idx inst;
+  core_ops_index_IndexMut_index_mut_back := alloc_vec_Vec_index_mut_back T Idx inst;
+|}.
+
+(*** Theorems *)
+
+Axiom alloc_vec_Vec_index_mut_back_eq : forall {a : Type} (v : alloc_vec_Vec a) (i : usize) (x : a),
+  alloc_vec_Vec_index_mut_back a usize (core_slice_index_usize_coresliceindexSliceIndexInst a) v i x =
+    alloc_vec_Vec_update_usize v i x.
+
+End Primitives.
diff --git a/tests/coq/traits/Traits.v b/tests/coq/traits/Traits.v
new file mode 100644
index 00000000..e104fb66
--- /dev/null
+++ b/tests/coq/traits/Traits.v
@@ -0,0 +1,520 @@
+(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
+(** [traits] *)
+Require Import Primitives.
+Import Primitives.
+Require Import Coq.ZArith.ZArith.
+Require Import List.
+Import ListNotations.
+Local Open Scope Primitives_scope.
+Module Traits.
+
+(** Trait declaration: [traits::BoolTrait] *)
+Record BoolTrait_t (Self : Type) := mkBoolTrait_t {
+  BoolTrait_t_get_bool : Self -> result bool;
+}.
+
+Arguments mkBoolTrait_t { _ }.
+Arguments BoolTrait_t_get_bool { _ }.
+
+(** [traits::Bool::{0}::get_bool]: forward function *)
+Definition bool_get_bool (self : bool) : result bool :=
+  Return self.
+
+(** Trait implementation: [traits::Bool::{0}] *)
+Definition Bool_BoolTraitInst : BoolTrait_t bool := {|
+  BoolTrait_t_get_bool := bool_get_bool;
+|}.
+
+(** [traits::BoolTrait::ret_true]: forward function *)
+Definition boolTrait_ret_true
+  {Self : Type} (self_clause : BoolTrait_t Self) (self : Self) : result bool :=
+  Return true
+.
+
+(** [traits::test_bool_trait_bool]: forward function *)
+Definition test_bool_trait_bool (x : bool) : result bool :=
+  b <- bool_get_bool x;
+  if b then boolTrait_ret_true Bool_BoolTraitInst x else Return false
+.
+
+(** [traits::Option::{1}::get_bool]: forward function *)
+Definition option_get_bool (T : Type) (self : option T) : result bool :=
+  match self with | None => Return false | Some t => Return true end
+.
+
+(** Trait implementation: [traits::Option::{1}] *)
+Definition Option_BoolTraitInst (T : Type) : BoolTrait_t (option T) := {|
+  BoolTrait_t_get_bool := option_get_bool T;
+|}.
+
+(** [traits::test_bool_trait_option]: forward function *)
+Definition test_bool_trait_option (T : Type) (x : option T) : result bool :=
+  b <- option_get_bool T x;
+  if b then boolTrait_ret_true (Option_BoolTraitInst T) x else Return false
+.
+
+(** [traits::test_bool_trait]: forward function *)
+Definition test_bool_trait
+  (T : Type) (inst : BoolTrait_t T) (x : T) : result bool :=
+  inst.(BoolTrait_t_get_bool) x
+.
+
+(** Trait declaration: [traits::ToU64] *)
+Record ToU64_t (Self : Type) := mkToU64_t {
+  ToU64_t_to_u64 : Self -> result u64;
+}.
+
+Arguments mkToU64_t { _ }.
+Arguments ToU64_t_to_u64 { _ }.
+
+(** [traits::u64::{2}::to_u64]: forward function *)
+Definition u64_to_u64 (self : u64) : result u64 :=
+  Return self.
+
+(** Trait implementation: [traits::u64::{2}] *)
+Definition u64_ToU64Inst : ToU64_t u64 := {| ToU64_t_to_u64 := u64_to_u64; |}.
+
+(** [traits::Tuple2::{3}::to_u64]: forward function *)
+Definition tuple2_to_u64
+  (A : Type) (inst : ToU64_t A) (self : (A * A)) : result u64 :=
+  let (t, t0) := self in
+  i <- inst.(ToU64_t_to_u64) t;
+  i0 <- inst.(ToU64_t_to_u64) t0;
+  u64_add i i0
+.
+
+(** Trait implementation: [traits::Tuple2::{3}] *)
+Definition Tuple2_ToU64Inst (A : Type) (inst : ToU64_t A) : ToU64_t (A * A)
+  := {|
+  ToU64_t_to_u64 := tuple2_to_u64 A inst;
+|}.
+
+(** [traits::f]: forward function *)
+Definition f (T : Type) (inst : ToU64_t T) (x : (T * T)) : result u64 :=
+  tuple2_to_u64 T inst x
+.
+
+(** [traits::g]: forward function *)
+Definition g (T : Type) (inst : ToU64_t (T * T)) (x : (T * T)) : result u64 :=
+  inst.(ToU64_t_to_u64) x
+.
+
+(** [traits::h0]: forward function *)
+Definition h0 (x : u64) : result u64 :=
+  u64_to_u64 x.
+
+(** [traits::Wrapper] *)
+Record Wrapper_t (T : Type) := mkWrapper_t { wrapper_x : T; }.
+
+Arguments mkWrapper_t { _ }.
+Arguments wrapper_x { _ }.
+
+(** [traits::Wrapper::{4}::to_u64]: forward function *)
+Definition wrapper_to_u64
+  (T : Type) (inst : ToU64_t T) (self : Wrapper_t T) : result u64 :=
+  inst.(ToU64_t_to_u64) self.(wrapper_x)
+.
+
+(** Trait implementation: [traits::Wrapper::{4}] *)
+Definition Wrapper_ToU64Inst (T : Type) (inst : ToU64_t T) : ToU64_t (Wrapper_t
+  T) := {|
+  ToU64_t_to_u64 := wrapper_to_u64 T inst;
+|}.
+
+(** [traits::h1]: forward function *)
+Definition h1 (x : Wrapper_t u64) : result u64 :=
+  wrapper_to_u64 u64 u64_ToU64Inst x
+.
+
+(** [traits::h2]: forward function *)
+Definition h2 (T : Type) (inst : ToU64_t T) (x : Wrapper_t T) : result u64 :=
+  wrapper_to_u64 T inst x
+.
+
+(** Trait declaration: [traits::ToType] *)
+Record ToType_t (Self T : Type) := mkToType_t {
+  ToType_t_to_type : Self -> result T;
+}.
+
+Arguments mkToType_t { _ _ }.
+Arguments ToType_t_to_type { _ _ }.
+
+(** [traits::u64::{5}::to_type]: forward function *)
+Definition u64_to_type (self : u64) : result bool :=
+  Return (self s> 0%u64).
+
+(** Trait implementation: [traits::u64::{5}] *)
+Definition u64_ToTypeInst : ToType_t u64 bool := {|
+  ToType_t_to_type := u64_to_type;
+|}.
+
+(** Trait declaration: [traits::OfType] *)
+Record OfType_t (Self : Type) := mkOfType_t {
+  OfType_t_of_type : forall (T : Type) (inst : ToType_t T Self), T -> result
+    Self;
+}.
+
+Arguments mkOfType_t { _ }.
+Arguments OfType_t_of_type { _ }.
+
+(** [traits::h3]: forward function *)
+Definition h3
+  (T1 T2 : Type) (inst : OfType_t T1) (inst0 : ToType_t T2 T1) (y : T2) :
+  result T1
+  :=
+  inst.(OfType_t_of_type) T2 inst0 y
+.
+
+(** Trait declaration: [traits::OfTypeBis] *)
+Record OfTypeBis_t (Self T : Type) := mkOfTypeBis_t {
+  OfTypeBis_tOfTypeBis_t_parent_clause_0 : ToType_t T Self;
+  OfTypeBis_t_of_type : T -> result Self;
+}.
+
+Arguments mkOfTypeBis_t { _ _ }.
+Arguments OfTypeBis_tOfTypeBis_t_parent_clause_0 { _ _ }.
+Arguments OfTypeBis_t_of_type { _ _ }.
+
+(** [traits::h4]: forward function *)
+Definition h4
+  (T1 T2 : Type) (inst : OfTypeBis_t T1 T2) (inst0 : ToType_t T2 T1) (y : T2) :
+  result T1
+  :=
+  inst.(OfTypeBis_t_of_type) y
+.
+
+(** [traits::TestType] *)
+Record TestType_t (T : Type) := mkTestType_t { testType_0 : T; }.
+
+Arguments mkTestType_t { _ }.
+Arguments testType_0 { _ }.
+
+(** [traits::TestType::{6}::test::TestType1] *)
+Record TestType_test_TestType1_t :=
+mkTestType_test_TestType1_t {
+  testType_test_TestType1_0 : u64;
+}
+.
+
+(** Trait declaration: [traits::TestType::{6}::test::TestTrait] *)
+Record TestType_test_TestTrait_t (Self : Type) := mkTestType_test_TestTrait_t {
+  TestType_test_TestTrait_t_test : Self -> result bool;
+}.
+
+Arguments mkTestType_test_TestTrait_t { _ }.
+Arguments TestType_test_TestTrait_t_test { _ }.
+
+(** [traits::TestType::{6}::test::TestType1::{0}::test]: forward function *)
+Definition testType_test_TestType1_test
+  (self : TestType_test_TestType1_t) : result bool :=
+  Return (self.(testType_test_TestType1_0) s> 1%u64)
+.
+
+(** Trait implementation: [traits::TestType::{6}::test::TestType1::{0}] *)
+Definition TestType_test_TestType1_TestType_test_TestTraitInst :
+  TestType_test_TestTrait_t TestType_test_TestType1_t := {|
+  TestType_test_TestTrait_t_test := testType_test_TestType1_test;
+|}.
+
+(** [traits::TestType::{6}::test]: forward function *)
+Definition testType_test
+  (T : Type) (inst : ToU64_t T) (self : TestType_t T) (x : T) : result bool :=
+  x0 <- inst.(ToU64_t_to_u64) x;
+  if x0 s> 0%u64
+  then testType_test_TestType1_test {| testType_test_TestType1_0 := 0%u64 |}
+  else Return false
+.
+
+(** [traits::BoolWrapper] *)
+Record BoolWrapper_t := mkBoolWrapper_t { boolWrapper_0 : bool; }.
+
+(** [traits::BoolWrapper::{7}::to_type]: forward function *)
+Definition boolWrapper_to_type
+  (T : Type) (inst : ToType_t bool T) (self : BoolWrapper_t) : result T :=
+  inst.(ToType_t_to_type) self.(boolWrapper_0)
+.
+
+(** Trait implementation: [traits::BoolWrapper::{7}] *)
+Definition BoolWrapper_ToTypeInst (T : Type) (inst : ToType_t bool T) :
+  ToType_t BoolWrapper_t T := {|
+  ToType_t_to_type := boolWrapper_to_type T inst;
+|}.
+
+(** [traits::WithConstTy::LEN2] *)
+Definition with_const_ty_len2_body : result usize := Return 32%usize.
+Definition with_const_ty_len2_c : usize := with_const_ty_len2_body%global.
+
+(** Trait declaration: [traits::WithConstTy] *)
+Record WithConstTy_t (Self : Type) (LEN : usize) := mkWithConstTy_t {
+  WithConstTy_tWithConstTy_t_LEN1 : usize;
+  WithConstTy_tWithConstTy_t_LEN2 : usize;
+  WithConstTy_tWithConstTy_t_V : Type;
+  WithConstTy_tWithConstTy_t_W : Type;
+  WithConstTy_tWithConstTy_t_W_clause_0 : ToU64_t WithConstTy_tWithConstTy_t_W;
+  WithConstTy_t_f : WithConstTy_tWithConstTy_t_W -> array u8 LEN -> result
+    WithConstTy_tWithConstTy_t_W;
+}.
+
+Arguments mkWithConstTy_t { _ _ }.
+Arguments WithConstTy_tWithConstTy_t_LEN1 { _ _ }.
+Arguments WithConstTy_tWithConstTy_t_LEN2 { _ _ }.
+Arguments WithConstTy_tWithConstTy_t_V { _ _ }.
+Arguments WithConstTy_tWithConstTy_t_W { _ _ }.
+Arguments WithConstTy_tWithConstTy_t_W_clause_0 { _ _ }.
+Arguments WithConstTy_t_f { _ _ }.
+
+(** [traits::Bool::{8}::LEN1] *)
+Definition bool_len1_body : result usize := Return 12%usize.
+Definition bool_len1_c : usize := bool_len1_body%global.
+
+(** [traits::Bool::{8}::f]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ()) *)
+Definition bool_f (i : u64) (a : array u8 32%usize) : result u64 :=
+  Return i.
+
+(** Trait implementation: [traits::Bool::{8}] *)
+Definition Bool_WithConstTyInst : WithConstTy_t bool 32%usize := {|
+  WithConstTy_tWithConstTy_t_LEN1 := bool_len1_c;
+  WithConstTy_tWithConstTy_t_LEN2 := with_const_ty_len2_c;
+  WithConstTy_tWithConstTy_t_V := u8;
+  WithConstTy_tWithConstTy_t_W := u64;
+  WithConstTy_tWithConstTy_t_W_clause_0 := u64_ToU64Inst;
+  WithConstTy_t_f := bool_f;
+|}.
+
+(** [traits::use_with_const_ty1]: forward function *)
+Definition use_with_const_ty1
+  (H : Type) (LEN : usize) (inst : WithConstTy_t H LEN) : result usize :=
+  let i := inst.(WithConstTy_tWithConstTy_t_LEN1) in Return i
+.
+
+(** [traits::use_with_const_ty2]: forward function *)
+Definition use_with_const_ty2
+  (H : Type) (LEN : usize) (inst : WithConstTy_t H LEN)
+  (w : inst.(WithConstTy_tWithConstTy_t_W)) :
+  result unit
+  :=
+  Return tt
+.
+
+(** [traits::use_with_const_ty3]: forward function *)
+Definition use_with_const_ty3
+  (H : Type) (LEN : usize) (inst : WithConstTy_t H LEN)
+  (x : inst.(WithConstTy_tWithConstTy_t_W)) :
+  result u64
+  :=
+  inst.(WithConstTy_tWithConstTy_t_W_clause_0).(ToU64_t_to_u64) x
+.
+
+(** [traits::test_where1]: forward function *)
+Definition test_where1 (T : Type) (_x : T) : result unit :=
+  Return tt.
+
+(** [traits::test_where2]: forward function *)
+Definition test_where2
+  (T : Type) (inst : WithConstTy_t T 32%usize) (_x : u32) : result unit :=
+  Return tt
+.
+
+(** [alloc::string::String] *)
+Axiom alloc_string_String_t : Type.
+
+(** Trait declaration: [traits::ParentTrait0] *)
+Record ParentTrait0_t (Self : Type) := mkParentTrait0_t {
+  ParentTrait0_tParentTrait0_t_W : Type;
+  ParentTrait0_t_get_name : Self -> result alloc_string_String_t;
+  ParentTrait0_t_get_w : Self -> result ParentTrait0_tParentTrait0_t_W;
+}.
+
+Arguments mkParentTrait0_t { _ }.
+Arguments ParentTrait0_tParentTrait0_t_W { _ }.
+Arguments ParentTrait0_t_get_name { _ }.
+Arguments ParentTrait0_t_get_w { _ }.
+
+(** Trait declaration: [traits::ParentTrait1] *)
+Record ParentTrait1_t (Self : Type) := mkParentTrait1_t{}.
+
+Arguments mkParentTrait1_t { _ }.
+
+(** Trait declaration: [traits::ChildTrait] *)
+Record ChildTrait_t (Self : Type) := mkChildTrait_t {
+  ChildTrait_tChildTrait_t_parent_clause_0 : ParentTrait0_t Self;
+  ChildTrait_tChildTrait_t_parent_clause_1 : ParentTrait1_t Self;
+}.
+
+Arguments mkChildTrait_t { _ }.
+Arguments ChildTrait_tChildTrait_t_parent_clause_0 { _ }.
+Arguments ChildTrait_tChildTrait_t_parent_clause_1 { _ }.
+
+(** [traits::test_child_trait1]: forward function *)
+Definition test_child_trait1
+  (T : Type) (inst : ChildTrait_t T) (x : T) : result alloc_string_String_t :=
+  inst.(ChildTrait_tChildTrait_t_parent_clause_0).(ParentTrait0_t_get_name) x
+.
+
+(** [traits::test_child_trait2]: forward function *)
+Definition test_child_trait2
+  (T : Type) (inst : ChildTrait_t T) (x : T) :
+  result
+    inst.(ChildTrait_tChildTrait_t_parent_clause_0).(ParentTrait0_tParentTrait0_t_W)
+  :=
+  inst.(ChildTrait_tChildTrait_t_parent_clause_0).(ParentTrait0_t_get_w) x
+.
+
+(** [traits::order1]: forward function *)
+Definition order1
+  (T U : Type) (inst : ParentTrait0_t T) (inst0 : ParentTrait0_t U) :
+  result unit
+  :=
+  Return tt
+.
+
+(** Trait declaration: [traits::ChildTrait1] *)
+Record ChildTrait1_t (Self : Type) := mkChildTrait1_t {
+  ChildTrait1_tChildTrait1_t_parent_clause_0 : ParentTrait1_t Self;
+}.
+
+Arguments mkChildTrait1_t { _ }.
+Arguments ChildTrait1_tChildTrait1_t_parent_clause_0 { _ }.
+
+(** Trait implementation: [traits::usize::{9}] *)
+Definition usize_ParentTrait1Inst : ParentTrait1_t usize := mkParentTrait1_t.
+
+(** Trait implementation: [traits::usize::{10}] *)
+Definition usize_ChildTrait1Inst : ChildTrait1_t usize := {|
+  ChildTrait1_tChildTrait1_t_parent_clause_0 := usize_ParentTrait1Inst;
+|}.
+
+(** Trait declaration: [traits::Iterator] *)
+Record Iterator_t (Self : Type) := mkIterator_t {
+  Iterator_tIterator_t_Item : Type;
+}.
+
+Arguments mkIterator_t { _ }.
+Arguments Iterator_tIterator_t_Item { _ }.
+
+(** Trait declaration: [traits::IntoIterator] *)
+Record IntoIterator_t (Self : Type) := mkIntoIterator_t {
+  IntoIterator_tIntoIterator_t_Item : Type;
+  IntoIterator_tIntoIterator_t_IntoIter : Type;
+  IntoIterator_tIntoIterator_t_IntoIter_clause_0 : Iterator_t
+    IntoIterator_tIntoIterator_t_IntoIter;
+  IntoIterator_t_into_iter : Self -> result
+    IntoIterator_tIntoIterator_t_IntoIter;
+}.
+
+Arguments mkIntoIterator_t { _ }.
+Arguments IntoIterator_tIntoIterator_t_Item { _ }.
+Arguments IntoIterator_tIntoIterator_t_IntoIter { _ }.
+Arguments IntoIterator_tIntoIterator_t_IntoIter_clause_0 { _ }.
+Arguments IntoIterator_t_into_iter { _ }.
+
+(** Trait declaration: [traits::FromResidual] *)
+Record FromResidual_t (Self T : Type) := mkFromResidual_t{}.
+
+Arguments mkFromResidual_t { _ _ }.
+
+(** Trait declaration: [traits::Try] *)
+Record Try_t (Self : Type) := mkTry_t {
+  Try_tTry_t_Residual : Type;
+  Try_tTry_t_parent_clause_0 : FromResidual_t Self Try_tTry_t_Residual;
+}.
+
+Arguments mkTry_t { _ }.
+Arguments Try_tTry_t_Residual { _ }.
+Arguments Try_tTry_t_parent_clause_0 { _ }.
+
+(** Trait declaration: [traits::WithTarget] *)
+Record WithTarget_t (Self : Type) := mkWithTarget_t {
+  WithTarget_tWithTarget_t_Target : Type;
+}.
+
+Arguments mkWithTarget_t { _ }.
+Arguments WithTarget_tWithTarget_t_Target { _ }.
+
+(** Trait declaration: [traits::ParentTrait2] *)
+Record ParentTrait2_t (Self : Type) := mkParentTrait2_t {
+  ParentTrait2_tParentTrait2_t_U : Type;
+  ParentTrait2_tParentTrait2_t_U_clause_0 : WithTarget_t
+    ParentTrait2_tParentTrait2_t_U;
+}.
+
+Arguments mkParentTrait2_t { _ }.
+Arguments ParentTrait2_tParentTrait2_t_U { _ }.
+Arguments ParentTrait2_tParentTrait2_t_U_clause_0 { _ }.
+
+(** Trait declaration: [traits::ChildTrait2] *)
+Record ChildTrait2_t (Self : Type) := mkChildTrait2_t {
+  ChildTrait2_tChildTrait2_t_parent_clause_0 : ParentTrait2_t Self;
+  ChildTrait2_t_convert :
+    (ChildTrait2_tChildTrait2_t_parent_clause_0).(ParentTrait2_tParentTrait2_t_U)
+    -> result
+    (ChildTrait2_tChildTrait2_t_parent_clause_0).(ParentTrait2_tParentTrait2_t_U_clause_0).(WithTarget_tWithTarget_t_Target);
+}.
+
+Arguments mkChildTrait2_t { _ }.
+Arguments ChildTrait2_tChildTrait2_t_parent_clause_0 { _ }.
+Arguments ChildTrait2_t_convert { _ }.
+
+(** Trait implementation: [traits::u32::{11}] *)
+Definition u32_WithTargetInst : WithTarget_t u32 := {|
+  WithTarget_tWithTarget_t_Target := u32;
+|}.
+
+(** Trait implementation: [traits::u32::{12}] *)
+Definition u32_ParentTrait2Inst : ParentTrait2_t u32 := {|
+  ParentTrait2_tParentTrait2_t_U := u32;
+  ParentTrait2_tParentTrait2_t_U_clause_0 := u32_WithTargetInst;
+|}.
+
+(** [traits::u32::{13}::convert]: forward function *)
+Definition u32_convert (x : u32) : result u32 :=
+  Return x.
+
+(** Trait implementation: [traits::u32::{13}] *)
+Definition u32_ChildTrait2Inst : ChildTrait2_t u32 := {|
+  ChildTrait2_tChildTrait2_t_parent_clause_0 := u32_ParentTrait2Inst;
+  ChildTrait2_t_convert := u32_convert;
+|}.
+
+(** [traits::incr_u32]: forward function *)
+Definition incr_u32 (x : u32) : result u32 :=
+  u32_add x 1%u32.
+
+(** Trait declaration: [traits::CFnOnce] *)
+Record CFnOnce_t (Self Args : Type) := mkCFnOnce_t {
+  CFnOnce_tCFnOnce_t_Output : Type;
+  CFnOnce_t_call_once : Self -> Args -> result CFnOnce_tCFnOnce_t_Output;
+}.
+
+Arguments mkCFnOnce_t { _ _ }.
+Arguments CFnOnce_tCFnOnce_t_Output { _ _ }.
+Arguments CFnOnce_t_call_once { _ _ }.
+
+(** Trait declaration: [traits::CFnMut] *)
+Record CFnMut_t (Self Args : Type) := mkCFnMut_t {
+  CFnMut_tCFnMut_t_parent_clause_0 : CFnOnce_t Self Args;
+  CFnMut_t_call_mut : Self -> Args -> result
+    (CFnMut_tCFnMut_t_parent_clause_0).(CFnOnce_tCFnOnce_t_Output);
+  CFnMut_t_call_mut_back : Self -> Args ->
+    (CFnMut_tCFnMut_t_parent_clause_0).(CFnOnce_tCFnOnce_t_Output) -> result
+    Self;
+}.
+
+Arguments mkCFnMut_t { _ _ }.
+Arguments CFnMut_tCFnMut_t_parent_clause_0 { _ _ }.
+Arguments CFnMut_t_call_mut { _ _ }.
+Arguments CFnMut_t_call_mut_back { _ _ }.
+
+(** Trait declaration: [traits::CFn] *)
+Record CFn_t (Self Args : Type) := mkCFn_t {
+  CFn_tCFn_t_parent_clause_0 : CFnMut_t Self Args;
+  CFn_t_call_mut : Self -> Args -> result
+    (CFn_tCFn_t_parent_clause_0).(CFnMut_tCFnMut_t_parent_clause_0).(CFnOnce_tCFnOnce_t_Output);
+}.
+
+Arguments mkCFn_t { _ _ }.
+Arguments CFn_tCFn_t_parent_clause_0 { _ _ }.
+Arguments CFn_t_call_mut { _ _ }.
+
+End Traits .
diff --git a/tests/coq/traits/_CoqProject b/tests/coq/traits/_CoqProject
new file mode 100644
index 00000000..5b6199fc
--- /dev/null
+++ b/tests/coq/traits/_CoqProject
@@ -0,0 +1,7 @@
+# This file was automatically generated - see ../Makefile
+-R . Lib
+-arg -w
+-arg all
+
+Traits.v
+Primitives.v
diff --git a/tests/fstar/array/Array.Clauses.Template.fst b/tests/fstar/array/Array.Clauses.Template.fst
index 8a15e230..06056d61 100644
--- a/tests/fstar/array/Array.Clauses.Template.fst
+++ b/tests/fstar/array/Array.Clauses.Template.fst
@@ -8,11 +8,12 @@ open Array.Types
 
 (** [array::sum]: decreases clause *)
 unfold
-let sum_loop_decreases (s : slice u32) (sum : u32) (i : usize) : nat = admit ()
+let sum_loop_decreases (s : slice u32) (sum0 : u32) (i : usize) : nat =
+  admit ()
 
 (** [array::sum2]: decreases clause *)
 unfold
-let sum2_loop_decreases (s : slice u32) (s2 : slice u32) (sum : u32)
+let sum2_loop_decreases (s : slice u32) (s2 : slice u32) (sum0 : u32)
   (i : usize) : nat =
   admit ()
 
diff --git a/tests/fstar/array/Array.Funs.fst b/tests/fstar/array/Array.Funs.fst
index 7c1d0b09..8f0bfbbd 100644
--- a/tests/fstar/array/Array.Funs.fst
+++ b/tests/fstar/array/Array.Funs.fst
@@ -7,349 +7,369 @@ include Array.Clauses
 
 #set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
 
+(** [array::incr]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ()) *)
+let incr (x : u32) : result u32 =
+  u32_add x 1
+
 (** [array::array_to_shared_slice_]: forward function *)
-let array_to_shared_slice__fwd
-  (t : Type0) (s : array t 32) : result (slice t) =
-  array_to_slice_shared t 32 s
+let array_to_shared_slice_ (t : Type0) (s : array t 32) : result (slice t) =
+  array_to_slice t 32 s
 
 (** [array::array_to_mut_slice_]: forward function *)
-let array_to_mut_slice__fwd (t : Type0) (s : array t 32) : result (slice t) =
-  array_to_slice_mut_fwd t 32 s
+let array_to_mut_slice_ (t : Type0) (s : array t 32) : result (slice t) =
+  array_to_slice t 32 s
 
 (** [array::array_to_mut_slice_]: backward function 0 *)
 let array_to_mut_slice__back
   (t : Type0) (s : array t 32) (ret : slice t) : result (array t 32) =
-  array_to_slice_mut_back t 32 s ret
+  array_from_slice t 32 s ret
 
 (** [array::array_len]: forward function *)
-let array_len_fwd (t : Type0) (s : array t 32) : result usize =
-  let* s0 = array_to_slice_shared t 32 s in let i = slice_len t s0 in Return i
+let array_len (t : Type0) (s : array t 32) : result usize =
+  let* s0 = array_to_slice t 32 s in let i = slice_len t s0 in Return i
 
 (** [array::shared_array_len]: forward function *)
-let shared_array_len_fwd (t : Type0) (s : array t 32) : result usize =
-  let* s0 = array_to_slice_shared t 32 s in let i = slice_len t s0 in Return i
+let shared_array_len (t : Type0) (s : array t 32) : result usize =
+  let* s0 = array_to_slice t 32 s in let i = slice_len t s0 in Return i
 
 (** [array::shared_slice_len]: forward function *)
-let shared_slice_len_fwd (t : Type0) (s : slice t) : result usize =
+let shared_slice_len (t : Type0) (s : slice t) : result usize =
   let i = slice_len t s in Return i
 
 (** [array::index_array_shared]: forward function *)
-let index_array_shared_fwd
-  (t : Type0) (s : array t 32) (i : usize) : result t =
-  array_index_shared t 32 s i
+let index_array_shared (t : Type0) (s : array t 32) (i : usize) : result t =
+  array_index_usize t 32 s i
 
 (** [array::index_array_u32]: forward function *)
-let index_array_u32_fwd (s : array u32 32) (i : usize) : result u32 =
-  array_index_shared u32 32 s i
-
-(** [array::index_array_generic]: forward function *)
-let index_array_generic_fwd
-  (n : usize) (s : array u32 n) (i : usize) : result u32 =
-  array_index_shared u32 n s i
-
-(** [array::index_array_generic_call]: forward function *)
-let index_array_generic_call_fwd
-  (n : usize) (s : array u32 n) (i : usize) : result u32 =
-  index_array_generic_fwd n s i
+let index_array_u32 (s : array u32 32) (i : usize) : result u32 =
+  array_index_usize u32 32 s i
 
 (** [array::index_array_copy]: forward function *)
-let index_array_copy_fwd (x : array u32 32) : result u32 =
-  array_index_shared u32 32 x 0
+let index_array_copy (x : array u32 32) : result u32 =
+  array_index_usize u32 32 x 0
 
 (** [array::index_mut_array]: forward function *)
-let index_mut_array_fwd (t : Type0) (s : array t 32) (i : usize) : result t =
-  array_index_mut_fwd t 32 s i
+let index_mut_array (t : Type0) (s : array t 32) (i : usize) : result t =
+  array_index_usize t 32 s i
 
 (** [array::index_mut_array]: backward function 0 *)
 let index_mut_array_back
   (t : Type0) (s : array t 32) (i : usize) (ret : t) : result (array t 32) =
-  array_index_mut_back t 32 s i ret
+  array_update_usize t 32 s i ret
 
 (** [array::index_slice]: forward function *)
-let index_slice_fwd (t : Type0) (s : slice t) (i : usize) : result t =
-  slice_index_shared t s i
+let index_slice (t : Type0) (s : slice t) (i : usize) : result t =
+  slice_index_usize t s i
 
 (** [array::index_mut_slice]: forward function *)
-let index_mut_slice_fwd (t : Type0) (s : slice t) (i : usize) : result t =
-  slice_index_mut_fwd t s i
+let index_mut_slice (t : Type0) (s : slice t) (i : usize) : result t =
+  slice_index_usize t s i
 
 (** [array::index_mut_slice]: backward function 0 *)
 let index_mut_slice_back
   (t : Type0) (s : slice t) (i : usize) (ret : t) : result (slice t) =
-  slice_index_mut_back t s i ret
+  slice_update_usize t s i ret
 
 (** [array::slice_subslice_shared_]: forward function *)
-let slice_subslice_shared__fwd
+let slice_subslice_shared_
   (x : slice u32) (y : usize) (z : usize) : result (slice u32) =
-  slice_subslice_shared u32 x (Mkrange y z)
+  core_slice_index_Slice_index u32 (core_ops_range_Range usize)
+    (core_slice_index_Range_coresliceindexSliceIndexInst u32) x
+    { start = y; end_ = z }
 
 (** [array::slice_subslice_mut_]: forward function *)
-let slice_subslice_mut__fwd
+let slice_subslice_mut_
   (x : slice u32) (y : usize) (z : usize) : result (slice u32) =
-  slice_subslice_mut_fwd u32 x (Mkrange y z)
+  core_slice_index_Slice_index_mut u32 (core_ops_range_Range usize)
+    (core_slice_index_Range_coresliceindexSliceIndexInst u32) x
+    { start = y; end_ = z }
 
 (** [array::slice_subslice_mut_]: backward function 0 *)
 let slice_subslice_mut__back
   (x : slice u32) (y : usize) (z : usize) (ret : slice u32) :
   result (slice u32)
   =
-  slice_subslice_mut_back u32 x (Mkrange y z) ret
+  core_slice_index_Slice_index_mut_back u32 (core_ops_range_Range usize)
+    (core_slice_index_Range_coresliceindexSliceIndexInst u32) x
+    { start = y; end_ = z } ret
 
 (** [array::array_to_slice_shared_]: forward function *)
-let array_to_slice_shared__fwd (x : array u32 32) : result (slice u32) =
-  array_to_slice_shared u32 32 x
+let array_to_slice_shared_ (x : array u32 32) : result (slice u32) =
+  array_to_slice u32 32 x
 
 (** [array::array_to_slice_mut_]: forward function *)
-let array_to_slice_mut__fwd (x : array u32 32) : result (slice u32) =
-  array_to_slice_mut_fwd u32 32 x
+let array_to_slice_mut_ (x : array u32 32) : result (slice u32) =
+  array_to_slice u32 32 x
 
 (** [array::array_to_slice_mut_]: backward function 0 *)
 let array_to_slice_mut__back
   (x : array u32 32) (ret : slice u32) : result (array u32 32) =
-  array_to_slice_mut_back u32 32 x ret
+  array_from_slice u32 32 x ret
 
 (** [array::array_subslice_shared_]: forward function *)
-let array_subslice_shared__fwd
+let array_subslice_shared_
   (x : array u32 32) (y : usize) (z : usize) : result (slice u32) =
-  array_subslice_shared u32 32 x (Mkrange y z)
+  core_array_Array_index u32 (core_ops_range_Range usize) 32
+    (core_slice_index_Slice_coreopsindexIndexInst u32 (core_ops_range_Range
+    usize) (core_slice_index_Range_coresliceindexSliceIndexInst u32)) x
+    { start = y; end_ = z }
 
 (** [array::array_subslice_mut_]: forward function *)
-let array_subslice_mut__fwd
+let array_subslice_mut_
   (x : array u32 32) (y : usize) (z : usize) : result (slice u32) =
-  array_subslice_mut_fwd u32 32 x (Mkrange y z)
+  core_array_Array_index_mut u32 (core_ops_range_Range usize) 32
+    (core_slice_index_Slice_coreopsindexIndexMutInst u32 (core_ops_range_Range
+    usize) (core_slice_index_Range_coresliceindexSliceIndexInst u32)) x
+    { start = y; end_ = z }
 
 (** [array::array_subslice_mut_]: backward function 0 *)
 let array_subslice_mut__back
   (x : array u32 32) (y : usize) (z : usize) (ret : slice u32) :
   result (array u32 32)
   =
-  array_subslice_mut_back u32 32 x (Mkrange y z) ret
+  core_array_Array_index_mut_back u32 (core_ops_range_Range usize) 32
+    (core_slice_index_Slice_coreopsindexIndexMutInst u32 (core_ops_range_Range
+    usize) (core_slice_index_Range_coresliceindexSliceIndexInst u32)) x
+    { start = y; end_ = z } ret
 
 (** [array::index_slice_0]: forward function *)
-let index_slice_0_fwd (t : Type0) (s : slice t) : result t =
-  slice_index_shared t s 0
+let index_slice_0 (t : Type0) (s : slice t) : result t =
+  slice_index_usize t s 0
 
 (** [array::index_array_0]: forward function *)
-let index_array_0_fwd (t : Type0) (s : array t 32) : result t =
-  array_index_shared t 32 s 0
+let index_array_0 (t : Type0) (s : array t 32) : result t =
+  array_index_usize t 32 s 0
 
 (** [array::index_index_array]: forward function *)
-let index_index_array_fwd
+let index_index_array
   (s : array (array u32 32) 32) (i : usize) (j : usize) : result u32 =
-  let* a = array_index_shared (array u32 32) 32 s i in
-  array_index_shared u32 32 a j
+  let* a = array_index_usize (array u32 32) 32 s i in
+  array_index_usize u32 32 a j
 
 (** [array::update_update_array]: forward function *)
-let update_update_array_fwd
+let update_update_array
   (s : array (array u32 32) 32) (i : usize) (j : usize) : result unit =
-  let* a = array_index_mut_fwd (array u32 32) 32 s i in
-  let* a0 = array_index_mut_back u32 32 a j 0 in
-  let* _ = array_index_mut_back (array u32 32) 32 s i a0 in
+  let* a = array_index_usize (array u32 32) 32 s i in
+  let* a0 = array_update_usize u32 32 a j 0 in
+  let* _ = array_update_usize (array u32 32) 32 s i a0 in
   Return ()
 
 (** [array::array_local_deep_copy]: forward function *)
-let array_local_deep_copy_fwd (x : array u32 32) : result unit =
+let array_local_deep_copy (x : array u32 32) : result unit =
   Return ()
 
 (** [array::take_array]: forward function *)
-let take_array_fwd (a : array u32 2) : result unit =
+let take_array (a : array u32 2) : result unit =
   Return ()
 
 (** [array::take_array_borrow]: forward function *)
-let take_array_borrow_fwd (a : array u32 2) : result unit =
+let take_array_borrow (a : array u32 2) : result unit =
   Return ()
 
 (** [array::take_slice]: forward function *)
-let take_slice_fwd (s : slice u32) : result unit =
+let take_slice (s : slice u32) : result unit =
   Return ()
 
 (** [array::take_mut_slice]: merged forward/backward function
     (there is a single backward function, and the forward function returns ()) *)
-let take_mut_slice_fwd_back (s : slice u32) : result (slice u32) =
+let take_mut_slice (s : slice u32) : result (slice u32) =
   Return s
 
 (** [array::take_all]: forward function *)
-let take_all_fwd : result unit =
-  let* _ = take_array_fwd (mk_array u32 2 [ 0; 0 ]) in
-  let* _ = take_array_borrow_fwd (mk_array u32 2 [ 0; 0 ]) in
-  let* s = array_to_slice_shared u32 2 (mk_array u32 2 [ 0; 0 ]) in
-  let* _ = take_slice_fwd s in
-  let* s0 = array_to_slice_mut_fwd u32 2 (mk_array u32 2 [ 0; 0 ]) in
-  let* s1 = take_mut_slice_fwd_back s0 in
-  let* _ = array_to_slice_mut_back u32 2 (mk_array u32 2 [ 0; 0 ]) s1 in
+let take_all : result unit =
+  let* _ = take_array (mk_array u32 2 [ 0; 0 ]) in
+  let* _ = take_array_borrow (mk_array u32 2 [ 0; 0 ]) in
+  let* s = array_to_slice u32 2 (mk_array u32 2 [ 0; 0 ]) in
+  let* _ = take_slice s in
+  let* s0 = array_to_slice u32 2 (mk_array u32 2 [ 0; 0 ]) in
+  let* s1 = take_mut_slice s0 in
+  let* _ = array_from_slice u32 2 (mk_array u32 2 [ 0; 0 ]) s1 in
   Return ()
 
 (** [array::index_array]: forward function *)
-let index_array_fwd (x : array u32 2) : result u32 =
-  array_index_shared u32 2 x 0
+let index_array (x : array u32 2) : result u32 =
+  array_index_usize u32 2 x 0
 
 (** [array::index_array_borrow]: forward function *)
-let index_array_borrow_fwd (x : array u32 2) : result u32 =
-  array_index_shared u32 2 x 0
+let index_array_borrow (x : array u32 2) : result u32 =
+  array_index_usize u32 2 x 0
 
 (** [array::index_slice_u32_0]: forward function *)
-let index_slice_u32_0_fwd (x : slice u32) : result u32 =
-  slice_index_shared u32 x 0
+let index_slice_u32_0 (x : slice u32) : result u32 =
+  slice_index_usize u32 x 0
 
 (** [array::index_mut_slice_u32_0]: forward function *)
-let index_mut_slice_u32_0_fwd (x : slice u32) : result u32 =
-  slice_index_shared u32 x 0
+let index_mut_slice_u32_0 (x : slice u32) : result u32 =
+  slice_index_usize u32 x 0
 
 (** [array::index_mut_slice_u32_0]: backward function 0 *)
 let index_mut_slice_u32_0_back (x : slice u32) : result (slice u32) =
-  let* _ = slice_index_shared u32 x 0 in Return x
+  let* _ = slice_index_usize u32 x 0 in Return x
 
 (** [array::index_all]: forward function *)
-let index_all_fwd : result u32 =
-  let* i = index_array_fwd (mk_array u32 2 [ 0; 0 ]) in
-  let* i0 = index_array_fwd (mk_array u32 2 [ 0; 0 ]) in
+let index_all : result u32 =
+  let* i = index_array (mk_array u32 2 [ 0; 0 ]) in
+  let* i0 = index_array (mk_array u32 2 [ 0; 0 ]) in
   let* i1 = u32_add i i0 in
-  let* i2 = index_array_borrow_fwd (mk_array u32 2 [ 0; 0 ]) in
+  let* i2 = index_array_borrow (mk_array u32 2 [ 0; 0 ]) in
   let* i3 = u32_add i1 i2 in
-  let* s = array_to_slice_shared u32 2 (mk_array u32 2 [ 0; 0 ]) in
-  let* i4 = index_slice_u32_0_fwd s in
+  let* s = array_to_slice u32 2 (mk_array u32 2 [ 0; 0 ]) in
+  let* i4 = index_slice_u32_0 s in
   let* i5 = u32_add i3 i4 in
-  let* s0 = array_to_slice_mut_fwd u32 2 (mk_array u32 2 [ 0; 0 ]) in
-  let* i6 = index_mut_slice_u32_0_fwd s0 in
+  let* s0 = array_to_slice u32 2 (mk_array u32 2 [ 0; 0 ]) in
+  let* i6 = index_mut_slice_u32_0 s0 in
   let* i7 = u32_add i5 i6 in
   let* s1 = index_mut_slice_u32_0_back s0 in
-  let* _ = array_to_slice_mut_back u32 2 (mk_array u32 2 [ 0; 0 ]) s1 in
+  let* _ = array_from_slice u32 2 (mk_array u32 2 [ 0; 0 ]) s1 in
   Return i7
 
 (** [array::update_array]: forward function *)
-let update_array_fwd (x : array u32 2) : result unit =
-  let* _ = array_index_mut_back u32 2 x 0 1 in Return ()
+let update_array (x : array u32 2) : result unit =
+  let* _ = array_update_usize u32 2 x 0 1 in Return ()
 
 (** [array::update_array_mut_borrow]: merged forward/backward function
     (there is a single backward function, and the forward function returns ()) *)
-let update_array_mut_borrow_fwd_back (x : array u32 2) : result (array u32 2) =
-  array_index_mut_back u32 2 x 0 1
+let update_array_mut_borrow (x : array u32 2) : result (array u32 2) =
+  array_update_usize u32 2 x 0 1
 
 (** [array::update_mut_slice]: merged forward/backward function
     (there is a single backward function, and the forward function returns ()) *)
-let update_mut_slice_fwd_back (x : slice u32) : result (slice u32) =
-  slice_index_mut_back u32 x 0 1
+let update_mut_slice (x : slice u32) : result (slice u32) =
+  slice_update_usize u32 x 0 1
 
 (** [array::update_all]: forward function *)
-let update_all_fwd : result unit =
-  let* _ = update_array_fwd (mk_array u32 2 [ 0; 0 ]) in
-  let* x = update_array_mut_borrow_fwd_back (mk_array u32 2 [ 0; 0 ]) in
-  let* s = array_to_slice_mut_fwd u32 2 x in
-  let* s0 = update_mut_slice_fwd_back s in
-  let* _ = array_to_slice_mut_back u32 2 x s0 in
+let update_all : result unit =
+  let* _ = update_array (mk_array u32 2 [ 0; 0 ]) in
+  let* x = update_array_mut_borrow (mk_array u32 2 [ 0; 0 ]) in
+  let* s = array_to_slice u32 2 x in
+  let* s0 = update_mut_slice s in
+  let* _ = array_from_slice u32 2 x s0 in
   Return ()
 
 (** [array::range_all]: forward function *)
-let range_all_fwd : result unit =
+let range_all : result unit =
   let* s =
-    array_subslice_mut_fwd u32 4 (mk_array u32 4 [ 0; 0; 0; 0 ]) (Mkrange 1 3)
-    in
-  let* s0 = update_mut_slice_fwd_back s in
+    core_array_Array_index_mut u32 (core_ops_range_Range usize) 4
+      (core_slice_index_Slice_coreopsindexIndexMutInst u32
+      (core_ops_range_Range usize)
+      (core_slice_index_Range_coresliceindexSliceIndexInst u32))
+      (mk_array u32 4 [ 0; 0; 0; 0 ]) { start = 1; end_ = 3 } in
+  let* s0 = update_mut_slice s in
   let* _ =
-    array_subslice_mut_back u32 4 (mk_array u32 4 [ 0; 0; 0; 0 ]) (Mkrange 1 3)
-      s0 in
+    core_array_Array_index_mut_back u32 (core_ops_range_Range usize) 4
+      (core_slice_index_Slice_coreopsindexIndexMutInst u32
+      (core_ops_range_Range usize)
+      (core_slice_index_Range_coresliceindexSliceIndexInst u32))
+      (mk_array u32 4 [ 0; 0; 0; 0 ]) { start = 1; end_ = 3 } s0 in
   Return ()
 
 (** [array::deref_array_borrow]: forward function *)
-let deref_array_borrow_fwd (x : array u32 2) : result u32 =
-  array_index_shared u32 2 x 0
+let deref_array_borrow (x : array u32 2) : result u32 =
+  array_index_usize u32 2 x 0
 
 (** [array::deref_array_mut_borrow]: forward function *)
-let deref_array_mut_borrow_fwd (x : array u32 2) : result u32 =
-  array_index_shared u32 2 x 0
+let deref_array_mut_borrow (x : array u32 2) : result u32 =
+  array_index_usize u32 2 x 0
 
 (** [array::deref_array_mut_borrow]: backward function 0 *)
 let deref_array_mut_borrow_back (x : array u32 2) : result (array u32 2) =
-  let* _ = array_index_shared u32 2 x 0 in Return x
+  let* _ = array_index_usize u32 2 x 0 in Return x
 
 (** [array::take_array_t]: forward function *)
-let take_array_t_fwd (a : array t_t 2) : result unit =
+let take_array_t (a : array aB_t 2) : result unit =
   Return ()
 
 (** [array::non_copyable_array]: forward function *)
-let non_copyable_array_fwd : result unit =
-  let* _ = take_array_t_fwd (mk_array t_t 2 [ TA; TB ]) in Return ()
+let non_copyable_array : result unit =
+  let* _ = take_array_t (mk_array aB_t 2 [ AB_A; AB_B ]) in Return ()
 
 (** [array::sum]: loop 0: forward function *)
-let rec sum_loop_fwd
-  (s : slice u32) (sum : u32) (i : usize) :
-  Tot (result u32) (decreases (sum_loop_decreases s sum i))
+let rec sum_loop
+  (s : slice u32) (sum0 : u32) (i : usize) :
+  Tot (result u32) (decreases (sum_loop_decreases s sum0 i))
   =
   let i0 = slice_len u32 s in
   if i < i0
   then
-    let* i1 = slice_index_shared u32 s i in
-    let* sum0 = u32_add sum i1 in
+    let* i1 = slice_index_usize u32 s i in
+    let* sum1 = u32_add sum0 i1 in
     let* i2 = usize_add i 1 in
-    sum_loop_fwd s sum0 i2
-  else Return sum
+    sum_loop s sum1 i2
+  else Return sum0
 
 (** [array::sum]: forward function *)
-let sum_fwd (s : slice u32) : result u32 =
-  sum_loop_fwd s 0 0
+let sum (s : slice u32) : result u32 =
+  sum_loop s 0 0
 
 (** [array::sum2]: loop 0: forward function *)
-let rec sum2_loop_fwd
-  (s : slice u32) (s2 : slice u32) (sum : u32) (i : usize) :
-  Tot (result u32) (decreases (sum2_loop_decreases s s2 sum i))
+let rec sum2_loop
+  (s : slice u32) (s2 : slice u32) (sum0 : u32) (i : usize) :
+  Tot (result u32) (decreases (sum2_loop_decreases s s2 sum0 i))
   =
   let i0 = slice_len u32 s in
   if i < i0
   then
-    let* i1 = slice_index_shared u32 s i in
-    let* i2 = slice_index_shared u32 s2 i in
+    let* i1 = slice_index_usize u32 s i in
+    let* i2 = slice_index_usize u32 s2 i in
     let* i3 = u32_add i1 i2 in
-    let* sum0 = u32_add sum i3 in
+    let* sum1 = u32_add sum0 i3 in
     let* i4 = usize_add i 1 in
-    sum2_loop_fwd s s2 sum0 i4
-  else Return sum
+    sum2_loop s s2 sum1 i4
+  else Return sum0
 
 (** [array::sum2]: forward function *)
-let sum2_fwd (s : slice u32) (s2 : slice u32) : result u32 =
+let sum2 (s : slice u32) (s2 : slice u32) : result u32 =
   let i = slice_len u32 s in
   let i0 = slice_len u32 s2 in
-  if not (i = i0) then Fail Failure else sum2_loop_fwd s s2 0 0
+  if not (i = i0) then Fail Failure else sum2_loop s s2 0 0
 
 (** [array::f0]: forward function *)
-let f0_fwd : result unit =
-  let* s = array_to_slice_mut_fwd u32 2 (mk_array u32 2 [ 1; 2 ]) in
-  let* s0 = slice_index_mut_back u32 s 0 1 in
-  let* _ = array_to_slice_mut_back u32 2 (mk_array u32 2 [ 1; 2 ]) s0 in
+let f0 : result unit =
+  let* s = array_to_slice u32 2 (mk_array u32 2 [ 1; 2 ]) in
+  let* s0 = slice_update_usize u32 s 0 1 in
+  let* _ = array_from_slice u32 2 (mk_array u32 2 [ 1; 2 ]) s0 in
   Return ()
 
 (** [array::f1]: forward function *)
-let f1_fwd : result unit =
-  let* _ = array_index_mut_back u32 2 (mk_array u32 2 [ 1; 2 ]) 0 1 in
-  Return ()
+let f1 : result unit =
+  let* _ = array_update_usize u32 2 (mk_array u32 2 [ 1; 2 ]) 0 1 in Return ()
 
 (** [array::f2]: forward function *)
-let f2_fwd (i : u32) : result unit =
+let f2 (i : u32) : result unit =
   Return ()
 
 (** [array::f4]: forward function *)
-let f4_fwd (x : array u32 32) (y : usize) (z : usize) : result (slice u32) =
-  array_subslice_shared u32 32 x (Mkrange y z)
+let f4 (x : array u32 32) (y : usize) (z : usize) : result (slice u32) =
+  core_array_Array_index u32 (core_ops_range_Range usize) 32
+    (core_slice_index_Slice_coreopsindexIndexInst u32 (core_ops_range_Range
+    usize) (core_slice_index_Range_coresliceindexSliceIndexInst u32)) x
+    { start = y; end_ = z }
 
 (** [array::f3]: forward function *)
-let f3_fwd : result u32 =
-  let* i = array_index_shared u32 2 (mk_array u32 2 [ 1; 2 ]) 0 in
-  let* _ = f2_fwd i in
-  let* s = array_to_slice_shared u32 2 (mk_array u32 2 [ 1; 2 ]) in
-  let* s0 =
-    f4_fwd
-      (mk_array u32 32 [
-        0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0;
-        0; 0; 0; 0; 0; 0; 0; 0
-        ]) 16 18 in
-  sum2_fwd s s0
+let f3 : result u32 =
+  let* i = array_index_usize u32 2 (mk_array u32 2 [ 1; 2 ]) 0 in
+  let* _ = f2 i in
+  let b = array_repeat u32 32 0 in
+  let* s = array_to_slice u32 2 (mk_array u32 2 [ 1; 2 ]) in
+  let* s0 = f4 b 16 18 in
+  sum2 s s0
+
+(** [array::SZ] *)
+let sz_body : result usize = Return 32
+let sz_c : usize = eval_global sz_body
+
+(** [array::f5]: forward function *)
+let f5 (x : array u32 32) : result u32 =
+  array_index_usize u32 32 x 0
 
 (** [array::ite]: forward function *)
-let ite_fwd : result unit =
-  let* s = array_to_slice_mut_fwd u32 2 (mk_array u32 2 [ 0; 0 ]) in
-  let* s0 = array_to_slice_mut_fwd u32 2 (mk_array u32 2 [ 0; 0 ]) in
+let ite : result unit =
+  let* s = array_to_slice u32 2 (mk_array u32 2 [ 0; 0 ]) in
+  let* s0 = array_to_slice u32 2 (mk_array u32 2 [ 0; 0 ]) in
   let* s1 = index_mut_slice_u32_0_back s0 in
-  let* _ = array_to_slice_mut_back u32 2 (mk_array u32 2 [ 0; 0 ]) s1 in
+  let* _ = array_from_slice u32 2 (mk_array u32 2 [ 0; 0 ]) s1 in
   let* s2 = index_mut_slice_u32_0_back s in
-  let* _ = array_to_slice_mut_back u32 2 (mk_array u32 2 [ 0; 0 ]) s2 in
+  let* _ = array_from_slice u32 2 (mk_array u32 2 [ 0; 0 ]) s2 in
   Return ()
 
diff --git a/tests/fstar/array/Array.Types.fst b/tests/fstar/array/Array.Types.fst
index 5e8e81d8..4e8d5566 100644
--- a/tests/fstar/array/Array.Types.fst
+++ b/tests/fstar/array/Array.Types.fst
@@ -5,6 +5,6 @@ open Primitives
 
 #set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
 
-(** [array::T] *)
-type t_t = | TA : t_t | TB : t_t
+(** [array::AB] *)
+type aB_t = | AB_A : aB_t | AB_B : aB_t
 
diff --git a/tests/fstar/array/Primitives.fst b/tests/fstar/array/Primitives.fst
index 9db82069..3297803c 100644
--- a/tests/fstar/array/Primitives.fst
+++ b/tests/fstar/array/Primitives.fst
@@ -55,8 +55,12 @@ type string = string
 let is_zero (n: nat) : bool = n = 0
 let decrease (n: nat{n > 0}) : nat = n - 1
 
-let mem_replace_fwd (a : Type0) (x : a) (y : a) : a = x
-let mem_replace_back (a : Type0) (x : a) (y : a) : a = y
+let core_mem_replace (a : Type0) (x : a) (y : a) : a = x
+let core_mem_replace_back (a : Type0) (x : a) (y : a) : a = y
+
+// We don't really use raw pointers for now
+type mut_raw_ptr (t : Type0) = { v : t }
+type const_raw_ptr (t : Type0) = { v : t }
 
 (*** Scalars *)
 /// Rem.: most of the following code was partially generated
@@ -100,6 +104,11 @@ type scalar_ty =
 | U64
 | U128
 
+let is_unsigned = function
+  | Isize | I8 | I16 | I32 | I64 | I128 -> false
+  | Usize | U8 | U16 | U32 | U64 | U128 -> true
+
+
 let scalar_min (ty : scalar_ty) : int =
   match ty with
   | Isize -> isize_min
@@ -162,6 +171,15 @@ let scalar_sub (#ty : scalar_ty) (x : scalar ty) (y : scalar ty) : result (scala
 let scalar_mul (#ty : scalar_ty) (x : scalar ty) (y : scalar ty) : result (scalar ty) =
   mk_scalar ty (x * y)
 
+let scalar_lxor (#ty : scalar_ty { is_unsigned ty && ty <> Usize })
+    (x : scalar ty) (y : scalar ty) : scalar ty =
+  match ty with
+  | U8 -> FStar.UInt.logxor #8 x y
+  | U16 -> FStar.UInt.logxor #16 x y
+  | U32 -> FStar.UInt.logxor #32 x y
+  | U64 -> FStar.UInt.logxor #64 x y
+  | U128 -> FStar.UInt.logxor #128 x y
+
 (** Cast an integer from a [src_ty] to a [tgt_ty] *)
 // TODO: check the semantics of casts in Rust
 let scalar_cast (src_ty : scalar_ty) (tgt_ty : scalar_ty) (x : scalar src_ty) : result (scalar tgt_ty) =
@@ -169,17 +187,44 @@ let scalar_cast (src_ty : scalar_ty) (tgt_ty : scalar_ty) (x : scalar src_ty) :
 
 /// The scalar types
 type isize : eqtype = scalar Isize
-type i8 : eqtype = scalar I8
-type i16 : eqtype = scalar I16
-type i32 : eqtype = scalar I32
-type i64 : eqtype = scalar I64
-type i128 : eqtype = scalar I128
+type i8    : eqtype = scalar I8
+type i16   : eqtype = scalar I16
+type i32   : eqtype = scalar I32
+type i64   : eqtype = scalar I64
+type i128  : eqtype = scalar I128
 type usize : eqtype = scalar Usize
-type u8 : eqtype = scalar U8
-type u16 : eqtype = scalar U16
-type u32 : eqtype = scalar U32
-type u64 : eqtype = scalar U64
-type u128 : eqtype = scalar U128
+type u8    : eqtype = scalar U8
+type u16   : eqtype = scalar U16
+type u32   : eqtype = scalar U32
+type u64   : eqtype = scalar U64
+type u128  : eqtype = scalar U128
+
+
+let core_isize_min : isize = isize_min
+let core_isize_max : isize = isize_max
+let core_i8_min    : i8 = i8_min
+let core_i8_max    : i8 = i8_max
+let core_i16_min   : i16 = i16_min
+let core_i16_max   : i16 = i16_max
+let core_i32_min   : i32 = i32_min
+let core_i32_max   : i32 = i32_max
+let core_i64_min   : i64 = i64_min
+let core_i64_max   : i64 = i64_max
+let core_i128_min  : i128 = i128_min
+let core_i128_max  : i128 = i128_max
+
+let core_usize_min : usize = usize_min
+let core_usize_max : usize = usize_max
+let core_u8_min    : u8 = u8_min
+let core_u8_max    : u8 = u8_max
+let core_u16_min   : u16 = u16_min
+let core_u16_max   : u16 = u16_max
+let core_u32_min   : u32 = u32_min
+let core_u32_max   : u32 = u32_max
+let core_u64_min   : u64 = u64_min
+let core_u64_max   : u64 = u64_max
+let core_u128_min  : u128 = u128_min
+let core_u128_max  : u128 = u128_max
 
 /// Negation
 let isize_neg = scalar_neg #Isize
@@ -231,7 +276,7 @@ let u32_add = scalar_add #U32
 let u64_add = scalar_add #U64
 let u128_add = scalar_add #U128
 
-/// Substraction
+/// Subtraction
 let isize_sub = scalar_sub #Isize
 let i8_sub = scalar_sub #I8
 let i16_sub = scalar_sub #I16
@@ -259,12 +304,65 @@ let u32_mul = scalar_mul #U32
 let u64_mul = scalar_mul #U64
 let u128_mul = scalar_mul #U128
 
-(*** Range *)
-type range (a : Type0) = {
+/// Logical operators, defined for unsigned types only, so far
+let u8_xor = scalar_lxor #U8
+let u16_xor = scalar_lxor #U16
+let u32_xor = scalar_lxor #U32
+let u64_xor = scalar_lxor #U64
+let u128_xor = scalar_lxor #U128
+
+(*** core::ops *)
+
+// Trait declaration: [core::ops::index::Index]
+noeq type core_ops_index_Index (self idx : Type0) = {
+  output : Type0;
+  index : self → idx → result output
+}
+
+// Trait declaration: [core::ops::index::IndexMut]
+noeq type core_ops_index_IndexMut (self idx : Type0) = {
+  indexInst : core_ops_index_Index self idx;
+  index_mut : self → idx → result indexInst.output;
+  index_mut_back : self → idx → indexInst.output → result self;
+}
+
+// Trait declaration [core::ops::deref::Deref]
+noeq type core_ops_deref_Deref (self : Type0) = {
+  target : Type0;
+  deref : self → result target;
+}
+
+// Trait declaration [core::ops::deref::DerefMut]
+noeq type core_ops_deref_DerefMut (self : Type0) = {
+  derefInst : core_ops_deref_Deref self;
+  deref_mut : self → result derefInst.target;
+  deref_mut_back : self → derefInst.target → result self;
+}
+
+type core_ops_range_Range (a : Type0) = {
   start : a;
   end_ : a;
 }
 
+(*** [alloc] *)
+
+let alloc_boxed_Box_deref (t : Type0) (x : t) : result t = Return x
+let alloc_boxed_Box_deref_mut (t : Type0) (x : t) : result t = Return x
+let alloc_boxed_Box_deref_mut_back (t : Type) (_ : t) (x : t) : result t = Return x
+
+// Trait instance
+let alloc_boxed_Box_coreOpsDerefInst (self : Type0) : core_ops_deref_Deref self = {
+  target = self;
+  deref = alloc_boxed_Box_deref self;
+}
+
+// Trait instance
+let alloc_boxed_Box_coreOpsDerefMutInst (self : Type0) : core_ops_deref_DerefMut self = {
+  derefInst = alloc_boxed_Box_coreOpsDerefInst self;
+  deref_mut = alloc_boxed_Box_deref_mut self;
+  deref_mut_back = alloc_boxed_Box_deref_mut_back self;
+}
+
 (*** Array *)
 type array (a : Type0) (n : usize) = s:list a{length s = n}
 
@@ -278,15 +376,11 @@ let mk_array (a : Type0) (n : usize)
   normalize_term_spec (FStar.List.Tot.length l);
   l
 
-let array_index_shared (a : Type0) (n : usize) (x : array a n) (i : usize) : result a =
-  if i < length x then Return (index x i)
-  else Fail Failure
-
-let array_index_mut_fwd (a : Type0) (n : usize) (x : array a n) (i : usize) : result a =
+let array_index_usize (a : Type0) (n : usize) (x : array a n) (i : usize) : result a =
   if i < length x then Return (index x i)
   else Fail Failure
 
-let array_index_mut_back (a : Type0) (n : usize) (x : array a n) (i : usize) (nx : a) : result (array a n) =
+let array_update_usize (a : Type0) (n : usize) (x : array a n) (i : usize) (nx : a) : result (array a n) =
   if i < length x then Return (list_update x i nx)
   else Fail Failure
 
@@ -295,55 +389,54 @@ type slice (a : Type0) = s:list a{length s <= usize_max}
 
 let slice_len (a : Type0) (s : slice a) : usize = length s
 
-let slice_index_shared (a : Type0) (x : slice a) (i : usize) : result a =
+let slice_index_usize (a : Type0) (x : slice a) (i : usize) : result a =
   if i < length x then Return (index x i)
   else Fail Failure
 
-let slice_index_mut_fwd (a : Type0) (x : slice a) (i : usize) : result a =
-  if i < length x then Return (index x i)
-  else Fail Failure
-
-let slice_index_mut_back (a : Type0) (x : slice a) (i : usize) (nx : a) : result (slice a) =
+let slice_update_usize (a : Type0) (x : slice a) (i : usize) (nx : a) : result (slice a) =
   if i < length x then Return (list_update x i nx)
   else Fail Failure
 
 (*** Subslices *)
 
-let array_to_slice_shared (a : Type0) (n : usize) (x : array a n) : result (slice a) = Return x
-let array_to_slice_mut_fwd (a : Type0) (n : usize) (x : array a n) : result (slice a) = Return x
-let array_to_slice_mut_back (a : Type0) (n : usize) (x : array a n) (s : slice a) : result (array a n) =
+let array_to_slice (a : Type0) (n : usize) (x : array a n) : result (slice a) = Return x
+let array_from_slice (a : Type0) (n : usize) (x : array a n) (s : slice a) : result (array a n) =
   if length s = n then Return s
   else Fail Failure
 
 // TODO: finish the definitions below (there lacks [List.drop] and [List.take] in the standard library *)
-let array_subslice_shared (a : Type0) (n : usize) (x : array a n) (r : range usize) : result (slice a) =
-  admit()
-
-let array_subslice_mut_fwd (a : Type0) (n : usize) (x : array a n) (r : range usize) : result (slice a) =
+let array_subslice (a : Type0) (n : usize) (x : array a n) (r : core_ops_range_Range usize) : result (slice a) =
   admit()
 
-let array_subslice_mut_back (a : Type0) (n : usize) (x : array a n) (r : range usize) (ns : slice a) : result (array a n) =
+let array_update_subslice (a : Type0) (n : usize) (x : array a n) (r : core_ops_range_Range usize) (ns : slice a) : result (array a n) =
   admit()
 
-let slice_subslice_shared (a : Type0) (x : slice a) (r : range usize) : result (slice a) =
+let array_repeat (a : Type0) (n : usize) (x : a) : array a n =
   admit()
 
-let slice_subslice_mut_fwd (a : Type0) (x : slice a) (r : range usize) : result (slice a) =
+let slice_subslice (a : Type0) (x : slice a) (r : core_ops_range_Range usize) : result (slice a) =
   admit()
 
-let slice_subslice_mut_back (a : Type0) (x : slice a) (r : range usize) (ns : slice a) : result (slice a) =
+let slice_update_subslice (a : Type0) (x : slice a) (r : core_ops_range_Range usize) (ns : slice a) : result (slice a) =
   admit()
 
 (*** Vector *)
-type vec (a : Type0) = v:list a{length v <= usize_max}
+type alloc_vec_Vec (a : Type0) = v:list a{length v <= usize_max}
 
-let vec_new (a  : Type0) : vec a = assert_norm(length #a [] == 0); []
-let vec_len (a : Type0) (v : vec a) : usize = length v
+let alloc_vec_Vec_new (a  : Type0) : alloc_vec_Vec a = assert_norm(length #a [] == 0); []
+let alloc_vec_Vec_len (a : Type0) (v : alloc_vec_Vec a) : usize = length v
+
+// Helper
+let alloc_vec_Vec_index_usize (#a : Type0) (v : alloc_vec_Vec a) (i : usize) : result a =
+  if i < length v then Return (index v i) else Fail Failure
+// Helper
+let alloc_vec_Vec_update_usize (#a : Type0) (v : alloc_vec_Vec a) (i : usize) (x : a) : result (alloc_vec_Vec a) =
+  if i < length v then Return (list_update v i x) else Fail Failure
 
 // The **forward** function shouldn't be used
-let vec_push_fwd (a  : Type0) (v : vec a) (x : a) : unit = ()
-let vec_push_back (a  : Type0) (v : vec a) (x : a) :
-  Pure (result (vec a))
+let alloc_vec_Vec_push_fwd (a  : Type0) (v : alloc_vec_Vec a) (x : a) : unit = ()
+let alloc_vec_Vec_push (a  : Type0) (v : alloc_vec_Vec a) (x : a) :
+  Pure (result (alloc_vec_Vec a))
   (requires True)
   (ensures (fun res ->
     match res with
@@ -358,18 +451,279 @@ let vec_push_back (a  : Type0) (v : vec a) (x : a) :
   else Fail Failure
 
 // The **forward** function shouldn't be used
-let vec_insert_fwd (a : Type0) (v : vec a) (i : usize) (x : a) : result unit =
+let alloc_vec_Vec_insert_fwd (a : Type0) (v : alloc_vec_Vec a) (i : usize) (x : a) : result unit =
   if i < length v then Return () else Fail Failure
-let vec_insert_back (a : Type0) (v : vec a) (i : usize) (x : a) : result (vec a) =
+let alloc_vec_Vec_insert (a : Type0) (v : alloc_vec_Vec a) (i : usize) (x : a) : result (alloc_vec_Vec a) =
   if i < length v then Return (list_update v i x) else Fail Failure
 
-// The **backward** function shouldn't be used
-let vec_index_fwd (a : Type0) (v : vec a) (i : usize) : result a =
-  if i < length v then Return (index v i) else Fail Failure
-let vec_index_back (a : Type0) (v : vec a) (i : usize) (x : a) : result unit =
-  if i < length v then Return () else Fail Failure
+// Trait declaration: [core::slice::index::private_slice_index::Sealed]
+type core_slice_index_private_slice_index_Sealed (self : Type0) = unit
+
+// Trait declaration: [core::slice::index::SliceIndex]
+noeq type core_slice_index_SliceIndex (self t : Type0) = {
+  sealedInst : core_slice_index_private_slice_index_Sealed self;
+  output : Type0;
+  get : self → t → result (option output);
+  get_mut : self → t → result (option output);
+  get_mut_back : self → t → option output → result t;
+  get_unchecked : self → const_raw_ptr t → result (const_raw_ptr output);
+  get_unchecked_mut : self → mut_raw_ptr t → result (mut_raw_ptr output);
+  index : self → t → result output;
+  index_mut : self → t → result output;
+  index_mut_back : self → t → output → result t;
+}
 
-let vec_index_mut_fwd (a : Type0) (v : vec a) (i : usize) : result a =
-  if i < length v then Return (index v i) else Fail Failure
-let vec_index_mut_back (a : Type0) (v : vec a) (i : usize) (nx : a) : result (vec a) =
-  if i < length v then Return (list_update v i nx) else Fail Failure
+// [core::slice::index::[T]::index]: forward function
+let core_slice_index_Slice_index
+  (t idx : Type0) (inst : core_slice_index_SliceIndex idx (slice t))
+  (s : slice t) (i : idx) : result inst.output =
+  let* x = inst.get i s in
+  match x with
+  | None -> Fail Failure
+  | Some x -> Return x
+
+// [core::slice::index::Range:::get]: forward function
+let core_slice_index_Range_get (t : Type0) (i : core_ops_range_Range usize) (s : slice t) :
+  result (option (slice t)) =
+  admit () // TODO
+
+// [core::slice::index::Range::get_mut]: forward function
+let core_slice_index_Range_get_mut
+  (t : Type0) : core_ops_range_Range usize → slice t → result (option (slice t)) =
+  admit () // TODO
+
+// [core::slice::index::Range::get_mut]: backward function 0
+let core_slice_index_Range_get_mut_back
+  (t : Type0) :
+  core_ops_range_Range usize → slice t → option (slice t) → result (slice t) =
+  admit () // TODO
+
+// [core::slice::index::Range::get_unchecked]: forward function
+let core_slice_index_Range_get_unchecked
+  (t : Type0) :
+  core_ops_range_Range usize → const_raw_ptr (slice t) → result (const_raw_ptr (slice t)) =
+  // Don't know what the model should be - for now we always fail to make
+  // sure code which uses it fails
+  fun _ _ -> Fail Failure
+
+// [core::slice::index::Range::get_unchecked_mut]: forward function
+let core_slice_index_Range_get_unchecked_mut
+  (t : Type0) :
+  core_ops_range_Range usize → mut_raw_ptr (slice t) → result (mut_raw_ptr (slice t)) =
+  // Don't know what the model should be - for now we always fail to make
+  // sure code which uses it fails
+  fun _ _ -> Fail Failure
+
+// [core::slice::index::Range::index]: forward function
+let core_slice_index_Range_index
+  (t : Type0) : core_ops_range_Range usize → slice t → result (slice t) =
+  admit () // TODO
+
+// [core::slice::index::Range::index_mut]: forward function
+let core_slice_index_Range_index_mut
+  (t : Type0) : core_ops_range_Range usize → slice t → result (slice t) =
+  admit () // TODO
+
+// [core::slice::index::Range::index_mut]: backward function 0
+let core_slice_index_Range_index_mut_back
+  (t : Type0) : core_ops_range_Range usize → slice t → slice t → result (slice t) =
+  admit () // TODO
+
+// [core::slice::index::[T]::index_mut]: forward function
+let core_slice_index_Slice_index_mut
+  (t idx : Type0) (inst : core_slice_index_SliceIndex idx (slice t)) :
+  slice t → idx → result inst.output =
+  admit () // 
+
+// [core::slice::index::[T]::index_mut]: backward function 0
+let core_slice_index_Slice_index_mut_back
+  (t idx : Type0) (inst : core_slice_index_SliceIndex idx (slice t)) :
+  slice t → idx → inst.output → result (slice t) =
+  admit () // TODO
+
+// [core::array::[T; N]::index]: forward function
+let core_array_Array_index
+  (t idx : Type0) (n : usize) (inst : core_ops_index_Index (slice t) idx)
+  (a : array t n) (i : idx) : result inst.output =
+  admit () // TODO
+
+// [core::array::[T; N]::index_mut]: forward function
+let core_array_Array_index_mut
+  (t idx : Type0) (n : usize) (inst : core_ops_index_IndexMut (slice t) idx)
+  (a : array t n) (i : idx) : result inst.indexInst.output =
+  admit () // TODO
+
+// [core::array::[T; N]::index_mut]: backward function 0
+let core_array_Array_index_mut_back
+  (t idx : Type0) (n : usize) (inst : core_ops_index_IndexMut (slice t) idx)
+  (a : array t n) (i : idx) (x : inst.indexInst.output) : result (array t n) =
+  admit () // TODO
+
+// Trait implementation: [core::slice::index::[T]]
+let core_slice_index_Slice_coreopsindexIndexInst (t idx : Type0)
+  (inst : core_slice_index_SliceIndex idx (slice t)) :
+  core_ops_index_Index (slice t) idx = {
+  output = inst.output;
+  index = core_slice_index_Slice_index t idx inst;
+}
+
+// Trait implementation: [core::slice::index::private_slice_index::Range]
+let core_slice_index_private_slice_index_Range_coresliceindexprivate_slice_indexSealedInst
+  : core_slice_index_private_slice_index_Sealed (core_ops_range_Range usize) = ()
+
+// Trait implementation: [core::slice::index::Range]
+let core_slice_index_Range_coresliceindexSliceIndexInst (t : Type0) :
+  core_slice_index_SliceIndex (core_ops_range_Range usize) (slice t) = {
+  sealedInst = core_slice_index_private_slice_index_Range_coresliceindexprivate_slice_indexSealedInst;
+  output = slice t;
+  get = core_slice_index_Range_get t;
+  get_mut = core_slice_index_Range_get_mut t;
+  get_mut_back = core_slice_index_Range_get_mut_back t;
+  get_unchecked = core_slice_index_Range_get_unchecked t;
+  get_unchecked_mut = core_slice_index_Range_get_unchecked_mut t;
+  index = core_slice_index_Range_index t;
+  index_mut = core_slice_index_Range_index_mut t;
+  index_mut_back = core_slice_index_Range_index_mut_back t;
+}
+
+// Trait implementation: [core::slice::index::[T]]
+let core_slice_index_Slice_coreopsindexIndexMutInst (t idx : Type0)
+  (inst : core_slice_index_SliceIndex idx (slice t)) :
+  core_ops_index_IndexMut (slice t) idx = {
+  indexInst = core_slice_index_Slice_coreopsindexIndexInst t idx inst;
+  index_mut = core_slice_index_Slice_index_mut t idx inst;
+  index_mut_back = core_slice_index_Slice_index_mut_back t idx inst;
+}
+
+// Trait implementation: [core::array::[T; N]]
+let core_array_Array_coreopsindexIndexInst (t idx : Type0) (n : usize)
+  (inst : core_ops_index_Index (slice t) idx) :
+  core_ops_index_Index (array t n) idx = {
+  output = inst.output;
+  index = core_array_Array_index t idx n inst;
+}
+
+// Trait implementation: [core::array::[T; N]]
+let core_array_Array_coreopsindexIndexMutInst (t idx : Type0) (n : usize)
+  (inst : core_ops_index_IndexMut (slice t) idx) :
+  core_ops_index_IndexMut (array t n) idx = {
+  indexInst = core_array_Array_coreopsindexIndexInst t idx n inst.indexInst;
+  index_mut = core_array_Array_index_mut t idx n inst;
+  index_mut_back = core_array_Array_index_mut_back t idx n inst;
+}
+
+// [core::slice::index::usize::get]: forward function
+let core_slice_index_usize_get
+  (t : Type0) : usize → slice t → result (option t) =
+  admit () // TODO
+
+// [core::slice::index::usize::get_mut]: forward function
+let core_slice_index_usize_get_mut
+  (t : Type0) : usize → slice t → result (option t) =
+  admit () // TODO
+
+// [core::slice::index::usize::get_mut]: backward function 0
+let core_slice_index_usize_get_mut_back
+  (t : Type0) : usize → slice t → option t → result (slice t) =
+  admit () // TODO
+
+// [core::slice::index::usize::get_unchecked]: forward function
+let core_slice_index_usize_get_unchecked
+  (t : Type0) : usize → const_raw_ptr (slice t) → result (const_raw_ptr t) =
+  admit () // TODO
+
+// [core::slice::index::usize::get_unchecked_mut]: forward function
+let core_slice_index_usize_get_unchecked_mut
+  (t : Type0) : usize → mut_raw_ptr (slice t) → result (mut_raw_ptr t) =
+  admit () // TODO
+
+// [core::slice::index::usize::index]: forward function
+let core_slice_index_usize_index (t : Type0) : usize → slice t → result t =
+  admit () // TODO
+
+// [core::slice::index::usize::index_mut]: forward function
+let core_slice_index_usize_index_mut (t : Type0) : usize → slice t → result t =
+  admit () // TODO
+
+// [core::slice::index::usize::index_mut]: backward function 0
+let core_slice_index_usize_index_mut_back
+  (t : Type0) : usize → slice t → t → result (slice t) =
+  admit () // TODO
+
+// Trait implementation: [core::slice::index::private_slice_index::usize]
+let core_slice_index_private_slice_index_usize_coresliceindexprivate_slice_indexSealedInst
+  : core_slice_index_private_slice_index_Sealed usize = ()
+
+// Trait implementation: [core::slice::index::usize]
+let core_slice_index_usize_coresliceindexSliceIndexInst (t : Type0) :
+  core_slice_index_SliceIndex usize (slice t) = {
+  sealedInst = core_slice_index_private_slice_index_usize_coresliceindexprivate_slice_indexSealedInst;
+  output = t;
+  get = core_slice_index_usize_get t;
+  get_mut = core_slice_index_usize_get_mut t;
+  get_mut_back = core_slice_index_usize_get_mut_back t;
+  get_unchecked = core_slice_index_usize_get_unchecked t;
+  get_unchecked_mut = core_slice_index_usize_get_unchecked_mut t;
+  index = core_slice_index_usize_index t;
+  index_mut = core_slice_index_usize_index_mut t;
+  index_mut_back = core_slice_index_usize_index_mut_back t;
+}
+
+// [alloc::vec::Vec::index]: forward function
+let alloc_vec_Vec_index (t idx : Type0) (inst : core_slice_index_SliceIndex idx (slice t))
+  (self : alloc_vec_Vec t) (i : idx) : result inst.output =
+  admit () // TODO
+
+// [alloc::vec::Vec::index_mut]: forward function
+let alloc_vec_Vec_index_mut (t idx : Type0) (inst : core_slice_index_SliceIndex idx (slice t))
+  (self : alloc_vec_Vec t) (i : idx) : result inst.output =
+  admit () // TODO
+
+// [alloc::vec::Vec::index_mut]: backward function 0
+let alloc_vec_Vec_index_mut_back
+  (t idx : Type0) (inst : core_slice_index_SliceIndex idx (slice t))
+  (self : alloc_vec_Vec t) (i : idx) (x : inst.output) : result (alloc_vec_Vec t) =
+  admit () // TODO
+
+// Trait implementation: [alloc::vec::Vec]
+let alloc_vec_Vec_coreopsindexIndexInst (t idx : Type0)
+  (inst : core_slice_index_SliceIndex idx (slice t)) :
+  core_ops_index_Index (alloc_vec_Vec t) idx = {
+  output = inst.output;
+  index = alloc_vec_Vec_index t idx inst;
+}
+
+// Trait implementation: [alloc::vec::Vec]
+let alloc_vec_Vec_coreopsindexIndexMutInst (t idx : Type0)
+  (inst : core_slice_index_SliceIndex idx (slice t)) :
+  core_ops_index_IndexMut (alloc_vec_Vec t) idx = {
+  indexInst = alloc_vec_Vec_coreopsindexIndexInst t idx inst;
+  index_mut = alloc_vec_Vec_index_mut t idx inst;
+  index_mut_back = alloc_vec_Vec_index_mut_back t idx inst;
+}
+
+(*** Theorems *)
+
+let alloc_vec_Vec_index_eq (#a : Type0) (v : alloc_vec_Vec a) (i : usize) :
+  Lemma (
+    alloc_vec_Vec_index a usize (core_slice_index_usize_coresliceindexSliceIndexInst a) v i ==
+      alloc_vec_Vec_index_usize v i)
+  [SMTPat (alloc_vec_Vec_index a usize (core_slice_index_usize_coresliceindexSliceIndexInst a) v i)]
+  =
+  admit()
+
+let alloc_vec_Vec_index_mut_eq (#a : Type0) (v : alloc_vec_Vec a) (i : usize) :
+  Lemma (
+    alloc_vec_Vec_index_mut a usize (core_slice_index_usize_coresliceindexSliceIndexInst a) v i ==
+      alloc_vec_Vec_index_usize v i)
+  [SMTPat (alloc_vec_Vec_index_mut a usize (core_slice_index_usize_coresliceindexSliceIndexInst a) v i)]
+  =
+  admit()
+
+let alloc_vec_Vec_index_mut_back_eq (#a : Type0) (v : alloc_vec_Vec a) (i : usize) (x : a) :
+  Lemma (
+    alloc_vec_Vec_index_mut_back a usize (core_slice_index_usize_coresliceindexSliceIndexInst a) v i x ==
+      alloc_vec_Vec_update_usize v i x)
+  [SMTPat (alloc_vec_Vec_index_mut_back a usize (core_slice_index_usize_coresliceindexSliceIndexInst a) v i x)]
+  =
+  admit()
diff --git a/tests/fstar/betree/BetreeMain.Clauses.Template.fst b/tests/fstar/betree/BetreeMain.Clauses.Template.fst
index 823df03a..8722f0bf 100644
--- a/tests/fstar/betree/BetreeMain.Clauses.Template.fst
+++ b/tests/fstar/betree/BetreeMain.Clauses.Template.fst
@@ -8,95 +8,95 @@ open BetreeMain.Types
 
 (** [betree_main::betree::List::{1}::len]: decreases clause *)
 unfold
-let betree_list_len_decreases (t : Type0) (self : betree_list_t t) : nat =
+let betree_List_len_decreases (t : Type0) (self : betree_List_t t) : nat =
   admit ()
 
 (** [betree_main::betree::List::{1}::split_at]: decreases clause *)
 unfold
-let betree_list_split_at_decreases (t : Type0) (self : betree_list_t t)
+let betree_List_split_at_decreases (t : Type0) (self : betree_List_t t)
   (n : u64) : nat =
   admit ()
 
 (** [betree_main::betree::List::{2}::partition_at_pivot]: decreases clause *)
 unfold
-let betree_list_partition_at_pivot_decreases (t : Type0)
-  (self : betree_list_t (u64 & t)) (pivot : u64) : nat =
+let betree_List_partition_at_pivot_decreases (t : Type0)
+  (self : betree_List_t (u64 & t)) (pivot : u64) : nat =
   admit ()
 
 (** [betree_main::betree::Node::{5}::lookup_first_message_for_key]: decreases clause *)
 unfold
-let betree_node_lookup_first_message_for_key_decreases (key : u64)
-  (msgs : betree_list_t (u64 & betree_message_t)) : nat =
+let betree_Node_lookup_first_message_for_key_decreases (key : u64)
+  (msgs : betree_List_t (u64 & betree_Message_t)) : nat =
   admit ()
 
 (** [betree_main::betree::Node::{5}::apply_upserts]: decreases clause *)
 unfold
-let betree_node_apply_upserts_decreases
-  (msgs : betree_list_t (u64 & betree_message_t)) (prev : option u64)
+let betree_Node_apply_upserts_decreases
+  (msgs : betree_List_t (u64 & betree_Message_t)) (prev : option u64)
   (key : u64) (st : state) : nat =
   admit ()
 
 (** [betree_main::betree::Node::{5}::lookup_in_bindings]: decreases clause *)
 unfold
-let betree_node_lookup_in_bindings_decreases (key : u64)
-  (bindings : betree_list_t (u64 & u64)) : nat =
+let betree_Node_lookup_in_bindings_decreases (key : u64)
+  (bindings : betree_List_t (u64 & u64)) : nat =
   admit ()
 
 (** [betree_main::betree::Internal::{4}::lookup_in_children]: decreases clause *)
 unfold
-let betree_internal_lookup_in_children_decreases (self : betree_internal_t)
+let betree_Internal_lookup_in_children_decreases (self : betree_Internal_t)
   (key : u64) (st : state) : nat =
   admit ()
 
 (** [betree_main::betree::Node::{5}::lookup]: decreases clause *)
 unfold
-let betree_node_lookup_decreases (self : betree_node_t) (key : u64)
+let betree_Node_lookup_decreases (self : betree_Node_t) (key : u64)
   (st : state) : nat =
   admit ()
 
 (** [betree_main::betree::Node::{5}::filter_messages_for_key]: decreases clause *)
 unfold
-let betree_node_filter_messages_for_key_decreases (key : u64)
-  (msgs : betree_list_t (u64 & betree_message_t)) : nat =
+let betree_Node_filter_messages_for_key_decreases (key : u64)
+  (msgs : betree_List_t (u64 & betree_Message_t)) : nat =
   admit ()
 
 (** [betree_main::betree::Node::{5}::lookup_first_message_after_key]: decreases clause *)
 unfold
-let betree_node_lookup_first_message_after_key_decreases (key : u64)
-  (msgs : betree_list_t (u64 & betree_message_t)) : nat =
+let betree_Node_lookup_first_message_after_key_decreases (key : u64)
+  (msgs : betree_List_t (u64 & betree_Message_t)) : nat =
   admit ()
 
 (** [betree_main::betree::Node::{5}::apply_messages_to_internal]: decreases clause *)
 unfold
-let betree_node_apply_messages_to_internal_decreases
-  (msgs : betree_list_t (u64 & betree_message_t))
-  (new_msgs : betree_list_t (u64 & betree_message_t)) : nat =
+let betree_Node_apply_messages_to_internal_decreases
+  (msgs : betree_List_t (u64 & betree_Message_t))
+  (new_msgs : betree_List_t (u64 & betree_Message_t)) : nat =
   admit ()
 
 (** [betree_main::betree::Node::{5}::lookup_mut_in_bindings]: decreases clause *)
 unfold
-let betree_node_lookup_mut_in_bindings_decreases (key : u64)
-  (bindings : betree_list_t (u64 & u64)) : nat =
+let betree_Node_lookup_mut_in_bindings_decreases (key : u64)
+  (bindings : betree_List_t (u64 & u64)) : nat =
   admit ()
 
 (** [betree_main::betree::Node::{5}::apply_messages_to_leaf]: decreases clause *)
 unfold
-let betree_node_apply_messages_to_leaf_decreases
-  (bindings : betree_list_t (u64 & u64))
-  (new_msgs : betree_list_t (u64 & betree_message_t)) : nat =
+let betree_Node_apply_messages_to_leaf_decreases
+  (bindings : betree_List_t (u64 & u64))
+  (new_msgs : betree_List_t (u64 & betree_Message_t)) : nat =
   admit ()
 
 (** [betree_main::betree::Internal::{4}::flush]: decreases clause *)
 unfold
-let betree_internal_flush_decreases (self : betree_internal_t)
-  (params : betree_params_t) (node_id_cnt : betree_node_id_counter_t)
-  (content : betree_list_t (u64 & betree_message_t)) (st : state) : nat =
+let betree_Internal_flush_decreases (self : betree_Internal_t)
+  (params : betree_Params_t) (node_id_cnt : betree_NodeIdCounter_t)
+  (content : betree_List_t (u64 & betree_Message_t)) (st : state) : nat =
   admit ()
 
 (** [betree_main::betree::Node::{5}::apply_messages]: decreases clause *)
 unfold
-let betree_node_apply_messages_decreases (self : betree_node_t)
-  (params : betree_params_t) (node_id_cnt : betree_node_id_counter_t)
-  (msgs : betree_list_t (u64 & betree_message_t)) (st : state) : nat =
+let betree_Node_apply_messages_decreases (self : betree_Node_t)
+  (params : betree_Params_t) (node_id_cnt : betree_NodeIdCounter_t)
+  (msgs : betree_List_t (u64 & betree_Message_t)) (st : state) : nat =
   admit ()
 
diff --git a/tests/fstar/betree/BetreeMain.Clauses.fst b/tests/fstar/betree/BetreeMain.Clauses.fst
index 07484711..cda7b920 100644
--- a/tests/fstar/betree/BetreeMain.Clauses.fst
+++ b/tests/fstar/betree/BetreeMain.Clauses.fst
@@ -8,8 +8,8 @@ open BetreeMain.Types
 (*** Well-founded relations *)
 
 (* We had a few issues when proving termination of the mutually recursive functions:
- * - betree_internal_flush
- * - betree_node_apply_messages
+ * - betree_Internal_flush
+ * - betree_Node_apply_messages
  *
  * The quantity which effectively decreases is:
  *   (betree_size, messages_length)
@@ -103,108 +103,108 @@ let wf_nat_pair_lem (p0 p1 : nat_pair) :
 
 (** [betree_main::betree::List::{1}::len]: decreases clause *)
 unfold
-let betree_list_len_decreases (t : Type0) (self : betree_list_t t) : betree_list_t t =
+let betree_List_len_decreases (t : Type0) (self : betree_List_t t) : betree_List_t t =
   self
 
 (** [betree_main::betree::List::{1}::split_at]: decreases clause *)
 unfold
-let betree_list_split_at_decreases (t : Type0) (self : betree_list_t t)
+let betree_List_split_at_decreases (t : Type0) (self : betree_List_t t)
   (n : u64) : nat =
   n
 
 (** [betree_main::betree::List::{2}::partition_at_pivot]: decreases clause *)
 unfold
-let betree_list_partition_at_pivot_decreases (t : Type0)
-  (self : betree_list_t (u64 & t)) (pivot : u64) : betree_list_t (u64 & t) =
+let betree_List_partition_at_pivot_decreases (t : Type0)
+  (self : betree_List_t (u64 & t)) (pivot : u64) : betree_List_t (u64 & t) =
   self
 
 (** [betree_main::betree::Node::{5}::lookup_in_bindings]: decreases clause *)
 unfold
-let betree_node_lookup_in_bindings_decreases (key : u64)
-  (bindings : betree_list_t (u64 & u64)) : betree_list_t (u64 & u64) =
+let betree_Node_lookup_in_bindings_decreases (key : u64)
+  (bindings : betree_List_t (u64 & u64)) : betree_List_t (u64 & u64) =
   bindings
 
 (** [betree_main::betree::Node::{5}::lookup_first_message_for_key]: decreases clause *)
 unfold
-let betree_node_lookup_first_message_for_key_decreases (key : u64)
-  (msgs : betree_list_t (u64 & betree_message_t)) : betree_list_t (u64 & betree_message_t) =
+let betree_Node_lookup_first_message_for_key_decreases (key : u64)
+  (msgs : betree_List_t (u64 & betree_Message_t)) : betree_List_t (u64 & betree_Message_t) =
   msgs
 
 (** [betree_main::betree::Node::{5}::apply_upserts]: decreases clause *)
 unfold
-let betree_node_apply_upserts_decreases
-  (msgs : betree_list_t (u64 & betree_message_t)) (prev : option u64)
-  (key : u64) (st : state) : betree_list_t (u64 & betree_message_t) =
+let betree_Node_apply_upserts_decreases
+  (msgs : betree_List_t (u64 & betree_Message_t)) (prev : option u64)
+  (key : u64) (st : state) : betree_List_t (u64 & betree_Message_t) =
   msgs
 
 (** [betree_main::betree::Internal::{4}::lookup_in_children]: decreases clause *)
 unfold
-let betree_internal_lookup_in_children_decreases (self : betree_internal_t)
-  (key : u64) (st : state) : betree_internal_t =
+let betree_Internal_lookup_in_children_decreases (self : betree_Internal_t)
+  (key : u64) (st : state) : betree_Internal_t =
   self
 
 (** [betree_main::betree::Node::{5}::lookup]: decreases clause *)
 unfold
-let betree_node_lookup_decreases (self : betree_node_t) (key : u64)
-  (st : state) : betree_node_t =
+let betree_Node_lookup_decreases (self : betree_Node_t) (key : u64)
+  (st : state) : betree_Node_t =
   self
 
 (** [betree_main::betree::Node::{5}::lookup_mut_in_bindings]: decreases clause *)
 unfold
-let betree_node_lookup_mut_in_bindings_decreases (key : u64)
-  (bindings : betree_list_t (u64 & u64)) : betree_list_t (u64 & u64) =
+let betree_Node_lookup_mut_in_bindings_decreases (key : u64)
+  (bindings : betree_List_t (u64 & u64)) : betree_List_t (u64 & u64) =
   bindings
 
 unfold
-let betree_node_apply_messages_to_leaf_decreases
-  (bindings : betree_list_t (u64 & u64))
-  (new_msgs : betree_list_t (u64 & betree_message_t)) : betree_list_t (u64 & betree_message_t) =
+let betree_Node_apply_messages_to_leaf_decreases
+  (bindings : betree_List_t (u64 & u64))
+  (new_msgs : betree_List_t (u64 & betree_Message_t)) : betree_List_t (u64 & betree_Message_t) =
   new_msgs
 
 (** [betree_main::betree::Node::{5}::filter_messages_for_key]: decreases clause *)
 unfold
-let betree_node_filter_messages_for_key_decreases (key : u64)
-  (msgs : betree_list_t (u64 & betree_message_t)) : betree_list_t (u64 & betree_message_t) =
+let betree_Node_filter_messages_for_key_decreases (key : u64)
+  (msgs : betree_List_t (u64 & betree_Message_t)) : betree_List_t (u64 & betree_Message_t) =
   msgs
 
 (** [betree_main::betree::Node::{5}::lookup_first_message_after_key]: decreases clause *)
 unfold
-let betree_node_lookup_first_message_after_key_decreases (key : u64)
-  (msgs : betree_list_t (u64 & betree_message_t)) : betree_list_t (u64 & betree_message_t) =
+let betree_Node_lookup_first_message_after_key_decreases (key : u64)
+  (msgs : betree_List_t (u64 & betree_Message_t)) : betree_List_t (u64 & betree_Message_t) =
   msgs
 
-let betree_node_apply_messages_to_internal_decreases
-  (msgs : betree_list_t (u64 & betree_message_t))
-  (new_msgs : betree_list_t (u64 & betree_message_t)) : betree_list_t (u64 & betree_message_t) =
+let betree_Node_apply_messages_to_internal_decreases
+  (msgs : betree_List_t (u64 & betree_Message_t))
+  (new_msgs : betree_List_t (u64 & betree_Message_t)) : betree_List_t (u64 & betree_Message_t) =
   new_msgs
 
 (*** Decrease clauses - nat_pair *)
 /// The following decrease clauses use the [nat_pair] definition and the well-founded
 /// relation proven above.
 
-let rec betree_size (bt : betree_node_t) : nat =
+let rec betree_size (bt : betree_Node_t) : nat =
   match bt with
-  | BetreeNodeInternal node -> 1 + betree_internal_size node
-  | BetreeNodeLeaf _ -> 1
+  | Betree_Node_Internal node -> 1 + betree_Internal_size node
+  | Betree_Node_Leaf _ -> 1
 
-and betree_internal_size (node : betree_internal_t) : nat =
-  1 + betree_size node.betree_internal_left + betree_size node.betree_internal_right
+and betree_Internal_size (node : betree_Internal_t) : nat =
+  1 + betree_size node.left + betree_size node.right
 
-let rec betree_list_len (#a : Type0) (ls : betree_list_t a) : nat =
+let rec betree_List_len (#a : Type0) (ls : betree_List_t a) : nat =
   match ls with
-  | BetreeListCons _ tl -> 1 + betree_list_len tl
-  | BetreeListNil -> 0
+  | Betree_List_Cons _ tl -> 1 + betree_List_len tl
+  | Betree_List_Nil -> 0
 
 (** [betree_main::betree::Internal::{4}::flush]: decreases clause *)
 unfold
-let betree_internal_flush_decreases (self : betree_internal_t)
-  (params : betree_params_t) (node_id_cnt : betree_node_id_counter_t)
-  (content : betree_list_t (u64 & betree_message_t)) (st : state) : nat_pair =
-  (|betree_internal_size self, 0|)
+let betree_Internal_flush_decreases (self : betree_Internal_t)
+  (params : betree_Params_t) (node_id_cnt : betree_NodeIdCounter_t)
+  (content : betree_List_t (u64 & betree_Message_t)) (st : state) : nat_pair =
+  (|betree_Internal_size self, 0|)
 
 (** [betree_main::betree::Node::{5}::apply_messages]: decreases clause *)
 unfold
-let betree_node_apply_messages_decreases (self : betree_node_t)
-  (params : betree_params_t) (node_id_cnt : betree_node_id_counter_t)
-  (msgs : betree_list_t (u64 & betree_message_t)) (st : state) : nat_pair =
-  (|betree_size self, betree_list_len msgs|)
+let betree_Node_apply_messages_decreases (self : betree_Node_t)
+  (params : betree_Params_t) (node_id_cnt : betree_NodeIdCounter_t)
+  (msgs : betree_List_t (u64 & betree_Message_t)) (st : state) : nat_pair =
+  (|betree_size self, betree_List_len msgs|)
diff --git a/tests/fstar/betree/BetreeMain.Funs.fst b/tests/fstar/betree/BetreeMain.Funs.fst
index 847dc865..d2bf5c7c 100644
--- a/tests/fstar/betree/BetreeMain.Funs.fst
+++ b/tests/fstar/betree/BetreeMain.Funs.fst
@@ -9,35 +9,35 @@ include BetreeMain.Clauses
 #set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
 
 (** [betree_main::betree::load_internal_node]: forward function *)
-let betree_load_internal_node_fwd
+let betree_load_internal_node
   (id : u64) (st : state) :
-  result (state & (betree_list_t (u64 & betree_message_t)))
+  result (state & (betree_List_t (u64 & betree_Message_t)))
   =
-  betree_utils_load_internal_node_fwd id st
+  betree_utils_load_internal_node id st
 
 (** [betree_main::betree::store_internal_node]: forward function *)
-let betree_store_internal_node_fwd
-  (id : u64) (content : betree_list_t (u64 & betree_message_t)) (st : state) :
+let betree_store_internal_node
+  (id : u64) (content : betree_List_t (u64 & betree_Message_t)) (st : state) :
   result (state & unit)
   =
-  let* (st0, _) = betree_utils_store_internal_node_fwd id content st in
+  let* (st0, _) = betree_utils_store_internal_node id content st in
   Return (st0, ())
 
 (** [betree_main::betree::load_leaf_node]: forward function *)
-let betree_load_leaf_node_fwd
-  (id : u64) (st : state) : result (state & (betree_list_t (u64 & u64))) =
-  betree_utils_load_leaf_node_fwd id st
+let betree_load_leaf_node
+  (id : u64) (st : state) : result (state & (betree_List_t (u64 & u64))) =
+  betree_utils_load_leaf_node id st
 
 (** [betree_main::betree::store_leaf_node]: forward function *)
-let betree_store_leaf_node_fwd
-  (id : u64) (content : betree_list_t (u64 & u64)) (st : state) :
+let betree_store_leaf_node
+  (id : u64) (content : betree_List_t (u64 & u64)) (st : state) :
   result (state & unit)
   =
-  let* (st0, _) = betree_utils_store_leaf_node_fwd id content st in
+  let* (st0, _) = betree_utils_store_leaf_node id content st in
   Return (st0, ())
 
 (** [betree_main::betree::fresh_node_id]: forward function *)
-let betree_fresh_node_id_fwd (counter : u64) : result u64 =
+let betree_fresh_node_id (counter : u64) : result u64 =
   let* _ = u64_add counter 1 in Return counter
 
 (** [betree_main::betree::fresh_node_id]: backward function 0 *)
@@ -45,976 +45,909 @@ let betree_fresh_node_id_back (counter : u64) : result u64 =
   u64_add counter 1
 
 (** [betree_main::betree::NodeIdCounter::{0}::new]: forward function *)
-let betree_node_id_counter_new_fwd : result betree_node_id_counter_t =
-  Return { betree_node_id_counter_next_node_id = 0 }
+let betree_NodeIdCounter_new : result betree_NodeIdCounter_t =
+  Return { next_node_id = 0 }
 
 (** [betree_main::betree::NodeIdCounter::{0}::fresh_id]: forward function *)
-let betree_node_id_counter_fresh_id_fwd
-  (self : betree_node_id_counter_t) : result u64 =
-  let* _ = u64_add self.betree_node_id_counter_next_node_id 1 in
-  Return self.betree_node_id_counter_next_node_id
+let betree_NodeIdCounter_fresh_id
+  (self : betree_NodeIdCounter_t) : result u64 =
+  let* _ = u64_add self.next_node_id 1 in Return self.next_node_id
 
 (** [betree_main::betree::NodeIdCounter::{0}::fresh_id]: backward function 0 *)
-let betree_node_id_counter_fresh_id_back
-  (self : betree_node_id_counter_t) : result betree_node_id_counter_t =
-  let* i = u64_add self.betree_node_id_counter_next_node_id 1 in
-  Return { betree_node_id_counter_next_node_id = i }
-
-(** [core::num::u64::{9}::MAX] *)
-let core_num_u64_max_body : result u64 = Return 18446744073709551615
-let core_num_u64_max_c : u64 = eval_global core_num_u64_max_body
+let betree_NodeIdCounter_fresh_id_back
+  (self : betree_NodeIdCounter_t) : result betree_NodeIdCounter_t =
+  let* i = u64_add self.next_node_id 1 in Return { next_node_id = i }
 
 (** [betree_main::betree::upsert_update]: forward function *)
-let betree_upsert_update_fwd
-  (prev : option u64) (st : betree_upsert_fun_state_t) : result u64 =
+let betree_upsert_update
+  (prev : option u64) (st : betree_UpsertFunState_t) : result u64 =
   begin match prev with
   | None ->
     begin match st with
-    | BetreeUpsertFunStateAdd v -> Return v
-    | BetreeUpsertFunStateSub i -> Return 0
+    | Betree_UpsertFunState_Add v -> Return v
+    | Betree_UpsertFunState_Sub i -> Return 0
     end
   | Some prev0 ->
     begin match st with
-    | BetreeUpsertFunStateAdd v ->
-      let* margin = u64_sub core_num_u64_max_c prev0 in
-      if margin >= v then u64_add prev0 v else Return core_num_u64_max_c
-    | BetreeUpsertFunStateSub v ->
+    | Betree_UpsertFunState_Add v ->
+      let* margin = u64_sub core_u64_max prev0 in
+      if margin >= v then u64_add prev0 v else Return core_u64_max
+    | Betree_UpsertFunState_Sub v ->
       if prev0 >= v then u64_sub prev0 v else Return 0
     end
   end
 
 (** [betree_main::betree::List::{1}::len]: forward function *)
-let rec betree_list_len_fwd
-  (t : Type0) (self : betree_list_t t) :
-  Tot (result u64) (decreases (betree_list_len_decreases t self))
+let rec betree_List_len
+  (t : Type0) (self : betree_List_t t) :
+  Tot (result u64) (decreases (betree_List_len_decreases t self))
   =
   begin match self with
-  | BetreeListCons x tl -> let* i = betree_list_len_fwd t tl in u64_add 1 i
-  | BetreeListNil -> Return 0
+  | Betree_List_Cons x tl -> let* i = betree_List_len t tl in u64_add 1 i
+  | Betree_List_Nil -> Return 0
   end
 
 (** [betree_main::betree::List::{1}::split_at]: forward function *)
-let rec betree_list_split_at_fwd
-  (t : Type0) (self : betree_list_t t) (n : u64) :
-  Tot (result ((betree_list_t t) & (betree_list_t t)))
-  (decreases (betree_list_split_at_decreases t self n))
+let rec betree_List_split_at
+  (t : Type0) (self : betree_List_t t) (n : u64) :
+  Tot (result ((betree_List_t t) & (betree_List_t t)))
+  (decreases (betree_List_split_at_decreases t self n))
   =
   if n = 0
-  then Return (BetreeListNil, self)
+  then Return (Betree_List_Nil, self)
   else
     begin match self with
-    | BetreeListCons hd tl ->
+    | Betree_List_Cons hd tl ->
       let* i = u64_sub n 1 in
-      let* p = betree_list_split_at_fwd t tl i in
+      let* p = betree_List_split_at t tl i in
       let (ls0, ls1) = p in
       let l = ls0 in
-      Return (BetreeListCons hd l, ls1)
-    | BetreeListNil -> Fail Failure
+      Return (Betree_List_Cons hd l, ls1)
+    | Betree_List_Nil -> Fail Failure
     end
 
 (** [betree_main::betree::List::{1}::push_front]: merged forward/backward function
     (there is a single backward function, and the forward function returns ()) *)
-let betree_list_push_front_fwd_back
-  (t : Type0) (self : betree_list_t t) (x : t) : result (betree_list_t t) =
-  let tl = mem_replace_fwd (betree_list_t t) self BetreeListNil in
+let betree_List_push_front
+  (t : Type0) (self : betree_List_t t) (x : t) : result (betree_List_t t) =
+  let tl = core_mem_replace (betree_List_t t) self Betree_List_Nil in
   let l = tl in
-  Return (BetreeListCons x l)
+  Return (Betree_List_Cons x l)
 
 (** [betree_main::betree::List::{1}::pop_front]: forward function *)
-let betree_list_pop_front_fwd (t : Type0) (self : betree_list_t t) : result t =
-  let ls = mem_replace_fwd (betree_list_t t) self BetreeListNil in
+let betree_List_pop_front (t : Type0) (self : betree_List_t t) : result t =
+  let ls = core_mem_replace (betree_List_t t) self Betree_List_Nil in
   begin match ls with
-  | BetreeListCons x tl -> Return x
-  | BetreeListNil -> Fail Failure
+  | Betree_List_Cons x tl -> Return x
+  | Betree_List_Nil -> Fail Failure
   end
 
 (** [betree_main::betree::List::{1}::pop_front]: backward function 0 *)
-let betree_list_pop_front_back
-  (t : Type0) (self : betree_list_t t) : result (betree_list_t t) =
-  let ls = mem_replace_fwd (betree_list_t t) self BetreeListNil in
+let betree_List_pop_front_back
+  (t : Type0) (self : betree_List_t t) : result (betree_List_t t) =
+  let ls = core_mem_replace (betree_List_t t) self Betree_List_Nil in
   begin match ls with
-  | BetreeListCons x tl -> Return tl
-  | BetreeListNil -> Fail Failure
+  | Betree_List_Cons x tl -> Return tl
+  | Betree_List_Nil -> Fail Failure
   end
 
 (** [betree_main::betree::List::{1}::hd]: forward function *)
-let betree_list_hd_fwd (t : Type0) (self : betree_list_t t) : result t =
+let betree_List_hd (t : Type0) (self : betree_List_t t) : result t =
   begin match self with
-  | BetreeListCons hd l -> Return hd
-  | BetreeListNil -> Fail Failure
+  | Betree_List_Cons hd l -> Return hd
+  | Betree_List_Nil -> Fail Failure
   end
 
 (** [betree_main::betree::List::{2}::head_has_key]: forward function *)
-let betree_list_head_has_key_fwd
-  (t : Type0) (self : betree_list_t (u64 & t)) (key : u64) : result bool =
+let betree_List_head_has_key
+  (t : Type0) (self : betree_List_t (u64 & t)) (key : u64) : result bool =
   begin match self with
-  | BetreeListCons hd l -> let (i, _) = hd in Return (i = key)
-  | BetreeListNil -> Return false
+  | Betree_List_Cons hd l -> let (i, _) = hd in Return (i = key)
+  | Betree_List_Nil -> Return false
   end
 
 (** [betree_main::betree::List::{2}::partition_at_pivot]: forward function *)
-let rec betree_list_partition_at_pivot_fwd
-  (t : Type0) (self : betree_list_t (u64 & t)) (pivot : u64) :
-  Tot (result ((betree_list_t (u64 & t)) & (betree_list_t (u64 & t))))
-  (decreases (betree_list_partition_at_pivot_decreases t self pivot))
+let rec betree_List_partition_at_pivot
+  (t : Type0) (self : betree_List_t (u64 & t)) (pivot : u64) :
+  Tot (result ((betree_List_t (u64 & t)) & (betree_List_t (u64 & t))))
+  (decreases (betree_List_partition_at_pivot_decreases t self pivot))
   =
   begin match self with
-  | BetreeListCons hd tl ->
+  | Betree_List_Cons hd tl ->
     let (i, x) = hd in
     if i >= pivot
-    then Return (BetreeListNil, BetreeListCons (i, x) tl)
+    then Return (Betree_List_Nil, Betree_List_Cons (i, x) tl)
     else
-      let* p = betree_list_partition_at_pivot_fwd t tl pivot in
+      let* p = betree_List_partition_at_pivot t tl pivot in
       let (ls0, ls1) = p in
       let l = ls0 in
-      Return (BetreeListCons (i, x) l, ls1)
-  | BetreeListNil -> Return (BetreeListNil, BetreeListNil)
+      Return (Betree_List_Cons (i, x) l, ls1)
+  | Betree_List_Nil -> Return (Betree_List_Nil, Betree_List_Nil)
   end
 
 (** [betree_main::betree::Leaf::{3}::split]: forward function *)
-let betree_leaf_split_fwd
-  (self : betree_leaf_t) (content : betree_list_t (u64 & u64))
-  (params : betree_params_t) (node_id_cnt : betree_node_id_counter_t)
+let betree_Leaf_split
+  (self : betree_Leaf_t) (content : betree_List_t (u64 & u64))
+  (params : betree_Params_t) (node_id_cnt : betree_NodeIdCounter_t)
   (st : state) :
-  result (state & betree_internal_t)
+  result (state & betree_Internal_t)
   =
-  let* p =
-    betree_list_split_at_fwd (u64 & u64) content
-      params.betree_params_split_size in
+  let* p = betree_List_split_at (u64 & u64) content params.split_size in
   let (content0, content1) = p in
-  let* p0 = betree_list_hd_fwd (u64 & u64) content1 in
+  let* p0 = betree_List_hd (u64 & u64) content1 in
   let (pivot, _) = p0 in
-  let* id0 = betree_node_id_counter_fresh_id_fwd node_id_cnt in
-  let* node_id_cnt0 = betree_node_id_counter_fresh_id_back node_id_cnt in
-  let* id1 = betree_node_id_counter_fresh_id_fwd node_id_cnt0 in
-  let* (st0, _) = betree_store_leaf_node_fwd id0 content0 st in
-  let* (st1, _) = betree_store_leaf_node_fwd id1 content1 st0 in
-  let n = BetreeNodeLeaf
-    { betree_leaf_id = id0; betree_leaf_size = params.betree_params_split_size
-    } in
-  let n0 = BetreeNodeLeaf
-    { betree_leaf_id = id1; betree_leaf_size = params.betree_params_split_size
-    } in
-  Return (st1,
-    {
-      betree_internal_id = self.betree_leaf_id;
-      betree_internal_pivot = pivot;
-      betree_internal_left = n;
-      betree_internal_right = n0
-    })
+  let* id0 = betree_NodeIdCounter_fresh_id node_id_cnt in
+  let* node_id_cnt0 = betree_NodeIdCounter_fresh_id_back node_id_cnt in
+  let* id1 = betree_NodeIdCounter_fresh_id node_id_cnt0 in
+  let* (st0, _) = betree_store_leaf_node id0 content0 st in
+  let* (st1, _) = betree_store_leaf_node id1 content1 st0 in
+  let n = Betree_Node_Leaf { id = id0; size = params.split_size } in
+  let n0 = Betree_Node_Leaf { id = id1; size = params.split_size } in
+  Return (st1, { id = self.id; pivot = pivot; left = n; right = n0 })
 
 (** [betree_main::betree::Leaf::{3}::split]: backward function 2 *)
-let betree_leaf_split_back
-  (self : betree_leaf_t) (content : betree_list_t (u64 & u64))
-  (params : betree_params_t) (node_id_cnt : betree_node_id_counter_t)
+let betree_Leaf_split_back
+  (self : betree_Leaf_t) (content : betree_List_t (u64 & u64))
+  (params : betree_Params_t) (node_id_cnt : betree_NodeIdCounter_t)
   (st : state) :
-  result betree_node_id_counter_t
+  result betree_NodeIdCounter_t
   =
-  let* p =
-    betree_list_split_at_fwd (u64 & u64) content
-      params.betree_params_split_size in
+  let* p = betree_List_split_at (u64 & u64) content params.split_size in
   let (content0, content1) = p in
-  let* _ = betree_list_hd_fwd (u64 & u64) content1 in
-  let* id0 = betree_node_id_counter_fresh_id_fwd node_id_cnt in
-  let* node_id_cnt0 = betree_node_id_counter_fresh_id_back node_id_cnt in
-  let* id1 = betree_node_id_counter_fresh_id_fwd node_id_cnt0 in
-  let* (st0, _) = betree_store_leaf_node_fwd id0 content0 st in
-  let* _ = betree_store_leaf_node_fwd id1 content1 st0 in
-  betree_node_id_counter_fresh_id_back node_id_cnt0
+  let* _ = betree_List_hd (u64 & u64) content1 in
+  let* id0 = betree_NodeIdCounter_fresh_id node_id_cnt in
+  let* node_id_cnt0 = betree_NodeIdCounter_fresh_id_back node_id_cnt in
+  let* id1 = betree_NodeIdCounter_fresh_id node_id_cnt0 in
+  let* (st0, _) = betree_store_leaf_node id0 content0 st in
+  let* _ = betree_store_leaf_node id1 content1 st0 in
+  betree_NodeIdCounter_fresh_id_back node_id_cnt0
 
 (** [betree_main::betree::Node::{5}::lookup_first_message_for_key]: forward function *)
-let rec betree_node_lookup_first_message_for_key_fwd
-  (key : u64) (msgs : betree_list_t (u64 & betree_message_t)) :
-  Tot (result (betree_list_t (u64 & betree_message_t)))
-  (decreases (betree_node_lookup_first_message_for_key_decreases key msgs))
+let rec betree_Node_lookup_first_message_for_key
+  (key : u64) (msgs : betree_List_t (u64 & betree_Message_t)) :
+  Tot (result (betree_List_t (u64 & betree_Message_t)))
+  (decreases (betree_Node_lookup_first_message_for_key_decreases key msgs))
   =
   begin match msgs with
-  | BetreeListCons x next_msgs ->
+  | Betree_List_Cons x next_msgs ->
     let (i, m) = x in
     if i >= key
-    then Return (BetreeListCons (i, m) next_msgs)
-    else betree_node_lookup_first_message_for_key_fwd key next_msgs
-  | BetreeListNil -> Return BetreeListNil
+    then Return (Betree_List_Cons (i, m) next_msgs)
+    else betree_Node_lookup_first_message_for_key key next_msgs
+  | Betree_List_Nil -> Return Betree_List_Nil
   end
 
 (** [betree_main::betree::Node::{5}::lookup_first_message_for_key]: backward function 0 *)
-let rec betree_node_lookup_first_message_for_key_back
-  (key : u64) (msgs : betree_list_t (u64 & betree_message_t))
-  (ret : betree_list_t (u64 & betree_message_t)) :
-  Tot (result (betree_list_t (u64 & betree_message_t)))
-  (decreases (betree_node_lookup_first_message_for_key_decreases key msgs))
+let rec betree_Node_lookup_first_message_for_key_back
+  (key : u64) (msgs : betree_List_t (u64 & betree_Message_t))
+  (ret : betree_List_t (u64 & betree_Message_t)) :
+  Tot (result (betree_List_t (u64 & betree_Message_t)))
+  (decreases (betree_Node_lookup_first_message_for_key_decreases key msgs))
   =
   begin match msgs with
-  | BetreeListCons x next_msgs ->
+  | Betree_List_Cons x next_msgs ->
     let (i, m) = x in
     if i >= key
     then Return ret
     else
       let* next_msgs0 =
-        betree_node_lookup_first_message_for_key_back key next_msgs ret in
-      Return (BetreeListCons (i, m) next_msgs0)
-  | BetreeListNil -> Return ret
+        betree_Node_lookup_first_message_for_key_back key next_msgs ret in
+      Return (Betree_List_Cons (i, m) next_msgs0)
+  | Betree_List_Nil -> Return ret
   end
 
 (** [betree_main::betree::Node::{5}::apply_upserts]: forward function *)
-let rec betree_node_apply_upserts_fwd
-  (msgs : betree_list_t (u64 & betree_message_t)) (prev : option u64)
+let rec betree_Node_apply_upserts
+  (msgs : betree_List_t (u64 & betree_Message_t)) (prev : option u64)
   (key : u64) (st : state) :
   Tot (result (state & u64))
-  (decreases (betree_node_apply_upserts_decreases msgs prev key st))
+  (decreases (betree_Node_apply_upserts_decreases msgs prev key st))
   =
-  let* b = betree_list_head_has_key_fwd betree_message_t msgs key in
+  let* b = betree_List_head_has_key betree_Message_t msgs key in
   if b
   then
-    let* msg = betree_list_pop_front_fwd (u64 & betree_message_t) msgs in
+    let* msg = betree_List_pop_front (u64 & betree_Message_t) msgs in
     let (_, m) = msg in
     begin match m with
-    | BetreeMessageInsert i -> Fail Failure
-    | BetreeMessageDelete -> Fail Failure
-    | BetreeMessageUpsert s ->
-      let* v = betree_upsert_update_fwd prev s in
-      let* msgs0 = betree_list_pop_front_back (u64 & betree_message_t) msgs in
-      betree_node_apply_upserts_fwd msgs0 (Some v) key st
+    | Betree_Message_Insert i -> Fail Failure
+    | Betree_Message_Delete -> Fail Failure
+    | Betree_Message_Upsert s ->
+      let* v = betree_upsert_update prev s in
+      let* msgs0 = betree_List_pop_front_back (u64 & betree_Message_t) msgs in
+      betree_Node_apply_upserts msgs0 (Some v) key st
     end
   else
-    let* (st0, v) = core_option_option_unwrap_fwd u64 prev st in
+    let* (st0, v) = core_option_Option_unwrap u64 prev st in
     let* _ =
-      betree_list_push_front_fwd_back (u64 & betree_message_t) msgs (key,
-        BetreeMessageInsert v) in
+      betree_List_push_front (u64 & betree_Message_t) msgs (key,
+        Betree_Message_Insert v) in
     Return (st0, v)
 
 (** [betree_main::betree::Node::{5}::apply_upserts]: backward function 0 *)
-let rec betree_node_apply_upserts_back
-  (msgs : betree_list_t (u64 & betree_message_t)) (prev : option u64)
+let rec betree_Node_apply_upserts_back
+  (msgs : betree_List_t (u64 & betree_Message_t)) (prev : option u64)
   (key : u64) (st : state) :
-  Tot (result (betree_list_t (u64 & betree_message_t)))
-  (decreases (betree_node_apply_upserts_decreases msgs prev key st))
+  Tot (result (betree_List_t (u64 & betree_Message_t)))
+  (decreases (betree_Node_apply_upserts_decreases msgs prev key st))
   =
-  let* b = betree_list_head_has_key_fwd betree_message_t msgs key in
+  let* b = betree_List_head_has_key betree_Message_t msgs key in
   if b
   then
-    let* msg = betree_list_pop_front_fwd (u64 & betree_message_t) msgs in
+    let* msg = betree_List_pop_front (u64 & betree_Message_t) msgs in
     let (_, m) = msg in
     begin match m with
-    | BetreeMessageInsert i -> Fail Failure
-    | BetreeMessageDelete -> Fail Failure
-    | BetreeMessageUpsert s ->
-      let* v = betree_upsert_update_fwd prev s in
-      let* msgs0 = betree_list_pop_front_back (u64 & betree_message_t) msgs in
-      betree_node_apply_upserts_back msgs0 (Some v) key st
+    | Betree_Message_Insert i -> Fail Failure
+    | Betree_Message_Delete -> Fail Failure
+    | Betree_Message_Upsert s ->
+      let* v = betree_upsert_update prev s in
+      let* msgs0 = betree_List_pop_front_back (u64 & betree_Message_t) msgs in
+      betree_Node_apply_upserts_back msgs0 (Some v) key st
     end
   else
-    let* (_, v) = core_option_option_unwrap_fwd u64 prev st in
-    betree_list_push_front_fwd_back (u64 & betree_message_t) msgs (key,
-      BetreeMessageInsert v)
+    let* (_, v) = core_option_Option_unwrap u64 prev st in
+    betree_List_push_front (u64 & betree_Message_t) msgs (key,
+      Betree_Message_Insert v)
 
 (** [betree_main::betree::Node::{5}::lookup_in_bindings]: forward function *)
-let rec betree_node_lookup_in_bindings_fwd
-  (key : u64) (bindings : betree_list_t (u64 & u64)) :
+let rec betree_Node_lookup_in_bindings
+  (key : u64) (bindings : betree_List_t (u64 & u64)) :
   Tot (result (option u64))
-  (decreases (betree_node_lookup_in_bindings_decreases key bindings))
+  (decreases (betree_Node_lookup_in_bindings_decreases key bindings))
   =
   begin match bindings with
-  | BetreeListCons hd tl ->
+  | Betree_List_Cons hd tl ->
     let (i, i0) = hd in
     if i = key
     then Return (Some i0)
-    else
-      if i > key
-      then Return None
-      else betree_node_lookup_in_bindings_fwd key tl
-  | BetreeListNil -> Return None
+    else if i > key then Return None else betree_Node_lookup_in_bindings key tl
+  | Betree_List_Nil -> Return None
   end
 
 (** [betree_main::betree::Internal::{4}::lookup_in_children]: forward function *)
-let rec betree_internal_lookup_in_children_fwd
-  (self : betree_internal_t) (key : u64) (st : state) :
+let rec betree_Internal_lookup_in_children
+  (self : betree_Internal_t) (key : u64) (st : state) :
   Tot (result (state & (option u64)))
-  (decreases (betree_internal_lookup_in_children_decreases self key st))
+  (decreases (betree_Internal_lookup_in_children_decreases self key st))
   =
-  if key < self.betree_internal_pivot
-  then betree_node_lookup_fwd self.betree_internal_left key st
-  else betree_node_lookup_fwd self.betree_internal_right key st
+  if key < self.pivot
+  then betree_Node_lookup self.left key st
+  else betree_Node_lookup self.right key st
 
 (** [betree_main::betree::Internal::{4}::lookup_in_children]: backward function 0 *)
-and betree_internal_lookup_in_children_back
-  (self : betree_internal_t) (key : u64) (st : state) :
-  Tot (result betree_internal_t)
-  (decreases (betree_internal_lookup_in_children_decreases self key st))
+and betree_Internal_lookup_in_children_back
+  (self : betree_Internal_t) (key : u64) (st : state) :
+  Tot (result betree_Internal_t)
+  (decreases (betree_Internal_lookup_in_children_decreases self key st))
   =
-  if key < self.betree_internal_pivot
+  if key < self.pivot
   then
-    let* n = betree_node_lookup_back self.betree_internal_left key st in
-    Return { self with betree_internal_left = n }
+    let* n = betree_Node_lookup_back self.left key st in
+    Return { self with left = n }
   else
-    let* n = betree_node_lookup_back self.betree_internal_right key st in
-    Return { self with betree_internal_right = n }
+    let* n = betree_Node_lookup_back self.right key st in
+    Return { self with right = n }
 
 (** [betree_main::betree::Node::{5}::lookup]: forward function *)
-and betree_node_lookup_fwd
-  (self : betree_node_t) (key : u64) (st : state) :
+and betree_Node_lookup
+  (self : betree_Node_t) (key : u64) (st : state) :
   Tot (result (state & (option u64)))
-  (decreases (betree_node_lookup_decreases self key st))
+  (decreases (betree_Node_lookup_decreases self key st))
   =
   begin match self with
-  | BetreeNodeInternal node ->
-    let* (st0, msgs) = betree_load_internal_node_fwd node.betree_internal_id st
-      in
-    let* pending = betree_node_lookup_first_message_for_key_fwd key msgs in
+  | Betree_Node_Internal node ->
+    let* (st0, msgs) = betree_load_internal_node node.id st in
+    let* pending = betree_Node_lookup_first_message_for_key key msgs in
     begin match pending with
-    | BetreeListCons p l ->
+    | Betree_List_Cons p l ->
       let (k, msg) = p in
       if k <> key
       then
-        let* (st1, opt) = betree_internal_lookup_in_children_fwd node key st0
-          in
+        let* (st1, o) = betree_Internal_lookup_in_children node key st0 in
         let* _ =
-          betree_node_lookup_first_message_for_key_back key msgs
-            (BetreeListCons (k, msg) l) in
-        Return (st1, opt)
+          betree_Node_lookup_first_message_for_key_back key msgs
+            (Betree_List_Cons (k, msg) l) in
+        Return (st1, o)
       else
         begin match msg with
-        | BetreeMessageInsert v ->
+        | Betree_Message_Insert v ->
           let* _ =
-            betree_node_lookup_first_message_for_key_back key msgs
-              (BetreeListCons (k, BetreeMessageInsert v) l) in
+            betree_Node_lookup_first_message_for_key_back key msgs
+              (Betree_List_Cons (k, Betree_Message_Insert v) l) in
           Return (st0, Some v)
-        | BetreeMessageDelete ->
+        | Betree_Message_Delete ->
           let* _ =
-            betree_node_lookup_first_message_for_key_back key msgs
-              (BetreeListCons (k, BetreeMessageDelete) l) in
+            betree_Node_lookup_first_message_for_key_back key msgs
+              (Betree_List_Cons (k, Betree_Message_Delete) l) in
           Return (st0, None)
-        | BetreeMessageUpsert ufs ->
-          let* (st1, v) = betree_internal_lookup_in_children_fwd node key st0
-            in
+        | Betree_Message_Upsert ufs ->
+          let* (st1, v) = betree_Internal_lookup_in_children node key st0 in
           let* (st2, v0) =
-            betree_node_apply_upserts_fwd (BetreeListCons (k,
-              BetreeMessageUpsert ufs) l) v key st1 in
-          let* node0 = betree_internal_lookup_in_children_back node key st0 in
+            betree_Node_apply_upserts (Betree_List_Cons (k,
+              Betree_Message_Upsert ufs) l) v key st1 in
+          let* node0 = betree_Internal_lookup_in_children_back node key st0 in
           let* pending0 =
-            betree_node_apply_upserts_back (BetreeListCons (k,
-              BetreeMessageUpsert ufs) l) v key st1 in
+            betree_Node_apply_upserts_back (Betree_List_Cons (k,
+              Betree_Message_Upsert ufs) l) v key st1 in
           let* msgs0 =
-            betree_node_lookup_first_message_for_key_back key msgs pending0 in
-          let* (st3, _) =
-            betree_store_internal_node_fwd node0.betree_internal_id msgs0 st2
-            in
+            betree_Node_lookup_first_message_for_key_back key msgs pending0 in
+          let* (st3, _) = betree_store_internal_node node0.id msgs0 st2 in
           Return (st3, Some v0)
         end
-    | BetreeListNil ->
-      let* (st1, opt) = betree_internal_lookup_in_children_fwd node key st0 in
+    | Betree_List_Nil ->
+      let* (st1, o) = betree_Internal_lookup_in_children node key st0 in
       let* _ =
-        betree_node_lookup_first_message_for_key_back key msgs BetreeListNil in
-      Return (st1, opt)
+        betree_Node_lookup_first_message_for_key_back key msgs Betree_List_Nil
+        in
+      Return (st1, o)
     end
-  | BetreeNodeLeaf node ->
-    let* (st0, bindings) = betree_load_leaf_node_fwd node.betree_leaf_id st in
-    let* opt = betree_node_lookup_in_bindings_fwd key bindings in
-    Return (st0, opt)
+  | Betree_Node_Leaf node ->
+    let* (st0, bindings) = betree_load_leaf_node node.id st in
+    let* o = betree_Node_lookup_in_bindings key bindings in
+    Return (st0, o)
   end
 
 (** [betree_main::betree::Node::{5}::lookup]: backward function 0 *)
-and betree_node_lookup_back
-  (self : betree_node_t) (key : u64) (st : state) :
-  Tot (result betree_node_t)
-  (decreases (betree_node_lookup_decreases self key st))
+and betree_Node_lookup_back
+  (self : betree_Node_t) (key : u64) (st : state) :
+  Tot (result betree_Node_t)
+  (decreases (betree_Node_lookup_decreases self key st))
   =
   begin match self with
-  | BetreeNodeInternal node ->
-    let* (st0, msgs) = betree_load_internal_node_fwd node.betree_internal_id st
-      in
-    let* pending = betree_node_lookup_first_message_for_key_fwd key msgs in
+  | Betree_Node_Internal node ->
+    let* (st0, msgs) = betree_load_internal_node node.id st in
+    let* pending = betree_Node_lookup_first_message_for_key key msgs in
     begin match pending with
-    | BetreeListCons p l ->
+    | Betree_List_Cons p l ->
       let (k, msg) = p in
       if k <> key
       then
         let* _ =
-          betree_node_lookup_first_message_for_key_back key msgs
-            (BetreeListCons (k, msg) l) in
-        let* node0 = betree_internal_lookup_in_children_back node key st0 in
-        Return (BetreeNodeInternal node0)
+          betree_Node_lookup_first_message_for_key_back key msgs
+            (Betree_List_Cons (k, msg) l) in
+        let* node0 = betree_Internal_lookup_in_children_back node key st0 in
+        Return (Betree_Node_Internal node0)
       else
         begin match msg with
-        | BetreeMessageInsert v ->
+        | Betree_Message_Insert v ->
           let* _ =
-            betree_node_lookup_first_message_for_key_back key msgs
-              (BetreeListCons (k, BetreeMessageInsert v) l) in
-          Return (BetreeNodeInternal node)
-        | BetreeMessageDelete ->
+            betree_Node_lookup_first_message_for_key_back key msgs
+              (Betree_List_Cons (k, Betree_Message_Insert v) l) in
+          Return (Betree_Node_Internal node)
+        | Betree_Message_Delete ->
           let* _ =
-            betree_node_lookup_first_message_for_key_back key msgs
-              (BetreeListCons (k, BetreeMessageDelete) l) in
-          Return (BetreeNodeInternal node)
-        | BetreeMessageUpsert ufs ->
-          let* (st1, v) = betree_internal_lookup_in_children_fwd node key st0
-            in
+            betree_Node_lookup_first_message_for_key_back key msgs
+              (Betree_List_Cons (k, Betree_Message_Delete) l) in
+          Return (Betree_Node_Internal node)
+        | Betree_Message_Upsert ufs ->
+          let* (st1, v) = betree_Internal_lookup_in_children node key st0 in
           let* (st2, _) =
-            betree_node_apply_upserts_fwd (BetreeListCons (k,
-              BetreeMessageUpsert ufs) l) v key st1 in
-          let* node0 = betree_internal_lookup_in_children_back node key st0 in
+            betree_Node_apply_upserts (Betree_List_Cons (k,
+              Betree_Message_Upsert ufs) l) v key st1 in
+          let* node0 = betree_Internal_lookup_in_children_back node key st0 in
           let* pending0 =
-            betree_node_apply_upserts_back (BetreeListCons (k,
-              BetreeMessageUpsert ufs) l) v key st1 in
+            betree_Node_apply_upserts_back (Betree_List_Cons (k,
+              Betree_Message_Upsert ufs) l) v key st1 in
           let* msgs0 =
-            betree_node_lookup_first_message_for_key_back key msgs pending0 in
-          let* _ =
-            betree_store_internal_node_fwd node0.betree_internal_id msgs0 st2
-            in
-          Return (BetreeNodeInternal node0)
+            betree_Node_lookup_first_message_for_key_back key msgs pending0 in
+          let* _ = betree_store_internal_node node0.id msgs0 st2 in
+          Return (Betree_Node_Internal node0)
         end
-    | BetreeListNil ->
+    | Betree_List_Nil ->
       let* _ =
-        betree_node_lookup_first_message_for_key_back key msgs BetreeListNil in
-      let* node0 = betree_internal_lookup_in_children_back node key st0 in
-      Return (BetreeNodeInternal node0)
+        betree_Node_lookup_first_message_for_key_back key msgs Betree_List_Nil
+        in
+      let* node0 = betree_Internal_lookup_in_children_back node key st0 in
+      Return (Betree_Node_Internal node0)
     end
-  | BetreeNodeLeaf node ->
-    let* (_, bindings) = betree_load_leaf_node_fwd node.betree_leaf_id st in
-    let* _ = betree_node_lookup_in_bindings_fwd key bindings in
-    Return (BetreeNodeLeaf node)
+  | Betree_Node_Leaf node ->
+    let* (_, bindings) = betree_load_leaf_node node.id st in
+    let* _ = betree_Node_lookup_in_bindings key bindings in
+    Return (Betree_Node_Leaf node)
   end
 
 (** [betree_main::betree::Node::{5}::filter_messages_for_key]: merged forward/backward function
     (there is a single backward function, and the forward function returns ()) *)
-let rec betree_node_filter_messages_for_key_fwd_back
-  (key : u64) (msgs : betree_list_t (u64 & betree_message_t)) :
-  Tot (result (betree_list_t (u64 & betree_message_t)))
-  (decreases (betree_node_filter_messages_for_key_decreases key msgs))
+let rec betree_Node_filter_messages_for_key
+  (key : u64) (msgs : betree_List_t (u64 & betree_Message_t)) :
+  Tot (result (betree_List_t (u64 & betree_Message_t)))
+  (decreases (betree_Node_filter_messages_for_key_decreases key msgs))
   =
   begin match msgs with
-  | BetreeListCons p l ->
+  | Betree_List_Cons p l ->
     let (k, m) = p in
     if k = key
     then
       let* msgs0 =
-        betree_list_pop_front_back (u64 & betree_message_t) (BetreeListCons (k,
-          m) l) in
-      betree_node_filter_messages_for_key_fwd_back key msgs0
-    else Return (BetreeListCons (k, m) l)
-  | BetreeListNil -> Return BetreeListNil
+        betree_List_pop_front_back (u64 & betree_Message_t) (Betree_List_Cons
+          (k, m) l) in
+      betree_Node_filter_messages_for_key key msgs0
+    else Return (Betree_List_Cons (k, m) l)
+  | Betree_List_Nil -> Return Betree_List_Nil
   end
 
 (** [betree_main::betree::Node::{5}::lookup_first_message_after_key]: forward function *)
-let rec betree_node_lookup_first_message_after_key_fwd
-  (key : u64) (msgs : betree_list_t (u64 & betree_message_t)) :
-  Tot (result (betree_list_t (u64 & betree_message_t)))
-  (decreases (betree_node_lookup_first_message_after_key_decreases key msgs))
+let rec betree_Node_lookup_first_message_after_key
+  (key : u64) (msgs : betree_List_t (u64 & betree_Message_t)) :
+  Tot (result (betree_List_t (u64 & betree_Message_t)))
+  (decreases (betree_Node_lookup_first_message_after_key_decreases key msgs))
   =
   begin match msgs with
-  | BetreeListCons p next_msgs ->
+  | Betree_List_Cons p next_msgs ->
     let (k, m) = p in
     if k = key
-    then betree_node_lookup_first_message_after_key_fwd key next_msgs
-    else Return (BetreeListCons (k, m) next_msgs)
-  | BetreeListNil -> Return BetreeListNil
+    then betree_Node_lookup_first_message_after_key key next_msgs
+    else Return (Betree_List_Cons (k, m) next_msgs)
+  | Betree_List_Nil -> Return Betree_List_Nil
   end
 
 (** [betree_main::betree::Node::{5}::lookup_first_message_after_key]: backward function 0 *)
-let rec betree_node_lookup_first_message_after_key_back
-  (key : u64) (msgs : betree_list_t (u64 & betree_message_t))
-  (ret : betree_list_t (u64 & betree_message_t)) :
-  Tot (result (betree_list_t (u64 & betree_message_t)))
-  (decreases (betree_node_lookup_first_message_after_key_decreases key msgs))
+let rec betree_Node_lookup_first_message_after_key_back
+  (key : u64) (msgs : betree_List_t (u64 & betree_Message_t))
+  (ret : betree_List_t (u64 & betree_Message_t)) :
+  Tot (result (betree_List_t (u64 & betree_Message_t)))
+  (decreases (betree_Node_lookup_first_message_after_key_decreases key msgs))
   =
   begin match msgs with
-  | BetreeListCons p next_msgs ->
+  | Betree_List_Cons p next_msgs ->
     let (k, m) = p in
     if k = key
     then
       let* next_msgs0 =
-        betree_node_lookup_first_message_after_key_back key next_msgs ret in
-      Return (BetreeListCons (k, m) next_msgs0)
+        betree_Node_lookup_first_message_after_key_back key next_msgs ret in
+      Return (Betree_List_Cons (k, m) next_msgs0)
     else Return ret
-  | BetreeListNil -> Return ret
+  | Betree_List_Nil -> Return ret
   end
 
 (** [betree_main::betree::Node::{5}::apply_to_internal]: merged forward/backward function
     (there is a single backward function, and the forward function returns ()) *)
-let betree_node_apply_to_internal_fwd_back
-  (msgs : betree_list_t (u64 & betree_message_t)) (key : u64)
-  (new_msg : betree_message_t) :
-  result (betree_list_t (u64 & betree_message_t))
+let betree_Node_apply_to_internal
+  (msgs : betree_List_t (u64 & betree_Message_t)) (key : u64)
+  (new_msg : betree_Message_t) :
+  result (betree_List_t (u64 & betree_Message_t))
   =
-  let* msgs0 = betree_node_lookup_first_message_for_key_fwd key msgs in
-  let* b = betree_list_head_has_key_fwd betree_message_t msgs0 key in
+  let* msgs0 = betree_Node_lookup_first_message_for_key key msgs in
+  let* b = betree_List_head_has_key betree_Message_t msgs0 key in
   if b
   then
     begin match new_msg with
-    | BetreeMessageInsert i ->
-      let* msgs1 = betree_node_filter_messages_for_key_fwd_back key msgs0 in
+    | Betree_Message_Insert i ->
+      let* msgs1 = betree_Node_filter_messages_for_key key msgs0 in
       let* msgs2 =
-        betree_list_push_front_fwd_back (u64 & betree_message_t) msgs1 (key,
-          BetreeMessageInsert i) in
-      betree_node_lookup_first_message_for_key_back key msgs msgs2
-    | BetreeMessageDelete ->
-      let* msgs1 = betree_node_filter_messages_for_key_fwd_back key msgs0 in
+        betree_List_push_front (u64 & betree_Message_t) msgs1 (key,
+          Betree_Message_Insert i) in
+      betree_Node_lookup_first_message_for_key_back key msgs msgs2
+    | Betree_Message_Delete ->
+      let* msgs1 = betree_Node_filter_messages_for_key key msgs0 in
       let* msgs2 =
-        betree_list_push_front_fwd_back (u64 & betree_message_t) msgs1 (key,
-          BetreeMessageDelete) in
-      betree_node_lookup_first_message_for_key_back key msgs msgs2
-    | BetreeMessageUpsert s ->
-      let* p = betree_list_hd_fwd (u64 & betree_message_t) msgs0 in
+        betree_List_push_front (u64 & betree_Message_t) msgs1 (key,
+          Betree_Message_Delete) in
+      betree_Node_lookup_first_message_for_key_back key msgs msgs2
+    | Betree_Message_Upsert s ->
+      let* p = betree_List_hd (u64 & betree_Message_t) msgs0 in
       let (_, m) = p in
       begin match m with
-      | BetreeMessageInsert prev ->
-        let* v = betree_upsert_update_fwd (Some prev) s in
-        let* msgs1 = betree_list_pop_front_back (u64 & betree_message_t) msgs0
+      | Betree_Message_Insert prev ->
+        let* v = betree_upsert_update (Some prev) s in
+        let* msgs1 = betree_List_pop_front_back (u64 & betree_Message_t) msgs0
           in
         let* msgs2 =
-          betree_list_push_front_fwd_back (u64 & betree_message_t) msgs1 (key,
-            BetreeMessageInsert v) in
-        betree_node_lookup_first_message_for_key_back key msgs msgs2
-      | BetreeMessageDelete ->
-        let* v = betree_upsert_update_fwd None s in
-        let* msgs1 = betree_list_pop_front_back (u64 & betree_message_t) msgs0
+          betree_List_push_front (u64 & betree_Message_t) msgs1 (key,
+            Betree_Message_Insert v) in
+        betree_Node_lookup_first_message_for_key_back key msgs msgs2
+      | Betree_Message_Delete ->
+        let* v = betree_upsert_update None s in
+        let* msgs1 = betree_List_pop_front_back (u64 & betree_Message_t) msgs0
           in
         let* msgs2 =
-          betree_list_push_front_fwd_back (u64 & betree_message_t) msgs1 (key,
-            BetreeMessageInsert v) in
-        betree_node_lookup_first_message_for_key_back key msgs msgs2
-      | BetreeMessageUpsert ufs ->
-        let* msgs1 = betree_node_lookup_first_message_after_key_fwd key msgs0
-          in
+          betree_List_push_front (u64 & betree_Message_t) msgs1 (key,
+            Betree_Message_Insert v) in
+        betree_Node_lookup_first_message_for_key_back key msgs msgs2
+      | Betree_Message_Upsert ufs ->
+        let* msgs1 = betree_Node_lookup_first_message_after_key key msgs0 in
         let* msgs2 =
-          betree_list_push_front_fwd_back (u64 & betree_message_t) msgs1 (key,
-            BetreeMessageUpsert s) in
+          betree_List_push_front (u64 & betree_Message_t) msgs1 (key,
+            Betree_Message_Upsert s) in
         let* msgs3 =
-          betree_node_lookup_first_message_after_key_back key msgs0 msgs2 in
-        betree_node_lookup_first_message_for_key_back key msgs msgs3
+          betree_Node_lookup_first_message_after_key_back key msgs0 msgs2 in
+        betree_Node_lookup_first_message_for_key_back key msgs msgs3
       end
     end
   else
     let* msgs1 =
-      betree_list_push_front_fwd_back (u64 & betree_message_t) msgs0 (key,
-        new_msg) in
-    betree_node_lookup_first_message_for_key_back key msgs msgs1
+      betree_List_push_front (u64 & betree_Message_t) msgs0 (key, new_msg) in
+    betree_Node_lookup_first_message_for_key_back key msgs msgs1
 
 (** [betree_main::betree::Node::{5}::apply_messages_to_internal]: merged forward/backward function
     (there is a single backward function, and the forward function returns ()) *)
-let rec betree_node_apply_messages_to_internal_fwd_back
-  (msgs : betree_list_t (u64 & betree_message_t))
-  (new_msgs : betree_list_t (u64 & betree_message_t)) :
-  Tot (result (betree_list_t (u64 & betree_message_t)))
-  (decreases (betree_node_apply_messages_to_internal_decreases msgs new_msgs))
+let rec betree_Node_apply_messages_to_internal
+  (msgs : betree_List_t (u64 & betree_Message_t))
+  (new_msgs : betree_List_t (u64 & betree_Message_t)) :
+  Tot (result (betree_List_t (u64 & betree_Message_t)))
+  (decreases (betree_Node_apply_messages_to_internal_decreases msgs new_msgs))
   =
   begin match new_msgs with
-  | BetreeListCons new_msg new_msgs_tl ->
+  | Betree_List_Cons new_msg new_msgs_tl ->
     let (i, m) = new_msg in
-    let* msgs0 = betree_node_apply_to_internal_fwd_back msgs i m in
-    betree_node_apply_messages_to_internal_fwd_back msgs0 new_msgs_tl
-  | BetreeListNil -> Return msgs
+    let* msgs0 = betree_Node_apply_to_internal msgs i m in
+    betree_Node_apply_messages_to_internal msgs0 new_msgs_tl
+  | Betree_List_Nil -> Return msgs
   end
 
 (** [betree_main::betree::Node::{5}::lookup_mut_in_bindings]: forward function *)
-let rec betree_node_lookup_mut_in_bindings_fwd
-  (key : u64) (bindings : betree_list_t (u64 & u64)) :
-  Tot (result (betree_list_t (u64 & u64)))
-  (decreases (betree_node_lookup_mut_in_bindings_decreases key bindings))
+let rec betree_Node_lookup_mut_in_bindings
+  (key : u64) (bindings : betree_List_t (u64 & u64)) :
+  Tot (result (betree_List_t (u64 & u64)))
+  (decreases (betree_Node_lookup_mut_in_bindings_decreases key bindings))
   =
   begin match bindings with
-  | BetreeListCons hd tl ->
+  | Betree_List_Cons hd tl ->
     let (i, i0) = hd in
     if i >= key
-    then Return (BetreeListCons (i, i0) tl)
-    else betree_node_lookup_mut_in_bindings_fwd key tl
-  | BetreeListNil -> Return BetreeListNil
+    then Return (Betree_List_Cons (i, i0) tl)
+    else betree_Node_lookup_mut_in_bindings key tl
+  | Betree_List_Nil -> Return Betree_List_Nil
   end
 
 (** [betree_main::betree::Node::{5}::lookup_mut_in_bindings]: backward function 0 *)
-let rec betree_node_lookup_mut_in_bindings_back
-  (key : u64) (bindings : betree_list_t (u64 & u64))
-  (ret : betree_list_t (u64 & u64)) :
-  Tot (result (betree_list_t (u64 & u64)))
-  (decreases (betree_node_lookup_mut_in_bindings_decreases key bindings))
+let rec betree_Node_lookup_mut_in_bindings_back
+  (key : u64) (bindings : betree_List_t (u64 & u64))
+  (ret : betree_List_t (u64 & u64)) :
+  Tot (result (betree_List_t (u64 & u64)))
+  (decreases (betree_Node_lookup_mut_in_bindings_decreases key bindings))
   =
   begin match bindings with
-  | BetreeListCons hd tl ->
+  | Betree_List_Cons hd tl ->
     let (i, i0) = hd in
     if i >= key
     then Return ret
     else
-      let* tl0 = betree_node_lookup_mut_in_bindings_back key tl ret in
-      Return (BetreeListCons (i, i0) tl0)
-  | BetreeListNil -> Return ret
+      let* tl0 = betree_Node_lookup_mut_in_bindings_back key tl ret in
+      Return (Betree_List_Cons (i, i0) tl0)
+  | Betree_List_Nil -> Return ret
   end
 
 (** [betree_main::betree::Node::{5}::apply_to_leaf]: merged forward/backward function
     (there is a single backward function, and the forward function returns ()) *)
-let betree_node_apply_to_leaf_fwd_back
-  (bindings : betree_list_t (u64 & u64)) (key : u64)
-  (new_msg : betree_message_t) :
-  result (betree_list_t (u64 & u64))
+let betree_Node_apply_to_leaf
+  (bindings : betree_List_t (u64 & u64)) (key : u64)
+  (new_msg : betree_Message_t) :
+  result (betree_List_t (u64 & u64))
   =
-  let* bindings0 = betree_node_lookup_mut_in_bindings_fwd key bindings in
-  let* b = betree_list_head_has_key_fwd u64 bindings0 key in
+  let* bindings0 = betree_Node_lookup_mut_in_bindings key bindings in
+  let* b = betree_List_head_has_key u64 bindings0 key in
   if b
   then
-    let* hd = betree_list_pop_front_fwd (u64 & u64) bindings0 in
+    let* hd = betree_List_pop_front (u64 & u64) bindings0 in
     begin match new_msg with
-    | BetreeMessageInsert v ->
-      let* bindings1 = betree_list_pop_front_back (u64 & u64) bindings0 in
-      let* bindings2 =
-        betree_list_push_front_fwd_back (u64 & u64) bindings1 (key, v) in
-      betree_node_lookup_mut_in_bindings_back key bindings bindings2
-    | BetreeMessageDelete ->
-      let* bindings1 = betree_list_pop_front_back (u64 & u64) bindings0 in
-      betree_node_lookup_mut_in_bindings_back key bindings bindings1
-    | BetreeMessageUpsert s ->
+    | Betree_Message_Insert v ->
+      let* bindings1 = betree_List_pop_front_back (u64 & u64) bindings0 in
+      let* bindings2 = betree_List_push_front (u64 & u64) bindings1 (key, v) in
+      betree_Node_lookup_mut_in_bindings_back key bindings bindings2
+    | Betree_Message_Delete ->
+      let* bindings1 = betree_List_pop_front_back (u64 & u64) bindings0 in
+      betree_Node_lookup_mut_in_bindings_back key bindings bindings1
+    | Betree_Message_Upsert s ->
       let (_, i) = hd in
-      let* v = betree_upsert_update_fwd (Some i) s in
-      let* bindings1 = betree_list_pop_front_back (u64 & u64) bindings0 in
-      let* bindings2 =
-        betree_list_push_front_fwd_back (u64 & u64) bindings1 (key, v) in
-      betree_node_lookup_mut_in_bindings_back key bindings bindings2
+      let* v = betree_upsert_update (Some i) s in
+      let* bindings1 = betree_List_pop_front_back (u64 & u64) bindings0 in
+      let* bindings2 = betree_List_push_front (u64 & u64) bindings1 (key, v) in
+      betree_Node_lookup_mut_in_bindings_back key bindings bindings2
     end
   else
     begin match new_msg with
-    | BetreeMessageInsert v ->
-      let* bindings1 =
-        betree_list_push_front_fwd_back (u64 & u64) bindings0 (key, v) in
-      betree_node_lookup_mut_in_bindings_back key bindings bindings1
-    | BetreeMessageDelete ->
-      betree_node_lookup_mut_in_bindings_back key bindings bindings0
-    | BetreeMessageUpsert s ->
-      let* v = betree_upsert_update_fwd None s in
-      let* bindings1 =
-        betree_list_push_front_fwd_back (u64 & u64) bindings0 (key, v) in
-      betree_node_lookup_mut_in_bindings_back key bindings bindings1
+    | Betree_Message_Insert v ->
+      let* bindings1 = betree_List_push_front (u64 & u64) bindings0 (key, v) in
+      betree_Node_lookup_mut_in_bindings_back key bindings bindings1
+    | Betree_Message_Delete ->
+      betree_Node_lookup_mut_in_bindings_back key bindings bindings0
+    | Betree_Message_Upsert s ->
+      let* v = betree_upsert_update None s in
+      let* bindings1 = betree_List_push_front (u64 & u64) bindings0 (key, v) in
+      betree_Node_lookup_mut_in_bindings_back key bindings bindings1
     end
 
 (** [betree_main::betree::Node::{5}::apply_messages_to_leaf]: merged forward/backward function
     (there is a single backward function, and the forward function returns ()) *)
-let rec betree_node_apply_messages_to_leaf_fwd_back
-  (bindings : betree_list_t (u64 & u64))
-  (new_msgs : betree_list_t (u64 & betree_message_t)) :
-  Tot (result (betree_list_t (u64 & u64)))
-  (decreases (betree_node_apply_messages_to_leaf_decreases bindings new_msgs))
+let rec betree_Node_apply_messages_to_leaf
+  (bindings : betree_List_t (u64 & u64))
+  (new_msgs : betree_List_t (u64 & betree_Message_t)) :
+  Tot (result (betree_List_t (u64 & u64)))
+  (decreases (betree_Node_apply_messages_to_leaf_decreases bindings new_msgs))
   =
   begin match new_msgs with
-  | BetreeListCons new_msg new_msgs_tl ->
+  | Betree_List_Cons new_msg new_msgs_tl ->
     let (i, m) = new_msg in
-    let* bindings0 = betree_node_apply_to_leaf_fwd_back bindings i m in
-    betree_node_apply_messages_to_leaf_fwd_back bindings0 new_msgs_tl
-  | BetreeListNil -> Return bindings
+    let* bindings0 = betree_Node_apply_to_leaf bindings i m in
+    betree_Node_apply_messages_to_leaf bindings0 new_msgs_tl
+  | Betree_List_Nil -> Return bindings
   end
 
 (** [betree_main::betree::Internal::{4}::flush]: forward function *)
-let rec betree_internal_flush_fwd
-  (self : betree_internal_t) (params : betree_params_t)
-  (node_id_cnt : betree_node_id_counter_t)
-  (content : betree_list_t (u64 & betree_message_t)) (st : state) :
-  Tot (result (state & (betree_list_t (u64 & betree_message_t))))
+let rec betree_Internal_flush
+  (self : betree_Internal_t) (params : betree_Params_t)
+  (node_id_cnt : betree_NodeIdCounter_t)
+  (content : betree_List_t (u64 & betree_Message_t)) (st : state) :
+  Tot (result (state & (betree_List_t (u64 & betree_Message_t))))
   (decreases (
-    betree_internal_flush_decreases self params node_id_cnt content st))
+    betree_Internal_flush_decreases self params node_id_cnt content st))
   =
-  let* p =
-    betree_list_partition_at_pivot_fwd betree_message_t content
-      self.betree_internal_pivot in
+  let* p = betree_List_partition_at_pivot betree_Message_t content self.pivot
+    in
   let (msgs_left, msgs_right) = p in
-  let* len_left = betree_list_len_fwd (u64 & betree_message_t) msgs_left in
-  if len_left >= params.betree_params_min_flush_size
+  let* len_left = betree_List_len (u64 & betree_Message_t) msgs_left in
+  if len_left >= params.min_flush_size
   then
     let* (st0, _) =
-      betree_node_apply_messages_fwd self.betree_internal_left params
-        node_id_cnt msgs_left st in
+      betree_Node_apply_messages self.left params node_id_cnt msgs_left st in
     let* (_, node_id_cnt0) =
-      betree_node_apply_messages_back self.betree_internal_left params
-        node_id_cnt msgs_left st in
-    let* len_right = betree_list_len_fwd (u64 & betree_message_t) msgs_right in
-    if len_right >= params.betree_params_min_flush_size
+      betree_Node_apply_messages_back self.left params node_id_cnt msgs_left st
+      in
+    let* len_right = betree_List_len (u64 & betree_Message_t) msgs_right in
+    if len_right >= params.min_flush_size
     then
       let* (st1, _) =
-        betree_node_apply_messages_fwd self.betree_internal_right params
-          node_id_cnt0 msgs_right st0 in
+        betree_Node_apply_messages self.right params node_id_cnt0 msgs_right
+          st0 in
       let* _ =
-        betree_node_apply_messages_back self.betree_internal_right params
-          node_id_cnt0 msgs_right st0 in
-      Return (st1, BetreeListNil)
+        betree_Node_apply_messages_back self.right params node_id_cnt0
+          msgs_right st0 in
+      Return (st1, Betree_List_Nil)
     else Return (st0, msgs_right)
   else
     let* (st0, _) =
-      betree_node_apply_messages_fwd self.betree_internal_right params
-        node_id_cnt msgs_right st in
+      betree_Node_apply_messages self.right params node_id_cnt msgs_right st in
     let* _ =
-      betree_node_apply_messages_back self.betree_internal_right params
-        node_id_cnt msgs_right st in
+      betree_Node_apply_messages_back self.right params node_id_cnt msgs_right
+        st in
     Return (st0, msgs_left)
 
 (** [betree_main::betree::Internal::{4}::flush]: backward function 0 *)
-and betree_internal_flush_back
-  (self : betree_internal_t) (params : betree_params_t)
-  (node_id_cnt : betree_node_id_counter_t)
-  (content : betree_list_t (u64 & betree_message_t)) (st : state) :
-  Tot (result (betree_internal_t & betree_node_id_counter_t))
+and betree_Internal_flush_back
+  (self : betree_Internal_t) (params : betree_Params_t)
+  (node_id_cnt : betree_NodeIdCounter_t)
+  (content : betree_List_t (u64 & betree_Message_t)) (st : state) :
+  Tot (result (betree_Internal_t & betree_NodeIdCounter_t))
   (decreases (
-    betree_internal_flush_decreases self params node_id_cnt content st))
+    betree_Internal_flush_decreases self params node_id_cnt content st))
   =
-  let* p =
-    betree_list_partition_at_pivot_fwd betree_message_t content
-      self.betree_internal_pivot in
+  let* p = betree_List_partition_at_pivot betree_Message_t content self.pivot
+    in
   let (msgs_left, msgs_right) = p in
-  let* len_left = betree_list_len_fwd (u64 & betree_message_t) msgs_left in
-  if len_left >= params.betree_params_min_flush_size
+  let* len_left = betree_List_len (u64 & betree_Message_t) msgs_left in
+  if len_left >= params.min_flush_size
   then
     let* (st0, _) =
-      betree_node_apply_messages_fwd self.betree_internal_left params
-        node_id_cnt msgs_left st in
+      betree_Node_apply_messages self.left params node_id_cnt msgs_left st in
     let* (n, node_id_cnt0) =
-      betree_node_apply_messages_back self.betree_internal_left params
-        node_id_cnt msgs_left st in
-    let* len_right = betree_list_len_fwd (u64 & betree_message_t) msgs_right in
-    if len_right >= params.betree_params_min_flush_size
+      betree_Node_apply_messages_back self.left params node_id_cnt msgs_left st
+      in
+    let* len_right = betree_List_len (u64 & betree_Message_t) msgs_right in
+    if len_right >= params.min_flush_size
     then
       let* (n0, node_id_cnt1) =
-        betree_node_apply_messages_back self.betree_internal_right params
-          node_id_cnt0 msgs_right st0 in
-      Return
-        ({ self with betree_internal_left = n; betree_internal_right = n0 },
-        node_id_cnt1)
-    else Return ({ self with betree_internal_left = n }, node_id_cnt0)
+        betree_Node_apply_messages_back self.right params node_id_cnt0
+          msgs_right st0 in
+      Return ({ self with left = n; right = n0 }, node_id_cnt1)
+    else Return ({ self with left = n }, node_id_cnt0)
   else
     let* (n, node_id_cnt0) =
-      betree_node_apply_messages_back self.betree_internal_right params
-        node_id_cnt msgs_right st in
-    Return ({ self with betree_internal_right = n }, node_id_cnt0)
+      betree_Node_apply_messages_back self.right params node_id_cnt msgs_right
+        st in
+    Return ({ self with right = n }, node_id_cnt0)
 
 (** [betree_main::betree::Node::{5}::apply_messages]: forward function *)
-and betree_node_apply_messages_fwd
-  (self : betree_node_t) (params : betree_params_t)
-  (node_id_cnt : betree_node_id_counter_t)
-  (msgs : betree_list_t (u64 & betree_message_t)) (st : state) :
+and betree_Node_apply_messages
+  (self : betree_Node_t) (params : betree_Params_t)
+  (node_id_cnt : betree_NodeIdCounter_t)
+  (msgs : betree_List_t (u64 & betree_Message_t)) (st : state) :
   Tot (result (state & unit))
   (decreases (
-    betree_node_apply_messages_decreases self params node_id_cnt msgs st))
+    betree_Node_apply_messages_decreases self params node_id_cnt msgs st))
   =
   begin match self with
-  | BetreeNodeInternal node ->
-    let* (st0, content) =
-      betree_load_internal_node_fwd node.betree_internal_id st in
-    let* content0 =
-      betree_node_apply_messages_to_internal_fwd_back content msgs in
-    let* num_msgs = betree_list_len_fwd (u64 & betree_message_t) content0 in
-    if num_msgs >= params.betree_params_min_flush_size
+  | Betree_Node_Internal node ->
+    let* (st0, content) = betree_load_internal_node node.id st in
+    let* content0 = betree_Node_apply_messages_to_internal content msgs in
+    let* num_msgs = betree_List_len (u64 & betree_Message_t) content0 in
+    if num_msgs >= params.min_flush_size
     then
       let* (st1, content1) =
-        betree_internal_flush_fwd node params node_id_cnt content0 st0 in
+        betree_Internal_flush node params node_id_cnt content0 st0 in
       let* (node0, _) =
-        betree_internal_flush_back node params node_id_cnt content0 st0 in
-      let* (st2, _) =
-        betree_store_internal_node_fwd node0.betree_internal_id content1 st1 in
+        betree_Internal_flush_back node params node_id_cnt content0 st0 in
+      let* (st2, _) = betree_store_internal_node node0.id content1 st1 in
       Return (st2, ())
     else
-      let* (st1, _) =
-        betree_store_internal_node_fwd node.betree_internal_id content0 st0 in
+      let* (st1, _) = betree_store_internal_node node.id content0 st0 in
       Return (st1, ())
-  | BetreeNodeLeaf node ->
-    let* (st0, content) = betree_load_leaf_node_fwd node.betree_leaf_id st in
-    let* content0 = betree_node_apply_messages_to_leaf_fwd_back content msgs in
-    let* len = betree_list_len_fwd (u64 & u64) content0 in
-    let* i = u64_mul 2 params.betree_params_split_size in
+  | Betree_Node_Leaf node ->
+    let* (st0, content) = betree_load_leaf_node node.id st in
+    let* content0 = betree_Node_apply_messages_to_leaf content msgs in
+    let* len = betree_List_len (u64 & u64) content0 in
+    let* i = u64_mul 2 params.split_size in
     if len >= i
     then
-      let* (st1, _) =
-        betree_leaf_split_fwd node content0 params node_id_cnt st0 in
-      let* (st2, _) =
-        betree_store_leaf_node_fwd node.betree_leaf_id BetreeListNil st1 in
+      let* (st1, _) = betree_Leaf_split node content0 params node_id_cnt st0 in
+      let* (st2, _) = betree_store_leaf_node node.id Betree_List_Nil st1 in
       Return (st2, ())
     else
-      let* (st1, _) =
-        betree_store_leaf_node_fwd node.betree_leaf_id content0 st0 in
+      let* (st1, _) = betree_store_leaf_node node.id content0 st0 in
       Return (st1, ())
   end
 
 (** [betree_main::betree::Node::{5}::apply_messages]: backward function 0 *)
-and betree_node_apply_messages_back
-  (self : betree_node_t) (params : betree_params_t)
-  (node_id_cnt : betree_node_id_counter_t)
-  (msgs : betree_list_t (u64 & betree_message_t)) (st : state) :
-  Tot (result (betree_node_t & betree_node_id_counter_t))
+and betree_Node_apply_messages_back
+  (self : betree_Node_t) (params : betree_Params_t)
+  (node_id_cnt : betree_NodeIdCounter_t)
+  (msgs : betree_List_t (u64 & betree_Message_t)) (st : state) :
+  Tot (result (betree_Node_t & betree_NodeIdCounter_t))
   (decreases (
-    betree_node_apply_messages_decreases self params node_id_cnt msgs st))
+    betree_Node_apply_messages_decreases self params node_id_cnt msgs st))
   =
   begin match self with
-  | BetreeNodeInternal node ->
-    let* (st0, content) =
-      betree_load_internal_node_fwd node.betree_internal_id st in
-    let* content0 =
-      betree_node_apply_messages_to_internal_fwd_back content msgs in
-    let* num_msgs = betree_list_len_fwd (u64 & betree_message_t) content0 in
-    if num_msgs >= params.betree_params_min_flush_size
+  | Betree_Node_Internal node ->
+    let* (st0, content) = betree_load_internal_node node.id st in
+    let* content0 = betree_Node_apply_messages_to_internal content msgs in
+    let* num_msgs = betree_List_len (u64 & betree_Message_t) content0 in
+    if num_msgs >= params.min_flush_size
     then
       let* (st1, content1) =
-        betree_internal_flush_fwd node params node_id_cnt content0 st0 in
+        betree_Internal_flush node params node_id_cnt content0 st0 in
       let* (node0, node_id_cnt0) =
-        betree_internal_flush_back node params node_id_cnt content0 st0 in
-      let* _ =
-        betree_store_internal_node_fwd node0.betree_internal_id content1 st1 in
-      Return (BetreeNodeInternal node0, node_id_cnt0)
+        betree_Internal_flush_back node params node_id_cnt content0 st0 in
+      let* _ = betree_store_internal_node node0.id content1 st1 in
+      Return (Betree_Node_Internal node0, node_id_cnt0)
     else
-      let* _ =
-        betree_store_internal_node_fwd node.betree_internal_id content0 st0 in
-      Return (BetreeNodeInternal node, node_id_cnt)
-  | BetreeNodeLeaf node ->
-    let* (st0, content) = betree_load_leaf_node_fwd node.betree_leaf_id st in
-    let* content0 = betree_node_apply_messages_to_leaf_fwd_back content msgs in
-    let* len = betree_list_len_fwd (u64 & u64) content0 in
-    let* i = u64_mul 2 params.betree_params_split_size in
+      let* _ = betree_store_internal_node node.id content0 st0 in
+      Return (Betree_Node_Internal node, node_id_cnt)
+  | Betree_Node_Leaf node ->
+    let* (st0, content) = betree_load_leaf_node node.id st in
+    let* content0 = betree_Node_apply_messages_to_leaf content msgs in
+    let* len = betree_List_len (u64 & u64) content0 in
+    let* i = u64_mul 2 params.split_size in
     if len >= i
     then
       let* (st1, new_node) =
-        betree_leaf_split_fwd node content0 params node_id_cnt st0 in
-      let* _ = betree_store_leaf_node_fwd node.betree_leaf_id BetreeListNil st1
-        in
+        betree_Leaf_split node content0 params node_id_cnt st0 in
+      let* _ = betree_store_leaf_node node.id Betree_List_Nil st1 in
       let* node_id_cnt0 =
-        betree_leaf_split_back node content0 params node_id_cnt st0 in
-      Return (BetreeNodeInternal new_node, node_id_cnt0)
+        betree_Leaf_split_back node content0 params node_id_cnt st0 in
+      Return (Betree_Node_Internal new_node, node_id_cnt0)
     else
-      let* _ = betree_store_leaf_node_fwd node.betree_leaf_id content0 st0 in
-      Return (BetreeNodeLeaf { node with betree_leaf_size = len }, node_id_cnt)
+      let* _ = betree_store_leaf_node node.id content0 st0 in
+      Return (Betree_Node_Leaf { node with size = len }, node_id_cnt)
   end
 
 (** [betree_main::betree::Node::{5}::apply]: forward function *)
-let betree_node_apply_fwd
-  (self : betree_node_t) (params : betree_params_t)
-  (node_id_cnt : betree_node_id_counter_t) (key : u64)
-  (new_msg : betree_message_t) (st : state) :
+let betree_Node_apply
+  (self : betree_Node_t) (params : betree_Params_t)
+  (node_id_cnt : betree_NodeIdCounter_t) (key : u64)
+  (new_msg : betree_Message_t) (st : state) :
   result (state & unit)
   =
-  let l = BetreeListNil in
+  let l = Betree_List_Nil in
   let* (st0, _) =
-    betree_node_apply_messages_fwd self params node_id_cnt (BetreeListCons
-      (key, new_msg) l) st in
+    betree_Node_apply_messages self params node_id_cnt (Betree_List_Cons (key,
+      new_msg) l) st in
   let* _ =
-    betree_node_apply_messages_back self params node_id_cnt (BetreeListCons
+    betree_Node_apply_messages_back self params node_id_cnt (Betree_List_Cons
       (key, new_msg) l) st in
   Return (st0, ())
 
 (** [betree_main::betree::Node::{5}::apply]: backward function 0 *)
-let betree_node_apply_back
-  (self : betree_node_t) (params : betree_params_t)
-  (node_id_cnt : betree_node_id_counter_t) (key : u64)
-  (new_msg : betree_message_t) (st : state) :
-  result (betree_node_t & betree_node_id_counter_t)
+let betree_Node_apply_back
+  (self : betree_Node_t) (params : betree_Params_t)
+  (node_id_cnt : betree_NodeIdCounter_t) (key : u64)
+  (new_msg : betree_Message_t) (st : state) :
+  result (betree_Node_t & betree_NodeIdCounter_t)
   =
-  let l = BetreeListNil in
-  betree_node_apply_messages_back self params node_id_cnt (BetreeListCons (key,
-    new_msg) l) st
+  let l = Betree_List_Nil in
+  betree_Node_apply_messages_back self params node_id_cnt (Betree_List_Cons
+    (key, new_msg) l) st
 
 (** [betree_main::betree::BeTree::{6}::new]: forward function *)
-let betree_be_tree_new_fwd
+let betree_BeTree_new
   (min_flush_size : u64) (split_size : u64) (st : state) :
-  result (state & betree_be_tree_t)
+  result (state & betree_BeTree_t)
   =
-  let* node_id_cnt = betree_node_id_counter_new_fwd in
-  let* id = betree_node_id_counter_fresh_id_fwd node_id_cnt in
-  let* (st0, _) = betree_store_leaf_node_fwd id BetreeListNil st in
-  let* node_id_cnt0 = betree_node_id_counter_fresh_id_back node_id_cnt in
+  let* node_id_cnt = betree_NodeIdCounter_new in
+  let* id = betree_NodeIdCounter_fresh_id node_id_cnt in
+  let* (st0, _) = betree_store_leaf_node id Betree_List_Nil st in
+  let* node_id_cnt0 = betree_NodeIdCounter_fresh_id_back node_id_cnt in
   Return (st0,
     {
-      betree_be_tree_params =
-        {
-          betree_params_min_flush_size = min_flush_size;
-          betree_params_split_size = split_size
-        };
-      betree_be_tree_node_id_cnt = node_id_cnt0;
-      betree_be_tree_root =
-        (BetreeNodeLeaf { betree_leaf_id = id; betree_leaf_size = 0 })
+      params = { min_flush_size = min_flush_size; split_size = split_size };
+      node_id_cnt = node_id_cnt0;
+      root = (Betree_Node_Leaf { id = id; size = 0 })
     })
 
 (** [betree_main::betree::BeTree::{6}::apply]: forward function *)
-let betree_be_tree_apply_fwd
-  (self : betree_be_tree_t) (key : u64) (msg : betree_message_t) (st : state) :
+let betree_BeTree_apply
+  (self : betree_BeTree_t) (key : u64) (msg : betree_Message_t) (st : state) :
   result (state & unit)
   =
   let* (st0, _) =
-    betree_node_apply_fwd self.betree_be_tree_root self.betree_be_tree_params
-      self.betree_be_tree_node_id_cnt key msg st in
+    betree_Node_apply self.root self.params self.node_id_cnt key msg st in
   let* _ =
-    betree_node_apply_back self.betree_be_tree_root self.betree_be_tree_params
-      self.betree_be_tree_node_id_cnt key msg st in
+    betree_Node_apply_back self.root self.params self.node_id_cnt key msg st in
   Return (st0, ())
 
 (** [betree_main::betree::BeTree::{6}::apply]: backward function 0 *)
-let betree_be_tree_apply_back
-  (self : betree_be_tree_t) (key : u64) (msg : betree_message_t) (st : state) :
-  result betree_be_tree_t
+let betree_BeTree_apply_back
+  (self : betree_BeTree_t) (key : u64) (msg : betree_Message_t) (st : state) :
+  result betree_BeTree_t
   =
   let* (n, nic) =
-    betree_node_apply_back self.betree_be_tree_root self.betree_be_tree_params
-      self.betree_be_tree_node_id_cnt key msg st in
-  Return
-    { self with betree_be_tree_node_id_cnt = nic; betree_be_tree_root = n }
+    betree_Node_apply_back self.root self.params self.node_id_cnt key msg st in
+  Return { self with node_id_cnt = nic; root = n }
 
 (** [betree_main::betree::BeTree::{6}::insert]: forward function *)
-let betree_be_tree_insert_fwd
-  (self : betree_be_tree_t) (key : u64) (value : u64) (st : state) :
+let betree_BeTree_insert
+  (self : betree_BeTree_t) (key : u64) (value : u64) (st : state) :
   result (state & unit)
   =
-  let* (st0, _) =
-    betree_be_tree_apply_fwd self key (BetreeMessageInsert value) st in
-  let* _ = betree_be_tree_apply_back self key (BetreeMessageInsert value) st in
+  let* (st0, _) = betree_BeTree_apply self key (Betree_Message_Insert value) st
+    in
+  let* _ = betree_BeTree_apply_back self key (Betree_Message_Insert value) st
+    in
   Return (st0, ())
 
 (** [betree_main::betree::BeTree::{6}::insert]: backward function 0 *)
-let betree_be_tree_insert_back
-  (self : betree_be_tree_t) (key : u64) (value : u64) (st : state) :
-  result betree_be_tree_t
+let betree_BeTree_insert_back
+  (self : betree_BeTree_t) (key : u64) (value : u64) (st : state) :
+  result betree_BeTree_t
   =
-  betree_be_tree_apply_back self key (BetreeMessageInsert value) st
+  betree_BeTree_apply_back self key (Betree_Message_Insert value) st
 
 (** [betree_main::betree::BeTree::{6}::delete]: forward function *)
-let betree_be_tree_delete_fwd
-  (self : betree_be_tree_t) (key : u64) (st : state) : result (state & unit) =
-  let* (st0, _) = betree_be_tree_apply_fwd self key BetreeMessageDelete st in
-  let* _ = betree_be_tree_apply_back self key BetreeMessageDelete st in
+let betree_BeTree_delete
+  (self : betree_BeTree_t) (key : u64) (st : state) : result (state & unit) =
+  let* (st0, _) = betree_BeTree_apply self key Betree_Message_Delete st in
+  let* _ = betree_BeTree_apply_back self key Betree_Message_Delete st in
   Return (st0, ())
 
 (** [betree_main::betree::BeTree::{6}::delete]: backward function 0 *)
-let betree_be_tree_delete_back
-  (self : betree_be_tree_t) (key : u64) (st : state) :
-  result betree_be_tree_t
-  =
-  betree_be_tree_apply_back self key BetreeMessageDelete st
+let betree_BeTree_delete_back
+  (self : betree_BeTree_t) (key : u64) (st : state) : result betree_BeTree_t =
+  betree_BeTree_apply_back self key Betree_Message_Delete st
 
 (** [betree_main::betree::BeTree::{6}::upsert]: forward function *)
-let betree_be_tree_upsert_fwd
-  (self : betree_be_tree_t) (key : u64) (upd : betree_upsert_fun_state_t)
+let betree_BeTree_upsert
+  (self : betree_BeTree_t) (key : u64) (upd : betree_UpsertFunState_t)
   (st : state) :
   result (state & unit)
   =
-  let* (st0, _) =
-    betree_be_tree_apply_fwd self key (BetreeMessageUpsert upd) st in
-  let* _ = betree_be_tree_apply_back self key (BetreeMessageUpsert upd) st in
+  let* (st0, _) = betree_BeTree_apply self key (Betree_Message_Upsert upd) st
+    in
+  let* _ = betree_BeTree_apply_back self key (Betree_Message_Upsert upd) st in
   Return (st0, ())
 
 (** [betree_main::betree::BeTree::{6}::upsert]: backward function 0 *)
-let betree_be_tree_upsert_back
-  (self : betree_be_tree_t) (key : u64) (upd : betree_upsert_fun_state_t)
+let betree_BeTree_upsert_back
+  (self : betree_BeTree_t) (key : u64) (upd : betree_UpsertFunState_t)
   (st : state) :
-  result betree_be_tree_t
+  result betree_BeTree_t
   =
-  betree_be_tree_apply_back self key (BetreeMessageUpsert upd) st
+  betree_BeTree_apply_back self key (Betree_Message_Upsert upd) st
 
 (** [betree_main::betree::BeTree::{6}::lookup]: forward function *)
-let betree_be_tree_lookup_fwd
-  (self : betree_be_tree_t) (key : u64) (st : state) :
+let betree_BeTree_lookup
+  (self : betree_BeTree_t) (key : u64) (st : state) :
   result (state & (option u64))
   =
-  betree_node_lookup_fwd self.betree_be_tree_root key st
+  betree_Node_lookup self.root key st
 
 (** [betree_main::betree::BeTree::{6}::lookup]: backward function 0 *)
-let betree_be_tree_lookup_back
-  (self : betree_be_tree_t) (key : u64) (st : state) :
-  result betree_be_tree_t
-  =
-  let* n = betree_node_lookup_back self.betree_be_tree_root key st in
-  Return { self with betree_be_tree_root = n }
+let betree_BeTree_lookup_back
+  (self : betree_BeTree_t) (key : u64) (st : state) : result betree_BeTree_t =
+  let* n = betree_Node_lookup_back self.root key st in
+  Return { self with root = n }
 
 (** [betree_main::main]: forward function *)
-let main_fwd : result unit =
+let main : result unit =
   Return ()
 
 (** Unit test for [betree_main::main] *)
-let _ = assert_norm (main_fwd = Return ())
+let _ = assert_norm (main = Return ())
 
diff --git a/tests/fstar/betree/BetreeMain.Opaque.fsti b/tests/fstar/betree/BetreeMain.Opaque.fsti
index c33cf225..c5d0a814 100644
--- a/tests/fstar/betree/BetreeMain.Opaque.fsti
+++ b/tests/fstar/betree/BetreeMain.Opaque.fsti
@@ -7,24 +7,24 @@ include BetreeMain.Types
 #set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
 
 (** [betree_main::betree_utils::load_internal_node]: forward function *)
-val betree_utils_load_internal_node_fwd
-  : u64 -> state -> result (state & (betree_list_t (u64 & betree_message_t)))
+val betree_utils_load_internal_node
+  : u64 -> state -> result (state & (betree_List_t (u64 & betree_Message_t)))
 
 (** [betree_main::betree_utils::store_internal_node]: forward function *)
-val betree_utils_store_internal_node_fwd
+val betree_utils_store_internal_node
   :
-  u64 -> betree_list_t (u64 & betree_message_t) -> state -> result (state &
+  u64 -> betree_List_t (u64 & betree_Message_t) -> state -> result (state &
     unit)
 
 (** [betree_main::betree_utils::load_leaf_node]: forward function *)
-val betree_utils_load_leaf_node_fwd
-  : u64 -> state -> result (state & (betree_list_t (u64 & u64)))
+val betree_utils_load_leaf_node
+  : u64 -> state -> result (state & (betree_List_t (u64 & u64)))
 
 (** [betree_main::betree_utils::store_leaf_node]: forward function *)
-val betree_utils_store_leaf_node_fwd
-  : u64 -> betree_list_t (u64 & u64) -> state -> result (state & unit)
+val betree_utils_store_leaf_node
+  : u64 -> betree_List_t (u64 & u64) -> state -> result (state & unit)
 
 (** [core::option::Option::{0}::unwrap]: forward function *)
-val core_option_option_unwrap_fwd
+val core_option_Option_unwrap
   (t : Type0) : option t -> state -> result (state & t)
 
diff --git a/tests/fstar/betree/BetreeMain.Types.fsti b/tests/fstar/betree/BetreeMain.Types.fsti
index a937c726..9320f6b7 100644
--- a/tests/fstar/betree/BetreeMain.Types.fsti
+++ b/tests/fstar/betree/BetreeMain.Types.fsti
@@ -6,53 +6,47 @@ open Primitives
 #set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
 
 (** [betree_main::betree::List] *)
-type betree_list_t (t : Type0) =
-| BetreeListCons : t -> betree_list_t t -> betree_list_t t
-| BetreeListNil : betree_list_t t
+type betree_List_t (t : Type0) =
+| Betree_List_Cons : t -> betree_List_t t -> betree_List_t t
+| Betree_List_Nil : betree_List_t t
 
 (** [betree_main::betree::UpsertFunState] *)
-type betree_upsert_fun_state_t =
-| BetreeUpsertFunStateAdd : u64 -> betree_upsert_fun_state_t
-| BetreeUpsertFunStateSub : u64 -> betree_upsert_fun_state_t
+type betree_UpsertFunState_t =
+| Betree_UpsertFunState_Add : u64 -> betree_UpsertFunState_t
+| Betree_UpsertFunState_Sub : u64 -> betree_UpsertFunState_t
 
 (** [betree_main::betree::Message] *)
-type betree_message_t =
-| BetreeMessageInsert : u64 -> betree_message_t
-| BetreeMessageDelete : betree_message_t
-| BetreeMessageUpsert : betree_upsert_fun_state_t -> betree_message_t
+type betree_Message_t =
+| Betree_Message_Insert : u64 -> betree_Message_t
+| Betree_Message_Delete : betree_Message_t
+| Betree_Message_Upsert : betree_UpsertFunState_t -> betree_Message_t
 
 (** [betree_main::betree::Leaf] *)
-type betree_leaf_t = { betree_leaf_id : u64; betree_leaf_size : u64; }
+type betree_Leaf_t = { id : u64; size : u64; }
 
 (** [betree_main::betree::Internal] *)
-type betree_internal_t =
+type betree_Internal_t =
 {
-  betree_internal_id : u64;
-  betree_internal_pivot : u64;
-  betree_internal_left : betree_node_t;
-  betree_internal_right : betree_node_t;
+  id : u64; pivot : u64; left : betree_Node_t; right : betree_Node_t;
 }
 
 (** [betree_main::betree::Node] *)
-and betree_node_t =
-| BetreeNodeInternal : betree_internal_t -> betree_node_t
-| BetreeNodeLeaf : betree_leaf_t -> betree_node_t
+and betree_Node_t =
+| Betree_Node_Internal : betree_Internal_t -> betree_Node_t
+| Betree_Node_Leaf : betree_Leaf_t -> betree_Node_t
 
 (** [betree_main::betree::Params] *)
-type betree_params_t =
-{
-  betree_params_min_flush_size : u64; betree_params_split_size : u64;
-}
+type betree_Params_t = { min_flush_size : u64; split_size : u64; }
 
 (** [betree_main::betree::NodeIdCounter] *)
-type betree_node_id_counter_t = { betree_node_id_counter_next_node_id : u64; }
+type betree_NodeIdCounter_t = { next_node_id : u64; }
 
 (** [betree_main::betree::BeTree] *)
-type betree_be_tree_t =
+type betree_BeTree_t =
 {
-  betree_be_tree_params : betree_params_t;
-  betree_be_tree_node_id_cnt : betree_node_id_counter_t;
-  betree_be_tree_root : betree_node_t;
+  params : betree_Params_t;
+  node_id_cnt : betree_NodeIdCounter_t;
+  root : betree_Node_t;
 }
 
 (** The state type used in the state-error monad *)
diff --git a/tests/fstar/betree/Primitives.fst b/tests/fstar/betree/Primitives.fst
index 9db82069..3297803c 100644
--- a/tests/fstar/betree/Primitives.fst
+++ b/tests/fstar/betree/Primitives.fst
@@ -55,8 +55,12 @@ type string = string
 let is_zero (n: nat) : bool = n = 0
 let decrease (n: nat{n > 0}) : nat = n - 1
 
-let mem_replace_fwd (a : Type0) (x : a) (y : a) : a = x
-let mem_replace_back (a : Type0) (x : a) (y : a) : a = y
+let core_mem_replace (a : Type0) (x : a) (y : a) : a = x
+let core_mem_replace_back (a : Type0) (x : a) (y : a) : a = y
+
+// We don't really use raw pointers for now
+type mut_raw_ptr (t : Type0) = { v : t }
+type const_raw_ptr (t : Type0) = { v : t }
 
 (*** Scalars *)
 /// Rem.: most of the following code was partially generated
@@ -100,6 +104,11 @@ type scalar_ty =
 | U64
 | U128
 
+let is_unsigned = function
+  | Isize | I8 | I16 | I32 | I64 | I128 -> false
+  | Usize | U8 | U16 | U32 | U64 | U128 -> true
+
+
 let scalar_min (ty : scalar_ty) : int =
   match ty with
   | Isize -> isize_min
@@ -162,6 +171,15 @@ let scalar_sub (#ty : scalar_ty) (x : scalar ty) (y : scalar ty) : result (scala
 let scalar_mul (#ty : scalar_ty) (x : scalar ty) (y : scalar ty) : result (scalar ty) =
   mk_scalar ty (x * y)
 
+let scalar_lxor (#ty : scalar_ty { is_unsigned ty && ty <> Usize })
+    (x : scalar ty) (y : scalar ty) : scalar ty =
+  match ty with
+  | U8 -> FStar.UInt.logxor #8 x y
+  | U16 -> FStar.UInt.logxor #16 x y
+  | U32 -> FStar.UInt.logxor #32 x y
+  | U64 -> FStar.UInt.logxor #64 x y
+  | U128 -> FStar.UInt.logxor #128 x y
+
 (** Cast an integer from a [src_ty] to a [tgt_ty] *)
 // TODO: check the semantics of casts in Rust
 let scalar_cast (src_ty : scalar_ty) (tgt_ty : scalar_ty) (x : scalar src_ty) : result (scalar tgt_ty) =
@@ -169,17 +187,44 @@ let scalar_cast (src_ty : scalar_ty) (tgt_ty : scalar_ty) (x : scalar src_ty) :
 
 /// The scalar types
 type isize : eqtype = scalar Isize
-type i8 : eqtype = scalar I8
-type i16 : eqtype = scalar I16
-type i32 : eqtype = scalar I32
-type i64 : eqtype = scalar I64
-type i128 : eqtype = scalar I128
+type i8    : eqtype = scalar I8
+type i16   : eqtype = scalar I16
+type i32   : eqtype = scalar I32
+type i64   : eqtype = scalar I64
+type i128  : eqtype = scalar I128
 type usize : eqtype = scalar Usize
-type u8 : eqtype = scalar U8
-type u16 : eqtype = scalar U16
-type u32 : eqtype = scalar U32
-type u64 : eqtype = scalar U64
-type u128 : eqtype = scalar U128
+type u8    : eqtype = scalar U8
+type u16   : eqtype = scalar U16
+type u32   : eqtype = scalar U32
+type u64   : eqtype = scalar U64
+type u128  : eqtype = scalar U128
+
+
+let core_isize_min : isize = isize_min
+let core_isize_max : isize = isize_max
+let core_i8_min    : i8 = i8_min
+let core_i8_max    : i8 = i8_max
+let core_i16_min   : i16 = i16_min
+let core_i16_max   : i16 = i16_max
+let core_i32_min   : i32 = i32_min
+let core_i32_max   : i32 = i32_max
+let core_i64_min   : i64 = i64_min
+let core_i64_max   : i64 = i64_max
+let core_i128_min  : i128 = i128_min
+let core_i128_max  : i128 = i128_max
+
+let core_usize_min : usize = usize_min
+let core_usize_max : usize = usize_max
+let core_u8_min    : u8 = u8_min
+let core_u8_max    : u8 = u8_max
+let core_u16_min   : u16 = u16_min
+let core_u16_max   : u16 = u16_max
+let core_u32_min   : u32 = u32_min
+let core_u32_max   : u32 = u32_max
+let core_u64_min   : u64 = u64_min
+let core_u64_max   : u64 = u64_max
+let core_u128_min  : u128 = u128_min
+let core_u128_max  : u128 = u128_max
 
 /// Negation
 let isize_neg = scalar_neg #Isize
@@ -231,7 +276,7 @@ let u32_add = scalar_add #U32
 let u64_add = scalar_add #U64
 let u128_add = scalar_add #U128
 
-/// Substraction
+/// Subtraction
 let isize_sub = scalar_sub #Isize
 let i8_sub = scalar_sub #I8
 let i16_sub = scalar_sub #I16
@@ -259,12 +304,65 @@ let u32_mul = scalar_mul #U32
 let u64_mul = scalar_mul #U64
 let u128_mul = scalar_mul #U128
 
-(*** Range *)
-type range (a : Type0) = {
+/// Logical operators, defined for unsigned types only, so far
+let u8_xor = scalar_lxor #U8
+let u16_xor = scalar_lxor #U16
+let u32_xor = scalar_lxor #U32
+let u64_xor = scalar_lxor #U64
+let u128_xor = scalar_lxor #U128
+
+(*** core::ops *)
+
+// Trait declaration: [core::ops::index::Index]
+noeq type core_ops_index_Index (self idx : Type0) = {
+  output : Type0;
+  index : self → idx → result output
+}
+
+// Trait declaration: [core::ops::index::IndexMut]
+noeq type core_ops_index_IndexMut (self idx : Type0) = {
+  indexInst : core_ops_index_Index self idx;
+  index_mut : self → idx → result indexInst.output;
+  index_mut_back : self → idx → indexInst.output → result self;
+}
+
+// Trait declaration [core::ops::deref::Deref]
+noeq type core_ops_deref_Deref (self : Type0) = {
+  target : Type0;
+  deref : self → result target;
+}
+
+// Trait declaration [core::ops::deref::DerefMut]
+noeq type core_ops_deref_DerefMut (self : Type0) = {
+  derefInst : core_ops_deref_Deref self;
+  deref_mut : self → result derefInst.target;
+  deref_mut_back : self → derefInst.target → result self;
+}
+
+type core_ops_range_Range (a : Type0) = {
   start : a;
   end_ : a;
 }
 
+(*** [alloc] *)
+
+let alloc_boxed_Box_deref (t : Type0) (x : t) : result t = Return x
+let alloc_boxed_Box_deref_mut (t : Type0) (x : t) : result t = Return x
+let alloc_boxed_Box_deref_mut_back (t : Type) (_ : t) (x : t) : result t = Return x
+
+// Trait instance
+let alloc_boxed_Box_coreOpsDerefInst (self : Type0) : core_ops_deref_Deref self = {
+  target = self;
+  deref = alloc_boxed_Box_deref self;
+}
+
+// Trait instance
+let alloc_boxed_Box_coreOpsDerefMutInst (self : Type0) : core_ops_deref_DerefMut self = {
+  derefInst = alloc_boxed_Box_coreOpsDerefInst self;
+  deref_mut = alloc_boxed_Box_deref_mut self;
+  deref_mut_back = alloc_boxed_Box_deref_mut_back self;
+}
+
 (*** Array *)
 type array (a : Type0) (n : usize) = s:list a{length s = n}
 
@@ -278,15 +376,11 @@ let mk_array (a : Type0) (n : usize)
   normalize_term_spec (FStar.List.Tot.length l);
   l
 
-let array_index_shared (a : Type0) (n : usize) (x : array a n) (i : usize) : result a =
-  if i < length x then Return (index x i)
-  else Fail Failure
-
-let array_index_mut_fwd (a : Type0) (n : usize) (x : array a n) (i : usize) : result a =
+let array_index_usize (a : Type0) (n : usize) (x : array a n) (i : usize) : result a =
   if i < length x then Return (index x i)
   else Fail Failure
 
-let array_index_mut_back (a : Type0) (n : usize) (x : array a n) (i : usize) (nx : a) : result (array a n) =
+let array_update_usize (a : Type0) (n : usize) (x : array a n) (i : usize) (nx : a) : result (array a n) =
   if i < length x then Return (list_update x i nx)
   else Fail Failure
 
@@ -295,55 +389,54 @@ type slice (a : Type0) = s:list a{length s <= usize_max}
 
 let slice_len (a : Type0) (s : slice a) : usize = length s
 
-let slice_index_shared (a : Type0) (x : slice a) (i : usize) : result a =
+let slice_index_usize (a : Type0) (x : slice a) (i : usize) : result a =
   if i < length x then Return (index x i)
   else Fail Failure
 
-let slice_index_mut_fwd (a : Type0) (x : slice a) (i : usize) : result a =
-  if i < length x then Return (index x i)
-  else Fail Failure
-
-let slice_index_mut_back (a : Type0) (x : slice a) (i : usize) (nx : a) : result (slice a) =
+let slice_update_usize (a : Type0) (x : slice a) (i : usize) (nx : a) : result (slice a) =
   if i < length x then Return (list_update x i nx)
   else Fail Failure
 
 (*** Subslices *)
 
-let array_to_slice_shared (a : Type0) (n : usize) (x : array a n) : result (slice a) = Return x
-let array_to_slice_mut_fwd (a : Type0) (n : usize) (x : array a n) : result (slice a) = Return x
-let array_to_slice_mut_back (a : Type0) (n : usize) (x : array a n) (s : slice a) : result (array a n) =
+let array_to_slice (a : Type0) (n : usize) (x : array a n) : result (slice a) = Return x
+let array_from_slice (a : Type0) (n : usize) (x : array a n) (s : slice a) : result (array a n) =
   if length s = n then Return s
   else Fail Failure
 
 // TODO: finish the definitions below (there lacks [List.drop] and [List.take] in the standard library *)
-let array_subslice_shared (a : Type0) (n : usize) (x : array a n) (r : range usize) : result (slice a) =
-  admit()
-
-let array_subslice_mut_fwd (a : Type0) (n : usize) (x : array a n) (r : range usize) : result (slice a) =
+let array_subslice (a : Type0) (n : usize) (x : array a n) (r : core_ops_range_Range usize) : result (slice a) =
   admit()
 
-let array_subslice_mut_back (a : Type0) (n : usize) (x : array a n) (r : range usize) (ns : slice a) : result (array a n) =
+let array_update_subslice (a : Type0) (n : usize) (x : array a n) (r : core_ops_range_Range usize) (ns : slice a) : result (array a n) =
   admit()
 
-let slice_subslice_shared (a : Type0) (x : slice a) (r : range usize) : result (slice a) =
+let array_repeat (a : Type0) (n : usize) (x : a) : array a n =
   admit()
 
-let slice_subslice_mut_fwd (a : Type0) (x : slice a) (r : range usize) : result (slice a) =
+let slice_subslice (a : Type0) (x : slice a) (r : core_ops_range_Range usize) : result (slice a) =
   admit()
 
-let slice_subslice_mut_back (a : Type0) (x : slice a) (r : range usize) (ns : slice a) : result (slice a) =
+let slice_update_subslice (a : Type0) (x : slice a) (r : core_ops_range_Range usize) (ns : slice a) : result (slice a) =
   admit()
 
 (*** Vector *)
-type vec (a : Type0) = v:list a{length v <= usize_max}
+type alloc_vec_Vec (a : Type0) = v:list a{length v <= usize_max}
 
-let vec_new (a  : Type0) : vec a = assert_norm(length #a [] == 0); []
-let vec_len (a : Type0) (v : vec a) : usize = length v
+let alloc_vec_Vec_new (a  : Type0) : alloc_vec_Vec a = assert_norm(length #a [] == 0); []
+let alloc_vec_Vec_len (a : Type0) (v : alloc_vec_Vec a) : usize = length v
+
+// Helper
+let alloc_vec_Vec_index_usize (#a : Type0) (v : alloc_vec_Vec a) (i : usize) : result a =
+  if i < length v then Return (index v i) else Fail Failure
+// Helper
+let alloc_vec_Vec_update_usize (#a : Type0) (v : alloc_vec_Vec a) (i : usize) (x : a) : result (alloc_vec_Vec a) =
+  if i < length v then Return (list_update v i x) else Fail Failure
 
 // The **forward** function shouldn't be used
-let vec_push_fwd (a  : Type0) (v : vec a) (x : a) : unit = ()
-let vec_push_back (a  : Type0) (v : vec a) (x : a) :
-  Pure (result (vec a))
+let alloc_vec_Vec_push_fwd (a  : Type0) (v : alloc_vec_Vec a) (x : a) : unit = ()
+let alloc_vec_Vec_push (a  : Type0) (v : alloc_vec_Vec a) (x : a) :
+  Pure (result (alloc_vec_Vec a))
   (requires True)
   (ensures (fun res ->
     match res with
@@ -358,18 +451,279 @@ let vec_push_back (a  : Type0) (v : vec a) (x : a) :
   else Fail Failure
 
 // The **forward** function shouldn't be used
-let vec_insert_fwd (a : Type0) (v : vec a) (i : usize) (x : a) : result unit =
+let alloc_vec_Vec_insert_fwd (a : Type0) (v : alloc_vec_Vec a) (i : usize) (x : a) : result unit =
   if i < length v then Return () else Fail Failure
-let vec_insert_back (a : Type0) (v : vec a) (i : usize) (x : a) : result (vec a) =
+let alloc_vec_Vec_insert (a : Type0) (v : alloc_vec_Vec a) (i : usize) (x : a) : result (alloc_vec_Vec a) =
   if i < length v then Return (list_update v i x) else Fail Failure
 
-// The **backward** function shouldn't be used
-let vec_index_fwd (a : Type0) (v : vec a) (i : usize) : result a =
-  if i < length v then Return (index v i) else Fail Failure
-let vec_index_back (a : Type0) (v : vec a) (i : usize) (x : a) : result unit =
-  if i < length v then Return () else Fail Failure
+// Trait declaration: [core::slice::index::private_slice_index::Sealed]
+type core_slice_index_private_slice_index_Sealed (self : Type0) = unit
+
+// Trait declaration: [core::slice::index::SliceIndex]
+noeq type core_slice_index_SliceIndex (self t : Type0) = {
+  sealedInst : core_slice_index_private_slice_index_Sealed self;
+  output : Type0;
+  get : self → t → result (option output);
+  get_mut : self → t → result (option output);
+  get_mut_back : self → t → option output → result t;
+  get_unchecked : self → const_raw_ptr t → result (const_raw_ptr output);
+  get_unchecked_mut : self → mut_raw_ptr t → result (mut_raw_ptr output);
+  index : self → t → result output;
+  index_mut : self → t → result output;
+  index_mut_back : self → t → output → result t;
+}
 
-let vec_index_mut_fwd (a : Type0) (v : vec a) (i : usize) : result a =
-  if i < length v then Return (index v i) else Fail Failure
-let vec_index_mut_back (a : Type0) (v : vec a) (i : usize) (nx : a) : result (vec a) =
-  if i < length v then Return (list_update v i nx) else Fail Failure
+// [core::slice::index::[T]::index]: forward function
+let core_slice_index_Slice_index
+  (t idx : Type0) (inst : core_slice_index_SliceIndex idx (slice t))
+  (s : slice t) (i : idx) : result inst.output =
+  let* x = inst.get i s in
+  match x with
+  | None -> Fail Failure
+  | Some x -> Return x
+
+// [core::slice::index::Range:::get]: forward function
+let core_slice_index_Range_get (t : Type0) (i : core_ops_range_Range usize) (s : slice t) :
+  result (option (slice t)) =
+  admit () // TODO
+
+// [core::slice::index::Range::get_mut]: forward function
+let core_slice_index_Range_get_mut
+  (t : Type0) : core_ops_range_Range usize → slice t → result (option (slice t)) =
+  admit () // TODO
+
+// [core::slice::index::Range::get_mut]: backward function 0
+let core_slice_index_Range_get_mut_back
+  (t : Type0) :
+  core_ops_range_Range usize → slice t → option (slice t) → result (slice t) =
+  admit () // TODO
+
+// [core::slice::index::Range::get_unchecked]: forward function
+let core_slice_index_Range_get_unchecked
+  (t : Type0) :
+  core_ops_range_Range usize → const_raw_ptr (slice t) → result (const_raw_ptr (slice t)) =
+  // Don't know what the model should be - for now we always fail to make
+  // sure code which uses it fails
+  fun _ _ -> Fail Failure
+
+// [core::slice::index::Range::get_unchecked_mut]: forward function
+let core_slice_index_Range_get_unchecked_mut
+  (t : Type0) :
+  core_ops_range_Range usize → mut_raw_ptr (slice t) → result (mut_raw_ptr (slice t)) =
+  // Don't know what the model should be - for now we always fail to make
+  // sure code which uses it fails
+  fun _ _ -> Fail Failure
+
+// [core::slice::index::Range::index]: forward function
+let core_slice_index_Range_index
+  (t : Type0) : core_ops_range_Range usize → slice t → result (slice t) =
+  admit () // TODO
+
+// [core::slice::index::Range::index_mut]: forward function
+let core_slice_index_Range_index_mut
+  (t : Type0) : core_ops_range_Range usize → slice t → result (slice t) =
+  admit () // TODO
+
+// [core::slice::index::Range::index_mut]: backward function 0
+let core_slice_index_Range_index_mut_back
+  (t : Type0) : core_ops_range_Range usize → slice t → slice t → result (slice t) =
+  admit () // TODO
+
+// [core::slice::index::[T]::index_mut]: forward function
+let core_slice_index_Slice_index_mut
+  (t idx : Type0) (inst : core_slice_index_SliceIndex idx (slice t)) :
+  slice t → idx → result inst.output =
+  admit () // 
+
+// [core::slice::index::[T]::index_mut]: backward function 0
+let core_slice_index_Slice_index_mut_back
+  (t idx : Type0) (inst : core_slice_index_SliceIndex idx (slice t)) :
+  slice t → idx → inst.output → result (slice t) =
+  admit () // TODO
+
+// [core::array::[T; N]::index]: forward function
+let core_array_Array_index
+  (t idx : Type0) (n : usize) (inst : core_ops_index_Index (slice t) idx)
+  (a : array t n) (i : idx) : result inst.output =
+  admit () // TODO
+
+// [core::array::[T; N]::index_mut]: forward function
+let core_array_Array_index_mut
+  (t idx : Type0) (n : usize) (inst : core_ops_index_IndexMut (slice t) idx)
+  (a : array t n) (i : idx) : result inst.indexInst.output =
+  admit () // TODO
+
+// [core::array::[T; N]::index_mut]: backward function 0
+let core_array_Array_index_mut_back
+  (t idx : Type0) (n : usize) (inst : core_ops_index_IndexMut (slice t) idx)
+  (a : array t n) (i : idx) (x : inst.indexInst.output) : result (array t n) =
+  admit () // TODO
+
+// Trait implementation: [core::slice::index::[T]]
+let core_slice_index_Slice_coreopsindexIndexInst (t idx : Type0)
+  (inst : core_slice_index_SliceIndex idx (slice t)) :
+  core_ops_index_Index (slice t) idx = {
+  output = inst.output;
+  index = core_slice_index_Slice_index t idx inst;
+}
+
+// Trait implementation: [core::slice::index::private_slice_index::Range]
+let core_slice_index_private_slice_index_Range_coresliceindexprivate_slice_indexSealedInst
+  : core_slice_index_private_slice_index_Sealed (core_ops_range_Range usize) = ()
+
+// Trait implementation: [core::slice::index::Range]
+let core_slice_index_Range_coresliceindexSliceIndexInst (t : Type0) :
+  core_slice_index_SliceIndex (core_ops_range_Range usize) (slice t) = {
+  sealedInst = core_slice_index_private_slice_index_Range_coresliceindexprivate_slice_indexSealedInst;
+  output = slice t;
+  get = core_slice_index_Range_get t;
+  get_mut = core_slice_index_Range_get_mut t;
+  get_mut_back = core_slice_index_Range_get_mut_back t;
+  get_unchecked = core_slice_index_Range_get_unchecked t;
+  get_unchecked_mut = core_slice_index_Range_get_unchecked_mut t;
+  index = core_slice_index_Range_index t;
+  index_mut = core_slice_index_Range_index_mut t;
+  index_mut_back = core_slice_index_Range_index_mut_back t;
+}
+
+// Trait implementation: [core::slice::index::[T]]
+let core_slice_index_Slice_coreopsindexIndexMutInst (t idx : Type0)
+  (inst : core_slice_index_SliceIndex idx (slice t)) :
+  core_ops_index_IndexMut (slice t) idx = {
+  indexInst = core_slice_index_Slice_coreopsindexIndexInst t idx inst;
+  index_mut = core_slice_index_Slice_index_mut t idx inst;
+  index_mut_back = core_slice_index_Slice_index_mut_back t idx inst;
+}
+
+// Trait implementation: [core::array::[T; N]]
+let core_array_Array_coreopsindexIndexInst (t idx : Type0) (n : usize)
+  (inst : core_ops_index_Index (slice t) idx) :
+  core_ops_index_Index (array t n) idx = {
+  output = inst.output;
+  index = core_array_Array_index t idx n inst;
+}
+
+// Trait implementation: [core::array::[T; N]]
+let core_array_Array_coreopsindexIndexMutInst (t idx : Type0) (n : usize)
+  (inst : core_ops_index_IndexMut (slice t) idx) :
+  core_ops_index_IndexMut (array t n) idx = {
+  indexInst = core_array_Array_coreopsindexIndexInst t idx n inst.indexInst;
+  index_mut = core_array_Array_index_mut t idx n inst;
+  index_mut_back = core_array_Array_index_mut_back t idx n inst;
+}
+
+// [core::slice::index::usize::get]: forward function
+let core_slice_index_usize_get
+  (t : Type0) : usize → slice t → result (option t) =
+  admit () // TODO
+
+// [core::slice::index::usize::get_mut]: forward function
+let core_slice_index_usize_get_mut
+  (t : Type0) : usize → slice t → result (option t) =
+  admit () // TODO
+
+// [core::slice::index::usize::get_mut]: backward function 0
+let core_slice_index_usize_get_mut_back
+  (t : Type0) : usize → slice t → option t → result (slice t) =
+  admit () // TODO
+
+// [core::slice::index::usize::get_unchecked]: forward function
+let core_slice_index_usize_get_unchecked
+  (t : Type0) : usize → const_raw_ptr (slice t) → result (const_raw_ptr t) =
+  admit () // TODO
+
+// [core::slice::index::usize::get_unchecked_mut]: forward function
+let core_slice_index_usize_get_unchecked_mut
+  (t : Type0) : usize → mut_raw_ptr (slice t) → result (mut_raw_ptr t) =
+  admit () // TODO
+
+// [core::slice::index::usize::index]: forward function
+let core_slice_index_usize_index (t : Type0) : usize → slice t → result t =
+  admit () // TODO
+
+// [core::slice::index::usize::index_mut]: forward function
+let core_slice_index_usize_index_mut (t : Type0) : usize → slice t → result t =
+  admit () // TODO
+
+// [core::slice::index::usize::index_mut]: backward function 0
+let core_slice_index_usize_index_mut_back
+  (t : Type0) : usize → slice t → t → result (slice t) =
+  admit () // TODO
+
+// Trait implementation: [core::slice::index::private_slice_index::usize]
+let core_slice_index_private_slice_index_usize_coresliceindexprivate_slice_indexSealedInst
+  : core_slice_index_private_slice_index_Sealed usize = ()
+
+// Trait implementation: [core::slice::index::usize]
+let core_slice_index_usize_coresliceindexSliceIndexInst (t : Type0) :
+  core_slice_index_SliceIndex usize (slice t) = {
+  sealedInst = core_slice_index_private_slice_index_usize_coresliceindexprivate_slice_indexSealedInst;
+  output = t;
+  get = core_slice_index_usize_get t;
+  get_mut = core_slice_index_usize_get_mut t;
+  get_mut_back = core_slice_index_usize_get_mut_back t;
+  get_unchecked = core_slice_index_usize_get_unchecked t;
+  get_unchecked_mut = core_slice_index_usize_get_unchecked_mut t;
+  index = core_slice_index_usize_index t;
+  index_mut = core_slice_index_usize_index_mut t;
+  index_mut_back = core_slice_index_usize_index_mut_back t;
+}
+
+// [alloc::vec::Vec::index]: forward function
+let alloc_vec_Vec_index (t idx : Type0) (inst : core_slice_index_SliceIndex idx (slice t))
+  (self : alloc_vec_Vec t) (i : idx) : result inst.output =
+  admit () // TODO
+
+// [alloc::vec::Vec::index_mut]: forward function
+let alloc_vec_Vec_index_mut (t idx : Type0) (inst : core_slice_index_SliceIndex idx (slice t))
+  (self : alloc_vec_Vec t) (i : idx) : result inst.output =
+  admit () // TODO
+
+// [alloc::vec::Vec::index_mut]: backward function 0
+let alloc_vec_Vec_index_mut_back
+  (t idx : Type0) (inst : core_slice_index_SliceIndex idx (slice t))
+  (self : alloc_vec_Vec t) (i : idx) (x : inst.output) : result (alloc_vec_Vec t) =
+  admit () // TODO
+
+// Trait implementation: [alloc::vec::Vec]
+let alloc_vec_Vec_coreopsindexIndexInst (t idx : Type0)
+  (inst : core_slice_index_SliceIndex idx (slice t)) :
+  core_ops_index_Index (alloc_vec_Vec t) idx = {
+  output = inst.output;
+  index = alloc_vec_Vec_index t idx inst;
+}
+
+// Trait implementation: [alloc::vec::Vec]
+let alloc_vec_Vec_coreopsindexIndexMutInst (t idx : Type0)
+  (inst : core_slice_index_SliceIndex idx (slice t)) :
+  core_ops_index_IndexMut (alloc_vec_Vec t) idx = {
+  indexInst = alloc_vec_Vec_coreopsindexIndexInst t idx inst;
+  index_mut = alloc_vec_Vec_index_mut t idx inst;
+  index_mut_back = alloc_vec_Vec_index_mut_back t idx inst;
+}
+
+(*** Theorems *)
+
+let alloc_vec_Vec_index_eq (#a : Type0) (v : alloc_vec_Vec a) (i : usize) :
+  Lemma (
+    alloc_vec_Vec_index a usize (core_slice_index_usize_coresliceindexSliceIndexInst a) v i ==
+      alloc_vec_Vec_index_usize v i)
+  [SMTPat (alloc_vec_Vec_index a usize (core_slice_index_usize_coresliceindexSliceIndexInst a) v i)]
+  =
+  admit()
+
+let alloc_vec_Vec_index_mut_eq (#a : Type0) (v : alloc_vec_Vec a) (i : usize) :
+  Lemma (
+    alloc_vec_Vec_index_mut a usize (core_slice_index_usize_coresliceindexSliceIndexInst a) v i ==
+      alloc_vec_Vec_index_usize v i)
+  [SMTPat (alloc_vec_Vec_index_mut a usize (core_slice_index_usize_coresliceindexSliceIndexInst a) v i)]
+  =
+  admit()
+
+let alloc_vec_Vec_index_mut_back_eq (#a : Type0) (v : alloc_vec_Vec a) (i : usize) (x : a) :
+  Lemma (
+    alloc_vec_Vec_index_mut_back a usize (core_slice_index_usize_coresliceindexSliceIndexInst a) v i x ==
+      alloc_vec_Vec_update_usize v i x)
+  [SMTPat (alloc_vec_Vec_index_mut_back a usize (core_slice_index_usize_coresliceindexSliceIndexInst a) v i x)]
+  =
+  admit()
diff --git a/tests/fstar/betree_back_stateful/BetreeMain.Clauses.Template.fst b/tests/fstar/betree_back_stateful/BetreeMain.Clauses.Template.fst
index 823df03a..8722f0bf 100644
--- a/tests/fstar/betree_back_stateful/BetreeMain.Clauses.Template.fst
+++ b/tests/fstar/betree_back_stateful/BetreeMain.Clauses.Template.fst
@@ -8,95 +8,95 @@ open BetreeMain.Types
 
 (** [betree_main::betree::List::{1}::len]: decreases clause *)
 unfold
-let betree_list_len_decreases (t : Type0) (self : betree_list_t t) : nat =
+let betree_List_len_decreases (t : Type0) (self : betree_List_t t) : nat =
   admit ()
 
 (** [betree_main::betree::List::{1}::split_at]: decreases clause *)
 unfold
-let betree_list_split_at_decreases (t : Type0) (self : betree_list_t t)
+let betree_List_split_at_decreases (t : Type0) (self : betree_List_t t)
   (n : u64) : nat =
   admit ()
 
 (** [betree_main::betree::List::{2}::partition_at_pivot]: decreases clause *)
 unfold
-let betree_list_partition_at_pivot_decreases (t : Type0)
-  (self : betree_list_t (u64 & t)) (pivot : u64) : nat =
+let betree_List_partition_at_pivot_decreases (t : Type0)
+  (self : betree_List_t (u64 & t)) (pivot : u64) : nat =
   admit ()
 
 (** [betree_main::betree::Node::{5}::lookup_first_message_for_key]: decreases clause *)
 unfold
-let betree_node_lookup_first_message_for_key_decreases (key : u64)
-  (msgs : betree_list_t (u64 & betree_message_t)) : nat =
+let betree_Node_lookup_first_message_for_key_decreases (key : u64)
+  (msgs : betree_List_t (u64 & betree_Message_t)) : nat =
   admit ()
 
 (** [betree_main::betree::Node::{5}::apply_upserts]: decreases clause *)
 unfold
-let betree_node_apply_upserts_decreases
-  (msgs : betree_list_t (u64 & betree_message_t)) (prev : option u64)
+let betree_Node_apply_upserts_decreases
+  (msgs : betree_List_t (u64 & betree_Message_t)) (prev : option u64)
   (key : u64) (st : state) : nat =
   admit ()
 
 (** [betree_main::betree::Node::{5}::lookup_in_bindings]: decreases clause *)
 unfold
-let betree_node_lookup_in_bindings_decreases (key : u64)
-  (bindings : betree_list_t (u64 & u64)) : nat =
+let betree_Node_lookup_in_bindings_decreases (key : u64)
+  (bindings : betree_List_t (u64 & u64)) : nat =
   admit ()
 
 (** [betree_main::betree::Internal::{4}::lookup_in_children]: decreases clause *)
 unfold
-let betree_internal_lookup_in_children_decreases (self : betree_internal_t)
+let betree_Internal_lookup_in_children_decreases (self : betree_Internal_t)
   (key : u64) (st : state) : nat =
   admit ()
 
 (** [betree_main::betree::Node::{5}::lookup]: decreases clause *)
 unfold
-let betree_node_lookup_decreases (self : betree_node_t) (key : u64)
+let betree_Node_lookup_decreases (self : betree_Node_t) (key : u64)
   (st : state) : nat =
   admit ()
 
 (** [betree_main::betree::Node::{5}::filter_messages_for_key]: decreases clause *)
 unfold
-let betree_node_filter_messages_for_key_decreases (key : u64)
-  (msgs : betree_list_t (u64 & betree_message_t)) : nat =
+let betree_Node_filter_messages_for_key_decreases (key : u64)
+  (msgs : betree_List_t (u64 & betree_Message_t)) : nat =
   admit ()
 
 (** [betree_main::betree::Node::{5}::lookup_first_message_after_key]: decreases clause *)
 unfold
-let betree_node_lookup_first_message_after_key_decreases (key : u64)
-  (msgs : betree_list_t (u64 & betree_message_t)) : nat =
+let betree_Node_lookup_first_message_after_key_decreases (key : u64)
+  (msgs : betree_List_t (u64 & betree_Message_t)) : nat =
   admit ()
 
 (** [betree_main::betree::Node::{5}::apply_messages_to_internal]: decreases clause *)
 unfold
-let betree_node_apply_messages_to_internal_decreases
-  (msgs : betree_list_t (u64 & betree_message_t))
-  (new_msgs : betree_list_t (u64 & betree_message_t)) : nat =
+let betree_Node_apply_messages_to_internal_decreases
+  (msgs : betree_List_t (u64 & betree_Message_t))
+  (new_msgs : betree_List_t (u64 & betree_Message_t)) : nat =
   admit ()
 
 (** [betree_main::betree::Node::{5}::lookup_mut_in_bindings]: decreases clause *)
 unfold
-let betree_node_lookup_mut_in_bindings_decreases (key : u64)
-  (bindings : betree_list_t (u64 & u64)) : nat =
+let betree_Node_lookup_mut_in_bindings_decreases (key : u64)
+  (bindings : betree_List_t (u64 & u64)) : nat =
   admit ()
 
 (** [betree_main::betree::Node::{5}::apply_messages_to_leaf]: decreases clause *)
 unfold
-let betree_node_apply_messages_to_leaf_decreases
-  (bindings : betree_list_t (u64 & u64))
-  (new_msgs : betree_list_t (u64 & betree_message_t)) : nat =
+let betree_Node_apply_messages_to_leaf_decreases
+  (bindings : betree_List_t (u64 & u64))
+  (new_msgs : betree_List_t (u64 & betree_Message_t)) : nat =
   admit ()
 
 (** [betree_main::betree::Internal::{4}::flush]: decreases clause *)
 unfold
-let betree_internal_flush_decreases (self : betree_internal_t)
-  (params : betree_params_t) (node_id_cnt : betree_node_id_counter_t)
-  (content : betree_list_t (u64 & betree_message_t)) (st : state) : nat =
+let betree_Internal_flush_decreases (self : betree_Internal_t)
+  (params : betree_Params_t) (node_id_cnt : betree_NodeIdCounter_t)
+  (content : betree_List_t (u64 & betree_Message_t)) (st : state) : nat =
   admit ()
 
 (** [betree_main::betree::Node::{5}::apply_messages]: decreases clause *)
 unfold
-let betree_node_apply_messages_decreases (self : betree_node_t)
-  (params : betree_params_t) (node_id_cnt : betree_node_id_counter_t)
-  (msgs : betree_list_t (u64 & betree_message_t)) (st : state) : nat =
+let betree_Node_apply_messages_decreases (self : betree_Node_t)
+  (params : betree_Params_t) (node_id_cnt : betree_NodeIdCounter_t)
+  (msgs : betree_List_t (u64 & betree_Message_t)) (st : state) : nat =
   admit ()
 
diff --git a/tests/fstar/betree_back_stateful/BetreeMain.Clauses.fst b/tests/fstar/betree_back_stateful/BetreeMain.Clauses.fst
index 07484711..cda7b920 100644
--- a/tests/fstar/betree_back_stateful/BetreeMain.Clauses.fst
+++ b/tests/fstar/betree_back_stateful/BetreeMain.Clauses.fst
@@ -8,8 +8,8 @@ open BetreeMain.Types
 (*** Well-founded relations *)
 
 (* We had a few issues when proving termination of the mutually recursive functions:
- * - betree_internal_flush
- * - betree_node_apply_messages
+ * - betree_Internal_flush
+ * - betree_Node_apply_messages
  *
  * The quantity which effectively decreases is:
  *   (betree_size, messages_length)
@@ -103,108 +103,108 @@ let wf_nat_pair_lem (p0 p1 : nat_pair) :
 
 (** [betree_main::betree::List::{1}::len]: decreases clause *)
 unfold
-let betree_list_len_decreases (t : Type0) (self : betree_list_t t) : betree_list_t t =
+let betree_List_len_decreases (t : Type0) (self : betree_List_t t) : betree_List_t t =
   self
 
 (** [betree_main::betree::List::{1}::split_at]: decreases clause *)
 unfold
-let betree_list_split_at_decreases (t : Type0) (self : betree_list_t t)
+let betree_List_split_at_decreases (t : Type0) (self : betree_List_t t)
   (n : u64) : nat =
   n
 
 (** [betree_main::betree::List::{2}::partition_at_pivot]: decreases clause *)
 unfold
-let betree_list_partition_at_pivot_decreases (t : Type0)
-  (self : betree_list_t (u64 & t)) (pivot : u64) : betree_list_t (u64 & t) =
+let betree_List_partition_at_pivot_decreases (t : Type0)
+  (self : betree_List_t (u64 & t)) (pivot : u64) : betree_List_t (u64 & t) =
   self
 
 (** [betree_main::betree::Node::{5}::lookup_in_bindings]: decreases clause *)
 unfold
-let betree_node_lookup_in_bindings_decreases (key : u64)
-  (bindings : betree_list_t (u64 & u64)) : betree_list_t (u64 & u64) =
+let betree_Node_lookup_in_bindings_decreases (key : u64)
+  (bindings : betree_List_t (u64 & u64)) : betree_List_t (u64 & u64) =
   bindings
 
 (** [betree_main::betree::Node::{5}::lookup_first_message_for_key]: decreases clause *)
 unfold
-let betree_node_lookup_first_message_for_key_decreases (key : u64)
-  (msgs : betree_list_t (u64 & betree_message_t)) : betree_list_t (u64 & betree_message_t) =
+let betree_Node_lookup_first_message_for_key_decreases (key : u64)
+  (msgs : betree_List_t (u64 & betree_Message_t)) : betree_List_t (u64 & betree_Message_t) =
   msgs
 
 (** [betree_main::betree::Node::{5}::apply_upserts]: decreases clause *)
 unfold
-let betree_node_apply_upserts_decreases
-  (msgs : betree_list_t (u64 & betree_message_t)) (prev : option u64)
-  (key : u64) (st : state) : betree_list_t (u64 & betree_message_t) =
+let betree_Node_apply_upserts_decreases
+  (msgs : betree_List_t (u64 & betree_Message_t)) (prev : option u64)
+  (key : u64) (st : state) : betree_List_t (u64 & betree_Message_t) =
   msgs
 
 (** [betree_main::betree::Internal::{4}::lookup_in_children]: decreases clause *)
 unfold
-let betree_internal_lookup_in_children_decreases (self : betree_internal_t)
-  (key : u64) (st : state) : betree_internal_t =
+let betree_Internal_lookup_in_children_decreases (self : betree_Internal_t)
+  (key : u64) (st : state) : betree_Internal_t =
   self
 
 (** [betree_main::betree::Node::{5}::lookup]: decreases clause *)
 unfold
-let betree_node_lookup_decreases (self : betree_node_t) (key : u64)
-  (st : state) : betree_node_t =
+let betree_Node_lookup_decreases (self : betree_Node_t) (key : u64)
+  (st : state) : betree_Node_t =
   self
 
 (** [betree_main::betree::Node::{5}::lookup_mut_in_bindings]: decreases clause *)
 unfold
-let betree_node_lookup_mut_in_bindings_decreases (key : u64)
-  (bindings : betree_list_t (u64 & u64)) : betree_list_t (u64 & u64) =
+let betree_Node_lookup_mut_in_bindings_decreases (key : u64)
+  (bindings : betree_List_t (u64 & u64)) : betree_List_t (u64 & u64) =
   bindings
 
 unfold
-let betree_node_apply_messages_to_leaf_decreases
-  (bindings : betree_list_t (u64 & u64))
-  (new_msgs : betree_list_t (u64 & betree_message_t)) : betree_list_t (u64 & betree_message_t) =
+let betree_Node_apply_messages_to_leaf_decreases
+  (bindings : betree_List_t (u64 & u64))
+  (new_msgs : betree_List_t (u64 & betree_Message_t)) : betree_List_t (u64 & betree_Message_t) =
   new_msgs
 
 (** [betree_main::betree::Node::{5}::filter_messages_for_key]: decreases clause *)
 unfold
-let betree_node_filter_messages_for_key_decreases (key : u64)
-  (msgs : betree_list_t (u64 & betree_message_t)) : betree_list_t (u64 & betree_message_t) =
+let betree_Node_filter_messages_for_key_decreases (key : u64)
+  (msgs : betree_List_t (u64 & betree_Message_t)) : betree_List_t (u64 & betree_Message_t) =
   msgs
 
 (** [betree_main::betree::Node::{5}::lookup_first_message_after_key]: decreases clause *)
 unfold
-let betree_node_lookup_first_message_after_key_decreases (key : u64)
-  (msgs : betree_list_t (u64 & betree_message_t)) : betree_list_t (u64 & betree_message_t) =
+let betree_Node_lookup_first_message_after_key_decreases (key : u64)
+  (msgs : betree_List_t (u64 & betree_Message_t)) : betree_List_t (u64 & betree_Message_t) =
   msgs
 
-let betree_node_apply_messages_to_internal_decreases
-  (msgs : betree_list_t (u64 & betree_message_t))
-  (new_msgs : betree_list_t (u64 & betree_message_t)) : betree_list_t (u64 & betree_message_t) =
+let betree_Node_apply_messages_to_internal_decreases
+  (msgs : betree_List_t (u64 & betree_Message_t))
+  (new_msgs : betree_List_t (u64 & betree_Message_t)) : betree_List_t (u64 & betree_Message_t) =
   new_msgs
 
 (*** Decrease clauses - nat_pair *)
 /// The following decrease clauses use the [nat_pair] definition and the well-founded
 /// relation proven above.
 
-let rec betree_size (bt : betree_node_t) : nat =
+let rec betree_size (bt : betree_Node_t) : nat =
   match bt with
-  | BetreeNodeInternal node -> 1 + betree_internal_size node
-  | BetreeNodeLeaf _ -> 1
+  | Betree_Node_Internal node -> 1 + betree_Internal_size node
+  | Betree_Node_Leaf _ -> 1
 
-and betree_internal_size (node : betree_internal_t) : nat =
-  1 + betree_size node.betree_internal_left + betree_size node.betree_internal_right
+and betree_Internal_size (node : betree_Internal_t) : nat =
+  1 + betree_size node.left + betree_size node.right
 
-let rec betree_list_len (#a : Type0) (ls : betree_list_t a) : nat =
+let rec betree_List_len (#a : Type0) (ls : betree_List_t a) : nat =
   match ls with
-  | BetreeListCons _ tl -> 1 + betree_list_len tl
-  | BetreeListNil -> 0
+  | Betree_List_Cons _ tl -> 1 + betree_List_len tl
+  | Betree_List_Nil -> 0
 
 (** [betree_main::betree::Internal::{4}::flush]: decreases clause *)
 unfold
-let betree_internal_flush_decreases (self : betree_internal_t)
-  (params : betree_params_t) (node_id_cnt : betree_node_id_counter_t)
-  (content : betree_list_t (u64 & betree_message_t)) (st : state) : nat_pair =
-  (|betree_internal_size self, 0|)
+let betree_Internal_flush_decreases (self : betree_Internal_t)
+  (params : betree_Params_t) (node_id_cnt : betree_NodeIdCounter_t)
+  (content : betree_List_t (u64 & betree_Message_t)) (st : state) : nat_pair =
+  (|betree_Internal_size self, 0|)
 
 (** [betree_main::betree::Node::{5}::apply_messages]: decreases clause *)
 unfold
-let betree_node_apply_messages_decreases (self : betree_node_t)
-  (params : betree_params_t) (node_id_cnt : betree_node_id_counter_t)
-  (msgs : betree_list_t (u64 & betree_message_t)) (st : state) : nat_pair =
-  (|betree_size self, betree_list_len msgs|)
+let betree_Node_apply_messages_decreases (self : betree_Node_t)
+  (params : betree_Params_t) (node_id_cnt : betree_NodeIdCounter_t)
+  (msgs : betree_List_t (u64 & betree_Message_t)) (st : state) : nat_pair =
+  (|betree_size self, betree_List_len msgs|)
diff --git a/tests/fstar/betree_back_stateful/BetreeMain.Funs.fst b/tests/fstar/betree_back_stateful/BetreeMain.Funs.fst
index 3d08cd3c..08c4f615 100644
--- a/tests/fstar/betree_back_stateful/BetreeMain.Funs.fst
+++ b/tests/fstar/betree_back_stateful/BetreeMain.Funs.fst
@@ -9,35 +9,35 @@ include BetreeMain.Clauses
 #set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
 
 (** [betree_main::betree::load_internal_node]: forward function *)
-let betree_load_internal_node_fwd
+let betree_load_internal_node
   (id : u64) (st : state) :
-  result (state & (betree_list_t (u64 & betree_message_t)))
+  result (state & (betree_List_t (u64 & betree_Message_t)))
   =
-  betree_utils_load_internal_node_fwd id st
+  betree_utils_load_internal_node id st
 
 (** [betree_main::betree::store_internal_node]: forward function *)
-let betree_store_internal_node_fwd
-  (id : u64) (content : betree_list_t (u64 & betree_message_t)) (st : state) :
+let betree_store_internal_node
+  (id : u64) (content : betree_List_t (u64 & betree_Message_t)) (st : state) :
   result (state & unit)
   =
-  let* (st0, _) = betree_utils_store_internal_node_fwd id content st in
+  let* (st0, _) = betree_utils_store_internal_node id content st in
   Return (st0, ())
 
 (** [betree_main::betree::load_leaf_node]: forward function *)
-let betree_load_leaf_node_fwd
-  (id : u64) (st : state) : result (state & (betree_list_t (u64 & u64))) =
-  betree_utils_load_leaf_node_fwd id st
+let betree_load_leaf_node
+  (id : u64) (st : state) : result (state & (betree_List_t (u64 & u64))) =
+  betree_utils_load_leaf_node id st
 
 (** [betree_main::betree::store_leaf_node]: forward function *)
-let betree_store_leaf_node_fwd
-  (id : u64) (content : betree_list_t (u64 & u64)) (st : state) :
+let betree_store_leaf_node
+  (id : u64) (content : betree_List_t (u64 & u64)) (st : state) :
   result (state & unit)
   =
-  let* (st0, _) = betree_utils_store_leaf_node_fwd id content st in
+  let* (st0, _) = betree_utils_store_leaf_node id content st in
   Return (st0, ())
 
 (** [betree_main::betree::fresh_node_id]: forward function *)
-let betree_fresh_node_id_fwd (counter : u64) : result u64 =
+let betree_fresh_node_id (counter : u64) : result u64 =
   let* _ = u64_add counter 1 in Return counter
 
 (** [betree_main::betree::fresh_node_id]: backward function 0 *)
@@ -45,1208 +45,1123 @@ let betree_fresh_node_id_back (counter : u64) : result u64 =
   u64_add counter 1
 
 (** [betree_main::betree::NodeIdCounter::{0}::new]: forward function *)
-let betree_node_id_counter_new_fwd : result betree_node_id_counter_t =
-  Return { betree_node_id_counter_next_node_id = 0 }
+let betree_NodeIdCounter_new : result betree_NodeIdCounter_t =
+  Return { next_node_id = 0 }
 
 (** [betree_main::betree::NodeIdCounter::{0}::fresh_id]: forward function *)
-let betree_node_id_counter_fresh_id_fwd
-  (self : betree_node_id_counter_t) : result u64 =
-  let* _ = u64_add self.betree_node_id_counter_next_node_id 1 in
-  Return self.betree_node_id_counter_next_node_id
+let betree_NodeIdCounter_fresh_id
+  (self : betree_NodeIdCounter_t) : result u64 =
+  let* _ = u64_add self.next_node_id 1 in Return self.next_node_id
 
 (** [betree_main::betree::NodeIdCounter::{0}::fresh_id]: backward function 0 *)
-let betree_node_id_counter_fresh_id_back
-  (self : betree_node_id_counter_t) : result betree_node_id_counter_t =
-  let* i = u64_add self.betree_node_id_counter_next_node_id 1 in
-  Return { betree_node_id_counter_next_node_id = i }
-
-(** [core::num::u64::{9}::MAX] *)
-let core_num_u64_max_body : result u64 = Return 18446744073709551615
-let core_num_u64_max_c : u64 = eval_global core_num_u64_max_body
+let betree_NodeIdCounter_fresh_id_back
+  (self : betree_NodeIdCounter_t) : result betree_NodeIdCounter_t =
+  let* i = u64_add self.next_node_id 1 in Return { next_node_id = i }
 
 (** [betree_main::betree::upsert_update]: forward function *)
-let betree_upsert_update_fwd
-  (prev : option u64) (st : betree_upsert_fun_state_t) : result u64 =
+let betree_upsert_update
+  (prev : option u64) (st : betree_UpsertFunState_t) : result u64 =
   begin match prev with
   | None ->
     begin match st with
-    | BetreeUpsertFunStateAdd v -> Return v
-    | BetreeUpsertFunStateSub i -> Return 0
+    | Betree_UpsertFunState_Add v -> Return v
+    | Betree_UpsertFunState_Sub i -> Return 0
     end
   | Some prev0 ->
     begin match st with
-    | BetreeUpsertFunStateAdd v ->
-      let* margin = u64_sub core_num_u64_max_c prev0 in
-      if margin >= v then u64_add prev0 v else Return core_num_u64_max_c
-    | BetreeUpsertFunStateSub v ->
+    | Betree_UpsertFunState_Add v ->
+      let* margin = u64_sub core_u64_max prev0 in
+      if margin >= v then u64_add prev0 v else Return core_u64_max
+    | Betree_UpsertFunState_Sub v ->
       if prev0 >= v then u64_sub prev0 v else Return 0
     end
   end
 
 (** [betree_main::betree::List::{1}::len]: forward function *)
-let rec betree_list_len_fwd
-  (t : Type0) (self : betree_list_t t) :
-  Tot (result u64) (decreases (betree_list_len_decreases t self))
+let rec betree_List_len
+  (t : Type0) (self : betree_List_t t) :
+  Tot (result u64) (decreases (betree_List_len_decreases t self))
   =
   begin match self with
-  | BetreeListCons x tl -> let* i = betree_list_len_fwd t tl in u64_add 1 i
-  | BetreeListNil -> Return 0
+  | Betree_List_Cons x tl -> let* i = betree_List_len t tl in u64_add 1 i
+  | Betree_List_Nil -> Return 0
   end
 
 (** [betree_main::betree::List::{1}::split_at]: forward function *)
-let rec betree_list_split_at_fwd
-  (t : Type0) (self : betree_list_t t) (n : u64) :
-  Tot (result ((betree_list_t t) & (betree_list_t t)))
-  (decreases (betree_list_split_at_decreases t self n))
+let rec betree_List_split_at
+  (t : Type0) (self : betree_List_t t) (n : u64) :
+  Tot (result ((betree_List_t t) & (betree_List_t t)))
+  (decreases (betree_List_split_at_decreases t self n))
   =
   if n = 0
-  then Return (BetreeListNil, self)
+  then Return (Betree_List_Nil, self)
   else
     begin match self with
-    | BetreeListCons hd tl ->
+    | Betree_List_Cons hd tl ->
       let* i = u64_sub n 1 in
-      let* p = betree_list_split_at_fwd t tl i in
+      let* p = betree_List_split_at t tl i in
       let (ls0, ls1) = p in
       let l = ls0 in
-      Return (BetreeListCons hd l, ls1)
-    | BetreeListNil -> Fail Failure
+      Return (Betree_List_Cons hd l, ls1)
+    | Betree_List_Nil -> Fail Failure
     end
 
 (** [betree_main::betree::List::{1}::push_front]: merged forward/backward function
     (there is a single backward function, and the forward function returns ()) *)
-let betree_list_push_front_fwd_back
-  (t : Type0) (self : betree_list_t t) (x : t) : result (betree_list_t t) =
-  let tl = mem_replace_fwd (betree_list_t t) self BetreeListNil in
+let betree_List_push_front
+  (t : Type0) (self : betree_List_t t) (x : t) : result (betree_List_t t) =
+  let tl = core_mem_replace (betree_List_t t) self Betree_List_Nil in
   let l = tl in
-  Return (BetreeListCons x l)
+  Return (Betree_List_Cons x l)
 
 (** [betree_main::betree::List::{1}::pop_front]: forward function *)
-let betree_list_pop_front_fwd (t : Type0) (self : betree_list_t t) : result t =
-  let ls = mem_replace_fwd (betree_list_t t) self BetreeListNil in
+let betree_List_pop_front (t : Type0) (self : betree_List_t t) : result t =
+  let ls = core_mem_replace (betree_List_t t) self Betree_List_Nil in
   begin match ls with
-  | BetreeListCons x tl -> Return x
-  | BetreeListNil -> Fail Failure
+  | Betree_List_Cons x tl -> Return x
+  | Betree_List_Nil -> Fail Failure
   end
 
 (** [betree_main::betree::List::{1}::pop_front]: backward function 0 *)
-let betree_list_pop_front_back
-  (t : Type0) (self : betree_list_t t) : result (betree_list_t t) =
-  let ls = mem_replace_fwd (betree_list_t t) self BetreeListNil in
+let betree_List_pop_front_back
+  (t : Type0) (self : betree_List_t t) : result (betree_List_t t) =
+  let ls = core_mem_replace (betree_List_t t) self Betree_List_Nil in
   begin match ls with
-  | BetreeListCons x tl -> Return tl
-  | BetreeListNil -> Fail Failure
+  | Betree_List_Cons x tl -> Return tl
+  | Betree_List_Nil -> Fail Failure
   end
 
 (** [betree_main::betree::List::{1}::hd]: forward function *)
-let betree_list_hd_fwd (t : Type0) (self : betree_list_t t) : result t =
+let betree_List_hd (t : Type0) (self : betree_List_t t) : result t =
   begin match self with
-  | BetreeListCons hd l -> Return hd
-  | BetreeListNil -> Fail Failure
+  | Betree_List_Cons hd l -> Return hd
+  | Betree_List_Nil -> Fail Failure
   end
 
 (** [betree_main::betree::List::{2}::head_has_key]: forward function *)
-let betree_list_head_has_key_fwd
-  (t : Type0) (self : betree_list_t (u64 & t)) (key : u64) : result bool =
+let betree_List_head_has_key
+  (t : Type0) (self : betree_List_t (u64 & t)) (key : u64) : result bool =
   begin match self with
-  | BetreeListCons hd l -> let (i, _) = hd in Return (i = key)
-  | BetreeListNil -> Return false
+  | Betree_List_Cons hd l -> let (i, _) = hd in Return (i = key)
+  | Betree_List_Nil -> Return false
   end
 
 (** [betree_main::betree::List::{2}::partition_at_pivot]: forward function *)
-let rec betree_list_partition_at_pivot_fwd
-  (t : Type0) (self : betree_list_t (u64 & t)) (pivot : u64) :
-  Tot (result ((betree_list_t (u64 & t)) & (betree_list_t (u64 & t))))
-  (decreases (betree_list_partition_at_pivot_decreases t self pivot))
+let rec betree_List_partition_at_pivot
+  (t : Type0) (self : betree_List_t (u64 & t)) (pivot : u64) :
+  Tot (result ((betree_List_t (u64 & t)) & (betree_List_t (u64 & t))))
+  (decreases (betree_List_partition_at_pivot_decreases t self pivot))
   =
   begin match self with
-  | BetreeListCons hd tl ->
+  | Betree_List_Cons hd tl ->
     let (i, x) = hd in
     if i >= pivot
-    then Return (BetreeListNil, BetreeListCons (i, x) tl)
+    then Return (Betree_List_Nil, Betree_List_Cons (i, x) tl)
     else
-      let* p = betree_list_partition_at_pivot_fwd t tl pivot in
+      let* p = betree_List_partition_at_pivot t tl pivot in
       let (ls0, ls1) = p in
       let l = ls0 in
-      Return (BetreeListCons (i, x) l, ls1)
-  | BetreeListNil -> Return (BetreeListNil, BetreeListNil)
+      Return (Betree_List_Cons (i, x) l, ls1)
+  | Betree_List_Nil -> Return (Betree_List_Nil, Betree_List_Nil)
   end
 
 (** [betree_main::betree::Leaf::{3}::split]: forward function *)
-let betree_leaf_split_fwd
-  (self : betree_leaf_t) (content : betree_list_t (u64 & u64))
-  (params : betree_params_t) (node_id_cnt : betree_node_id_counter_t)
+let betree_Leaf_split
+  (self : betree_Leaf_t) (content : betree_List_t (u64 & u64))
+  (params : betree_Params_t) (node_id_cnt : betree_NodeIdCounter_t)
   (st : state) :
-  result (state & betree_internal_t)
+  result (state & betree_Internal_t)
   =
-  let* p =
-    betree_list_split_at_fwd (u64 & u64) content
-      params.betree_params_split_size in
+  let* p = betree_List_split_at (u64 & u64) content params.split_size in
   let (content0, content1) = p in
-  let* p0 = betree_list_hd_fwd (u64 & u64) content1 in
+  let* p0 = betree_List_hd (u64 & u64) content1 in
   let (pivot, _) = p0 in
-  let* id0 = betree_node_id_counter_fresh_id_fwd node_id_cnt in
-  let* node_id_cnt0 = betree_node_id_counter_fresh_id_back node_id_cnt in
-  let* id1 = betree_node_id_counter_fresh_id_fwd node_id_cnt0 in
-  let* (st0, _) = betree_store_leaf_node_fwd id0 content0 st in
-  let* (st1, _) = betree_store_leaf_node_fwd id1 content1 st0 in
-  let n = BetreeNodeLeaf
-    { betree_leaf_id = id0; betree_leaf_size = params.betree_params_split_size
-    } in
-  let n0 = BetreeNodeLeaf
-    { betree_leaf_id = id1; betree_leaf_size = params.betree_params_split_size
-    } in
-  Return (st1,
-    {
-      betree_internal_id = self.betree_leaf_id;
-      betree_internal_pivot = pivot;
-      betree_internal_left = n;
-      betree_internal_right = n0
-    })
+  let* id0 = betree_NodeIdCounter_fresh_id node_id_cnt in
+  let* node_id_cnt0 = betree_NodeIdCounter_fresh_id_back node_id_cnt in
+  let* id1 = betree_NodeIdCounter_fresh_id node_id_cnt0 in
+  let* (st0, _) = betree_store_leaf_node id0 content0 st in
+  let* (st1, _) = betree_store_leaf_node id1 content1 st0 in
+  let n = Betree_Node_Leaf { id = id0; size = params.split_size } in
+  let n0 = Betree_Node_Leaf { id = id1; size = params.split_size } in
+  Return (st1, { id = self.id; pivot = pivot; left = n; right = n0 })
 
 (** [betree_main::betree::Leaf::{3}::split]: backward function 0 *)
-let betree_leaf_split_back0
-  (self : betree_leaf_t) (content : betree_list_t (u64 & u64))
-  (params : betree_params_t) (node_id_cnt : betree_node_id_counter_t)
+let betree_Leaf_split_back0
+  (self : betree_Leaf_t) (content : betree_List_t (u64 & u64))
+  (params : betree_Params_t) (node_id_cnt : betree_NodeIdCounter_t)
   (st : state) (st0 : state) :
   result (state & unit)
   =
-  let* p =
-    betree_list_split_at_fwd (u64 & u64) content
-      params.betree_params_split_size in
+  let* p = betree_List_split_at (u64 & u64) content params.split_size in
   let (content0, content1) = p in
-  let* _ = betree_list_hd_fwd (u64 & u64) content1 in
-  let* id0 = betree_node_id_counter_fresh_id_fwd node_id_cnt in
-  let* node_id_cnt0 = betree_node_id_counter_fresh_id_back node_id_cnt in
-  let* id1 = betree_node_id_counter_fresh_id_fwd node_id_cnt0 in
-  let* (st1, _) = betree_store_leaf_node_fwd id0 content0 st in
-  let* _ = betree_store_leaf_node_fwd id1 content1 st1 in
+  let* _ = betree_List_hd (u64 & u64) content1 in
+  let* id0 = betree_NodeIdCounter_fresh_id node_id_cnt in
+  let* node_id_cnt0 = betree_NodeIdCounter_fresh_id_back node_id_cnt in
+  let* id1 = betree_NodeIdCounter_fresh_id node_id_cnt0 in
+  let* (st1, _) = betree_store_leaf_node id0 content0 st in
+  let* _ = betree_store_leaf_node id1 content1 st1 in
   Return (st0, ())
 
 (** [betree_main::betree::Leaf::{3}::split]: backward function 1 *)
-let betree_leaf_split_back1
-  (self : betree_leaf_t) (content : betree_list_t (u64 & u64))
-  (params : betree_params_t) (node_id_cnt : betree_node_id_counter_t)
+let betree_Leaf_split_back1
+  (self : betree_Leaf_t) (content : betree_List_t (u64 & u64))
+  (params : betree_Params_t) (node_id_cnt : betree_NodeIdCounter_t)
   (st : state) (st0 : state) :
   result (state & unit)
   =
-  let* p =
-    betree_list_split_at_fwd (u64 & u64) content
-      params.betree_params_split_size in
+  let* p = betree_List_split_at (u64 & u64) content params.split_size in
   let (content0, content1) = p in
-  let* _ = betree_list_hd_fwd (u64 & u64) content1 in
-  let* id0 = betree_node_id_counter_fresh_id_fwd node_id_cnt in
-  let* node_id_cnt0 = betree_node_id_counter_fresh_id_back node_id_cnt in
-  let* id1 = betree_node_id_counter_fresh_id_fwd node_id_cnt0 in
-  let* (st1, _) = betree_store_leaf_node_fwd id0 content0 st in
-  let* _ = betree_store_leaf_node_fwd id1 content1 st1 in
+  let* _ = betree_List_hd (u64 & u64) content1 in
+  let* id0 = betree_NodeIdCounter_fresh_id node_id_cnt in
+  let* node_id_cnt0 = betree_NodeIdCounter_fresh_id_back node_id_cnt in
+  let* id1 = betree_NodeIdCounter_fresh_id node_id_cnt0 in
+  let* (st1, _) = betree_store_leaf_node id0 content0 st in
+  let* _ = betree_store_leaf_node id1 content1 st1 in
   Return (st0, ())
 
 (** [betree_main::betree::Leaf::{3}::split]: backward function 2 *)
-let betree_leaf_split_back2
-  (self : betree_leaf_t) (content : betree_list_t (u64 & u64))
-  (params : betree_params_t) (node_id_cnt : betree_node_id_counter_t)
+let betree_Leaf_split_back2
+  (self : betree_Leaf_t) (content : betree_List_t (u64 & u64))
+  (params : betree_Params_t) (node_id_cnt : betree_NodeIdCounter_t)
   (st : state) (st0 : state) :
-  result (state & betree_node_id_counter_t)
+  result (state & betree_NodeIdCounter_t)
   =
-  let* p =
-    betree_list_split_at_fwd (u64 & u64) content
-      params.betree_params_split_size in
+  let* p = betree_List_split_at (u64 & u64) content params.split_size in
   let (content0, content1) = p in
-  let* _ = betree_list_hd_fwd (u64 & u64) content1 in
-  let* id0 = betree_node_id_counter_fresh_id_fwd node_id_cnt in
-  let* node_id_cnt0 = betree_node_id_counter_fresh_id_back node_id_cnt in
-  let* id1 = betree_node_id_counter_fresh_id_fwd node_id_cnt0 in
-  let* (st1, _) = betree_store_leaf_node_fwd id0 content0 st in
-  let* _ = betree_store_leaf_node_fwd id1 content1 st1 in
-  let* node_id_cnt1 = betree_node_id_counter_fresh_id_back node_id_cnt0 in
+  let* _ = betree_List_hd (u64 & u64) content1 in
+  let* id0 = betree_NodeIdCounter_fresh_id node_id_cnt in
+  let* node_id_cnt0 = betree_NodeIdCounter_fresh_id_back node_id_cnt in
+  let* id1 = betree_NodeIdCounter_fresh_id node_id_cnt0 in
+  let* (st1, _) = betree_store_leaf_node id0 content0 st in
+  let* _ = betree_store_leaf_node id1 content1 st1 in
+  let* node_id_cnt1 = betree_NodeIdCounter_fresh_id_back node_id_cnt0 in
   Return (st0, node_id_cnt1)
 
 (** [betree_main::betree::Node::{5}::lookup_first_message_for_key]: forward function *)
-let rec betree_node_lookup_first_message_for_key_fwd
-  (key : u64) (msgs : betree_list_t (u64 & betree_message_t)) :
-  Tot (result (betree_list_t (u64 & betree_message_t)))
-  (decreases (betree_node_lookup_first_message_for_key_decreases key msgs))
+let rec betree_Node_lookup_first_message_for_key
+  (key : u64) (msgs : betree_List_t (u64 & betree_Message_t)) :
+  Tot (result (betree_List_t (u64 & betree_Message_t)))
+  (decreases (betree_Node_lookup_first_message_for_key_decreases key msgs))
   =
   begin match msgs with
-  | BetreeListCons x next_msgs ->
+  | Betree_List_Cons x next_msgs ->
     let (i, m) = x in
     if i >= key
-    then Return (BetreeListCons (i, m) next_msgs)
-    else betree_node_lookup_first_message_for_key_fwd key next_msgs
-  | BetreeListNil -> Return BetreeListNil
+    then Return (Betree_List_Cons (i, m) next_msgs)
+    else betree_Node_lookup_first_message_for_key key next_msgs
+  | Betree_List_Nil -> Return Betree_List_Nil
   end
 
 (** [betree_main::betree::Node::{5}::lookup_first_message_for_key]: backward function 0 *)
-let rec betree_node_lookup_first_message_for_key_back
-  (key : u64) (msgs : betree_list_t (u64 & betree_message_t))
-  (ret : betree_list_t (u64 & betree_message_t)) :
-  Tot (result (betree_list_t (u64 & betree_message_t)))
-  (decreases (betree_node_lookup_first_message_for_key_decreases key msgs))
+let rec betree_Node_lookup_first_message_for_key_back
+  (key : u64) (msgs : betree_List_t (u64 & betree_Message_t))
+  (ret : betree_List_t (u64 & betree_Message_t)) :
+  Tot (result (betree_List_t (u64 & betree_Message_t)))
+  (decreases (betree_Node_lookup_first_message_for_key_decreases key msgs))
   =
   begin match msgs with
-  | BetreeListCons x next_msgs ->
+  | Betree_List_Cons x next_msgs ->
     let (i, m) = x in
     if i >= key
     then Return ret
     else
       let* next_msgs0 =
-        betree_node_lookup_first_message_for_key_back key next_msgs ret in
-      Return (BetreeListCons (i, m) next_msgs0)
-  | BetreeListNil -> Return ret
+        betree_Node_lookup_first_message_for_key_back key next_msgs ret in
+      Return (Betree_List_Cons (i, m) next_msgs0)
+  | Betree_List_Nil -> Return ret
   end
 
 (** [betree_main::betree::Node::{5}::apply_upserts]: forward function *)
-let rec betree_node_apply_upserts_fwd
-  (msgs : betree_list_t (u64 & betree_message_t)) (prev : option u64)
+let rec betree_Node_apply_upserts
+  (msgs : betree_List_t (u64 & betree_Message_t)) (prev : option u64)
   (key : u64) (st : state) :
   Tot (result (state & u64))
-  (decreases (betree_node_apply_upserts_decreases msgs prev key st))
+  (decreases (betree_Node_apply_upserts_decreases msgs prev key st))
   =
-  let* b = betree_list_head_has_key_fwd betree_message_t msgs key in
+  let* b = betree_List_head_has_key betree_Message_t msgs key in
   if b
   then
-    let* msg = betree_list_pop_front_fwd (u64 & betree_message_t) msgs in
+    let* msg = betree_List_pop_front (u64 & betree_Message_t) msgs in
     let (_, m) = msg in
     begin match m with
-    | BetreeMessageInsert i -> Fail Failure
-    | BetreeMessageDelete -> Fail Failure
-    | BetreeMessageUpsert s ->
-      let* v = betree_upsert_update_fwd prev s in
-      let* msgs0 = betree_list_pop_front_back (u64 & betree_message_t) msgs in
-      betree_node_apply_upserts_fwd msgs0 (Some v) key st
+    | Betree_Message_Insert i -> Fail Failure
+    | Betree_Message_Delete -> Fail Failure
+    | Betree_Message_Upsert s ->
+      let* v = betree_upsert_update prev s in
+      let* msgs0 = betree_List_pop_front_back (u64 & betree_Message_t) msgs in
+      betree_Node_apply_upserts msgs0 (Some v) key st
     end
   else
-    let* (st0, v) = core_option_option_unwrap_fwd u64 prev st in
+    let* (st0, v) = core_option_Option_unwrap u64 prev st in
     let* _ =
-      betree_list_push_front_fwd_back (u64 & betree_message_t) msgs (key,
-        BetreeMessageInsert v) in
+      betree_List_push_front (u64 & betree_Message_t) msgs (key,
+        Betree_Message_Insert v) in
     Return (st0, v)
 
 (** [betree_main::betree::Node::{5}::apply_upserts]: backward function 0 *)
-let rec betree_node_apply_upserts_back
-  (msgs : betree_list_t (u64 & betree_message_t)) (prev : option u64)
+let rec betree_Node_apply_upserts_back
+  (msgs : betree_List_t (u64 & betree_Message_t)) (prev : option u64)
   (key : u64) (st : state) (st0 : state) :
-  Tot (result (state & (betree_list_t (u64 & betree_message_t))))
-  (decreases (betree_node_apply_upserts_decreases msgs prev key st))
+  Tot (result (state & (betree_List_t (u64 & betree_Message_t))))
+  (decreases (betree_Node_apply_upserts_decreases msgs prev key st))
   =
-  let* b = betree_list_head_has_key_fwd betree_message_t msgs key in
+  let* b = betree_List_head_has_key betree_Message_t msgs key in
   if b
   then
-    let* msg = betree_list_pop_front_fwd (u64 & betree_message_t) msgs in
+    let* msg = betree_List_pop_front (u64 & betree_Message_t) msgs in
     let (_, m) = msg in
     begin match m with
-    | BetreeMessageInsert i -> Fail Failure
-    | BetreeMessageDelete -> Fail Failure
-    | BetreeMessageUpsert s ->
-      let* v = betree_upsert_update_fwd prev s in
-      let* msgs0 = betree_list_pop_front_back (u64 & betree_message_t) msgs in
-      betree_node_apply_upserts_back msgs0 (Some v) key st st0
+    | Betree_Message_Insert i -> Fail Failure
+    | Betree_Message_Delete -> Fail Failure
+    | Betree_Message_Upsert s ->
+      let* v = betree_upsert_update prev s in
+      let* msgs0 = betree_List_pop_front_back (u64 & betree_Message_t) msgs in
+      betree_Node_apply_upserts_back msgs0 (Some v) key st st0
     end
   else
-    let* (_, v) = core_option_option_unwrap_fwd u64 prev st in
+    let* (_, v) = core_option_Option_unwrap u64 prev st in
     let* msgs0 =
-      betree_list_push_front_fwd_back (u64 & betree_message_t) msgs (key,
-        BetreeMessageInsert v) in
+      betree_List_push_front (u64 & betree_Message_t) msgs (key,
+        Betree_Message_Insert v) in
     Return (st0, msgs0)
 
 (** [betree_main::betree::Node::{5}::lookup_in_bindings]: forward function *)
-let rec betree_node_lookup_in_bindings_fwd
-  (key : u64) (bindings : betree_list_t (u64 & u64)) :
+let rec betree_Node_lookup_in_bindings
+  (key : u64) (bindings : betree_List_t (u64 & u64)) :
   Tot (result (option u64))
-  (decreases (betree_node_lookup_in_bindings_decreases key bindings))
+  (decreases (betree_Node_lookup_in_bindings_decreases key bindings))
   =
   begin match bindings with
-  | BetreeListCons hd tl ->
+  | Betree_List_Cons hd tl ->
     let (i, i0) = hd in
     if i = key
     then Return (Some i0)
-    else
-      if i > key
-      then Return None
-      else betree_node_lookup_in_bindings_fwd key tl
-  | BetreeListNil -> Return None
+    else if i > key then Return None else betree_Node_lookup_in_bindings key tl
+  | Betree_List_Nil -> Return None
   end
 
 (** [betree_main::betree::Internal::{4}::lookup_in_children]: forward function *)
-let rec betree_internal_lookup_in_children_fwd
-  (self : betree_internal_t) (key : u64) (st : state) :
+let rec betree_Internal_lookup_in_children
+  (self : betree_Internal_t) (key : u64) (st : state) :
   Tot (result (state & (option u64)))
-  (decreases (betree_internal_lookup_in_children_decreases self key st))
+  (decreases (betree_Internal_lookup_in_children_decreases self key st))
   =
-  if key < self.betree_internal_pivot
-  then betree_node_lookup_fwd self.betree_internal_left key st
-  else betree_node_lookup_fwd self.betree_internal_right key st
+  if key < self.pivot
+  then betree_Node_lookup self.left key st
+  else betree_Node_lookup self.right key st
 
 (** [betree_main::betree::Internal::{4}::lookup_in_children]: backward function 0 *)
-and betree_internal_lookup_in_children_back
-  (self : betree_internal_t) (key : u64) (st : state) (st0 : state) :
-  Tot (result (state & betree_internal_t))
-  (decreases (betree_internal_lookup_in_children_decreases self key st))
+and betree_Internal_lookup_in_children_back
+  (self : betree_Internal_t) (key : u64) (st : state) (st0 : state) :
+  Tot (result (state & betree_Internal_t))
+  (decreases (betree_Internal_lookup_in_children_decreases self key st))
   =
-  if key < self.betree_internal_pivot
+  if key < self.pivot
   then
-    let* (st1, n) =
-      betree_node_lookup_back self.betree_internal_left key st st0 in
-    Return (st1, { self with betree_internal_left = n })
+    let* (st1, n) = betree_Node_lookup_back self.left key st st0 in
+    Return (st1, { self with left = n })
   else
-    let* (st1, n) =
-      betree_node_lookup_back self.betree_internal_right key st st0 in
-    Return (st1, { self with betree_internal_right = n })
+    let* (st1, n) = betree_Node_lookup_back self.right key st st0 in
+    Return (st1, { self with right = n })
 
 (** [betree_main::betree::Node::{5}::lookup]: forward function *)
-and betree_node_lookup_fwd
-  (self : betree_node_t) (key : u64) (st : state) :
+and betree_Node_lookup
+  (self : betree_Node_t) (key : u64) (st : state) :
   Tot (result (state & (option u64)))
-  (decreases (betree_node_lookup_decreases self key st))
+  (decreases (betree_Node_lookup_decreases self key st))
   =
   begin match self with
-  | BetreeNodeInternal node ->
-    let* (st0, msgs) = betree_load_internal_node_fwd node.betree_internal_id st
-      in
-    let* pending = betree_node_lookup_first_message_for_key_fwd key msgs in
+  | Betree_Node_Internal node ->
+    let* (st0, msgs) = betree_load_internal_node node.id st in
+    let* pending = betree_Node_lookup_first_message_for_key key msgs in
     begin match pending with
-    | BetreeListCons p l ->
+    | Betree_List_Cons p l ->
       let (k, msg) = p in
       if k <> key
       then
-        let* (st1, opt) = betree_internal_lookup_in_children_fwd node key st0
-          in
+        let* (st1, o) = betree_Internal_lookup_in_children node key st0 in
         let* _ =
-          betree_node_lookup_first_message_for_key_back key msgs
-            (BetreeListCons (k, msg) l) in
-        Return (st1, opt)
+          betree_Node_lookup_first_message_for_key_back key msgs
+            (Betree_List_Cons (k, msg) l) in
+        Return (st1, o)
       else
         begin match msg with
-        | BetreeMessageInsert v ->
+        | Betree_Message_Insert v ->
           let* _ =
-            betree_node_lookup_first_message_for_key_back key msgs
-              (BetreeListCons (k, BetreeMessageInsert v) l) in
+            betree_Node_lookup_first_message_for_key_back key msgs
+              (Betree_List_Cons (k, Betree_Message_Insert v) l) in
           Return (st0, Some v)
-        | BetreeMessageDelete ->
+        | Betree_Message_Delete ->
           let* _ =
-            betree_node_lookup_first_message_for_key_back key msgs
-              (BetreeListCons (k, BetreeMessageDelete) l) in
+            betree_Node_lookup_first_message_for_key_back key msgs
+              (Betree_List_Cons (k, Betree_Message_Delete) l) in
           Return (st0, None)
-        | BetreeMessageUpsert ufs ->
-          let* (st1, v) = betree_internal_lookup_in_children_fwd node key st0
-            in
+        | Betree_Message_Upsert ufs ->
+          let* (st1, v) = betree_Internal_lookup_in_children node key st0 in
           let* (st2, v0) =
-            betree_node_apply_upserts_fwd (BetreeListCons (k,
-              BetreeMessageUpsert ufs) l) v key st1 in
+            betree_Node_apply_upserts (Betree_List_Cons (k,
+              Betree_Message_Upsert ufs) l) v key st1 in
           let* (st3, node0) =
-            betree_internal_lookup_in_children_back node key st0 st2 in
+            betree_Internal_lookup_in_children_back node key st0 st2 in
           let* (st4, pending0) =
-            betree_node_apply_upserts_back (BetreeListCons (k,
-              BetreeMessageUpsert ufs) l) v key st1 st3 in
+            betree_Node_apply_upserts_back (Betree_List_Cons (k,
+              Betree_Message_Upsert ufs) l) v key st1 st3 in
           let* msgs0 =
-            betree_node_lookup_first_message_for_key_back key msgs pending0 in
-          let* (st5, _) =
-            betree_store_internal_node_fwd node0.betree_internal_id msgs0 st4
-            in
+            betree_Node_lookup_first_message_for_key_back key msgs pending0 in
+          let* (st5, _) = betree_store_internal_node node0.id msgs0 st4 in
           Return (st5, Some v0)
         end
-    | BetreeListNil ->
-      let* (st1, opt) = betree_internal_lookup_in_children_fwd node key st0 in
+    | Betree_List_Nil ->
+      let* (st1, o) = betree_Internal_lookup_in_children node key st0 in
       let* _ =
-        betree_node_lookup_first_message_for_key_back key msgs BetreeListNil in
-      Return (st1, opt)
+        betree_Node_lookup_first_message_for_key_back key msgs Betree_List_Nil
+        in
+      Return (st1, o)
     end
-  | BetreeNodeLeaf node ->
-    let* (st0, bindings) = betree_load_leaf_node_fwd node.betree_leaf_id st in
-    let* opt = betree_node_lookup_in_bindings_fwd key bindings in
-    Return (st0, opt)
+  | Betree_Node_Leaf node ->
+    let* (st0, bindings) = betree_load_leaf_node node.id st in
+    let* o = betree_Node_lookup_in_bindings key bindings in
+    Return (st0, o)
   end
 
 (** [betree_main::betree::Node::{5}::lookup]: backward function 0 *)
-and betree_node_lookup_back
-  (self : betree_node_t) (key : u64) (st : state) (st0 : state) :
-  Tot (result (state & betree_node_t))
-  (decreases (betree_node_lookup_decreases self key st))
+and betree_Node_lookup_back
+  (self : betree_Node_t) (key : u64) (st : state) (st0 : state) :
+  Tot (result (state & betree_Node_t))
+  (decreases (betree_Node_lookup_decreases self key st))
   =
   begin match self with
-  | BetreeNodeInternal node ->
-    let* (st1, msgs) = betree_load_internal_node_fwd node.betree_internal_id st
-      in
-    let* pending = betree_node_lookup_first_message_for_key_fwd key msgs in
+  | Betree_Node_Internal node ->
+    let* (st1, msgs) = betree_load_internal_node node.id st in
+    let* pending = betree_Node_lookup_first_message_for_key key msgs in
     begin match pending with
-    | BetreeListCons p l ->
+    | Betree_List_Cons p l ->
       let (k, msg) = p in
       if k <> key
       then
         let* _ =
-          betree_node_lookup_first_message_for_key_back key msgs
-            (BetreeListCons (k, msg) l) in
+          betree_Node_lookup_first_message_for_key_back key msgs
+            (Betree_List_Cons (k, msg) l) in
         let* (st2, node0) =
-          betree_internal_lookup_in_children_back node key st1 st0 in
-        Return (st2, BetreeNodeInternal node0)
+          betree_Internal_lookup_in_children_back node key st1 st0 in
+        Return (st2, Betree_Node_Internal node0)
       else
         begin match msg with
-        | BetreeMessageInsert v ->
+        | Betree_Message_Insert v ->
           let* _ =
-            betree_node_lookup_first_message_for_key_back key msgs
-              (BetreeListCons (k, BetreeMessageInsert v) l) in
-          Return (st0, BetreeNodeInternal node)
-        | BetreeMessageDelete ->
+            betree_Node_lookup_first_message_for_key_back key msgs
+              (Betree_List_Cons (k, Betree_Message_Insert v) l) in
+          Return (st0, Betree_Node_Internal node)
+        | Betree_Message_Delete ->
           let* _ =
-            betree_node_lookup_first_message_for_key_back key msgs
-              (BetreeListCons (k, BetreeMessageDelete) l) in
-          Return (st0, BetreeNodeInternal node)
-        | BetreeMessageUpsert ufs ->
-          let* (st2, v) = betree_internal_lookup_in_children_fwd node key st1
-            in
+            betree_Node_lookup_first_message_for_key_back key msgs
+              (Betree_List_Cons (k, Betree_Message_Delete) l) in
+          Return (st0, Betree_Node_Internal node)
+        | Betree_Message_Upsert ufs ->
+          let* (st2, v) = betree_Internal_lookup_in_children node key st1 in
           let* (st3, _) =
-            betree_node_apply_upserts_fwd (BetreeListCons (k,
-              BetreeMessageUpsert ufs) l) v key st2 in
+            betree_Node_apply_upserts (Betree_List_Cons (k,
+              Betree_Message_Upsert ufs) l) v key st2 in
           let* (st4, node0) =
-            betree_internal_lookup_in_children_back node key st1 st3 in
+            betree_Internal_lookup_in_children_back node key st1 st3 in
           let* (st5, pending0) =
-            betree_node_apply_upserts_back (BetreeListCons (k,
-              BetreeMessageUpsert ufs) l) v key st2 st4 in
+            betree_Node_apply_upserts_back (Betree_List_Cons (k,
+              Betree_Message_Upsert ufs) l) v key st2 st4 in
           let* msgs0 =
-            betree_node_lookup_first_message_for_key_back key msgs pending0 in
-          let* _ =
-            betree_store_internal_node_fwd node0.betree_internal_id msgs0 st5
-            in
-          Return (st0, BetreeNodeInternal node0)
+            betree_Node_lookup_first_message_for_key_back key msgs pending0 in
+          let* _ = betree_store_internal_node node0.id msgs0 st5 in
+          Return (st0, Betree_Node_Internal node0)
         end
-    | BetreeListNil ->
+    | Betree_List_Nil ->
       let* _ =
-        betree_node_lookup_first_message_for_key_back key msgs BetreeListNil in
+        betree_Node_lookup_first_message_for_key_back key msgs Betree_List_Nil
+        in
       let* (st2, node0) =
-        betree_internal_lookup_in_children_back node key st1 st0 in
-      Return (st2, BetreeNodeInternal node0)
+        betree_Internal_lookup_in_children_back node key st1 st0 in
+      Return (st2, Betree_Node_Internal node0)
     end
-  | BetreeNodeLeaf node ->
-    let* (_, bindings) = betree_load_leaf_node_fwd node.betree_leaf_id st in
-    let* _ = betree_node_lookup_in_bindings_fwd key bindings in
-    Return (st0, BetreeNodeLeaf node)
+  | Betree_Node_Leaf node ->
+    let* (_, bindings) = betree_load_leaf_node node.id st in
+    let* _ = betree_Node_lookup_in_bindings key bindings in
+    Return (st0, Betree_Node_Leaf node)
   end
 
 (** [betree_main::betree::Node::{5}::filter_messages_for_key]: merged forward/backward function
     (there is a single backward function, and the forward function returns ()) *)
-let rec betree_node_filter_messages_for_key_fwd_back
-  (key : u64) (msgs : betree_list_t (u64 & betree_message_t)) :
-  Tot (result (betree_list_t (u64 & betree_message_t)))
-  (decreases (betree_node_filter_messages_for_key_decreases key msgs))
+let rec betree_Node_filter_messages_for_key
+  (key : u64) (msgs : betree_List_t (u64 & betree_Message_t)) :
+  Tot (result (betree_List_t (u64 & betree_Message_t)))
+  (decreases (betree_Node_filter_messages_for_key_decreases key msgs))
   =
   begin match msgs with
-  | BetreeListCons p l ->
+  | Betree_List_Cons p l ->
     let (k, m) = p in
     if k = key
     then
       let* msgs0 =
-        betree_list_pop_front_back (u64 & betree_message_t) (BetreeListCons (k,
-          m) l) in
-      betree_node_filter_messages_for_key_fwd_back key msgs0
-    else Return (BetreeListCons (k, m) l)
-  | BetreeListNil -> Return BetreeListNil
+        betree_List_pop_front_back (u64 & betree_Message_t) (Betree_List_Cons
+          (k, m) l) in
+      betree_Node_filter_messages_for_key key msgs0
+    else Return (Betree_List_Cons (k, m) l)
+  | Betree_List_Nil -> Return Betree_List_Nil
   end
 
 (** [betree_main::betree::Node::{5}::lookup_first_message_after_key]: forward function *)
-let rec betree_node_lookup_first_message_after_key_fwd
-  (key : u64) (msgs : betree_list_t (u64 & betree_message_t)) :
-  Tot (result (betree_list_t (u64 & betree_message_t)))
-  (decreases (betree_node_lookup_first_message_after_key_decreases key msgs))
+let rec betree_Node_lookup_first_message_after_key
+  (key : u64) (msgs : betree_List_t (u64 & betree_Message_t)) :
+  Tot (result (betree_List_t (u64 & betree_Message_t)))
+  (decreases (betree_Node_lookup_first_message_after_key_decreases key msgs))
   =
   begin match msgs with
-  | BetreeListCons p next_msgs ->
+  | Betree_List_Cons p next_msgs ->
     let (k, m) = p in
     if k = key
-    then betree_node_lookup_first_message_after_key_fwd key next_msgs
-    else Return (BetreeListCons (k, m) next_msgs)
-  | BetreeListNil -> Return BetreeListNil
+    then betree_Node_lookup_first_message_after_key key next_msgs
+    else Return (Betree_List_Cons (k, m) next_msgs)
+  | Betree_List_Nil -> Return Betree_List_Nil
   end
 
 (** [betree_main::betree::Node::{5}::lookup_first_message_after_key]: backward function 0 *)
-let rec betree_node_lookup_first_message_after_key_back
-  (key : u64) (msgs : betree_list_t (u64 & betree_message_t))
-  (ret : betree_list_t (u64 & betree_message_t)) :
-  Tot (result (betree_list_t (u64 & betree_message_t)))
-  (decreases (betree_node_lookup_first_message_after_key_decreases key msgs))
+let rec betree_Node_lookup_first_message_after_key_back
+  (key : u64) (msgs : betree_List_t (u64 & betree_Message_t))
+  (ret : betree_List_t (u64 & betree_Message_t)) :
+  Tot (result (betree_List_t (u64 & betree_Message_t)))
+  (decreases (betree_Node_lookup_first_message_after_key_decreases key msgs))
   =
   begin match msgs with
-  | BetreeListCons p next_msgs ->
+  | Betree_List_Cons p next_msgs ->
     let (k, m) = p in
     if k = key
     then
       let* next_msgs0 =
-        betree_node_lookup_first_message_after_key_back key next_msgs ret in
-      Return (BetreeListCons (k, m) next_msgs0)
+        betree_Node_lookup_first_message_after_key_back key next_msgs ret in
+      Return (Betree_List_Cons (k, m) next_msgs0)
     else Return ret
-  | BetreeListNil -> Return ret
+  | Betree_List_Nil -> Return ret
   end
 
 (** [betree_main::betree::Node::{5}::apply_to_internal]: merged forward/backward function
     (there is a single backward function, and the forward function returns ()) *)
-let betree_node_apply_to_internal_fwd_back
-  (msgs : betree_list_t (u64 & betree_message_t)) (key : u64)
-  (new_msg : betree_message_t) :
-  result (betree_list_t (u64 & betree_message_t))
+let betree_Node_apply_to_internal
+  (msgs : betree_List_t (u64 & betree_Message_t)) (key : u64)
+  (new_msg : betree_Message_t) :
+  result (betree_List_t (u64 & betree_Message_t))
   =
-  let* msgs0 = betree_node_lookup_first_message_for_key_fwd key msgs in
-  let* b = betree_list_head_has_key_fwd betree_message_t msgs0 key in
+  let* msgs0 = betree_Node_lookup_first_message_for_key key msgs in
+  let* b = betree_List_head_has_key betree_Message_t msgs0 key in
   if b
   then
     begin match new_msg with
-    | BetreeMessageInsert i ->
-      let* msgs1 = betree_node_filter_messages_for_key_fwd_back key msgs0 in
+    | Betree_Message_Insert i ->
+      let* msgs1 = betree_Node_filter_messages_for_key key msgs0 in
       let* msgs2 =
-        betree_list_push_front_fwd_back (u64 & betree_message_t) msgs1 (key,
-          BetreeMessageInsert i) in
-      betree_node_lookup_first_message_for_key_back key msgs msgs2
-    | BetreeMessageDelete ->
-      let* msgs1 = betree_node_filter_messages_for_key_fwd_back key msgs0 in
+        betree_List_push_front (u64 & betree_Message_t) msgs1 (key,
+          Betree_Message_Insert i) in
+      betree_Node_lookup_first_message_for_key_back key msgs msgs2
+    | Betree_Message_Delete ->
+      let* msgs1 = betree_Node_filter_messages_for_key key msgs0 in
       let* msgs2 =
-        betree_list_push_front_fwd_back (u64 & betree_message_t) msgs1 (key,
-          BetreeMessageDelete) in
-      betree_node_lookup_first_message_for_key_back key msgs msgs2
-    | BetreeMessageUpsert s ->
-      let* p = betree_list_hd_fwd (u64 & betree_message_t) msgs0 in
+        betree_List_push_front (u64 & betree_Message_t) msgs1 (key,
+          Betree_Message_Delete) in
+      betree_Node_lookup_first_message_for_key_back key msgs msgs2
+    | Betree_Message_Upsert s ->
+      let* p = betree_List_hd (u64 & betree_Message_t) msgs0 in
       let (_, m) = p in
       begin match m with
-      | BetreeMessageInsert prev ->
-        let* v = betree_upsert_update_fwd (Some prev) s in
-        let* msgs1 = betree_list_pop_front_back (u64 & betree_message_t) msgs0
+      | Betree_Message_Insert prev ->
+        let* v = betree_upsert_update (Some prev) s in
+        let* msgs1 = betree_List_pop_front_back (u64 & betree_Message_t) msgs0
           in
         let* msgs2 =
-          betree_list_push_front_fwd_back (u64 & betree_message_t) msgs1 (key,
-            BetreeMessageInsert v) in
-        betree_node_lookup_first_message_for_key_back key msgs msgs2
-      | BetreeMessageDelete ->
-        let* v = betree_upsert_update_fwd None s in
-        let* msgs1 = betree_list_pop_front_back (u64 & betree_message_t) msgs0
+          betree_List_push_front (u64 & betree_Message_t) msgs1 (key,
+            Betree_Message_Insert v) in
+        betree_Node_lookup_first_message_for_key_back key msgs msgs2
+      | Betree_Message_Delete ->
+        let* v = betree_upsert_update None s in
+        let* msgs1 = betree_List_pop_front_back (u64 & betree_Message_t) msgs0
           in
         let* msgs2 =
-          betree_list_push_front_fwd_back (u64 & betree_message_t) msgs1 (key,
-            BetreeMessageInsert v) in
-        betree_node_lookup_first_message_for_key_back key msgs msgs2
-      | BetreeMessageUpsert ufs ->
-        let* msgs1 = betree_node_lookup_first_message_after_key_fwd key msgs0
-          in
+          betree_List_push_front (u64 & betree_Message_t) msgs1 (key,
+            Betree_Message_Insert v) in
+        betree_Node_lookup_first_message_for_key_back key msgs msgs2
+      | Betree_Message_Upsert ufs ->
+        let* msgs1 = betree_Node_lookup_first_message_after_key key msgs0 in
         let* msgs2 =
-          betree_list_push_front_fwd_back (u64 & betree_message_t) msgs1 (key,
-            BetreeMessageUpsert s) in
+          betree_List_push_front (u64 & betree_Message_t) msgs1 (key,
+            Betree_Message_Upsert s) in
         let* msgs3 =
-          betree_node_lookup_first_message_after_key_back key msgs0 msgs2 in
-        betree_node_lookup_first_message_for_key_back key msgs msgs3
+          betree_Node_lookup_first_message_after_key_back key msgs0 msgs2 in
+        betree_Node_lookup_first_message_for_key_back key msgs msgs3
       end
     end
   else
     let* msgs1 =
-      betree_list_push_front_fwd_back (u64 & betree_message_t) msgs0 (key,
-        new_msg) in
-    betree_node_lookup_first_message_for_key_back key msgs msgs1
+      betree_List_push_front (u64 & betree_Message_t) msgs0 (key, new_msg) in
+    betree_Node_lookup_first_message_for_key_back key msgs msgs1
 
 (** [betree_main::betree::Node::{5}::apply_messages_to_internal]: merged forward/backward function
     (there is a single backward function, and the forward function returns ()) *)
-let rec betree_node_apply_messages_to_internal_fwd_back
-  (msgs : betree_list_t (u64 & betree_message_t))
-  (new_msgs : betree_list_t (u64 & betree_message_t)) :
-  Tot (result (betree_list_t (u64 & betree_message_t)))
-  (decreases (betree_node_apply_messages_to_internal_decreases msgs new_msgs))
+let rec betree_Node_apply_messages_to_internal
+  (msgs : betree_List_t (u64 & betree_Message_t))
+  (new_msgs : betree_List_t (u64 & betree_Message_t)) :
+  Tot (result (betree_List_t (u64 & betree_Message_t)))
+  (decreases (betree_Node_apply_messages_to_internal_decreases msgs new_msgs))
   =
   begin match new_msgs with
-  | BetreeListCons new_msg new_msgs_tl ->
+  | Betree_List_Cons new_msg new_msgs_tl ->
     let (i, m) = new_msg in
-    let* msgs0 = betree_node_apply_to_internal_fwd_back msgs i m in
-    betree_node_apply_messages_to_internal_fwd_back msgs0 new_msgs_tl
-  | BetreeListNil -> Return msgs
+    let* msgs0 = betree_Node_apply_to_internal msgs i m in
+    betree_Node_apply_messages_to_internal msgs0 new_msgs_tl
+  | Betree_List_Nil -> Return msgs
   end
 
 (** [betree_main::betree::Node::{5}::lookup_mut_in_bindings]: forward function *)
-let rec betree_node_lookup_mut_in_bindings_fwd
-  (key : u64) (bindings : betree_list_t (u64 & u64)) :
-  Tot (result (betree_list_t (u64 & u64)))
-  (decreases (betree_node_lookup_mut_in_bindings_decreases key bindings))
+let rec betree_Node_lookup_mut_in_bindings
+  (key : u64) (bindings : betree_List_t (u64 & u64)) :
+  Tot (result (betree_List_t (u64 & u64)))
+  (decreases (betree_Node_lookup_mut_in_bindings_decreases key bindings))
   =
   begin match bindings with
-  | BetreeListCons hd tl ->
+  | Betree_List_Cons hd tl ->
     let (i, i0) = hd in
     if i >= key
-    then Return (BetreeListCons (i, i0) tl)
-    else betree_node_lookup_mut_in_bindings_fwd key tl
-  | BetreeListNil -> Return BetreeListNil
+    then Return (Betree_List_Cons (i, i0) tl)
+    else betree_Node_lookup_mut_in_bindings key tl
+  | Betree_List_Nil -> Return Betree_List_Nil
   end
 
 (** [betree_main::betree::Node::{5}::lookup_mut_in_bindings]: backward function 0 *)
-let rec betree_node_lookup_mut_in_bindings_back
-  (key : u64) (bindings : betree_list_t (u64 & u64))
-  (ret : betree_list_t (u64 & u64)) :
-  Tot (result (betree_list_t (u64 & u64)))
-  (decreases (betree_node_lookup_mut_in_bindings_decreases key bindings))
+let rec betree_Node_lookup_mut_in_bindings_back
+  (key : u64) (bindings : betree_List_t (u64 & u64))
+  (ret : betree_List_t (u64 & u64)) :
+  Tot (result (betree_List_t (u64 & u64)))
+  (decreases (betree_Node_lookup_mut_in_bindings_decreases key bindings))
   =
   begin match bindings with
-  | BetreeListCons hd tl ->
+  | Betree_List_Cons hd tl ->
     let (i, i0) = hd in
     if i >= key
     then Return ret
     else
-      let* tl0 = betree_node_lookup_mut_in_bindings_back key tl ret in
-      Return (BetreeListCons (i, i0) tl0)
-  | BetreeListNil -> Return ret
+      let* tl0 = betree_Node_lookup_mut_in_bindings_back key tl ret in
+      Return (Betree_List_Cons (i, i0) tl0)
+  | Betree_List_Nil -> Return ret
   end
 
 (** [betree_main::betree::Node::{5}::apply_to_leaf]: merged forward/backward function
     (there is a single backward function, and the forward function returns ()) *)
-let betree_node_apply_to_leaf_fwd_back
-  (bindings : betree_list_t (u64 & u64)) (key : u64)
-  (new_msg : betree_message_t) :
-  result (betree_list_t (u64 & u64))
+let betree_Node_apply_to_leaf
+  (bindings : betree_List_t (u64 & u64)) (key : u64)
+  (new_msg : betree_Message_t) :
+  result (betree_List_t (u64 & u64))
   =
-  let* bindings0 = betree_node_lookup_mut_in_bindings_fwd key bindings in
-  let* b = betree_list_head_has_key_fwd u64 bindings0 key in
+  let* bindings0 = betree_Node_lookup_mut_in_bindings key bindings in
+  let* b = betree_List_head_has_key u64 bindings0 key in
   if b
   then
-    let* hd = betree_list_pop_front_fwd (u64 & u64) bindings0 in
+    let* hd = betree_List_pop_front (u64 & u64) bindings0 in
     begin match new_msg with
-    | BetreeMessageInsert v ->
-      let* bindings1 = betree_list_pop_front_back (u64 & u64) bindings0 in
-      let* bindings2 =
-        betree_list_push_front_fwd_back (u64 & u64) bindings1 (key, v) in
-      betree_node_lookup_mut_in_bindings_back key bindings bindings2
-    | BetreeMessageDelete ->
-      let* bindings1 = betree_list_pop_front_back (u64 & u64) bindings0 in
-      betree_node_lookup_mut_in_bindings_back key bindings bindings1
-    | BetreeMessageUpsert s ->
+    | Betree_Message_Insert v ->
+      let* bindings1 = betree_List_pop_front_back (u64 & u64) bindings0 in
+      let* bindings2 = betree_List_push_front (u64 & u64) bindings1 (key, v) in
+      betree_Node_lookup_mut_in_bindings_back key bindings bindings2
+    | Betree_Message_Delete ->
+      let* bindings1 = betree_List_pop_front_back (u64 & u64) bindings0 in
+      betree_Node_lookup_mut_in_bindings_back key bindings bindings1
+    | Betree_Message_Upsert s ->
       let (_, i) = hd in
-      let* v = betree_upsert_update_fwd (Some i) s in
-      let* bindings1 = betree_list_pop_front_back (u64 & u64) bindings0 in
-      let* bindings2 =
-        betree_list_push_front_fwd_back (u64 & u64) bindings1 (key, v) in
-      betree_node_lookup_mut_in_bindings_back key bindings bindings2
+      let* v = betree_upsert_update (Some i) s in
+      let* bindings1 = betree_List_pop_front_back (u64 & u64) bindings0 in
+      let* bindings2 = betree_List_push_front (u64 & u64) bindings1 (key, v) in
+      betree_Node_lookup_mut_in_bindings_back key bindings bindings2
     end
   else
     begin match new_msg with
-    | BetreeMessageInsert v ->
-      let* bindings1 =
-        betree_list_push_front_fwd_back (u64 & u64) bindings0 (key, v) in
-      betree_node_lookup_mut_in_bindings_back key bindings bindings1
-    | BetreeMessageDelete ->
-      betree_node_lookup_mut_in_bindings_back key bindings bindings0
-    | BetreeMessageUpsert s ->
-      let* v = betree_upsert_update_fwd None s in
-      let* bindings1 =
-        betree_list_push_front_fwd_back (u64 & u64) bindings0 (key, v) in
-      betree_node_lookup_mut_in_bindings_back key bindings bindings1
+    | Betree_Message_Insert v ->
+      let* bindings1 = betree_List_push_front (u64 & u64) bindings0 (key, v) in
+      betree_Node_lookup_mut_in_bindings_back key bindings bindings1
+    | Betree_Message_Delete ->
+      betree_Node_lookup_mut_in_bindings_back key bindings bindings0
+    | Betree_Message_Upsert s ->
+      let* v = betree_upsert_update None s in
+      let* bindings1 = betree_List_push_front (u64 & u64) bindings0 (key, v) in
+      betree_Node_lookup_mut_in_bindings_back key bindings bindings1
     end
 
 (** [betree_main::betree::Node::{5}::apply_messages_to_leaf]: merged forward/backward function
     (there is a single backward function, and the forward function returns ()) *)
-let rec betree_node_apply_messages_to_leaf_fwd_back
-  (bindings : betree_list_t (u64 & u64))
-  (new_msgs : betree_list_t (u64 & betree_message_t)) :
-  Tot (result (betree_list_t (u64 & u64)))
-  (decreases (betree_node_apply_messages_to_leaf_decreases bindings new_msgs))
+let rec betree_Node_apply_messages_to_leaf
+  (bindings : betree_List_t (u64 & u64))
+  (new_msgs : betree_List_t (u64 & betree_Message_t)) :
+  Tot (result (betree_List_t (u64 & u64)))
+  (decreases (betree_Node_apply_messages_to_leaf_decreases bindings new_msgs))
   =
   begin match new_msgs with
-  | BetreeListCons new_msg new_msgs_tl ->
+  | Betree_List_Cons new_msg new_msgs_tl ->
     let (i, m) = new_msg in
-    let* bindings0 = betree_node_apply_to_leaf_fwd_back bindings i m in
-    betree_node_apply_messages_to_leaf_fwd_back bindings0 new_msgs_tl
-  | BetreeListNil -> Return bindings
+    let* bindings0 = betree_Node_apply_to_leaf bindings i m in
+    betree_Node_apply_messages_to_leaf bindings0 new_msgs_tl
+  | Betree_List_Nil -> Return bindings
   end
 
 (** [betree_main::betree::Internal::{4}::flush]: forward function *)
-let rec betree_internal_flush_fwd
-  (self : betree_internal_t) (params : betree_params_t)
-  (node_id_cnt : betree_node_id_counter_t)
-  (content : betree_list_t (u64 & betree_message_t)) (st : state) :
-  Tot (result (state & (betree_list_t (u64 & betree_message_t))))
+let rec betree_Internal_flush
+  (self : betree_Internal_t) (params : betree_Params_t)
+  (node_id_cnt : betree_NodeIdCounter_t)
+  (content : betree_List_t (u64 & betree_Message_t)) (st : state) :
+  Tot (result (state & (betree_List_t (u64 & betree_Message_t))))
   (decreases (
-    betree_internal_flush_decreases self params node_id_cnt content st))
+    betree_Internal_flush_decreases self params node_id_cnt content st))
   =
-  let* p =
-    betree_list_partition_at_pivot_fwd betree_message_t content
-      self.betree_internal_pivot in
+  let* p = betree_List_partition_at_pivot betree_Message_t content self.pivot
+    in
   let (msgs_left, msgs_right) = p in
-  let* len_left = betree_list_len_fwd (u64 & betree_message_t) msgs_left in
-  if len_left >= params.betree_params_min_flush_size
+  let* len_left = betree_List_len (u64 & betree_Message_t) msgs_left in
+  if len_left >= params.min_flush_size
   then
     let* (st0, _) =
-      betree_node_apply_messages_fwd self.betree_internal_left params
-        node_id_cnt msgs_left st in
+      betree_Node_apply_messages self.left params node_id_cnt msgs_left st in
     let* (st1, (_, node_id_cnt0)) =
-      betree_node_apply_messages_back'a self.betree_internal_left params
-        node_id_cnt msgs_left st st0 in
+      betree_Node_apply_messages_back'a self.left params node_id_cnt msgs_left
+        st st0 in
     let* (st2, ()) =
-      betree_node_apply_messages_back1 self.betree_internal_left params
-        node_id_cnt msgs_left st st1 in
-    let* len_right = betree_list_len_fwd (u64 & betree_message_t) msgs_right in
-    if len_right >= params.betree_params_min_flush_size
+      betree_Node_apply_messages_back1 self.left params node_id_cnt msgs_left
+        st st1 in
+    let* len_right = betree_List_len (u64 & betree_Message_t) msgs_right in
+    if len_right >= params.min_flush_size
     then
       let* (st3, _) =
-        betree_node_apply_messages_fwd self.betree_internal_right params
-          node_id_cnt0 msgs_right st2 in
+        betree_Node_apply_messages self.right params node_id_cnt0 msgs_right
+          st2 in
       let* (st4, (_, _)) =
-        betree_node_apply_messages_back'a self.betree_internal_right params
-          node_id_cnt0 msgs_right st2 st3 in
+        betree_Node_apply_messages_back'a self.right params node_id_cnt0
+          msgs_right st2 st3 in
       let* (st5, ()) =
-        betree_node_apply_messages_back1 self.betree_internal_right params
-          node_id_cnt0 msgs_right st2 st4 in
-      Return (st5, BetreeListNil)
+        betree_Node_apply_messages_back1 self.right params node_id_cnt0
+          msgs_right st2 st4 in
+      Return (st5, Betree_List_Nil)
     else Return (st2, msgs_right)
   else
     let* (st0, _) =
-      betree_node_apply_messages_fwd self.betree_internal_right params
-        node_id_cnt msgs_right st in
+      betree_Node_apply_messages self.right params node_id_cnt msgs_right st in
     let* (st1, (_, _)) =
-      betree_node_apply_messages_back'a self.betree_internal_right params
-        node_id_cnt msgs_right st st0 in
+      betree_Node_apply_messages_back'a self.right params node_id_cnt
+        msgs_right st st0 in
     let* (st2, ()) =
-      betree_node_apply_messages_back1 self.betree_internal_right params
-        node_id_cnt msgs_right st st1 in
+      betree_Node_apply_messages_back1 self.right params node_id_cnt msgs_right
+        st st1 in
     Return (st2, msgs_left)
 
 (** [betree_main::betree::Internal::{4}::flush]: backward function 0 *)
-and betree_internal_flush_back'a
-  (self : betree_internal_t) (params : betree_params_t)
-  (node_id_cnt : betree_node_id_counter_t)
-  (content : betree_list_t (u64 & betree_message_t)) (st : state) (st0 : state)
+and betree_Internal_flush_back'a
+  (self : betree_Internal_t) (params : betree_Params_t)
+  (node_id_cnt : betree_NodeIdCounter_t)
+  (content : betree_List_t (u64 & betree_Message_t)) (st : state) (st0 : state)
   :
-  Tot (result (state & (betree_internal_t & betree_node_id_counter_t)))
+  Tot (result (state & (betree_Internal_t & betree_NodeIdCounter_t)))
   (decreases (
-    betree_internal_flush_decreases self params node_id_cnt content st))
+    betree_Internal_flush_decreases self params node_id_cnt content st))
   =
-  let* p =
-    betree_list_partition_at_pivot_fwd betree_message_t content
-      self.betree_internal_pivot in
+  let* p = betree_List_partition_at_pivot betree_Message_t content self.pivot
+    in
   let (msgs_left, msgs_right) = p in
-  let* len_left = betree_list_len_fwd (u64 & betree_message_t) msgs_left in
-  if len_left >= params.betree_params_min_flush_size
+  let* len_left = betree_List_len (u64 & betree_Message_t) msgs_left in
+  if len_left >= params.min_flush_size
   then
     let* (st1, _) =
-      betree_node_apply_messages_fwd self.betree_internal_left params
-        node_id_cnt msgs_left st in
+      betree_Node_apply_messages self.left params node_id_cnt msgs_left st in
     let* (st2, (n, node_id_cnt0)) =
-      betree_node_apply_messages_back'a self.betree_internal_left params
-        node_id_cnt msgs_left st st1 in
+      betree_Node_apply_messages_back'a self.left params node_id_cnt msgs_left
+        st st1 in
     let* (st3, ()) =
-      betree_node_apply_messages_back1 self.betree_internal_left params
-        node_id_cnt msgs_left st st2 in
-    let* len_right = betree_list_len_fwd (u64 & betree_message_t) msgs_right in
-    if len_right >= params.betree_params_min_flush_size
+      betree_Node_apply_messages_back1 self.left params node_id_cnt msgs_left
+        st st2 in
+    let* len_right = betree_List_len (u64 & betree_Message_t) msgs_right in
+    if len_right >= params.min_flush_size
     then
       let* (st4, _) =
-        betree_node_apply_messages_fwd self.betree_internal_right params
-          node_id_cnt0 msgs_right st3 in
+        betree_Node_apply_messages self.right params node_id_cnt0 msgs_right
+          st3 in
       let* (st5, (n0, node_id_cnt1)) =
-        betree_node_apply_messages_back'a self.betree_internal_right params
-          node_id_cnt0 msgs_right st3 st4 in
+        betree_Node_apply_messages_back'a self.right params node_id_cnt0
+          msgs_right st3 st4 in
       let* _ =
-        betree_node_apply_messages_back1 self.betree_internal_right params
-          node_id_cnt0 msgs_right st3 st5 in
-      Return (st0,
-        ({ self with betree_internal_left = n; betree_internal_right = n0 },
-        node_id_cnt1))
-    else Return (st0, ({ self with betree_internal_left = n }, node_id_cnt0))
+        betree_Node_apply_messages_back1 self.right params node_id_cnt0
+          msgs_right st3 st5 in
+      Return (st0, ({ self with left = n; right = n0 }, node_id_cnt1))
+    else Return (st0, ({ self with left = n }, node_id_cnt0))
   else
     let* (st1, _) =
-      betree_node_apply_messages_fwd self.betree_internal_right params
-        node_id_cnt msgs_right st in
+      betree_Node_apply_messages self.right params node_id_cnt msgs_right st in
     let* (st2, (n, node_id_cnt0)) =
-      betree_node_apply_messages_back'a self.betree_internal_right params
-        node_id_cnt msgs_right st st1 in
+      betree_Node_apply_messages_back'a self.right params node_id_cnt
+        msgs_right st st1 in
     let* _ =
-      betree_node_apply_messages_back1 self.betree_internal_right params
-        node_id_cnt msgs_right st st2 in
-    Return (st0, ({ self with betree_internal_right = n }, node_id_cnt0))
+      betree_Node_apply_messages_back1 self.right params node_id_cnt msgs_right
+        st st2 in
+    Return (st0, ({ self with right = n }, node_id_cnt0))
 
 (** [betree_main::betree::Internal::{4}::flush]: backward function 1 *)
-and betree_internal_flush_back1
-  (self : betree_internal_t) (params : betree_params_t)
-  (node_id_cnt : betree_node_id_counter_t)
-  (content : betree_list_t (u64 & betree_message_t)) (st : state) (st0 : state)
+and betree_Internal_flush_back1
+  (self : betree_Internal_t) (params : betree_Params_t)
+  (node_id_cnt : betree_NodeIdCounter_t)
+  (content : betree_List_t (u64 & betree_Message_t)) (st : state) (st0 : state)
   :
   Tot (result (state & unit))
   (decreases (
-    betree_internal_flush_decreases self params node_id_cnt content st))
+    betree_Internal_flush_decreases self params node_id_cnt content st))
   =
-  let* p =
-    betree_list_partition_at_pivot_fwd betree_message_t content
-      self.betree_internal_pivot in
+  let* p = betree_List_partition_at_pivot betree_Message_t content self.pivot
+    in
   let (msgs_left, msgs_right) = p in
-  let* len_left = betree_list_len_fwd (u64 & betree_message_t) msgs_left in
-  if len_left >= params.betree_params_min_flush_size
+  let* len_left = betree_List_len (u64 & betree_Message_t) msgs_left in
+  if len_left >= params.min_flush_size
   then
     let* (st1, _) =
-      betree_node_apply_messages_fwd self.betree_internal_left params
-        node_id_cnt msgs_left st in
+      betree_Node_apply_messages self.left params node_id_cnt msgs_left st in
     let* (st2, (_, node_id_cnt0)) =
-      betree_node_apply_messages_back'a self.betree_internal_left params
-        node_id_cnt msgs_left st st1 in
+      betree_Node_apply_messages_back'a self.left params node_id_cnt msgs_left
+        st st1 in
     let* (st3, ()) =
-      betree_node_apply_messages_back1 self.betree_internal_left params
-        node_id_cnt msgs_left st st2 in
-    let* len_right = betree_list_len_fwd (u64 & betree_message_t) msgs_right in
-    if len_right >= params.betree_params_min_flush_size
+      betree_Node_apply_messages_back1 self.left params node_id_cnt msgs_left
+        st st2 in
+    let* len_right = betree_List_len (u64 & betree_Message_t) msgs_right in
+    if len_right >= params.min_flush_size
     then
       let* (st4, _) =
-        betree_node_apply_messages_fwd self.betree_internal_right params
-          node_id_cnt0 msgs_right st3 in
+        betree_Node_apply_messages self.right params node_id_cnt0 msgs_right
+          st3 in
       let* (st5, (_, _)) =
-        betree_node_apply_messages_back'a self.betree_internal_right params
-          node_id_cnt0 msgs_right st3 st4 in
+        betree_Node_apply_messages_back'a self.right params node_id_cnt0
+          msgs_right st3 st4 in
       let* _ =
-        betree_node_apply_messages_back1 self.betree_internal_right params
-          node_id_cnt0 msgs_right st3 st5 in
+        betree_Node_apply_messages_back1 self.right params node_id_cnt0
+          msgs_right st3 st5 in
       Return (st0, ())
     else Return (st0, ())
   else
     let* (st1, _) =
-      betree_node_apply_messages_fwd self.betree_internal_right params
-        node_id_cnt msgs_right st in
+      betree_Node_apply_messages self.right params node_id_cnt msgs_right st in
     let* (st2, (_, _)) =
-      betree_node_apply_messages_back'a self.betree_internal_right params
-        node_id_cnt msgs_right st st1 in
+      betree_Node_apply_messages_back'a self.right params node_id_cnt
+        msgs_right st st1 in
     let* _ =
-      betree_node_apply_messages_back1 self.betree_internal_right params
-        node_id_cnt msgs_right st st2 in
+      betree_Node_apply_messages_back1 self.right params node_id_cnt msgs_right
+        st st2 in
     Return (st0, ())
 
 (** [betree_main::betree::Node::{5}::apply_messages]: forward function *)
-and betree_node_apply_messages_fwd
-  (self : betree_node_t) (params : betree_params_t)
-  (node_id_cnt : betree_node_id_counter_t)
-  (msgs : betree_list_t (u64 & betree_message_t)) (st : state) :
+and betree_Node_apply_messages
+  (self : betree_Node_t) (params : betree_Params_t)
+  (node_id_cnt : betree_NodeIdCounter_t)
+  (msgs : betree_List_t (u64 & betree_Message_t)) (st : state) :
   Tot (result (state & unit))
   (decreases (
-    betree_node_apply_messages_decreases self params node_id_cnt msgs st))
+    betree_Node_apply_messages_decreases self params node_id_cnt msgs st))
   =
   begin match self with
-  | BetreeNodeInternal node ->
-    let* (st0, content) =
-      betree_load_internal_node_fwd node.betree_internal_id st in
-    let* content0 =
-      betree_node_apply_messages_to_internal_fwd_back content msgs in
-    let* num_msgs = betree_list_len_fwd (u64 & betree_message_t) content0 in
-    if num_msgs >= params.betree_params_min_flush_size
+  | Betree_Node_Internal node ->
+    let* (st0, content) = betree_load_internal_node node.id st in
+    let* content0 = betree_Node_apply_messages_to_internal content msgs in
+    let* num_msgs = betree_List_len (u64 & betree_Message_t) content0 in
+    if num_msgs >= params.min_flush_size
     then
       let* (st1, content1) =
-        betree_internal_flush_fwd node params node_id_cnt content0 st0 in
+        betree_Internal_flush node params node_id_cnt content0 st0 in
       let* (st2, (node0, _)) =
-        betree_internal_flush_back'a node params node_id_cnt content0 st0 st1
+        betree_Internal_flush_back'a node params node_id_cnt content0 st0 st1
         in
-      let* (st3, _) =
-        betree_store_internal_node_fwd node0.betree_internal_id content1 st2 in
+      let* (st3, _) = betree_store_internal_node node0.id content1 st2 in
       Return (st3, ())
     else
-      let* (st1, _) =
-        betree_store_internal_node_fwd node.betree_internal_id content0 st0 in
+      let* (st1, _) = betree_store_internal_node node.id content0 st0 in
       Return (st1, ())
-  | BetreeNodeLeaf node ->
-    let* (st0, content) = betree_load_leaf_node_fwd node.betree_leaf_id st in
-    let* content0 = betree_node_apply_messages_to_leaf_fwd_back content msgs in
-    let* len = betree_list_len_fwd (u64 & u64) content0 in
-    let* i = u64_mul 2 params.betree_params_split_size in
+  | Betree_Node_Leaf node ->
+    let* (st0, content) = betree_load_leaf_node node.id st in
+    let* content0 = betree_Node_apply_messages_to_leaf content msgs in
+    let* len = betree_List_len (u64 & u64) content0 in
+    let* i = u64_mul 2 params.split_size in
     if len >= i
     then
-      let* (st1, _) =
-        betree_leaf_split_fwd node content0 params node_id_cnt st0 in
-      let* (st2, _) =
-        betree_store_leaf_node_fwd node.betree_leaf_id BetreeListNil st1 in
-      betree_leaf_split_back0 node content0 params node_id_cnt st0 st2
+      let* (st1, _) = betree_Leaf_split node content0 params node_id_cnt st0 in
+      let* (st2, _) = betree_store_leaf_node node.id Betree_List_Nil st1 in
+      betree_Leaf_split_back0 node content0 params node_id_cnt st0 st2
     else
-      let* (st1, _) =
-        betree_store_leaf_node_fwd node.betree_leaf_id content0 st0 in
+      let* (st1, _) = betree_store_leaf_node node.id content0 st0 in
       Return (st1, ())
   end
 
 (** [betree_main::betree::Node::{5}::apply_messages]: backward function 0 *)
-and betree_node_apply_messages_back'a
-  (self : betree_node_t) (params : betree_params_t)
-  (node_id_cnt : betree_node_id_counter_t)
-  (msgs : betree_list_t (u64 & betree_message_t)) (st : state) (st0 : state) :
-  Tot (result (state & (betree_node_t & betree_node_id_counter_t)))
+and betree_Node_apply_messages_back'a
+  (self : betree_Node_t) (params : betree_Params_t)
+  (node_id_cnt : betree_NodeIdCounter_t)
+  (msgs : betree_List_t (u64 & betree_Message_t)) (st : state) (st0 : state) :
+  Tot (result (state & (betree_Node_t & betree_NodeIdCounter_t)))
   (decreases (
-    betree_node_apply_messages_decreases self params node_id_cnt msgs st))
+    betree_Node_apply_messages_decreases self params node_id_cnt msgs st))
   =
   begin match self with
-  | BetreeNodeInternal node ->
-    let* (st1, content) =
-      betree_load_internal_node_fwd node.betree_internal_id st in
-    let* content0 =
-      betree_node_apply_messages_to_internal_fwd_back content msgs in
-    let* num_msgs = betree_list_len_fwd (u64 & betree_message_t) content0 in
-    if num_msgs >= params.betree_params_min_flush_size
+  | Betree_Node_Internal node ->
+    let* (st1, content) = betree_load_internal_node node.id st in
+    let* content0 = betree_Node_apply_messages_to_internal content msgs in
+    let* num_msgs = betree_List_len (u64 & betree_Message_t) content0 in
+    if num_msgs >= params.min_flush_size
     then
       let* (st2, content1) =
-        betree_internal_flush_fwd node params node_id_cnt content0 st1 in
+        betree_Internal_flush node params node_id_cnt content0 st1 in
       let* (st3, (node0, node_id_cnt0)) =
-        betree_internal_flush_back'a node params node_id_cnt content0 st1 st2
+        betree_Internal_flush_back'a node params node_id_cnt content0 st1 st2
         in
-      let* _ =
-        betree_store_internal_node_fwd node0.betree_internal_id content1 st3 in
-      Return (st0, (BetreeNodeInternal node0, node_id_cnt0))
+      let* _ = betree_store_internal_node node0.id content1 st3 in
+      Return (st0, (Betree_Node_Internal node0, node_id_cnt0))
     else
-      let* _ =
-        betree_store_internal_node_fwd node.betree_internal_id content0 st1 in
-      Return (st0, (BetreeNodeInternal node, node_id_cnt))
-  | BetreeNodeLeaf node ->
-    let* (st1, content) = betree_load_leaf_node_fwd node.betree_leaf_id st in
-    let* content0 = betree_node_apply_messages_to_leaf_fwd_back content msgs in
-    let* len = betree_list_len_fwd (u64 & u64) content0 in
-    let* i = u64_mul 2 params.betree_params_split_size in
+      let* _ = betree_store_internal_node node.id content0 st1 in
+      Return (st0, (Betree_Node_Internal node, node_id_cnt))
+  | Betree_Node_Leaf node ->
+    let* (st1, content) = betree_load_leaf_node node.id st in
+    let* content0 = betree_Node_apply_messages_to_leaf content msgs in
+    let* len = betree_List_len (u64 & u64) content0 in
+    let* i = u64_mul 2 params.split_size in
     if len >= i
     then
       let* (st2, new_node) =
-        betree_leaf_split_fwd node content0 params node_id_cnt st1 in
-      let* (st3, _) =
-        betree_store_leaf_node_fwd node.betree_leaf_id BetreeListNil st2 in
-      let* _ = betree_leaf_split_back0 node content0 params node_id_cnt st1 st3
+        betree_Leaf_split node content0 params node_id_cnt st1 in
+      let* (st3, _) = betree_store_leaf_node node.id Betree_List_Nil st2 in
+      let* _ = betree_Leaf_split_back0 node content0 params node_id_cnt st1 st3
         in
       let* (st4, node_id_cnt0) =
-        betree_leaf_split_back2 node content0 params node_id_cnt st1 st0 in
-      Return (st4, (BetreeNodeInternal new_node, node_id_cnt0))
+        betree_Leaf_split_back2 node content0 params node_id_cnt st1 st0 in
+      Return (st4, (Betree_Node_Internal new_node, node_id_cnt0))
     else
-      let* _ = betree_store_leaf_node_fwd node.betree_leaf_id content0 st1 in
-      Return (st0, (BetreeNodeLeaf { node with betree_leaf_size = len },
-        node_id_cnt))
+      let* _ = betree_store_leaf_node node.id content0 st1 in
+      Return (st0, (Betree_Node_Leaf { node with size = len }, node_id_cnt))
   end
 
 (** [betree_main::betree::Node::{5}::apply_messages]: backward function 1 *)
-and betree_node_apply_messages_back1
-  (self : betree_node_t) (params : betree_params_t)
-  (node_id_cnt : betree_node_id_counter_t)
-  (msgs : betree_list_t (u64 & betree_message_t)) (st : state) (st0 : state) :
+and betree_Node_apply_messages_back1
+  (self : betree_Node_t) (params : betree_Params_t)
+  (node_id_cnt : betree_NodeIdCounter_t)
+  (msgs : betree_List_t (u64 & betree_Message_t)) (st : state) (st0 : state) :
   Tot (result (state & unit))
   (decreases (
-    betree_node_apply_messages_decreases self params node_id_cnt msgs st))
+    betree_Node_apply_messages_decreases self params node_id_cnt msgs st))
   =
   begin match self with
-  | BetreeNodeInternal node ->
-    let* (st1, content) =
-      betree_load_internal_node_fwd node.betree_internal_id st in
-    let* content0 =
-      betree_node_apply_messages_to_internal_fwd_back content msgs in
-    let* num_msgs = betree_list_len_fwd (u64 & betree_message_t) content0 in
-    if num_msgs >= params.betree_params_min_flush_size
+  | Betree_Node_Internal node ->
+    let* (st1, content) = betree_load_internal_node node.id st in
+    let* content0 = betree_Node_apply_messages_to_internal content msgs in
+    let* num_msgs = betree_List_len (u64 & betree_Message_t) content0 in
+    if num_msgs >= params.min_flush_size
     then
       let* (st2, content1) =
-        betree_internal_flush_fwd node params node_id_cnt content0 st1 in
+        betree_Internal_flush node params node_id_cnt content0 st1 in
       let* (st3, (node0, _)) =
-        betree_internal_flush_back'a node params node_id_cnt content0 st1 st2
+        betree_Internal_flush_back'a node params node_id_cnt content0 st1 st2
         in
-      let* _ =
-        betree_store_internal_node_fwd node0.betree_internal_id content1 st3 in
-      betree_internal_flush_back1 node params node_id_cnt content0 st1 st0
+      let* _ = betree_store_internal_node node0.id content1 st3 in
+      betree_Internal_flush_back1 node params node_id_cnt content0 st1 st0
     else
-      let* _ =
-        betree_store_internal_node_fwd node.betree_internal_id content0 st1 in
+      let* _ = betree_store_internal_node node.id content0 st1 in
       Return (st0, ())
-  | BetreeNodeLeaf node ->
-    let* (st1, content) = betree_load_leaf_node_fwd node.betree_leaf_id st in
-    let* content0 = betree_node_apply_messages_to_leaf_fwd_back content msgs in
-    let* len = betree_list_len_fwd (u64 & u64) content0 in
-    let* i = u64_mul 2 params.betree_params_split_size in
+  | Betree_Node_Leaf node ->
+    let* (st1, content) = betree_load_leaf_node node.id st in
+    let* content0 = betree_Node_apply_messages_to_leaf content msgs in
+    let* len = betree_List_len (u64 & u64) content0 in
+    let* i = u64_mul 2 params.split_size in
     if len >= i
     then
-      let* (st2, _) =
-        betree_leaf_split_fwd node content0 params node_id_cnt st1 in
-      let* (st3, _) =
-        betree_store_leaf_node_fwd node.betree_leaf_id BetreeListNil st2 in
-      let* _ = betree_leaf_split_back0 node content0 params node_id_cnt st1 st3
+      let* (st2, _) = betree_Leaf_split node content0 params node_id_cnt st1 in
+      let* (st3, _) = betree_store_leaf_node node.id Betree_List_Nil st2 in
+      let* _ = betree_Leaf_split_back0 node content0 params node_id_cnt st1 st3
         in
-      betree_leaf_split_back1 node content0 params node_id_cnt st1 st0
+      betree_Leaf_split_back1 node content0 params node_id_cnt st1 st0
     else
-      let* _ = betree_store_leaf_node_fwd node.betree_leaf_id content0 st1 in
-      Return (st0, ())
+      let* _ = betree_store_leaf_node node.id content0 st1 in Return (st0, ())
   end
 
 (** [betree_main::betree::Node::{5}::apply]: forward function *)
-let betree_node_apply_fwd
-  (self : betree_node_t) (params : betree_params_t)
-  (node_id_cnt : betree_node_id_counter_t) (key : u64)
-  (new_msg : betree_message_t) (st : state) :
+let betree_Node_apply
+  (self : betree_Node_t) (params : betree_Params_t)
+  (node_id_cnt : betree_NodeIdCounter_t) (key : u64)
+  (new_msg : betree_Message_t) (st : state) :
   result (state & unit)
   =
-  let l = BetreeListNil in
+  let l = Betree_List_Nil in
   let* (st0, _) =
-    betree_node_apply_messages_fwd self params node_id_cnt (BetreeListCons
-      (key, new_msg) l) st in
+    betree_Node_apply_messages self params node_id_cnt (Betree_List_Cons (key,
+      new_msg) l) st in
   let* (st1, (_, _)) =
-    betree_node_apply_messages_back'a self params node_id_cnt (BetreeListCons
+    betree_Node_apply_messages_back'a self params node_id_cnt (Betree_List_Cons
       (key, new_msg) l) st st0 in
-  betree_node_apply_messages_back1 self params node_id_cnt (BetreeListCons
+  betree_Node_apply_messages_back1 self params node_id_cnt (Betree_List_Cons
     (key, new_msg) l) st st1
 
 (** [betree_main::betree::Node::{5}::apply]: backward function 0 *)
-let betree_node_apply_back'a
-  (self : betree_node_t) (params : betree_params_t)
-  (node_id_cnt : betree_node_id_counter_t) (key : u64)
-  (new_msg : betree_message_t) (st : state) (st0 : state) :
-  result (state & (betree_node_t & betree_node_id_counter_t))
+let betree_Node_apply_back'a
+  (self : betree_Node_t) (params : betree_Params_t)
+  (node_id_cnt : betree_NodeIdCounter_t) (key : u64)
+  (new_msg : betree_Message_t) (st : state) (st0 : state) :
+  result (state & (betree_Node_t & betree_NodeIdCounter_t))
   =
-  let l = BetreeListNil in
+  let l = Betree_List_Nil in
   let* (st1, _) =
-    betree_node_apply_messages_fwd self params node_id_cnt (BetreeListCons
-      (key, new_msg) l) st in
+    betree_Node_apply_messages self params node_id_cnt (Betree_List_Cons (key,
+      new_msg) l) st in
   let* (st2, (self0, node_id_cnt0)) =
-    betree_node_apply_messages_back'a self params node_id_cnt (BetreeListCons
+    betree_Node_apply_messages_back'a self params node_id_cnt (Betree_List_Cons
       (key, new_msg) l) st st1 in
   let* _ =
-    betree_node_apply_messages_back1 self params node_id_cnt (BetreeListCons
+    betree_Node_apply_messages_back1 self params node_id_cnt (Betree_List_Cons
       (key, new_msg) l) st st2 in
   Return (st0, (self0, node_id_cnt0))
 
 (** [betree_main::betree::Node::{5}::apply]: backward function 1 *)
-let betree_node_apply_back1
-  (self : betree_node_t) (params : betree_params_t)
-  (node_id_cnt : betree_node_id_counter_t) (key : u64)
-  (new_msg : betree_message_t) (st : state) (st0 : state) :
+let betree_Node_apply_back1
+  (self : betree_Node_t) (params : betree_Params_t)
+  (node_id_cnt : betree_NodeIdCounter_t) (key : u64)
+  (new_msg : betree_Message_t) (st : state) (st0 : state) :
   result (state & unit)
   =
-  let l = BetreeListNil in
+  let l = Betree_List_Nil in
   let* (st1, _) =
-    betree_node_apply_messages_fwd self params node_id_cnt (BetreeListCons
-      (key, new_msg) l) st in
+    betree_Node_apply_messages self params node_id_cnt (Betree_List_Cons (key,
+      new_msg) l) st in
   let* (st2, (_, _)) =
-    betree_node_apply_messages_back'a self params node_id_cnt (BetreeListCons
+    betree_Node_apply_messages_back'a self params node_id_cnt (Betree_List_Cons
       (key, new_msg) l) st st1 in
   let* _ =
-    betree_node_apply_messages_back1 self params node_id_cnt (BetreeListCons
+    betree_Node_apply_messages_back1 self params node_id_cnt (Betree_List_Cons
       (key, new_msg) l) st st2 in
   Return (st0, ())
 
 (** [betree_main::betree::BeTree::{6}::new]: forward function *)
-let betree_be_tree_new_fwd
+let betree_BeTree_new
   (min_flush_size : u64) (split_size : u64) (st : state) :
-  result (state & betree_be_tree_t)
+  result (state & betree_BeTree_t)
   =
-  let* node_id_cnt = betree_node_id_counter_new_fwd in
-  let* id = betree_node_id_counter_fresh_id_fwd node_id_cnt in
-  let* (st0, _) = betree_store_leaf_node_fwd id BetreeListNil st in
-  let* node_id_cnt0 = betree_node_id_counter_fresh_id_back node_id_cnt in
+  let* node_id_cnt = betree_NodeIdCounter_new in
+  let* id = betree_NodeIdCounter_fresh_id node_id_cnt in
+  let* (st0, _) = betree_store_leaf_node id Betree_List_Nil st in
+  let* node_id_cnt0 = betree_NodeIdCounter_fresh_id_back node_id_cnt in
   Return (st0,
     {
-      betree_be_tree_params =
-        {
-          betree_params_min_flush_size = min_flush_size;
-          betree_params_split_size = split_size
-        };
-      betree_be_tree_node_id_cnt = node_id_cnt0;
-      betree_be_tree_root =
-        (BetreeNodeLeaf { betree_leaf_id = id; betree_leaf_size = 0 })
+      params = { min_flush_size = min_flush_size; split_size = split_size };
+      node_id_cnt = node_id_cnt0;
+      root = (Betree_Node_Leaf { id = id; size = 0 })
     })
 
 (** [betree_main::betree::BeTree::{6}::apply]: forward function *)
-let betree_be_tree_apply_fwd
-  (self : betree_be_tree_t) (key : u64) (msg : betree_message_t) (st : state) :
+let betree_BeTree_apply
+  (self : betree_BeTree_t) (key : u64) (msg : betree_Message_t) (st : state) :
   result (state & unit)
   =
   let* (st0, _) =
-    betree_node_apply_fwd self.betree_be_tree_root self.betree_be_tree_params
-      self.betree_be_tree_node_id_cnt key msg st in
+    betree_Node_apply self.root self.params self.node_id_cnt key msg st in
   let* (st1, (_, _)) =
-    betree_node_apply_back'a self.betree_be_tree_root
-      self.betree_be_tree_params self.betree_be_tree_node_id_cnt key msg st st0
-    in
-  betree_node_apply_back1 self.betree_be_tree_root self.betree_be_tree_params
-    self.betree_be_tree_node_id_cnt key msg st st1
+    betree_Node_apply_back'a self.root self.params self.node_id_cnt key msg st
+      st0 in
+  betree_Node_apply_back1 self.root self.params self.node_id_cnt key msg st st1
 
 (** [betree_main::betree::BeTree::{6}::apply]: backward function 0 *)
-let betree_be_tree_apply_back
-  (self : betree_be_tree_t) (key : u64) (msg : betree_message_t) (st : state)
+let betree_BeTree_apply_back
+  (self : betree_BeTree_t) (key : u64) (msg : betree_Message_t) (st : state)
   (st0 : state) :
-  result (state & betree_be_tree_t)
+  result (state & betree_BeTree_t)
   =
   let* (st1, _) =
-    betree_node_apply_fwd self.betree_be_tree_root self.betree_be_tree_params
-      self.betree_be_tree_node_id_cnt key msg st in
+    betree_Node_apply self.root self.params self.node_id_cnt key msg st in
   let* (st2, (n, nic)) =
-    betree_node_apply_back'a self.betree_be_tree_root
-      self.betree_be_tree_params self.betree_be_tree_node_id_cnt key msg st st1
-    in
+    betree_Node_apply_back'a self.root self.params self.node_id_cnt key msg st
+      st1 in
   let* _ =
-    betree_node_apply_back1 self.betree_be_tree_root self.betree_be_tree_params
-      self.betree_be_tree_node_id_cnt key msg st st2 in
-  Return (st0,
-    { self with betree_be_tree_node_id_cnt = nic; betree_be_tree_root = n })
+    betree_Node_apply_back1 self.root self.params self.node_id_cnt key msg st
+      st2 in
+  Return (st0, { self with node_id_cnt = nic; root = n })
 
 (** [betree_main::betree::BeTree::{6}::insert]: forward function *)
-let betree_be_tree_insert_fwd
-  (self : betree_be_tree_t) (key : u64) (value : u64) (st : state) :
+let betree_BeTree_insert
+  (self : betree_BeTree_t) (key : u64) (value : u64) (st : state) :
   result (state & unit)
   =
-  let* (st0, _) =
-    betree_be_tree_apply_fwd self key (BetreeMessageInsert value) st in
+  let* (st0, _) = betree_BeTree_apply self key (Betree_Message_Insert value) st
+    in
   let* (st1, _) =
-    betree_be_tree_apply_back self key (BetreeMessageInsert value) st st0 in
+    betree_BeTree_apply_back self key (Betree_Message_Insert value) st st0 in
   Return (st1, ())
 
 (** [betree_main::betree::BeTree::{6}::insert]: backward function 0 *)
-let betree_be_tree_insert_back
-  (self : betree_be_tree_t) (key : u64) (value : u64) (st : state)
-  (st0 : state) :
-  result (state & betree_be_tree_t)
+let betree_BeTree_insert_back
+  (self : betree_BeTree_t) (key : u64) (value : u64) (st : state) (st0 : state)
+  :
+  result (state & betree_BeTree_t)
   =
-  let* (st1, _) =
-    betree_be_tree_apply_fwd self key (BetreeMessageInsert value) st in
+  let* (st1, _) = betree_BeTree_apply self key (Betree_Message_Insert value) st
+    in
   let* (_, self0) =
-    betree_be_tree_apply_back self key (BetreeMessageInsert value) st st1 in
+    betree_BeTree_apply_back self key (Betree_Message_Insert value) st st1 in
   Return (st0, self0)
 
 (** [betree_main::betree::BeTree::{6}::delete]: forward function *)
-let betree_be_tree_delete_fwd
-  (self : betree_be_tree_t) (key : u64) (st : state) : result (state & unit) =
-  let* (st0, _) = betree_be_tree_apply_fwd self key BetreeMessageDelete st in
-  let* (st1, _) = betree_be_tree_apply_back self key BetreeMessageDelete st st0
-    in
+let betree_BeTree_delete
+  (self : betree_BeTree_t) (key : u64) (st : state) : result (state & unit) =
+  let* (st0, _) = betree_BeTree_apply self key Betree_Message_Delete st in
+  let* (st1, _) =
+    betree_BeTree_apply_back self key Betree_Message_Delete st st0 in
   Return (st1, ())
 
 (** [betree_main::betree::BeTree::{6}::delete]: backward function 0 *)
-let betree_be_tree_delete_back
-  (self : betree_be_tree_t) (key : u64) (st : state) (st0 : state) :
-  result (state & betree_be_tree_t)
+let betree_BeTree_delete_back
+  (self : betree_BeTree_t) (key : u64) (st : state) (st0 : state) :
+  result (state & betree_BeTree_t)
   =
-  let* (st1, _) = betree_be_tree_apply_fwd self key BetreeMessageDelete st in
+  let* (st1, _) = betree_BeTree_apply self key Betree_Message_Delete st in
   let* (_, self0) =
-    betree_be_tree_apply_back self key BetreeMessageDelete st st1 in
+    betree_BeTree_apply_back self key Betree_Message_Delete st st1 in
   Return (st0, self0)
 
 (** [betree_main::betree::BeTree::{6}::upsert]: forward function *)
-let betree_be_tree_upsert_fwd
-  (self : betree_be_tree_t) (key : u64) (upd : betree_upsert_fun_state_t)
+let betree_BeTree_upsert
+  (self : betree_BeTree_t) (key : u64) (upd : betree_UpsertFunState_t)
   (st : state) :
   result (state & unit)
   =
-  let* (st0, _) =
-    betree_be_tree_apply_fwd self key (BetreeMessageUpsert upd) st in
+  let* (st0, _) = betree_BeTree_apply self key (Betree_Message_Upsert upd) st
+    in
   let* (st1, _) =
-    betree_be_tree_apply_back self key (BetreeMessageUpsert upd) st st0 in
+    betree_BeTree_apply_back self key (Betree_Message_Upsert upd) st st0 in
   Return (st1, ())
 
 (** [betree_main::betree::BeTree::{6}::upsert]: backward function 0 *)
-let betree_be_tree_upsert_back
-  (self : betree_be_tree_t) (key : u64) (upd : betree_upsert_fun_state_t)
+let betree_BeTree_upsert_back
+  (self : betree_BeTree_t) (key : u64) (upd : betree_UpsertFunState_t)
   (st : state) (st0 : state) :
-  result (state & betree_be_tree_t)
+  result (state & betree_BeTree_t)
   =
-  let* (st1, _) =
-    betree_be_tree_apply_fwd self key (BetreeMessageUpsert upd) st in
+  let* (st1, _) = betree_BeTree_apply self key (Betree_Message_Upsert upd) st
+    in
   let* (_, self0) =
-    betree_be_tree_apply_back self key (BetreeMessageUpsert upd) st st1 in
+    betree_BeTree_apply_back self key (Betree_Message_Upsert upd) st st1 in
   Return (st0, self0)
 
 (** [betree_main::betree::BeTree::{6}::lookup]: forward function *)
-let betree_be_tree_lookup_fwd
-  (self : betree_be_tree_t) (key : u64) (st : state) :
+let betree_BeTree_lookup
+  (self : betree_BeTree_t) (key : u64) (st : state) :
   result (state & (option u64))
   =
-  betree_node_lookup_fwd self.betree_be_tree_root key st
+  betree_Node_lookup self.root key st
 
 (** [betree_main::betree::BeTree::{6}::lookup]: backward function 0 *)
-let betree_be_tree_lookup_back
-  (self : betree_be_tree_t) (key : u64) (st : state) (st0 : state) :
-  result (state & betree_be_tree_t)
+let betree_BeTree_lookup_back
+  (self : betree_BeTree_t) (key : u64) (st : state) (st0 : state) :
+  result (state & betree_BeTree_t)
   =
-  let* (st1, n) = betree_node_lookup_back self.betree_be_tree_root key st st0
-    in
-  Return (st1, { self with betree_be_tree_root = n })
+  let* (st1, n) = betree_Node_lookup_back self.root key st st0 in
+  Return (st1, { self with root = n })
 
 (** [betree_main::main]: forward function *)
-let main_fwd : result unit =
+let main : result unit =
   Return ()
 
 (** Unit test for [betree_main::main] *)
-let _ = assert_norm (main_fwd = Return ())
+let _ = assert_norm (main = Return ())
 
diff --git a/tests/fstar/betree_back_stateful/BetreeMain.Opaque.fsti b/tests/fstar/betree_back_stateful/BetreeMain.Opaque.fsti
index c33cf225..c5d0a814 100644
--- a/tests/fstar/betree_back_stateful/BetreeMain.Opaque.fsti
+++ b/tests/fstar/betree_back_stateful/BetreeMain.Opaque.fsti
@@ -7,24 +7,24 @@ include BetreeMain.Types
 #set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
 
 (** [betree_main::betree_utils::load_internal_node]: forward function *)
-val betree_utils_load_internal_node_fwd
-  : u64 -> state -> result (state & (betree_list_t (u64 & betree_message_t)))
+val betree_utils_load_internal_node
+  : u64 -> state -> result (state & (betree_List_t (u64 & betree_Message_t)))
 
 (** [betree_main::betree_utils::store_internal_node]: forward function *)
-val betree_utils_store_internal_node_fwd
+val betree_utils_store_internal_node
   :
-  u64 -> betree_list_t (u64 & betree_message_t) -> state -> result (state &
+  u64 -> betree_List_t (u64 & betree_Message_t) -> state -> result (state &
     unit)
 
 (** [betree_main::betree_utils::load_leaf_node]: forward function *)
-val betree_utils_load_leaf_node_fwd
-  : u64 -> state -> result (state & (betree_list_t (u64 & u64)))
+val betree_utils_load_leaf_node
+  : u64 -> state -> result (state & (betree_List_t (u64 & u64)))
 
 (** [betree_main::betree_utils::store_leaf_node]: forward function *)
-val betree_utils_store_leaf_node_fwd
-  : u64 -> betree_list_t (u64 & u64) -> state -> result (state & unit)
+val betree_utils_store_leaf_node
+  : u64 -> betree_List_t (u64 & u64) -> state -> result (state & unit)
 
 (** [core::option::Option::{0}::unwrap]: forward function *)
-val core_option_option_unwrap_fwd
+val core_option_Option_unwrap
   (t : Type0) : option t -> state -> result (state & t)
 
diff --git a/tests/fstar/betree_back_stateful/BetreeMain.Types.fsti b/tests/fstar/betree_back_stateful/BetreeMain.Types.fsti
index a937c726..9320f6b7 100644
--- a/tests/fstar/betree_back_stateful/BetreeMain.Types.fsti
+++ b/tests/fstar/betree_back_stateful/BetreeMain.Types.fsti
@@ -6,53 +6,47 @@ open Primitives
 #set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
 
 (** [betree_main::betree::List] *)
-type betree_list_t (t : Type0) =
-| BetreeListCons : t -> betree_list_t t -> betree_list_t t
-| BetreeListNil : betree_list_t t
+type betree_List_t (t : Type0) =
+| Betree_List_Cons : t -> betree_List_t t -> betree_List_t t
+| Betree_List_Nil : betree_List_t t
 
 (** [betree_main::betree::UpsertFunState] *)
-type betree_upsert_fun_state_t =
-| BetreeUpsertFunStateAdd : u64 -> betree_upsert_fun_state_t
-| BetreeUpsertFunStateSub : u64 -> betree_upsert_fun_state_t
+type betree_UpsertFunState_t =
+| Betree_UpsertFunState_Add : u64 -> betree_UpsertFunState_t
+| Betree_UpsertFunState_Sub : u64 -> betree_UpsertFunState_t
 
 (** [betree_main::betree::Message] *)
-type betree_message_t =
-| BetreeMessageInsert : u64 -> betree_message_t
-| BetreeMessageDelete : betree_message_t
-| BetreeMessageUpsert : betree_upsert_fun_state_t -> betree_message_t
+type betree_Message_t =
+| Betree_Message_Insert : u64 -> betree_Message_t
+| Betree_Message_Delete : betree_Message_t
+| Betree_Message_Upsert : betree_UpsertFunState_t -> betree_Message_t
 
 (** [betree_main::betree::Leaf] *)
-type betree_leaf_t = { betree_leaf_id : u64; betree_leaf_size : u64; }
+type betree_Leaf_t = { id : u64; size : u64; }
 
 (** [betree_main::betree::Internal] *)
-type betree_internal_t =
+type betree_Internal_t =
 {
-  betree_internal_id : u64;
-  betree_internal_pivot : u64;
-  betree_internal_left : betree_node_t;
-  betree_internal_right : betree_node_t;
+  id : u64; pivot : u64; left : betree_Node_t; right : betree_Node_t;
 }
 
 (** [betree_main::betree::Node] *)
-and betree_node_t =
-| BetreeNodeInternal : betree_internal_t -> betree_node_t
-| BetreeNodeLeaf : betree_leaf_t -> betree_node_t
+and betree_Node_t =
+| Betree_Node_Internal : betree_Internal_t -> betree_Node_t
+| Betree_Node_Leaf : betree_Leaf_t -> betree_Node_t
 
 (** [betree_main::betree::Params] *)
-type betree_params_t =
-{
-  betree_params_min_flush_size : u64; betree_params_split_size : u64;
-}
+type betree_Params_t = { min_flush_size : u64; split_size : u64; }
 
 (** [betree_main::betree::NodeIdCounter] *)
-type betree_node_id_counter_t = { betree_node_id_counter_next_node_id : u64; }
+type betree_NodeIdCounter_t = { next_node_id : u64; }
 
 (** [betree_main::betree::BeTree] *)
-type betree_be_tree_t =
+type betree_BeTree_t =
 {
-  betree_be_tree_params : betree_params_t;
-  betree_be_tree_node_id_cnt : betree_node_id_counter_t;
-  betree_be_tree_root : betree_node_t;
+  params : betree_Params_t;
+  node_id_cnt : betree_NodeIdCounter_t;
+  root : betree_Node_t;
 }
 
 (** The state type used in the state-error monad *)
diff --git a/tests/fstar/betree_back_stateful/Primitives.fst b/tests/fstar/betree_back_stateful/Primitives.fst
index 9db82069..3297803c 100644
--- a/tests/fstar/betree_back_stateful/Primitives.fst
+++ b/tests/fstar/betree_back_stateful/Primitives.fst
@@ -55,8 +55,12 @@ type string = string
 let is_zero (n: nat) : bool = n = 0
 let decrease (n: nat{n > 0}) : nat = n - 1
 
-let mem_replace_fwd (a : Type0) (x : a) (y : a) : a = x
-let mem_replace_back (a : Type0) (x : a) (y : a) : a = y
+let core_mem_replace (a : Type0) (x : a) (y : a) : a = x
+let core_mem_replace_back (a : Type0) (x : a) (y : a) : a = y
+
+// We don't really use raw pointers for now
+type mut_raw_ptr (t : Type0) = { v : t }
+type const_raw_ptr (t : Type0) = { v : t }
 
 (*** Scalars *)
 /// Rem.: most of the following code was partially generated
@@ -100,6 +104,11 @@ type scalar_ty =
 | U64
 | U128
 
+let is_unsigned = function
+  | Isize | I8 | I16 | I32 | I64 | I128 -> false
+  | Usize | U8 | U16 | U32 | U64 | U128 -> true
+
+
 let scalar_min (ty : scalar_ty) : int =
   match ty with
   | Isize -> isize_min
@@ -162,6 +171,15 @@ let scalar_sub (#ty : scalar_ty) (x : scalar ty) (y : scalar ty) : result (scala
 let scalar_mul (#ty : scalar_ty) (x : scalar ty) (y : scalar ty) : result (scalar ty) =
   mk_scalar ty (x * y)
 
+let scalar_lxor (#ty : scalar_ty { is_unsigned ty && ty <> Usize })
+    (x : scalar ty) (y : scalar ty) : scalar ty =
+  match ty with
+  | U8 -> FStar.UInt.logxor #8 x y
+  | U16 -> FStar.UInt.logxor #16 x y
+  | U32 -> FStar.UInt.logxor #32 x y
+  | U64 -> FStar.UInt.logxor #64 x y
+  | U128 -> FStar.UInt.logxor #128 x y
+
 (** Cast an integer from a [src_ty] to a [tgt_ty] *)
 // TODO: check the semantics of casts in Rust
 let scalar_cast (src_ty : scalar_ty) (tgt_ty : scalar_ty) (x : scalar src_ty) : result (scalar tgt_ty) =
@@ -169,17 +187,44 @@ let scalar_cast (src_ty : scalar_ty) (tgt_ty : scalar_ty) (x : scalar src_ty) :
 
 /// The scalar types
 type isize : eqtype = scalar Isize
-type i8 : eqtype = scalar I8
-type i16 : eqtype = scalar I16
-type i32 : eqtype = scalar I32
-type i64 : eqtype = scalar I64
-type i128 : eqtype = scalar I128
+type i8    : eqtype = scalar I8
+type i16   : eqtype = scalar I16
+type i32   : eqtype = scalar I32
+type i64   : eqtype = scalar I64
+type i128  : eqtype = scalar I128
 type usize : eqtype = scalar Usize
-type u8 : eqtype = scalar U8
-type u16 : eqtype = scalar U16
-type u32 : eqtype = scalar U32
-type u64 : eqtype = scalar U64
-type u128 : eqtype = scalar U128
+type u8    : eqtype = scalar U8
+type u16   : eqtype = scalar U16
+type u32   : eqtype = scalar U32
+type u64   : eqtype = scalar U64
+type u128  : eqtype = scalar U128
+
+
+let core_isize_min : isize = isize_min
+let core_isize_max : isize = isize_max
+let core_i8_min    : i8 = i8_min
+let core_i8_max    : i8 = i8_max
+let core_i16_min   : i16 = i16_min
+let core_i16_max   : i16 = i16_max
+let core_i32_min   : i32 = i32_min
+let core_i32_max   : i32 = i32_max
+let core_i64_min   : i64 = i64_min
+let core_i64_max   : i64 = i64_max
+let core_i128_min  : i128 = i128_min
+let core_i128_max  : i128 = i128_max
+
+let core_usize_min : usize = usize_min
+let core_usize_max : usize = usize_max
+let core_u8_min    : u8 = u8_min
+let core_u8_max    : u8 = u8_max
+let core_u16_min   : u16 = u16_min
+let core_u16_max   : u16 = u16_max
+let core_u32_min   : u32 = u32_min
+let core_u32_max   : u32 = u32_max
+let core_u64_min   : u64 = u64_min
+let core_u64_max   : u64 = u64_max
+let core_u128_min  : u128 = u128_min
+let core_u128_max  : u128 = u128_max
 
 /// Negation
 let isize_neg = scalar_neg #Isize
@@ -231,7 +276,7 @@ let u32_add = scalar_add #U32
 let u64_add = scalar_add #U64
 let u128_add = scalar_add #U128
 
-/// Substraction
+/// Subtraction
 let isize_sub = scalar_sub #Isize
 let i8_sub = scalar_sub #I8
 let i16_sub = scalar_sub #I16
@@ -259,12 +304,65 @@ let u32_mul = scalar_mul #U32
 let u64_mul = scalar_mul #U64
 let u128_mul = scalar_mul #U128
 
-(*** Range *)
-type range (a : Type0) = {
+/// Logical operators, defined for unsigned types only, so far
+let u8_xor = scalar_lxor #U8
+let u16_xor = scalar_lxor #U16
+let u32_xor = scalar_lxor #U32
+let u64_xor = scalar_lxor #U64
+let u128_xor = scalar_lxor #U128
+
+(*** core::ops *)
+
+// Trait declaration: [core::ops::index::Index]
+noeq type core_ops_index_Index (self idx : Type0) = {
+  output : Type0;
+  index : self → idx → result output
+}
+
+// Trait declaration: [core::ops::index::IndexMut]
+noeq type core_ops_index_IndexMut (self idx : Type0) = {
+  indexInst : core_ops_index_Index self idx;
+  index_mut : self → idx → result indexInst.output;
+  index_mut_back : self → idx → indexInst.output → result self;
+}
+
+// Trait declaration [core::ops::deref::Deref]
+noeq type core_ops_deref_Deref (self : Type0) = {
+  target : Type0;
+  deref : self → result target;
+}
+
+// Trait declaration [core::ops::deref::DerefMut]
+noeq type core_ops_deref_DerefMut (self : Type0) = {
+  derefInst : core_ops_deref_Deref self;
+  deref_mut : self → result derefInst.target;
+  deref_mut_back : self → derefInst.target → result self;
+}
+
+type core_ops_range_Range (a : Type0) = {
   start : a;
   end_ : a;
 }
 
+(*** [alloc] *)
+
+let alloc_boxed_Box_deref (t : Type0) (x : t) : result t = Return x
+let alloc_boxed_Box_deref_mut (t : Type0) (x : t) : result t = Return x
+let alloc_boxed_Box_deref_mut_back (t : Type) (_ : t) (x : t) : result t = Return x
+
+// Trait instance
+let alloc_boxed_Box_coreOpsDerefInst (self : Type0) : core_ops_deref_Deref self = {
+  target = self;
+  deref = alloc_boxed_Box_deref self;
+}
+
+// Trait instance
+let alloc_boxed_Box_coreOpsDerefMutInst (self : Type0) : core_ops_deref_DerefMut self = {
+  derefInst = alloc_boxed_Box_coreOpsDerefInst self;
+  deref_mut = alloc_boxed_Box_deref_mut self;
+  deref_mut_back = alloc_boxed_Box_deref_mut_back self;
+}
+
 (*** Array *)
 type array (a : Type0) (n : usize) = s:list a{length s = n}
 
@@ -278,15 +376,11 @@ let mk_array (a : Type0) (n : usize)
   normalize_term_spec (FStar.List.Tot.length l);
   l
 
-let array_index_shared (a : Type0) (n : usize) (x : array a n) (i : usize) : result a =
-  if i < length x then Return (index x i)
-  else Fail Failure
-
-let array_index_mut_fwd (a : Type0) (n : usize) (x : array a n) (i : usize) : result a =
+let array_index_usize (a : Type0) (n : usize) (x : array a n) (i : usize) : result a =
   if i < length x then Return (index x i)
   else Fail Failure
 
-let array_index_mut_back (a : Type0) (n : usize) (x : array a n) (i : usize) (nx : a) : result (array a n) =
+let array_update_usize (a : Type0) (n : usize) (x : array a n) (i : usize) (nx : a) : result (array a n) =
   if i < length x then Return (list_update x i nx)
   else Fail Failure
 
@@ -295,55 +389,54 @@ type slice (a : Type0) = s:list a{length s <= usize_max}
 
 let slice_len (a : Type0) (s : slice a) : usize = length s
 
-let slice_index_shared (a : Type0) (x : slice a) (i : usize) : result a =
+let slice_index_usize (a : Type0) (x : slice a) (i : usize) : result a =
   if i < length x then Return (index x i)
   else Fail Failure
 
-let slice_index_mut_fwd (a : Type0) (x : slice a) (i : usize) : result a =
-  if i < length x then Return (index x i)
-  else Fail Failure
-
-let slice_index_mut_back (a : Type0) (x : slice a) (i : usize) (nx : a) : result (slice a) =
+let slice_update_usize (a : Type0) (x : slice a) (i : usize) (nx : a) : result (slice a) =
   if i < length x then Return (list_update x i nx)
   else Fail Failure
 
 (*** Subslices *)
 
-let array_to_slice_shared (a : Type0) (n : usize) (x : array a n) : result (slice a) = Return x
-let array_to_slice_mut_fwd (a : Type0) (n : usize) (x : array a n) : result (slice a) = Return x
-let array_to_slice_mut_back (a : Type0) (n : usize) (x : array a n) (s : slice a) : result (array a n) =
+let array_to_slice (a : Type0) (n : usize) (x : array a n) : result (slice a) = Return x
+let array_from_slice (a : Type0) (n : usize) (x : array a n) (s : slice a) : result (array a n) =
   if length s = n then Return s
   else Fail Failure
 
 // TODO: finish the definitions below (there lacks [List.drop] and [List.take] in the standard library *)
-let array_subslice_shared (a : Type0) (n : usize) (x : array a n) (r : range usize) : result (slice a) =
-  admit()
-
-let array_subslice_mut_fwd (a : Type0) (n : usize) (x : array a n) (r : range usize) : result (slice a) =
+let array_subslice (a : Type0) (n : usize) (x : array a n) (r : core_ops_range_Range usize) : result (slice a) =
   admit()
 
-let array_subslice_mut_back (a : Type0) (n : usize) (x : array a n) (r : range usize) (ns : slice a) : result (array a n) =
+let array_update_subslice (a : Type0) (n : usize) (x : array a n) (r : core_ops_range_Range usize) (ns : slice a) : result (array a n) =
   admit()
 
-let slice_subslice_shared (a : Type0) (x : slice a) (r : range usize) : result (slice a) =
+let array_repeat (a : Type0) (n : usize) (x : a) : array a n =
   admit()
 
-let slice_subslice_mut_fwd (a : Type0) (x : slice a) (r : range usize) : result (slice a) =
+let slice_subslice (a : Type0) (x : slice a) (r : core_ops_range_Range usize) : result (slice a) =
   admit()
 
-let slice_subslice_mut_back (a : Type0) (x : slice a) (r : range usize) (ns : slice a) : result (slice a) =
+let slice_update_subslice (a : Type0) (x : slice a) (r : core_ops_range_Range usize) (ns : slice a) : result (slice a) =
   admit()
 
 (*** Vector *)
-type vec (a : Type0) = v:list a{length v <= usize_max}
+type alloc_vec_Vec (a : Type0) = v:list a{length v <= usize_max}
 
-let vec_new (a  : Type0) : vec a = assert_norm(length #a [] == 0); []
-let vec_len (a : Type0) (v : vec a) : usize = length v
+let alloc_vec_Vec_new (a  : Type0) : alloc_vec_Vec a = assert_norm(length #a [] == 0); []
+let alloc_vec_Vec_len (a : Type0) (v : alloc_vec_Vec a) : usize = length v
+
+// Helper
+let alloc_vec_Vec_index_usize (#a : Type0) (v : alloc_vec_Vec a) (i : usize) : result a =
+  if i < length v then Return (index v i) else Fail Failure
+// Helper
+let alloc_vec_Vec_update_usize (#a : Type0) (v : alloc_vec_Vec a) (i : usize) (x : a) : result (alloc_vec_Vec a) =
+  if i < length v then Return (list_update v i x) else Fail Failure
 
 // The **forward** function shouldn't be used
-let vec_push_fwd (a  : Type0) (v : vec a) (x : a) : unit = ()
-let vec_push_back (a  : Type0) (v : vec a) (x : a) :
-  Pure (result (vec a))
+let alloc_vec_Vec_push_fwd (a  : Type0) (v : alloc_vec_Vec a) (x : a) : unit = ()
+let alloc_vec_Vec_push (a  : Type0) (v : alloc_vec_Vec a) (x : a) :
+  Pure (result (alloc_vec_Vec a))
   (requires True)
   (ensures (fun res ->
     match res with
@@ -358,18 +451,279 @@ let vec_push_back (a  : Type0) (v : vec a) (x : a) :
   else Fail Failure
 
 // The **forward** function shouldn't be used
-let vec_insert_fwd (a : Type0) (v : vec a) (i : usize) (x : a) : result unit =
+let alloc_vec_Vec_insert_fwd (a : Type0) (v : alloc_vec_Vec a) (i : usize) (x : a) : result unit =
   if i < length v then Return () else Fail Failure
-let vec_insert_back (a : Type0) (v : vec a) (i : usize) (x : a) : result (vec a) =
+let alloc_vec_Vec_insert (a : Type0) (v : alloc_vec_Vec a) (i : usize) (x : a) : result (alloc_vec_Vec a) =
   if i < length v then Return (list_update v i x) else Fail Failure
 
-// The **backward** function shouldn't be used
-let vec_index_fwd (a : Type0) (v : vec a) (i : usize) : result a =
-  if i < length v then Return (index v i) else Fail Failure
-let vec_index_back (a : Type0) (v : vec a) (i : usize) (x : a) : result unit =
-  if i < length v then Return () else Fail Failure
+// Trait declaration: [core::slice::index::private_slice_index::Sealed]
+type core_slice_index_private_slice_index_Sealed (self : Type0) = unit
+
+// Trait declaration: [core::slice::index::SliceIndex]
+noeq type core_slice_index_SliceIndex (self t : Type0) = {
+  sealedInst : core_slice_index_private_slice_index_Sealed self;
+  output : Type0;
+  get : self → t → result (option output);
+  get_mut : self → t → result (option output);
+  get_mut_back : self → t → option output → result t;
+  get_unchecked : self → const_raw_ptr t → result (const_raw_ptr output);
+  get_unchecked_mut : self → mut_raw_ptr t → result (mut_raw_ptr output);
+  index : self → t → result output;
+  index_mut : self → t → result output;
+  index_mut_back : self → t → output → result t;
+}
 
-let vec_index_mut_fwd (a : Type0) (v : vec a) (i : usize) : result a =
-  if i < length v then Return (index v i) else Fail Failure
-let vec_index_mut_back (a : Type0) (v : vec a) (i : usize) (nx : a) : result (vec a) =
-  if i < length v then Return (list_update v i nx) else Fail Failure
+// [core::slice::index::[T]::index]: forward function
+let core_slice_index_Slice_index
+  (t idx : Type0) (inst : core_slice_index_SliceIndex idx (slice t))
+  (s : slice t) (i : idx) : result inst.output =
+  let* x = inst.get i s in
+  match x with
+  | None -> Fail Failure
+  | Some x -> Return x
+
+// [core::slice::index::Range:::get]: forward function
+let core_slice_index_Range_get (t : Type0) (i : core_ops_range_Range usize) (s : slice t) :
+  result (option (slice t)) =
+  admit () // TODO
+
+// [core::slice::index::Range::get_mut]: forward function
+let core_slice_index_Range_get_mut
+  (t : Type0) : core_ops_range_Range usize → slice t → result (option (slice t)) =
+  admit () // TODO
+
+// [core::slice::index::Range::get_mut]: backward function 0
+let core_slice_index_Range_get_mut_back
+  (t : Type0) :
+  core_ops_range_Range usize → slice t → option (slice t) → result (slice t) =
+  admit () // TODO
+
+// [core::slice::index::Range::get_unchecked]: forward function
+let core_slice_index_Range_get_unchecked
+  (t : Type0) :
+  core_ops_range_Range usize → const_raw_ptr (slice t) → result (const_raw_ptr (slice t)) =
+  // Don't know what the model should be - for now we always fail to make
+  // sure code which uses it fails
+  fun _ _ -> Fail Failure
+
+// [core::slice::index::Range::get_unchecked_mut]: forward function
+let core_slice_index_Range_get_unchecked_mut
+  (t : Type0) :
+  core_ops_range_Range usize → mut_raw_ptr (slice t) → result (mut_raw_ptr (slice t)) =
+  // Don't know what the model should be - for now we always fail to make
+  // sure code which uses it fails
+  fun _ _ -> Fail Failure
+
+// [core::slice::index::Range::index]: forward function
+let core_slice_index_Range_index
+  (t : Type0) : core_ops_range_Range usize → slice t → result (slice t) =
+  admit () // TODO
+
+// [core::slice::index::Range::index_mut]: forward function
+let core_slice_index_Range_index_mut
+  (t : Type0) : core_ops_range_Range usize → slice t → result (slice t) =
+  admit () // TODO
+
+// [core::slice::index::Range::index_mut]: backward function 0
+let core_slice_index_Range_index_mut_back
+  (t : Type0) : core_ops_range_Range usize → slice t → slice t → result (slice t) =
+  admit () // TODO
+
+// [core::slice::index::[T]::index_mut]: forward function
+let core_slice_index_Slice_index_mut
+  (t idx : Type0) (inst : core_slice_index_SliceIndex idx (slice t)) :
+  slice t → idx → result inst.output =
+  admit () // 
+
+// [core::slice::index::[T]::index_mut]: backward function 0
+let core_slice_index_Slice_index_mut_back
+  (t idx : Type0) (inst : core_slice_index_SliceIndex idx (slice t)) :
+  slice t → idx → inst.output → result (slice t) =
+  admit () // TODO
+
+// [core::array::[T; N]::index]: forward function
+let core_array_Array_index
+  (t idx : Type0) (n : usize) (inst : core_ops_index_Index (slice t) idx)
+  (a : array t n) (i : idx) : result inst.output =
+  admit () // TODO
+
+// [core::array::[T; N]::index_mut]: forward function
+let core_array_Array_index_mut
+  (t idx : Type0) (n : usize) (inst : core_ops_index_IndexMut (slice t) idx)
+  (a : array t n) (i : idx) : result inst.indexInst.output =
+  admit () // TODO
+
+// [core::array::[T; N]::index_mut]: backward function 0
+let core_array_Array_index_mut_back
+  (t idx : Type0) (n : usize) (inst : core_ops_index_IndexMut (slice t) idx)
+  (a : array t n) (i : idx) (x : inst.indexInst.output) : result (array t n) =
+  admit () // TODO
+
+// Trait implementation: [core::slice::index::[T]]
+let core_slice_index_Slice_coreopsindexIndexInst (t idx : Type0)
+  (inst : core_slice_index_SliceIndex idx (slice t)) :
+  core_ops_index_Index (slice t) idx = {
+  output = inst.output;
+  index = core_slice_index_Slice_index t idx inst;
+}
+
+// Trait implementation: [core::slice::index::private_slice_index::Range]
+let core_slice_index_private_slice_index_Range_coresliceindexprivate_slice_indexSealedInst
+  : core_slice_index_private_slice_index_Sealed (core_ops_range_Range usize) = ()
+
+// Trait implementation: [core::slice::index::Range]
+let core_slice_index_Range_coresliceindexSliceIndexInst (t : Type0) :
+  core_slice_index_SliceIndex (core_ops_range_Range usize) (slice t) = {
+  sealedInst = core_slice_index_private_slice_index_Range_coresliceindexprivate_slice_indexSealedInst;
+  output = slice t;
+  get = core_slice_index_Range_get t;
+  get_mut = core_slice_index_Range_get_mut t;
+  get_mut_back = core_slice_index_Range_get_mut_back t;
+  get_unchecked = core_slice_index_Range_get_unchecked t;
+  get_unchecked_mut = core_slice_index_Range_get_unchecked_mut t;
+  index = core_slice_index_Range_index t;
+  index_mut = core_slice_index_Range_index_mut t;
+  index_mut_back = core_slice_index_Range_index_mut_back t;
+}
+
+// Trait implementation: [core::slice::index::[T]]
+let core_slice_index_Slice_coreopsindexIndexMutInst (t idx : Type0)
+  (inst : core_slice_index_SliceIndex idx (slice t)) :
+  core_ops_index_IndexMut (slice t) idx = {
+  indexInst = core_slice_index_Slice_coreopsindexIndexInst t idx inst;
+  index_mut = core_slice_index_Slice_index_mut t idx inst;
+  index_mut_back = core_slice_index_Slice_index_mut_back t idx inst;
+}
+
+// Trait implementation: [core::array::[T; N]]
+let core_array_Array_coreopsindexIndexInst (t idx : Type0) (n : usize)
+  (inst : core_ops_index_Index (slice t) idx) :
+  core_ops_index_Index (array t n) idx = {
+  output = inst.output;
+  index = core_array_Array_index t idx n inst;
+}
+
+// Trait implementation: [core::array::[T; N]]
+let core_array_Array_coreopsindexIndexMutInst (t idx : Type0) (n : usize)
+  (inst : core_ops_index_IndexMut (slice t) idx) :
+  core_ops_index_IndexMut (array t n) idx = {
+  indexInst = core_array_Array_coreopsindexIndexInst t idx n inst.indexInst;
+  index_mut = core_array_Array_index_mut t idx n inst;
+  index_mut_back = core_array_Array_index_mut_back t idx n inst;
+}
+
+// [core::slice::index::usize::get]: forward function
+let core_slice_index_usize_get
+  (t : Type0) : usize → slice t → result (option t) =
+  admit () // TODO
+
+// [core::slice::index::usize::get_mut]: forward function
+let core_slice_index_usize_get_mut
+  (t : Type0) : usize → slice t → result (option t) =
+  admit () // TODO
+
+// [core::slice::index::usize::get_mut]: backward function 0
+let core_slice_index_usize_get_mut_back
+  (t : Type0) : usize → slice t → option t → result (slice t) =
+  admit () // TODO
+
+// [core::slice::index::usize::get_unchecked]: forward function
+let core_slice_index_usize_get_unchecked
+  (t : Type0) : usize → const_raw_ptr (slice t) → result (const_raw_ptr t) =
+  admit () // TODO
+
+// [core::slice::index::usize::get_unchecked_mut]: forward function
+let core_slice_index_usize_get_unchecked_mut
+  (t : Type0) : usize → mut_raw_ptr (slice t) → result (mut_raw_ptr t) =
+  admit () // TODO
+
+// [core::slice::index::usize::index]: forward function
+let core_slice_index_usize_index (t : Type0) : usize → slice t → result t =
+  admit () // TODO
+
+// [core::slice::index::usize::index_mut]: forward function
+let core_slice_index_usize_index_mut (t : Type0) : usize → slice t → result t =
+  admit () // TODO
+
+// [core::slice::index::usize::index_mut]: backward function 0
+let core_slice_index_usize_index_mut_back
+  (t : Type0) : usize → slice t → t → result (slice t) =
+  admit () // TODO
+
+// Trait implementation: [core::slice::index::private_slice_index::usize]
+let core_slice_index_private_slice_index_usize_coresliceindexprivate_slice_indexSealedInst
+  : core_slice_index_private_slice_index_Sealed usize = ()
+
+// Trait implementation: [core::slice::index::usize]
+let core_slice_index_usize_coresliceindexSliceIndexInst (t : Type0) :
+  core_slice_index_SliceIndex usize (slice t) = {
+  sealedInst = core_slice_index_private_slice_index_usize_coresliceindexprivate_slice_indexSealedInst;
+  output = t;
+  get = core_slice_index_usize_get t;
+  get_mut = core_slice_index_usize_get_mut t;
+  get_mut_back = core_slice_index_usize_get_mut_back t;
+  get_unchecked = core_slice_index_usize_get_unchecked t;
+  get_unchecked_mut = core_slice_index_usize_get_unchecked_mut t;
+  index = core_slice_index_usize_index t;
+  index_mut = core_slice_index_usize_index_mut t;
+  index_mut_back = core_slice_index_usize_index_mut_back t;
+}
+
+// [alloc::vec::Vec::index]: forward function
+let alloc_vec_Vec_index (t idx : Type0) (inst : core_slice_index_SliceIndex idx (slice t))
+  (self : alloc_vec_Vec t) (i : idx) : result inst.output =
+  admit () // TODO
+
+// [alloc::vec::Vec::index_mut]: forward function
+let alloc_vec_Vec_index_mut (t idx : Type0) (inst : core_slice_index_SliceIndex idx (slice t))
+  (self : alloc_vec_Vec t) (i : idx) : result inst.output =
+  admit () // TODO
+
+// [alloc::vec::Vec::index_mut]: backward function 0
+let alloc_vec_Vec_index_mut_back
+  (t idx : Type0) (inst : core_slice_index_SliceIndex idx (slice t))
+  (self : alloc_vec_Vec t) (i : idx) (x : inst.output) : result (alloc_vec_Vec t) =
+  admit () // TODO
+
+// Trait implementation: [alloc::vec::Vec]
+let alloc_vec_Vec_coreopsindexIndexInst (t idx : Type0)
+  (inst : core_slice_index_SliceIndex idx (slice t)) :
+  core_ops_index_Index (alloc_vec_Vec t) idx = {
+  output = inst.output;
+  index = alloc_vec_Vec_index t idx inst;
+}
+
+// Trait implementation: [alloc::vec::Vec]
+let alloc_vec_Vec_coreopsindexIndexMutInst (t idx : Type0)
+  (inst : core_slice_index_SliceIndex idx (slice t)) :
+  core_ops_index_IndexMut (alloc_vec_Vec t) idx = {
+  indexInst = alloc_vec_Vec_coreopsindexIndexInst t idx inst;
+  index_mut = alloc_vec_Vec_index_mut t idx inst;
+  index_mut_back = alloc_vec_Vec_index_mut_back t idx inst;
+}
+
+(*** Theorems *)
+
+let alloc_vec_Vec_index_eq (#a : Type0) (v : alloc_vec_Vec a) (i : usize) :
+  Lemma (
+    alloc_vec_Vec_index a usize (core_slice_index_usize_coresliceindexSliceIndexInst a) v i ==
+      alloc_vec_Vec_index_usize v i)
+  [SMTPat (alloc_vec_Vec_index a usize (core_slice_index_usize_coresliceindexSliceIndexInst a) v i)]
+  =
+  admit()
+
+let alloc_vec_Vec_index_mut_eq (#a : Type0) (v : alloc_vec_Vec a) (i : usize) :
+  Lemma (
+    alloc_vec_Vec_index_mut a usize (core_slice_index_usize_coresliceindexSliceIndexInst a) v i ==
+      alloc_vec_Vec_index_usize v i)
+  [SMTPat (alloc_vec_Vec_index_mut a usize (core_slice_index_usize_coresliceindexSliceIndexInst a) v i)]
+  =
+  admit()
+
+let alloc_vec_Vec_index_mut_back_eq (#a : Type0) (v : alloc_vec_Vec a) (i : usize) (x : a) :
+  Lemma (
+    alloc_vec_Vec_index_mut_back a usize (core_slice_index_usize_coresliceindexSliceIndexInst a) v i x ==
+      alloc_vec_Vec_update_usize v i x)
+  [SMTPat (alloc_vec_Vec_index_mut_back a usize (core_slice_index_usize_coresliceindexSliceIndexInst a) v i x)]
+  =
+  admit()
diff --git a/tests/fstar/hashmap/Hashmap.Clauses.Template.fst b/tests/fstar/hashmap/Hashmap.Clauses.Template.fst
index 640ae783..a1f81666 100644
--- a/tests/fstar/hashmap/Hashmap.Clauses.Template.fst
+++ b/tests/fstar/hashmap/Hashmap.Clauses.Template.fst
@@ -8,55 +8,55 @@ open Hashmap.Types
 
 (** [hashmap::HashMap::{0}::allocate_slots]: decreases clause *)
 unfold
-let hash_map_allocate_slots_loop_decreases (t : Type0) (slots : vec (list_t t))
-  (n : usize) : nat =
+let hashMap_allocate_slots_loop_decreases (t : Type0)
+  (slots : alloc_vec_Vec (list_t t)) (n : usize) : nat =
   admit ()
 
 (** [hashmap::HashMap::{0}::clear]: decreases clause *)
 unfold
-let hash_map_clear_loop_decreases (t : Type0) (slots : vec (list_t t))
+let hashMap_clear_loop_decreases (t : Type0) (slots : alloc_vec_Vec (list_t t))
   (i : usize) : nat =
   admit ()
 
 (** [hashmap::HashMap::{0}::insert_in_list]: decreases clause *)
 unfold
-let hash_map_insert_in_list_loop_decreases (t : Type0) (key : usize)
-  (value : t) (ls : list_t t) : nat =
+let hashMap_insert_in_list_loop_decreases (t : Type0) (key : usize) (value : t)
+  (ls : list_t t) : nat =
   admit ()
 
 (** [hashmap::HashMap::{0}::move_elements_from_list]: decreases clause *)
 unfold
-let hash_map_move_elements_from_list_loop_decreases (t : Type0)
-  (ntable : hash_map_t t) (ls : list_t t) : nat =
+let hashMap_move_elements_from_list_loop_decreases (t : Type0)
+  (ntable : hashMap_t t) (ls : list_t t) : nat =
   admit ()
 
 (** [hashmap::HashMap::{0}::move_elements]: decreases clause *)
 unfold
-let hash_map_move_elements_loop_decreases (t : Type0) (ntable : hash_map_t t)
-  (slots : vec (list_t t)) (i : usize) : nat =
+let hashMap_move_elements_loop_decreases (t : Type0) (ntable : hashMap_t t)
+  (slots : alloc_vec_Vec (list_t t)) (i : usize) : nat =
   admit ()
 
 (** [hashmap::HashMap::{0}::contains_key_in_list]: decreases clause *)
 unfold
-let hash_map_contains_key_in_list_loop_decreases (t : Type0) (key : usize)
+let hashMap_contains_key_in_list_loop_decreases (t : Type0) (key : usize)
   (ls : list_t t) : nat =
   admit ()
 
 (** [hashmap::HashMap::{0}::get_in_list]: decreases clause *)
 unfold
-let hash_map_get_in_list_loop_decreases (t : Type0) (key : usize)
+let hashMap_get_in_list_loop_decreases (t : Type0) (key : usize)
   (ls : list_t t) : nat =
   admit ()
 
 (** [hashmap::HashMap::{0}::get_mut_in_list]: decreases clause *)
 unfold
-let hash_map_get_mut_in_list_loop_decreases (t : Type0) (ls : list_t t)
+let hashMap_get_mut_in_list_loop_decreases (t : Type0) (ls : list_t t)
   (key : usize) : nat =
   admit ()
 
 (** [hashmap::HashMap::{0}::remove_from_list]: decreases clause *)
 unfold
-let hash_map_remove_from_list_loop_decreases (t : Type0) (key : usize)
+let hashMap_remove_from_list_loop_decreases (t : Type0) (key : usize)
   (ls : list_t t) : nat =
   admit ()
 
diff --git a/tests/fstar/hashmap/Hashmap.Clauses.fst b/tests/fstar/hashmap/Hashmap.Clauses.fst
index d8bb8d20..6c699d05 100644
--- a/tests/fstar/hashmap/Hashmap.Clauses.fst
+++ b/tests/fstar/hashmap/Hashmap.Clauses.fst
@@ -8,54 +8,54 @@ open Hashmap.Types
 
 (** [hashmap::HashMap::allocate_slots]: decreases clause *)
 unfold
-let hash_map_allocate_slots_loop_decreases (t : Type0) (slots : vec (list_t t))
-  (n : usize) : nat = n
+let hashMap_allocate_slots_loop_decreases (t : Type0)
+  (slots : alloc_vec_Vec (list_t t)) (n : usize) : nat = n
 
 (** [hashmap::HashMap::clear]: decreases clause *)
 unfold
-let hash_map_clear_loop_decreases (t : Type0) (slots : vec (list_t t))
+let hashMap_clear_loop_decreases (t : Type0) (slots : alloc_vec_Vec (list_t t))
   (i : usize) : nat =
   if i < length slots then length slots - i else 0
 
 (** [hashmap::HashMap::insert_in_list]: decreases clause *)
 unfold
-let hash_map_insert_in_list_loop_decreases (t : Type0) (key : usize) (value : t)
+let hashMap_insert_in_list_loop_decreases (t : Type0) (key : usize) (value : t)
   (ls : list_t t) : list_t t =
   ls
 
 (** [hashmap::HashMap::move_elements_from_list]: decreases clause *)
 unfold
-let hash_map_move_elements_from_list_loop_decreases (t : Type0)
-  (ntable : hash_map_t t) (ls : list_t t) : list_t t =
+let hashMap_move_elements_from_list_loop_decreases (t : Type0)
+  (ntable : hashMap_t t) (ls : list_t t) : list_t t =
   ls
 
 (** [hashmap::HashMap::move_elements]: decreases clause *)
 unfold
-let hash_map_move_elements_loop_decreases (t : Type0) (ntable : hash_map_t t)
-  (slots : vec (list_t t)) (i : usize) : nat =
+let hashMap_move_elements_loop_decreases (t : Type0) (ntable : hashMap_t t)
+  (slots : alloc_vec_Vec (list_t t)) (i : usize) : nat =
   if i < length slots then length slots - i else 0
 
 (** [hashmap::HashMap::contains_key_in_list]: decreases clause *)
 unfold
-let hash_map_contains_key_in_list_loop_decreases (t : Type0) (key : usize)
+let hashMap_contains_key_in_list_loop_decreases (t : Type0) (key : usize)
   (ls : list_t t) : list_t t =
   ls
 
 (** [hashmap::HashMap::get_in_list]: decreases clause *)
 unfold
-let hash_map_get_in_list_loop_decreases (t : Type0) (key : usize) (ls : list_t t) :
+let hashMap_get_in_list_loop_decreases (t : Type0) (key : usize) (ls : list_t t) :
   list_t t =
   ls
 
 (** [hashmap::HashMap::get_mut_in_list]: decreases clause *)
 unfold
-let hash_map_get_mut_in_list_loop_decreases (t : Type0) (ls : list_t t)
+let hashMap_get_mut_in_list_loop_decreases (t : Type0) (ls : list_t t)
   (key : usize) : list_t t =
   ls
 
 (** [hashmap::HashMap::remove_from_list]: decreases clause *)
 unfold
-let hash_map_remove_from_list_loop_decreases (t : Type0) (key : usize)
+let hashMap_remove_from_list_loop_decreases (t : Type0) (key : usize)
   (ls : list_t t) : list_t t =
   ls
 
diff --git a/tests/fstar/hashmap/Hashmap.Funs.fst b/tests/fstar/hashmap/Hashmap.Funs.fst
index f4c13a7b..0e31e364 100644
--- a/tests/fstar/hashmap/Hashmap.Funs.fst
+++ b/tests/fstar/hashmap/Hashmap.Funs.fst
@@ -8,460 +8,486 @@ include Hashmap.Clauses
 #set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
 
 (** [hashmap::hash_key]: forward function *)
-let hash_key_fwd (k : usize) : result usize =
+let hash_key (k : usize) : result usize =
   Return k
 
 (** [hashmap::HashMap::{0}::allocate_slots]: loop 0: forward function *)
-let rec hash_map_allocate_slots_loop_fwd
-  (t : Type0) (slots : vec (list_t t)) (n : usize) :
-  Tot (result (vec (list_t t)))
-  (decreases (hash_map_allocate_slots_loop_decreases t slots n))
+let rec hashMap_allocate_slots_loop
+  (t : Type0) (slots : alloc_vec_Vec (list_t t)) (n : usize) :
+  Tot (result (alloc_vec_Vec (list_t t)))
+  (decreases (hashMap_allocate_slots_loop_decreases t slots n))
   =
   if n > 0
   then
-    let* slots0 = vec_push_back (list_t t) slots ListNil in
+    let* slots0 = alloc_vec_Vec_push (list_t t) slots List_Nil in
     let* n0 = usize_sub n 1 in
-    hash_map_allocate_slots_loop_fwd t slots0 n0
+    hashMap_allocate_slots_loop t slots0 n0
   else Return slots
 
 (** [hashmap::HashMap::{0}::allocate_slots]: forward function *)
-let hash_map_allocate_slots_fwd
-  (t : Type0) (slots : vec (list_t t)) (n : usize) : result (vec (list_t t)) =
-  hash_map_allocate_slots_loop_fwd t slots n
+let hashMap_allocate_slots
+  (t : Type0) (slots : alloc_vec_Vec (list_t t)) (n : usize) :
+  result (alloc_vec_Vec (list_t t))
+  =
+  hashMap_allocate_slots_loop t slots n
 
 (** [hashmap::HashMap::{0}::new_with_capacity]: forward function *)
-let hash_map_new_with_capacity_fwd
+let hashMap_new_with_capacity
   (t : Type0) (capacity : usize) (max_load_dividend : usize)
   (max_load_divisor : usize) :
-  result (hash_map_t t)
+  result (hashMap_t t)
   =
-  let v = vec_new (list_t t) in
-  let* slots = hash_map_allocate_slots_fwd t v capacity in
+  let v = alloc_vec_Vec_new (list_t t) in
+  let* slots = hashMap_allocate_slots t v capacity in
   let* i = usize_mul capacity max_load_dividend in
   let* i0 = usize_div i max_load_divisor in
   Return
     {
-      hash_map_num_entries = 0;
-      hash_map_max_load_factor = (max_load_dividend, max_load_divisor);
-      hash_map_max_load = i0;
-      hash_map_slots = slots
+      num_entries = 0;
+      max_load_factor = (max_load_dividend, max_load_divisor);
+      max_load = i0;
+      slots = slots
     }
 
 (** [hashmap::HashMap::{0}::new]: forward function *)
-let hash_map_new_fwd (t : Type0) : result (hash_map_t t) =
-  hash_map_new_with_capacity_fwd t 32 4 5
+let hashMap_new (t : Type0) : result (hashMap_t t) =
+  hashMap_new_with_capacity t 32 4 5
 
 (** [hashmap::HashMap::{0}::clear]: loop 0: merged forward/backward function
     (there is a single backward function, and the forward function returns ()) *)
-let rec hash_map_clear_loop_fwd_back
-  (t : Type0) (slots : vec (list_t t)) (i : usize) :
-  Tot (result (vec (list_t t)))
-  (decreases (hash_map_clear_loop_decreases t slots i))
+let rec hashMap_clear_loop
+  (t : Type0) (slots : alloc_vec_Vec (list_t t)) (i : usize) :
+  Tot (result (alloc_vec_Vec (list_t t)))
+  (decreases (hashMap_clear_loop_decreases t slots i))
   =
-  let i0 = vec_len (list_t t) slots in
+  let i0 = alloc_vec_Vec_len (list_t t) slots in
   if i < i0
   then
     let* i1 = usize_add i 1 in
-    let* slots0 = vec_index_mut_back (list_t t) slots i ListNil in
-    hash_map_clear_loop_fwd_back t slots0 i1
+    let* slots0 =
+      alloc_vec_Vec_index_mut_back (list_t t) usize
+        (core_slice_index_usize_coresliceindexSliceIndexInst (list_t t)) slots
+        i List_Nil in
+    hashMap_clear_loop t slots0 i1
   else Return slots
 
 (** [hashmap::HashMap::{0}::clear]: merged forward/backward function
     (there is a single backward function, and the forward function returns ()) *)
-let hash_map_clear_fwd_back
-  (t : Type0) (self : hash_map_t t) : result (hash_map_t t) =
-  let* v = hash_map_clear_loop_fwd_back t self.hash_map_slots 0 in
-  Return { self with hash_map_num_entries = 0; hash_map_slots = v }
+let hashMap_clear (t : Type0) (self : hashMap_t t) : result (hashMap_t t) =
+  let* v = hashMap_clear_loop t self.slots 0 in
+  Return { self with num_entries = 0; slots = v }
 
 (** [hashmap::HashMap::{0}::len]: forward function *)
-let hash_map_len_fwd (t : Type0) (self : hash_map_t t) : result usize =
-  Return self.hash_map_num_entries
+let hashMap_len (t : Type0) (self : hashMap_t t) : result usize =
+  Return self.num_entries
 
 (** [hashmap::HashMap::{0}::insert_in_list]: loop 0: forward function *)
-let rec hash_map_insert_in_list_loop_fwd
+let rec hashMap_insert_in_list_loop
   (t : Type0) (key : usize) (value : t) (ls : list_t t) :
   Tot (result bool)
-  (decreases (hash_map_insert_in_list_loop_decreases t key value ls))
+  (decreases (hashMap_insert_in_list_loop_decreases t key value ls))
   =
   begin match ls with
-  | ListCons ckey cvalue tl ->
+  | List_Cons ckey cvalue tl ->
     if ckey = key
     then Return false
-    else hash_map_insert_in_list_loop_fwd t key value tl
-  | ListNil -> Return true
+    else hashMap_insert_in_list_loop t key value tl
+  | List_Nil -> Return true
   end
 
 (** [hashmap::HashMap::{0}::insert_in_list]: forward function *)
-let hash_map_insert_in_list_fwd
+let hashMap_insert_in_list
   (t : Type0) (key : usize) (value : t) (ls : list_t t) : result bool =
-  hash_map_insert_in_list_loop_fwd t key value ls
+  hashMap_insert_in_list_loop t key value ls
 
 (** [hashmap::HashMap::{0}::insert_in_list]: loop 0: backward function 0 *)
-let rec hash_map_insert_in_list_loop_back
+let rec hashMap_insert_in_list_loop_back
   (t : Type0) (key : usize) (value : t) (ls : list_t t) :
   Tot (result (list_t t))
-  (decreases (hash_map_insert_in_list_loop_decreases t key value ls))
+  (decreases (hashMap_insert_in_list_loop_decreases t key value ls))
   =
   begin match ls with
-  | ListCons ckey cvalue tl ->
+  | List_Cons ckey cvalue tl ->
     if ckey = key
-    then Return (ListCons ckey value tl)
+    then Return (List_Cons ckey value tl)
     else
-      let* tl0 = hash_map_insert_in_list_loop_back t key value tl in
-      Return (ListCons ckey cvalue tl0)
-  | ListNil -> let l = ListNil in Return (ListCons key value l)
+      let* tl0 = hashMap_insert_in_list_loop_back t key value tl in
+      Return (List_Cons ckey cvalue tl0)
+  | List_Nil -> let l = List_Nil in Return (List_Cons key value l)
   end
 
 (** [hashmap::HashMap::{0}::insert_in_list]: backward function 0 *)
-let hash_map_insert_in_list_back
+let hashMap_insert_in_list_back
   (t : Type0) (key : usize) (value : t) (ls : list_t t) : result (list_t t) =
-  hash_map_insert_in_list_loop_back t key value ls
+  hashMap_insert_in_list_loop_back t key value ls
 
 (** [hashmap::HashMap::{0}::insert_no_resize]: merged forward/backward function
     (there is a single backward function, and the forward function returns ()) *)
-let hash_map_insert_no_resize_fwd_back
-  (t : Type0) (self : hash_map_t t) (key : usize) (value : t) :
-  result (hash_map_t t)
+let hashMap_insert_no_resize
+  (t : Type0) (self : hashMap_t t) (key : usize) (value : t) :
+  result (hashMap_t t)
   =
-  let* hash = hash_key_fwd key in
-  let i = vec_len (list_t t) self.hash_map_slots in
+  let* hash = hash_key key in
+  let i = alloc_vec_Vec_len (list_t t) self.slots in
   let* hash_mod = usize_rem hash i in
-  let* l = vec_index_mut_fwd (list_t t) self.hash_map_slots hash_mod in
-  let* inserted = hash_map_insert_in_list_fwd t key value l in
+  let* l =
+    alloc_vec_Vec_index_mut (list_t t) usize
+      (core_slice_index_usize_coresliceindexSliceIndexInst (list_t t))
+      self.slots hash_mod in
+  let* inserted = hashMap_insert_in_list t key value l in
   if inserted
   then
-    let* i0 = usize_add self.hash_map_num_entries 1 in
-    let* l0 = hash_map_insert_in_list_back t key value l in
-    let* v = vec_index_mut_back (list_t t) self.hash_map_slots hash_mod l0 in
-    Return { self with hash_map_num_entries = i0; hash_map_slots = v }
+    let* i0 = usize_add self.num_entries 1 in
+    let* l0 = hashMap_insert_in_list_back t key value l in
+    let* v =
+      alloc_vec_Vec_index_mut_back (list_t t) usize
+        (core_slice_index_usize_coresliceindexSliceIndexInst (list_t t))
+        self.slots hash_mod l0 in
+    Return { self with num_entries = i0; slots = v }
   else
-    let* l0 = hash_map_insert_in_list_back t key value l in
-    let* v = vec_index_mut_back (list_t t) self.hash_map_slots hash_mod l0 in
-    Return { self with hash_map_slots = v }
-
-(** [core::num::u32::{8}::MAX] *)
-let core_num_u32_max_body : result u32 = Return 4294967295
-let core_num_u32_max_c : u32 = eval_global core_num_u32_max_body
+    let* l0 = hashMap_insert_in_list_back t key value l in
+    let* v =
+      alloc_vec_Vec_index_mut_back (list_t t) usize
+        (core_slice_index_usize_coresliceindexSliceIndexInst (list_t t))
+        self.slots hash_mod l0 in
+    Return { self with slots = v }
 
 (** [hashmap::HashMap::{0}::move_elements_from_list]: loop 0: merged forward/backward function
     (there is a single backward function, and the forward function returns ()) *)
-let rec hash_map_move_elements_from_list_loop_fwd_back
-  (t : Type0) (ntable : hash_map_t t) (ls : list_t t) :
-  Tot (result (hash_map_t t))
-  (decreases (hash_map_move_elements_from_list_loop_decreases t ntable ls))
+let rec hashMap_move_elements_from_list_loop
+  (t : Type0) (ntable : hashMap_t t) (ls : list_t t) :
+  Tot (result (hashMap_t t))
+  (decreases (hashMap_move_elements_from_list_loop_decreases t ntable ls))
   =
   begin match ls with
-  | ListCons k v tl ->
-    let* ntable0 = hash_map_insert_no_resize_fwd_back t ntable k v in
-    hash_map_move_elements_from_list_loop_fwd_back t ntable0 tl
-  | ListNil -> Return ntable
+  | List_Cons k v tl ->
+    let* ntable0 = hashMap_insert_no_resize t ntable k v in
+    hashMap_move_elements_from_list_loop t ntable0 tl
+  | List_Nil -> Return ntable
   end
 
 (** [hashmap::HashMap::{0}::move_elements_from_list]: merged forward/backward function
     (there is a single backward function, and the forward function returns ()) *)
-let hash_map_move_elements_from_list_fwd_back
-  (t : Type0) (ntable : hash_map_t t) (ls : list_t t) : result (hash_map_t t) =
-  hash_map_move_elements_from_list_loop_fwd_back t ntable ls
+let hashMap_move_elements_from_list
+  (t : Type0) (ntable : hashMap_t t) (ls : list_t t) : result (hashMap_t t) =
+  hashMap_move_elements_from_list_loop t ntable ls
 
 (** [hashmap::HashMap::{0}::move_elements]: loop 0: merged forward/backward function
     (there is a single backward function, and the forward function returns ()) *)
-let rec hash_map_move_elements_loop_fwd_back
-  (t : Type0) (ntable : hash_map_t t) (slots : vec (list_t t)) (i : usize) :
-  Tot (result ((hash_map_t t) & (vec (list_t t))))
-  (decreases (hash_map_move_elements_loop_decreases t ntable slots i))
+let rec hashMap_move_elements_loop
+  (t : Type0) (ntable : hashMap_t t) (slots : alloc_vec_Vec (list_t t))
+  (i : usize) :
+  Tot (result ((hashMap_t t) & (alloc_vec_Vec (list_t t))))
+  (decreases (hashMap_move_elements_loop_decreases t ntable slots i))
   =
-  let i0 = vec_len (list_t t) slots in
+  let i0 = alloc_vec_Vec_len (list_t t) slots in
   if i < i0
   then
-    let* l = vec_index_mut_fwd (list_t t) slots i in
-    let ls = mem_replace_fwd (list_t t) l ListNil in
-    let* ntable0 = hash_map_move_elements_from_list_fwd_back t ntable ls in
+    let* l =
+      alloc_vec_Vec_index_mut (list_t t) usize
+        (core_slice_index_usize_coresliceindexSliceIndexInst (list_t t)) slots
+        i in
+    let ls = core_mem_replace (list_t t) l List_Nil in
+    let* ntable0 = hashMap_move_elements_from_list t ntable ls in
     let* i1 = usize_add i 1 in
-    let l0 = mem_replace_back (list_t t) l ListNil in
-    let* slots0 = vec_index_mut_back (list_t t) slots i l0 in
-    hash_map_move_elements_loop_fwd_back t ntable0 slots0 i1
+    let l0 = core_mem_replace_back (list_t t) l List_Nil in
+    let* slots0 =
+      alloc_vec_Vec_index_mut_back (list_t t) usize
+        (core_slice_index_usize_coresliceindexSliceIndexInst (list_t t)) slots
+        i l0 in
+    hashMap_move_elements_loop t ntable0 slots0 i1
   else Return (ntable, slots)
 
 (** [hashmap::HashMap::{0}::move_elements]: merged forward/backward function
     (there is a single backward function, and the forward function returns ()) *)
-let hash_map_move_elements_fwd_back
-  (t : Type0) (ntable : hash_map_t t) (slots : vec (list_t t)) (i : usize) :
-  result ((hash_map_t t) & (vec (list_t t)))
+let hashMap_move_elements
+  (t : Type0) (ntable : hashMap_t t) (slots : alloc_vec_Vec (list_t t))
+  (i : usize) :
+  result ((hashMap_t t) & (alloc_vec_Vec (list_t t)))
   =
-  hash_map_move_elements_loop_fwd_back t ntable slots i
+  hashMap_move_elements_loop t ntable slots i
 
 (** [hashmap::HashMap::{0}::try_resize]: merged forward/backward function
     (there is a single backward function, and the forward function returns ()) *)
-let hash_map_try_resize_fwd_back
-  (t : Type0) (self : hash_map_t t) : result (hash_map_t t) =
-  let* max_usize = scalar_cast U32 Usize core_num_u32_max_c in
-  let capacity = vec_len (list_t t) self.hash_map_slots in
+let hashMap_try_resize
+  (t : Type0) (self : hashMap_t t) : result (hashMap_t t) =
+  let* max_usize = scalar_cast U32 Usize core_u32_max in
+  let capacity = alloc_vec_Vec_len (list_t t) self.slots in
   let* n1 = usize_div max_usize 2 in
-  let (i, i0) = self.hash_map_max_load_factor in
+  let (i, i0) = self.max_load_factor in
   let* i1 = usize_div n1 i in
   if capacity <= i1
   then
     let* i2 = usize_mul capacity 2 in
-    let* ntable = hash_map_new_with_capacity_fwd t i2 i i0 in
-    let* (ntable0, _) =
-      hash_map_move_elements_fwd_back t ntable self.hash_map_slots 0 in
+    let* ntable = hashMap_new_with_capacity t i2 i i0 in
+    let* (ntable0, _) = hashMap_move_elements t ntable self.slots 0 in
     Return
-      {
-        ntable0
-          with
-          hash_map_num_entries = self.hash_map_num_entries;
-          hash_map_max_load_factor = (i, i0)
+      { ntable0 with num_entries = self.num_entries; max_load_factor = (i, i0)
       }
-  else Return { self with hash_map_max_load_factor = (i, i0) }
+  else Return { self with max_load_factor = (i, i0) }
 
 (** [hashmap::HashMap::{0}::insert]: merged forward/backward function
     (there is a single backward function, and the forward function returns ()) *)
-let hash_map_insert_fwd_back
-  (t : Type0) (self : hash_map_t t) (key : usize) (value : t) :
-  result (hash_map_t t)
+let hashMap_insert
+  (t : Type0) (self : hashMap_t t) (key : usize) (value : t) :
+  result (hashMap_t t)
   =
-  let* self0 = hash_map_insert_no_resize_fwd_back t self key value in
-  let* i = hash_map_len_fwd t self0 in
-  if i > self0.hash_map_max_load
-  then hash_map_try_resize_fwd_back t self0
-  else Return self0
+  let* self0 = hashMap_insert_no_resize t self key value in
+  let* i = hashMap_len t self0 in
+  if i > self0.max_load then hashMap_try_resize t self0 else Return self0
 
 (** [hashmap::HashMap::{0}::contains_key_in_list]: loop 0: forward function *)
-let rec hash_map_contains_key_in_list_loop_fwd
+let rec hashMap_contains_key_in_list_loop
   (t : Type0) (key : usize) (ls : list_t t) :
   Tot (result bool)
-  (decreases (hash_map_contains_key_in_list_loop_decreases t key ls))
+  (decreases (hashMap_contains_key_in_list_loop_decreases t key ls))
   =
   begin match ls with
-  | ListCons ckey x tl ->
+  | List_Cons ckey x tl ->
     if ckey = key
     then Return true
-    else hash_map_contains_key_in_list_loop_fwd t key tl
-  | ListNil -> Return false
+    else hashMap_contains_key_in_list_loop t key tl
+  | List_Nil -> Return false
   end
 
 (** [hashmap::HashMap::{0}::contains_key_in_list]: forward function *)
-let hash_map_contains_key_in_list_fwd
+let hashMap_contains_key_in_list
   (t : Type0) (key : usize) (ls : list_t t) : result bool =
-  hash_map_contains_key_in_list_loop_fwd t key ls
+  hashMap_contains_key_in_list_loop t key ls
 
 (** [hashmap::HashMap::{0}::contains_key]: forward function *)
-let hash_map_contains_key_fwd
-  (t : Type0) (self : hash_map_t t) (key : usize) : result bool =
-  let* hash = hash_key_fwd key in
-  let i = vec_len (list_t t) self.hash_map_slots in
+let hashMap_contains_key
+  (t : Type0) (self : hashMap_t t) (key : usize) : result bool =
+  let* hash = hash_key key in
+  let i = alloc_vec_Vec_len (list_t t) self.slots in
   let* hash_mod = usize_rem hash i in
-  let* l = vec_index_fwd (list_t t) self.hash_map_slots hash_mod in
-  hash_map_contains_key_in_list_fwd t key l
+  let* l =
+    alloc_vec_Vec_index (list_t t) usize
+      (core_slice_index_usize_coresliceindexSliceIndexInst (list_t t))
+      self.slots hash_mod in
+  hashMap_contains_key_in_list t key l
 
 (** [hashmap::HashMap::{0}::get_in_list]: loop 0: forward function *)
-let rec hash_map_get_in_list_loop_fwd
+let rec hashMap_get_in_list_loop
   (t : Type0) (key : usize) (ls : list_t t) :
-  Tot (result t) (decreases (hash_map_get_in_list_loop_decreases t key ls))
+  Tot (result t) (decreases (hashMap_get_in_list_loop_decreases t key ls))
   =
   begin match ls with
-  | ListCons ckey cvalue tl ->
-    if ckey = key
-    then Return cvalue
-    else hash_map_get_in_list_loop_fwd t key tl
-  | ListNil -> Fail Failure
+  | List_Cons ckey cvalue tl ->
+    if ckey = key then Return cvalue else hashMap_get_in_list_loop t key tl
+  | List_Nil -> Fail Failure
   end
 
 (** [hashmap::HashMap::{0}::get_in_list]: forward function *)
-let hash_map_get_in_list_fwd
-  (t : Type0) (key : usize) (ls : list_t t) : result t =
-  hash_map_get_in_list_loop_fwd t key ls
+let hashMap_get_in_list (t : Type0) (key : usize) (ls : list_t t) : result t =
+  hashMap_get_in_list_loop t key ls
 
 (** [hashmap::HashMap::{0}::get]: forward function *)
-let hash_map_get_fwd
-  (t : Type0) (self : hash_map_t t) (key : usize) : result t =
-  let* hash = hash_key_fwd key in
-  let i = vec_len (list_t t) self.hash_map_slots in
+let hashMap_get (t : Type0) (self : hashMap_t t) (key : usize) : result t =
+  let* hash = hash_key key in
+  let i = alloc_vec_Vec_len (list_t t) self.slots in
   let* hash_mod = usize_rem hash i in
-  let* l = vec_index_fwd (list_t t) self.hash_map_slots hash_mod in
-  hash_map_get_in_list_fwd t key l
+  let* l =
+    alloc_vec_Vec_index (list_t t) usize
+      (core_slice_index_usize_coresliceindexSliceIndexInst (list_t t))
+      self.slots hash_mod in
+  hashMap_get_in_list t key l
 
 (** [hashmap::HashMap::{0}::get_mut_in_list]: loop 0: forward function *)
-let rec hash_map_get_mut_in_list_loop_fwd
+let rec hashMap_get_mut_in_list_loop
   (t : Type0) (ls : list_t t) (key : usize) :
-  Tot (result t) (decreases (hash_map_get_mut_in_list_loop_decreases t ls key))
+  Tot (result t) (decreases (hashMap_get_mut_in_list_loop_decreases t ls key))
   =
   begin match ls with
-  | ListCons ckey cvalue tl ->
-    if ckey = key
-    then Return cvalue
-    else hash_map_get_mut_in_list_loop_fwd t tl key
-  | ListNil -> Fail Failure
+  | List_Cons ckey cvalue tl ->
+    if ckey = key then Return cvalue else hashMap_get_mut_in_list_loop t tl key
+  | List_Nil -> Fail Failure
   end
 
 (** [hashmap::HashMap::{0}::get_mut_in_list]: forward function *)
-let hash_map_get_mut_in_list_fwd
+let hashMap_get_mut_in_list
   (t : Type0) (ls : list_t t) (key : usize) : result t =
-  hash_map_get_mut_in_list_loop_fwd t ls key
+  hashMap_get_mut_in_list_loop t ls key
 
 (** [hashmap::HashMap::{0}::get_mut_in_list]: loop 0: backward function 0 *)
-let rec hash_map_get_mut_in_list_loop_back
+let rec hashMap_get_mut_in_list_loop_back
   (t : Type0) (ls : list_t t) (key : usize) (ret : t) :
   Tot (result (list_t t))
-  (decreases (hash_map_get_mut_in_list_loop_decreases t ls key))
+  (decreases (hashMap_get_mut_in_list_loop_decreases t ls key))
   =
   begin match ls with
-  | ListCons ckey cvalue tl ->
+  | List_Cons ckey cvalue tl ->
     if ckey = key
-    then Return (ListCons ckey ret tl)
+    then Return (List_Cons ckey ret tl)
     else
-      let* tl0 = hash_map_get_mut_in_list_loop_back t tl key ret in
-      Return (ListCons ckey cvalue tl0)
-  | ListNil -> Fail Failure
+      let* tl0 = hashMap_get_mut_in_list_loop_back t tl key ret in
+      Return (List_Cons ckey cvalue tl0)
+  | List_Nil -> Fail Failure
   end
 
 (** [hashmap::HashMap::{0}::get_mut_in_list]: backward function 0 *)
-let hash_map_get_mut_in_list_back
+let hashMap_get_mut_in_list_back
   (t : Type0) (ls : list_t t) (key : usize) (ret : t) : result (list_t t) =
-  hash_map_get_mut_in_list_loop_back t ls key ret
+  hashMap_get_mut_in_list_loop_back t ls key ret
 
 (** [hashmap::HashMap::{0}::get_mut]: forward function *)
-let hash_map_get_mut_fwd
-  (t : Type0) (self : hash_map_t t) (key : usize) : result t =
-  let* hash = hash_key_fwd key in
-  let i = vec_len (list_t t) self.hash_map_slots in
+let hashMap_get_mut (t : Type0) (self : hashMap_t t) (key : usize) : result t =
+  let* hash = hash_key key in
+  let i = alloc_vec_Vec_len (list_t t) self.slots in
   let* hash_mod = usize_rem hash i in
-  let* l = vec_index_mut_fwd (list_t t) self.hash_map_slots hash_mod in
-  hash_map_get_mut_in_list_fwd t l key
+  let* l =
+    alloc_vec_Vec_index_mut (list_t t) usize
+      (core_slice_index_usize_coresliceindexSliceIndexInst (list_t t))
+      self.slots hash_mod in
+  hashMap_get_mut_in_list t l key
 
 (** [hashmap::HashMap::{0}::get_mut]: backward function 0 *)
-let hash_map_get_mut_back
-  (t : Type0) (self : hash_map_t t) (key : usize) (ret : t) :
-  result (hash_map_t t)
+let hashMap_get_mut_back
+  (t : Type0) (self : hashMap_t t) (key : usize) (ret : t) :
+  result (hashMap_t t)
   =
-  let* hash = hash_key_fwd key in
-  let i = vec_len (list_t t) self.hash_map_slots in
+  let* hash = hash_key key in
+  let i = alloc_vec_Vec_len (list_t t) self.slots in
   let* hash_mod = usize_rem hash i in
-  let* l = vec_index_mut_fwd (list_t t) self.hash_map_slots hash_mod in
-  let* l0 = hash_map_get_mut_in_list_back t l key ret in
-  let* v = vec_index_mut_back (list_t t) self.hash_map_slots hash_mod l0 in
-  Return { self with hash_map_slots = v }
+  let* l =
+    alloc_vec_Vec_index_mut (list_t t) usize
+      (core_slice_index_usize_coresliceindexSliceIndexInst (list_t t))
+      self.slots hash_mod in
+  let* l0 = hashMap_get_mut_in_list_back t l key ret in
+  let* v =
+    alloc_vec_Vec_index_mut_back (list_t t) usize
+      (core_slice_index_usize_coresliceindexSliceIndexInst (list_t t))
+      self.slots hash_mod l0 in
+  Return { self with slots = v }
 
 (** [hashmap::HashMap::{0}::remove_from_list]: loop 0: forward function *)
-let rec hash_map_remove_from_list_loop_fwd
+let rec hashMap_remove_from_list_loop
   (t : Type0) (key : usize) (ls : list_t t) :
   Tot (result (option t))
-  (decreases (hash_map_remove_from_list_loop_decreases t key ls))
+  (decreases (hashMap_remove_from_list_loop_decreases t key ls))
   =
   begin match ls with
-  | ListCons ckey x tl ->
+  | List_Cons ckey x tl ->
     if ckey = key
     then
-      let mv_ls = mem_replace_fwd (list_t t) (ListCons ckey x tl) ListNil in
+      let mv_ls = core_mem_replace (list_t t) (List_Cons ckey x tl) List_Nil in
       begin match mv_ls with
-      | ListCons i cvalue tl0 -> Return (Some cvalue)
-      | ListNil -> Fail Failure
+      | List_Cons i cvalue tl0 -> Return (Some cvalue)
+      | List_Nil -> Fail Failure
       end
-    else hash_map_remove_from_list_loop_fwd t key tl
-  | ListNil -> Return None
+    else hashMap_remove_from_list_loop t key tl
+  | List_Nil -> Return None
   end
 
 (** [hashmap::HashMap::{0}::remove_from_list]: forward function *)
-let hash_map_remove_from_list_fwd
+let hashMap_remove_from_list
   (t : Type0) (key : usize) (ls : list_t t) : result (option t) =
-  hash_map_remove_from_list_loop_fwd t key ls
+  hashMap_remove_from_list_loop t key ls
 
 (** [hashmap::HashMap::{0}::remove_from_list]: loop 0: backward function 1 *)
-let rec hash_map_remove_from_list_loop_back
+let rec hashMap_remove_from_list_loop_back
   (t : Type0) (key : usize) (ls : list_t t) :
   Tot (result (list_t t))
-  (decreases (hash_map_remove_from_list_loop_decreases t key ls))
+  (decreases (hashMap_remove_from_list_loop_decreases t key ls))
   =
   begin match ls with
-  | ListCons ckey x tl ->
+  | List_Cons ckey x tl ->
     if ckey = key
     then
-      let mv_ls = mem_replace_fwd (list_t t) (ListCons ckey x tl) ListNil in
+      let mv_ls = core_mem_replace (list_t t) (List_Cons ckey x tl) List_Nil in
       begin match mv_ls with
-      | ListCons i cvalue tl0 -> Return tl0
-      | ListNil -> Fail Failure
+      | List_Cons i cvalue tl0 -> Return tl0
+      | List_Nil -> Fail Failure
       end
     else
-      let* tl0 = hash_map_remove_from_list_loop_back t key tl in
-      Return (ListCons ckey x tl0)
-  | ListNil -> Return ListNil
+      let* tl0 = hashMap_remove_from_list_loop_back t key tl in
+      Return (List_Cons ckey x tl0)
+  | List_Nil -> Return List_Nil
   end
 
 (** [hashmap::HashMap::{0}::remove_from_list]: backward function 1 *)
-let hash_map_remove_from_list_back
+let hashMap_remove_from_list_back
   (t : Type0) (key : usize) (ls : list_t t) : result (list_t t) =
-  hash_map_remove_from_list_loop_back t key ls
+  hashMap_remove_from_list_loop_back t key ls
 
 (** [hashmap::HashMap::{0}::remove]: forward function *)
-let hash_map_remove_fwd
-  (t : Type0) (self : hash_map_t t) (key : usize) : result (option t) =
-  let* hash = hash_key_fwd key in
-  let i = vec_len (list_t t) self.hash_map_slots in
+let hashMap_remove
+  (t : Type0) (self : hashMap_t t) (key : usize) : result (option t) =
+  let* hash = hash_key key in
+  let i = alloc_vec_Vec_len (list_t t) self.slots in
   let* hash_mod = usize_rem hash i in
-  let* l = vec_index_mut_fwd (list_t t) self.hash_map_slots hash_mod in
-  let* x = hash_map_remove_from_list_fwd t key l in
+  let* l =
+    alloc_vec_Vec_index_mut (list_t t) usize
+      (core_slice_index_usize_coresliceindexSliceIndexInst (list_t t))
+      self.slots hash_mod in
+  let* x = hashMap_remove_from_list t key l in
   begin match x with
   | None -> Return None
-  | Some x0 ->
-    let* _ = usize_sub self.hash_map_num_entries 1 in Return (Some x0)
+  | Some x0 -> let* _ = usize_sub self.num_entries 1 in Return (Some x0)
   end
 
 (** [hashmap::HashMap::{0}::remove]: backward function 0 *)
-let hash_map_remove_back
-  (t : Type0) (self : hash_map_t t) (key : usize) : result (hash_map_t t) =
-  let* hash = hash_key_fwd key in
-  let i = vec_len (list_t t) self.hash_map_slots in
+let hashMap_remove_back
+  (t : Type0) (self : hashMap_t t) (key : usize) : result (hashMap_t t) =
+  let* hash = hash_key key in
+  let i = alloc_vec_Vec_len (list_t t) self.slots in
   let* hash_mod = usize_rem hash i in
-  let* l = vec_index_mut_fwd (list_t t) self.hash_map_slots hash_mod in
-  let* x = hash_map_remove_from_list_fwd t key l in
+  let* l =
+    alloc_vec_Vec_index_mut (list_t t) usize
+      (core_slice_index_usize_coresliceindexSliceIndexInst (list_t t))
+      self.slots hash_mod in
+  let* x = hashMap_remove_from_list t key l in
   begin match x with
   | None ->
-    let* l0 = hash_map_remove_from_list_back t key l in
-    let* v = vec_index_mut_back (list_t t) self.hash_map_slots hash_mod l0 in
-    Return { self with hash_map_slots = v }
+    let* l0 = hashMap_remove_from_list_back t key l in
+    let* v =
+      alloc_vec_Vec_index_mut_back (list_t t) usize
+        (core_slice_index_usize_coresliceindexSliceIndexInst (list_t t))
+        self.slots hash_mod l0 in
+    Return { self with slots = v }
   | Some x0 ->
-    let* i0 = usize_sub self.hash_map_num_entries 1 in
-    let* l0 = hash_map_remove_from_list_back t key l in
-    let* v = vec_index_mut_back (list_t t) self.hash_map_slots hash_mod l0 in
-    Return { self with hash_map_num_entries = i0; hash_map_slots = v }
+    let* i0 = usize_sub self.num_entries 1 in
+    let* l0 = hashMap_remove_from_list_back t key l in
+    let* v =
+      alloc_vec_Vec_index_mut_back (list_t t) usize
+        (core_slice_index_usize_coresliceindexSliceIndexInst (list_t t))
+        self.slots hash_mod l0 in
+    Return { self with num_entries = i0; slots = v }
   end
 
 (** [hashmap::test1]: forward function *)
-let test1_fwd : result unit =
-  let* hm = hash_map_new_fwd u64 in
-  let* hm0 = hash_map_insert_fwd_back u64 hm 0 42 in
-  let* hm1 = hash_map_insert_fwd_back u64 hm0 128 18 in
-  let* hm2 = hash_map_insert_fwd_back u64 hm1 1024 138 in
-  let* hm3 = hash_map_insert_fwd_back u64 hm2 1056 256 in
-  let* i = hash_map_get_fwd u64 hm3 128 in
+let test1 : result unit =
+  let* hm = hashMap_new u64 in
+  let* hm0 = hashMap_insert u64 hm 0 42 in
+  let* hm1 = hashMap_insert u64 hm0 128 18 in
+  let* hm2 = hashMap_insert u64 hm1 1024 138 in
+  let* hm3 = hashMap_insert u64 hm2 1056 256 in
+  let* i = hashMap_get u64 hm3 128 in
   if not (i = 18)
   then Fail Failure
   else
-    let* hm4 = hash_map_get_mut_back u64 hm3 1024 56 in
-    let* i0 = hash_map_get_fwd u64 hm4 1024 in
+    let* hm4 = hashMap_get_mut_back u64 hm3 1024 56 in
+    let* i0 = hashMap_get u64 hm4 1024 in
     if not (i0 = 56)
     then Fail Failure
     else
-      let* x = hash_map_remove_fwd u64 hm4 1024 in
+      let* x = hashMap_remove u64 hm4 1024 in
       begin match x with
       | None -> Fail Failure
       | Some x0 ->
         if not (x0 = 56)
         then Fail Failure
         else
-          let* hm5 = hash_map_remove_back u64 hm4 1024 in
-          let* i1 = hash_map_get_fwd u64 hm5 0 in
+          let* hm5 = hashMap_remove_back u64 hm4 1024 in
+          let* i1 = hashMap_get u64 hm5 0 in
           if not (i1 = 42)
           then Fail Failure
           else
-            let* i2 = hash_map_get_fwd u64 hm5 128 in
+            let* i2 = hashMap_get u64 hm5 128 in
             if not (i2 = 18)
             then Fail Failure
             else
-              let* i3 = hash_map_get_fwd u64 hm5 1056 in
+              let* i3 = hashMap_get u64 hm5 1056 in
               if not (i3 = 256) then Fail Failure else Return ()
       end
 
-(** Unit test for [hashmap::test1] *)
-let _ = assert_norm (test1_fwd = Return ())
-
diff --git a/tests/fstar/hashmap/Hashmap.Properties.fst b/tests/fstar/hashmap/Hashmap.Properties.fst
index 49d96cd5..def520f0 100644
--- a/tests/fstar/hashmap/Hashmap.Properties.fst
+++ b/tests/fstar/hashmap/Hashmap.Properties.fst
@@ -272,7 +272,7 @@ type pos_usize = x:usize{x > 0}
 
 type binding (t : Type0) = key & t
 
-type slots_t (t : Type0) = vec (list_t t)
+type slots_t (t : Type0) = alloc_vec_Vec (list_t t)
 
 /// We represent hash maps as associative lists
 type assoc_list (t : Type0) = list (binding t)
@@ -280,8 +280,8 @@ type assoc_list (t : Type0) = list (binding t)
 /// Representation function for [list_t]
 let rec list_t_v (#t : Type0) (ls : list_t t) : assoc_list t =
   match ls with
-  | ListNil -> []
-  | ListCons k v tl -> (k,v) :: list_t_v tl
+  | List_Nil -> []
+  | List_Cons k v tl -> (k,v) :: list_t_v tl
 
 let list_t_len (#t : Type0) (ls : list_t t) : nat = length (list_t_v ls)
 let list_t_index (#t : Type0) (ls : list_t t) (i : nat{i < list_t_len ls}) : binding t =
@@ -305,30 +305,30 @@ let slots_t_al_v (#t : Type0) (slots : slots_t t) : assoc_list t =
 /// list per slot). This is the representation we use most, internally. Note that
 /// we later introduce a [map_s] representation, which is the one used in the
 /// lemmas shown to the user.
-type hash_map_s t = list (slot_s t)
+type hashMap_s t = list (slot_s t)
 
 // TODO: why not always have the condition on the length?
 // 'nes': "non-empty slots"
-type hash_map_s_nes (t : Type0) : Type0 =
-  hm:hash_map_s t{is_pos_usize (length hm)}
+type hashMap_s_nes (t : Type0) : Type0 =
+  hm:hashMap_s t{is_pos_usize (length hm)}
 
-/// Representation function for [hash_map_t] as a list of slots
-let hash_map_t_v (#t : Type0) (hm : hash_map_t t) : hash_map_s t =
-  map list_t_v hm.hash_map_slots
+/// Representation function for [hashMap_t] as a list of slots
+let hashMap_t_v (#t : Type0) (hm : hashMap_t t) : hashMap_s t =
+  map list_t_v hm.slots
 
-/// Representation function for [hash_map_t] as an associative list
-let hash_map_t_al_v (#t : Type0) (hm : hash_map_t t) : assoc_list t =
-  flatten (hash_map_t_v hm)
+/// Representation function for [hashMap_t] as an associative list
+let hashMap_t_al_v (#t : Type0) (hm : hashMap_t t) : assoc_list t =
+  flatten (hashMap_t_v hm)
 
 // 'nes': "non-empty slots"
-type hash_map_t_nes (t : Type0) : Type0 =
-  hm:hash_map_t t{is_pos_usize (length hm.hash_map_slots)}
+type hashMap_t_nes (t : Type0) : Type0 =
+  hm:hashMap_t t{is_pos_usize (length hm.slots)}
 
-let hash_key (k : key) : hash =
-  Return?.v (hash_key_fwd k)
+let hash_key_s (k : key) : hash =
+  Return?.v (hash_key k)
 
 let hash_mod_key (k : key) (len : usize{len > 0}) : hash =
-  (hash_key k) % len
+  (hash_key_s k) % len
 
 let not_same_key (#t : Type0) (k : key) (b : binding t) : bool = fst b <> k
 let same_key (#t : Type0) (k : key) (b : binding t) : bool = fst b = k
@@ -339,8 +339,8 @@ let same_hash_mod_key (#t : Type0) (len : usize{len > 0}) (h : nat) (b : binding
 
 let binding_neq (#t : Type0) (b0 b1 : binding t) : bool = fst b0 <> fst b1
 
-let hash_map_t_len_s (#t : Type0) (hm : hash_map_t t) : nat =
-  hm.hash_map_num_entries
+let hashMap_t_len_s (#t : Type0) (hm : hashMap_t t) : nat =
+  hm.num_entries
 
 let assoc_list_find (#t : Type0) (k : key) (slot : assoc_list t) : option t =
   match find (same_key k) slot with
@@ -354,26 +354,26 @@ let slot_t_find_s (#t : Type0) (k : key) (slot : list_t t) : option t =
   slot_s_find k (slot_t_v slot)
 
 // This is a simpler version of the "find" function, which captures the essence
-// of what happens and operates on [hash_map_s].
-let hash_map_s_find
-  (#t : Type0) (hm : hash_map_s_nes t)
+// of what happens and operates on [hashMap_s].
+let hashMap_s_find
+  (#t : Type0) (hm : hashMap_s_nes t)
   (k : key) : option t =
   let i = hash_mod_key k (length hm) in
   let slot = index hm i in
   slot_s_find k slot
 
-let hash_map_s_len
-  (#t : Type0) (hm : hash_map_s t) :
+let hashMap_s_len
+  (#t : Type0) (hm : hashMap_s t) :
   nat =
   length (flatten hm)
 
-// Same as above, but operates on [hash_map_t]
+// Same as above, but operates on [hashMap_t]
 // Note that we don't reuse the above function on purpose: converting to a
-// [hash_map_s] then looking up an element is not the same as what we
+// [hashMap_s] then looking up an element is not the same as what we
 // wrote below.
-let hash_map_t_find_s
-  (#t : Type0) (hm : hash_map_t t{length hm.hash_map_slots > 0}) (k : key) : option t =
-  let slots = hm.hash_map_slots in
+let hashMap_t_find_s
+  (#t : Type0) (hm : hashMap_t t{length hm.slots > 0}) (k : key) : option t =
+  let slots = hm.slots in
   let i = hash_mod_key k (length slots) in
   let slot = index slots i in
   slot_t_find_s k slot
@@ -404,74 +404,74 @@ let slots_t_inv (#t : Type0) (slots : slots_t t{length slots <= usize_max}) : Ty
   {:pattern index slots i}
   slot_t_inv (length slots) i (index slots i)
 
-let hash_map_s_inv (#t : Type0) (hm : hash_map_s t) : Type0 =
+let hashMap_s_inv (#t : Type0) (hm : hashMap_s t) : Type0 =
   length hm <= usize_max /\
   length hm > 0 /\
   slots_s_inv hm
 
 /// Base invariant for the hashmap (the complete invariant can be temporarily
 /// broken between the moment we inserted an element and the moment we resize)
-let hash_map_t_base_inv (#t : Type0) (hm : hash_map_t t) : Type0 =
-  let al = hash_map_t_al_v hm in
+let hashMap_t_base_inv (#t : Type0) (hm : hashMap_t t) : Type0 =
+  let al = hashMap_t_al_v hm in
   // [num_entries] correctly tracks the number of entries in the table
   // Note that it gives us that the length of the slots array is <= usize_max:
   // [> length <= usize_max
-  // (because hash_map_num_entries has type `usize`)
-  hm.hash_map_num_entries = length al /\
+  // (because hashMap_num_entries has type `usize`)
+  hm.num_entries = length al /\
   // Slots invariant
-  slots_t_inv hm.hash_map_slots /\
+  slots_t_inv hm.slots /\
   // The capacity must be > 0 (otherwise we can't resize, because we
   // multiply the capacity by two!)
-  length hm.hash_map_slots > 0 /\
+  length hm.slots > 0 /\
   // Load computation
   begin
-  let capacity = length hm.hash_map_slots in
-  let (dividend, divisor) = hm.hash_map_max_load_factor in
+  let capacity = length hm.slots in
+  let (dividend, divisor) = hm.max_load_factor in
   0 < dividend /\ dividend < divisor /\
   capacity * dividend >= divisor /\
-  hm.hash_map_max_load = (capacity * dividend) / divisor
+  hm.max_load = (capacity * dividend) / divisor
   end
 
 /// We often need to frame some values
-let hash_map_t_same_params (#t : Type0) (hm0 hm1 : hash_map_t t) : Type0 =
-  length hm0.hash_map_slots = length hm1.hash_map_slots /\
-  hm0.hash_map_max_load = hm1.hash_map_max_load /\
-  hm0.hash_map_max_load_factor = hm1.hash_map_max_load_factor
+let hashMap_t_same_params (#t : Type0) (hm0 hm1 : hashMap_t t) : Type0 =
+  length hm0.slots = length hm1.slots /\
+  hm0.max_load = hm1.max_load /\
+  hm0.max_load_factor = hm1.max_load_factor
 
 /// The following invariants, etc. are meant to be revealed to the user through
 /// the .fsti.
 
 /// Invariant for the hashmap
-let hash_map_t_inv (#t : Type0) (hm : hash_map_t t) : Type0 =
+let hashMap_t_inv (#t : Type0) (hm : hashMap_t t) : Type0 =
   // Base invariant
-  hash_map_t_base_inv hm /\
+  hashMap_t_base_inv hm /\
   // The hash map is either: not overloaded, or we can't resize it
   begin
-  let (dividend, divisor) = hm.hash_map_max_load_factor in
-  hm.hash_map_num_entries <= hm.hash_map_max_load
-  || length hm.hash_map_slots * 2 * dividend > usize_max
+  let (dividend, divisor) = hm.max_load_factor in
+  hm.num_entries <= hm.max_load
+  || length hm.slots * 2 * dividend > usize_max
   end
 
 (*** .fsti *)
 /// We reveal slightly different version of the above functions to the user
 
-let len_s (#t : Type0) (hm : hash_map_t t) : nat = hash_map_t_len_s hm
+let len_s (#t : Type0) (hm : hashMap_t t) : nat = hashMap_t_len_s hm
 
-/// This version doesn't take any precondition (contrary to [hash_map_t_find_s])
-let find_s (#t : Type0) (hm : hash_map_t t) (k : key) : option t =
-  if length hm.hash_map_slots = 0 then None
-  else hash_map_t_find_s hm k
+/// This version doesn't take any precondition (contrary to [hashMap_t_find_s])
+let find_s (#t : Type0) (hm : hashMap_t t) (k : key) : option t =
+  if length hm.slots = 0 then None
+  else hashMap_t_find_s hm k
 
 (*** Overloading *)
 
-let hash_map_not_overloaded_lem #t hm = ()
+let hashMap_not_overloaded_lem #t hm = ()
 
 (*** allocate_slots *)
 
 /// Auxiliary lemma
 val slots_t_all_nil_inv_lem
-  (#t : Type0) (slots : vec (list_t t){length slots <= usize_max}) :
-  Lemma (requires (forall (i:nat{i < length slots}). index slots i == ListNil))
+  (#t : Type0) (slots : alloc_vec_Vec (list_t t){length slots <= usize_max}) :
+  Lemma (requires (forall (i:nat{i < length slots}). index slots i == List_Nil))
   (ensures (slots_t_inv slots))
 
 #push-options "--fuel 1"
@@ -479,8 +479,8 @@ let slots_t_all_nil_inv_lem #t slots = ()
 #pop-options
 
 val slots_t_al_v_all_nil_is_empty_lem
-  (#t : Type0) (slots : vec (list_t t)) :
-  Lemma (requires (forall (i:nat{i < length slots}). index slots i == ListNil))
+  (#t : Type0) (slots : alloc_vec_Vec (list_t t)) :
+  Lemma (requires (forall (i:nat{i < length slots}). index slots i == List_Nil))
   (ensures (slots_t_al_v slots == []))
 
 #push-options "--fuel 1"
@@ -492,44 +492,44 @@ let rec slots_t_al_v_all_nil_is_empty_lem #t slots =
    slots_t_al_v_all_nil_is_empty_lem #t slots';
    assert(slots_t_al_v slots == list_t_v s @ slots_t_al_v slots');
    assert(slots_t_al_v slots == list_t_v s);
-   assert(index slots 0 == ListNil)
+   assert(index slots 0 == List_Nil)
 #pop-options
 
 /// [allocate_slots]
-val hash_map_allocate_slots_fwd_lem
-  (t : Type0) (slots : vec (list_t t)) (n : usize) :
+val hashMap_allocate_slots_lem
+  (t : Type0) (slots : alloc_vec_Vec (list_t t)) (n : usize) :
   Lemma
   (requires (length slots + n <= usize_max))
   (ensures (
-   match hash_map_allocate_slots_fwd t slots n with
+   match hashMap_allocate_slots t slots n with
    | Fail _ -> False
    | Return slots' ->
      length slots' = length slots + n /\
      // We leave the already allocated slots unchanged
      (forall (i:nat{i < length slots}). index slots' i == index slots i) /\
      // We allocate n additional empty slots
-     (forall (i:nat{length slots <= i /\ i < length slots'}). index slots' i == ListNil)))
-  (decreases (hash_map_allocate_slots_loop_decreases t slots n))
+     (forall (i:nat{length slots <= i /\ i < length slots'}). index slots' i == List_Nil)))
+  (decreases (hashMap_allocate_slots_loop_decreases t slots n))
 
 #push-options "--fuel 1"
-let rec hash_map_allocate_slots_fwd_lem t slots n =
+let rec hashMap_allocate_slots_lem t slots n =
   begin match n with
   | 0 -> ()
   | _ ->
-    begin match vec_push_back (list_t t) slots ListNil with
+    begin match alloc_vec_Vec_push (list_t t) slots List_Nil with
     | Fail _ -> ()
     | Return slots1 ->
       begin match usize_sub n 1 with
       | Fail _ -> ()
       | Return i ->
-        hash_map_allocate_slots_fwd_lem t slots1 i;
-        begin match hash_map_allocate_slots_fwd t slots1 i with
+        hashMap_allocate_slots_lem t slots1 i;
+        begin match hashMap_allocate_slots t slots1 i with
         | Fail _ -> ()
         | Return slots2 ->
           assert(length slots1 = length slots + 1);
-          assert(slots1 == slots @ [ListNil]); // Triggers patterns
-          assert(index slots1 (length slots) == index [ListNil] 0); // Triggers patterns
-          assert(index slots1 (length slots) == ListNil)
+          assert(slots1 == slots @ [List_Nil]); // Triggers patterns
+          assert(index slots1 (length slots) == index [List_Nil] 0); // Triggers patterns
+          assert(index slots1 (length slots) == List_Nil)
         end
       end
     end
@@ -538,7 +538,7 @@ let rec hash_map_allocate_slots_fwd_lem t slots n =
 
 (*** new_with_capacity *)
 /// Under proper conditions, [new_with_capacity] doesn't fail and returns an empty hash map.
-val hash_map_new_with_capacity_fwd_lem
+val hashMap_new_with_capacity_lem
   (t : Type0) (capacity : usize)
   (max_load_dividend : usize) (max_load_divisor : usize) :
   Lemma
@@ -549,31 +549,31 @@ val hash_map_new_with_capacity_fwd_lem
     capacity * max_load_dividend >= max_load_divisor /\
     capacity * max_load_dividend <= usize_max))
   (ensures (
-    match hash_map_new_with_capacity_fwd t capacity max_load_dividend max_load_divisor with
+    match hashMap_new_with_capacity t capacity max_load_dividend max_load_divisor with
     | Fail _ -> False
     | Return hm ->
       // The hash map invariant is satisfied
-      hash_map_t_inv hm /\
+      hashMap_t_inv hm /\
       // The parameters are correct
-      hm.hash_map_max_load_factor = (max_load_dividend, max_load_divisor) /\
-      hm.hash_map_max_load = (capacity * max_load_dividend) / max_load_divisor /\
+      hm.max_load_factor = (max_load_dividend, max_load_divisor) /\
+      hm.max_load = (capacity * max_load_dividend) / max_load_divisor /\
       // The hash map has the specified capacity - we need to reveal this
-      // otherwise the pre of [hash_map_t_find_s] is not satisfied.
-      length hm.hash_map_slots = capacity /\
+      // otherwise the pre of [hashMap_t_find_s] is not satisfied.
+      length hm.slots = capacity /\
       // The hash map has 0 values
-      hash_map_t_len_s hm = 0 /\
+      hashMap_t_len_s hm = 0 /\
       // It contains no bindings
-      (forall k. hash_map_t_find_s hm k == None) /\
+      (forall k. hashMap_t_find_s hm k == None) /\
       // We need this low-level property for the invariant
-      (forall(i:nat{i < length hm.hash_map_slots}). index hm.hash_map_slots i == ListNil)))
+      (forall(i:nat{i < length hm.slots}). index hm.slots i == List_Nil)))
 
 #push-options "--z3rlimit 50 --fuel 1"
-let hash_map_new_with_capacity_fwd_lem (t : Type0) (capacity : usize)
+let hashMap_new_with_capacity_lem (t : Type0) (capacity : usize)
   (max_load_dividend : usize) (max_load_divisor : usize) =
-  let v = vec_new (list_t t) in
+  let v = alloc_vec_Vec_new (list_t t) in
   assert(length v = 0);
-  hash_map_allocate_slots_fwd_lem t v capacity;
-  begin match hash_map_allocate_slots_fwd t v capacity with
+  hashMap_allocate_slots_lem t v capacity;
+  begin match hashMap_allocate_slots t v capacity with
   | Fail _ -> assert(False)
   | Return v0 ->
     begin match usize_mul capacity max_load_dividend with
@@ -582,9 +582,9 @@ let hash_map_new_with_capacity_fwd_lem (t : Type0) (capacity : usize)
       begin match usize_div i max_load_divisor with
       | Fail _ -> assert(False)
       | Return i0 ->
-          let hm = Mkhash_map_t 0 (max_load_dividend, max_load_divisor) i0 v0 in
+          let hm = MkhashMap_t 0 (max_load_dividend, max_load_divisor) i0 v0 in
           slots_t_all_nil_inv_lem v0;
-          slots_t_al_v_all_nil_is_empty_lem hm.hash_map_slots
+          slots_t_al_v_all_nil_is_empty_lem hm.slots
       end
     end
   end
@@ -593,65 +593,65 @@ let hash_map_new_with_capacity_fwd_lem (t : Type0) (capacity : usize)
 (*** new *)
 
 /// [new] doesn't fail and returns an empty hash map
-val hash_map_new_fwd_lem_aux (t : Type0) :
+val hashMap_new_lem_aux (t : Type0) :
   Lemma
   (ensures (
-    match hash_map_new_fwd t with
+    match hashMap_new t with
     | Fail _ -> False
     | Return hm ->
       // The hash map invariant is satisfied
-      hash_map_t_inv hm /\
+      hashMap_t_inv hm /\
       // The hash map has 0 values
-      hash_map_t_len_s hm = 0 /\
+      hashMap_t_len_s hm = 0 /\
       // It contains no bindings
-      (forall k. hash_map_t_find_s hm k == None)))
+      (forall k. hashMap_t_find_s hm k == None)))
 
 #push-options "--fuel 1"
-let hash_map_new_fwd_lem_aux t =
-  hash_map_new_with_capacity_fwd_lem t 32 4 5;
-  match hash_map_new_with_capacity_fwd t 32 4 5 with
+let hashMap_new_lem_aux t =
+  hashMap_new_with_capacity_lem t 32 4 5;
+  match hashMap_new_with_capacity t 32 4 5 with
   | Fail _ -> ()
   | Return hm -> ()
 #pop-options
 
 /// The lemma we reveal in the .fsti
-let hash_map_new_fwd_lem t = hash_map_new_fwd_lem_aux t
+let hashMap_new_lem t = hashMap_new_lem_aux t
 
 (*** clear *)
 /// [clear]: the loop doesn't fail and simply clears the slots starting at index i
 #push-options "--fuel 1"
-let rec hash_map_clear_loop_fwd_back_lem
-  (t : Type0) (slots : vec (list_t t)) (i : usize) :
+let rec hashMap_clear_loop_lem
+  (t : Type0) (slots : alloc_vec_Vec (list_t t)) (i : usize) :
   Lemma
   (ensures (
-    match hash_map_clear_loop_fwd_back t slots i with
+    match hashMap_clear_loop t slots i with
     | Fail _ -> False
     | Return slots' ->
       // The length is preserved
       length slots' == length slots /\
       // The slots before i are left unchanged
       (forall (j:nat{j < i /\ j < length slots}). index slots' j == index slots j) /\
-      // The slots after i are set to ListNil
-      (forall (j:nat{i <= j /\ j < length slots}). index slots' j == ListNil)))
-  (decreases (hash_map_clear_loop_decreases t slots i))
+      // The slots after i are set to List_Nil
+      (forall (j:nat{i <= j /\ j < length slots}). index slots' j == List_Nil)))
+  (decreases (hashMap_clear_loop_decreases t slots i))
   =
-  let i0 = vec_len (list_t t) slots in
+  let i0 = alloc_vec_Vec_len (list_t t) slots in
   let b = i < i0 in
   if b
   then
-    begin match vec_index_mut_back (list_t t) slots i ListNil with
+    begin match alloc_vec_Vec_update_usize slots i List_Nil with
     | Fail _ -> ()
     | Return v ->
       begin match usize_add i 1 with
       | Fail _ -> ()
       | Return i1 ->
-        hash_map_clear_loop_fwd_back_lem t v i1;
-        begin match hash_map_clear_loop_fwd_back t v i1 with
+        hashMap_clear_loop_lem t v i1;
+        begin match hashMap_clear_loop t v i1 with
         | Fail _ -> ()
         | Return slots1 ->
           assert(length slots1 == length slots);
-          assert(forall (j:nat{i+1 <= j /\ j < length slots}). index slots1 j == ListNil);
-          assert(index slots1 i == ListNil)
+          assert(forall (j:nat{i+1 <= j /\ j < length slots}). index slots1 j == List_Nil);
+          assert(index slots1 i == List_Nil)
         end
       end
     end
@@ -659,80 +659,80 @@ let rec hash_map_clear_loop_fwd_back_lem
 #pop-options
 
 /// [clear] doesn't fail and turns the hash map into an empty map
-val hash_map_clear_fwd_back_lem_aux
-  (#t : Type0) (self : hash_map_t t) :
+val hashMap_clear_lem_aux
+  (#t : Type0) (self : hashMap_t t) :
   Lemma
-  (requires (hash_map_t_base_inv self))
+  (requires (hashMap_t_base_inv self))
   (ensures (
-    match hash_map_clear_fwd_back t self with
+    match hashMap_clear t self with
     | Fail _ -> False
     | Return hm ->
       // The hash map invariant is satisfied
-      hash_map_t_base_inv hm /\
+      hashMap_t_base_inv hm /\
       // We preserved the parameters
-      hash_map_t_same_params hm self /\
+      hashMap_t_same_params hm self /\
       // The hash map has 0 values
-      hash_map_t_len_s hm = 0 /\
+      hashMap_t_len_s hm = 0 /\
       // It contains no bindings
-      (forall k. hash_map_t_find_s hm k == None)))
+      (forall k. hashMap_t_find_s hm k == None)))
 
 // Being lazy: fuel 1 helps a lot...
 #push-options "--fuel 1"
-let hash_map_clear_fwd_back_lem_aux #t self =
-  let p = self.hash_map_max_load_factor in
-  let i = self.hash_map_max_load in
-  let v = self.hash_map_slots in
-  hash_map_clear_loop_fwd_back_lem t v 0;
-  begin match hash_map_clear_loop_fwd_back t v 0 with
+let hashMap_clear_lem_aux #t self =
+  let p = self.max_load_factor in
+  let i = self.max_load in
+  let v = self.slots in
+  hashMap_clear_loop_lem t v 0;
+  begin match hashMap_clear_loop t v 0 with
   | Fail _ -> ()
   | Return slots1 ->
     slots_t_al_v_all_nil_is_empty_lem slots1;
-    let hm1 = Mkhash_map_t 0 p i slots1 in
-    assert(hash_map_t_base_inv hm1);
-    assert(hash_map_t_inv hm1)
+    let hm1 = MkhashMap_t 0 p i slots1 in
+    assert(hashMap_t_base_inv hm1);
+    assert(hashMap_t_inv hm1)
   end
 #pop-options
 
-let hash_map_clear_fwd_back_lem #t self = hash_map_clear_fwd_back_lem_aux #t self
+let hashMap_clear_lem #t self = hashMap_clear_lem_aux #t self
 
 (*** len *)
 
 /// [len]: we link it to a non-failing function.
 /// Rk.: we might want to make an analysis to not use an error monad to translate
 /// functions which statically can't fail.
-let hash_map_len_fwd_lem #t self = ()
+let hashMap_len_lem #t self = ()
 
 
 (*** insert_in_list *)
 
 (**** insert_in_list'fwd *)
 
-/// [insert_in_list_fwd]: returns true iff the key is not in the list (functional version)
-val hash_map_insert_in_list_fwd_lem
+/// [insert_in_list]: returns true iff the key is not in the list (functional version)
+val hashMap_insert_in_list_lem
   (t : Type0) (key : usize) (value : t) (ls : list_t t) :
   Lemma
   (ensures (
-    match hash_map_insert_in_list_fwd t key value ls with
+    match hashMap_insert_in_list t key value ls with
     | Fail _ -> False
     | Return b ->
       b <==> (slot_t_find_s key ls == None)))
-  (decreases (hash_map_insert_in_list_loop_decreases t key value ls))
+  (decreases (hashMap_insert_in_list_loop_decreases t key value ls))
 
 #push-options "--fuel 1"
-let rec hash_map_insert_in_list_fwd_lem t key value ls =
+let rec hashMap_insert_in_list_lem t key value ls =
   begin match ls with
-  | ListCons ckey cvalue ls0 ->
+  | List_Cons ckey cvalue ls0 ->
     let b = ckey = key in
     if b
     then ()
     else
       begin
-      hash_map_insert_in_list_fwd_lem t key value ls0;
-      match hash_map_insert_in_list_fwd t key value ls0 with
+      hashMap_insert_in_list_lem t key value ls0;
+      match hashMap_insert_in_list t key value ls0 with
       | Fail _ -> ()
       | Return b0 -> ()
       end
-  | ListNil ->
+  | List_Nil ->
     assert(list_t_v ls == []);
     assert_norm(find (same_key #t key) [] == None)
   end
@@ -748,7 +748,7 @@ let rec hash_map_insert_in_list_fwd_lem t key value ls =
 /// We write a helper which "captures" what [insert_in_list] does.
 /// We then reason about this helper to prove the high-level properties we want
 /// (functional properties, preservation of invariants, etc.).
-let hash_map_insert_in_list_s
+let hashMap_insert_in_list_s
   (#t : Type0) (key : usize) (value : t) (ls : list (binding t)) :
   list (binding t) =
   // Check if there is already a binding for the key
@@ -761,86 +761,86 @@ let hash_map_insert_in_list_s
     find_update (same_key key) ls (key,value)
 
 /// [insert_in_list]: if the key is not in the map, appends a new bindings (functional version)
-val hash_map_insert_in_list_back_lem_append_s
+val hashMap_insert_in_list_back_lem_append_s
   (t : Type0) (key : usize) (value : t) (ls : list_t t) :
   Lemma
   (requires (
     slot_t_find_s key ls == None))
   (ensures (
-    match hash_map_insert_in_list_back t key value ls with
+    match hashMap_insert_in_list_back t key value ls with
     | Fail _ -> False
     | Return ls' ->
       list_t_v ls' == list_t_v ls @ [(key,value)]))
-  (decreases (hash_map_insert_in_list_loop_decreases t key value ls))
+  (decreases (hashMap_insert_in_list_loop_decreases t key value ls))
 
 #push-options "--fuel 1"
-let rec hash_map_insert_in_list_back_lem_append_s t key value ls =
+let rec hashMap_insert_in_list_back_lem_append_s t key value ls =
   begin match ls with
-  | ListCons ckey cvalue ls0 ->
+  | List_Cons ckey cvalue ls0 ->
     let b = ckey = key in
     if b
     then ()
     else
       begin
-      hash_map_insert_in_list_back_lem_append_s t key value ls0;
-      match hash_map_insert_in_list_back t key value ls0 with
+      hashMap_insert_in_list_back_lem_append_s t key value ls0;
+      match hashMap_insert_in_list_back t key value ls0 with
       | Fail _ -> ()
       | Return l -> ()
       end
-  | ListNil -> ()
+  | List_Nil -> ()
   end
 #pop-options
 
 /// [insert_in_list]: if the key is in the map, we update the binding (functional version)
-val hash_map_insert_in_list_back_lem_update_s
+val hashMap_insert_in_list_back_lem_update_s
   (t : Type0) (key : usize) (value : t) (ls : list_t t) :
   Lemma
   (requires (
     Some? (find (same_key key) (list_t_v ls))))
   (ensures (
-    match hash_map_insert_in_list_back t key value ls with
+    match hashMap_insert_in_list_back t key value ls with
     | Fail _ -> False
     | Return ls' ->
       list_t_v ls' == find_update (same_key key) (list_t_v ls) (key,value)))
-  (decreases (hash_map_insert_in_list_loop_decreases t key value ls))
+  (decreases (hashMap_insert_in_list_loop_decreases t key value ls))
 
 #push-options "--fuel 1"
-let rec hash_map_insert_in_list_back_lem_update_s t key value ls =
+let rec hashMap_insert_in_list_back_lem_update_s t key value ls =
   begin match ls with
-  | ListCons ckey cvalue ls0 ->
+  | List_Cons ckey cvalue ls0 ->
     let b = ckey = key in
     if b
     then ()
     else
       begin
-      hash_map_insert_in_list_back_lem_update_s t key value ls0;
-      match hash_map_insert_in_list_back t key value ls0 with
+      hashMap_insert_in_list_back_lem_update_s t key value ls0;
+      match hashMap_insert_in_list_back t key value ls0 with
       | Fail _ -> ()
       | Return l -> ()
       end
-  | ListNil -> ()
+  | List_Nil -> ()
   end
 #pop-options
 
 /// Put everything together
-val hash_map_insert_in_list_back_lem_s
+val hashMap_insert_in_list_back_lem_s
   (t : Type0) (key : usize) (value : t) (ls : list_t t) :
   Lemma
   (ensures (
-    match hash_map_insert_in_list_back t key value ls with
+    match hashMap_insert_in_list_back t key value ls with
     | Fail _ -> False
     | Return ls' ->
-      list_t_v ls' == hash_map_insert_in_list_s key value (list_t_v ls)))
+      list_t_v ls' == hashMap_insert_in_list_s key value (list_t_v ls)))
 
-let hash_map_insert_in_list_back_lem_s t key value ls =
+let hashMap_insert_in_list_back_lem_s t key value ls =
   match find (same_key key) (list_t_v ls) with
-  | None -> hash_map_insert_in_list_back_lem_append_s t key value ls
-  | Some _ -> hash_map_insert_in_list_back_lem_update_s t key value ls
+  | None -> hashMap_insert_in_list_back_lem_append_s t key value ls
+  | Some _ -> hashMap_insert_in_list_back_lem_update_s t key value ls
 
 (**** Invariants of insert_in_list_s *)
 
 /// Auxiliary lemmas
-/// We work on [hash_map_insert_in_list_s], the "high-level" version of [insert_in_list'back].
+/// We work on [hashMap_insert_in_list_s], the "high-level" version of [insert_in_list'back].
 ///
 /// Note that in F* we can't have recursive proofs inside of other proofs, contrary
 /// to Coq, which makes it a bit cumbersome to prove auxiliary results like the
@@ -893,14 +893,14 @@ let rec slot_s_inv_not_find_append_end_inv_lem t len key value ls =
 #pop-options
 
 /// [insert_in_list]: if the key is not in the map, appends a new bindings
-val hash_map_insert_in_list_s_lem_append
+val hashMap_insert_in_list_s_lem_append
   (t : Type0) (len : usize{len > 0}) (key : usize) (value : t) (ls : list (binding t)) :
   Lemma
   (requires (
     slot_s_inv len (hash_mod_key key len) ls /\
     slot_s_find key ls == None))
   (ensures (
-    let ls' = hash_map_insert_in_list_s key value ls in
+    let ls' = hashMap_insert_in_list_s key value ls in
     ls' == ls @ [(key,value)] /\
     // The invariant is preserved
     slot_s_inv len (hash_mod_key key len) ls' /\
@@ -909,20 +909,20 @@ val hash_map_insert_in_list_s_lem_append
     // The other bindings are preserved
     (forall k'. k' <> key ==> slot_s_find k' ls' == slot_s_find k' ls)))
 
-let hash_map_insert_in_list_s_lem_append t len key value ls =
+let hashMap_insert_in_list_s_lem_append t len key value ls =
   slot_s_inv_not_find_append_end_inv_lem t len key value ls
 
 /// [insert_in_list]: if the key is not in the map, appends a new bindings (quantifiers)
 /// Rk.: we don't use this lemma.
 /// TODO: remove?
-val hash_map_insert_in_list_back_lem_append
+val hashMap_insert_in_list_back_lem_append
   (t : Type0) (len : usize{len > 0}) (key : usize) (value : t) (ls : list_t t) :
   Lemma
   (requires (
     slot_t_inv len (hash_mod_key key len) ls /\
     slot_t_find_s key ls == None))
   (ensures (
-    match hash_map_insert_in_list_back t key value ls with
+    match hashMap_insert_in_list_back t key value ls with
     | Fail _ -> False
     | Return ls' ->
       list_t_v ls' == list_t_v ls @ [(key,value)] /\
@@ -933,9 +933,9 @@ val hash_map_insert_in_list_back_lem_append
       // The other bindings are preserved
       (forall k'. k' <> key ==> slot_t_find_s k' ls' == slot_t_find_s k' ls)))
 
-let hash_map_insert_in_list_back_lem_append t len key value ls =
-  hash_map_insert_in_list_back_lem_s t key value ls;
-  hash_map_insert_in_list_s_lem_append t len key value (list_t_v ls)
+let hashMap_insert_in_list_back_lem_append t len key value ls =
+  hashMap_insert_in_list_back_lem_s t key value ls;
+  hashMap_insert_in_list_s_lem_append t len key value (list_t_v ls)
 
 (** Auxiliary lemmas: update case *)
 
@@ -1013,14 +1013,14 @@ let rec slot_s_inv_find_append_end_inv_lem t len key value ls =
 #pop-options
 
 /// [insert_in_list]: if the key is in the map, update the bindings
-val hash_map_insert_in_list_s_lem_update
+val hashMap_insert_in_list_s_lem_update
   (t : Type0) (len : usize{len > 0}) (key : usize) (value : t) (ls : list (binding t)) :
   Lemma
   (requires (
     slot_s_inv len (hash_mod_key key len) ls /\
     Some? (slot_s_find key ls)))
   (ensures (
-    let ls' = hash_map_insert_in_list_s key value ls in
+    let ls' = hashMap_insert_in_list_s key value ls in
     ls' == find_update (same_key key) ls (key,value) /\
     // The invariant is preserved
     slot_s_inv len (hash_mod_key key len) ls' /\
@@ -1029,20 +1029,20 @@ val hash_map_insert_in_list_s_lem_update
     // The other bindings are preserved
     (forall k'. k' <> key ==> slot_s_find k' ls' == slot_s_find k' ls)))
 
-let hash_map_insert_in_list_s_lem_update t len key value ls =
+let hashMap_insert_in_list_s_lem_update t len key value ls =
   slot_s_inv_find_append_end_inv_lem t len key value ls
 
 
 /// [insert_in_list]: if the key is in the map, update the bindings
 /// TODO: not used: remove?
-val hash_map_insert_in_list_back_lem_update
+val hashMap_insert_in_list_back_lem_update
   (t : Type0) (len : usize{len > 0}) (key : usize) (value : t) (ls : list_t t) :
   Lemma
   (requires (
     slot_t_inv len (hash_mod_key key len) ls /\
     Some? (slot_t_find_s key ls)))
   (ensures (
-    match hash_map_insert_in_list_back t key value ls with
+    match hashMap_insert_in_list_back t key value ls with
     | Fail _ -> False
     | Return ls' ->
       let als = list_t_v ls in
@@ -1054,20 +1054,20 @@ val hash_map_insert_in_list_back_lem_update
       // The other bindings are preserved
       (forall k'. k' <> key ==> slot_t_find_s k' ls' == slot_t_find_s k' ls)))
 
-let hash_map_insert_in_list_back_lem_update t len key value ls =
-  hash_map_insert_in_list_back_lem_s t key value ls;
-  hash_map_insert_in_list_s_lem_update t len key value (list_t_v ls)
+let hashMap_insert_in_list_back_lem_update t len key value ls =
+  hashMap_insert_in_list_back_lem_s t key value ls;
+  hashMap_insert_in_list_s_lem_update t len key value (list_t_v ls)
 
 (** Final lemmas about [insert_in_list] *)
 
 /// High-level version
-val hash_map_insert_in_list_s_lem
+val hashMap_insert_in_list_s_lem
   (t : Type0) (len : usize{len > 0}) (key : usize) (value : t) (ls : list (binding t)) :
   Lemma
   (requires (
     slot_s_inv len (hash_mod_key key len) ls))
   (ensures (
-    let ls' = hash_map_insert_in_list_s key value ls in
+    let ls' = hashMap_insert_in_list_s key value ls in
     // The invariant is preserved
     slot_s_inv len (hash_mod_key key len) ls' /\
     // [key] maps to [value]
@@ -1079,22 +1079,22 @@ val hash_map_insert_in_list_s_lem
      | None -> length ls' = length ls + 1
      | Some _ -> length ls' = length ls)))
 
-let hash_map_insert_in_list_s_lem t len key value ls =
+let hashMap_insert_in_list_s_lem t len key value ls =
   match slot_s_find key ls with
   | None ->
     assert_norm(length [(key,value)] = 1);
-    hash_map_insert_in_list_s_lem_append t len key value ls
+    hashMap_insert_in_list_s_lem_append t len key value ls
   | Some _ ->
-    hash_map_insert_in_list_s_lem_update t len key value ls
+    hashMap_insert_in_list_s_lem_update t len key value ls
 
 /// [insert_in_list]
 /// TODO: not used: remove?
-val hash_map_insert_in_list_back_lem
+val hashMap_insert_in_list_back_lem
   (t : Type0) (len : usize{len > 0}) (key : usize) (value : t) (ls : list_t t) :
   Lemma
   (requires (slot_t_inv len (hash_mod_key key len) ls))
   (ensures (
-    match hash_map_insert_in_list_back t key value ls with
+    match hashMap_insert_in_list_back t key value ls with
     | Fail _ -> False
     | Return ls' ->
       // The invariant is preserved
@@ -1111,127 +1111,127 @@ val hash_map_insert_in_list_back_lem
        | Some _ ->
          list_t_v ls' == find_update (same_key key) (list_t_v ls) (key,value) /\
          list_t_len ls' = list_t_len ls)))
-  (decreases (hash_map_insert_in_list_loop_decreases t key value ls))
+  (decreases (hashMap_insert_in_list_loop_decreases t key value ls))
 
-let hash_map_insert_in_list_back_lem t len key value ls =
-  hash_map_insert_in_list_back_lem_s t key value ls;
-  hash_map_insert_in_list_s_lem t len key value (list_t_v ls)
+let hashMap_insert_in_list_back_lem t len key value ls =
+  hashMap_insert_in_list_back_lem_s t key value ls;
+  hashMap_insert_in_list_s_lem t len key value (list_t_v ls)
 
 (*** insert_no_resize *)
 
 (**** Refinement proof *)
 /// Same strategy as for [insert_in_list]: we introduce a high-level version of
 /// the function, and reason about it.
-/// We work on [hash_map_s] (we use a higher-level view of the hash-map, but
+/// We work on [hashMap_s] (we use a higher-level view of the hash-map, but
 /// not too high).
 
 /// A high-level version of insert, which doesn't check if the table is saturated
-let hash_map_insert_no_fail_s
-  (#t : Type0) (hm : hash_map_s_nes t)
+let hashMap_insert_no_fail_s
+  (#t : Type0) (hm : hashMap_s_nes t)
   (key : usize) (value : t) :
-  hash_map_s t =
+  hashMap_s t =
   let len = length hm in
   let i = hash_mod_key key len in
   let slot = index hm i in
-  let slot' = hash_map_insert_in_list_s key value slot in
+  let slot' = hashMap_insert_in_list_s key value slot in
   let hm' = list_update hm i slot' in
   hm'
 
-// TODO: at some point I used hash_map_s_nes and it broke proofs...x
-let hash_map_insert_no_resize_s
-  (#t : Type0) (hm : hash_map_s_nes t)
+// TODO: at some point I used hashMap_s_nes and it broke proofs...x
+let hashMap_insert_no_resize_s
+  (#t : Type0) (hm : hashMap_s_nes t)
   (key : usize) (value : t) :
-  result (hash_map_s t) =
+  result (hashMap_s t) =
   // Check if the table is saturated (too many entries, and we need to insert one)
   let num_entries = length (flatten hm) in
-  if None? (hash_map_s_find hm key) && num_entries = usize_max then Fail Failure
-  else Return (hash_map_insert_no_fail_s hm key value)
+  if None? (hashMap_s_find hm key) && num_entries = usize_max then Fail Failure
+  else Return (hashMap_insert_no_fail_s hm key value)
 
-/// Prove that [hash_map_insert_no_resize_s] is refined by
-/// [hash_map_insert_no_resize'fwd_back]
-val hash_map_insert_no_resize_fwd_back_lem_s
-  (t : Type0) (self : hash_map_t t) (key : usize) (value : t) :
+/// Prove that [hashMap_insert_no_resize_s] is refined by
+/// [hashMap_insert_no_resize'fwd_back]
+val hashMap_insert_no_resize_lem_s
+  (t : Type0) (self : hashMap_t t) (key : usize) (value : t) :
   Lemma
   (requires (
-    hash_map_t_base_inv self /\
-    hash_map_s_len (hash_map_t_v self) = hash_map_t_len_s self))
+    hashMap_t_base_inv self /\
+    hashMap_s_len (hashMap_t_v self) = hashMap_t_len_s self))
   (ensures (
     begin
-    match hash_map_insert_no_resize_fwd_back t self key value,
-          hash_map_insert_no_resize_s (hash_map_t_v self) key value
+    match hashMap_insert_no_resize t self key value,
+          hashMap_insert_no_resize_s (hashMap_t_v self) key value
     with
     | Fail _, Fail _ -> True
     | Return hm, Return hm_v ->
-      hash_map_t_base_inv hm /\
-      hash_map_t_same_params hm self /\
-      hash_map_t_v hm == hm_v /\
-      hash_map_s_len hm_v == hash_map_t_len_s hm
+      hashMap_t_base_inv hm /\
+      hashMap_t_same_params hm self /\
+      hashMap_t_v hm == hm_v /\
+      hashMap_s_len hm_v == hashMap_t_len_s hm
     | _ -> False
     end))
 
-let hash_map_insert_no_resize_fwd_back_lem_s t self key value =
-  begin match hash_key_fwd key with
+let hashMap_insert_no_resize_lem_s t self key value =
+  begin match hash_key key with
   | Fail _ -> ()
   | Return i ->
-    let i0 = self.hash_map_num_entries in
-    let p = self.hash_map_max_load_factor in
-    let i1 = self.hash_map_max_load in
-    let v = self.hash_map_slots in
-    let i2 = vec_len (list_t t) v in
+    let i0 = self.num_entries in
+    let p = self.max_load_factor in
+    let i1 = self.max_load in
+    let v = self.slots in
+    let i2 = alloc_vec_Vec_len (list_t t) v in
     let len = length v in
     begin match usize_rem i i2 with
     | Fail _ -> ()
     | Return hash_mod ->
-      begin match vec_index_mut_fwd (list_t t) v hash_mod with
+      begin match alloc_vec_Vec_index_usize v hash_mod with
       | Fail _ -> ()
       | Return l ->
         begin
-        // Checking that: list_t_v (index ...) == index (hash_map_t_v ...) ...
-        assert(list_t_v l == index (hash_map_t_v self) hash_mod);
-        hash_map_insert_in_list_fwd_lem t key value l;
-        match hash_map_insert_in_list_fwd t key value l with
+        // Checking that: list_t_v (index ...) == index (hashMap_t_v ...) ...
+        assert(list_t_v l == index (hashMap_t_v self) hash_mod);
+        hashMap_insert_in_list_lem t key value l;
+        match hashMap_insert_in_list t key value l with
         | Fail _ -> ()
         | Return b ->
           assert(b = None? (slot_s_find key (list_t_v l)));
-          hash_map_insert_in_list_back_lem t len key value l;
+          hashMap_insert_in_list_back_lem t len key value l;
           if b
           then
             begin match usize_add i0 1 with
             | Fail _ -> ()
             | Return i3 ->
               begin
-              match hash_map_insert_in_list_back t key value l with
+              match hashMap_insert_in_list_back t key value l with
               | Fail _ -> ()
               | Return l0 ->
-                begin match vec_index_mut_back (list_t t) v hash_mod l0 with
+                begin match alloc_vec_Vec_update_usize v hash_mod l0 with
                 | Fail _ -> ()
                 | Return v0 ->
-                  let self_v = hash_map_t_v self in
-                  let hm = Mkhash_map_t i3 p i1 v0 in
-                  let hm_v = hash_map_t_v hm in
+                  let self_v = hashMap_t_v self in
+                  let hm = MkhashMap_t i3 p i1 v0 in
+                  let hm_v = hashMap_t_v hm in
                   assert(hm_v == list_update self_v hash_mod (list_t_v l0));
                   assert_norm(length [(key,value)] = 1);
                   assert(length (list_t_v l0) = length (list_t_v l) + 1);
                   length_flatten_update self_v hash_mod (list_t_v l0);
-                  assert(hash_map_s_len hm_v = hash_map_t_len_s hm)
+                  assert(hashMap_s_len hm_v = hashMap_t_len_s hm)
                 end
               end
             end
           else
             begin
-            match hash_map_insert_in_list_back t key value l with
+            match hashMap_insert_in_list_back t key value l with
             | Fail _ -> ()
             | Return l0 ->
-              begin match vec_index_mut_back (list_t t) v hash_mod l0 with
+              begin match alloc_vec_Vec_update_usize v hash_mod l0 with
               | Fail _ -> ()
               | Return v0 ->
-                let self_v = hash_map_t_v self in
-                let hm = Mkhash_map_t i0 p i1 v0 in
-                let hm_v = hash_map_t_v hm in
+                let self_v = hashMap_t_v self in
+                let hm = MkhashMap_t i0 p i1 v0 in
+                let hm_v = hashMap_t_v hm in
                 assert(hm_v == list_update self_v hash_mod (list_t_v l0));
                 assert(length (list_t_v l0) = length (list_t_v l));
                 length_flatten_update self_v hash_mod (list_t_v l0);
-                assert(hash_map_s_len hm_v = hash_map_t_len_s hm)
+                assert(hashMap_s_len hm_v = hashMap_t_len_s hm)
               end
             end
         end
@@ -1241,108 +1241,108 @@ let hash_map_insert_no_resize_fwd_back_lem_s t self key value =
 
 (**** insert_{no_fail,no_resize}: invariants *)
 
-let hash_map_s_updated_binding
-  (#t : Type0) (hm : hash_map_s_nes t)
-  (key : usize) (opt_value : option t) (hm' : hash_map_s_nes t) : Type0 =
+let hashMap_s_updated_binding
+  (#t : Type0) (hm : hashMap_s_nes t)
+  (key : usize) (opt_value : option t) (hm' : hashMap_s_nes t) : Type0 =
   // [key] maps to [value]
-  hash_map_s_find hm' key == opt_value /\
+  hashMap_s_find hm' key == opt_value /\
   // The other bindings are preserved
-  (forall k'. k' <> key ==> hash_map_s_find hm' k' == hash_map_s_find hm k')
+  (forall k'. k' <> key ==> hashMap_s_find hm' k' == hashMap_s_find hm k')
 
-let insert_post (#t : Type0) (hm : hash_map_s_nes t)
-  (key : usize) (value : t) (hm' : hash_map_s_nes t) : Type0 =
+let insert_post (#t : Type0) (hm : hashMap_s_nes t)
+  (key : usize) (value : t) (hm' : hashMap_s_nes t) : Type0 =
   // The invariant is preserved
-  hash_map_s_inv hm' /\
+  hashMap_s_inv hm' /\
   // [key] maps to [value] and the other bindings are preserved
-  hash_map_s_updated_binding hm key (Some value) hm' /\
+  hashMap_s_updated_binding hm key (Some value) hm' /\
   // The length is incremented, iff we inserted a new key
-  (match hash_map_s_find hm key with
-   | None -> hash_map_s_len hm' = hash_map_s_len hm + 1
-   | Some _ -> hash_map_s_len hm' = hash_map_s_len hm)
+  (match hashMap_s_find hm key with
+   | None -> hashMap_s_len hm' = hashMap_s_len hm + 1
+   | Some _ -> hashMap_s_len hm' = hashMap_s_len hm)
 
-val hash_map_insert_no_fail_s_lem
-  (#t : Type0) (hm : hash_map_s_nes t)
+val hashMap_insert_no_fail_s_lem
+  (#t : Type0) (hm : hashMap_s_nes t)
   (key : usize) (value : t) :
   Lemma
-  (requires (hash_map_s_inv hm))
+  (requires (hashMap_s_inv hm))
   (ensures (
-    let hm' = hash_map_insert_no_fail_s hm key value in
+    let hm' = hashMap_insert_no_fail_s hm key value in
     insert_post hm key value hm'))
 
-let hash_map_insert_no_fail_s_lem #t hm key value =
+let hashMap_insert_no_fail_s_lem #t hm key value =
   let len = length hm in
   let i = hash_mod_key key len in
   let slot = index hm i in
-  hash_map_insert_in_list_s_lem t len key value slot;
-  let slot' = hash_map_insert_in_list_s key value slot in
+  hashMap_insert_in_list_s_lem t len key value slot;
+  let slot' = hashMap_insert_in_list_s key value slot in
   length_flatten_update hm i slot'
 
-val hash_map_insert_no_resize_s_lem
-  (#t : Type0) (hm : hash_map_s_nes t)
+val hashMap_insert_no_resize_s_lem
+  (#t : Type0) (hm : hashMap_s_nes t)
   (key : usize) (value : t) :
   Lemma
-  (requires (hash_map_s_inv hm))
+  (requires (hashMap_s_inv hm))
   (ensures (
-    match hash_map_insert_no_resize_s hm key value with
+    match hashMap_insert_no_resize_s hm key value with
     | Fail _ ->
       // Can fail only if we need to create a new binding in
       // an already saturated map
-      hash_map_s_len hm = usize_max /\
-      None? (hash_map_s_find hm key)
+      hashMap_s_len hm = usize_max /\
+      None? (hashMap_s_find hm key)
     | Return hm' ->
       insert_post hm key value hm'))
 
-let hash_map_insert_no_resize_s_lem #t hm key value =
+let hashMap_insert_no_resize_s_lem #t hm key value =
   let num_entries = length (flatten hm) in
-  if None? (hash_map_s_find hm key) && num_entries = usize_max then ()
-  else hash_map_insert_no_fail_s_lem hm key value
+  if None? (hashMap_s_find hm key) && num_entries = usize_max then ()
+  else hashMap_insert_no_fail_s_lem hm key value
 
 
 (**** find after insert *)
 /// Lemmas about what happens if we call [find] after an insertion
 
-val hash_map_insert_no_resize_s_get_same_lem
-  (#t : Type0) (hm : hash_map_s t)
+val hashMap_insert_no_resize_s_get_same_lem
+  (#t : Type0) (hm : hashMap_s t)
   (key : usize) (value : t) :
-  Lemma (requires (hash_map_s_inv hm))
+  Lemma (requires (hashMap_s_inv hm))
   (ensures (
-    match hash_map_insert_no_resize_s hm key value with
+    match hashMap_insert_no_resize_s hm key value with
     | Fail _ -> True
     | Return hm' ->
-      hash_map_s_find hm' key == Some value))
+      hashMap_s_find hm' key == Some value))
 
-let hash_map_insert_no_resize_s_get_same_lem #t hm key value =
+let hashMap_insert_no_resize_s_get_same_lem #t hm key value =
   let num_entries = length (flatten hm) in
-  if None? (hash_map_s_find hm key) && num_entries = usize_max then ()
+  if None? (hashMap_s_find hm key) && num_entries = usize_max then ()
   else
     begin
-    let hm' = Return?.v (hash_map_insert_no_resize_s hm key value) in
+    let hm' = Return?.v (hashMap_insert_no_resize_s hm key value) in
     let len = length hm in
     let i = hash_mod_key key len in
     let slot = index hm i in
-    hash_map_insert_in_list_s_lem t len key value slot
+    hashMap_insert_in_list_s_lem t len key value slot
    end
 
-val hash_map_insert_no_resize_s_get_diff_lem
-  (#t : Type0) (hm : hash_map_s t)
+val hashMap_insert_no_resize_s_get_diff_lem
+  (#t : Type0) (hm : hashMap_s t)
   (key : usize) (value : t) (key' : usize{key' <> key}) :
-  Lemma (requires (hash_map_s_inv hm))
+  Lemma (requires (hashMap_s_inv hm))
   (ensures (
-    match hash_map_insert_no_resize_s hm key value with
+    match hashMap_insert_no_resize_s hm key value with
     | Fail _ -> True
     | Return hm' ->
-      hash_map_s_find hm' key' == hash_map_s_find hm key'))
+      hashMap_s_find hm' key' == hashMap_s_find hm key'))
 
-let hash_map_insert_no_resize_s_get_diff_lem #t hm key value key' =
+let hashMap_insert_no_resize_s_get_diff_lem #t hm key value key' =
   let num_entries = length (flatten hm) in
-  if None? (hash_map_s_find hm key) && num_entries = usize_max then ()
+  if None? (hashMap_s_find hm key) && num_entries = usize_max then ()
   else
     begin
-    let hm' = Return?.v (hash_map_insert_no_resize_s hm key value) in
+    let hm' = Return?.v (hashMap_insert_no_resize_s hm key value) in
     let len = length hm in
     let i = hash_mod_key key len in
     let slot = index hm i in
-    hash_map_insert_in_list_s_lem t len key value slot;
+    hashMap_insert_in_list_s_lem t len key value slot;
     let i' = hash_mod_key key' len in
     if i <> i' then ()
     else
@@ -1354,116 +1354,116 @@ let hash_map_insert_no_resize_s_get_diff_lem #t hm key value key' =
 
 (*** move_elements_from_list *)
 
-/// Having a great time here: if we use `result (hash_map_s_res t)` as the
-/// return type for [hash_map_move_elements_from_list_s] instead of having this
-/// awkward match, the proof of [hash_map_move_elements_fwd_back_lem_refin] fails.
+/// Having a great time here: if we use `result (hashMap_s_res t)` as the
+/// return type for [hashMap_move_elements_from_list_s] instead of having this
+/// awkward match, the proof of [hashMap_move_elements_lem_refin] fails.
 /// I guess it comes from F*'s poor subtyping.
-/// Followingly, I'm not taking any chance and using [result_hash_map_s]
+/// Followingly, I'm not taking any chance and using [result_hashMap_s]
 /// everywhere.
-type result_hash_map_s_nes (t : Type0) : Type0 =
-  res:result (hash_map_s t) {
+type result_hashMap_s_nes (t : Type0) : Type0 =
+  res:result (hashMap_s t) {
     match res with
     | Fail _ -> True
     | Return hm -> is_pos_usize (length hm)
   }
 
-let rec hash_map_move_elements_from_list_s
-  (#t : Type0) (hm : hash_map_s_nes t)
+let rec hashMap_move_elements_from_list_s
+  (#t : Type0) (hm : hashMap_s_nes t)
   (ls : slot_s t) :
-  // Do *NOT* use `result (hash_map_s t)`
-  Tot (result_hash_map_s_nes t)
+  // Do *NOT* use `result (hashMap_s t)`
+  Tot (result_hashMap_s_nes t)
   (decreases ls) =
   match ls with
   | [] -> Return hm
   | (key, value) :: ls' ->
-    match hash_map_insert_no_resize_s hm key value with
+    match hashMap_insert_no_resize_s hm key value with
     | Fail e -> Fail e
     | Return hm' ->
-      hash_map_move_elements_from_list_s hm' ls'
+      hashMap_move_elements_from_list_s hm' ls'
 
 /// Refinement lemma
-val hash_map_move_elements_from_list_fwd_back_lem
-  (t : Type0) (ntable : hash_map_t_nes t) (ls : list_t t) :
-  Lemma (requires (hash_map_t_base_inv ntable))
+val hashMap_move_elements_from_list_lem
+  (t : Type0) (ntable : hashMap_t_nes t) (ls : list_t t) :
+  Lemma (requires (hashMap_t_base_inv ntable))
   (ensures (
-    match hash_map_move_elements_from_list_fwd_back t ntable ls,
-          hash_map_move_elements_from_list_s (hash_map_t_v ntable) (slot_t_v ls)
+    match hashMap_move_elements_from_list t ntable ls,
+          hashMap_move_elements_from_list_s (hashMap_t_v ntable) (slot_t_v ls)
     with
     | Fail _, Fail _ -> True
     | Return hm', Return hm_v ->
-      hash_map_t_base_inv hm' /\
-      hash_map_t_v hm' == hm_v /\
-      hash_map_t_same_params hm' ntable
+      hashMap_t_base_inv hm' /\
+      hashMap_t_v hm' == hm_v /\
+      hashMap_t_same_params hm' ntable
     | _ -> False))
-  (decreases (hash_map_move_elements_from_list_loop_decreases t ntable ls))
+  (decreases (hashMap_move_elements_from_list_loop_decreases t ntable ls))
 
 #push-options "--fuel 1"
-let rec hash_map_move_elements_from_list_fwd_back_lem t ntable ls =
+let rec hashMap_move_elements_from_list_lem t ntable ls =
   begin match ls with
-  | ListCons k v tl ->
+  | List_Cons k v tl ->
     assert(list_t_v ls == (k, v) :: list_t_v tl);
     let ls_v = list_t_v ls in
     let (_,_) :: tl_v = ls_v in
-    hash_map_insert_no_resize_fwd_back_lem_s t ntable k v;
-    begin match hash_map_insert_no_resize_fwd_back t ntable k v with
+    hashMap_insert_no_resize_lem_s t ntable k v;
+    begin match hashMap_insert_no_resize t ntable k v with
     | Fail _ -> ()
     | Return h ->
-      let h_v = Return?.v (hash_map_insert_no_resize_s (hash_map_t_v ntable) k v) in
-      assert(hash_map_t_v h == h_v);
-      hash_map_move_elements_from_list_fwd_back_lem t h tl;
-      begin match hash_map_move_elements_from_list_fwd_back t h tl with
+      let h_v = Return?.v (hashMap_insert_no_resize_s (hashMap_t_v ntable) k v) in
+      assert(hashMap_t_v h == h_v);
+      hashMap_move_elements_from_list_lem t h tl;
+      begin match hashMap_move_elements_from_list t h tl with
       | Fail _ -> ()
       | Return h0 -> ()
       end
     end
-  | ListNil -> ()
+  | List_Nil -> ()
   end
 #pop-options
 
 (*** move_elements *)
 
 (**** move_elements: refinement 0 *)
-/// The proof for [hash_map_move_elements_fwd_back_lem_refin] broke so many times
+/// The proof for [hashMap_move_elements_lem_refin] broke so many times
 /// (while it is supposed to be super simple!) that we decided to add one refinement
 /// level, to really do things step by step...
 /// Doing this refinement layer made me notice that maybe the problem came from
-/// the fact that at some point we have to prove `list_t_v ListNil == []`: I
+/// the fact that at some point we have to prove `list_t_v List_Nil == []`: I
 /// added the corresponding assert to help Z3 and everything became stable.
 /// I finally didn't use this "simple" refinement lemma, but I still keep it here
-/// because it allows for easy comparisons with [hash_map_move_elements_s].
+/// because it allows for easy comparisons with [hashMap_move_elements_s].
 
-/// [hash_map_move_elements_fwd] refines this function, which is actually almost
+/// [hashMap_move_elements] refines this function, which is actually almost
 /// the same (just a little bit shorter and cleaner, and has a pre).
 ///
 /// The way I wrote the high-level model is the following:
-/// - I copy-pasted the definition of [hash_map_move_elements_fwd], wrote the
-///   signature which links this new definition to [hash_map_move_elements_fwd] and
+/// - I copy-pasted the definition of [hashMap_move_elements], wrote the
+///   signature which links this new definition to [hashMap_move_elements] and
 ///   checked that the proof passed
 /// - I gradually simplified it, while making sure the proof still passes
 #push-options "--fuel 1"
-let rec hash_map_move_elements_s_simpl
-  (t : Type0) (ntable : hash_map_t t)
-  (slots : vec (list_t t))
+let rec hashMap_move_elements_s_simpl
+  (t : Type0) (ntable : hashMap_t t)
+  (slots : alloc_vec_Vec (list_t t))
   (i : usize{i <= length slots /\ length slots <= usize_max}) :
-  Pure (result ((hash_map_t t) & (vec (list_t t))))
+  Pure (result ((hashMap_t t) & (alloc_vec_Vec (list_t t))))
   (requires (True))
   (ensures (fun res ->
-    match res, hash_map_move_elements_fwd_back t ntable slots i with
+    match res, hashMap_move_elements t ntable slots i with
     | Fail _, Fail _ -> True
     | Return (ntable1, slots1), Return (ntable2, slots2) ->
       ntable1 == ntable2 /\
       slots1 == slots2
     | _ -> False))
-  (decreases (hash_map_move_elements_loop_decreases t ntable slots i))
+  (decreases (hashMap_move_elements_loop_decreases t ntable slots i))
   =
   if i < length slots
   then
     let slot = index slots i in
-    begin match hash_map_move_elements_from_list_fwd_back t ntable slot with
+    begin match hashMap_move_elements_from_list t ntable slot with
     | Fail e -> Fail e
     | Return hm' ->
-      let slots' = list_update slots i ListNil in
-      hash_map_move_elements_s_simpl t hm' slots' (i+1)
+      let slots' = list_update slots i List_Nil in
+      hashMap_move_elements_s_simpl t hm' slots' (i+1)
     end
   else Return (ntable, slots)
 #pop-options
@@ -1476,71 +1476,71 @@ let rec hash_map_move_elements_s_simpl
 // Note that we ignore the returned slots (we thus don't return a pair:
 // only the new hash map in which we moved the elements from the slots):
 // this returned value is not used.
-let rec hash_map_move_elements_s
-  (#t : Type0) (hm : hash_map_s_nes t)
+let rec hashMap_move_elements_s
+  (#t : Type0) (hm : hashMap_s_nes t)
   (slots : slots_s t) (i : usize{i <= length slots /\ length slots <= usize_max}) :
-  Tot (result_hash_map_s_nes t)
+  Tot (result_hashMap_s_nes t)
   (decreases (length slots - i)) =
   let len = length slots in
   if i < len then
     begin
     let slot = index slots i in
-    match hash_map_move_elements_from_list_s hm slot with
+    match hashMap_move_elements_from_list_s hm slot with
     | Fail e -> Fail e
     | Return hm' ->
       let slots' = list_update slots i [] in
-      hash_map_move_elements_s hm' slots' (i+1)
+      hashMap_move_elements_s hm' slots' (i+1)
     end
   else Return hm
 
-val hash_map_move_elements_fwd_back_lem_refin
-  (t : Type0) (ntable : hash_map_t t)
-  (slots : vec (list_t t)) (i : usize{i <= length slots}) :
+val hashMap_move_elements_lem_refin
+  (t : Type0) (ntable : hashMap_t t)
+  (slots : alloc_vec_Vec (list_t t)) (i : usize{i <= length slots}) :
   Lemma
   (requires (
-    hash_map_t_base_inv ntable))
+    hashMap_t_base_inv ntable))
   (ensures (
-    match hash_map_move_elements_fwd_back t ntable slots i,
-          hash_map_move_elements_s (hash_map_t_v ntable) (slots_t_v slots) i
+    match hashMap_move_elements t ntable slots i,
+          hashMap_move_elements_s (hashMap_t_v ntable) (slots_t_v slots) i
     with
     | Fail _, Fail _ -> True // We will prove later that this is not possible
     | Return (ntable', _), Return ntable'_v ->
-      hash_map_t_base_inv ntable' /\
-      hash_map_t_v ntable' == ntable'_v /\
-      hash_map_t_same_params ntable' ntable
+      hashMap_t_base_inv ntable' /\
+      hashMap_t_v ntable' == ntable'_v /\
+      hashMap_t_same_params ntable' ntable
     | _ -> False))
  (decreases (length slots - i))
 
 #restart-solver
 #push-options "--fuel 1"
-let rec hash_map_move_elements_fwd_back_lem_refin t ntable slots i =
-  assert(hash_map_t_base_inv ntable);
-  let i0 = vec_len (list_t t) slots in
+let rec hashMap_move_elements_lem_refin t ntable slots i =
+  assert(hashMap_t_base_inv ntable);
+  let i0 = alloc_vec_Vec_len (list_t t) slots in
   let b = i < i0 in
   if b
   then
-    begin match vec_index_mut_fwd (list_t t) slots i with
+    begin match alloc_vec_Vec_index_usize slots i with
     | Fail _ -> ()
     | Return l ->
-      let l0 = mem_replace_fwd (list_t t) l ListNil in
+      let l0 = core_mem_replace (list_t t) l List_Nil in
       assert(l0 == l);
-      hash_map_move_elements_from_list_fwd_back_lem t ntable l0;
-      begin match hash_map_move_elements_from_list_fwd_back t ntable l0 with
+      hashMap_move_elements_from_list_lem t ntable l0;
+      begin match hashMap_move_elements_from_list t ntable l0 with
       | Fail _ -> ()
       | Return h ->
-        let l1 = mem_replace_back (list_t t) l ListNil in
-        assert(l1 == ListNil);
-        assert(slot_t_v #t ListNil == []); // THIS IS IMPORTANT
-        begin match vec_index_mut_back (list_t t) slots i l1 with
+        let l1 = core_mem_replace_back (list_t t) l List_Nil in
+        assert(l1 == List_Nil);
+        assert(slot_t_v #t List_Nil == []); // THIS IS IMPORTANT
+        begin match alloc_vec_Vec_update_usize slots i l1 with
         | Fail _ -> ()
         | Return v ->
           begin match usize_add i 1 with
           | Fail _ -> ()
           | Return i1 ->
-            hash_map_move_elements_fwd_back_lem_refin t h v i1;
-            begin match hash_map_move_elements_fwd_back t h v i1 with
+            hashMap_move_elements_lem_refin t h v i1;
+            begin match hashMap_move_elements t h v i1 with
             | Fail _ ->
-              assert(Fail? (hash_map_move_elements_fwd_back t ntable slots i));
+              assert(Fail? (hashMap_move_elements t ntable slots i));
               ()
             | Return (ntable', v0) -> ()
             end
@@ -1560,19 +1560,19 @@ let rec hash_map_move_elements_fwd_back_lem_refin t ntable slots i =
 /// [ntable] is the hash map to which we move the elements
 /// [slots] is the current hash map, from which we remove the elements, and seen
 ///         as a "flat" associative list (and not a list of lists)
-/// This is actually exactly [hash_map_move_elements_from_list_s]...
-let rec hash_map_move_elements_s_flat
-  (#t : Type0) (ntable : hash_map_s_nes t)
+/// This is actually exactly [hashMap_move_elements_from_list_s]...
+let rec hashMap_move_elements_s_flat
+  (#t : Type0) (ntable : hashMap_s_nes t)
   (slots : assoc_list t) :
-  Tot (result_hash_map_s_nes t)
+  Tot (result_hashMap_s_nes t)
   (decreases slots) =
   match slots with
   | [] -> Return ntable
   | (k,v) :: slots' ->
-    match hash_map_insert_no_resize_s ntable k v with
+    match hashMap_insert_no_resize_s ntable k v with
     | Fail e -> Fail e
     | Return ntable' ->
-      hash_map_move_elements_s_flat ntable' slots'
+      hashMap_move_elements_s_flat ntable' slots'
 
 /// The refinment lemmas
 /// First, auxiliary helpers.
@@ -1656,42 +1656,42 @@ let rec flatten_nil_prefix_as_flatten_i #a l i =
 
 /// The proof is trivial, the functions are the same.
 /// Just keeping two definitions to allow changes...
-val hash_map_move_elements_from_list_s_as_flat_lem
-  (#t : Type0) (hm : hash_map_s_nes t)
+val hashMap_move_elements_from_list_s_as_flat_lem
+  (#t : Type0) (hm : hashMap_s_nes t)
   (ls : slot_s t) :
   Lemma
   (ensures (
-    hash_map_move_elements_from_list_s hm ls ==
-    hash_map_move_elements_s_flat hm ls))
+    hashMap_move_elements_from_list_s hm ls ==
+    hashMap_move_elements_s_flat hm ls))
   (decreases ls)
 
 #push-options "--fuel 1"
-let rec hash_map_move_elements_from_list_s_as_flat_lem #t hm ls =
+let rec hashMap_move_elements_from_list_s_as_flat_lem #t hm ls =
   match ls with
   | [] -> ()
   | (key, value) :: ls' ->
-    match hash_map_insert_no_resize_s hm key value with
+    match hashMap_insert_no_resize_s hm key value with
     | Fail _ -> ()
     | Return hm' ->
-      hash_map_move_elements_from_list_s_as_flat_lem hm' ls'
+      hashMap_move_elements_from_list_s_as_flat_lem hm' ls'
 #pop-options
 
-/// Composition of two calls to [hash_map_move_elements_s_flat]
-let hash_map_move_elements_s_flat_comp
-  (#t : Type0) (hm : hash_map_s_nes t) (slot0 slot1 : slot_s t) :
-  Tot (result_hash_map_s_nes t) =
-  match hash_map_move_elements_s_flat hm slot0 with
+/// Composition of two calls to [hashMap_move_elements_s_flat]
+let hashMap_move_elements_s_flat_comp
+  (#t : Type0) (hm : hashMap_s_nes t) (slot0 slot1 : slot_s t) :
+  Tot (result_hashMap_s_nes t) =
+  match hashMap_move_elements_s_flat hm slot0 with
   | Fail e -> Fail e
-  | Return hm1 -> hash_map_move_elements_s_flat hm1 slot1
+  | Return hm1 -> hashMap_move_elements_s_flat hm1 slot1
 
 /// High-level desc:
 /// move_elements (move_elements hm slot0) slo1 == move_elements hm (slot0 @ slot1)
-val hash_map_move_elements_s_flat_append_lem
-  (#t : Type0) (hm : hash_map_s_nes t) (slot0 slot1 : slot_s t) :
+val hashMap_move_elements_s_flat_append_lem
+  (#t : Type0) (hm : hashMap_s_nes t) (slot0 slot1 : slot_s t) :
   Lemma
   (ensures (
-    match hash_map_move_elements_s_flat_comp hm slot0 slot1,
-          hash_map_move_elements_s_flat hm (slot0 @ slot1)
+    match hashMap_move_elements_s_flat_comp hm slot0 slot1,
+          hashMap_move_elements_s_flat hm (slot0 @ slot1)
     with
     | Fail _, Fail _ -> True
     | Return hm1, Return hm2 -> hm1 == hm2
@@ -1699,14 +1699,14 @@ val hash_map_move_elements_s_flat_append_lem
   (decreases (slot0))
 
 #push-options "--fuel 1"
-let rec hash_map_move_elements_s_flat_append_lem #t hm slot0 slot1 =
+let rec hashMap_move_elements_s_flat_append_lem #t hm slot0 slot1 =
   match slot0 with
   | [] -> ()
   | (k,v) :: slot0' ->
-    match hash_map_insert_no_resize_s hm k v with
+    match hashMap_insert_no_resize_s hm k v with
     | Fail _ -> ()
     | Return hm' ->
-      hash_map_move_elements_s_flat_append_lem hm' slot0' slot1
+      hashMap_move_elements_s_flat_append_lem hm' slot0' slot1
 #pop-options
 
 val flatten_i_same_suffix (#a : Type) (l0 l1 : list (list a)) (i : nat) :
@@ -1726,16 +1726,16 @@ let rec flatten_i_same_suffix #a l0 l1 i =
 #pop-options
 
 /// Refinement lemma:
-/// [hash_map_move_elements_s] refines [hash_map_move_elements_s_flat]
+/// [hashMap_move_elements_s] refines [hashMap_move_elements_s_flat]
 /// (actually the functions are equal on all inputs).
-val hash_map_move_elements_s_lem_refin_flat
-  (#t : Type0) (hm : hash_map_s_nes t)
+val hashMap_move_elements_s_lem_refin_flat
+  (#t : Type0) (hm : hashMap_s_nes t)
   (slots : slots_s t)
   (i : nat{i <= length slots /\ length slots <= usize_max}) :
   Lemma
   (ensures (
-    match hash_map_move_elements_s hm slots i,
-          hash_map_move_elements_s_flat hm (flatten_i slots i)
+    match hashMap_move_elements_s hm slots i,
+          hashMap_move_elements_s_flat hm (flatten_i slots i)
     with
     | Fail _, Fail _ -> True
     | Return hm, Return hm' -> hm == hm'
@@ -1743,22 +1743,22 @@ val hash_map_move_elements_s_lem_refin_flat
   (decreases (length slots - i))
 
 #push-options "--fuel 1"
-let rec hash_map_move_elements_s_lem_refin_flat #t hm slots i =
+let rec hashMap_move_elements_s_lem_refin_flat #t hm slots i =
   let len = length slots in
   if i < len then
     begin
     let slot = index slots i in
-    hash_map_move_elements_from_list_s_as_flat_lem hm slot;
-    match hash_map_move_elements_from_list_s hm slot with
+    hashMap_move_elements_from_list_s_as_flat_lem hm slot;
+    match hashMap_move_elements_from_list_s hm slot with
     | Fail _ ->
       assert(flatten_i slots i == slot @ flatten_i slots (i+1));
-      hash_map_move_elements_s_flat_append_lem hm slot (flatten_i slots (i+1));
-      assert(Fail? (hash_map_move_elements_s_flat hm (flatten_i slots i)))
+      hashMap_move_elements_s_flat_append_lem hm slot (flatten_i slots (i+1));
+      assert(Fail? (hashMap_move_elements_s_flat hm (flatten_i slots i)))
     | Return hm' ->
       let slots' = list_update slots i [] in
       flatten_i_same_suffix slots slots' (i+1);
-      hash_map_move_elements_s_lem_refin_flat hm' slots' (i+1);
-      hash_map_move_elements_s_flat_append_lem hm slot (flatten_i slots' (i+1));
+      hashMap_move_elements_s_lem_refin_flat hm' slots' (i+1);
+      hashMap_move_elements_s_flat_append_lem hm slot (flatten_i slots' (i+1));
       ()
     end
   else ()
@@ -1769,21 +1769,21 @@ let assoc_list_inv (#t : Type0) (al : assoc_list t) : Type0 =
   pairwise_rel binding_neq al
 
 let disjoint_hm_al_on_key
-  (#t : Type0) (hm : hash_map_s_nes t) (al : assoc_list t) (k : key) : Type0 =
-  match hash_map_s_find hm k, assoc_list_find k al with
+  (#t : Type0) (hm : hashMap_s_nes t) (al : assoc_list t) (k : key) : Type0 =
+  match hashMap_s_find hm k, assoc_list_find k al with
   | Some _, None
   | None, Some _
   | None, None -> True
   | Some _, Some _ -> False
 
 /// Playing a dangerous game here: using forall quantifiers
-let disjoint_hm_al (#t : Type0) (hm : hash_map_s_nes t) (al : assoc_list t) : Type0 =
+let disjoint_hm_al (#t : Type0) (hm : hashMap_s_nes t) (al : assoc_list t) : Type0 =
   forall (k:key). disjoint_hm_al_on_key hm al k
 
 let find_in_union_hm_al
-  (#t : Type0) (hm : hash_map_s_nes t) (al : assoc_list t) (k : key) :
+  (#t : Type0) (hm : hashMap_s_nes t) (al : assoc_list t) (k : key) :
   option t =
-  match hash_map_s_find hm k with
+  match hashMap_s_find hm k with
   | Some b -> Some b
   | None -> assoc_list_find k al
 
@@ -1799,58 +1799,58 @@ let rec for_all_binding_neq_find_lem #t k v al =
   | b :: al' -> for_all_binding_neq_find_lem k v al'
 #pop-options
 
-val hash_map_move_elements_s_flat_lem
-  (#t : Type0) (hm : hash_map_s_nes t) (al : assoc_list t) :
+val hashMap_move_elements_s_flat_lem
+  (#t : Type0) (hm : hashMap_s_nes t) (al : assoc_list t) :
   Lemma
   (requires (
     // Invariants
-    hash_map_s_inv hm /\
+    hashMap_s_inv hm /\
     assoc_list_inv al /\
     // The two are disjoint
     disjoint_hm_al hm al /\
     // We can add all the elements to the hashmap
-    hash_map_s_len hm + length al <= usize_max))
+    hashMap_s_len hm + length al <= usize_max))
   (ensures (
-    match hash_map_move_elements_s_flat hm al with
+    match hashMap_move_elements_s_flat hm al with
     | Fail _ -> False // We can't fail
     | Return hm' ->
       // The invariant is preserved
-      hash_map_s_inv hm' /\
+      hashMap_s_inv hm' /\
       // The new hash map is the union of the two maps
-      (forall (k:key). hash_map_s_find hm' k == find_in_union_hm_al hm al k) /\
-      hash_map_s_len hm' = hash_map_s_len hm + length al))
+      (forall (k:key). hashMap_s_find hm' k == find_in_union_hm_al hm al k) /\
+      hashMap_s_len hm' = hashMap_s_len hm + length al))
   (decreases al)
 
 #restart-solver
 #push-options "--z3rlimit 200 --fuel 1"
-let rec hash_map_move_elements_s_flat_lem #t hm al =
+let rec hashMap_move_elements_s_flat_lem #t hm al =
   match al with
   | [] -> ()
   | (k,v) :: al' ->
-    hash_map_insert_no_resize_s_lem hm k v;
-    match hash_map_insert_no_resize_s hm k v with
+    hashMap_insert_no_resize_s_lem hm k v;
+    match hashMap_insert_no_resize_s hm k v with
     | Fail _ -> ()
     | Return hm' ->
-      assert(hash_map_s_inv hm');
+      assert(hashMap_s_inv hm');
       assert(assoc_list_inv al');
       let disjoint_lem (k' : key) :
         Lemma (disjoint_hm_al_on_key hm' al' k')
         [SMTPat (disjoint_hm_al_on_key hm' al' k')] =
         if k' = k then
           begin
-          assert(hash_map_s_find hm' k' == Some v);
+          assert(hashMap_s_find hm' k' == Some v);
           for_all_binding_neq_find_lem k v al';
           assert(assoc_list_find k' al' == None)
           end
         else
           begin
-          assert(hash_map_s_find hm' k' == hash_map_s_find hm k');
+          assert(hashMap_s_find hm' k' == hashMap_s_find hm k');
           assert(assoc_list_find k' al' == assoc_list_find k' al)
           end
       in
       assert(disjoint_hm_al hm' al');
-      assert(hash_map_s_len hm' + length al' <= usize_max);
-      hash_map_move_elements_s_flat_lem hm' al'
+      assert(hashMap_s_len hm' + length al' <= usize_max);
+      hashMap_move_elements_s_flat_lem hm' al'
 #pop-options
 
 /// We need to prove that the invariants on the "low-level" representations of
@@ -1866,18 +1866,18 @@ let slots_t_inv_implies_slots_s_inv #t slots =
   // Problem is: I can never really predict for sure with F*...
   ()
 
-val hash_map_t_base_inv_implies_hash_map_s_inv
-  (#t : Type0) (hm : hash_map_t t) :
-  Lemma (requires (hash_map_t_base_inv hm))
-  (ensures (hash_map_s_inv (hash_map_t_v hm)))
+val hashMap_t_base_inv_implies_hashMap_s_inv
+  (#t : Type0) (hm : hashMap_t t) :
+  Lemma (requires (hashMap_t_base_inv hm))
+  (ensures (hashMap_s_inv (hashMap_t_v hm)))
 
-let hash_map_t_base_inv_implies_hash_map_s_inv #t hm = () // same as previous
+let hashMap_t_base_inv_implies_hashMap_s_inv #t hm = () // same as previous
 
 /// Introducing a "partial" version of the hash map invariant, which operates on
 /// a suffix of the hash map.
-let partial_hash_map_s_inv
+let partial_hashMap_s_inv
   (#t : Type0) (len : usize{len > 0}) (offset : usize)
-  (hm : hash_map_s t{offset + length hm <= usize_max}) : Type0 =
+  (hm : hashMap_s t{offset + length hm <= usize_max}) : Type0 =
   forall(i:nat{i < length hm}). {:pattern index hm i} slot_s_inv len (offset + i) (index hm i)
 
 /// Auxiliary lemma.
@@ -1887,13 +1887,13 @@ val binding_in_previous_slot_implies_neq
   (#t : Type0) (len : usize{len > 0})
   (i : usize) (b : binding t)
   (offset : usize{i < offset})
-  (slots : hash_map_s t{offset + length slots <= usize_max}) :
+  (slots : hashMap_s t{offset + length slots <= usize_max}) :
   Lemma
   (requires (
     // The binding comes from a slot not in [slots]
     hash_mod_key (fst b) len = i /\
     // The slots are the well-formed suffix of a hash map
-    partial_hash_map_s_inv len offset slots))
+    partial_hashMap_s_inv len offset slots))
   (ensures (
     for_all (binding_neq b) (flatten slots)))
   (decreases slots)
@@ -1924,17 +1924,17 @@ let rec binding_in_previous_slot_implies_neq #t len i b offset slots =
     for_all_append (binding_neq b) s (flatten slots')    
 #pop-options
 
-val partial_hash_map_s_inv_implies_assoc_list_lem
+val partial_hashMap_s_inv_implies_assoc_list_lem
   (#t : Type0) (len : usize{len > 0}) (offset : usize)
-  (hm : hash_map_s t{offset + length hm <= usize_max}) :
+  (hm : hashMap_s t{offset + length hm <= usize_max}) :
   Lemma
   (requires (
-    partial_hash_map_s_inv len offset hm))
+    partial_hashMap_s_inv len offset hm))
   (ensures (assoc_list_inv (flatten hm)))
   (decreases (length hm + length (flatten hm)))
 
 #push-options "--fuel 1"
-let rec partial_hash_map_s_inv_implies_assoc_list_lem #t len offset hm =
+let rec partial_hashMap_s_inv_implies_assoc_list_lem #t len offset hm =
   match hm with
   | [] -> ()
   | slot :: hm' ->
@@ -1943,8 +1943,8 @@ let rec partial_hash_map_s_inv_implies_assoc_list_lem #t len offset hm =
     match slot with
     | [] ->
       assert(flatten hm == flatten hm');
-      assert(partial_hash_map_s_inv len (offset+1) hm'); // Triggers instantiations
-      partial_hash_map_s_inv_implies_assoc_list_lem len (offset+1) hm'
+      assert(partial_hashMap_s_inv len (offset+1) hm'); // Triggers instantiations
+      partial_hashMap_s_inv_implies_assoc_list_lem len (offset+1) hm'
     | x :: slot' ->
       assert(flatten (slot' :: hm') == slot' @ flatten hm');
       let hm'' = slot' :: hm' in
@@ -1953,45 +1953,45 @@ let rec partial_hash_map_s_inv_implies_assoc_list_lem #t len offset hm =
       assert(index hm 0 == slot); // Triggers instantiations
       assert(slot_s_inv len offset slot);
       assert(slot_s_inv len offset slot');
-      assert(partial_hash_map_s_inv len offset hm'');
-      partial_hash_map_s_inv_implies_assoc_list_lem len offset (slot' :: hm');
+      assert(partial_hashMap_s_inv len offset hm'');
+      partial_hashMap_s_inv_implies_assoc_list_lem len offset (slot' :: hm');
       // Proving that the key in `x` is different from all the other keys in
       // the flattened map
       assert(for_all (binding_neq x) slot');
       for_all_append (binding_neq x) slot' (flatten hm');
-      assert(partial_hash_map_s_inv len (offset+1) hm');
+      assert(partial_hashMap_s_inv len (offset+1) hm');
       binding_in_previous_slot_implies_neq #t len offset x (offset+1) hm';
       assert(for_all (binding_neq x) (flatten hm'));
       assert(for_all (binding_neq x) (flatten (slot' :: hm')))
 #pop-options
 
-val hash_map_s_inv_implies_assoc_list_lem
-  (#t : Type0) (hm : hash_map_s t) :
-  Lemma (requires (hash_map_s_inv hm))
+val hashMap_s_inv_implies_assoc_list_lem
+  (#t : Type0) (hm : hashMap_s t) :
+  Lemma (requires (hashMap_s_inv hm))
   (ensures (assoc_list_inv (flatten hm)))
 
-let hash_map_s_inv_implies_assoc_list_lem #t hm =
-  partial_hash_map_s_inv_implies_assoc_list_lem (length hm) 0 hm
+let hashMap_s_inv_implies_assoc_list_lem #t hm =
+  partial_hashMap_s_inv_implies_assoc_list_lem (length hm) 0 hm
 
-val hash_map_t_base_inv_implies_assoc_list_lem
-  (#t : Type0) (hm : hash_map_t t):
-  Lemma (requires (hash_map_t_base_inv hm))
-  (ensures (assoc_list_inv (hash_map_t_al_v hm)))
+val hashMap_t_base_inv_implies_assoc_list_lem
+  (#t : Type0) (hm : hashMap_t t):
+  Lemma (requires (hashMap_t_base_inv hm))
+  (ensures (assoc_list_inv (hashMap_t_al_v hm)))
 
-let hash_map_t_base_inv_implies_assoc_list_lem #t hm =
-  hash_map_s_inv_implies_assoc_list_lem (hash_map_t_v hm)
+let hashMap_t_base_inv_implies_assoc_list_lem #t hm =
+  hashMap_s_inv_implies_assoc_list_lem (hashMap_t_v hm)
 
 /// For some reason, we can't write the below [forall] directly in the [ensures]
 /// clause of the next lemma: it makes Z3 fails even with a huge rlimit.
 /// I have no idea what's going on.
-let hash_map_is_assoc_list
-  (#t : Type0) (ntable : hash_map_t t{length ntable.hash_map_slots > 0})
+let hashMap_is_assoc_list
+  (#t : Type0) (ntable : hashMap_t t{length ntable.slots > 0})
   (al : assoc_list t) : Type0 =
-  (forall (k:key). hash_map_t_find_s ntable k == assoc_list_find k al)
+  (forall (k:key). hashMap_t_find_s ntable k == assoc_list_find k al)
 
-let partial_hash_map_s_find
+let partial_hashMap_s_find
   (#t : Type0) (len : usize{len > 0}) (offset : usize)
-  (hm : hash_map_s_nes t{offset + length hm = len})
+  (hm : hashMap_s_nes t{offset + length hm = len})
   (k : key{hash_mod_key k len >= offset}) : option t =
   let i = hash_mod_key k len in
   let slot = index hm (i - offset) in
@@ -2021,13 +2021,13 @@ val key_in_previous_slot_implies_not_found
   (#t : Type0) (len : usize{len > 0})
   (k : key)
   (offset : usize)
-  (slots : hash_map_s t{offset + length slots = len}) :
+  (slots : hashMap_s t{offset + length slots = len}) :
   Lemma
   (requires (
     // The binding comes from a slot not in [slots]
     hash_mod_key k len < offset /\
     // The slots are the well-formed suffix of a hash map
-    partial_hash_map_s_inv len offset slots))
+    partial_hashMap_s_inv len offset slots))
   (ensures (
     assoc_list_find k (flatten slots) == None))
   (decreases slots)
@@ -2045,19 +2045,19 @@ let rec key_in_previous_slot_implies_not_found #t len k offset slots =
     key_in_previous_slot_implies_not_found len k (offset+1) slots'
 #pop-options  
 
-val partial_hash_map_s_is_assoc_list_lem
+val partial_hashMap_s_is_assoc_list_lem
   (#t : Type0) (len : usize{len > 0}) (offset : usize)
-  (hm : hash_map_s_nes t{offset + length hm = len})
+  (hm : hashMap_s_nes t{offset + length hm = len})
   (k : key{hash_mod_key k len >= offset}) :
   Lemma
   (requires (
-    partial_hash_map_s_inv len offset hm))
+    partial_hashMap_s_inv len offset hm))
   (ensures (
-    partial_hash_map_s_find len offset hm k == assoc_list_find k (flatten hm)))
+    partial_hashMap_s_find len offset hm k == assoc_list_find k (flatten hm)))
   (decreases hm)
 
 #push-options "--fuel 1"
-let rec partial_hash_map_s_is_assoc_list_lem #t len offset hm k =
+let rec partial_hashMap_s_is_assoc_list_lem #t len offset hm k =
   match hm with
   | [] -> ()
   | slot :: hm' ->
@@ -2066,7 +2066,7 @@ let rec partial_hash_map_s_is_assoc_list_lem #t len offset hm k =
     if i = 0 then
       begin
       // We must look in the current slot
-      assert(partial_hash_map_s_find len offset hm k == slot_s_find k slot);
+      assert(partial_hashMap_s_find len offset hm k == slot_s_find k slot);
       find_append (same_key k) slot (flatten hm');
       assert(forall (i:nat{i < length hm'}). index hm' i == index hm (i+1)); // Triggers instantiations
       key_in_previous_slot_implies_not_found #t len k (offset+1) hm';
@@ -2085,64 +2085,64 @@ let rec partial_hash_map_s_is_assoc_list_lem #t len offset hm k =
     else
       begin
       // We must ignore the current slot
-      assert(partial_hash_map_s_find len offset hm k ==
-             partial_hash_map_s_find len (offset+1) hm' k);
+      assert(partial_hashMap_s_find len offset hm k ==
+             partial_hashMap_s_find len (offset+1) hm' k);
       find_append (same_key k) slot (flatten hm');
       assert(index hm 0 == slot); // Triggers instantiations
       not_same_hash_key_not_found_in_slot #t len k offset slot;
       assert(forall (i:nat{i < length hm'}). index hm' i == index hm (i+1)); // Triggers instantiations
-      partial_hash_map_s_is_assoc_list_lem #t len (offset+1) hm' k
+      partial_hashMap_s_is_assoc_list_lem #t len (offset+1) hm' k
       end
 #pop-options
 
-val hash_map_is_assoc_list_lem (#t : Type0) (hm : hash_map_t t) :
-  Lemma (requires (hash_map_t_base_inv hm))
-  (ensures (hash_map_is_assoc_list hm (hash_map_t_al_v hm)))
+val hashMap_is_assoc_list_lem (#t : Type0) (hm : hashMap_t t) :
+  Lemma (requires (hashMap_t_base_inv hm))
+  (ensures (hashMap_is_assoc_list hm (hashMap_t_al_v hm)))
 
-let hash_map_is_assoc_list_lem #t hm =
+let hashMap_is_assoc_list_lem #t hm =
   let aux (k:key) :
-    Lemma (hash_map_t_find_s hm k == assoc_list_find k (hash_map_t_al_v hm))
-    [SMTPat (hash_map_t_find_s hm k)] =
-    let hm_v = hash_map_t_v hm in
+    Lemma (hashMap_t_find_s hm k == assoc_list_find k (hashMap_t_al_v hm))
+    [SMTPat (hashMap_t_find_s hm k)] =
+    let hm_v = hashMap_t_v hm in
     let len = length hm_v in
-    partial_hash_map_s_is_assoc_list_lem #t len 0 hm_v k
+    partial_hashMap_s_is_assoc_list_lem #t len 0 hm_v k
   in
   ()
 
 /// The final lemma about [move_elements]: calling it on an empty hash table moves
 /// all the elements to this empty table.
-val hash_map_move_elements_fwd_back_lem
-  (t : Type0) (ntable : hash_map_t t) (slots : vec (list_t t)) :
+val hashMap_move_elements_lem
+  (t : Type0) (ntable : hashMap_t t) (slots : alloc_vec_Vec (list_t t)) :
   Lemma
   (requires (
     let al = flatten (slots_t_v slots) in
-    hash_map_t_base_inv ntable /\
+    hashMap_t_base_inv ntable /\
     length al <= usize_max /\
     assoc_list_inv al /\
     // The table is empty
-    hash_map_t_len_s ntable = 0 /\
-    (forall (k:key). hash_map_t_find_s ntable k  == None)))
+    hashMap_t_len_s ntable = 0 /\
+    (forall (k:key). hashMap_t_find_s ntable k  == None)))
   (ensures (
     let al = flatten (slots_t_v slots) in
-    match hash_map_move_elements_fwd_back t ntable slots 0,
-          hash_map_move_elements_s_flat (hash_map_t_v ntable) al
+    match hashMap_move_elements t ntable slots 0,
+          hashMap_move_elements_s_flat (hashMap_t_v ntable) al
     with
     | Return (ntable', _), Return ntable'_v ->
       // The invariant is preserved
-      hash_map_t_base_inv ntable' /\
+      hashMap_t_base_inv ntable' /\
       // We preserved the parameters
-      hash_map_t_same_params ntable' ntable /\
+      hashMap_t_same_params ntable' ntable /\
       // The table has the same number of slots
-      length ntable'.hash_map_slots = length ntable.hash_map_slots /\
+      length ntable'.slots = length ntable.slots /\
       // The count is good
-      hash_map_t_len_s ntable' = length al /\
+      hashMap_t_len_s ntable' = length al /\
       // The table can be linked to its model (we need this only to reveal
       // "pretty" functional lemmas to the user in the fsti - so that we
       // can write lemmas with SMT patterns - this is very F* specific)
-      hash_map_t_v ntable' == ntable'_v /\
+      hashMap_t_v ntable' == ntable'_v /\
       // The new table contains exactly all the bindings from the slots
-      // Rk.: see the comment for [hash_map_is_assoc_list]
-      hash_map_is_assoc_list ntable' al
+      // Rk.: see the comment for [hashMap_is_assoc_list]
+      hashMap_is_assoc_list ntable' al
     | _ -> False // We can only succeed
     ))
 
@@ -2154,41 +2154,41 @@ val hash_map_move_elements_fwd_back_lem
 // lack of ifuel (this kind of proofs is annoying, really).
 #restart-solver
 #push-options "--z3rlimit 100"
-let hash_map_move_elements_fwd_back_lem t ntable slots =
-  let ntable_v = hash_map_t_v ntable in
+let hashMap_move_elements_lem t ntable slots =
+  let ntable_v = hashMap_t_v ntable in
   let slots_v = slots_t_v slots in
   let al = flatten slots_v in
-  hash_map_move_elements_fwd_back_lem_refin t ntable slots 0;
+  hashMap_move_elements_lem_refin t ntable slots 0;
   begin
-  match hash_map_move_elements_fwd_back t ntable slots 0,
-        hash_map_move_elements_s ntable_v slots_v 0
+  match hashMap_move_elements t ntable slots 0,
+        hashMap_move_elements_s ntable_v slots_v 0
   with
   | Fail _, Fail _ -> ()
   | Return (ntable', _), Return ntable'_v ->
-    assert(hash_map_t_base_inv ntable');
-    assert(hash_map_t_v ntable' == ntable'_v)
+    assert(hashMap_t_base_inv ntable');
+    assert(hashMap_t_v ntable' == ntable'_v)
   | _ -> assert(False)
   end;
-  hash_map_move_elements_s_lem_refin_flat ntable_v slots_v 0;
+  hashMap_move_elements_s_lem_refin_flat ntable_v slots_v 0;
   begin
-  match hash_map_move_elements_s ntable_v slots_v 0,
-        hash_map_move_elements_s_flat ntable_v (flatten_i slots_v 0)
+  match hashMap_move_elements_s ntable_v slots_v 0,
+        hashMap_move_elements_s_flat ntable_v (flatten_i slots_v 0)
   with
   | Fail _, Fail _ -> ()
   | Return hm, Return hm' -> assert(hm == hm')
   | _ -> assert(False)
   end;
   flatten_0_is_flatten slots_v; // flatten_i slots_v 0 == flatten slots_v
-  hash_map_move_elements_s_flat_lem ntable_v al;
-  match hash_map_move_elements_fwd_back t ntable slots 0,
-        hash_map_move_elements_s_flat ntable_v al
+  hashMap_move_elements_s_flat_lem ntable_v al;
+  match hashMap_move_elements t ntable slots 0,
+        hashMap_move_elements_s_flat ntable_v al
   with
   | Return (ntable', _), Return ntable'_v ->
-    assert(hash_map_t_base_inv ntable');
-    assert(length ntable'.hash_map_slots = length ntable.hash_map_slots);
-    assert(hash_map_t_len_s ntable' = length al);
-    assert(hash_map_t_v ntable' == ntable'_v);
-    assert(hash_map_is_assoc_list ntable' al)
+    assert(hashMap_t_base_inv ntable');
+    assert(length ntable'.slots = length ntable.slots);
+    assert(hashMap_t_len_s ntable' = length al);
+    assert(hashMap_t_v ntable' == ntable'_v);
+    assert(hashMap_is_assoc_list ntable' al)
   | _ -> assert(False)
 #pop-options
 
@@ -2197,47 +2197,47 @@ let hash_map_move_elements_fwd_back_lem t ntable slots =
 /// High-level model 1.
 /// This is one is slightly "crude": we just simplify a bit the function.
 
-let hash_map_try_resize_s_simpl
+let hashMap_try_resize_s_simpl
   (#t : Type0)
-  (hm : hash_map_t t) :
-  Pure  (result (hash_map_t t))
+  (hm : hashMap_t t) :
+  Pure  (result (hashMap_t t))
   (requires (
-    let (divid, divis) = hm.hash_map_max_load_factor in
+    let (divid, divis) = hm.max_load_factor in
     divid > 0 /\ divis > 0))
   (ensures (fun _ -> True)) =
-  let capacity = length hm.hash_map_slots in
-  let (divid, divis) = hm.hash_map_max_load_factor in
+  let capacity = length hm.slots in
+  let (divid, divis) = hm.max_load_factor in
   if capacity <= (usize_max / 2) / divid then
     let ncapacity : usize = capacity * 2 in
-    begin match hash_map_new_with_capacity_fwd t ncapacity divid divis with
+    begin match hashMap_new_with_capacity t ncapacity divid divis with
     | Fail e -> Fail e
     | Return ntable ->
-      match hash_map_move_elements_fwd_back t ntable hm.hash_map_slots 0 with
+      match hashMap_move_elements t ntable hm.slots 0 with
       | Fail e -> Fail e
       | Return (ntable', _) ->
         let hm =
-          { hm with hash_map_slots = ntable'.hash_map_slots;
-                    hash_map_max_load = ntable'.hash_map_max_load }
+          { hm with slots = ntable'.slots;
+                    max_load = ntable'.max_load }
         in
         Return hm
     end
   else Return hm
 
-val hash_map_try_resize_fwd_back_lem_refin
-  (t : Type0) (self : hash_map_t t) :
+val hashMap_try_resize_lem_refin
+  (t : Type0) (self : hashMap_t t) :
   Lemma
   (requires (
-    let (divid, divis) = self.hash_map_max_load_factor in
+    let (divid, divis) = self.max_load_factor in
     divid > 0 /\ divis > 0))
   (ensures (
-    match hash_map_try_resize_fwd_back t self,
-          hash_map_try_resize_s_simpl self
+    match hashMap_try_resize t self,
+          hashMap_try_resize_s_simpl self
     with
     | Fail _, Fail _ -> True
     | Return hm1, Return hm2 -> hm1 == hm2
     | _ -> False))
 
-let hash_map_try_resize_fwd_back_lem_refin t self = ()
+let hashMap_try_resize_lem_refin t self = ()
 
 /// Isolating arithmetic proofs
 
@@ -2342,78 +2342,78 @@ let new_max_load_lem len capacity divid divis =
   assert(nmax_load >= max_load + 1)
 #pop-options
 
-val hash_map_try_resize_s_simpl_lem (#t : Type0) (hm : hash_map_t t) :
+val hashMap_try_resize_s_simpl_lem (#t : Type0) (hm : hashMap_t t) :
   Lemma
   (requires (
     // The base invariant is satisfied
-    hash_map_t_base_inv hm /\
+    hashMap_t_base_inv hm /\
     // However, the "full" invariant is broken, as we call [try_resize]
     // only if the current number of entries is > the max load.
     // 
     // There are two situations:
     // - either we just reached the max load
     // - or we were already saturated and can't resize
-    (let (dividend, divisor) = hm.hash_map_max_load_factor in
-     hm.hash_map_num_entries == hm.hash_map_max_load + 1 \/
-     length hm.hash_map_slots * 2 * dividend > usize_max)
+    (let (dividend, divisor) = hm.max_load_factor in
+     hm.num_entries == hm.max_load + 1 \/
+     length hm.slots * 2 * dividend > usize_max)
   ))
   (ensures (
-    match hash_map_try_resize_s_simpl hm with
+    match hashMap_try_resize_s_simpl hm with
     | Fail _ -> False
     | Return hm' ->
       // The full invariant is now satisfied (the full invariant is "base
       // invariant" + the map is not overloaded (or can't be resized because
       // already too big)
-      hash_map_t_inv hm' /\
+      hashMap_t_inv hm' /\
       // It contains the same bindings as the initial map
-      (forall (k:key). hash_map_t_find_s hm' k == hash_map_t_find_s hm k)))
+      (forall (k:key). hashMap_t_find_s hm' k == hashMap_t_find_s hm k)))
 
 #restart-solver
 #push-options "--z3rlimit 400"
-let hash_map_try_resize_s_simpl_lem #t hm =
-  let capacity = length hm.hash_map_slots in
-  let (divid, divis) = hm.hash_map_max_load_factor in
+let hashMap_try_resize_s_simpl_lem #t hm =
+  let capacity = length hm.slots in
+  let (divid, divis) = hm.max_load_factor in
   if capacity <= (usize_max / 2) / divid then
     begin
     let ncapacity : usize = capacity * 2 in
     assert(ncapacity * divid <= usize_max);
-    assert(hash_map_t_len_s hm = hm.hash_map_max_load + 1);
-    new_max_load_lem (hash_map_t_len_s hm) capacity divid divis;
-    hash_map_new_with_capacity_fwd_lem t ncapacity divid divis;
-    match hash_map_new_with_capacity_fwd t ncapacity divid divis with
+    assert(hashMap_t_len_s hm = hm.max_load + 1);
+    new_max_load_lem (hashMap_t_len_s hm) capacity divid divis;
+    hashMap_new_with_capacity_lem t ncapacity divid divis;
+    match hashMap_new_with_capacity t ncapacity divid divis with
     | Fail _ -> ()
     | Return ntable ->
-      let slots = hm.hash_map_slots in
+      let slots = hm.slots in
       let al = flatten (slots_t_v slots) in
-      // Proving that: length al = hm.hash_map_num_entries
+      // Proving that: length al = hm.num_entries
       assert(al == flatten (map slot_t_v slots));
       assert(al == flatten (map list_t_v slots));
-      assert(hash_map_t_al_v hm == flatten (hash_map_t_v hm));
-      assert(hash_map_t_al_v hm == flatten (map list_t_v hm.hash_map_slots));
-      assert(al == hash_map_t_al_v hm);
-      assert(hash_map_t_base_inv ntable);
-      assert(length al = hm.hash_map_num_entries);
+      assert(hashMap_t_al_v hm == flatten (hashMap_t_v hm));
+      assert(hashMap_t_al_v hm == flatten (map list_t_v hm.slots));
+      assert(al == hashMap_t_al_v hm);
+      assert(hashMap_t_base_inv ntable);
+      assert(length al = hm.num_entries);
       assert(length al <= usize_max);
-      hash_map_t_base_inv_implies_assoc_list_lem hm;
+      hashMap_t_base_inv_implies_assoc_list_lem hm;
       assert(assoc_list_inv al);
-      assert(hash_map_t_len_s ntable = 0);
-      assert(forall (k:key). hash_map_t_find_s ntable k  == None);
-      hash_map_move_elements_fwd_back_lem t ntable hm.hash_map_slots;
-      match hash_map_move_elements_fwd_back t ntable hm.hash_map_slots 0 with
+      assert(hashMap_t_len_s ntable = 0);
+      assert(forall (k:key). hashMap_t_find_s ntable k  == None);
+      hashMap_move_elements_lem t ntable hm.slots;
+      match hashMap_move_elements t ntable hm.slots 0 with
       | Fail _ -> ()
       | Return (ntable', _) ->
-        hash_map_is_assoc_list_lem hm;
-        assert(hash_map_is_assoc_list hm (hash_map_t_al_v hm));
+        hashMap_is_assoc_list_lem hm;
+        assert(hashMap_is_assoc_list hm (hashMap_t_al_v hm));
         let hm' =
-          { hm with hash_map_slots = ntable'.hash_map_slots;
-                    hash_map_max_load = ntable'.hash_map_max_load }
+          { hm with slots = ntable'.slots;
+                    max_load = ntable'.max_load }
         in
-        assert(hash_map_t_base_inv ntable');
-        assert(hash_map_t_base_inv hm');
-        assert(hash_map_t_len_s hm' = hash_map_t_len_s hm);
-        new_max_load_lem (hash_map_t_len_s hm') capacity divid divis;
-        assert(hash_map_t_len_s hm' <= hm'.hash_map_max_load); // Requires a lemma
-        assert(hash_map_t_inv hm')
+        assert(hashMap_t_base_inv ntable');
+        assert(hashMap_t_base_inv hm');
+        assert(hashMap_t_len_s hm' = hashMap_t_len_s hm);
+        new_max_load_lem (hashMap_t_len_s hm') capacity divid divis;
+        assert(hashMap_t_len_s hm' <= hm'.max_load); // Requires a lemma
+        assert(hashMap_t_inv hm')
     end
   else
     begin
@@ -2422,203 +2422,203 @@ let hash_map_try_resize_s_simpl_lem #t hm =
     end
 #pop-options
 
-let hash_map_t_same_bindings  (#t : Type0) (hm hm' : hash_map_t_nes t) : Type0 =
-  forall (k:key). hash_map_t_find_s hm k == hash_map_t_find_s hm' k
+let hashMap_t_same_bindings  (#t : Type0) (hm hm' : hashMap_t_nes t) : Type0 =
+  forall (k:key). hashMap_t_find_s hm k == hashMap_t_find_s hm' k
 
 /// The final lemma about [try_resize]
-val hash_map_try_resize_fwd_back_lem (#t : Type0) (hm : hash_map_t t) :
+val hashMap_try_resize_lem (#t : Type0) (hm : hashMap_t t) :
   Lemma
   (requires (
-    hash_map_t_base_inv hm /\
+    hashMap_t_base_inv hm /\
     // However, the "full" invariant is broken, as we call [try_resize]
     // only if the current number of entries is > the max load.
     // 
     // There are two situations:
     // - either we just reached the max load
     // - or we were already saturated and can't resize
-    (let (dividend, divisor) = hm.hash_map_max_load_factor in
-     hm.hash_map_num_entries == hm.hash_map_max_load + 1 \/
-     length hm.hash_map_slots * 2 * dividend > usize_max)))
+    (let (dividend, divisor) = hm.max_load_factor in
+     hm.num_entries == hm.max_load + 1 \/
+     length hm.slots * 2 * dividend > usize_max)))
   (ensures (
-    match hash_map_try_resize_fwd_back t hm with
+    match hashMap_try_resize t hm with
     | Fail _ -> False
     | Return hm' ->
       // The full invariant is now satisfied (the full invariant is "base
       // invariant" + the map is not overloaded (or can't be resized because
       // already too big)
-      hash_map_t_inv hm' /\
+      hashMap_t_inv hm' /\
       // The length is the same
-      hash_map_t_len_s hm' = hash_map_t_len_s hm /\
+      hashMap_t_len_s hm' = hashMap_t_len_s hm /\
       // It contains the same bindings as the initial map
-      hash_map_t_same_bindings hm' hm))
+      hashMap_t_same_bindings hm' hm))
 
-let hash_map_try_resize_fwd_back_lem #t hm =
-  hash_map_try_resize_fwd_back_lem_refin t hm;
-  hash_map_try_resize_s_simpl_lem hm
+let hashMap_try_resize_lem #t hm =
+  hashMap_try_resize_lem_refin t hm;
+  hashMap_try_resize_s_simpl_lem hm
 
 (*** insert *)
 
 /// The high-level model (very close to the original function: we don't need something
 /// very high level, just to clean it a bit)
-let hash_map_insert_s
-  (#t : Type0) (self : hash_map_t t) (key : usize) (value : t) :
-  result (hash_map_t t) =
-  match hash_map_insert_no_resize_fwd_back t self key value with
+let hashMap_insert_s
+  (#t : Type0) (self : hashMap_t t) (key : usize) (value : t) :
+  result (hashMap_t t) =
+  match hashMap_insert_no_resize t self key value with
   | Fail e -> Fail e
   | Return hm' ->
-    if hash_map_t_len_s hm' > hm'.hash_map_max_load then
-      hash_map_try_resize_fwd_back t hm'
+    if hashMap_t_len_s hm' > hm'.max_load then
+      hashMap_try_resize t hm'
     else Return hm'
 
-val hash_map_insert_fwd_back_lem_refin
-  (t : Type0) (self : hash_map_t t) (key : usize) (value : t) :
+val hashMap_insert_lem_refin
+  (t : Type0) (self : hashMap_t t) (key : usize) (value : t) :
   Lemma (requires True)
   (ensures (
-    match hash_map_insert_fwd_back t self key value,
-          hash_map_insert_s self key value
+    match hashMap_insert t self key value,
+          hashMap_insert_s self key value
     with
     | Fail _, Fail _ -> True
     | Return hm1, Return hm2 -> hm1 == hm2
     | _ -> False))
 
-let hash_map_insert_fwd_back_lem_refin t self key value = ()
+let hashMap_insert_lem_refin t self key value = ()
 
 /// Helper
-let hash_map_insert_fwd_back_bindings_lem
-  (t : Type0) (self : hash_map_t_nes t) (key : usize) (value : t)
-  (hm' hm'' : hash_map_t_nes t) :
+let hashMap_insert_bindings_lem
+  (t : Type0) (self : hashMap_t_nes t) (key : usize) (value : t)
+  (hm' hm'' : hashMap_t_nes t) :
   Lemma
   (requires (
-     hash_map_s_updated_binding (hash_map_t_v self) key
-                                (Some value) (hash_map_t_v hm') /\
-     hash_map_t_same_bindings hm' hm''))
+     hashMap_s_updated_binding (hashMap_t_v self) key
+                                (Some value) (hashMap_t_v hm') /\
+     hashMap_t_same_bindings hm' hm''))
   (ensures (
-     hash_map_s_updated_binding (hash_map_t_v self) key
-                                (Some value) (hash_map_t_v hm'')))
+     hashMap_s_updated_binding (hashMap_t_v self) key
+                                (Some value) (hashMap_t_v hm'')))
   = ()
 
-val hash_map_insert_fwd_back_lem_aux
-  (#t : Type0) (self : hash_map_t t) (key : usize) (value : t) :
-  Lemma (requires (hash_map_t_inv self))
+val hashMap_insert_lem_aux
+  (#t : Type0) (self : hashMap_t t) (key : usize) (value : t) :
+  Lemma (requires (hashMap_t_inv self))
   (ensures (
-    match hash_map_insert_fwd_back t self key value with
+    match hashMap_insert t self key value with
     | Fail _ ->
       // We can fail only if:
       // - the key is not in the map and we need to add it
       // - we are already saturated
-      hash_map_t_len_s self = usize_max /\
-      None? (hash_map_t_find_s self key)
+      hashMap_t_len_s self = usize_max /\
+      None? (hashMap_t_find_s self key)
     | Return hm' ->
       // The invariant is preserved
-      hash_map_t_inv hm' /\
+      hashMap_t_inv hm' /\
       // [key] maps to [value] and the other bindings are preserved
-      hash_map_s_updated_binding (hash_map_t_v self) key (Some value) (hash_map_t_v hm') /\
+      hashMap_s_updated_binding (hashMap_t_v self) key (Some value) (hashMap_t_v hm') /\
       // The length is incremented, iff we inserted a new key
-      (match hash_map_t_find_s self key with
-       | None -> hash_map_t_len_s hm' = hash_map_t_len_s self + 1
-       | Some _ -> hash_map_t_len_s hm' = hash_map_t_len_s self)))
+      (match hashMap_t_find_s self key with
+       | None -> hashMap_t_len_s hm' = hashMap_t_len_s self + 1
+       | Some _ -> hashMap_t_len_s hm' = hashMap_t_len_s self)))
 
 #restart-solver
 #push-options "--z3rlimit 200"
-let hash_map_insert_fwd_back_lem_aux #t self key value =
-  hash_map_insert_no_resize_fwd_back_lem_s t self key value;
-  hash_map_insert_no_resize_s_lem (hash_map_t_v self) key value;
-  match hash_map_insert_no_resize_fwd_back t self key value with
+let hashMap_insert_lem_aux #t self key value =
+  hashMap_insert_no_resize_lem_s t self key value;
+  hashMap_insert_no_resize_s_lem (hashMap_t_v self) key value;
+  match hashMap_insert_no_resize t self key value with
   | Fail _ -> ()
   | Return hm' ->
-    // Expanding the post of [hash_map_insert_no_resize_fwd_back_lem_s]
-    let self_v = hash_map_t_v self in
-    let hm'_v = Return?.v (hash_map_insert_no_resize_s self_v key value) in
-    assert(hash_map_t_base_inv hm');
-    assert(hash_map_t_same_params hm' self);
-    assert(hash_map_t_v hm' == hm'_v);
-    assert(hash_map_s_len hm'_v == hash_map_t_len_s hm');
-    // Expanding the post of [hash_map_insert_no_resize_s_lem]
+    // Expanding the post of [hashMap_insert_no_resize_lem_s]
+    let self_v = hashMap_t_v self in
+    let hm'_v = Return?.v (hashMap_insert_no_resize_s self_v key value) in
+    assert(hashMap_t_base_inv hm');
+    assert(hashMap_t_same_params hm' self);
+    assert(hashMap_t_v hm' == hm'_v);
+    assert(hashMap_s_len hm'_v == hashMap_t_len_s hm');
+    // Expanding the post of [hashMap_insert_no_resize_s_lem]
     assert(insert_post self_v key value hm'_v);
     // Expanding [insert_post]
-    assert(hash_map_s_inv hm'_v);
+    assert(hashMap_s_inv hm'_v);
     assert(
-      match hash_map_s_find self_v key with
-      | None -> hash_map_s_len hm'_v = hash_map_s_len self_v + 1
-      | Some _ -> hash_map_s_len hm'_v = hash_map_s_len self_v);
-    if hash_map_t_len_s hm' > hm'.hash_map_max_load then
+      match hashMap_s_find self_v key with
+      | None -> hashMap_s_len hm'_v = hashMap_s_len self_v + 1
+      | Some _ -> hashMap_s_len hm'_v = hashMap_s_len self_v);
+    if hashMap_t_len_s hm' > hm'.max_load then
       begin
-      hash_map_try_resize_fwd_back_lem hm';
-      // Expanding the post of [hash_map_try_resize_fwd_back_lem]
-      let hm'' = Return?.v (hash_map_try_resize_fwd_back t hm') in
-      assert(hash_map_t_inv hm'');
-      let hm''_v = hash_map_t_v hm'' in
-      assert(forall k. hash_map_t_find_s hm'' k == hash_map_t_find_s hm' k);
-      assert(hash_map_t_len_s hm'' = hash_map_t_len_s hm'); // TODO
+      hashMap_try_resize_lem hm';
+      // Expanding the post of [hashMap_try_resize_lem]
+      let hm'' = Return?.v (hashMap_try_resize t hm') in
+      assert(hashMap_t_inv hm'');
+      let hm''_v = hashMap_t_v hm'' in
+      assert(forall k. hashMap_t_find_s hm'' k == hashMap_t_find_s hm' k);
+      assert(hashMap_t_len_s hm'' = hashMap_t_len_s hm'); // TODO
       // Proving the post
-      assert(hash_map_t_inv hm'');
-      hash_map_insert_fwd_back_bindings_lem t self key value hm' hm'';
+      assert(hashMap_t_inv hm'');
+      hashMap_insert_bindings_lem t self key value hm' hm'';
       assert(
-        match hash_map_t_find_s self key with
-         | None -> hash_map_t_len_s hm'' = hash_map_t_len_s self + 1
-         | Some _ -> hash_map_t_len_s hm'' = hash_map_t_len_s self)
+        match hashMap_t_find_s self key with
+         | None -> hashMap_t_len_s hm'' = hashMap_t_len_s self + 1
+         | Some _ -> hashMap_t_len_s hm'' = hashMap_t_len_s self)
       end
     else ()
 #pop-options
 
-let hash_map_insert_fwd_back_lem #t self key value =
-  hash_map_insert_fwd_back_lem_aux #t self key value
+let hashMap_insert_lem #t self key value =
+  hashMap_insert_lem_aux #t self key value
 
 (*** contains_key *)
 
 (**** contains_key_in_list *)
 
-val hash_map_contains_key_in_list_fwd_lem
+val hashMap_contains_key_in_list_lem
   (#t : Type0) (key : usize) (ls : list_t t) :
   Lemma
   (ensures (
-    match hash_map_contains_key_in_list_fwd t key ls with
+    match hashMap_contains_key_in_list t key ls with
     | Fail _ -> False
     | Return b ->
       b = Some? (slot_t_find_s key ls)))
 
 
 #push-options "--fuel 1"
-let rec hash_map_contains_key_in_list_fwd_lem #t key ls =
+let rec hashMap_contains_key_in_list_lem #t key ls =
   match ls with
-  | ListCons ckey x ls0 ->
+  | List_Cons ckey x ls0 ->
     let b = ckey = key in
     if b
     then ()
     else
       begin
-      hash_map_contains_key_in_list_fwd_lem key ls0;
-      match hash_map_contains_key_in_list_fwd t key ls0 with
+      hashMap_contains_key_in_list_lem key ls0;
+      match hashMap_contains_key_in_list t key ls0 with
       | Fail _ -> ()
       | Return b0 -> ()
       end
-  | ListNil -> ()
+  | List_Nil -> ()
 #pop-options
 
 (**** contains_key *)
 
-val hash_map_contains_key_fwd_lem_aux
-  (#t : Type0) (self : hash_map_t_nes t) (key : usize) :
+val hashMap_contains_key_lem_aux
+  (#t : Type0) (self : hashMap_t_nes t) (key : usize) :
   Lemma
   (ensures (
-    match hash_map_contains_key_fwd t self key with
+    match hashMap_contains_key t self key with
     | Fail _ -> False
-    | Return b -> b = Some? (hash_map_t_find_s self key)))
+    | Return b -> b = Some? (hashMap_t_find_s self key)))
 
-let hash_map_contains_key_fwd_lem_aux #t self key =
-  begin match hash_key_fwd key with
+let hashMap_contains_key_lem_aux #t self key =
+  begin match hash_key key with
   | Fail _ -> ()
   | Return i ->
-    let v = self.hash_map_slots in
-    let i0 = vec_len (list_t t) v in
+    let v = self.slots in
+    let i0 = alloc_vec_Vec_len (list_t t) v in
     begin match usize_rem i i0 with
     | Fail _ -> ()
     | Return hash_mod ->
-      begin match vec_index_fwd (list_t t) v hash_mod with
+      begin match alloc_vec_Vec_index_usize v hash_mod with
       | Fail _ -> ()
       | Return l ->
-        hash_map_contains_key_in_list_fwd_lem key l;
-        begin match hash_map_contains_key_in_list_fwd t key l with
+        hashMap_contains_key_in_list_lem key l;
+        begin match hashMap_contains_key_in_list t key l with
         | Fail _ -> ()
         | Return b -> ()
         end
@@ -2627,66 +2627,66 @@ let hash_map_contains_key_fwd_lem_aux #t self key =
   end
 
 /// The lemma in the .fsti
-let hash_map_contains_key_fwd_lem #t self key =
-  hash_map_contains_key_fwd_lem_aux #t self key
+let hashMap_contains_key_lem #t self key =
+  hashMap_contains_key_lem_aux #t self key
 
 (*** get *)
 
 (**** get_in_list *)
 
-val hash_map_get_in_list_fwd_lem
+val hashMap_get_in_list_lem
   (#t : Type0) (key : usize) (ls : list_t t) :
   Lemma
   (ensures (
-    match hash_map_get_in_list_fwd t key ls, slot_t_find_s key ls with
+    match hashMap_get_in_list t key ls, slot_t_find_s key ls with
     | Fail _, None -> True
     | Return x, Some x' -> x == x'
     | _ -> False))
 
 #push-options "--fuel 1"
-let rec hash_map_get_in_list_fwd_lem #t key ls =
+let rec hashMap_get_in_list_lem #t key ls =
   begin match ls with
-  | ListCons ckey cvalue ls0 ->
+  | List_Cons ckey cvalue ls0 ->
     let b = ckey = key in
     if b
     then ()
     else
       begin
-      hash_map_get_in_list_fwd_lem key ls0;
-      match hash_map_get_in_list_fwd t key ls0 with
+      hashMap_get_in_list_lem key ls0;
+      match hashMap_get_in_list t key ls0 with
       | Fail _ -> ()
       | Return x -> ()
       end
-  | ListNil -> ()
+  | List_Nil -> ()
   end
 #pop-options
 
 (**** get *)
 
-val hash_map_get_fwd_lem_aux
-  (#t : Type0) (self : hash_map_t_nes t) (key : usize) :
+val hashMap_get_lem_aux
+  (#t : Type0) (self : hashMap_t_nes t) (key : usize) :
   Lemma
   (ensures (
-    match hash_map_get_fwd t self key, hash_map_t_find_s self key with
+    match hashMap_get t self key, hashMap_t_find_s self key with
     | Fail _, None -> True
     | Return x, Some x' -> x == x'
     | _ -> False))
 
-let hash_map_get_fwd_lem_aux #t self key =
-  begin match hash_key_fwd key with
+let hashMap_get_lem_aux #t self key =
+  begin match hash_key key with
   | Fail _ -> ()
   | Return i ->
-    let v = self.hash_map_slots in
-    let i0 = vec_len (list_t t) v in
+    let v = self.slots in
+    let i0 = alloc_vec_Vec_len (list_t t) v in
     begin match usize_rem i i0 with
     | Fail _ -> ()
     | Return hash_mod ->
-      begin match vec_index_fwd (list_t t) v hash_mod with
+      begin match alloc_vec_Vec_index_usize v hash_mod with
       | Fail _ -> ()
       | Return l ->
         begin
-        hash_map_get_in_list_fwd_lem key l;
-        match hash_map_get_in_list_fwd t key l with
+        hashMap_get_in_list_lem key l;
+        match hashMap_get_in_list t key l with
         | Fail _ -> ()
         | Return x -> ()
         end
@@ -2695,66 +2695,66 @@ let hash_map_get_fwd_lem_aux #t self key =
   end
 
 /// .fsti
-let hash_map_get_fwd_lem #t self key = hash_map_get_fwd_lem_aux #t self key
+let hashMap_get_lem #t self key = hashMap_get_lem_aux #t self key
 
 (*** get_mut'fwd *)
 
 
 (**** get_mut_in_list'fwd *)
 
-val hash_map_get_mut_in_list_loop_fwd_lem
+val hashMap_get_mut_in_list_loop_lem
   (#t : Type0) (ls : list_t t) (key : usize) :
   Lemma
   (ensures (
-    match hash_map_get_mut_in_list_loop_fwd t ls key, slot_t_find_s key ls with
+    match hashMap_get_mut_in_list_loop t ls key, slot_t_find_s key ls with
     | Fail _, None -> True
     | Return x, Some x' -> x == x'
     | _ -> False))
 
 #push-options "--fuel 1"
-let rec hash_map_get_mut_in_list_loop_fwd_lem #t ls key =
+let rec hashMap_get_mut_in_list_loop_lem #t ls key =
   begin match ls with
-  | ListCons ckey cvalue ls0 ->
+  | List_Cons ckey cvalue ls0 ->
     let b = ckey = key in
     if b
     then ()
     else
       begin
-      hash_map_get_mut_in_list_loop_fwd_lem ls0 key;
-      match hash_map_get_mut_in_list_loop_fwd t ls0 key with
+      hashMap_get_mut_in_list_loop_lem ls0 key;
+      match hashMap_get_mut_in_list_loop t ls0 key with
       | Fail _ -> ()
       | Return x -> ()
       end
-  | ListNil -> ()
+  | List_Nil -> ()
   end
 #pop-options
 
 (**** get_mut'fwd *)
 
-val hash_map_get_mut_fwd_lem_aux
-  (#t : Type0) (self : hash_map_t_nes t) (key : usize) :
+val hashMap_get_mut_lem_aux
+  (#t : Type0) (self : hashMap_t_nes t) (key : usize) :
   Lemma
   (ensures (
-    match hash_map_get_mut_fwd t self key, hash_map_t_find_s self key with
+    match hashMap_get_mut t self key, hashMap_t_find_s self key with
     | Fail _, None -> True
     | Return x, Some x' -> x == x'
     | _ -> False))
 
-let hash_map_get_mut_fwd_lem_aux #t self key =
-  begin match hash_key_fwd key with
+let hashMap_get_mut_lem_aux #t self key =
+  begin match hash_key key with
   | Fail _ -> ()
   | Return i ->
-    let v = self.hash_map_slots in
-    let i0 = vec_len (list_t t) v in
+    let v = self.slots in
+    let i0 = alloc_vec_Vec_len (list_t t) v in
     begin match usize_rem i i0 with
     | Fail _ -> ()
     | Return hash_mod ->
-      begin match vec_index_fwd (list_t t) v hash_mod with
+      begin match alloc_vec_Vec_index_usize v hash_mod with
       | Fail _ -> ()
       | Return l ->
         begin
-        hash_map_get_mut_in_list_loop_fwd_lem l key;
-        match hash_map_get_mut_in_list_loop_fwd t l key with
+        hashMap_get_mut_in_list_loop_lem l key;
+        match hashMap_get_mut_in_list_loop t l key with
         | Fail _ -> ()
         | Return x -> ()
         end
@@ -2762,78 +2762,78 @@ let hash_map_get_mut_fwd_lem_aux #t self key =
     end
   end
 
-let hash_map_get_mut_fwd_lem #t self key =
-  hash_map_get_mut_fwd_lem_aux #t self key
+let hashMap_get_mut_lem #t self key =
+  hashMap_get_mut_lem_aux #t self key
 
 (*** get_mut'back *)
 
 (**** get_mut_in_list'back *)
 
-val hash_map_get_mut_in_list_loop_back_lem
+val hashMap_get_mut_in_list_loop_back_lem
   (#t : Type0) (ls : list_t t) (key : usize) (ret : t) :
   Lemma
   (requires (Some? (slot_t_find_s key ls)))
   (ensures (
-    match hash_map_get_mut_in_list_loop_back t ls key ret with
+    match hashMap_get_mut_in_list_loop_back t ls key ret with
     | Fail _ -> False
     | Return ls' -> list_t_v ls' == find_update (same_key key) (list_t_v ls) (key,ret)
     | _ -> False))
 
 #push-options "--fuel 1"
-let rec hash_map_get_mut_in_list_loop_back_lem #t ls key ret =
+let rec hashMap_get_mut_in_list_loop_back_lem #t ls key ret =
   begin match ls with
-  | ListCons ckey cvalue ls0 ->
+  | List_Cons ckey cvalue ls0 ->
     let b = ckey = key in
     if b
-    then let ls1 = ListCons ckey ret ls0 in ()
+    then let ls1 = List_Cons ckey ret ls0 in ()
     else
       begin
-      hash_map_get_mut_in_list_loop_back_lem ls0 key ret;
-      match hash_map_get_mut_in_list_loop_back t ls0 key ret with
+      hashMap_get_mut_in_list_loop_back_lem ls0 key ret;
+      match hashMap_get_mut_in_list_loop_back t ls0 key ret with
       | Fail _ -> ()
-      | Return l -> let ls1 = ListCons ckey cvalue l in ()
+      | Return l -> let ls1 = List_Cons ckey cvalue l in ()
       end
-  | ListNil -> ()
+  | List_Nil -> ()
   end
 #pop-options
 
 (**** get_mut'back *)
 
 /// Refinement lemma
-val hash_map_get_mut_back_lem_refin
-  (#t : Type0) (self : hash_map_t t{length self.hash_map_slots > 0})
+val hashMap_get_mut_back_lem_refin
+  (#t : Type0) (self : hashMap_t t{length self.slots > 0})
   (key : usize) (ret : t) :
   Lemma
-  (requires (Some? (hash_map_t_find_s self key)))
+  (requires (Some? (hashMap_t_find_s self key)))
   (ensures (
-    match hash_map_get_mut_back t self key ret with
+    match hashMap_get_mut_back t self key ret with
     | Fail _ -> False
     | Return hm' ->
-      hash_map_t_v hm' == hash_map_insert_no_fail_s (hash_map_t_v self) key ret))
+      hashMap_t_v hm' == hashMap_insert_no_fail_s (hashMap_t_v self) key ret))
 
-let hash_map_get_mut_back_lem_refin #t self key ret =
-  begin match hash_key_fwd key with
+let hashMap_get_mut_back_lem_refin #t self key ret =
+  begin match hash_key key with
   | Fail _ -> ()
   | Return i ->
-    let i0 = self.hash_map_num_entries in
-    let p = self.hash_map_max_load_factor in
-    let i1 = self.hash_map_max_load in
-    let v = self.hash_map_slots in
-    let i2 = vec_len (list_t t) v in
+    let i0 = self.num_entries in
+    let p = self.max_load_factor in
+    let i1 = self.max_load in
+    let v = self.slots in
+    let i2 = alloc_vec_Vec_len (list_t t) v in
     begin match usize_rem i i2 with
     | Fail _ -> ()
     | Return hash_mod ->
-      begin match vec_index_mut_fwd (list_t t) v hash_mod with
+      begin match alloc_vec_Vec_index_usize v hash_mod with
       | Fail _ -> ()
       | Return l ->
         begin
-        hash_map_get_mut_in_list_loop_back_lem l key ret;
-        match hash_map_get_mut_in_list_loop_back t l key ret with
+        hashMap_get_mut_in_list_loop_back_lem l key ret;
+        match hashMap_get_mut_in_list_loop_back t l key ret with
         | Fail _ -> ()
         | Return l0 ->
-          begin match vec_index_mut_back (list_t t) v hash_mod l0 with
+          begin match alloc_vec_Vec_update_usize v hash_mod l0 with
           | Fail _ -> ()
-          | Return v0 -> let self0 = Mkhash_map_t i0 p i1 v0 in ()
+          | Return v0 -> let self0 = MkhashMap_t i0 p i1 v0 in ()
           end
         end
       end
@@ -2841,102 +2841,102 @@ let hash_map_get_mut_back_lem_refin #t self key ret =
   end
 
 /// Final lemma
-val hash_map_get_mut_back_lem_aux
-  (#t : Type0) (hm : hash_map_t t)
+val hashMap_get_mut_back_lem_aux
+  (#t : Type0) (hm : hashMap_t t)
   (key : usize) (ret : t) :
   Lemma
   (requires (
-    hash_map_t_inv hm /\
-    Some? (hash_map_t_find_s hm key)))
+    hashMap_t_inv hm /\
+    Some? (hashMap_t_find_s hm key)))
   (ensures (
-    match hash_map_get_mut_back t hm key ret with
+    match hashMap_get_mut_back t hm key ret with
     | Fail _ -> False
     | Return hm' ->
       // Functional spec
-      hash_map_t_v hm' == hash_map_insert_no_fail_s (hash_map_t_v hm) key ret /\
+      hashMap_t_v hm' == hashMap_insert_no_fail_s (hashMap_t_v hm) key ret /\
      // The invariant is preserved
-     hash_map_t_inv hm' /\
+     hashMap_t_inv hm' /\
      // The length is preserved
-     hash_map_t_len_s hm' = hash_map_t_len_s hm /\
+     hashMap_t_len_s hm' = hashMap_t_len_s hm /\
      // [key] maps to [value]
-     hash_map_t_find_s hm' key == Some ret /\
+     hashMap_t_find_s hm' key == Some ret /\
      // The other bindings are preserved
-     (forall k'. k' <> key ==> hash_map_t_find_s hm' k' == hash_map_t_find_s hm k')))
+     (forall k'. k' <> key ==> hashMap_t_find_s hm' k' == hashMap_t_find_s hm k')))
 
-let hash_map_get_mut_back_lem_aux #t hm key ret =
-  let hm_v = hash_map_t_v hm in
-  hash_map_get_mut_back_lem_refin hm key ret;
-  match hash_map_get_mut_back t hm key ret with
+let hashMap_get_mut_back_lem_aux #t hm key ret =
+  let hm_v = hashMap_t_v hm in
+  hashMap_get_mut_back_lem_refin hm key ret;
+  match hashMap_get_mut_back t hm key ret with
   | Fail _ -> assert(False)
   | Return hm' ->
-    hash_map_insert_no_fail_s_lem hm_v key ret
+    hashMap_insert_no_fail_s_lem hm_v key ret
 
 /// .fsti
-let hash_map_get_mut_back_lem #t hm key ret = hash_map_get_mut_back_lem_aux hm key ret
+let hashMap_get_mut_back_lem #t hm key ret = hashMap_get_mut_back_lem_aux hm key ret
 
 (*** remove'fwd *)
 
-val hash_map_remove_from_list_fwd_lem
+val hashMap_remove_from_list_lem
   (#t : Type0) (key : usize) (ls : list_t t) :
   Lemma
   (ensures (
-    match hash_map_remove_from_list_fwd t key ls with
+    match hashMap_remove_from_list t key ls with
     | Fail _ -> False
     | Return opt_x ->
       opt_x == slot_t_find_s key ls /\
       (Some? opt_x ==> length (slot_t_v ls) > 0)))
 
 #push-options "--fuel 1"
-let rec hash_map_remove_from_list_fwd_lem #t key ls =
+let rec hashMap_remove_from_list_lem #t key ls =
   begin match ls with
-  | ListCons ckey x tl ->
+  | List_Cons ckey x tl ->
     let b = ckey = key in
     if b
     then
-      let mv_ls = mem_replace_fwd (list_t t) (ListCons ckey x tl) ListNil in
+      let mv_ls = core_mem_replace (list_t t) (List_Cons ckey x tl) List_Nil in
       begin match mv_ls with
-      | ListCons i cvalue tl0 -> ()
-      | ListNil -> ()
+      | List_Cons i cvalue tl0 -> ()
+      | List_Nil -> ()
       end
     else
       begin
-      hash_map_remove_from_list_fwd_lem key tl;
-      match hash_map_remove_from_list_fwd t key tl with
+      hashMap_remove_from_list_lem key tl;
+      match hashMap_remove_from_list t key tl with
       | Fail _ -> ()
       | Return opt -> ()
       end
-  | ListNil -> ()
+  | List_Nil -> ()
   end
 #pop-options
 
-val hash_map_remove_fwd_lem_aux
-  (#t : Type0) (self : hash_map_t t) (key : usize) :
+val hashMap_remove_lem_aux
+  (#t : Type0) (self : hashMap_t t) (key : usize) :
   Lemma
   (requires (
     // We need the invariant to prove that upon decrementing the entries counter,
     // the counter doesn't become negative
-    hash_map_t_inv self))
+    hashMap_t_inv self))
   (ensures (
-    match hash_map_remove_fwd t self key with
+    match hashMap_remove t self key with
     | Fail _ -> False
-    | Return opt_x -> opt_x == hash_map_t_find_s self key))
+    | Return opt_x -> opt_x == hashMap_t_find_s self key))
 
-let hash_map_remove_fwd_lem_aux #t self key =
-  begin match hash_key_fwd key with
+let hashMap_remove_lem_aux #t self key =
+  begin match hash_key key with
   | Fail _ -> ()
   | Return i ->
-    let i0 = self.hash_map_num_entries in
-    let v = self.hash_map_slots in
-    let i1 = vec_len (list_t t) v in
+    let i0 = self.num_entries in
+    let v = self.slots in
+    let i1 = alloc_vec_Vec_len (list_t t) v in
     begin match usize_rem i i1 with
     | Fail _ -> ()
     | Return hash_mod ->
-      begin match vec_index_mut_fwd (list_t t) v hash_mod with
+      begin match alloc_vec_Vec_index_usize v hash_mod with
       | Fail _ -> ()
       | Return l ->
         begin
-        hash_map_remove_from_list_fwd_lem key l;
-        match hash_map_remove_from_list_fwd t key l with
+        hashMap_remove_from_list_lem key l;
+        match hashMap_remove_from_list t key l with
         | Fail _ -> ()
         | Return x ->
           begin match x with
@@ -2945,7 +2945,7 @@ let hash_map_remove_fwd_lem_aux #t self key =
             begin
             assert(l == index v hash_mod);
             assert(length (list_t_v #t l) > 0);
-            length_flatten_index (hash_map_t_v self) hash_mod;
+            length_flatten_index (hashMap_t_v self) hash_mod;
             match usize_sub i0 1 with
             | Fail _ -> ()
             | Return _ -> ()
@@ -2957,27 +2957,27 @@ let hash_map_remove_fwd_lem_aux #t self key =
   end
 
 /// .fsti
-let hash_map_remove_fwd_lem #t self key = hash_map_remove_fwd_lem_aux #t self key
+let hashMap_remove_lem #t self key = hashMap_remove_lem_aux #t self key
 
 (*** remove'back *)
 
 (**** Refinement proofs *)
 
 /// High-level model for [remove_from_list'back]
-let hash_map_remove_from_list_s
+let hashMap_remove_from_list_s
   (#t : Type0) (key : usize) (ls : slot_s t) :
   slot_s t =
   filter_one (not_same_key key) ls
 
 /// Refinement lemma
-val hash_map_remove_from_list_back_lem_refin
+val hashMap_remove_from_list_back_lem_refin
   (#t : Type0) (key : usize) (ls : list_t t) :
   Lemma
   (ensures (
-    match hash_map_remove_from_list_back t key ls with
+    match hashMap_remove_from_list_back t key ls with
     | Fail _ -> False
     | Return ls' ->
-      list_t_v ls' == hash_map_remove_from_list_s key (list_t_v ls) /\
+      list_t_v ls' == hashMap_remove_from_list_s key (list_t_v ls) /\
       // The length is decremented, iff the key was in the slot
       (let len = length (list_t_v ls) in
        let len' = length (list_t_v ls') in
@@ -2986,89 +2986,89 @@ val hash_map_remove_from_list_back_lem_refin
        | Some _ -> len = len' + 1)))
 
 #push-options "--fuel 1"
-let rec hash_map_remove_from_list_back_lem_refin #t key ls =
+let rec hashMap_remove_from_list_back_lem_refin #t key ls =
   begin match ls with
-  | ListCons ckey x tl ->
+  | List_Cons ckey x tl ->
     let b = ckey = key in
     if b
     then
-      let mv_ls = mem_replace_fwd (list_t t) (ListCons ckey x tl) ListNil in
+      let mv_ls = core_mem_replace (list_t t) (List_Cons ckey x tl) List_Nil in
       begin match mv_ls with
-      | ListCons i cvalue tl0 -> ()
-      | ListNil -> ()
+      | List_Cons i cvalue tl0 -> ()
+      | List_Nil -> ()
       end
     else
       begin
-      hash_map_remove_from_list_back_lem_refin key tl;
-      match hash_map_remove_from_list_back t key tl with
+      hashMap_remove_from_list_back_lem_refin key tl;
+      match hashMap_remove_from_list_back t key tl with
       | Fail _ -> ()
-      | Return l -> let ls0 = ListCons ckey x l in ()
+      | Return l -> let ls0 = List_Cons ckey x l in ()
       end
-  | ListNil -> ()
+  | List_Nil -> ()
   end
 #pop-options
 
 /// High-level model for [remove_from_list'back]
-let hash_map_remove_s
-  (#t : Type0) (self : hash_map_s_nes t) (key : usize) :
-  hash_map_s t =
+let hashMap_remove_s
+  (#t : Type0) (self : hashMap_s_nes t) (key : usize) :
+  hashMap_s t =
   let len = length self in
   let hash = hash_mod_key key len in
   let slot = index self hash in
-  let slot' = hash_map_remove_from_list_s key slot in
+  let slot' = hashMap_remove_from_list_s key slot in
   list_update self hash slot'
 
 /// Refinement lemma
-val hash_map_remove_back_lem_refin
-  (#t : Type0) (self : hash_map_t_nes t) (key : usize) :
+val hashMap_remove_back_lem_refin
+  (#t : Type0) (self : hashMap_t_nes t) (key : usize) :
   Lemma
   (requires (
     // We need the invariant to prove that upon decrementing the entries counter,
     // the counter doesn't become negative
-    hash_map_t_inv self))
+    hashMap_t_inv self))
   (ensures (
-    match hash_map_remove_back t self key with
+    match hashMap_remove_back t self key with
     | Fail _ -> False
     | Return hm' ->
-      hash_map_t_same_params hm' self /\
-      hash_map_t_v hm' == hash_map_remove_s (hash_map_t_v self) key /\
+      hashMap_t_same_params hm' self /\
+      hashMap_t_v hm' == hashMap_remove_s (hashMap_t_v self) key /\
       // The length is decremented iff the key was in the map
-      (let len = hash_map_t_len_s self in
-       let len' = hash_map_t_len_s hm' in
-       match hash_map_t_find_s self key with
+      (let len = hashMap_t_len_s self in
+       let len' = hashMap_t_len_s hm' in
+       match hashMap_t_find_s self key with
        | None -> len = len'
        | Some _ -> len = len' + 1)))
 
-let hash_map_remove_back_lem_refin #t self key =
-  begin match hash_key_fwd key with
+let hashMap_remove_back_lem_refin #t self key =
+  begin match hash_key key with
   | Fail _ -> ()
   | Return i ->
-    let i0 = self.hash_map_num_entries in
-    let p = self.hash_map_max_load_factor in
-    let i1 = self.hash_map_max_load in
-    let v = self.hash_map_slots in
-    let i2 = vec_len (list_t t) v in
+    let i0 = self.num_entries in
+    let p = self.max_load_factor in
+    let i1 = self.max_load in
+    let v = self.slots in
+    let i2 = alloc_vec_Vec_len (list_t t) v in
     begin match usize_rem i i2 with
     | Fail _ -> ()
     | Return hash_mod ->
-      begin match vec_index_mut_fwd (list_t t) v hash_mod with
+      begin match alloc_vec_Vec_index_usize v hash_mod with
       | Fail _ -> ()
       | Return l ->
         begin
-        hash_map_remove_from_list_fwd_lem key l;
-        match hash_map_remove_from_list_fwd t key l with
+        hashMap_remove_from_list_lem key l;
+        match hashMap_remove_from_list t key l with
         | Fail _ -> ()
         | Return x ->
           begin match x with
           | None ->
             begin
-            hash_map_remove_from_list_back_lem_refin key l;
-            match hash_map_remove_from_list_back t key l with
+            hashMap_remove_from_list_back_lem_refin key l;
+            match hashMap_remove_from_list_back t key l with
             | Fail _ -> ()
             | Return l0 ->
               begin
               length_flatten_update (slots_t_v v) hash_mod (list_t_v l0);
-              match vec_index_mut_back (list_t t) v hash_mod l0 with
+              match alloc_vec_Vec_update_usize v hash_mod l0 with
               | Fail _ -> ()
               | Return v0 -> ()
               end
@@ -3077,18 +3077,18 @@ let hash_map_remove_back_lem_refin #t self key =
             begin
             assert(l == index v hash_mod);
             assert(length (list_t_v #t l) > 0);
-            length_flatten_index (hash_map_t_v self) hash_mod;
+            length_flatten_index (hashMap_t_v self) hash_mod;
             match usize_sub i0 1 with
             | Fail _ -> ()
             | Return i3 ->
               begin
-              hash_map_remove_from_list_back_lem_refin key l;
-              match hash_map_remove_from_list_back t key l with
+              hashMap_remove_from_list_back_lem_refin key l;
+              match hashMap_remove_from_list_back t key l with
               | Fail _ -> ()
               | Return l0 ->
                 begin
                 length_flatten_update (slots_t_v v) hash_mod (list_t_v l0);
-                match vec_index_mut_back (list_t t) v hash_mod l0 with
+                match alloc_vec_Vec_update_usize v hash_mod l0 with
                 | Fail _ -> ()
                 | Return v0 -> ()
                 end
@@ -3102,12 +3102,12 @@ let hash_map_remove_back_lem_refin #t self key =
 
 (**** Invariants, high-level properties *)
 
-val hash_map_remove_from_list_s_lem
+val hashMap_remove_from_list_s_lem
   (#t : Type0) (k : usize) (slot : slot_s t) (len : usize{len > 0}) (i : usize) :
   Lemma
   (requires (slot_s_inv len i slot))
   (ensures (
-    let slot' = hash_map_remove_from_list_s k slot in
+    let slot' = hashMap_remove_from_list_s k slot in
     slot_s_inv len i slot' /\
     slot_s_find k slot' == None /\
     (forall (k':key{k' <> k}). slot_s_find k' slot' == slot_s_find k' slot) /\
@@ -3117,14 +3117,14 @@ val hash_map_remove_from_list_s_lem
   ))
 
 #push-options "--fuel 1"
-let rec hash_map_remove_from_list_s_lem #t key slot len i =
+let rec hashMap_remove_from_list_s_lem #t key slot len i =
   match slot with
   | [] -> ()
   | (k',v) :: slot' ->
     if k' <> key then
       begin
-      hash_map_remove_from_list_s_lem key slot' len i;
-      let slot'' = hash_map_remove_from_list_s key slot' in
+      hashMap_remove_from_list_s_lem key slot' len i;
+      let slot'' = hashMap_remove_from_list_s key slot' in
       assert(for_all (same_hash_mod_key len i) ((k',v)::slot''));
       assert(for_all (binding_neq (k',v)) slot'); // Triggers instanciation
       assert(for_all (binding_neq (k',v)) slot'')
@@ -3136,51 +3136,51 @@ let rec hash_map_remove_from_list_s_lem #t key slot len i =
       end
 #pop-options
 
-val hash_map_remove_s_lem
-  (#t : Type0) (self : hash_map_s_nes t) (key : usize) :
+val hashMap_remove_s_lem
+  (#t : Type0) (self : hashMap_s_nes t) (key : usize) :
   Lemma
-  (requires (hash_map_s_inv self))
+  (requires (hashMap_s_inv self))
   (ensures (
-    let hm' = hash_map_remove_s self key in
+    let hm' = hashMap_remove_s self key in
     // The invariant is preserved
-    hash_map_s_inv hm' /\
+    hashMap_s_inv hm' /\
     // We updated the binding
-    hash_map_s_updated_binding self key None hm'))
+    hashMap_s_updated_binding self key None hm'))
 
-let hash_map_remove_s_lem #t self key =
+let hashMap_remove_s_lem #t self key =
   let len = length self in
   let hash = hash_mod_key key len in
   let slot = index self hash in
-  hash_map_remove_from_list_s_lem key slot len hash;
-  let slot' = hash_map_remove_from_list_s key slot in
+  hashMap_remove_from_list_s_lem key slot len hash;
+  let slot' = hashMap_remove_from_list_s key slot in
   let hm' = list_update self hash slot' in
-  assert(hash_map_s_inv self)
+  assert(hashMap_s_inv self)
 
 /// Final lemma about [remove'back]
-val hash_map_remove_back_lem_aux
-  (#t : Type0) (self : hash_map_t t) (key : usize) :
+val hashMap_remove_back_lem_aux
+  (#t : Type0) (self : hashMap_t t) (key : usize) :
   Lemma
-  (requires (hash_map_t_inv self))
+  (requires (hashMap_t_inv self))
   (ensures (
-    match hash_map_remove_back t self key with
+    match hashMap_remove_back t self key with
     | Fail _ -> False
     | Return hm' ->
-      hash_map_t_inv self /\
-      hash_map_t_same_params hm' self /\
+      hashMap_t_inv self /\
+      hashMap_t_same_params hm' self /\
       // We updated the binding
-      hash_map_s_updated_binding (hash_map_t_v self) key None (hash_map_t_v hm') /\
-      hash_map_t_v hm' == hash_map_remove_s (hash_map_t_v self) key /\
+      hashMap_s_updated_binding (hashMap_t_v self) key None (hashMap_t_v hm') /\
+      hashMap_t_v hm' == hashMap_remove_s (hashMap_t_v self) key /\
       // The length is decremented iff the key was in the map
-      (let len = hash_map_t_len_s self in
-       let len' = hash_map_t_len_s hm' in
-       match hash_map_t_find_s self key with
+      (let len = hashMap_t_len_s self in
+       let len' = hashMap_t_len_s hm' in
+       match hashMap_t_find_s self key with
        | None -> len = len'
        | Some _ -> len = len' + 1)))
 
-let hash_map_remove_back_lem_aux #t self key =
-  hash_map_remove_back_lem_refin self key;
-  hash_map_remove_s_lem (hash_map_t_v self) key
+let hashMap_remove_back_lem_aux #t self key =
+  hashMap_remove_back_lem_refin self key;
+  hashMap_remove_s_lem (hashMap_t_v self) key
 
 /// .fsti
-let hash_map_remove_back_lem #t self key =
-  hash_map_remove_back_lem_aux #t self key
+let hashMap_remove_back_lem #t self key =
+  hashMap_remove_back_lem_aux #t self key
diff --git a/tests/fstar/hashmap/Hashmap.Properties.fsti b/tests/fstar/hashmap/Hashmap.Properties.fsti
index 0a4f0134..26c0ec06 100644
--- a/tests/fstar/hashmap/Hashmap.Properties.fsti
+++ b/tests/fstar/hashmap/Hashmap.Properties.fsti
@@ -18,11 +18,11 @@ type key : eqtype = usize
 
 type hash : eqtype = usize
 
-val hash_map_t_inv (#t : Type0) (hm : hash_map_t t) : Type0
+val hashMap_t_inv (#t : Type0) (hm : hashMap_t t) : Type0
 
-val len_s (#t : Type0) (hm : hash_map_t t) : nat
+val len_s (#t : Type0) (hm : hashMap_t t) : nat
 
-val find_s (#t : Type0) (hm : hash_map_t t) (k : key) : option t
+val find_s (#t : Type0) (hm : hashMap_t t) (k : key) : option t
 
 (*** Overloading *)
 
@@ -32,16 +32,16 @@ val find_s (#t : Type0) (hm : hash_map_t t) (k : key) : option t
 /// limiting the hash collisions.
 /// This is expressed by the following property, which is maintained in the hash
 /// map invariant.
-val hash_map_not_overloaded_lem (#t : Type0) (hm : hash_map_t t) :
+val hashMap_not_overloaded_lem (#t : Type0) (hm : hashMap_t t) :
   Lemma
-  (requires (hash_map_t_inv hm))
+  (requires (hashMap_t_inv hm))
   (ensures (
     // The capacity is the number of slots
-    let capacity = length hm.hash_map_slots in
+    let capacity = length hm.slots in
     // The max load factor defines a threshold on the number of entries:
     // if there are more entries than a given fraction of the number of slots,
     // we resize the slots vector to limit the hash collisions
-    let (dividend, divisor) = hm.hash_map_max_load_factor in
+    let (dividend, divisor) = hm.max_load_factor in
     // technicality: this postcondition won't typecheck if we don't reveal
     // that divisor > 0 (because of the division)
     divisor > 0 /\
@@ -63,14 +63,14 @@ val hash_map_not_overloaded_lem (#t : Type0) (hm : hash_map_t t) :
 (**** [new'fwd] *)
 
 /// [new] doesn't fail and returns an empty hash map
-val hash_map_new_fwd_lem (t : Type0) :
+val hashMap_new_lem (t : Type0) :
   Lemma
   (ensures (
-    match hash_map_new_fwd t with
+    match hashMap_new t with
     | Fail _ -> False
     | Return hm ->
       // The hash map invariant is satisfied
-      hash_map_t_inv hm /\
+      hashMap_t_inv hm /\
       // The hash map has a length of 0
       len_s hm = 0 /\
       // It contains no bindings
@@ -79,16 +79,16 @@ val hash_map_new_fwd_lem (t : Type0) :
 (**** [clear] *)
 
 /// [clear] doesn't fail and turns the hash map into an empty map
-val hash_map_clear_fwd_back_lem
-  (#t : Type0) (self : hash_map_t t) :
+val hashMap_clear_lem
+  (#t : Type0) (self : hashMap_t t) :
   Lemma
-  (requires (hash_map_t_inv self))
+  (requires (hashMap_t_inv self))
   (ensures (
-    match hash_map_clear_fwd_back t self with
+    match hashMap_clear t self with
     | Fail _ -> False
     | Return hm ->
       // The hash map invariant is satisfied
-      hash_map_t_inv hm /\
+      hashMap_t_inv hm /\
       // The hash map has a length of 0
       len_s hm = 0 /\
       // It contains no bindings
@@ -97,11 +97,11 @@ val hash_map_clear_fwd_back_lem
 (**** [len] *)
 
 /// [len] can't fail and returns the length (the number of elements) of the hash map
-val hash_map_len_fwd_lem (#t : Type0) (self : hash_map_t t) :
+val hashMap_len_lem (#t : Type0) (self : hashMap_t t) :
   Lemma
-  (requires (hash_map_t_inv self))
+  (requires (hashMap_t_inv self))
   (ensures (
-    match hash_map_len_fwd t self with
+    match hashMap_len t self with
     | Fail _ -> False
     | Return l -> l = len_s self))
 
@@ -114,12 +114,12 @@ val hash_map_len_fwd_lem (#t : Type0) (self : hash_map_t t) :
 /// entirely encompassed by the effect of the backward function alone).
 /// 
 /// [insert'fwd_back] simply inserts a binding.
-val hash_map_insert_fwd_back_lem
-  (#t : Type0) (self : hash_map_t t) (key : usize) (value : t) :
+val hashMap_insert_lem
+  (#t : Type0) (self : hashMap_t t) (key : usize) (value : t) :
   Lemma
-  (requires (hash_map_t_inv self))
+  (requires (hashMap_t_inv self))
   (ensures (
-    match hash_map_insert_fwd_back t self key value with
+    match hashMap_insert t self key value with
     | Fail _ ->
       // We can fail only if:
       // - the key is not in the map and we thus need to add it
@@ -128,7 +128,7 @@ val hash_map_insert_fwd_back_lem
       len_s self = usize_max
     | Return hm' ->
       // The invariant is preserved
-      hash_map_t_inv hm' /\
+      hashMap_t_inv hm' /\
       // [key] maps to [value]
       find_s hm' key == Some value /\
       // The other bindings are preserved
@@ -145,24 +145,24 @@ val hash_map_insert_fwd_back_lem
 
 /// [contains_key'fwd] can't fail and returns `true` if and only if there is
 /// a binding for key [key]
-val hash_map_contains_key_fwd_lem
-  (#t : Type0) (self : hash_map_t t) (key : usize) :
+val hashMap_contains_key_lem
+  (#t : Type0) (self : hashMap_t t) (key : usize) :
   Lemma
-  (requires (hash_map_t_inv self))
+  (requires (hashMap_t_inv self))
   (ensures (
-    match hash_map_contains_key_fwd t self key with
+    match hashMap_contains_key t self key with
     | Fail _ -> False
     | Return b -> b = Some? (find_s self key)))
 
 (**** [get'fwd] *)
 
 /// [get] returns (a shared borrow to) the binding for key [key]
-val hash_map_get_fwd_lem
-  (#t : Type0) (self : hash_map_t t) (key : usize) :
+val hashMap_get_lem
+  (#t : Type0) (self : hashMap_t t) (key : usize) :
   Lemma
-  (requires (hash_map_t_inv self))
+  (requires (hashMap_t_inv self))
   (ensures (
-    match hash_map_get_fwd t self key, find_s self key with
+    match hashMap_get t self key, find_s self key with
     | Fail _, None -> True
     | Return x, Some x' -> x == x'
     | _ -> False))
@@ -175,12 +175,12 @@ val hash_map_get_fwd_lem
 /// in Rust, which gives the possibility of modifying this element in place. Then,
 /// upon ending the borrow, the effect of the modification is modelled in the
 /// translation through a call to the backward function.
-val hash_map_get_mut_fwd_lem
-  (#t : Type0) (self : hash_map_t t) (key : usize) :
+val hashMap_get_mut_lem
+  (#t : Type0) (self : hashMap_t t) (key : usize) :
   Lemma
-  (requires (hash_map_t_inv self))
+  (requires (hashMap_t_inv self))
   (ensures (
-    match hash_map_get_mut_fwd t self key, find_s self key with
+    match hashMap_get_mut t self key, find_s self key with
     | Fail _, None -> True
     | Return x, Some x' -> x == x'
     | _ -> False))
@@ -192,11 +192,11 @@ val hash_map_get_mut_fwd_lem
 /// A call to [get_mut'back] must follow a call to [get_mut'fwd], which gives
 /// us that there must be a binding for key [key] in the map (otherwise we
 /// can't prove the absence of failure).
-val hash_map_get_mut_back_lem
-  (#t : Type0) (hm : hash_map_t t) (key : usize) (ret : t) :
+val hashMap_get_mut_back_lem
+  (#t : Type0) (hm : hashMap_t t) (key : usize) (ret : t) :
   Lemma
   (requires (
-    hash_map_t_inv hm /\
+    hashMap_t_inv hm /\
     // A call to the backward function must follow a call to the forward
     // function, whose success gives us that there is a binding for the key.
     // In the case of *forward* functions, "success" has to be understood as
@@ -207,14 +207,14 @@ val hash_map_get_mut_back_lem
     // "failure" is to be understood as the semantics getting stuck.
     // This is of course true unless we filtered the call to the forward function
     // because its effect is encompassed by the backward function, as with
-    // [hash_map_clear_fwd_back]).
+    // [hashMap_clear]).
     Some? (find_s hm key)))
   (ensures (
-    match hash_map_get_mut_back t hm key ret with
+    match hashMap_get_mut_back t hm key ret with
     | Fail _ -> False // Can't fail
     | Return hm' ->
      // The invariant is preserved
-     hash_map_t_inv hm' /\
+     hashMap_t_inv hm' /\
      // The length is preserved
      len_s hm' = len_s hm /\
      // [key] maps to the update value, [ret]
@@ -228,12 +228,12 @@ val hash_map_get_mut_back_lem
 /// (the rust function *moves* it out of the map). Note that the effect of the update
 /// on the map is modelles through the call to [remove'back] ([remove] takes a
 /// mutable borrow to the hash map as parameter).
-val hash_map_remove_fwd_lem
-  (#t : Type0) (self : hash_map_t t) (key : usize) :
+val hashMap_remove_lem
+  (#t : Type0) (self : hashMap_t t) (key : usize) :
   Lemma
-  (requires (hash_map_t_inv self))
+  (requires (hashMap_t_inv self))
   (ensures (
-    match hash_map_remove_fwd t self key with
+    match hashMap_remove t self key with
     | Fail _ -> False
     | Return opt_x -> opt_x == find_s self key))
 
@@ -243,16 +243,16 @@ val hash_map_remove_fwd_lem
 /// The hash map given as parameter to [remove] is given through a mutable borrow:
 /// hence the backward function which gives back the updated map, without the
 /// binding.
-val hash_map_remove_back_lem
-  (#t : Type0) (self : hash_map_t t) (key : usize) :
+val hashMap_remove_back_lem
+  (#t : Type0) (self : hashMap_t t) (key : usize) :
   Lemma
-  (requires (hash_map_t_inv self))
+  (requires (hashMap_t_inv self))
   (ensures (
-    match hash_map_remove_back t self key with
+    match hashMap_remove_back t self key with
     | Fail _ -> False
     | Return hm' ->
       // The invariant is preserved
-      hash_map_t_inv self /\
+      hashMap_t_inv self /\
       // The binding for [key] is not there anymore
       find_s hm' key == None /\
       // The other bindings are preserved
diff --git a/tests/fstar/hashmap/Hashmap.Types.fst b/tests/fstar/hashmap/Hashmap.Types.fst
index 91ee26c6..753730fe 100644
--- a/tests/fstar/hashmap/Hashmap.Types.fst
+++ b/tests/fstar/hashmap/Hashmap.Types.fst
@@ -7,15 +7,15 @@ open Primitives
 
 (** [hashmap::List] *)
 type list_t (t : Type0) =
-| ListCons : usize -> t -> list_t t -> list_t t
-| ListNil : list_t t
+| List_Cons : usize -> t -> list_t t -> list_t t
+| List_Nil : list_t t
 
 (** [hashmap::HashMap] *)
-type hash_map_t (t : Type0) =
+type hashMap_t (t : Type0) =
 {
-  hash_map_num_entries : usize;
-  hash_map_max_load_factor : (usize & usize);
-  hash_map_max_load : usize;
-  hash_map_slots : vec (list_t t);
+  num_entries : usize;
+  max_load_factor : (usize & usize);
+  max_load : usize;
+  slots : alloc_vec_Vec (list_t t);
 }
 
diff --git a/tests/fstar/hashmap/Primitives.fst b/tests/fstar/hashmap/Primitives.fst
index 9db82069..3297803c 100644
--- a/tests/fstar/hashmap/Primitives.fst
+++ b/tests/fstar/hashmap/Primitives.fst
@@ -55,8 +55,12 @@ type string = string
 let is_zero (n: nat) : bool = n = 0
 let decrease (n: nat{n > 0}) : nat = n - 1
 
-let mem_replace_fwd (a : Type0) (x : a) (y : a) : a = x
-let mem_replace_back (a : Type0) (x : a) (y : a) : a = y
+let core_mem_replace (a : Type0) (x : a) (y : a) : a = x
+let core_mem_replace_back (a : Type0) (x : a) (y : a) : a = y
+
+// We don't really use raw pointers for now
+type mut_raw_ptr (t : Type0) = { v : t }
+type const_raw_ptr (t : Type0) = { v : t }
 
 (*** Scalars *)
 /// Rem.: most of the following code was partially generated
@@ -100,6 +104,11 @@ type scalar_ty =
 | U64
 | U128
 
+let is_unsigned = function
+  | Isize | I8 | I16 | I32 | I64 | I128 -> false
+  | Usize | U8 | U16 | U32 | U64 | U128 -> true
+
+
 let scalar_min (ty : scalar_ty) : int =
   match ty with
   | Isize -> isize_min
@@ -162,6 +171,15 @@ let scalar_sub (#ty : scalar_ty) (x : scalar ty) (y : scalar ty) : result (scala
 let scalar_mul (#ty : scalar_ty) (x : scalar ty) (y : scalar ty) : result (scalar ty) =
   mk_scalar ty (x * y)
 
+let scalar_lxor (#ty : scalar_ty { is_unsigned ty && ty <> Usize })
+    (x : scalar ty) (y : scalar ty) : scalar ty =
+  match ty with
+  | U8 -> FStar.UInt.logxor #8 x y
+  | U16 -> FStar.UInt.logxor #16 x y
+  | U32 -> FStar.UInt.logxor #32 x y
+  | U64 -> FStar.UInt.logxor #64 x y
+  | U128 -> FStar.UInt.logxor #128 x y
+
 (** Cast an integer from a [src_ty] to a [tgt_ty] *)
 // TODO: check the semantics of casts in Rust
 let scalar_cast (src_ty : scalar_ty) (tgt_ty : scalar_ty) (x : scalar src_ty) : result (scalar tgt_ty) =
@@ -169,17 +187,44 @@ let scalar_cast (src_ty : scalar_ty) (tgt_ty : scalar_ty) (x : scalar src_ty) :
 
 /// The scalar types
 type isize : eqtype = scalar Isize
-type i8 : eqtype = scalar I8
-type i16 : eqtype = scalar I16
-type i32 : eqtype = scalar I32
-type i64 : eqtype = scalar I64
-type i128 : eqtype = scalar I128
+type i8    : eqtype = scalar I8
+type i16   : eqtype = scalar I16
+type i32   : eqtype = scalar I32
+type i64   : eqtype = scalar I64
+type i128  : eqtype = scalar I128
 type usize : eqtype = scalar Usize
-type u8 : eqtype = scalar U8
-type u16 : eqtype = scalar U16
-type u32 : eqtype = scalar U32
-type u64 : eqtype = scalar U64
-type u128 : eqtype = scalar U128
+type u8    : eqtype = scalar U8
+type u16   : eqtype = scalar U16
+type u32   : eqtype = scalar U32
+type u64   : eqtype = scalar U64
+type u128  : eqtype = scalar U128
+
+
+let core_isize_min : isize = isize_min
+let core_isize_max : isize = isize_max
+let core_i8_min    : i8 = i8_min
+let core_i8_max    : i8 = i8_max
+let core_i16_min   : i16 = i16_min
+let core_i16_max   : i16 = i16_max
+let core_i32_min   : i32 = i32_min
+let core_i32_max   : i32 = i32_max
+let core_i64_min   : i64 = i64_min
+let core_i64_max   : i64 = i64_max
+let core_i128_min  : i128 = i128_min
+let core_i128_max  : i128 = i128_max
+
+let core_usize_min : usize = usize_min
+let core_usize_max : usize = usize_max
+let core_u8_min    : u8 = u8_min
+let core_u8_max    : u8 = u8_max
+let core_u16_min   : u16 = u16_min
+let core_u16_max   : u16 = u16_max
+let core_u32_min   : u32 = u32_min
+let core_u32_max   : u32 = u32_max
+let core_u64_min   : u64 = u64_min
+let core_u64_max   : u64 = u64_max
+let core_u128_min  : u128 = u128_min
+let core_u128_max  : u128 = u128_max
 
 /// Negation
 let isize_neg = scalar_neg #Isize
@@ -231,7 +276,7 @@ let u32_add = scalar_add #U32
 let u64_add = scalar_add #U64
 let u128_add = scalar_add #U128
 
-/// Substraction
+/// Subtraction
 let isize_sub = scalar_sub #Isize
 let i8_sub = scalar_sub #I8
 let i16_sub = scalar_sub #I16
@@ -259,12 +304,65 @@ let u32_mul = scalar_mul #U32
 let u64_mul = scalar_mul #U64
 let u128_mul = scalar_mul #U128
 
-(*** Range *)
-type range (a : Type0) = {
+/// Logical operators, defined for unsigned types only, so far
+let u8_xor = scalar_lxor #U8
+let u16_xor = scalar_lxor #U16
+let u32_xor = scalar_lxor #U32
+let u64_xor = scalar_lxor #U64
+let u128_xor = scalar_lxor #U128
+
+(*** core::ops *)
+
+// Trait declaration: [core::ops::index::Index]
+noeq type core_ops_index_Index (self idx : Type0) = {
+  output : Type0;
+  index : self → idx → result output
+}
+
+// Trait declaration: [core::ops::index::IndexMut]
+noeq type core_ops_index_IndexMut (self idx : Type0) = {
+  indexInst : core_ops_index_Index self idx;
+  index_mut : self → idx → result indexInst.output;
+  index_mut_back : self → idx → indexInst.output → result self;
+}
+
+// Trait declaration [core::ops::deref::Deref]
+noeq type core_ops_deref_Deref (self : Type0) = {
+  target : Type0;
+  deref : self → result target;
+}
+
+// Trait declaration [core::ops::deref::DerefMut]
+noeq type core_ops_deref_DerefMut (self : Type0) = {
+  derefInst : core_ops_deref_Deref self;
+  deref_mut : self → result derefInst.target;
+  deref_mut_back : self → derefInst.target → result self;
+}
+
+type core_ops_range_Range (a : Type0) = {
   start : a;
   end_ : a;
 }
 
+(*** [alloc] *)
+
+let alloc_boxed_Box_deref (t : Type0) (x : t) : result t = Return x
+let alloc_boxed_Box_deref_mut (t : Type0) (x : t) : result t = Return x
+let alloc_boxed_Box_deref_mut_back (t : Type) (_ : t) (x : t) : result t = Return x
+
+// Trait instance
+let alloc_boxed_Box_coreOpsDerefInst (self : Type0) : core_ops_deref_Deref self = {
+  target = self;
+  deref = alloc_boxed_Box_deref self;
+}
+
+// Trait instance
+let alloc_boxed_Box_coreOpsDerefMutInst (self : Type0) : core_ops_deref_DerefMut self = {
+  derefInst = alloc_boxed_Box_coreOpsDerefInst self;
+  deref_mut = alloc_boxed_Box_deref_mut self;
+  deref_mut_back = alloc_boxed_Box_deref_mut_back self;
+}
+
 (*** Array *)
 type array (a : Type0) (n : usize) = s:list a{length s = n}
 
@@ -278,15 +376,11 @@ let mk_array (a : Type0) (n : usize)
   normalize_term_spec (FStar.List.Tot.length l);
   l
 
-let array_index_shared (a : Type0) (n : usize) (x : array a n) (i : usize) : result a =
-  if i < length x then Return (index x i)
-  else Fail Failure
-
-let array_index_mut_fwd (a : Type0) (n : usize) (x : array a n) (i : usize) : result a =
+let array_index_usize (a : Type0) (n : usize) (x : array a n) (i : usize) : result a =
   if i < length x then Return (index x i)
   else Fail Failure
 
-let array_index_mut_back (a : Type0) (n : usize) (x : array a n) (i : usize) (nx : a) : result (array a n) =
+let array_update_usize (a : Type0) (n : usize) (x : array a n) (i : usize) (nx : a) : result (array a n) =
   if i < length x then Return (list_update x i nx)
   else Fail Failure
 
@@ -295,55 +389,54 @@ type slice (a : Type0) = s:list a{length s <= usize_max}
 
 let slice_len (a : Type0) (s : slice a) : usize = length s
 
-let slice_index_shared (a : Type0) (x : slice a) (i : usize) : result a =
+let slice_index_usize (a : Type0) (x : slice a) (i : usize) : result a =
   if i < length x then Return (index x i)
   else Fail Failure
 
-let slice_index_mut_fwd (a : Type0) (x : slice a) (i : usize) : result a =
-  if i < length x then Return (index x i)
-  else Fail Failure
-
-let slice_index_mut_back (a : Type0) (x : slice a) (i : usize) (nx : a) : result (slice a) =
+let slice_update_usize (a : Type0) (x : slice a) (i : usize) (nx : a) : result (slice a) =
   if i < length x then Return (list_update x i nx)
   else Fail Failure
 
 (*** Subslices *)
 
-let array_to_slice_shared (a : Type0) (n : usize) (x : array a n) : result (slice a) = Return x
-let array_to_slice_mut_fwd (a : Type0) (n : usize) (x : array a n) : result (slice a) = Return x
-let array_to_slice_mut_back (a : Type0) (n : usize) (x : array a n) (s : slice a) : result (array a n) =
+let array_to_slice (a : Type0) (n : usize) (x : array a n) : result (slice a) = Return x
+let array_from_slice (a : Type0) (n : usize) (x : array a n) (s : slice a) : result (array a n) =
   if length s = n then Return s
   else Fail Failure
 
 // TODO: finish the definitions below (there lacks [List.drop] and [List.take] in the standard library *)
-let array_subslice_shared (a : Type0) (n : usize) (x : array a n) (r : range usize) : result (slice a) =
-  admit()
-
-let array_subslice_mut_fwd (a : Type0) (n : usize) (x : array a n) (r : range usize) : result (slice a) =
+let array_subslice (a : Type0) (n : usize) (x : array a n) (r : core_ops_range_Range usize) : result (slice a) =
   admit()
 
-let array_subslice_mut_back (a : Type0) (n : usize) (x : array a n) (r : range usize) (ns : slice a) : result (array a n) =
+let array_update_subslice (a : Type0) (n : usize) (x : array a n) (r : core_ops_range_Range usize) (ns : slice a) : result (array a n) =
   admit()
 
-let slice_subslice_shared (a : Type0) (x : slice a) (r : range usize) : result (slice a) =
+let array_repeat (a : Type0) (n : usize) (x : a) : array a n =
   admit()
 
-let slice_subslice_mut_fwd (a : Type0) (x : slice a) (r : range usize) : result (slice a) =
+let slice_subslice (a : Type0) (x : slice a) (r : core_ops_range_Range usize) : result (slice a) =
   admit()
 
-let slice_subslice_mut_back (a : Type0) (x : slice a) (r : range usize) (ns : slice a) : result (slice a) =
+let slice_update_subslice (a : Type0) (x : slice a) (r : core_ops_range_Range usize) (ns : slice a) : result (slice a) =
   admit()
 
 (*** Vector *)
-type vec (a : Type0) = v:list a{length v <= usize_max}
+type alloc_vec_Vec (a : Type0) = v:list a{length v <= usize_max}
 
-let vec_new (a  : Type0) : vec a = assert_norm(length #a [] == 0); []
-let vec_len (a : Type0) (v : vec a) : usize = length v
+let alloc_vec_Vec_new (a  : Type0) : alloc_vec_Vec a = assert_norm(length #a [] == 0); []
+let alloc_vec_Vec_len (a : Type0) (v : alloc_vec_Vec a) : usize = length v
+
+// Helper
+let alloc_vec_Vec_index_usize (#a : Type0) (v : alloc_vec_Vec a) (i : usize) : result a =
+  if i < length v then Return (index v i) else Fail Failure
+// Helper
+let alloc_vec_Vec_update_usize (#a : Type0) (v : alloc_vec_Vec a) (i : usize) (x : a) : result (alloc_vec_Vec a) =
+  if i < length v then Return (list_update v i x) else Fail Failure
 
 // The **forward** function shouldn't be used
-let vec_push_fwd (a  : Type0) (v : vec a) (x : a) : unit = ()
-let vec_push_back (a  : Type0) (v : vec a) (x : a) :
-  Pure (result (vec a))
+let alloc_vec_Vec_push_fwd (a  : Type0) (v : alloc_vec_Vec a) (x : a) : unit = ()
+let alloc_vec_Vec_push (a  : Type0) (v : alloc_vec_Vec a) (x : a) :
+  Pure (result (alloc_vec_Vec a))
   (requires True)
   (ensures (fun res ->
     match res with
@@ -358,18 +451,279 @@ let vec_push_back (a  : Type0) (v : vec a) (x : a) :
   else Fail Failure
 
 // The **forward** function shouldn't be used
-let vec_insert_fwd (a : Type0) (v : vec a) (i : usize) (x : a) : result unit =
+let alloc_vec_Vec_insert_fwd (a : Type0) (v : alloc_vec_Vec a) (i : usize) (x : a) : result unit =
   if i < length v then Return () else Fail Failure
-let vec_insert_back (a : Type0) (v : vec a) (i : usize) (x : a) : result (vec a) =
+let alloc_vec_Vec_insert (a : Type0) (v : alloc_vec_Vec a) (i : usize) (x : a) : result (alloc_vec_Vec a) =
   if i < length v then Return (list_update v i x) else Fail Failure
 
-// The **backward** function shouldn't be used
-let vec_index_fwd (a : Type0) (v : vec a) (i : usize) : result a =
-  if i < length v then Return (index v i) else Fail Failure
-let vec_index_back (a : Type0) (v : vec a) (i : usize) (x : a) : result unit =
-  if i < length v then Return () else Fail Failure
+// Trait declaration: [core::slice::index::private_slice_index::Sealed]
+type core_slice_index_private_slice_index_Sealed (self : Type0) = unit
+
+// Trait declaration: [core::slice::index::SliceIndex]
+noeq type core_slice_index_SliceIndex (self t : Type0) = {
+  sealedInst : core_slice_index_private_slice_index_Sealed self;
+  output : Type0;
+  get : self → t → result (option output);
+  get_mut : self → t → result (option output);
+  get_mut_back : self → t → option output → result t;
+  get_unchecked : self → const_raw_ptr t → result (const_raw_ptr output);
+  get_unchecked_mut : self → mut_raw_ptr t → result (mut_raw_ptr output);
+  index : self → t → result output;
+  index_mut : self → t → result output;
+  index_mut_back : self → t → output → result t;
+}
 
-let vec_index_mut_fwd (a : Type0) (v : vec a) (i : usize) : result a =
-  if i < length v then Return (index v i) else Fail Failure
-let vec_index_mut_back (a : Type0) (v : vec a) (i : usize) (nx : a) : result (vec a) =
-  if i < length v then Return (list_update v i nx) else Fail Failure
+// [core::slice::index::[T]::index]: forward function
+let core_slice_index_Slice_index
+  (t idx : Type0) (inst : core_slice_index_SliceIndex idx (slice t))
+  (s : slice t) (i : idx) : result inst.output =
+  let* x = inst.get i s in
+  match x with
+  | None -> Fail Failure
+  | Some x -> Return x
+
+// [core::slice::index::Range:::get]: forward function
+let core_slice_index_Range_get (t : Type0) (i : core_ops_range_Range usize) (s : slice t) :
+  result (option (slice t)) =
+  admit () // TODO
+
+// [core::slice::index::Range::get_mut]: forward function
+let core_slice_index_Range_get_mut
+  (t : Type0) : core_ops_range_Range usize → slice t → result (option (slice t)) =
+  admit () // TODO
+
+// [core::slice::index::Range::get_mut]: backward function 0
+let core_slice_index_Range_get_mut_back
+  (t : Type0) :
+  core_ops_range_Range usize → slice t → option (slice t) → result (slice t) =
+  admit () // TODO
+
+// [core::slice::index::Range::get_unchecked]: forward function
+let core_slice_index_Range_get_unchecked
+  (t : Type0) :
+  core_ops_range_Range usize → const_raw_ptr (slice t) → result (const_raw_ptr (slice t)) =
+  // Don't know what the model should be - for now we always fail to make
+  // sure code which uses it fails
+  fun _ _ -> Fail Failure
+
+// [core::slice::index::Range::get_unchecked_mut]: forward function
+let core_slice_index_Range_get_unchecked_mut
+  (t : Type0) :
+  core_ops_range_Range usize → mut_raw_ptr (slice t) → result (mut_raw_ptr (slice t)) =
+  // Don't know what the model should be - for now we always fail to make
+  // sure code which uses it fails
+  fun _ _ -> Fail Failure
+
+// [core::slice::index::Range::index]: forward function
+let core_slice_index_Range_index
+  (t : Type0) : core_ops_range_Range usize → slice t → result (slice t) =
+  admit () // TODO
+
+// [core::slice::index::Range::index_mut]: forward function
+let core_slice_index_Range_index_mut
+  (t : Type0) : core_ops_range_Range usize → slice t → result (slice t) =
+  admit () // TODO
+
+// [core::slice::index::Range::index_mut]: backward function 0
+let core_slice_index_Range_index_mut_back
+  (t : Type0) : core_ops_range_Range usize → slice t → slice t → result (slice t) =
+  admit () // TODO
+
+// [core::slice::index::[T]::index_mut]: forward function
+let core_slice_index_Slice_index_mut
+  (t idx : Type0) (inst : core_slice_index_SliceIndex idx (slice t)) :
+  slice t → idx → result inst.output =
+  admit () // 
+
+// [core::slice::index::[T]::index_mut]: backward function 0
+let core_slice_index_Slice_index_mut_back
+  (t idx : Type0) (inst : core_slice_index_SliceIndex idx (slice t)) :
+  slice t → idx → inst.output → result (slice t) =
+  admit () // TODO
+
+// [core::array::[T; N]::index]: forward function
+let core_array_Array_index
+  (t idx : Type0) (n : usize) (inst : core_ops_index_Index (slice t) idx)
+  (a : array t n) (i : idx) : result inst.output =
+  admit () // TODO
+
+// [core::array::[T; N]::index_mut]: forward function
+let core_array_Array_index_mut
+  (t idx : Type0) (n : usize) (inst : core_ops_index_IndexMut (slice t) idx)
+  (a : array t n) (i : idx) : result inst.indexInst.output =
+  admit () // TODO
+
+// [core::array::[T; N]::index_mut]: backward function 0
+let core_array_Array_index_mut_back
+  (t idx : Type0) (n : usize) (inst : core_ops_index_IndexMut (slice t) idx)
+  (a : array t n) (i : idx) (x : inst.indexInst.output) : result (array t n) =
+  admit () // TODO
+
+// Trait implementation: [core::slice::index::[T]]
+let core_slice_index_Slice_coreopsindexIndexInst (t idx : Type0)
+  (inst : core_slice_index_SliceIndex idx (slice t)) :
+  core_ops_index_Index (slice t) idx = {
+  output = inst.output;
+  index = core_slice_index_Slice_index t idx inst;
+}
+
+// Trait implementation: [core::slice::index::private_slice_index::Range]
+let core_slice_index_private_slice_index_Range_coresliceindexprivate_slice_indexSealedInst
+  : core_slice_index_private_slice_index_Sealed (core_ops_range_Range usize) = ()
+
+// Trait implementation: [core::slice::index::Range]
+let core_slice_index_Range_coresliceindexSliceIndexInst (t : Type0) :
+  core_slice_index_SliceIndex (core_ops_range_Range usize) (slice t) = {
+  sealedInst = core_slice_index_private_slice_index_Range_coresliceindexprivate_slice_indexSealedInst;
+  output = slice t;
+  get = core_slice_index_Range_get t;
+  get_mut = core_slice_index_Range_get_mut t;
+  get_mut_back = core_slice_index_Range_get_mut_back t;
+  get_unchecked = core_slice_index_Range_get_unchecked t;
+  get_unchecked_mut = core_slice_index_Range_get_unchecked_mut t;
+  index = core_slice_index_Range_index t;
+  index_mut = core_slice_index_Range_index_mut t;
+  index_mut_back = core_slice_index_Range_index_mut_back t;
+}
+
+// Trait implementation: [core::slice::index::[T]]
+let core_slice_index_Slice_coreopsindexIndexMutInst (t idx : Type0)
+  (inst : core_slice_index_SliceIndex idx (slice t)) :
+  core_ops_index_IndexMut (slice t) idx = {
+  indexInst = core_slice_index_Slice_coreopsindexIndexInst t idx inst;
+  index_mut = core_slice_index_Slice_index_mut t idx inst;
+  index_mut_back = core_slice_index_Slice_index_mut_back t idx inst;
+}
+
+// Trait implementation: [core::array::[T; N]]
+let core_array_Array_coreopsindexIndexInst (t idx : Type0) (n : usize)
+  (inst : core_ops_index_Index (slice t) idx) :
+  core_ops_index_Index (array t n) idx = {
+  output = inst.output;
+  index = core_array_Array_index t idx n inst;
+}
+
+// Trait implementation: [core::array::[T; N]]
+let core_array_Array_coreopsindexIndexMutInst (t idx : Type0) (n : usize)
+  (inst : core_ops_index_IndexMut (slice t) idx) :
+  core_ops_index_IndexMut (array t n) idx = {
+  indexInst = core_array_Array_coreopsindexIndexInst t idx n inst.indexInst;
+  index_mut = core_array_Array_index_mut t idx n inst;
+  index_mut_back = core_array_Array_index_mut_back t idx n inst;
+}
+
+// [core::slice::index::usize::get]: forward function
+let core_slice_index_usize_get
+  (t : Type0) : usize → slice t → result (option t) =
+  admit () // TODO
+
+// [core::slice::index::usize::get_mut]: forward function
+let core_slice_index_usize_get_mut
+  (t : Type0) : usize → slice t → result (option t) =
+  admit () // TODO
+
+// [core::slice::index::usize::get_mut]: backward function 0
+let core_slice_index_usize_get_mut_back
+  (t : Type0) : usize → slice t → option t → result (slice t) =
+  admit () // TODO
+
+// [core::slice::index::usize::get_unchecked]: forward function
+let core_slice_index_usize_get_unchecked
+  (t : Type0) : usize → const_raw_ptr (slice t) → result (const_raw_ptr t) =
+  admit () // TODO
+
+// [core::slice::index::usize::get_unchecked_mut]: forward function
+let core_slice_index_usize_get_unchecked_mut
+  (t : Type0) : usize → mut_raw_ptr (slice t) → result (mut_raw_ptr t) =
+  admit () // TODO
+
+// [core::slice::index::usize::index]: forward function
+let core_slice_index_usize_index (t : Type0) : usize → slice t → result t =
+  admit () // TODO
+
+// [core::slice::index::usize::index_mut]: forward function
+let core_slice_index_usize_index_mut (t : Type0) : usize → slice t → result t =
+  admit () // TODO
+
+// [core::slice::index::usize::index_mut]: backward function 0
+let core_slice_index_usize_index_mut_back
+  (t : Type0) : usize → slice t → t → result (slice t) =
+  admit () // TODO
+
+// Trait implementation: [core::slice::index::private_slice_index::usize]
+let core_slice_index_private_slice_index_usize_coresliceindexprivate_slice_indexSealedInst
+  : core_slice_index_private_slice_index_Sealed usize = ()
+
+// Trait implementation: [core::slice::index::usize]
+let core_slice_index_usize_coresliceindexSliceIndexInst (t : Type0) :
+  core_slice_index_SliceIndex usize (slice t) = {
+  sealedInst = core_slice_index_private_slice_index_usize_coresliceindexprivate_slice_indexSealedInst;
+  output = t;
+  get = core_slice_index_usize_get t;
+  get_mut = core_slice_index_usize_get_mut t;
+  get_mut_back = core_slice_index_usize_get_mut_back t;
+  get_unchecked = core_slice_index_usize_get_unchecked t;
+  get_unchecked_mut = core_slice_index_usize_get_unchecked_mut t;
+  index = core_slice_index_usize_index t;
+  index_mut = core_slice_index_usize_index_mut t;
+  index_mut_back = core_slice_index_usize_index_mut_back t;
+}
+
+// [alloc::vec::Vec::index]: forward function
+let alloc_vec_Vec_index (t idx : Type0) (inst : core_slice_index_SliceIndex idx (slice t))
+  (self : alloc_vec_Vec t) (i : idx) : result inst.output =
+  admit () // TODO
+
+// [alloc::vec::Vec::index_mut]: forward function
+let alloc_vec_Vec_index_mut (t idx : Type0) (inst : core_slice_index_SliceIndex idx (slice t))
+  (self : alloc_vec_Vec t) (i : idx) : result inst.output =
+  admit () // TODO
+
+// [alloc::vec::Vec::index_mut]: backward function 0
+let alloc_vec_Vec_index_mut_back
+  (t idx : Type0) (inst : core_slice_index_SliceIndex idx (slice t))
+  (self : alloc_vec_Vec t) (i : idx) (x : inst.output) : result (alloc_vec_Vec t) =
+  admit () // TODO
+
+// Trait implementation: [alloc::vec::Vec]
+let alloc_vec_Vec_coreopsindexIndexInst (t idx : Type0)
+  (inst : core_slice_index_SliceIndex idx (slice t)) :
+  core_ops_index_Index (alloc_vec_Vec t) idx = {
+  output = inst.output;
+  index = alloc_vec_Vec_index t idx inst;
+}
+
+// Trait implementation: [alloc::vec::Vec]
+let alloc_vec_Vec_coreopsindexIndexMutInst (t idx : Type0)
+  (inst : core_slice_index_SliceIndex idx (slice t)) :
+  core_ops_index_IndexMut (alloc_vec_Vec t) idx = {
+  indexInst = alloc_vec_Vec_coreopsindexIndexInst t idx inst;
+  index_mut = alloc_vec_Vec_index_mut t idx inst;
+  index_mut_back = alloc_vec_Vec_index_mut_back t idx inst;
+}
+
+(*** Theorems *)
+
+let alloc_vec_Vec_index_eq (#a : Type0) (v : alloc_vec_Vec a) (i : usize) :
+  Lemma (
+    alloc_vec_Vec_index a usize (core_slice_index_usize_coresliceindexSliceIndexInst a) v i ==
+      alloc_vec_Vec_index_usize v i)
+  [SMTPat (alloc_vec_Vec_index a usize (core_slice_index_usize_coresliceindexSliceIndexInst a) v i)]
+  =
+  admit()
+
+let alloc_vec_Vec_index_mut_eq (#a : Type0) (v : alloc_vec_Vec a) (i : usize) :
+  Lemma (
+    alloc_vec_Vec_index_mut a usize (core_slice_index_usize_coresliceindexSliceIndexInst a) v i ==
+      alloc_vec_Vec_index_usize v i)
+  [SMTPat (alloc_vec_Vec_index_mut a usize (core_slice_index_usize_coresliceindexSliceIndexInst a) v i)]
+  =
+  admit()
+
+let alloc_vec_Vec_index_mut_back_eq (#a : Type0) (v : alloc_vec_Vec a) (i : usize) (x : a) :
+  Lemma (
+    alloc_vec_Vec_index_mut_back a usize (core_slice_index_usize_coresliceindexSliceIndexInst a) v i x ==
+      alloc_vec_Vec_update_usize v i x)
+  [SMTPat (alloc_vec_Vec_index_mut_back a usize (core_slice_index_usize_coresliceindexSliceIndexInst a) v i x)]
+  =
+  admit()
diff --git a/tests/fstar/hashmap_on_disk/HashmapMain.Clauses.Template.fst b/tests/fstar/hashmap_on_disk/HashmapMain.Clauses.Template.fst
index 615c670d..61885ac7 100644
--- a/tests/fstar/hashmap_on_disk/HashmapMain.Clauses.Template.fst
+++ b/tests/fstar/hashmap_on_disk/HashmapMain.Clauses.Template.fst
@@ -8,56 +8,56 @@ open HashmapMain.Types
 
 (** [hashmap_main::hashmap::HashMap::{0}::allocate_slots]: decreases clause *)
 unfold
-let hashmap_hash_map_allocate_slots_loop_decreases (t : Type0)
-  (slots : vec (hashmap_list_t t)) (n : usize) : nat =
+let hashmap_HashMap_allocate_slots_loop_decreases (t : Type0)
+  (slots : alloc_vec_Vec (hashmap_List_t t)) (n : usize) : nat =
   admit ()
 
 (** [hashmap_main::hashmap::HashMap::{0}::clear]: decreases clause *)
 unfold
-let hashmap_hash_map_clear_loop_decreases (t : Type0)
-  (slots : vec (hashmap_list_t t)) (i : usize) : nat =
+let hashmap_HashMap_clear_loop_decreases (t : Type0)
+  (slots : alloc_vec_Vec (hashmap_List_t t)) (i : usize) : nat =
   admit ()
 
 (** [hashmap_main::hashmap::HashMap::{0}::insert_in_list]: decreases clause *)
 unfold
-let hashmap_hash_map_insert_in_list_loop_decreases (t : Type0) (key : usize)
-  (value : t) (ls : hashmap_list_t t) : nat =
+let hashmap_HashMap_insert_in_list_loop_decreases (t : Type0) (key : usize)
+  (value : t) (ls : hashmap_List_t t) : nat =
   admit ()
 
 (** [hashmap_main::hashmap::HashMap::{0}::move_elements_from_list]: decreases clause *)
 unfold
-let hashmap_hash_map_move_elements_from_list_loop_decreases (t : Type0)
-  (ntable : hashmap_hash_map_t t) (ls : hashmap_list_t t) : nat =
+let hashmap_HashMap_move_elements_from_list_loop_decreases (t : Type0)
+  (ntable : hashmap_HashMap_t t) (ls : hashmap_List_t t) : nat =
   admit ()
 
 (** [hashmap_main::hashmap::HashMap::{0}::move_elements]: decreases clause *)
 unfold
-let hashmap_hash_map_move_elements_loop_decreases (t : Type0)
-  (ntable : hashmap_hash_map_t t) (slots : vec (hashmap_list_t t)) (i : usize)
-  : nat =
+let hashmap_HashMap_move_elements_loop_decreases (t : Type0)
+  (ntable : hashmap_HashMap_t t) (slots : alloc_vec_Vec (hashmap_List_t t))
+  (i : usize) : nat =
   admit ()
 
 (** [hashmap_main::hashmap::HashMap::{0}::contains_key_in_list]: decreases clause *)
 unfold
-let hashmap_hash_map_contains_key_in_list_loop_decreases (t : Type0)
-  (key : usize) (ls : hashmap_list_t t) : nat =
+let hashmap_HashMap_contains_key_in_list_loop_decreases (t : Type0)
+  (key : usize) (ls : hashmap_List_t t) : nat =
   admit ()
 
 (** [hashmap_main::hashmap::HashMap::{0}::get_in_list]: decreases clause *)
 unfold
-let hashmap_hash_map_get_in_list_loop_decreases (t : Type0) (key : usize)
-  (ls : hashmap_list_t t) : nat =
+let hashmap_HashMap_get_in_list_loop_decreases (t : Type0) (key : usize)
+  (ls : hashmap_List_t t) : nat =
   admit ()
 
 (** [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list]: decreases clause *)
 unfold
-let hashmap_hash_map_get_mut_in_list_loop_decreases (t : Type0)
-  (ls : hashmap_list_t t) (key : usize) : nat =
+let hashmap_HashMap_get_mut_in_list_loop_decreases (t : Type0)
+  (ls : hashmap_List_t t) (key : usize) : nat =
   admit ()
 
 (** [hashmap_main::hashmap::HashMap::{0}::remove_from_list]: decreases clause *)
 unfold
-let hashmap_hash_map_remove_from_list_loop_decreases (t : Type0) (key : usize)
-  (ls : hashmap_list_t t) : nat =
+let hashmap_HashMap_remove_from_list_loop_decreases (t : Type0) (key : usize)
+  (ls : hashmap_List_t t) : nat =
   admit ()
 
diff --git a/tests/fstar/hashmap_on_disk/HashmapMain.Clauses.fst b/tests/fstar/hashmap_on_disk/HashmapMain.Clauses.fst
index 699ff3b2..be5a4ab1 100644
--- a/tests/fstar/hashmap_on_disk/HashmapMain.Clauses.fst
+++ b/tests/fstar/hashmap_on_disk/HashmapMain.Clauses.fst
@@ -8,54 +8,54 @@ open HashmapMain.Types
 
 (** [hashmap::HashMap::allocate_slots]: decreases clause *)
 unfold
-let hashmap_hash_map_allocate_slots_loop_decreases (t : Type0) (slots : vec (hashmap_list_t t))
+let hashmap_HashMap_allocate_slots_loop_decreases (t : Type0) (slots : alloc_vec_Vec (hashmap_List_t t))
   (n : usize) : nat = n
 
 (** [hashmap::HashMap::clear]: decreases clause *)
 unfold
-let hashmap_hash_map_clear_loop_decreases (t : Type0) (slots : vec (hashmap_list_t t))
+let hashmap_HashMap_clear_loop_decreases (t : Type0) (slots : alloc_vec_Vec (hashmap_List_t t))
   (i : usize) : nat =
   if i < length slots then length slots - i else 0
 
 (** [hashmap::HashMap::insert_in_list]: decreases clause *)
 unfold
-let hashmap_hash_map_insert_in_list_loop_decreases (t : Type0) (key : usize) (value : t)
-  (ls : hashmap_list_t t) : hashmap_list_t t =
+let hashmap_HashMap_insert_in_list_loop_decreases (t : Type0) (key : usize) (value : t)
+  (ls : hashmap_List_t t) : hashmap_List_t t =
   ls
 
 (** [hashmap::HashMap::move_elements_from_list]: decreases clause *)
 unfold
-let hashmap_hash_map_move_elements_from_list_loop_decreases (t : Type0)
-  (ntable : hashmap_hash_map_t t) (ls : hashmap_list_t t) : hashmap_list_t t =
+let hashmap_HashMap_move_elements_from_list_loop_decreases (t : Type0)
+  (ntable : hashmap_HashMap_t t) (ls : hashmap_List_t t) : hashmap_List_t t =
   ls
 
 (** [hashmap::HashMap::move_elements]: decreases clause *)
 unfold
-let hashmap_hash_map_move_elements_loop_decreases (t : Type0) (ntable : hashmap_hash_map_t t)
-  (slots : vec (hashmap_list_t t)) (i : usize) : nat =
+let hashmap_HashMap_move_elements_loop_decreases (t : Type0) (ntable : hashmap_HashMap_t t)
+  (slots : alloc_vec_Vec (hashmap_List_t t)) (i : usize) : nat =
   if i < length slots then length slots - i else 0
 
 (** [hashmap::HashMap::contains_key_in_list]: decreases clause *)
 unfold
-let hashmap_hash_map_contains_key_in_list_loop_decreases (t : Type0) (key : usize)
-  (ls : hashmap_list_t t) : hashmap_list_t t =
+let hashmap_HashMap_contains_key_in_list_loop_decreases (t : Type0) (key : usize)
+  (ls : hashmap_List_t t) : hashmap_List_t t =
   ls
 
 (** [hashmap::HashMap::get_in_list]: decreases clause *)
 unfold
-let hashmap_hash_map_get_in_list_loop_decreases (t : Type0) (key : usize) (ls : hashmap_list_t t) :
-  hashmap_list_t t =
+let hashmap_HashMap_get_in_list_loop_decreases (t : Type0) (key : usize) (ls : hashmap_List_t t) :
+  hashmap_List_t t =
   ls
 
 (** [hashmap::HashMap::get_mut_in_list]: decreases clause *)
 unfold
-let hashmap_hash_map_get_mut_in_list_loop_decreases (t : Type0)
-  (ls : hashmap_list_t t) (key : usize) : hashmap_list_t t =
+let hashmap_HashMap_get_mut_in_list_loop_decreases (t : Type0)
+  (ls : hashmap_List_t t) (key : usize) : hashmap_List_t t =
   ls
 
 (** [hashmap::HashMap::remove_from_list]: decreases clause *)
 unfold
-let hashmap_hash_map_remove_from_list_loop_decreases (t : Type0) (key : usize)
-  (ls : hashmap_list_t t) : hashmap_list_t t =
+let hashmap_HashMap_remove_from_list_loop_decreases (t : Type0) (key : usize)
+  (ls : hashmap_List_t t) : hashmap_List_t t =
   ls
 
diff --git a/tests/fstar/hashmap_on_disk/HashmapMain.Funs.fst b/tests/fstar/hashmap_on_disk/HashmapMain.Funs.fst
index 1c94209c..5f227596 100644
--- a/tests/fstar/hashmap_on_disk/HashmapMain.Funs.fst
+++ b/tests/fstar/hashmap_on_disk/HashmapMain.Funs.fst
@@ -9,529 +9,528 @@ include HashmapMain.Clauses
 #set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
 
 (** [hashmap_main::hashmap::hash_key]: forward function *)
-let hashmap_hash_key_fwd (k : usize) : result usize =
+let hashmap_hash_key (k : usize) : result usize =
   Return k
 
 (** [hashmap_main::hashmap::HashMap::{0}::allocate_slots]: loop 0: forward function *)
-let rec hashmap_hash_map_allocate_slots_loop_fwd
-  (t : Type0) (slots : vec (hashmap_list_t t)) (n : usize) :
-  Tot (result (vec (hashmap_list_t t)))
-  (decreases (hashmap_hash_map_allocate_slots_loop_decreases t slots n))
+let rec hashmap_HashMap_allocate_slots_loop
+  (t : Type0) (slots : alloc_vec_Vec (hashmap_List_t t)) (n : usize) :
+  Tot (result (alloc_vec_Vec (hashmap_List_t t)))
+  (decreases (hashmap_HashMap_allocate_slots_loop_decreases t slots n))
   =
   if n > 0
   then
-    let* slots0 = vec_push_back (hashmap_list_t t) slots HashmapListNil in
+    let* slots0 = alloc_vec_Vec_push (hashmap_List_t t) slots Hashmap_List_Nil
+      in
     let* n0 = usize_sub n 1 in
-    hashmap_hash_map_allocate_slots_loop_fwd t slots0 n0
+    hashmap_HashMap_allocate_slots_loop t slots0 n0
   else Return slots
 
 (** [hashmap_main::hashmap::HashMap::{0}::allocate_slots]: forward function *)
-let hashmap_hash_map_allocate_slots_fwd
-  (t : Type0) (slots : vec (hashmap_list_t t)) (n : usize) :
-  result (vec (hashmap_list_t t))
+let hashmap_HashMap_allocate_slots
+  (t : Type0) (slots : alloc_vec_Vec (hashmap_List_t t)) (n : usize) :
+  result (alloc_vec_Vec (hashmap_List_t t))
   =
-  hashmap_hash_map_allocate_slots_loop_fwd t slots n
+  hashmap_HashMap_allocate_slots_loop t slots n
 
 (** [hashmap_main::hashmap::HashMap::{0}::new_with_capacity]: forward function *)
-let hashmap_hash_map_new_with_capacity_fwd
+let hashmap_HashMap_new_with_capacity
   (t : Type0) (capacity : usize) (max_load_dividend : usize)
   (max_load_divisor : usize) :
-  result (hashmap_hash_map_t t)
+  result (hashmap_HashMap_t t)
   =
-  let v = vec_new (hashmap_list_t t) in
-  let* slots = hashmap_hash_map_allocate_slots_fwd t v capacity in
+  let v = alloc_vec_Vec_new (hashmap_List_t t) in
+  let* slots = hashmap_HashMap_allocate_slots t v capacity in
   let* i = usize_mul capacity max_load_dividend in
   let* i0 = usize_div i max_load_divisor in
   Return
     {
-      hashmap_hash_map_num_entries = 0;
-      hashmap_hash_map_max_load_factor = (max_load_dividend, max_load_divisor);
-      hashmap_hash_map_max_load = i0;
-      hashmap_hash_map_slots = slots
+      num_entries = 0;
+      max_load_factor = (max_load_dividend, max_load_divisor);
+      max_load = i0;
+      slots = slots
     }
 
 (** [hashmap_main::hashmap::HashMap::{0}::new]: forward function *)
-let hashmap_hash_map_new_fwd (t : Type0) : result (hashmap_hash_map_t t) =
-  hashmap_hash_map_new_with_capacity_fwd t 32 4 5
+let hashmap_HashMap_new (t : Type0) : result (hashmap_HashMap_t t) =
+  hashmap_HashMap_new_with_capacity t 32 4 5
 
 (** [hashmap_main::hashmap::HashMap::{0}::clear]: loop 0: merged forward/backward function
     (there is a single backward function, and the forward function returns ()) *)
-let rec hashmap_hash_map_clear_loop_fwd_back
-  (t : Type0) (slots : vec (hashmap_list_t t)) (i : usize) :
-  Tot (result (vec (hashmap_list_t t)))
-  (decreases (hashmap_hash_map_clear_loop_decreases t slots i))
+let rec hashmap_HashMap_clear_loop
+  (t : Type0) (slots : alloc_vec_Vec (hashmap_List_t t)) (i : usize) :
+  Tot (result (alloc_vec_Vec (hashmap_List_t t)))
+  (decreases (hashmap_HashMap_clear_loop_decreases t slots i))
   =
-  let i0 = vec_len (hashmap_list_t t) slots in
+  let i0 = alloc_vec_Vec_len (hashmap_List_t t) slots in
   if i < i0
   then
     let* i1 = usize_add i 1 in
-    let* slots0 = vec_index_mut_back (hashmap_list_t t) slots i HashmapListNil
-      in
-    hashmap_hash_map_clear_loop_fwd_back t slots0 i1
+    let* slots0 =
+      alloc_vec_Vec_index_mut_back (hashmap_List_t t) usize
+        (core_slice_index_usize_coresliceindexSliceIndexInst (hashmap_List_t
+        t)) slots i Hashmap_List_Nil in
+    hashmap_HashMap_clear_loop t slots0 i1
   else Return slots
 
 (** [hashmap_main::hashmap::HashMap::{0}::clear]: merged forward/backward function
     (there is a single backward function, and the forward function returns ()) *)
-let hashmap_hash_map_clear_fwd_back
-  (t : Type0) (self : hashmap_hash_map_t t) : result (hashmap_hash_map_t t) =
-  let* v = hashmap_hash_map_clear_loop_fwd_back t self.hashmap_hash_map_slots 0
-    in
-  Return
-    { self with hashmap_hash_map_num_entries = 0; hashmap_hash_map_slots = v }
+let hashmap_HashMap_clear
+  (t : Type0) (self : hashmap_HashMap_t t) : result (hashmap_HashMap_t t) =
+  let* v = hashmap_HashMap_clear_loop t self.slots 0 in
+  Return { self with num_entries = 0; slots = v }
 
 (** [hashmap_main::hashmap::HashMap::{0}::len]: forward function *)
-let hashmap_hash_map_len_fwd
-  (t : Type0) (self : hashmap_hash_map_t t) : result usize =
-  Return self.hashmap_hash_map_num_entries
+let hashmap_HashMap_len
+  (t : Type0) (self : hashmap_HashMap_t t) : result usize =
+  Return self.num_entries
 
 (** [hashmap_main::hashmap::HashMap::{0}::insert_in_list]: loop 0: forward function *)
-let rec hashmap_hash_map_insert_in_list_loop_fwd
-  (t : Type0) (key : usize) (value : t) (ls : hashmap_list_t t) :
+let rec hashmap_HashMap_insert_in_list_loop
+  (t : Type0) (key : usize) (value : t) (ls : hashmap_List_t t) :
   Tot (result bool)
-  (decreases (hashmap_hash_map_insert_in_list_loop_decreases t key value ls))
+  (decreases (hashmap_HashMap_insert_in_list_loop_decreases t key value ls))
   =
   begin match ls with
-  | HashmapListCons ckey cvalue tl ->
+  | Hashmap_List_Cons ckey cvalue tl ->
     if ckey = key
     then Return false
-    else hashmap_hash_map_insert_in_list_loop_fwd t key value tl
-  | HashmapListNil -> Return true
+    else hashmap_HashMap_insert_in_list_loop t key value tl
+  | Hashmap_List_Nil -> Return true
   end
 
 (** [hashmap_main::hashmap::HashMap::{0}::insert_in_list]: forward function *)
-let hashmap_hash_map_insert_in_list_fwd
-  (t : Type0) (key : usize) (value : t) (ls : hashmap_list_t t) : result bool =
-  hashmap_hash_map_insert_in_list_loop_fwd t key value ls
+let hashmap_HashMap_insert_in_list
+  (t : Type0) (key : usize) (value : t) (ls : hashmap_List_t t) : result bool =
+  hashmap_HashMap_insert_in_list_loop t key value ls
 
 (** [hashmap_main::hashmap::HashMap::{0}::insert_in_list]: loop 0: backward function 0 *)
-let rec hashmap_hash_map_insert_in_list_loop_back
-  (t : Type0) (key : usize) (value : t) (ls : hashmap_list_t t) :
-  Tot (result (hashmap_list_t t))
-  (decreases (hashmap_hash_map_insert_in_list_loop_decreases t key value ls))
+let rec hashmap_HashMap_insert_in_list_loop_back
+  (t : Type0) (key : usize) (value : t) (ls : hashmap_List_t t) :
+  Tot (result (hashmap_List_t t))
+  (decreases (hashmap_HashMap_insert_in_list_loop_decreases t key value ls))
   =
   begin match ls with
-  | HashmapListCons ckey cvalue tl ->
+  | Hashmap_List_Cons ckey cvalue tl ->
     if ckey = key
-    then Return (HashmapListCons ckey value tl)
+    then Return (Hashmap_List_Cons ckey value tl)
     else
-      let* tl0 = hashmap_hash_map_insert_in_list_loop_back t key value tl in
-      Return (HashmapListCons ckey cvalue tl0)
-  | HashmapListNil ->
-    let l = HashmapListNil in Return (HashmapListCons key value l)
+      let* tl0 = hashmap_HashMap_insert_in_list_loop_back t key value tl in
+      Return (Hashmap_List_Cons ckey cvalue tl0)
+  | Hashmap_List_Nil ->
+    let l = Hashmap_List_Nil in Return (Hashmap_List_Cons key value l)
   end
 
 (** [hashmap_main::hashmap::HashMap::{0}::insert_in_list]: backward function 0 *)
-let hashmap_hash_map_insert_in_list_back
-  (t : Type0) (key : usize) (value : t) (ls : hashmap_list_t t) :
-  result (hashmap_list_t t)
+let hashmap_HashMap_insert_in_list_back
+  (t : Type0) (key : usize) (value : t) (ls : hashmap_List_t t) :
+  result (hashmap_List_t t)
   =
-  hashmap_hash_map_insert_in_list_loop_back t key value ls
+  hashmap_HashMap_insert_in_list_loop_back t key value ls
 
 (** [hashmap_main::hashmap::HashMap::{0}::insert_no_resize]: merged forward/backward function
     (there is a single backward function, and the forward function returns ()) *)
-let hashmap_hash_map_insert_no_resize_fwd_back
-  (t : Type0) (self : hashmap_hash_map_t t) (key : usize) (value : t) :
-  result (hashmap_hash_map_t t)
+let hashmap_HashMap_insert_no_resize
+  (t : Type0) (self : hashmap_HashMap_t t) (key : usize) (value : t) :
+  result (hashmap_HashMap_t t)
   =
-  let* hash = hashmap_hash_key_fwd key in
-  let i = vec_len (hashmap_list_t t) self.hashmap_hash_map_slots in
+  let* hash = hashmap_hash_key key in
+  let i = alloc_vec_Vec_len (hashmap_List_t t) self.slots in
   let* hash_mod = usize_rem hash i in
   let* l =
-    vec_index_mut_fwd (hashmap_list_t t) self.hashmap_hash_map_slots hash_mod
-    in
-  let* inserted = hashmap_hash_map_insert_in_list_fwd t key value l in
+    alloc_vec_Vec_index_mut (hashmap_List_t t) usize
+      (core_slice_index_usize_coresliceindexSliceIndexInst (hashmap_List_t t))
+      self.slots hash_mod in
+  let* inserted = hashmap_HashMap_insert_in_list t key value l in
   if inserted
   then
-    let* i0 = usize_add self.hashmap_hash_map_num_entries 1 in
-    let* l0 = hashmap_hash_map_insert_in_list_back t key value l in
+    let* i0 = usize_add self.num_entries 1 in
+    let* l0 = hashmap_HashMap_insert_in_list_back t key value l in
     let* v =
-      vec_index_mut_back (hashmap_list_t t) self.hashmap_hash_map_slots
-        hash_mod l0 in
-    Return
-      { self with hashmap_hash_map_num_entries = i0; hashmap_hash_map_slots = v
-      }
+      alloc_vec_Vec_index_mut_back (hashmap_List_t t) usize
+        (core_slice_index_usize_coresliceindexSliceIndexInst (hashmap_List_t
+        t)) self.slots hash_mod l0 in
+    Return { self with num_entries = i0; slots = v }
   else
-    let* l0 = hashmap_hash_map_insert_in_list_back t key value l in
+    let* l0 = hashmap_HashMap_insert_in_list_back t key value l in
     let* v =
-      vec_index_mut_back (hashmap_list_t t) self.hashmap_hash_map_slots
-        hash_mod l0 in
-    Return { self with hashmap_hash_map_slots = v }
-
-(** [core::num::u32::{8}::MAX] *)
-let core_num_u32_max_body : result u32 = Return 4294967295
-let core_num_u32_max_c : u32 = eval_global core_num_u32_max_body
+      alloc_vec_Vec_index_mut_back (hashmap_List_t t) usize
+        (core_slice_index_usize_coresliceindexSliceIndexInst (hashmap_List_t
+        t)) self.slots hash_mod l0 in
+    Return { self with slots = v }
 
 (** [hashmap_main::hashmap::HashMap::{0}::move_elements_from_list]: loop 0: merged forward/backward function
     (there is a single backward function, and the forward function returns ()) *)
-let rec hashmap_hash_map_move_elements_from_list_loop_fwd_back
-  (t : Type0) (ntable : hashmap_hash_map_t t) (ls : hashmap_list_t t) :
-  Tot (result (hashmap_hash_map_t t))
+let rec hashmap_HashMap_move_elements_from_list_loop
+  (t : Type0) (ntable : hashmap_HashMap_t t) (ls : hashmap_List_t t) :
+  Tot (result (hashmap_HashMap_t t))
   (decreases (
-    hashmap_hash_map_move_elements_from_list_loop_decreases t ntable ls))
+    hashmap_HashMap_move_elements_from_list_loop_decreases t ntable ls))
   =
   begin match ls with
-  | HashmapListCons k v tl ->
-    let* ntable0 = hashmap_hash_map_insert_no_resize_fwd_back t ntable k v in
-    hashmap_hash_map_move_elements_from_list_loop_fwd_back t ntable0 tl
-  | HashmapListNil -> Return ntable
+  | Hashmap_List_Cons k v tl ->
+    let* ntable0 = hashmap_HashMap_insert_no_resize t ntable k v in
+    hashmap_HashMap_move_elements_from_list_loop t ntable0 tl
+  | Hashmap_List_Nil -> Return ntable
   end
 
 (** [hashmap_main::hashmap::HashMap::{0}::move_elements_from_list]: merged forward/backward function
     (there is a single backward function, and the forward function returns ()) *)
-let hashmap_hash_map_move_elements_from_list_fwd_back
-  (t : Type0) (ntable : hashmap_hash_map_t t) (ls : hashmap_list_t t) :
-  result (hashmap_hash_map_t t)
+let hashmap_HashMap_move_elements_from_list
+  (t : Type0) (ntable : hashmap_HashMap_t t) (ls : hashmap_List_t t) :
+  result (hashmap_HashMap_t t)
   =
-  hashmap_hash_map_move_elements_from_list_loop_fwd_back t ntable ls
+  hashmap_HashMap_move_elements_from_list_loop t ntable ls
 
 (** [hashmap_main::hashmap::HashMap::{0}::move_elements]: loop 0: merged forward/backward function
     (there is a single backward function, and the forward function returns ()) *)
-let rec hashmap_hash_map_move_elements_loop_fwd_back
-  (t : Type0) (ntable : hashmap_hash_map_t t) (slots : vec (hashmap_list_t t))
-  (i : usize) :
-  Tot (result ((hashmap_hash_map_t t) & (vec (hashmap_list_t t))))
-  (decreases (hashmap_hash_map_move_elements_loop_decreases t ntable slots i))
+let rec hashmap_HashMap_move_elements_loop
+  (t : Type0) (ntable : hashmap_HashMap_t t)
+  (slots : alloc_vec_Vec (hashmap_List_t t)) (i : usize) :
+  Tot (result ((hashmap_HashMap_t t) & (alloc_vec_Vec (hashmap_List_t t))))
+  (decreases (hashmap_HashMap_move_elements_loop_decreases t ntable slots i))
   =
-  let i0 = vec_len (hashmap_list_t t) slots in
+  let i0 = alloc_vec_Vec_len (hashmap_List_t t) slots in
   if i < i0
   then
-    let* l = vec_index_mut_fwd (hashmap_list_t t) slots i in
-    let ls = mem_replace_fwd (hashmap_list_t t) l HashmapListNil in
-    let* ntable0 =
-      hashmap_hash_map_move_elements_from_list_fwd_back t ntable ls in
+    let* l =
+      alloc_vec_Vec_index_mut (hashmap_List_t t) usize
+        (core_slice_index_usize_coresliceindexSliceIndexInst (hashmap_List_t
+        t)) slots i in
+    let ls = core_mem_replace (hashmap_List_t t) l Hashmap_List_Nil in
+    let* ntable0 = hashmap_HashMap_move_elements_from_list t ntable ls in
     let* i1 = usize_add i 1 in
-    let l0 = mem_replace_back (hashmap_list_t t) l HashmapListNil in
-    let* slots0 = vec_index_mut_back (hashmap_list_t t) slots i l0 in
-    hashmap_hash_map_move_elements_loop_fwd_back t ntable0 slots0 i1
+    let l0 = core_mem_replace_back (hashmap_List_t t) l Hashmap_List_Nil in
+    let* slots0 =
+      alloc_vec_Vec_index_mut_back (hashmap_List_t t) usize
+        (core_slice_index_usize_coresliceindexSliceIndexInst (hashmap_List_t
+        t)) slots i l0 in
+    hashmap_HashMap_move_elements_loop t ntable0 slots0 i1
   else Return (ntable, slots)
 
 (** [hashmap_main::hashmap::HashMap::{0}::move_elements]: merged forward/backward function
     (there is a single backward function, and the forward function returns ()) *)
-let hashmap_hash_map_move_elements_fwd_back
-  (t : Type0) (ntable : hashmap_hash_map_t t) (slots : vec (hashmap_list_t t))
-  (i : usize) :
-  result ((hashmap_hash_map_t t) & (vec (hashmap_list_t t)))
+let hashmap_HashMap_move_elements
+  (t : Type0) (ntable : hashmap_HashMap_t t)
+  (slots : alloc_vec_Vec (hashmap_List_t t)) (i : usize) :
+  result ((hashmap_HashMap_t t) & (alloc_vec_Vec (hashmap_List_t t)))
   =
-  hashmap_hash_map_move_elements_loop_fwd_back t ntable slots i
+  hashmap_HashMap_move_elements_loop t ntable slots i
 
 (** [hashmap_main::hashmap::HashMap::{0}::try_resize]: merged forward/backward function
     (there is a single backward function, and the forward function returns ()) *)
-let hashmap_hash_map_try_resize_fwd_back
-  (t : Type0) (self : hashmap_hash_map_t t) : result (hashmap_hash_map_t t) =
-  let* max_usize = scalar_cast U32 Usize core_num_u32_max_c in
-  let capacity = vec_len (hashmap_list_t t) self.hashmap_hash_map_slots in
+let hashmap_HashMap_try_resize
+  (t : Type0) (self : hashmap_HashMap_t t) : result (hashmap_HashMap_t t) =
+  let* max_usize = scalar_cast U32 Usize core_u32_max in
+  let capacity = alloc_vec_Vec_len (hashmap_List_t t) self.slots in
   let* n1 = usize_div max_usize 2 in
-  let (i, i0) = self.hashmap_hash_map_max_load_factor in
+  let (i, i0) = self.max_load_factor in
   let* i1 = usize_div n1 i in
   if capacity <= i1
   then
     let* i2 = usize_mul capacity 2 in
-    let* ntable = hashmap_hash_map_new_with_capacity_fwd t i2 i i0 in
-    let* (ntable0, _) =
-      hashmap_hash_map_move_elements_fwd_back t ntable
-        self.hashmap_hash_map_slots 0 in
+    let* ntable = hashmap_HashMap_new_with_capacity t i2 i i0 in
+    let* (ntable0, _) = hashmap_HashMap_move_elements t ntable self.slots 0 in
     Return
-      {
-        ntable0
-          with
-          hashmap_hash_map_num_entries = self.hashmap_hash_map_num_entries;
-          hashmap_hash_map_max_load_factor = (i, i0)
+      { ntable0 with num_entries = self.num_entries; max_load_factor = (i, i0)
       }
-  else Return { self with hashmap_hash_map_max_load_factor = (i, i0) }
+  else Return { self with max_load_factor = (i, i0) }
 
 (** [hashmap_main::hashmap::HashMap::{0}::insert]: merged forward/backward function
     (there is a single backward function, and the forward function returns ()) *)
-let hashmap_hash_map_insert_fwd_back
-  (t : Type0) (self : hashmap_hash_map_t t) (key : usize) (value : t) :
-  result (hashmap_hash_map_t t)
+let hashmap_HashMap_insert
+  (t : Type0) (self : hashmap_HashMap_t t) (key : usize) (value : t) :
+  result (hashmap_HashMap_t t)
   =
-  let* self0 = hashmap_hash_map_insert_no_resize_fwd_back t self key value in
-  let* i = hashmap_hash_map_len_fwd t self0 in
-  if i > self0.hashmap_hash_map_max_load
-  then hashmap_hash_map_try_resize_fwd_back t self0
+  let* self0 = hashmap_HashMap_insert_no_resize t self key value in
+  let* i = hashmap_HashMap_len t self0 in
+  if i > self0.max_load
+  then hashmap_HashMap_try_resize t self0
   else Return self0
 
 (** [hashmap_main::hashmap::HashMap::{0}::contains_key_in_list]: loop 0: forward function *)
-let rec hashmap_hash_map_contains_key_in_list_loop_fwd
-  (t : Type0) (key : usize) (ls : hashmap_list_t t) :
+let rec hashmap_HashMap_contains_key_in_list_loop
+  (t : Type0) (key : usize) (ls : hashmap_List_t t) :
   Tot (result bool)
-  (decreases (hashmap_hash_map_contains_key_in_list_loop_decreases t key ls))
+  (decreases (hashmap_HashMap_contains_key_in_list_loop_decreases t key ls))
   =
   begin match ls with
-  | HashmapListCons ckey x tl ->
+  | Hashmap_List_Cons ckey x tl ->
     if ckey = key
     then Return true
-    else hashmap_hash_map_contains_key_in_list_loop_fwd t key tl
-  | HashmapListNil -> Return false
+    else hashmap_HashMap_contains_key_in_list_loop t key tl
+  | Hashmap_List_Nil -> Return false
   end
 
 (** [hashmap_main::hashmap::HashMap::{0}::contains_key_in_list]: forward function *)
-let hashmap_hash_map_contains_key_in_list_fwd
-  (t : Type0) (key : usize) (ls : hashmap_list_t t) : result bool =
-  hashmap_hash_map_contains_key_in_list_loop_fwd t key ls
+let hashmap_HashMap_contains_key_in_list
+  (t : Type0) (key : usize) (ls : hashmap_List_t t) : result bool =
+  hashmap_HashMap_contains_key_in_list_loop t key ls
 
 (** [hashmap_main::hashmap::HashMap::{0}::contains_key]: forward function *)
-let hashmap_hash_map_contains_key_fwd
-  (t : Type0) (self : hashmap_hash_map_t t) (key : usize) : result bool =
-  let* hash = hashmap_hash_key_fwd key in
-  let i = vec_len (hashmap_list_t t) self.hashmap_hash_map_slots in
+let hashmap_HashMap_contains_key
+  (t : Type0) (self : hashmap_HashMap_t t) (key : usize) : result bool =
+  let* hash = hashmap_hash_key key in
+  let i = alloc_vec_Vec_len (hashmap_List_t t) self.slots in
   let* hash_mod = usize_rem hash i in
   let* l =
-    vec_index_fwd (hashmap_list_t t) self.hashmap_hash_map_slots hash_mod in
-  hashmap_hash_map_contains_key_in_list_fwd t key l
+    alloc_vec_Vec_index (hashmap_List_t t) usize
+      (core_slice_index_usize_coresliceindexSliceIndexInst (hashmap_List_t t))
+      self.slots hash_mod in
+  hashmap_HashMap_contains_key_in_list t key l
 
 (** [hashmap_main::hashmap::HashMap::{0}::get_in_list]: loop 0: forward function *)
-let rec hashmap_hash_map_get_in_list_loop_fwd
-  (t : Type0) (key : usize) (ls : hashmap_list_t t) :
+let rec hashmap_HashMap_get_in_list_loop
+  (t : Type0) (key : usize) (ls : hashmap_List_t t) :
   Tot (result t)
-  (decreases (hashmap_hash_map_get_in_list_loop_decreases t key ls))
+  (decreases (hashmap_HashMap_get_in_list_loop_decreases t key ls))
   =
   begin match ls with
-  | HashmapListCons ckey cvalue tl ->
+  | Hashmap_List_Cons ckey cvalue tl ->
     if ckey = key
     then Return cvalue
-    else hashmap_hash_map_get_in_list_loop_fwd t key tl
-  | HashmapListNil -> Fail Failure
+    else hashmap_HashMap_get_in_list_loop t key tl
+  | Hashmap_List_Nil -> Fail Failure
   end
 
 (** [hashmap_main::hashmap::HashMap::{0}::get_in_list]: forward function *)
-let hashmap_hash_map_get_in_list_fwd
-  (t : Type0) (key : usize) (ls : hashmap_list_t t) : result t =
-  hashmap_hash_map_get_in_list_loop_fwd t key ls
+let hashmap_HashMap_get_in_list
+  (t : Type0) (key : usize) (ls : hashmap_List_t t) : result t =
+  hashmap_HashMap_get_in_list_loop t key ls
 
 (** [hashmap_main::hashmap::HashMap::{0}::get]: forward function *)
-let hashmap_hash_map_get_fwd
-  (t : Type0) (self : hashmap_hash_map_t t) (key : usize) : result t =
-  let* hash = hashmap_hash_key_fwd key in
-  let i = vec_len (hashmap_list_t t) self.hashmap_hash_map_slots in
+let hashmap_HashMap_get
+  (t : Type0) (self : hashmap_HashMap_t t) (key : usize) : result t =
+  let* hash = hashmap_hash_key key in
+  let i = alloc_vec_Vec_len (hashmap_List_t t) self.slots in
   let* hash_mod = usize_rem hash i in
   let* l =
-    vec_index_fwd (hashmap_list_t t) self.hashmap_hash_map_slots hash_mod in
-  hashmap_hash_map_get_in_list_fwd t key l
+    alloc_vec_Vec_index (hashmap_List_t t) usize
+      (core_slice_index_usize_coresliceindexSliceIndexInst (hashmap_List_t t))
+      self.slots hash_mod in
+  hashmap_HashMap_get_in_list t key l
 
 (** [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list]: loop 0: forward function *)
-let rec hashmap_hash_map_get_mut_in_list_loop_fwd
-  (t : Type0) (ls : hashmap_list_t t) (key : usize) :
+let rec hashmap_HashMap_get_mut_in_list_loop
+  (t : Type0) (ls : hashmap_List_t t) (key : usize) :
   Tot (result t)
-  (decreases (hashmap_hash_map_get_mut_in_list_loop_decreases t ls key))
+  (decreases (hashmap_HashMap_get_mut_in_list_loop_decreases t ls key))
   =
   begin match ls with
-  | HashmapListCons ckey cvalue tl ->
+  | Hashmap_List_Cons ckey cvalue tl ->
     if ckey = key
     then Return cvalue
-    else hashmap_hash_map_get_mut_in_list_loop_fwd t tl key
-  | HashmapListNil -> Fail Failure
+    else hashmap_HashMap_get_mut_in_list_loop t tl key
+  | Hashmap_List_Nil -> Fail Failure
   end
 
 (** [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list]: forward function *)
-let hashmap_hash_map_get_mut_in_list_fwd
-  (t : Type0) (ls : hashmap_list_t t) (key : usize) : result t =
-  hashmap_hash_map_get_mut_in_list_loop_fwd t ls key
+let hashmap_HashMap_get_mut_in_list
+  (t : Type0) (ls : hashmap_List_t t) (key : usize) : result t =
+  hashmap_HashMap_get_mut_in_list_loop t ls key
 
 (** [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list]: loop 0: backward function 0 *)
-let rec hashmap_hash_map_get_mut_in_list_loop_back
-  (t : Type0) (ls : hashmap_list_t t) (key : usize) (ret : t) :
-  Tot (result (hashmap_list_t t))
-  (decreases (hashmap_hash_map_get_mut_in_list_loop_decreases t ls key))
+let rec hashmap_HashMap_get_mut_in_list_loop_back
+  (t : Type0) (ls : hashmap_List_t t) (key : usize) (ret : t) :
+  Tot (result (hashmap_List_t t))
+  (decreases (hashmap_HashMap_get_mut_in_list_loop_decreases t ls key))
   =
   begin match ls with
-  | HashmapListCons ckey cvalue tl ->
+  | Hashmap_List_Cons ckey cvalue tl ->
     if ckey = key
-    then Return (HashmapListCons ckey ret tl)
+    then Return (Hashmap_List_Cons ckey ret tl)
     else
-      let* tl0 = hashmap_hash_map_get_mut_in_list_loop_back t tl key ret in
-      Return (HashmapListCons ckey cvalue tl0)
-  | HashmapListNil -> Fail Failure
+      let* tl0 = hashmap_HashMap_get_mut_in_list_loop_back t tl key ret in
+      Return (Hashmap_List_Cons ckey cvalue tl0)
+  | Hashmap_List_Nil -> Fail Failure
   end
 
 (** [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list]: backward function 0 *)
-let hashmap_hash_map_get_mut_in_list_back
-  (t : Type0) (ls : hashmap_list_t t) (key : usize) (ret : t) :
-  result (hashmap_list_t t)
+let hashmap_HashMap_get_mut_in_list_back
+  (t : Type0) (ls : hashmap_List_t t) (key : usize) (ret : t) :
+  result (hashmap_List_t t)
   =
-  hashmap_hash_map_get_mut_in_list_loop_back t ls key ret
+  hashmap_HashMap_get_mut_in_list_loop_back t ls key ret
 
 (** [hashmap_main::hashmap::HashMap::{0}::get_mut]: forward function *)
-let hashmap_hash_map_get_mut_fwd
-  (t : Type0) (self : hashmap_hash_map_t t) (key : usize) : result t =
-  let* hash = hashmap_hash_key_fwd key in
-  let i = vec_len (hashmap_list_t t) self.hashmap_hash_map_slots in
+let hashmap_HashMap_get_mut
+  (t : Type0) (self : hashmap_HashMap_t t) (key : usize) : result t =
+  let* hash = hashmap_hash_key key in
+  let i = alloc_vec_Vec_len (hashmap_List_t t) self.slots in
   let* hash_mod = usize_rem hash i in
   let* l =
-    vec_index_mut_fwd (hashmap_list_t t) self.hashmap_hash_map_slots hash_mod
-    in
-  hashmap_hash_map_get_mut_in_list_fwd t l key
+    alloc_vec_Vec_index_mut (hashmap_List_t t) usize
+      (core_slice_index_usize_coresliceindexSliceIndexInst (hashmap_List_t t))
+      self.slots hash_mod in
+  hashmap_HashMap_get_mut_in_list t l key
 
 (** [hashmap_main::hashmap::HashMap::{0}::get_mut]: backward function 0 *)
-let hashmap_hash_map_get_mut_back
-  (t : Type0) (self : hashmap_hash_map_t t) (key : usize) (ret : t) :
-  result (hashmap_hash_map_t t)
+let hashmap_HashMap_get_mut_back
+  (t : Type0) (self : hashmap_HashMap_t t) (key : usize) (ret : t) :
+  result (hashmap_HashMap_t t)
   =
-  let* hash = hashmap_hash_key_fwd key in
-  let i = vec_len (hashmap_list_t t) self.hashmap_hash_map_slots in
+  let* hash = hashmap_hash_key key in
+  let i = alloc_vec_Vec_len (hashmap_List_t t) self.slots in
   let* hash_mod = usize_rem hash i in
   let* l =
-    vec_index_mut_fwd (hashmap_list_t t) self.hashmap_hash_map_slots hash_mod
-    in
-  let* l0 = hashmap_hash_map_get_mut_in_list_back t l key ret in
+    alloc_vec_Vec_index_mut (hashmap_List_t t) usize
+      (core_slice_index_usize_coresliceindexSliceIndexInst (hashmap_List_t t))
+      self.slots hash_mod in
+  let* l0 = hashmap_HashMap_get_mut_in_list_back t l key ret in
   let* v =
-    vec_index_mut_back (hashmap_list_t t) self.hashmap_hash_map_slots hash_mod
-      l0 in
-  Return { self with hashmap_hash_map_slots = v }
+    alloc_vec_Vec_index_mut_back (hashmap_List_t t) usize
+      (core_slice_index_usize_coresliceindexSliceIndexInst (hashmap_List_t t))
+      self.slots hash_mod l0 in
+  Return { self with slots = v }
 
 (** [hashmap_main::hashmap::HashMap::{0}::remove_from_list]: loop 0: forward function *)
-let rec hashmap_hash_map_remove_from_list_loop_fwd
-  (t : Type0) (key : usize) (ls : hashmap_list_t t) :
+let rec hashmap_HashMap_remove_from_list_loop
+  (t : Type0) (key : usize) (ls : hashmap_List_t t) :
   Tot (result (option t))
-  (decreases (hashmap_hash_map_remove_from_list_loop_decreases t key ls))
+  (decreases (hashmap_HashMap_remove_from_list_loop_decreases t key ls))
   =
   begin match ls with
-  | HashmapListCons ckey x tl ->
+  | Hashmap_List_Cons ckey x tl ->
     if ckey = key
     then
       let mv_ls =
-        mem_replace_fwd (hashmap_list_t t) (HashmapListCons ckey x tl)
-          HashmapListNil in
+        core_mem_replace (hashmap_List_t t) (Hashmap_List_Cons ckey x tl)
+          Hashmap_List_Nil in
       begin match mv_ls with
-      | HashmapListCons i cvalue tl0 -> Return (Some cvalue)
-      | HashmapListNil -> Fail Failure
+      | Hashmap_List_Cons i cvalue tl0 -> Return (Some cvalue)
+      | Hashmap_List_Nil -> Fail Failure
       end
-    else hashmap_hash_map_remove_from_list_loop_fwd t key tl
-  | HashmapListNil -> Return None
+    else hashmap_HashMap_remove_from_list_loop t key tl
+  | Hashmap_List_Nil -> Return None
   end
 
 (** [hashmap_main::hashmap::HashMap::{0}::remove_from_list]: forward function *)
-let hashmap_hash_map_remove_from_list_fwd
-  (t : Type0) (key : usize) (ls : hashmap_list_t t) : result (option t) =
-  hashmap_hash_map_remove_from_list_loop_fwd t key ls
+let hashmap_HashMap_remove_from_list
+  (t : Type0) (key : usize) (ls : hashmap_List_t t) : result (option t) =
+  hashmap_HashMap_remove_from_list_loop t key ls
 
 (** [hashmap_main::hashmap::HashMap::{0}::remove_from_list]: loop 0: backward function 1 *)
-let rec hashmap_hash_map_remove_from_list_loop_back
-  (t : Type0) (key : usize) (ls : hashmap_list_t t) :
-  Tot (result (hashmap_list_t t))
-  (decreases (hashmap_hash_map_remove_from_list_loop_decreases t key ls))
+let rec hashmap_HashMap_remove_from_list_loop_back
+  (t : Type0) (key : usize) (ls : hashmap_List_t t) :
+  Tot (result (hashmap_List_t t))
+  (decreases (hashmap_HashMap_remove_from_list_loop_decreases t key ls))
   =
   begin match ls with
-  | HashmapListCons ckey x tl ->
+  | Hashmap_List_Cons ckey x tl ->
     if ckey = key
     then
       let mv_ls =
-        mem_replace_fwd (hashmap_list_t t) (HashmapListCons ckey x tl)
-          HashmapListNil in
+        core_mem_replace (hashmap_List_t t) (Hashmap_List_Cons ckey x tl)
+          Hashmap_List_Nil in
       begin match mv_ls with
-      | HashmapListCons i cvalue tl0 -> Return tl0
-      | HashmapListNil -> Fail Failure
+      | Hashmap_List_Cons i cvalue tl0 -> Return tl0
+      | Hashmap_List_Nil -> Fail Failure
       end
     else
-      let* tl0 = hashmap_hash_map_remove_from_list_loop_back t key tl in
-      Return (HashmapListCons ckey x tl0)
-  | HashmapListNil -> Return HashmapListNil
+      let* tl0 = hashmap_HashMap_remove_from_list_loop_back t key tl in
+      Return (Hashmap_List_Cons ckey x tl0)
+  | Hashmap_List_Nil -> Return Hashmap_List_Nil
   end
 
 (** [hashmap_main::hashmap::HashMap::{0}::remove_from_list]: backward function 1 *)
-let hashmap_hash_map_remove_from_list_back
-  (t : Type0) (key : usize) (ls : hashmap_list_t t) :
-  result (hashmap_list_t t)
+let hashmap_HashMap_remove_from_list_back
+  (t : Type0) (key : usize) (ls : hashmap_List_t t) :
+  result (hashmap_List_t t)
   =
-  hashmap_hash_map_remove_from_list_loop_back t key ls
+  hashmap_HashMap_remove_from_list_loop_back t key ls
 
 (** [hashmap_main::hashmap::HashMap::{0}::remove]: forward function *)
-let hashmap_hash_map_remove_fwd
-  (t : Type0) (self : hashmap_hash_map_t t) (key : usize) : result (option t) =
-  let* hash = hashmap_hash_key_fwd key in
-  let i = vec_len (hashmap_list_t t) self.hashmap_hash_map_slots in
+let hashmap_HashMap_remove
+  (t : Type0) (self : hashmap_HashMap_t t) (key : usize) : result (option t) =
+  let* hash = hashmap_hash_key key in
+  let i = alloc_vec_Vec_len (hashmap_List_t t) self.slots in
   let* hash_mod = usize_rem hash i in
   let* l =
-    vec_index_mut_fwd (hashmap_list_t t) self.hashmap_hash_map_slots hash_mod
-    in
-  let* x = hashmap_hash_map_remove_from_list_fwd t key l in
+    alloc_vec_Vec_index_mut (hashmap_List_t t) usize
+      (core_slice_index_usize_coresliceindexSliceIndexInst (hashmap_List_t t))
+      self.slots hash_mod in
+  let* x = hashmap_HashMap_remove_from_list t key l in
   begin match x with
   | None -> Return None
-  | Some x0 ->
-    let* _ = usize_sub self.hashmap_hash_map_num_entries 1 in Return (Some x0)
+  | Some x0 -> let* _ = usize_sub self.num_entries 1 in Return (Some x0)
   end
 
 (** [hashmap_main::hashmap::HashMap::{0}::remove]: backward function 0 *)
-let hashmap_hash_map_remove_back
-  (t : Type0) (self : hashmap_hash_map_t t) (key : usize) :
-  result (hashmap_hash_map_t t)
+let hashmap_HashMap_remove_back
+  (t : Type0) (self : hashmap_HashMap_t t) (key : usize) :
+  result (hashmap_HashMap_t t)
   =
-  let* hash = hashmap_hash_key_fwd key in
-  let i = vec_len (hashmap_list_t t) self.hashmap_hash_map_slots in
+  let* hash = hashmap_hash_key key in
+  let i = alloc_vec_Vec_len (hashmap_List_t t) self.slots in
   let* hash_mod = usize_rem hash i in
   let* l =
-    vec_index_mut_fwd (hashmap_list_t t) self.hashmap_hash_map_slots hash_mod
-    in
-  let* x = hashmap_hash_map_remove_from_list_fwd t key l in
+    alloc_vec_Vec_index_mut (hashmap_List_t t) usize
+      (core_slice_index_usize_coresliceindexSliceIndexInst (hashmap_List_t t))
+      self.slots hash_mod in
+  let* x = hashmap_HashMap_remove_from_list t key l in
   begin match x with
   | None ->
-    let* l0 = hashmap_hash_map_remove_from_list_back t key l in
+    let* l0 = hashmap_HashMap_remove_from_list_back t key l in
     let* v =
-      vec_index_mut_back (hashmap_list_t t) self.hashmap_hash_map_slots
-        hash_mod l0 in
-    Return { self with hashmap_hash_map_slots = v }
+      alloc_vec_Vec_index_mut_back (hashmap_List_t t) usize
+        (core_slice_index_usize_coresliceindexSliceIndexInst (hashmap_List_t
+        t)) self.slots hash_mod l0 in
+    Return { self with slots = v }
   | Some x0 ->
-    let* i0 = usize_sub self.hashmap_hash_map_num_entries 1 in
-    let* l0 = hashmap_hash_map_remove_from_list_back t key l in
+    let* i0 = usize_sub self.num_entries 1 in
+    let* l0 = hashmap_HashMap_remove_from_list_back t key l in
     let* v =
-      vec_index_mut_back (hashmap_list_t t) self.hashmap_hash_map_slots
-        hash_mod l0 in
-    Return
-      { self with hashmap_hash_map_num_entries = i0; hashmap_hash_map_slots = v
-      }
+      alloc_vec_Vec_index_mut_back (hashmap_List_t t) usize
+        (core_slice_index_usize_coresliceindexSliceIndexInst (hashmap_List_t
+        t)) self.slots hash_mod l0 in
+    Return { self with num_entries = i0; slots = v }
   end
 
 (** [hashmap_main::hashmap::test1]: forward function *)
-let hashmap_test1_fwd : result unit =
-  let* hm = hashmap_hash_map_new_fwd u64 in
-  let* hm0 = hashmap_hash_map_insert_fwd_back u64 hm 0 42 in
-  let* hm1 = hashmap_hash_map_insert_fwd_back u64 hm0 128 18 in
-  let* hm2 = hashmap_hash_map_insert_fwd_back u64 hm1 1024 138 in
-  let* hm3 = hashmap_hash_map_insert_fwd_back u64 hm2 1056 256 in
-  let* i = hashmap_hash_map_get_fwd u64 hm3 128 in
+let hashmap_test1 : result unit =
+  let* hm = hashmap_HashMap_new u64 in
+  let* hm0 = hashmap_HashMap_insert u64 hm 0 42 in
+  let* hm1 = hashmap_HashMap_insert u64 hm0 128 18 in
+  let* hm2 = hashmap_HashMap_insert u64 hm1 1024 138 in
+  let* hm3 = hashmap_HashMap_insert u64 hm2 1056 256 in
+  let* i = hashmap_HashMap_get u64 hm3 128 in
   if not (i = 18)
   then Fail Failure
   else
-    let* hm4 = hashmap_hash_map_get_mut_back u64 hm3 1024 56 in
-    let* i0 = hashmap_hash_map_get_fwd u64 hm4 1024 in
+    let* hm4 = hashmap_HashMap_get_mut_back u64 hm3 1024 56 in
+    let* i0 = hashmap_HashMap_get u64 hm4 1024 in
     if not (i0 = 56)
     then Fail Failure
     else
-      let* x = hashmap_hash_map_remove_fwd u64 hm4 1024 in
+      let* x = hashmap_HashMap_remove u64 hm4 1024 in
       begin match x with
       | None -> Fail Failure
       | Some x0 ->
         if not (x0 = 56)
         then Fail Failure
         else
-          let* hm5 = hashmap_hash_map_remove_back u64 hm4 1024 in
-          let* i1 = hashmap_hash_map_get_fwd u64 hm5 0 in
+          let* hm5 = hashmap_HashMap_remove_back u64 hm4 1024 in
+          let* i1 = hashmap_HashMap_get u64 hm5 0 in
           if not (i1 = 42)
           then Fail Failure
           else
-            let* i2 = hashmap_hash_map_get_fwd u64 hm5 128 in
+            let* i2 = hashmap_HashMap_get u64 hm5 128 in
             if not (i2 = 18)
             then Fail Failure
             else
-              let* i3 = hashmap_hash_map_get_fwd u64 hm5 1056 in
+              let* i3 = hashmap_HashMap_get u64 hm5 1056 in
               if not (i3 = 256) then Fail Failure else Return ()
       end
 
-(** Unit test for [hashmap_main::hashmap::test1] *)
-let _ = assert_norm (hashmap_test1_fwd = Return ())
-
 (** [hashmap_main::insert_on_disk]: forward function *)
-let insert_on_disk_fwd
+let insert_on_disk
   (key : usize) (value : u64) (st : state) : result (state & unit) =
-  let* (st0, hm) = hashmap_utils_deserialize_fwd st in
-  let* hm0 = hashmap_hash_map_insert_fwd_back u64 hm key value in
-  let* (st1, _) = hashmap_utils_serialize_fwd hm0 st0 in
+  let* (st0, hm) = hashmap_utils_deserialize st in
+  let* hm0 = hashmap_HashMap_insert u64 hm key value in
+  let* (st1, _) = hashmap_utils_serialize hm0 st0 in
   Return (st1, ())
 
 (** [hashmap_main::main]: forward function *)
-let main_fwd : result unit =
+let main : result unit =
   Return ()
 
-(** Unit test for [hashmap_main::main] *)
-let _ = assert_norm (main_fwd = Return ())
-
diff --git a/tests/fstar/hashmap_on_disk/HashmapMain.Opaque.fsti b/tests/fstar/hashmap_on_disk/HashmapMain.Opaque.fsti
index 78a6c3ba..d6cecf36 100644
--- a/tests/fstar/hashmap_on_disk/HashmapMain.Opaque.fsti
+++ b/tests/fstar/hashmap_on_disk/HashmapMain.Opaque.fsti
@@ -7,10 +7,10 @@ include HashmapMain.Types
 #set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
 
 (** [hashmap_main::hashmap_utils::deserialize]: forward function *)
-val hashmap_utils_deserialize_fwd
-  : state -> result (state & (hashmap_hash_map_t u64))
+val hashmap_utils_deserialize
+  : state -> result (state & (hashmap_HashMap_t u64))
 
 (** [hashmap_main::hashmap_utils::serialize]: forward function *)
-val hashmap_utils_serialize_fwd
-  : hashmap_hash_map_t u64 -> state -> result (state & unit)
+val hashmap_utils_serialize
+  : hashmap_HashMap_t u64 -> state -> result (state & unit)
 
diff --git a/tests/fstar/hashmap_on_disk/HashmapMain.Properties.fst b/tests/fstar/hashmap_on_disk/HashmapMain.Properties.fst
index 106fe05a..358df29e 100644
--- a/tests/fstar/hashmap_on_disk/HashmapMain.Properties.fst
+++ b/tests/fstar/hashmap_on_disk/HashmapMain.Properties.fst
@@ -13,36 +13,36 @@ open HashmapMain.Funs
 
 /// [state_v] gives us the hash map currently stored on disk
 assume
-val state_v : state -> hashmap_hash_map_t u64
+val state_v : state -> hashmap_HashMap_t u64
 
 /// [serialize] updates the hash map stored on disk
 assume
-val serialize_lem (hm : hashmap_hash_map_t u64) (st : state) : Lemma (
-  match hashmap_utils_serialize_fwd hm st with
+val serialize_lem (hm : hashmap_HashMap_t u64) (st : state) : Lemma (
+  match hashmap_utils_serialize hm st with
   | Fail _ -> True
   | Return (st', ()) -> state_v st' == hm)
-  [SMTPat (hashmap_utils_serialize_fwd hm st)]
+  [SMTPat (hashmap_utils_serialize hm st)]
 
 /// [deserialize] gives us the hash map stored on disk, without updating it
 assume
 val deserialize_lem (st : state) : Lemma (
-  match hashmap_utils_deserialize_fwd st with
+  match hashmap_utils_deserialize st with
   | Fail _ -> True
   | Return (st', hm) -> hm == state_v st /\ st' == st)
-  [SMTPat (hashmap_utils_deserialize_fwd st)]
+  [SMTPat (hashmap_utils_deserialize st)]
 
 (*** Lemmas *)
 
 /// The obvious lemma about [insert_on_disk]: the updated hash map stored on disk
 /// is exactly the hash map produced from inserting the binding ([key], [value])
 /// in the hash map previously stored on disk.
-val insert_on_disk_fwd_lem (key : usize) (value : u64) (st : state) : Lemma (
-  match insert_on_disk_fwd key value st with
+val insert_on_disk_lem (key : usize) (value : u64) (st : state) : Lemma (
+  match insert_on_disk key value st with
   | Fail _ -> True
   | Return (st', ()) ->
     let hm = state_v st in
-    match hashmap_hash_map_insert_fwd_back u64 hm key value with
+    match hashmap_HashMap_insert u64 hm key value with
     | Fail _ -> False
     | Return hm' -> hm' == state_v st')
 
-let insert_on_disk_fwd_lem key value st = ()
+let insert_on_disk_lem key value st = ()
diff --git a/tests/fstar/hashmap_on_disk/HashmapMain.Types.fsti b/tests/fstar/hashmap_on_disk/HashmapMain.Types.fsti
index e289174b..24b78c2a 100644
--- a/tests/fstar/hashmap_on_disk/HashmapMain.Types.fsti
+++ b/tests/fstar/hashmap_on_disk/HashmapMain.Types.fsti
@@ -6,17 +6,17 @@ open Primitives
 #set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
 
 (** [hashmap_main::hashmap::List] *)
-type hashmap_list_t (t : Type0) =
-| HashmapListCons : usize -> t -> hashmap_list_t t -> hashmap_list_t t
-| HashmapListNil : hashmap_list_t t
+type hashmap_List_t (t : Type0) =
+| Hashmap_List_Cons : usize -> t -> hashmap_List_t t -> hashmap_List_t t
+| Hashmap_List_Nil : hashmap_List_t t
 
 (** [hashmap_main::hashmap::HashMap] *)
-type hashmap_hash_map_t (t : Type0) =
+type hashmap_HashMap_t (t : Type0) =
 {
-  hashmap_hash_map_num_entries : usize;
-  hashmap_hash_map_max_load_factor : (usize & usize);
-  hashmap_hash_map_max_load : usize;
-  hashmap_hash_map_slots : vec (hashmap_list_t t);
+  num_entries : usize;
+  max_load_factor : (usize & usize);
+  max_load : usize;
+  slots : alloc_vec_Vec (hashmap_List_t t);
 }
 
 (** The state type used in the state-error monad *)
diff --git a/tests/fstar/hashmap_on_disk/Primitives.fst b/tests/fstar/hashmap_on_disk/Primitives.fst
index 9db82069..3297803c 100644
--- a/tests/fstar/hashmap_on_disk/Primitives.fst
+++ b/tests/fstar/hashmap_on_disk/Primitives.fst
@@ -55,8 +55,12 @@ type string = string
 let is_zero (n: nat) : bool = n = 0
 let decrease (n: nat{n > 0}) : nat = n - 1
 
-let mem_replace_fwd (a : Type0) (x : a) (y : a) : a = x
-let mem_replace_back (a : Type0) (x : a) (y : a) : a = y
+let core_mem_replace (a : Type0) (x : a) (y : a) : a = x
+let core_mem_replace_back (a : Type0) (x : a) (y : a) : a = y
+
+// We don't really use raw pointers for now
+type mut_raw_ptr (t : Type0) = { v : t }
+type const_raw_ptr (t : Type0) = { v : t }
 
 (*** Scalars *)
 /// Rem.: most of the following code was partially generated
@@ -100,6 +104,11 @@ type scalar_ty =
 | U64
 | U128
 
+let is_unsigned = function
+  | Isize | I8 | I16 | I32 | I64 | I128 -> false
+  | Usize | U8 | U16 | U32 | U64 | U128 -> true
+
+
 let scalar_min (ty : scalar_ty) : int =
   match ty with
   | Isize -> isize_min
@@ -162,6 +171,15 @@ let scalar_sub (#ty : scalar_ty) (x : scalar ty) (y : scalar ty) : result (scala
 let scalar_mul (#ty : scalar_ty) (x : scalar ty) (y : scalar ty) : result (scalar ty) =
   mk_scalar ty (x * y)
 
+let scalar_lxor (#ty : scalar_ty { is_unsigned ty && ty <> Usize })
+    (x : scalar ty) (y : scalar ty) : scalar ty =
+  match ty with
+  | U8 -> FStar.UInt.logxor #8 x y
+  | U16 -> FStar.UInt.logxor #16 x y
+  | U32 -> FStar.UInt.logxor #32 x y
+  | U64 -> FStar.UInt.logxor #64 x y
+  | U128 -> FStar.UInt.logxor #128 x y
+
 (** Cast an integer from a [src_ty] to a [tgt_ty] *)
 // TODO: check the semantics of casts in Rust
 let scalar_cast (src_ty : scalar_ty) (tgt_ty : scalar_ty) (x : scalar src_ty) : result (scalar tgt_ty) =
@@ -169,17 +187,44 @@ let scalar_cast (src_ty : scalar_ty) (tgt_ty : scalar_ty) (x : scalar src_ty) :
 
 /// The scalar types
 type isize : eqtype = scalar Isize
-type i8 : eqtype = scalar I8
-type i16 : eqtype = scalar I16
-type i32 : eqtype = scalar I32
-type i64 : eqtype = scalar I64
-type i128 : eqtype = scalar I128
+type i8    : eqtype = scalar I8
+type i16   : eqtype = scalar I16
+type i32   : eqtype = scalar I32
+type i64   : eqtype = scalar I64
+type i128  : eqtype = scalar I128
 type usize : eqtype = scalar Usize
-type u8 : eqtype = scalar U8
-type u16 : eqtype = scalar U16
-type u32 : eqtype = scalar U32
-type u64 : eqtype = scalar U64
-type u128 : eqtype = scalar U128
+type u8    : eqtype = scalar U8
+type u16   : eqtype = scalar U16
+type u32   : eqtype = scalar U32
+type u64   : eqtype = scalar U64
+type u128  : eqtype = scalar U128
+
+
+let core_isize_min : isize = isize_min
+let core_isize_max : isize = isize_max
+let core_i8_min    : i8 = i8_min
+let core_i8_max    : i8 = i8_max
+let core_i16_min   : i16 = i16_min
+let core_i16_max   : i16 = i16_max
+let core_i32_min   : i32 = i32_min
+let core_i32_max   : i32 = i32_max
+let core_i64_min   : i64 = i64_min
+let core_i64_max   : i64 = i64_max
+let core_i128_min  : i128 = i128_min
+let core_i128_max  : i128 = i128_max
+
+let core_usize_min : usize = usize_min
+let core_usize_max : usize = usize_max
+let core_u8_min    : u8 = u8_min
+let core_u8_max    : u8 = u8_max
+let core_u16_min   : u16 = u16_min
+let core_u16_max   : u16 = u16_max
+let core_u32_min   : u32 = u32_min
+let core_u32_max   : u32 = u32_max
+let core_u64_min   : u64 = u64_min
+let core_u64_max   : u64 = u64_max
+let core_u128_min  : u128 = u128_min
+let core_u128_max  : u128 = u128_max
 
 /// Negation
 let isize_neg = scalar_neg #Isize
@@ -231,7 +276,7 @@ let u32_add = scalar_add #U32
 let u64_add = scalar_add #U64
 let u128_add = scalar_add #U128
 
-/// Substraction
+/// Subtraction
 let isize_sub = scalar_sub #Isize
 let i8_sub = scalar_sub #I8
 let i16_sub = scalar_sub #I16
@@ -259,12 +304,65 @@ let u32_mul = scalar_mul #U32
 let u64_mul = scalar_mul #U64
 let u128_mul = scalar_mul #U128
 
-(*** Range *)
-type range (a : Type0) = {
+/// Logical operators, defined for unsigned types only, so far
+let u8_xor = scalar_lxor #U8
+let u16_xor = scalar_lxor #U16
+let u32_xor = scalar_lxor #U32
+let u64_xor = scalar_lxor #U64
+let u128_xor = scalar_lxor #U128
+
+(*** core::ops *)
+
+// Trait declaration: [core::ops::index::Index]
+noeq type core_ops_index_Index (self idx : Type0) = {
+  output : Type0;
+  index : self → idx → result output
+}
+
+// Trait declaration: [core::ops::index::IndexMut]
+noeq type core_ops_index_IndexMut (self idx : Type0) = {
+  indexInst : core_ops_index_Index self idx;
+  index_mut : self → idx → result indexInst.output;
+  index_mut_back : self → idx → indexInst.output → result self;
+}
+
+// Trait declaration [core::ops::deref::Deref]
+noeq type core_ops_deref_Deref (self : Type0) = {
+  target : Type0;
+  deref : self → result target;
+}
+
+// Trait declaration [core::ops::deref::DerefMut]
+noeq type core_ops_deref_DerefMut (self : Type0) = {
+  derefInst : core_ops_deref_Deref self;
+  deref_mut : self → result derefInst.target;
+  deref_mut_back : self → derefInst.target → result self;
+}
+
+type core_ops_range_Range (a : Type0) = {
   start : a;
   end_ : a;
 }
 
+(*** [alloc] *)
+
+let alloc_boxed_Box_deref (t : Type0) (x : t) : result t = Return x
+let alloc_boxed_Box_deref_mut (t : Type0) (x : t) : result t = Return x
+let alloc_boxed_Box_deref_mut_back (t : Type) (_ : t) (x : t) : result t = Return x
+
+// Trait instance
+let alloc_boxed_Box_coreOpsDerefInst (self : Type0) : core_ops_deref_Deref self = {
+  target = self;
+  deref = alloc_boxed_Box_deref self;
+}
+
+// Trait instance
+let alloc_boxed_Box_coreOpsDerefMutInst (self : Type0) : core_ops_deref_DerefMut self = {
+  derefInst = alloc_boxed_Box_coreOpsDerefInst self;
+  deref_mut = alloc_boxed_Box_deref_mut self;
+  deref_mut_back = alloc_boxed_Box_deref_mut_back self;
+}
+
 (*** Array *)
 type array (a : Type0) (n : usize) = s:list a{length s = n}
 
@@ -278,15 +376,11 @@ let mk_array (a : Type0) (n : usize)
   normalize_term_spec (FStar.List.Tot.length l);
   l
 
-let array_index_shared (a : Type0) (n : usize) (x : array a n) (i : usize) : result a =
-  if i < length x then Return (index x i)
-  else Fail Failure
-
-let array_index_mut_fwd (a : Type0) (n : usize) (x : array a n) (i : usize) : result a =
+let array_index_usize (a : Type0) (n : usize) (x : array a n) (i : usize) : result a =
   if i < length x then Return (index x i)
   else Fail Failure
 
-let array_index_mut_back (a : Type0) (n : usize) (x : array a n) (i : usize) (nx : a) : result (array a n) =
+let array_update_usize (a : Type0) (n : usize) (x : array a n) (i : usize) (nx : a) : result (array a n) =
   if i < length x then Return (list_update x i nx)
   else Fail Failure
 
@@ -295,55 +389,54 @@ type slice (a : Type0) = s:list a{length s <= usize_max}
 
 let slice_len (a : Type0) (s : slice a) : usize = length s
 
-let slice_index_shared (a : Type0) (x : slice a) (i : usize) : result a =
+let slice_index_usize (a : Type0) (x : slice a) (i : usize) : result a =
   if i < length x then Return (index x i)
   else Fail Failure
 
-let slice_index_mut_fwd (a : Type0) (x : slice a) (i : usize) : result a =
-  if i < length x then Return (index x i)
-  else Fail Failure
-
-let slice_index_mut_back (a : Type0) (x : slice a) (i : usize) (nx : a) : result (slice a) =
+let slice_update_usize (a : Type0) (x : slice a) (i : usize) (nx : a) : result (slice a) =
   if i < length x then Return (list_update x i nx)
   else Fail Failure
 
 (*** Subslices *)
 
-let array_to_slice_shared (a : Type0) (n : usize) (x : array a n) : result (slice a) = Return x
-let array_to_slice_mut_fwd (a : Type0) (n : usize) (x : array a n) : result (slice a) = Return x
-let array_to_slice_mut_back (a : Type0) (n : usize) (x : array a n) (s : slice a) : result (array a n) =
+let array_to_slice (a : Type0) (n : usize) (x : array a n) : result (slice a) = Return x
+let array_from_slice (a : Type0) (n : usize) (x : array a n) (s : slice a) : result (array a n) =
   if length s = n then Return s
   else Fail Failure
 
 // TODO: finish the definitions below (there lacks [List.drop] and [List.take] in the standard library *)
-let array_subslice_shared (a : Type0) (n : usize) (x : array a n) (r : range usize) : result (slice a) =
-  admit()
-
-let array_subslice_mut_fwd (a : Type0) (n : usize) (x : array a n) (r : range usize) : result (slice a) =
+let array_subslice (a : Type0) (n : usize) (x : array a n) (r : core_ops_range_Range usize) : result (slice a) =
   admit()
 
-let array_subslice_mut_back (a : Type0) (n : usize) (x : array a n) (r : range usize) (ns : slice a) : result (array a n) =
+let array_update_subslice (a : Type0) (n : usize) (x : array a n) (r : core_ops_range_Range usize) (ns : slice a) : result (array a n) =
   admit()
 
-let slice_subslice_shared (a : Type0) (x : slice a) (r : range usize) : result (slice a) =
+let array_repeat (a : Type0) (n : usize) (x : a) : array a n =
   admit()
 
-let slice_subslice_mut_fwd (a : Type0) (x : slice a) (r : range usize) : result (slice a) =
+let slice_subslice (a : Type0) (x : slice a) (r : core_ops_range_Range usize) : result (slice a) =
   admit()
 
-let slice_subslice_mut_back (a : Type0) (x : slice a) (r : range usize) (ns : slice a) : result (slice a) =
+let slice_update_subslice (a : Type0) (x : slice a) (r : core_ops_range_Range usize) (ns : slice a) : result (slice a) =
   admit()
 
 (*** Vector *)
-type vec (a : Type0) = v:list a{length v <= usize_max}
+type alloc_vec_Vec (a : Type0) = v:list a{length v <= usize_max}
 
-let vec_new (a  : Type0) : vec a = assert_norm(length #a [] == 0); []
-let vec_len (a : Type0) (v : vec a) : usize = length v
+let alloc_vec_Vec_new (a  : Type0) : alloc_vec_Vec a = assert_norm(length #a [] == 0); []
+let alloc_vec_Vec_len (a : Type0) (v : alloc_vec_Vec a) : usize = length v
+
+// Helper
+let alloc_vec_Vec_index_usize (#a : Type0) (v : alloc_vec_Vec a) (i : usize) : result a =
+  if i < length v then Return (index v i) else Fail Failure
+// Helper
+let alloc_vec_Vec_update_usize (#a : Type0) (v : alloc_vec_Vec a) (i : usize) (x : a) : result (alloc_vec_Vec a) =
+  if i < length v then Return (list_update v i x) else Fail Failure
 
 // The **forward** function shouldn't be used
-let vec_push_fwd (a  : Type0) (v : vec a) (x : a) : unit = ()
-let vec_push_back (a  : Type0) (v : vec a) (x : a) :
-  Pure (result (vec a))
+let alloc_vec_Vec_push_fwd (a  : Type0) (v : alloc_vec_Vec a) (x : a) : unit = ()
+let alloc_vec_Vec_push (a  : Type0) (v : alloc_vec_Vec a) (x : a) :
+  Pure (result (alloc_vec_Vec a))
   (requires True)
   (ensures (fun res ->
     match res with
@@ -358,18 +451,279 @@ let vec_push_back (a  : Type0) (v : vec a) (x : a) :
   else Fail Failure
 
 // The **forward** function shouldn't be used
-let vec_insert_fwd (a : Type0) (v : vec a) (i : usize) (x : a) : result unit =
+let alloc_vec_Vec_insert_fwd (a : Type0) (v : alloc_vec_Vec a) (i : usize) (x : a) : result unit =
   if i < length v then Return () else Fail Failure
-let vec_insert_back (a : Type0) (v : vec a) (i : usize) (x : a) : result (vec a) =
+let alloc_vec_Vec_insert (a : Type0) (v : alloc_vec_Vec a) (i : usize) (x : a) : result (alloc_vec_Vec a) =
   if i < length v then Return (list_update v i x) else Fail Failure
 
-// The **backward** function shouldn't be used
-let vec_index_fwd (a : Type0) (v : vec a) (i : usize) : result a =
-  if i < length v then Return (index v i) else Fail Failure
-let vec_index_back (a : Type0) (v : vec a) (i : usize) (x : a) : result unit =
-  if i < length v then Return () else Fail Failure
+// Trait declaration: [core::slice::index::private_slice_index::Sealed]
+type core_slice_index_private_slice_index_Sealed (self : Type0) = unit
+
+// Trait declaration: [core::slice::index::SliceIndex]
+noeq type core_slice_index_SliceIndex (self t : Type0) = {
+  sealedInst : core_slice_index_private_slice_index_Sealed self;
+  output : Type0;
+  get : self → t → result (option output);
+  get_mut : self → t → result (option output);
+  get_mut_back : self → t → option output → result t;
+  get_unchecked : self → const_raw_ptr t → result (const_raw_ptr output);
+  get_unchecked_mut : self → mut_raw_ptr t → result (mut_raw_ptr output);
+  index : self → t → result output;
+  index_mut : self → t → result output;
+  index_mut_back : self → t → output → result t;
+}
 
-let vec_index_mut_fwd (a : Type0) (v : vec a) (i : usize) : result a =
-  if i < length v then Return (index v i) else Fail Failure
-let vec_index_mut_back (a : Type0) (v : vec a) (i : usize) (nx : a) : result (vec a) =
-  if i < length v then Return (list_update v i nx) else Fail Failure
+// [core::slice::index::[T]::index]: forward function
+let core_slice_index_Slice_index
+  (t idx : Type0) (inst : core_slice_index_SliceIndex idx (slice t))
+  (s : slice t) (i : idx) : result inst.output =
+  let* x = inst.get i s in
+  match x with
+  | None -> Fail Failure
+  | Some x -> Return x
+
+// [core::slice::index::Range:::get]: forward function
+let core_slice_index_Range_get (t : Type0) (i : core_ops_range_Range usize) (s : slice t) :
+  result (option (slice t)) =
+  admit () // TODO
+
+// [core::slice::index::Range::get_mut]: forward function
+let core_slice_index_Range_get_mut
+  (t : Type0) : core_ops_range_Range usize → slice t → result (option (slice t)) =
+  admit () // TODO
+
+// [core::slice::index::Range::get_mut]: backward function 0
+let core_slice_index_Range_get_mut_back
+  (t : Type0) :
+  core_ops_range_Range usize → slice t → option (slice t) → result (slice t) =
+  admit () // TODO
+
+// [core::slice::index::Range::get_unchecked]: forward function
+let core_slice_index_Range_get_unchecked
+  (t : Type0) :
+  core_ops_range_Range usize → const_raw_ptr (slice t) → result (const_raw_ptr (slice t)) =
+  // Don't know what the model should be - for now we always fail to make
+  // sure code which uses it fails
+  fun _ _ -> Fail Failure
+
+// [core::slice::index::Range::get_unchecked_mut]: forward function
+let core_slice_index_Range_get_unchecked_mut
+  (t : Type0) :
+  core_ops_range_Range usize → mut_raw_ptr (slice t) → result (mut_raw_ptr (slice t)) =
+  // Don't know what the model should be - for now we always fail to make
+  // sure code which uses it fails
+  fun _ _ -> Fail Failure
+
+// [core::slice::index::Range::index]: forward function
+let core_slice_index_Range_index
+  (t : Type0) : core_ops_range_Range usize → slice t → result (slice t) =
+  admit () // TODO
+
+// [core::slice::index::Range::index_mut]: forward function
+let core_slice_index_Range_index_mut
+  (t : Type0) : core_ops_range_Range usize → slice t → result (slice t) =
+  admit () // TODO
+
+// [core::slice::index::Range::index_mut]: backward function 0
+let core_slice_index_Range_index_mut_back
+  (t : Type0) : core_ops_range_Range usize → slice t → slice t → result (slice t) =
+  admit () // TODO
+
+// [core::slice::index::[T]::index_mut]: forward function
+let core_slice_index_Slice_index_mut
+  (t idx : Type0) (inst : core_slice_index_SliceIndex idx (slice t)) :
+  slice t → idx → result inst.output =
+  admit () // 
+
+// [core::slice::index::[T]::index_mut]: backward function 0
+let core_slice_index_Slice_index_mut_back
+  (t idx : Type0) (inst : core_slice_index_SliceIndex idx (slice t)) :
+  slice t → idx → inst.output → result (slice t) =
+  admit () // TODO
+
+// [core::array::[T; N]::index]: forward function
+let core_array_Array_index
+  (t idx : Type0) (n : usize) (inst : core_ops_index_Index (slice t) idx)
+  (a : array t n) (i : idx) : result inst.output =
+  admit () // TODO
+
+// [core::array::[T; N]::index_mut]: forward function
+let core_array_Array_index_mut
+  (t idx : Type0) (n : usize) (inst : core_ops_index_IndexMut (slice t) idx)
+  (a : array t n) (i : idx) : result inst.indexInst.output =
+  admit () // TODO
+
+// [core::array::[T; N]::index_mut]: backward function 0
+let core_array_Array_index_mut_back
+  (t idx : Type0) (n : usize) (inst : core_ops_index_IndexMut (slice t) idx)
+  (a : array t n) (i : idx) (x : inst.indexInst.output) : result (array t n) =
+  admit () // TODO
+
+// Trait implementation: [core::slice::index::[T]]
+let core_slice_index_Slice_coreopsindexIndexInst (t idx : Type0)
+  (inst : core_slice_index_SliceIndex idx (slice t)) :
+  core_ops_index_Index (slice t) idx = {
+  output = inst.output;
+  index = core_slice_index_Slice_index t idx inst;
+}
+
+// Trait implementation: [core::slice::index::private_slice_index::Range]
+let core_slice_index_private_slice_index_Range_coresliceindexprivate_slice_indexSealedInst
+  : core_slice_index_private_slice_index_Sealed (core_ops_range_Range usize) = ()
+
+// Trait implementation: [core::slice::index::Range]
+let core_slice_index_Range_coresliceindexSliceIndexInst (t : Type0) :
+  core_slice_index_SliceIndex (core_ops_range_Range usize) (slice t) = {
+  sealedInst = core_slice_index_private_slice_index_Range_coresliceindexprivate_slice_indexSealedInst;
+  output = slice t;
+  get = core_slice_index_Range_get t;
+  get_mut = core_slice_index_Range_get_mut t;
+  get_mut_back = core_slice_index_Range_get_mut_back t;
+  get_unchecked = core_slice_index_Range_get_unchecked t;
+  get_unchecked_mut = core_slice_index_Range_get_unchecked_mut t;
+  index = core_slice_index_Range_index t;
+  index_mut = core_slice_index_Range_index_mut t;
+  index_mut_back = core_slice_index_Range_index_mut_back t;
+}
+
+// Trait implementation: [core::slice::index::[T]]
+let core_slice_index_Slice_coreopsindexIndexMutInst (t idx : Type0)
+  (inst : core_slice_index_SliceIndex idx (slice t)) :
+  core_ops_index_IndexMut (slice t) idx = {
+  indexInst = core_slice_index_Slice_coreopsindexIndexInst t idx inst;
+  index_mut = core_slice_index_Slice_index_mut t idx inst;
+  index_mut_back = core_slice_index_Slice_index_mut_back t idx inst;
+}
+
+// Trait implementation: [core::array::[T; N]]
+let core_array_Array_coreopsindexIndexInst (t idx : Type0) (n : usize)
+  (inst : core_ops_index_Index (slice t) idx) :
+  core_ops_index_Index (array t n) idx = {
+  output = inst.output;
+  index = core_array_Array_index t idx n inst;
+}
+
+// Trait implementation: [core::array::[T; N]]
+let core_array_Array_coreopsindexIndexMutInst (t idx : Type0) (n : usize)
+  (inst : core_ops_index_IndexMut (slice t) idx) :
+  core_ops_index_IndexMut (array t n) idx = {
+  indexInst = core_array_Array_coreopsindexIndexInst t idx n inst.indexInst;
+  index_mut = core_array_Array_index_mut t idx n inst;
+  index_mut_back = core_array_Array_index_mut_back t idx n inst;
+}
+
+// [core::slice::index::usize::get]: forward function
+let core_slice_index_usize_get
+  (t : Type0) : usize → slice t → result (option t) =
+  admit () // TODO
+
+// [core::slice::index::usize::get_mut]: forward function
+let core_slice_index_usize_get_mut
+  (t : Type0) : usize → slice t → result (option t) =
+  admit () // TODO
+
+// [core::slice::index::usize::get_mut]: backward function 0
+let core_slice_index_usize_get_mut_back
+  (t : Type0) : usize → slice t → option t → result (slice t) =
+  admit () // TODO
+
+// [core::slice::index::usize::get_unchecked]: forward function
+let core_slice_index_usize_get_unchecked
+  (t : Type0) : usize → const_raw_ptr (slice t) → result (const_raw_ptr t) =
+  admit () // TODO
+
+// [core::slice::index::usize::get_unchecked_mut]: forward function
+let core_slice_index_usize_get_unchecked_mut
+  (t : Type0) : usize → mut_raw_ptr (slice t) → result (mut_raw_ptr t) =
+  admit () // TODO
+
+// [core::slice::index::usize::index]: forward function
+let core_slice_index_usize_index (t : Type0) : usize → slice t → result t =
+  admit () // TODO
+
+// [core::slice::index::usize::index_mut]: forward function
+let core_slice_index_usize_index_mut (t : Type0) : usize → slice t → result t =
+  admit () // TODO
+
+// [core::slice::index::usize::index_mut]: backward function 0
+let core_slice_index_usize_index_mut_back
+  (t : Type0) : usize → slice t → t → result (slice t) =
+  admit () // TODO
+
+// Trait implementation: [core::slice::index::private_slice_index::usize]
+let core_slice_index_private_slice_index_usize_coresliceindexprivate_slice_indexSealedInst
+  : core_slice_index_private_slice_index_Sealed usize = ()
+
+// Trait implementation: [core::slice::index::usize]
+let core_slice_index_usize_coresliceindexSliceIndexInst (t : Type0) :
+  core_slice_index_SliceIndex usize (slice t) = {
+  sealedInst = core_slice_index_private_slice_index_usize_coresliceindexprivate_slice_indexSealedInst;
+  output = t;
+  get = core_slice_index_usize_get t;
+  get_mut = core_slice_index_usize_get_mut t;
+  get_mut_back = core_slice_index_usize_get_mut_back t;
+  get_unchecked = core_slice_index_usize_get_unchecked t;
+  get_unchecked_mut = core_slice_index_usize_get_unchecked_mut t;
+  index = core_slice_index_usize_index t;
+  index_mut = core_slice_index_usize_index_mut t;
+  index_mut_back = core_slice_index_usize_index_mut_back t;
+}
+
+// [alloc::vec::Vec::index]: forward function
+let alloc_vec_Vec_index (t idx : Type0) (inst : core_slice_index_SliceIndex idx (slice t))
+  (self : alloc_vec_Vec t) (i : idx) : result inst.output =
+  admit () // TODO
+
+// [alloc::vec::Vec::index_mut]: forward function
+let alloc_vec_Vec_index_mut (t idx : Type0) (inst : core_slice_index_SliceIndex idx (slice t))
+  (self : alloc_vec_Vec t) (i : idx) : result inst.output =
+  admit () // TODO
+
+// [alloc::vec::Vec::index_mut]: backward function 0
+let alloc_vec_Vec_index_mut_back
+  (t idx : Type0) (inst : core_slice_index_SliceIndex idx (slice t))
+  (self : alloc_vec_Vec t) (i : idx) (x : inst.output) : result (alloc_vec_Vec t) =
+  admit () // TODO
+
+// Trait implementation: [alloc::vec::Vec]
+let alloc_vec_Vec_coreopsindexIndexInst (t idx : Type0)
+  (inst : core_slice_index_SliceIndex idx (slice t)) :
+  core_ops_index_Index (alloc_vec_Vec t) idx = {
+  output = inst.output;
+  index = alloc_vec_Vec_index t idx inst;
+}
+
+// Trait implementation: [alloc::vec::Vec]
+let alloc_vec_Vec_coreopsindexIndexMutInst (t idx : Type0)
+  (inst : core_slice_index_SliceIndex idx (slice t)) :
+  core_ops_index_IndexMut (alloc_vec_Vec t) idx = {
+  indexInst = alloc_vec_Vec_coreopsindexIndexInst t idx inst;
+  index_mut = alloc_vec_Vec_index_mut t idx inst;
+  index_mut_back = alloc_vec_Vec_index_mut_back t idx inst;
+}
+
+(*** Theorems *)
+
+let alloc_vec_Vec_index_eq (#a : Type0) (v : alloc_vec_Vec a) (i : usize) :
+  Lemma (
+    alloc_vec_Vec_index a usize (core_slice_index_usize_coresliceindexSliceIndexInst a) v i ==
+      alloc_vec_Vec_index_usize v i)
+  [SMTPat (alloc_vec_Vec_index a usize (core_slice_index_usize_coresliceindexSliceIndexInst a) v i)]
+  =
+  admit()
+
+let alloc_vec_Vec_index_mut_eq (#a : Type0) (v : alloc_vec_Vec a) (i : usize) :
+  Lemma (
+    alloc_vec_Vec_index_mut a usize (core_slice_index_usize_coresliceindexSliceIndexInst a) v i ==
+      alloc_vec_Vec_index_usize v i)
+  [SMTPat (alloc_vec_Vec_index_mut a usize (core_slice_index_usize_coresliceindexSliceIndexInst a) v i)]
+  =
+  admit()
+
+let alloc_vec_Vec_index_mut_back_eq (#a : Type0) (v : alloc_vec_Vec a) (i : usize) (x : a) :
+  Lemma (
+    alloc_vec_Vec_index_mut_back a usize (core_slice_index_usize_coresliceindexSliceIndexInst a) v i x ==
+      alloc_vec_Vec_update_usize v i x)
+  [SMTPat (alloc_vec_Vec_index_mut_back a usize (core_slice_index_usize_coresliceindexSliceIndexInst a) v i x)]
+  =
+  admit()
diff --git a/tests/fstar/misc/Constants.fst b/tests/fstar/misc/Constants.fst
index d2b0415e..c21d6a5f 100644
--- a/tests/fstar/misc/Constants.fst
+++ b/tests/fstar/misc/Constants.fst
@@ -9,12 +9,8 @@ open Primitives
 let x0_body : result u32 = Return 0
 let x0_c : u32 = eval_global x0_body
 
-(** [core::num::u32::{8}::MAX] *)
-let core_num_u32_max_body : result u32 = Return 4294967295
-let core_num_u32_max_c : u32 = eval_global core_num_u32_max_body
-
 (** [constants::X1] *)
-let x1_body : result u32 = Return core_num_u32_max_c
+let x1_body : result u32 = Return core_u32_max
 let x1_c : u32 = eval_global x1_body
 
 (** [constants::X2] *)
@@ -22,30 +18,30 @@ let x2_body : result u32 = Return 3
 let x2_c : u32 = eval_global x2_body
 
 (** [constants::incr]: forward function *)
-let incr_fwd (n : u32) : result u32 =
+let incr (n : u32) : result u32 =
   u32_add n 1
 
 (** [constants::X3] *)
-let x3_body : result u32 = incr_fwd 32
+let x3_body : result u32 = incr 32
 let x3_c : u32 = eval_global x3_body
 
 (** [constants::mk_pair0]: forward function *)
-let mk_pair0_fwd (x : u32) (y : u32) : result (u32 & u32) =
+let mk_pair0 (x : u32) (y : u32) : result (u32 & u32) =
   Return (x, y)
 
 (** [constants::Pair] *)
-type pair_t (t1 t2 : Type0) = { pair_x : t1; pair_y : t2; }
+type pair_t (t1 t2 : Type0) = { x : t1; y : t2; }
 
 (** [constants::mk_pair1]: forward function *)
-let mk_pair1_fwd (x : u32) (y : u32) : result (pair_t u32 u32) =
-  Return { pair_x = x; pair_y = y }
+let mk_pair1 (x : u32) (y : u32) : result (pair_t u32 u32) =
+  Return { x = x; y = y }
 
 (** [constants::P0] *)
-let p0_body : result (u32 & u32) = mk_pair0_fwd 0 1
+let p0_body : result (u32 & u32) = mk_pair0 0 1
 let p0_c : (u32 & u32) = eval_global p0_body
 
 (** [constants::P1] *)
-let p1_body : result (pair_t u32 u32) = mk_pair1_fwd 0 1
+let p1_body : result (pair_t u32 u32) = mk_pair1 0 1
 let p1_c : pair_t u32 u32 = eval_global p1_body
 
 (** [constants::P2] *)
@@ -53,26 +49,26 @@ let p2_body : result (u32 & u32) = Return (0, 1)
 let p2_c : (u32 & u32) = eval_global p2_body
 
 (** [constants::P3] *)
-let p3_body : result (pair_t u32 u32) = Return { pair_x = 0; pair_y = 1 }
+let p3_body : result (pair_t u32 u32) = Return { x = 0; y = 1 }
 let p3_c : pair_t u32 u32 = eval_global p3_body
 
 (** [constants::Wrap] *)
-type wrap_t (t : Type0) = { wrap_val : t; }
+type wrap_t (t : Type0) = { value : t; }
 
 (** [constants::Wrap::{0}::new]: forward function *)
-let wrap_new_fwd (t : Type0) (val0 : t) : result (wrap_t t) =
-  Return { wrap_val = val0 }
+let wrap_new (t : Type0) (value : t) : result (wrap_t t) =
+  Return { value = value }
 
 (** [constants::Y] *)
-let y_body : result (wrap_t i32) = wrap_new_fwd i32 2
+let y_body : result (wrap_t i32) = wrap_new i32 2
 let y_c : wrap_t i32 = eval_global y_body
 
 (** [constants::unwrap_y]: forward function *)
-let unwrap_y_fwd : result i32 =
-  Return y_c.wrap_val
+let unwrap_y : result i32 =
+  Return y_c.value
 
 (** [constants::YVAL] *)
-let yval_body : result i32 = unwrap_y_fwd
+let yval_body : result i32 = unwrap_y
 let yval_c : i32 = eval_global yval_body
 
 (** [constants::get_z1::Z1] *)
@@ -80,11 +76,11 @@ let get_z1_z1_body : result i32 = Return 3
 let get_z1_z1_c : i32 = eval_global get_z1_z1_body
 
 (** [constants::get_z1]: forward function *)
-let get_z1_fwd : result i32 =
+let get_z1 : result i32 =
   Return get_z1_z1_c
 
 (** [constants::add]: forward function *)
-let add_fwd (a : i32) (b : i32) : result i32 =
+let add (a : i32) (b : i32) : result i32 =
   i32_add a b
 
 (** [constants::Q1] *)
@@ -96,19 +92,19 @@ let q2_body : result i32 = Return q1_c
 let q2_c : i32 = eval_global q2_body
 
 (** [constants::Q3] *)
-let q3_body : result i32 = add_fwd q2_c 3
+let q3_body : result i32 = add q2_c 3
 let q3_c : i32 = eval_global q3_body
 
 (** [constants::get_z2]: forward function *)
-let get_z2_fwd : result i32 =
-  let* i = get_z1_fwd in let* i0 = add_fwd i q3_c in add_fwd q1_c i0
+let get_z2 : result i32 =
+  let* i = get_z1 in let* i0 = add i q3_c in add q1_c i0
 
 (** [constants::S1] *)
 let s1_body : result u32 = Return 6
 let s1_c : u32 = eval_global s1_body
 
 (** [constants::S2] *)
-let s2_body : result u32 = incr_fwd s1_c
+let s2_body : result u32 = incr s1_c
 let s2_c : u32 = eval_global s2_body
 
 (** [constants::S3] *)
@@ -116,6 +112,6 @@ let s3_body : result (pair_t u32 u32) = Return p3_c
 let s3_c : pair_t u32 u32 = eval_global s3_body
 
 (** [constants::S4] *)
-let s4_body : result (pair_t u32 u32) = mk_pair1_fwd 7 8
+let s4_body : result (pair_t u32 u32) = mk_pair1 7 8
 let s4_c : pair_t u32 u32 = eval_global s4_body
 
diff --git a/tests/fstar/misc/External.Funs.fst b/tests/fstar/misc/External.Funs.fst
index f118a2cf..e26014ac 100644
--- a/tests/fstar/misc/External.Funs.fst
+++ b/tests/fstar/misc/External.Funs.fst
@@ -8,8 +8,8 @@ include External.Opaque
 #set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
 
 (** [external::swap]: forward function *)
-let swap_fwd (t : Type0) (x : t) (y : t) (st : state) : result (state & unit) =
-  let* (st0, _) = core_mem_swap_fwd t x y st in
+let swap (t : Type0) (x : t) (y : t) (st : state) : result (state & unit) =
+  let* (st0, _) = core_mem_swap t x y st in
   let* (st1, _) = core_mem_swap_back0 t x y st st0 in
   let* (st2, _) = core_mem_swap_back1 t x y st st1 in
   Return (st2, ())
@@ -19,28 +19,29 @@ let swap_back
   (t : Type0) (x : t) (y : t) (st : state) (st0 : state) :
   result (state & (t & t))
   =
-  let* (st1, _) = core_mem_swap_fwd t x y st in
+  let* (st1, _) = core_mem_swap t x y st in
   let* (st2, x0) = core_mem_swap_back0 t x y st st1 in
   let* (_, y0) = core_mem_swap_back1 t x y st st2 in
   Return (st0, (x0, y0))
 
 (** [external::test_new_non_zero_u32]: forward function *)
-let test_new_non_zero_u32_fwd
-  (x : u32) (st : state) : result (state & core_num_nonzero_non_zero_u32_t) =
-  let* (st0, opt) = core_num_nonzero_non_zero_u32_new_fwd x st in
-  core_option_option_unwrap_fwd core_num_nonzero_non_zero_u32_t opt st0
+let test_new_non_zero_u32
+  (x : u32) (st : state) : result (state & core_num_nonzero_NonZeroU32_t) =
+  let* (st0, o) = core_num_nonzero_NonZeroU32_new x st in
+  core_option_Option_unwrap core_num_nonzero_NonZeroU32_t o st0
 
 (** [external::test_vec]: forward function *)
-let test_vec_fwd : result unit =
-  let v = vec_new u32 in let* _ = vec_push_back u32 v 0 in Return ()
+let test_vec : result unit =
+  let v = alloc_vec_Vec_new u32 in
+  let* _ = alloc_vec_Vec_push u32 v 0 in
+  Return ()
 
 (** Unit test for [external::test_vec] *)
-let _ = assert_norm (test_vec_fwd = Return ())
+let _ = assert_norm (test_vec = Return ())
 
 (** [external::custom_swap]: forward function *)
-let custom_swap_fwd
-  (t : Type0) (x : t) (y : t) (st : state) : result (state & t) =
-  let* (st0, _) = core_mem_swap_fwd t x y st in
+let custom_swap (t : Type0) (x : t) (y : t) (st : state) : result (state & t) =
+  let* (st0, _) = core_mem_swap t x y st in
   let* (st1, x0) = core_mem_swap_back0 t x y st st0 in
   let* (st2, _) = core_mem_swap_back1 t x y st st1 in
   Return (st2, x0)
@@ -50,15 +51,14 @@ let custom_swap_back
   (t : Type0) (x : t) (y : t) (st : state) (ret : t) (st0 : state) :
   result (state & (t & t))
   =
-  let* (st1, _) = core_mem_swap_fwd t x y st in
+  let* (st1, _) = core_mem_swap t x y st in
   let* (st2, _) = core_mem_swap_back0 t x y st st1 in
   let* (_, y0) = core_mem_swap_back1 t x y st st2 in
   Return (st0, (ret, y0))
 
 (** [external::test_custom_swap]: forward function *)
-let test_custom_swap_fwd
-  (x : u32) (y : u32) (st : state) : result (state & unit) =
-  let* (st0, _) = custom_swap_fwd u32 x y st in Return (st0, ())
+let test_custom_swap (x : u32) (y : u32) (st : state) : result (state & unit) =
+  let* (st0, _) = custom_swap u32 x y st in Return (st0, ())
 
 (** [external::test_custom_swap]: backward function 0 *)
 let test_custom_swap_back
@@ -68,8 +68,8 @@ let test_custom_swap_back
   custom_swap_back u32 x y st 1 st0
 
 (** [external::test_swap_non_zero]: forward function *)
-let test_swap_non_zero_fwd (x : u32) (st : state) : result (state & u32) =
-  let* (st0, _) = swap_fwd u32 x 0 st in
+let test_swap_non_zero (x : u32) (st : state) : result (state & u32) =
+  let* (st0, _) = swap u32 x 0 st in
   let* (st1, (x0, _)) = swap_back u32 x 0 st st0 in
   if x0 = 0 then Fail Failure else Return (st1, x0)
 
diff --git a/tests/fstar/misc/External.Opaque.fsti b/tests/fstar/misc/External.Opaque.fsti
index 2e19f767..85cf285c 100644
--- a/tests/fstar/misc/External.Opaque.fsti
+++ b/tests/fstar/misc/External.Opaque.fsti
@@ -7,7 +7,7 @@ include External.Types
 #set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
 
 (** [core::mem::swap]: forward function *)
-val core_mem_swap_fwd (t : Type0) : t -> t -> state -> result (state & unit)
+val core_mem_swap (t : Type0) : t -> t -> state -> result (state & unit)
 
 (** [core::mem::swap]: backward function 0 *)
 val core_mem_swap_back0
@@ -18,10 +18,10 @@ val core_mem_swap_back1
   (t : Type0) : t -> t -> state -> state -> result (state & t)
 
 (** [core::num::nonzero::NonZeroU32::{14}::new]: forward function *)
-val core_num_nonzero_non_zero_u32_new_fwd
-  : u32 -> state -> result (state & (option core_num_nonzero_non_zero_u32_t))
+val core_num_nonzero_NonZeroU32_new
+  : u32 -> state -> result (state & (option core_num_nonzero_NonZeroU32_t))
 
 (** [core::option::Option::{0}::unwrap]: forward function *)
-val core_option_option_unwrap_fwd
+val core_option_Option_unwrap
   (t : Type0) : option t -> state -> result (state & t)
 
diff --git a/tests/fstar/misc/External.Types.fsti b/tests/fstar/misc/External.Types.fsti
index 4a13a744..78b5228d 100644
--- a/tests/fstar/misc/External.Types.fsti
+++ b/tests/fstar/misc/External.Types.fsti
@@ -6,7 +6,7 @@ open Primitives
 #set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
 
 (** [core::num::nonzero::NonZeroU32] *)
-val core_num_nonzero_non_zero_u32_t : Type0
+val core_num_nonzero_NonZeroU32_t : Type0
 
 (** The state type used in the state-error monad *)
 val state : Type0
diff --git a/tests/fstar/misc/Loops.Clauses.Template.fst b/tests/fstar/misc/Loops.Clauses.Template.fst
index 053b7663..9920bdc1 100644
--- a/tests/fstar/misc/Loops.Clauses.Template.fst
+++ b/tests/fstar/misc/Loops.Clauses.Template.fst
@@ -22,7 +22,8 @@ let sum_with_shared_borrows_loop_decreases (max : u32) (i : u32) (s : u32) :
   admit ()
 
 (** [loops::clear]: decreases clause *)
-unfold let clear_loop_decreases (v : vec u32) (i : usize) : nat = admit ()
+unfold
+let clear_loop_decreases (v : alloc_vec_Vec u32) (i : usize) : nat = admit ()
 
 (** [loops::list_mem]: decreases clause *)
 unfold let list_mem_loop_decreases (x : u32) (ls : list_t u32) : nat = admit ()
diff --git a/tests/fstar/misc/Loops.Clauses.fst b/tests/fstar/misc/Loops.Clauses.fst
index 82f34de1..75194437 100644
--- a/tests/fstar/misc/Loops.Clauses.fst
+++ b/tests/fstar/misc/Loops.Clauses.fst
@@ -20,7 +20,7 @@ let sum_with_shared_borrows_loop_decreases (max : u32) (i : u32) (s : u32) : nat
   if max >= i then max - i else 0
 
 (** [loops::clear]: decreases clause *)
-unfold let clear_loop_decreases (v : vec u32) (i : usize) : nat =
+unfold let clear_loop_decreases (v : alloc_vec_Vec u32) (i : usize) : nat =
   if i <= List.Tot.length v then List.Tot.length v - i else 0
 
 (** [loops::list_mem]: decreases clause *)
diff --git a/tests/fstar/misc/Loops.Funs.fst b/tests/fstar/misc/Loops.Funs.fst
index 9a80f415..0f755351 100644
--- a/tests/fstar/misc/Loops.Funs.fst
+++ b/tests/fstar/misc/Loops.Funs.fst
@@ -8,20 +8,20 @@ include Loops.Clauses
 #set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
 
 (** [loops::sum]: loop 0: forward function *)
-let rec sum_loop_fwd
+let rec sum_loop
   (max : u32) (i : u32) (s : u32) :
   Tot (result u32) (decreases (sum_loop_decreases max i s))
   =
   if i < max
-  then let* s0 = u32_add s i in let* i0 = u32_add i 1 in sum_loop_fwd max i0 s0
+  then let* s0 = u32_add s i in let* i0 = u32_add i 1 in sum_loop max i0 s0
   else u32_mul s 2
 
 (** [loops::sum]: forward function *)
-let sum_fwd (max : u32) : result u32 =
-  sum_loop_fwd max 0 0
+let sum (max : u32) : result u32 =
+  sum_loop max 0 0
 
 (** [loops::sum_with_mut_borrows]: loop 0: forward function *)
-let rec sum_with_mut_borrows_loop_fwd
+let rec sum_with_mut_borrows_loop
   (max : u32) (mi : u32) (ms : u32) :
   Tot (result u32) (decreases (sum_with_mut_borrows_loop_decreases max mi ms))
   =
@@ -29,15 +29,15 @@ let rec sum_with_mut_borrows_loop_fwd
   then
     let* ms0 = u32_add ms mi in
     let* mi0 = u32_add mi 1 in
-    sum_with_mut_borrows_loop_fwd max mi0 ms0
+    sum_with_mut_borrows_loop max mi0 ms0
   else u32_mul ms 2
 
 (** [loops::sum_with_mut_borrows]: forward function *)
-let sum_with_mut_borrows_fwd (max : u32) : result u32 =
-  sum_with_mut_borrows_loop_fwd max 0 0
+let sum_with_mut_borrows (max : u32) : result u32 =
+  sum_with_mut_borrows_loop max 0 0
 
 (** [loops::sum_with_shared_borrows]: loop 0: forward function *)
-let rec sum_with_shared_borrows_loop_fwd
+let rec sum_with_shared_borrows_loop
   (max : u32) (i : u32) (s : u32) :
   Tot (result u32) (decreases (sum_with_shared_borrows_loop_decreases max i s))
   =
@@ -45,62 +45,64 @@ let rec sum_with_shared_borrows_loop_fwd
   then
     let* i0 = u32_add i 1 in
     let* s0 = u32_add s i0 in
-    sum_with_shared_borrows_loop_fwd max i0 s0
+    sum_with_shared_borrows_loop max i0 s0
   else u32_mul s 2
 
 (** [loops::sum_with_shared_borrows]: forward function *)
-let sum_with_shared_borrows_fwd (max : u32) : result u32 =
-  sum_with_shared_borrows_loop_fwd max 0 0
+let sum_with_shared_borrows (max : u32) : result u32 =
+  sum_with_shared_borrows_loop max 0 0
 
 (** [loops::clear]: loop 0: merged forward/backward function
     (there is a single backward function, and the forward function returns ()) *)
-let rec clear_loop_fwd_back
-  (v : vec u32) (i : usize) :
-  Tot (result (vec u32)) (decreases (clear_loop_decreases v i))
+let rec clear_loop
+  (v : alloc_vec_Vec u32) (i : usize) :
+  Tot (result (alloc_vec_Vec u32)) (decreases (clear_loop_decreases v i))
   =
-  let i0 = vec_len u32 v in
+  let i0 = alloc_vec_Vec_len u32 v in
   if i < i0
   then
     let* i1 = usize_add i 1 in
-    let* v0 = vec_index_mut_back u32 v i 0 in
-    clear_loop_fwd_back v0 i1
+    let* v0 =
+      alloc_vec_Vec_index_mut_back u32 usize
+        (core_slice_index_usize_coresliceindexSliceIndexInst u32) v i 0 in
+    clear_loop v0 i1
   else Return v
 
 (** [loops::clear]: merged forward/backward function
     (there is a single backward function, and the forward function returns ()) *)
-let clear_fwd_back (v : vec u32) : result (vec u32) =
-  clear_loop_fwd_back v 0
+let clear (v : alloc_vec_Vec u32) : result (alloc_vec_Vec u32) =
+  clear_loop v 0
 
 (** [loops::list_mem]: loop 0: forward function *)
-let rec list_mem_loop_fwd
+let rec list_mem_loop
   (x : u32) (ls : list_t u32) :
   Tot (result bool) (decreases (list_mem_loop_decreases x ls))
   =
   begin match ls with
-  | ListCons y tl -> if y = x then Return true else list_mem_loop_fwd x tl
-  | ListNil -> Return false
+  | List_Cons y tl -> if y = x then Return true else list_mem_loop x tl
+  | List_Nil -> Return false
   end
 
 (** [loops::list_mem]: forward function *)
-let list_mem_fwd (x : u32) (ls : list_t u32) : result bool =
-  list_mem_loop_fwd x ls
+let list_mem (x : u32) (ls : list_t u32) : result bool =
+  list_mem_loop x ls
 
 (** [loops::list_nth_mut_loop]: loop 0: forward function *)
-let rec list_nth_mut_loop_loop_fwd
+let rec list_nth_mut_loop_loop
   (t : Type0) (ls : list_t t) (i : u32) :
   Tot (result t) (decreases (list_nth_mut_loop_loop_decreases t ls i))
   =
   begin match ls with
-  | ListCons x tl ->
+  | List_Cons x tl ->
     if i = 0
     then Return x
-    else let* i0 = u32_sub i 1 in list_nth_mut_loop_loop_fwd t tl i0
-  | ListNil -> Fail Failure
+    else let* i0 = u32_sub i 1 in list_nth_mut_loop_loop t tl i0
+  | List_Nil -> Fail Failure
   end
 
 (** [loops::list_nth_mut_loop]: forward function *)
-let list_nth_mut_loop_fwd (t : Type0) (ls : list_t t) (i : u32) : result t =
-  list_nth_mut_loop_loop_fwd t ls i
+let list_nth_mut_loop (t : Type0) (ls : list_t t) (i : u32) : result t =
+  list_nth_mut_loop_loop t ls i
 
 (** [loops::list_nth_mut_loop]: loop 0: backward function 0 *)
 let rec list_nth_mut_loop_loop_back
@@ -108,14 +110,14 @@ let rec list_nth_mut_loop_loop_back
   Tot (result (list_t t)) (decreases (list_nth_mut_loop_loop_decreases t ls i))
   =
   begin match ls with
-  | ListCons x tl ->
+  | List_Cons x tl ->
     if i = 0
-    then Return (ListCons ret tl)
+    then Return (List_Cons ret tl)
     else
       let* i0 = u32_sub i 1 in
       let* tl0 = list_nth_mut_loop_loop_back t tl i0 ret in
-      Return (ListCons x tl0)
-  | ListNil -> Fail Failure
+      Return (List_Cons x tl0)
+  | List_Nil -> Fail Failure
   end
 
 (** [loops::list_nth_mut_loop]: backward function 0 *)
@@ -124,36 +126,40 @@ let list_nth_mut_loop_back
   list_nth_mut_loop_loop_back t ls i ret
 
 (** [loops::list_nth_shared_loop]: loop 0: forward function *)
-let rec list_nth_shared_loop_loop_fwd
+let rec list_nth_shared_loop_loop
   (t : Type0) (ls : list_t t) (i : u32) :
   Tot (result t) (decreases (list_nth_shared_loop_loop_decreases t ls i))
   =
   begin match ls with
-  | ListCons x tl ->
+  | List_Cons x tl ->
     if i = 0
     then Return x
-    else let* i0 = u32_sub i 1 in list_nth_shared_loop_loop_fwd t tl i0
-  | ListNil -> Fail Failure
+    else let* i0 = u32_sub i 1 in list_nth_shared_loop_loop t tl i0
+  | List_Nil -> Fail Failure
   end
 
 (** [loops::list_nth_shared_loop]: forward function *)
-let list_nth_shared_loop_fwd (t : Type0) (ls : list_t t) (i : u32) : result t =
-  list_nth_shared_loop_loop_fwd t ls i
+let list_nth_shared_loop (t : Type0) (ls : list_t t) (i : u32) : result t =
+  list_nth_shared_loop_loop t ls i
 
 (** [loops::get_elem_mut]: loop 0: forward function *)
-let rec get_elem_mut_loop_fwd
+let rec get_elem_mut_loop
   (x : usize) (ls : list_t usize) :
   Tot (result usize) (decreases (get_elem_mut_loop_decreases x ls))
   =
   begin match ls with
-  | ListCons y tl -> if y = x then Return y else get_elem_mut_loop_fwd x tl
-  | ListNil -> Fail Failure
+  | List_Cons y tl -> if y = x then Return y else get_elem_mut_loop x tl
+  | List_Nil -> Fail Failure
   end
 
 (** [loops::get_elem_mut]: forward function *)
-let get_elem_mut_fwd (slots : vec (list_t usize)) (x : usize) : result usize =
-  let* l = vec_index_mut_fwd (list_t usize) slots 0 in
-  get_elem_mut_loop_fwd x l
+let get_elem_mut
+  (slots : alloc_vec_Vec (list_t usize)) (x : usize) : result usize =
+  let* l =
+    alloc_vec_Vec_index_mut (list_t usize) usize
+      (core_slice_index_usize_coresliceindexSliceIndexInst (list_t usize))
+      slots 0 in
+  get_elem_mut_loop x l
 
 (** [loops::get_elem_mut]: loop 0: backward function 0 *)
 let rec get_elem_mut_loop_back
@@ -161,39 +167,48 @@ let rec get_elem_mut_loop_back
   Tot (result (list_t usize)) (decreases (get_elem_mut_loop_decreases x ls))
   =
   begin match ls with
-  | ListCons y tl ->
+  | List_Cons y tl ->
     if y = x
-    then Return (ListCons ret tl)
-    else let* tl0 = get_elem_mut_loop_back x tl ret in Return (ListCons y tl0)
-  | ListNil -> Fail Failure
+    then Return (List_Cons ret tl)
+    else let* tl0 = get_elem_mut_loop_back x tl ret in Return (List_Cons y tl0)
+  | List_Nil -> Fail Failure
   end
 
 (** [loops::get_elem_mut]: backward function 0 *)
 let get_elem_mut_back
-  (slots : vec (list_t usize)) (x : usize) (ret : usize) :
-  result (vec (list_t usize))
+  (slots : alloc_vec_Vec (list_t usize)) (x : usize) (ret : usize) :
+  result (alloc_vec_Vec (list_t usize))
   =
-  let* l = vec_index_mut_fwd (list_t usize) slots 0 in
+  let* l =
+    alloc_vec_Vec_index_mut (list_t usize) usize
+      (core_slice_index_usize_coresliceindexSliceIndexInst (list_t usize))
+      slots 0 in
   let* l0 = get_elem_mut_loop_back x l ret in
-  vec_index_mut_back (list_t usize) slots 0 l0
+  alloc_vec_Vec_index_mut_back (list_t usize) usize
+    (core_slice_index_usize_coresliceindexSliceIndexInst (list_t usize)) slots
+    0 l0
 
 (** [loops::get_elem_shared]: loop 0: forward function *)
-let rec get_elem_shared_loop_fwd
+let rec get_elem_shared_loop
   (x : usize) (ls : list_t usize) :
   Tot (result usize) (decreases (get_elem_shared_loop_decreases x ls))
   =
   begin match ls with
-  | ListCons y tl -> if y = x then Return y else get_elem_shared_loop_fwd x tl
-  | ListNil -> Fail Failure
+  | List_Cons y tl -> if y = x then Return y else get_elem_shared_loop x tl
+  | List_Nil -> Fail Failure
   end
 
 (** [loops::get_elem_shared]: forward function *)
-let get_elem_shared_fwd
-  (slots : vec (list_t usize)) (x : usize) : result usize =
-  let* l = vec_index_fwd (list_t usize) slots 0 in get_elem_shared_loop_fwd x l
+let get_elem_shared
+  (slots : alloc_vec_Vec (list_t usize)) (x : usize) : result usize =
+  let* l =
+    alloc_vec_Vec_index (list_t usize) usize
+      (core_slice_index_usize_coresliceindexSliceIndexInst (list_t usize))
+      slots 0 in
+  get_elem_shared_loop x l
 
 (** [loops::id_mut]: forward function *)
-let id_mut_fwd (t : Type0) (ls : list_t t) : result (list_t t) =
+let id_mut (t : Type0) (ls : list_t t) : result (list_t t) =
   Return ls
 
 (** [loops::id_mut]: backward function 0 *)
@@ -202,26 +217,26 @@ let id_mut_back
   Return ret
 
 (** [loops::id_shared]: forward function *)
-let id_shared_fwd (t : Type0) (ls : list_t t) : result (list_t t) =
+let id_shared (t : Type0) (ls : list_t t) : result (list_t t) =
   Return ls
 
 (** [loops::list_nth_mut_loop_with_id]: loop 0: forward function *)
-let rec list_nth_mut_loop_with_id_loop_fwd
+let rec list_nth_mut_loop_with_id_loop
   (t : Type0) (i : u32) (ls : list_t t) :
   Tot (result t) (decreases (list_nth_mut_loop_with_id_loop_decreases t i ls))
   =
   begin match ls with
-  | ListCons x tl ->
+  | List_Cons x tl ->
     if i = 0
     then Return x
-    else let* i0 = u32_sub i 1 in list_nth_mut_loop_with_id_loop_fwd t i0 tl
-  | ListNil -> Fail Failure
+    else let* i0 = u32_sub i 1 in list_nth_mut_loop_with_id_loop t i0 tl
+  | List_Nil -> Fail Failure
   end
 
 (** [loops::list_nth_mut_loop_with_id]: forward function *)
-let list_nth_mut_loop_with_id_fwd
+let list_nth_mut_loop_with_id
   (t : Type0) (ls : list_t t) (i : u32) : result t =
-  let* ls0 = id_mut_fwd t ls in list_nth_mut_loop_with_id_loop_fwd t i ls0
+  let* ls0 = id_mut t ls in list_nth_mut_loop_with_id_loop t i ls0
 
 (** [loops::list_nth_mut_loop_with_id]: loop 0: backward function 0 *)
 let rec list_nth_mut_loop_with_id_loop_back
@@ -230,66 +245,64 @@ let rec list_nth_mut_loop_with_id_loop_back
   (decreases (list_nth_mut_loop_with_id_loop_decreases t i ls))
   =
   begin match ls with
-  | ListCons x tl ->
+  | List_Cons x tl ->
     if i = 0
-    then Return (ListCons ret tl)
+    then Return (List_Cons ret tl)
     else
       let* i0 = u32_sub i 1 in
       let* tl0 = list_nth_mut_loop_with_id_loop_back t i0 tl ret in
-      Return (ListCons x tl0)
-  | ListNil -> Fail Failure
+      Return (List_Cons x tl0)
+  | List_Nil -> Fail Failure
   end
 
 (** [loops::list_nth_mut_loop_with_id]: backward function 0 *)
 let list_nth_mut_loop_with_id_back
   (t : Type0) (ls : list_t t) (i : u32) (ret : t) : result (list_t t) =
-  let* ls0 = id_mut_fwd t ls in
+  let* ls0 = id_mut t ls in
   let* l = list_nth_mut_loop_with_id_loop_back t i ls0 ret in
   id_mut_back t ls l
 
 (** [loops::list_nth_shared_loop_with_id]: loop 0: forward function *)
-let rec list_nth_shared_loop_with_id_loop_fwd
+let rec list_nth_shared_loop_with_id_loop
   (t : Type0) (i : u32) (ls : list_t t) :
   Tot (result t)
   (decreases (list_nth_shared_loop_with_id_loop_decreases t i ls))
   =
   begin match ls with
-  | ListCons x tl ->
+  | List_Cons x tl ->
     if i = 0
     then Return x
-    else let* i0 = u32_sub i 1 in list_nth_shared_loop_with_id_loop_fwd t i0 tl
-  | ListNil -> Fail Failure
+    else let* i0 = u32_sub i 1 in list_nth_shared_loop_with_id_loop t i0 tl
+  | List_Nil -> Fail Failure
   end
 
 (** [loops::list_nth_shared_loop_with_id]: forward function *)
-let list_nth_shared_loop_with_id_fwd
+let list_nth_shared_loop_with_id
   (t : Type0) (ls : list_t t) (i : u32) : result t =
-  let* ls0 = id_shared_fwd t ls in
-  list_nth_shared_loop_with_id_loop_fwd t i ls0
+  let* ls0 = id_shared t ls in list_nth_shared_loop_with_id_loop t i ls0
 
 (** [loops::list_nth_mut_loop_pair]: loop 0: forward function *)
-let rec list_nth_mut_loop_pair_loop_fwd
+let rec list_nth_mut_loop_pair_loop
   (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) :
   Tot (result (t & t))
   (decreases (list_nth_mut_loop_pair_loop_decreases t ls0 ls1 i))
   =
   begin match ls0 with
-  | ListCons x0 tl0 ->
+  | List_Cons x0 tl0 ->
     begin match ls1 with
-    | ListCons x1 tl1 ->
+    | List_Cons x1 tl1 ->
       if i = 0
       then Return (x0, x1)
-      else
-        let* i0 = u32_sub i 1 in list_nth_mut_loop_pair_loop_fwd t tl0 tl1 i0
-    | ListNil -> Fail Failure
+      else let* i0 = u32_sub i 1 in list_nth_mut_loop_pair_loop t tl0 tl1 i0
+    | List_Nil -> Fail Failure
     end
-  | ListNil -> Fail Failure
+  | List_Nil -> Fail Failure
   end
 
 (** [loops::list_nth_mut_loop_pair]: forward function *)
-let list_nth_mut_loop_pair_fwd
+let list_nth_mut_loop_pair
   (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) : result (t & t) =
-  list_nth_mut_loop_pair_loop_fwd t ls0 ls1 i
+  list_nth_mut_loop_pair_loop t ls0 ls1 i
 
 (** [loops::list_nth_mut_loop_pair]: loop 0: backward function 0 *)
 let rec list_nth_mut_loop_pair_loop_back'a
@@ -298,18 +311,18 @@ let rec list_nth_mut_loop_pair_loop_back'a
   (decreases (list_nth_mut_loop_pair_loop_decreases t ls0 ls1 i))
   =
   begin match ls0 with
-  | ListCons x0 tl0 ->
+  | List_Cons x0 tl0 ->
     begin match ls1 with
-    | ListCons x1 tl1 ->
+    | List_Cons x1 tl1 ->
       if i = 0
-      then Return (ListCons ret tl0)
+      then Return (List_Cons ret tl0)
       else
         let* i0 = u32_sub i 1 in
         let* tl00 = list_nth_mut_loop_pair_loop_back'a t tl0 tl1 i0 ret in
-        Return (ListCons x0 tl00)
-    | ListNil -> Fail Failure
+        Return (List_Cons x0 tl00)
+    | List_Nil -> Fail Failure
     end
-  | ListNil -> Fail Failure
+  | List_Nil -> Fail Failure
   end
 
 (** [loops::list_nth_mut_loop_pair]: backward function 0 *)
@@ -326,18 +339,18 @@ let rec list_nth_mut_loop_pair_loop_back'b
   (decreases (list_nth_mut_loop_pair_loop_decreases t ls0 ls1 i))
   =
   begin match ls0 with
-  | ListCons x0 tl0 ->
+  | List_Cons x0 tl0 ->
     begin match ls1 with
-    | ListCons x1 tl1 ->
+    | List_Cons x1 tl1 ->
       if i = 0
-      then Return (ListCons ret tl1)
+      then Return (List_Cons ret tl1)
       else
         let* i0 = u32_sub i 1 in
         let* tl10 = list_nth_mut_loop_pair_loop_back'b t tl0 tl1 i0 ret in
-        Return (ListCons x1 tl10)
-    | ListNil -> Fail Failure
+        Return (List_Cons x1 tl10)
+    | List_Nil -> Fail Failure
     end
-  | ListNil -> Fail Failure
+  | List_Nil -> Fail Failure
   end
 
 (** [loops::list_nth_mut_loop_pair]: backward function 1 *)
@@ -348,54 +361,51 @@ let list_nth_mut_loop_pair_back'b
   list_nth_mut_loop_pair_loop_back'b t ls0 ls1 i ret
 
 (** [loops::list_nth_shared_loop_pair]: loop 0: forward function *)
-let rec list_nth_shared_loop_pair_loop_fwd
+let rec list_nth_shared_loop_pair_loop
   (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) :
   Tot (result (t & t))
   (decreases (list_nth_shared_loop_pair_loop_decreases t ls0 ls1 i))
   =
   begin match ls0 with
-  | ListCons x0 tl0 ->
+  | List_Cons x0 tl0 ->
     begin match ls1 with
-    | ListCons x1 tl1 ->
+    | List_Cons x1 tl1 ->
       if i = 0
       then Return (x0, x1)
-      else
-        let* i0 = u32_sub i 1 in
-        list_nth_shared_loop_pair_loop_fwd t tl0 tl1 i0
-    | ListNil -> Fail Failure
+      else let* i0 = u32_sub i 1 in list_nth_shared_loop_pair_loop t tl0 tl1 i0
+    | List_Nil -> Fail Failure
     end
-  | ListNil -> Fail Failure
+  | List_Nil -> Fail Failure
   end
 
 (** [loops::list_nth_shared_loop_pair]: forward function *)
-let list_nth_shared_loop_pair_fwd
+let list_nth_shared_loop_pair
   (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) : result (t & t) =
-  list_nth_shared_loop_pair_loop_fwd t ls0 ls1 i
+  list_nth_shared_loop_pair_loop t ls0 ls1 i
 
 (** [loops::list_nth_mut_loop_pair_merge]: loop 0: forward function *)
-let rec list_nth_mut_loop_pair_merge_loop_fwd
+let rec list_nth_mut_loop_pair_merge_loop
   (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) :
   Tot (result (t & t))
   (decreases (list_nth_mut_loop_pair_merge_loop_decreases t ls0 ls1 i))
   =
   begin match ls0 with
-  | ListCons x0 tl0 ->
+  | List_Cons x0 tl0 ->
     begin match ls1 with
-    | ListCons x1 tl1 ->
+    | List_Cons x1 tl1 ->
       if i = 0
       then Return (x0, x1)
       else
-        let* i0 = u32_sub i 1 in
-        list_nth_mut_loop_pair_merge_loop_fwd t tl0 tl1 i0
-    | ListNil -> Fail Failure
+        let* i0 = u32_sub i 1 in list_nth_mut_loop_pair_merge_loop t tl0 tl1 i0
+    | List_Nil -> Fail Failure
     end
-  | ListNil -> Fail Failure
+  | List_Nil -> Fail Failure
   end
 
 (** [loops::list_nth_mut_loop_pair_merge]: forward function *)
-let list_nth_mut_loop_pair_merge_fwd
+let list_nth_mut_loop_pair_merge
   (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) : result (t & t) =
-  list_nth_mut_loop_pair_merge_loop_fwd t ls0 ls1 i
+  list_nth_mut_loop_pair_merge_loop t ls0 ls1 i
 
 (** [loops::list_nth_mut_loop_pair_merge]: loop 0: backward function 0 *)
 let rec list_nth_mut_loop_pair_merge_loop_back
@@ -404,19 +414,19 @@ let rec list_nth_mut_loop_pair_merge_loop_back
   (decreases (list_nth_mut_loop_pair_merge_loop_decreases t ls0 ls1 i))
   =
   begin match ls0 with
-  | ListCons x0 tl0 ->
+  | List_Cons x0 tl0 ->
     begin match ls1 with
-    | ListCons x1 tl1 ->
+    | List_Cons x1 tl1 ->
       if i = 0
-      then let (x, x2) = ret in Return (ListCons x tl0, ListCons x2 tl1)
+      then let (x, x2) = ret in Return (List_Cons x tl0, List_Cons x2 tl1)
       else
         let* i0 = u32_sub i 1 in
         let* (tl00, tl10) =
           list_nth_mut_loop_pair_merge_loop_back t tl0 tl1 i0 ret in
-        Return (ListCons x0 tl00, ListCons x1 tl10)
-    | ListNil -> Fail Failure
+        Return (List_Cons x0 tl00, List_Cons x1 tl10)
+    | List_Nil -> Fail Failure
     end
-  | ListNil -> Fail Failure
+  | List_Nil -> Fail Failure
   end
 
 (** [loops::list_nth_mut_loop_pair_merge]: backward function 0 *)
@@ -427,54 +437,54 @@ let list_nth_mut_loop_pair_merge_back
   list_nth_mut_loop_pair_merge_loop_back t ls0 ls1 i ret
 
 (** [loops::list_nth_shared_loop_pair_merge]: loop 0: forward function *)
-let rec list_nth_shared_loop_pair_merge_loop_fwd
+let rec list_nth_shared_loop_pair_merge_loop
   (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) :
   Tot (result (t & t))
   (decreases (list_nth_shared_loop_pair_merge_loop_decreases t ls0 ls1 i))
   =
   begin match ls0 with
-  | ListCons x0 tl0 ->
+  | List_Cons x0 tl0 ->
     begin match ls1 with
-    | ListCons x1 tl1 ->
+    | List_Cons x1 tl1 ->
       if i = 0
       then Return (x0, x1)
       else
         let* i0 = u32_sub i 1 in
-        list_nth_shared_loop_pair_merge_loop_fwd t tl0 tl1 i0
-    | ListNil -> Fail Failure
+        list_nth_shared_loop_pair_merge_loop t tl0 tl1 i0
+    | List_Nil -> Fail Failure
     end
-  | ListNil -> Fail Failure
+  | List_Nil -> Fail Failure
   end
 
 (** [loops::list_nth_shared_loop_pair_merge]: forward function *)
-let list_nth_shared_loop_pair_merge_fwd
+let list_nth_shared_loop_pair_merge
   (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) : result (t & t) =
-  list_nth_shared_loop_pair_merge_loop_fwd t ls0 ls1 i
+  list_nth_shared_loop_pair_merge_loop t ls0 ls1 i
 
 (** [loops::list_nth_mut_shared_loop_pair]: loop 0: forward function *)
-let rec list_nth_mut_shared_loop_pair_loop_fwd
+let rec list_nth_mut_shared_loop_pair_loop
   (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) :
   Tot (result (t & t))
   (decreases (list_nth_mut_shared_loop_pair_loop_decreases t ls0 ls1 i))
   =
   begin match ls0 with
-  | ListCons x0 tl0 ->
+  | List_Cons x0 tl0 ->
     begin match ls1 with
-    | ListCons x1 tl1 ->
+    | List_Cons x1 tl1 ->
       if i = 0
       then Return (x0, x1)
       else
         let* i0 = u32_sub i 1 in
-        list_nth_mut_shared_loop_pair_loop_fwd t tl0 tl1 i0
-    | ListNil -> Fail Failure
+        list_nth_mut_shared_loop_pair_loop t tl0 tl1 i0
+    | List_Nil -> Fail Failure
     end
-  | ListNil -> Fail Failure
+  | List_Nil -> Fail Failure
   end
 
 (** [loops::list_nth_mut_shared_loop_pair]: forward function *)
-let list_nth_mut_shared_loop_pair_fwd
+let list_nth_mut_shared_loop_pair
   (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) : result (t & t) =
-  list_nth_mut_shared_loop_pair_loop_fwd t ls0 ls1 i
+  list_nth_mut_shared_loop_pair_loop t ls0 ls1 i
 
 (** [loops::list_nth_mut_shared_loop_pair]: loop 0: backward function 0 *)
 let rec list_nth_mut_shared_loop_pair_loop_back
@@ -483,18 +493,18 @@ let rec list_nth_mut_shared_loop_pair_loop_back
   (decreases (list_nth_mut_shared_loop_pair_loop_decreases t ls0 ls1 i))
   =
   begin match ls0 with
-  | ListCons x0 tl0 ->
+  | List_Cons x0 tl0 ->
     begin match ls1 with
-    | ListCons x1 tl1 ->
+    | List_Cons x1 tl1 ->
       if i = 0
-      then Return (ListCons ret tl0)
+      then Return (List_Cons ret tl0)
       else
         let* i0 = u32_sub i 1 in
         let* tl00 = list_nth_mut_shared_loop_pair_loop_back t tl0 tl1 i0 ret in
-        Return (ListCons x0 tl00)
-    | ListNil -> Fail Failure
+        Return (List_Cons x0 tl00)
+    | List_Nil -> Fail Failure
     end
-  | ListNil -> Fail Failure
+  | List_Nil -> Fail Failure
   end
 
 (** [loops::list_nth_mut_shared_loop_pair]: backward function 0 *)
@@ -505,29 +515,29 @@ let list_nth_mut_shared_loop_pair_back
   list_nth_mut_shared_loop_pair_loop_back t ls0 ls1 i ret
 
 (** [loops::list_nth_mut_shared_loop_pair_merge]: loop 0: forward function *)
-let rec list_nth_mut_shared_loop_pair_merge_loop_fwd
+let rec list_nth_mut_shared_loop_pair_merge_loop
   (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) :
   Tot (result (t & t))
   (decreases (list_nth_mut_shared_loop_pair_merge_loop_decreases t ls0 ls1 i))
   =
   begin match ls0 with
-  | ListCons x0 tl0 ->
+  | List_Cons x0 tl0 ->
     begin match ls1 with
-    | ListCons x1 tl1 ->
+    | List_Cons x1 tl1 ->
       if i = 0
       then Return (x0, x1)
       else
         let* i0 = u32_sub i 1 in
-        list_nth_mut_shared_loop_pair_merge_loop_fwd t tl0 tl1 i0
-    | ListNil -> Fail Failure
+        list_nth_mut_shared_loop_pair_merge_loop t tl0 tl1 i0
+    | List_Nil -> Fail Failure
     end
-  | ListNil -> Fail Failure
+  | List_Nil -> Fail Failure
   end
 
 (** [loops::list_nth_mut_shared_loop_pair_merge]: forward function *)
-let list_nth_mut_shared_loop_pair_merge_fwd
+let list_nth_mut_shared_loop_pair_merge
   (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) : result (t & t) =
-  list_nth_mut_shared_loop_pair_merge_loop_fwd t ls0 ls1 i
+  list_nth_mut_shared_loop_pair_merge_loop t ls0 ls1 i
 
 (** [loops::list_nth_mut_shared_loop_pair_merge]: loop 0: backward function 0 *)
 let rec list_nth_mut_shared_loop_pair_merge_loop_back
@@ -536,19 +546,19 @@ let rec list_nth_mut_shared_loop_pair_merge_loop_back
   (decreases (list_nth_mut_shared_loop_pair_merge_loop_decreases t ls0 ls1 i))
   =
   begin match ls0 with
-  | ListCons x0 tl0 ->
+  | List_Cons x0 tl0 ->
     begin match ls1 with
-    | ListCons x1 tl1 ->
+    | List_Cons x1 tl1 ->
       if i = 0
-      then Return (ListCons ret tl0)
+      then Return (List_Cons ret tl0)
       else
         let* i0 = u32_sub i 1 in
         let* tl00 =
           list_nth_mut_shared_loop_pair_merge_loop_back t tl0 tl1 i0 ret in
-        Return (ListCons x0 tl00)
-    | ListNil -> Fail Failure
+        Return (List_Cons x0 tl00)
+    | List_Nil -> Fail Failure
     end
-  | ListNil -> Fail Failure
+  | List_Nil -> Fail Failure
   end
 
 (** [loops::list_nth_mut_shared_loop_pair_merge]: backward function 0 *)
@@ -559,29 +569,29 @@ let list_nth_mut_shared_loop_pair_merge_back
   list_nth_mut_shared_loop_pair_merge_loop_back t ls0 ls1 i ret
 
 (** [loops::list_nth_shared_mut_loop_pair]: loop 0: forward function *)
-let rec list_nth_shared_mut_loop_pair_loop_fwd
+let rec list_nth_shared_mut_loop_pair_loop
   (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) :
   Tot (result (t & t))
   (decreases (list_nth_shared_mut_loop_pair_loop_decreases t ls0 ls1 i))
   =
   begin match ls0 with
-  | ListCons x0 tl0 ->
+  | List_Cons x0 tl0 ->
     begin match ls1 with
-    | ListCons x1 tl1 ->
+    | List_Cons x1 tl1 ->
       if i = 0
       then Return (x0, x1)
       else
         let* i0 = u32_sub i 1 in
-        list_nth_shared_mut_loop_pair_loop_fwd t tl0 tl1 i0
-    | ListNil -> Fail Failure
+        list_nth_shared_mut_loop_pair_loop t tl0 tl1 i0
+    | List_Nil -> Fail Failure
     end
-  | ListNil -> Fail Failure
+  | List_Nil -> Fail Failure
   end
 
 (** [loops::list_nth_shared_mut_loop_pair]: forward function *)
-let list_nth_shared_mut_loop_pair_fwd
+let list_nth_shared_mut_loop_pair
   (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) : result (t & t) =
-  list_nth_shared_mut_loop_pair_loop_fwd t ls0 ls1 i
+  list_nth_shared_mut_loop_pair_loop t ls0 ls1 i
 
 (** [loops::list_nth_shared_mut_loop_pair]: loop 0: backward function 1 *)
 let rec list_nth_shared_mut_loop_pair_loop_back
@@ -590,18 +600,18 @@ let rec list_nth_shared_mut_loop_pair_loop_back
   (decreases (list_nth_shared_mut_loop_pair_loop_decreases t ls0 ls1 i))
   =
   begin match ls0 with
-  | ListCons x0 tl0 ->
+  | List_Cons x0 tl0 ->
     begin match ls1 with
-    | ListCons x1 tl1 ->
+    | List_Cons x1 tl1 ->
       if i = 0
-      then Return (ListCons ret tl1)
+      then Return (List_Cons ret tl1)
       else
         let* i0 = u32_sub i 1 in
         let* tl10 = list_nth_shared_mut_loop_pair_loop_back t tl0 tl1 i0 ret in
-        Return (ListCons x1 tl10)
-    | ListNil -> Fail Failure
+        Return (List_Cons x1 tl10)
+    | List_Nil -> Fail Failure
     end
-  | ListNil -> Fail Failure
+  | List_Nil -> Fail Failure
   end
 
 (** [loops::list_nth_shared_mut_loop_pair]: backward function 1 *)
@@ -612,29 +622,29 @@ let list_nth_shared_mut_loop_pair_back
   list_nth_shared_mut_loop_pair_loop_back t ls0 ls1 i ret
 
 (** [loops::list_nth_shared_mut_loop_pair_merge]: loop 0: forward function *)
-let rec list_nth_shared_mut_loop_pair_merge_loop_fwd
+let rec list_nth_shared_mut_loop_pair_merge_loop
   (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) :
   Tot (result (t & t))
   (decreases (list_nth_shared_mut_loop_pair_merge_loop_decreases t ls0 ls1 i))
   =
   begin match ls0 with
-  | ListCons x0 tl0 ->
+  | List_Cons x0 tl0 ->
     begin match ls1 with
-    | ListCons x1 tl1 ->
+    | List_Cons x1 tl1 ->
       if i = 0
       then Return (x0, x1)
       else
         let* i0 = u32_sub i 1 in
-        list_nth_shared_mut_loop_pair_merge_loop_fwd t tl0 tl1 i0
-    | ListNil -> Fail Failure
+        list_nth_shared_mut_loop_pair_merge_loop t tl0 tl1 i0
+    | List_Nil -> Fail Failure
     end
-  | ListNil -> Fail Failure
+  | List_Nil -> Fail Failure
   end
 
 (** [loops::list_nth_shared_mut_loop_pair_merge]: forward function *)
-let list_nth_shared_mut_loop_pair_merge_fwd
+let list_nth_shared_mut_loop_pair_merge
   (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) : result (t & t) =
-  list_nth_shared_mut_loop_pair_merge_loop_fwd t ls0 ls1 i
+  list_nth_shared_mut_loop_pair_merge_loop t ls0 ls1 i
 
 (** [loops::list_nth_shared_mut_loop_pair_merge]: loop 0: backward function 0 *)
 let rec list_nth_shared_mut_loop_pair_merge_loop_back
@@ -643,19 +653,19 @@ let rec list_nth_shared_mut_loop_pair_merge_loop_back
   (decreases (list_nth_shared_mut_loop_pair_merge_loop_decreases t ls0 ls1 i))
   =
   begin match ls0 with
-  | ListCons x0 tl0 ->
+  | List_Cons x0 tl0 ->
     begin match ls1 with
-    | ListCons x1 tl1 ->
+    | List_Cons x1 tl1 ->
       if i = 0
-      then Return (ListCons ret tl1)
+      then Return (List_Cons ret tl1)
       else
         let* i0 = u32_sub i 1 in
         let* tl10 =
           list_nth_shared_mut_loop_pair_merge_loop_back t tl0 tl1 i0 ret in
-        Return (ListCons x1 tl10)
-    | ListNil -> Fail Failure
+        Return (List_Cons x1 tl10)
+    | List_Nil -> Fail Failure
     end
-  | ListNil -> Fail Failure
+  | List_Nil -> Fail Failure
   end
 
 (** [loops::list_nth_shared_mut_loop_pair_merge]: backward function 0 *)
diff --git a/tests/fstar/misc/Loops.Types.fst b/tests/fstar/misc/Loops.Types.fst
index 2e032fe7..c622c548 100644
--- a/tests/fstar/misc/Loops.Types.fst
+++ b/tests/fstar/misc/Loops.Types.fst
@@ -7,6 +7,6 @@ open Primitives
 
 (** [loops::List] *)
 type list_t (t : Type0) =
-| ListCons : t -> list_t t -> list_t t
-| ListNil : list_t t
+| List_Cons : t -> list_t t -> list_t t
+| List_Nil : list_t t
 
diff --git a/tests/fstar/misc/NoNestedBorrows.fst b/tests/fstar/misc/NoNestedBorrows.fst
index 2cdd6e21..e97927aa 100644
--- a/tests/fstar/misc/NoNestedBorrows.fst
+++ b/tests/fstar/misc/NoNestedBorrows.fst
@@ -6,95 +6,107 @@ open Primitives
 #set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
 
 (** [no_nested_borrows::Pair] *)
-type pair_t (t1 t2 : Type0) = { pair_x : t1; pair_y : t2; }
+type pair_t (t1 t2 : Type0) = { x : t1; y : t2; }
 
 (** [no_nested_borrows::List] *)
 type list_t (t : Type0) =
-| ListCons : t -> list_t t -> list_t t
-| ListNil : list_t t
+| List_Cons : t -> list_t t -> list_t t
+| List_Nil : list_t t
 
 (** [no_nested_borrows::One] *)
-type one_t (t1 : Type0) = | OneOne : t1 -> one_t t1
+type one_t (t1 : Type0) = | One_One : t1 -> one_t t1
 
 (** [no_nested_borrows::EmptyEnum] *)
-type empty_enum_t = | EmptyEnumEmpty : empty_enum_t
+type emptyEnum_t = | EmptyEnum_Empty : emptyEnum_t
 
 (** [no_nested_borrows::Enum] *)
-type enum_t = | EnumVariant1 : enum_t | EnumVariant2 : enum_t
+type enum_t = | Enum_Variant1 : enum_t | Enum_Variant2 : enum_t
 
 (** [no_nested_borrows::EmptyStruct] *)
-type empty_struct_t = unit
+type emptyStruct_t = unit
 
 (** [no_nested_borrows::Sum] *)
 type sum_t (t1 t2 : Type0) =
-| SumLeft : t1 -> sum_t t1 t2
-| SumRight : t2 -> sum_t t1 t2
+| Sum_Left : t1 -> sum_t t1 t2
+| Sum_Right : t2 -> sum_t t1 t2
 
 (** [no_nested_borrows::neg_test]: forward function *)
-let neg_test_fwd (x : i32) : result i32 =
+let neg_test (x : i32) : result i32 =
   i32_neg x
 
 (** [no_nested_borrows::add_test]: forward function *)
-let add_test_fwd (x : u32) (y : u32) : result u32 =
+let add_test (x : u32) (y : u32) : result u32 =
   u32_add x y
 
 (** [no_nested_borrows::subs_test]: forward function *)
-let subs_test_fwd (x : u32) (y : u32) : result u32 =
+let subs_test (x : u32) (y : u32) : result u32 =
   u32_sub x y
 
 (** [no_nested_borrows::div_test]: forward function *)
-let div_test_fwd (x : u32) (y : u32) : result u32 =
+let div_test (x : u32) (y : u32) : result u32 =
   u32_div x y
 
 (** [no_nested_borrows::div_test1]: forward function *)
-let div_test1_fwd (x : u32) : result u32 =
+let div_test1 (x : u32) : result u32 =
   u32_div x 2
 
 (** [no_nested_borrows::rem_test]: forward function *)
-let rem_test_fwd (x : u32) (y : u32) : result u32 =
+let rem_test (x : u32) (y : u32) : result u32 =
   u32_rem x y
 
+(** [no_nested_borrows::mul_test]: forward function *)
+let mul_test (x : u32) (y : u32) : result u32 =
+  u32_mul x y
+
+(** [no_nested_borrows::CONST0] *)
+let const0_body : result usize = usize_add 1 1
+let const0_c : usize = eval_global const0_body
+
+(** [no_nested_borrows::CONST1] *)
+let const1_body : result usize = usize_mul 2 2
+let const1_c : usize = eval_global const1_body
+
 (** [no_nested_borrows::cast_test]: forward function *)
-let cast_test_fwd (x : u32) : result i32 =
+let cast_test (x : u32) : result i32 =
   scalar_cast U32 I32 x
 
 (** [no_nested_borrows::test2]: forward function *)
-let test2_fwd : result unit =
+let test2 : result unit =
   let* _ = u32_add 23 44 in Return ()
 
 (** Unit test for [no_nested_borrows::test2] *)
-let _ = assert_norm (test2_fwd = Return ())
+let _ = assert_norm (test2 = Return ())
 
 (** [no_nested_borrows::get_max]: forward function *)
-let get_max_fwd (x : u32) (y : u32) : result u32 =
+let get_max (x : u32) (y : u32) : result u32 =
   if x >= y then Return x else Return y
 
 (** [no_nested_borrows::test3]: forward function *)
-let test3_fwd : result unit =
-  let* x = get_max_fwd 4 3 in
-  let* y = get_max_fwd 10 11 in
+let test3 : result unit =
+  let* x = get_max 4 3 in
+  let* y = get_max 10 11 in
   let* z = u32_add x y in
   if not (z = 15) then Fail Failure else Return ()
 
 (** Unit test for [no_nested_borrows::test3] *)
-let _ = assert_norm (test3_fwd = Return ())
+let _ = assert_norm (test3 = Return ())
 
 (** [no_nested_borrows::test_neg1]: forward function *)
-let test_neg1_fwd : result unit =
+let test_neg1 : result unit =
   let* y = i32_neg 3 in if not (y = -3) then Fail Failure else Return ()
 
 (** Unit test for [no_nested_borrows::test_neg1] *)
-let _ = assert_norm (test_neg1_fwd = Return ())
+let _ = assert_norm (test_neg1 = Return ())
 
 (** [no_nested_borrows::refs_test1]: forward function *)
-let refs_test1_fwd : result unit =
+let refs_test1 : result unit =
   if not (1 = 1) then Fail Failure else Return ()
 
 (** Unit test for [no_nested_borrows::refs_test1] *)
-let _ = assert_norm (refs_test1_fwd = Return ())
+let _ = assert_norm (refs_test1 = Return ())
 
 (** [no_nested_borrows::refs_test2]: forward function *)
-let refs_test2_fwd : result unit =
+let refs_test2 : result unit =
   if not (2 = 2)
   then Fail Failure
   else
@@ -106,76 +118,76 @@ let refs_test2_fwd : result unit =
       else if not (2 = 2) then Fail Failure else Return ()
 
 (** Unit test for [no_nested_borrows::refs_test2] *)
-let _ = assert_norm (refs_test2_fwd = Return ())
+let _ = assert_norm (refs_test2 = Return ())
 
 (** [no_nested_borrows::test_list1]: forward function *)
-let test_list1_fwd : result unit =
+let test_list1 : result unit =
   Return ()
 
 (** Unit test for [no_nested_borrows::test_list1] *)
-let _ = assert_norm (test_list1_fwd = Return ())
+let _ = assert_norm (test_list1 = Return ())
 
 (** [no_nested_borrows::test_box1]: forward function *)
-let test_box1_fwd : result unit =
+let test_box1 : result unit =
   let b = 1 in let x = b in if not (x = 1) then Fail Failure else Return ()
 
 (** Unit test for [no_nested_borrows::test_box1] *)
-let _ = assert_norm (test_box1_fwd = Return ())
+let _ = assert_norm (test_box1 = Return ())
 
 (** [no_nested_borrows::copy_int]: forward function *)
-let copy_int_fwd (x : i32) : result i32 =
+let copy_int (x : i32) : result i32 =
   Return x
 
 (** [no_nested_borrows::test_unreachable]: forward function *)
-let test_unreachable_fwd (b : bool) : result unit =
+let test_unreachable (b : bool) : result unit =
   if b then Fail Failure else Return ()
 
 (** [no_nested_borrows::test_panic]: forward function *)
-let test_panic_fwd (b : bool) : result unit =
+let test_panic (b : bool) : result unit =
   if b then Fail Failure else Return ()
 
 (** [no_nested_borrows::test_copy_int]: forward function *)
-let test_copy_int_fwd : result unit =
-  let* y = copy_int_fwd 0 in if not (0 = y) then Fail Failure else Return ()
+let test_copy_int : result unit =
+  let* y = copy_int 0 in if not (0 = y) then Fail Failure else Return ()
 
 (** Unit test for [no_nested_borrows::test_copy_int] *)
-let _ = assert_norm (test_copy_int_fwd = Return ())
+let _ = assert_norm (test_copy_int = Return ())
 
 (** [no_nested_borrows::is_cons]: forward function *)
-let is_cons_fwd (t : Type0) (l : list_t t) : result bool =
+let is_cons (t : Type0) (l : list_t t) : result bool =
   begin match l with
-  | ListCons x l0 -> Return true
-  | ListNil -> Return false
+  | List_Cons x l0 -> Return true
+  | List_Nil -> Return false
   end
 
 (** [no_nested_borrows::test_is_cons]: forward function *)
-let test_is_cons_fwd : result unit =
-  let l = ListNil in
-  let* b = is_cons_fwd i32 (ListCons 0 l) in
+let test_is_cons : result unit =
+  let l = List_Nil in
+  let* b = is_cons i32 (List_Cons 0 l) in
   if not b then Fail Failure else Return ()
 
 (** Unit test for [no_nested_borrows::test_is_cons] *)
-let _ = assert_norm (test_is_cons_fwd = Return ())
+let _ = assert_norm (test_is_cons = Return ())
 
 (** [no_nested_borrows::split_list]: forward function *)
-let split_list_fwd (t : Type0) (l : list_t t) : result (t & (list_t t)) =
+let split_list (t : Type0) (l : list_t t) : result (t & (list_t t)) =
   begin match l with
-  | ListCons hd tl -> Return (hd, tl)
-  | ListNil -> Fail Failure
+  | List_Cons hd tl -> Return (hd, tl)
+  | List_Nil -> Fail Failure
   end
 
 (** [no_nested_borrows::test_split_list]: forward function *)
-let test_split_list_fwd : result unit =
-  let l = ListNil in
-  let* p = split_list_fwd i32 (ListCons 0 l) in
+let test_split_list : result unit =
+  let l = List_Nil in
+  let* p = split_list i32 (List_Cons 0 l) in
   let (hd, _) = p in
   if not (hd = 0) then Fail Failure else Return ()
 
 (** Unit test for [no_nested_borrows::test_split_list] *)
-let _ = assert_norm (test_split_list_fwd = Return ())
+let _ = assert_norm (test_split_list = Return ())
 
 (** [no_nested_borrows::choose]: forward function *)
-let choose_fwd (t : Type0) (b : bool) (x : t) (y : t) : result t =
+let choose (t : Type0) (b : bool) (x : t) (y : t) : result t =
   if b then Return x else Return y
 
 (** [no_nested_borrows::choose]: backward function 0 *)
@@ -184,8 +196,8 @@ let choose_back
   if b then Return (ret, y) else Return (x, ret)
 
 (** [no_nested_borrows::choose_test]: forward function *)
-let choose_test_fwd : result unit =
-  let* z = choose_fwd i32 true 0 0 in
+let choose_test : result unit =
+  let* z = choose i32 true 0 0 in
   let* z0 = i32_add z 1 in
   if not (z0 = 1)
   then Fail Failure
@@ -196,115 +208,112 @@ let choose_test_fwd : result unit =
     else if not (y = 0) then Fail Failure else Return ()
 
 (** Unit test for [no_nested_borrows::choose_test] *)
-let _ = assert_norm (choose_test_fwd = Return ())
+let _ = assert_norm (choose_test = Return ())
 
 (** [no_nested_borrows::test_char]: forward function *)
-let test_char_fwd : result char =
+let test_char : result char =
   Return 'a'
 
 (** [no_nested_borrows::Tree] *)
 type tree_t (t : Type0) =
-| TreeLeaf : t -> tree_t t
-| TreeNode : t -> node_elem_t t -> tree_t t -> tree_t t
+| Tree_Leaf : t -> tree_t t
+| Tree_Node : t -> nodeElem_t t -> tree_t t -> tree_t t
 
 (** [no_nested_borrows::NodeElem] *)
-and node_elem_t (t : Type0) =
-| NodeElemCons : tree_t t -> node_elem_t t -> node_elem_t t
-| NodeElemNil : node_elem_t t
+and nodeElem_t (t : Type0) =
+| NodeElem_Cons : tree_t t -> nodeElem_t t -> nodeElem_t t
+| NodeElem_Nil : nodeElem_t t
 
 (** [no_nested_borrows::list_length]: forward function *)
-let rec list_length_fwd (t : Type0) (l : list_t t) : result u32 =
+let rec list_length (t : Type0) (l : list_t t) : result u32 =
   begin match l with
-  | ListCons x l1 -> let* i = list_length_fwd t l1 in u32_add 1 i
-  | ListNil -> Return 0
+  | List_Cons x l1 -> let* i = list_length t l1 in u32_add 1 i
+  | List_Nil -> Return 0
   end
 
 (** [no_nested_borrows::list_nth_shared]: forward function *)
-let rec list_nth_shared_fwd (t : Type0) (l : list_t t) (i : u32) : result t =
+let rec list_nth_shared (t : Type0) (l : list_t t) (i : u32) : result t =
   begin match l with
-  | ListCons x tl ->
+  | List_Cons x tl ->
     if i = 0
     then Return x
-    else let* i0 = u32_sub i 1 in list_nth_shared_fwd t tl i0
-  | ListNil -> Fail Failure
+    else let* i0 = u32_sub i 1 in list_nth_shared t tl i0
+  | List_Nil -> Fail Failure
   end
 
 (** [no_nested_borrows::list_nth_mut]: forward function *)
-let rec list_nth_mut_fwd (t : Type0) (l : list_t t) (i : u32) : result t =
+let rec list_nth_mut (t : Type0) (l : list_t t) (i : u32) : result t =
   begin match l with
-  | ListCons x tl ->
-    if i = 0
-    then Return x
-    else let* i0 = u32_sub i 1 in list_nth_mut_fwd t tl i0
-  | ListNil -> Fail Failure
+  | List_Cons x tl ->
+    if i = 0 then Return x else let* i0 = u32_sub i 1 in list_nth_mut t tl i0
+  | List_Nil -> Fail Failure
   end
 
 (** [no_nested_borrows::list_nth_mut]: backward function 0 *)
 let rec list_nth_mut_back
   (t : Type0) (l : list_t t) (i : u32) (ret : t) : result (list_t t) =
   begin match l with
-  | ListCons x tl ->
+  | List_Cons x tl ->
     if i = 0
-    then Return (ListCons ret tl)
+    then Return (List_Cons ret tl)
     else
       let* i0 = u32_sub i 1 in
       let* tl0 = list_nth_mut_back t tl i0 ret in
-      Return (ListCons x tl0)
-  | ListNil -> Fail Failure
+      Return (List_Cons x tl0)
+  | List_Nil -> Fail Failure
   end
 
 (** [no_nested_borrows::list_rev_aux]: forward function *)
-let rec list_rev_aux_fwd
+let rec list_rev_aux
   (t : Type0) (li : list_t t) (lo : list_t t) : result (list_t t) =
   begin match li with
-  | ListCons hd tl -> list_rev_aux_fwd t tl (ListCons hd lo)
-  | ListNil -> Return lo
+  | List_Cons hd tl -> list_rev_aux t tl (List_Cons hd lo)
+  | List_Nil -> Return lo
   end
 
 (** [no_nested_borrows::list_rev]: merged forward/backward function
     (there is a single backward function, and the forward function returns ()) *)
-let list_rev_fwd_back (t : Type0) (l : list_t t) : result (list_t t) =
-  let li = mem_replace_fwd (list_t t) l ListNil in
-  list_rev_aux_fwd t li ListNil
+let list_rev (t : Type0) (l : list_t t) : result (list_t t) =
+  let li = core_mem_replace (list_t t) l List_Nil in list_rev_aux t li List_Nil
 
 (** [no_nested_borrows::test_list_functions]: forward function *)
-let test_list_functions_fwd : result unit =
-  let l = ListNil in
-  let l0 = ListCons 2 l in
-  let l1 = ListCons 1 l0 in
-  let* i = list_length_fwd i32 (ListCons 0 l1) in
+let test_list_functions : result unit =
+  let l = List_Nil in
+  let l0 = List_Cons 2 l in
+  let l1 = List_Cons 1 l0 in
+  let* i = list_length i32 (List_Cons 0 l1) in
   if not (i = 3)
   then Fail Failure
   else
-    let* i0 = list_nth_shared_fwd i32 (ListCons 0 l1) 0 in
+    let* i0 = list_nth_shared i32 (List_Cons 0 l1) 0 in
     if not (i0 = 0)
     then Fail Failure
     else
-      let* i1 = list_nth_shared_fwd i32 (ListCons 0 l1) 1 in
+      let* i1 = list_nth_shared i32 (List_Cons 0 l1) 1 in
       if not (i1 = 1)
       then Fail Failure
       else
-        let* i2 = list_nth_shared_fwd i32 (ListCons 0 l1) 2 in
+        let* i2 = list_nth_shared i32 (List_Cons 0 l1) 2 in
         if not (i2 = 2)
         then Fail Failure
         else
-          let* ls = list_nth_mut_back i32 (ListCons 0 l1) 1 3 in
-          let* i3 = list_nth_shared_fwd i32 ls 0 in
+          let* ls = list_nth_mut_back i32 (List_Cons 0 l1) 1 3 in
+          let* i3 = list_nth_shared i32 ls 0 in
           if not (i3 = 0)
           then Fail Failure
           else
-            let* i4 = list_nth_shared_fwd i32 ls 1 in
+            let* i4 = list_nth_shared i32 ls 1 in
             if not (i4 = 3)
             then Fail Failure
             else
-              let* i5 = list_nth_shared_fwd i32 ls 2 in
+              let* i5 = list_nth_shared i32 ls 2 in
               if not (i5 = 2) then Fail Failure else Return ()
 
 (** Unit test for [no_nested_borrows::test_list_functions] *)
-let _ = assert_norm (test_list_functions_fwd = Return ())
+let _ = assert_norm (test_list_functions = Return ())
 
 (** [no_nested_borrows::id_mut_pair1]: forward function *)
-let id_mut_pair1_fwd (t1 t2 : Type0) (x : t1) (y : t2) : result (t1 & t2) =
+let id_mut_pair1 (t1 t2 : Type0) (x : t1) (y : t2) : result (t1 & t2) =
   Return (x, y)
 
 (** [no_nested_borrows::id_mut_pair1]: backward function 0 *)
@@ -313,7 +322,7 @@ let id_mut_pair1_back
   let (x0, x1) = ret in Return (x0, x1)
 
 (** [no_nested_borrows::id_mut_pair2]: forward function *)
-let id_mut_pair2_fwd (t1 t2 : Type0) (p : (t1 & t2)) : result (t1 & t2) =
+let id_mut_pair2 (t1 t2 : Type0) (p : (t1 & t2)) : result (t1 & t2) =
   let (x, x0) = p in Return (x, x0)
 
 (** [no_nested_borrows::id_mut_pair2]: backward function 0 *)
@@ -322,7 +331,7 @@ let id_mut_pair2_back
   let (x, x0) = ret in Return (x, x0)
 
 (** [no_nested_borrows::id_mut_pair3]: forward function *)
-let id_mut_pair3_fwd (t1 t2 : Type0) (x : t1) (y : t2) : result (t1 & t2) =
+let id_mut_pair3 (t1 t2 : Type0) (x : t1) (y : t2) : result (t1 & t2) =
   Return (x, y)
 
 (** [no_nested_borrows::id_mut_pair3]: backward function 0 *)
@@ -336,7 +345,7 @@ let id_mut_pair3_back'b
   Return ret
 
 (** [no_nested_borrows::id_mut_pair4]: forward function *)
-let id_mut_pair4_fwd (t1 t2 : Type0) (p : (t1 & t2)) : result (t1 & t2) =
+let id_mut_pair4 (t1 t2 : Type0) (p : (t1 & t2)) : result (t1 & t2) =
   let (x, x0) = p in Return (x, x0)
 
 (** [no_nested_borrows::id_mut_pair4]: backward function 0 *)
@@ -350,81 +359,76 @@ let id_mut_pair4_back'b
   Return ret
 
 (** [no_nested_borrows::StructWithTuple] *)
-type struct_with_tuple_t (t1 t2 : Type0) = { struct_with_tuple_p : (t1 & t2); }
+type structWithTuple_t (t1 t2 : Type0) = { p : (t1 & t2); }
 
 (** [no_nested_borrows::new_tuple1]: forward function *)
-let new_tuple1_fwd : result (struct_with_tuple_t u32 u32) =
-  Return { struct_with_tuple_p = (1, 2) }
+let new_tuple1 : result (structWithTuple_t u32 u32) =
+  Return { p = (1, 2) }
 
 (** [no_nested_borrows::new_tuple2]: forward function *)
-let new_tuple2_fwd : result (struct_with_tuple_t i16 i16) =
-  Return { struct_with_tuple_p = (1, 2) }
+let new_tuple2 : result (structWithTuple_t i16 i16) =
+  Return { p = (1, 2) }
 
 (** [no_nested_borrows::new_tuple3]: forward function *)
-let new_tuple3_fwd : result (struct_with_tuple_t u64 i64) =
-  Return { struct_with_tuple_p = (1, 2) }
+let new_tuple3 : result (structWithTuple_t u64 i64) =
+  Return { p = (1, 2) }
 
 (** [no_nested_borrows::StructWithPair] *)
-type struct_with_pair_t (t1 t2 : Type0) =
-{
-  struct_with_pair_p : pair_t t1 t2;
-}
+type structWithPair_t (t1 t2 : Type0) = { p : pair_t t1 t2; }
 
 (** [no_nested_borrows::new_pair1]: forward function *)
-let new_pair1_fwd : result (struct_with_pair_t u32 u32) =
-  Return { struct_with_pair_p = { pair_x = 1; pair_y = 2 } }
+let new_pair1 : result (structWithPair_t u32 u32) =
+  Return { p = { x = 1; y = 2 } }
 
 (** [no_nested_borrows::test_constants]: forward function *)
-let test_constants_fwd : result unit =
-  let* swt = new_tuple1_fwd in
-  let (i, _) = swt.struct_with_tuple_p in
+let test_constants : result unit =
+  let* swt = new_tuple1 in
+  let (i, _) = swt.p in
   if not (i = 1)
   then Fail Failure
   else
-    let* swt0 = new_tuple2_fwd in
-    let (i0, _) = swt0.struct_with_tuple_p in
+    let* swt0 = new_tuple2 in
+    let (i0, _) = swt0.p in
     if not (i0 = 1)
     then Fail Failure
     else
-      let* swt1 = new_tuple3_fwd in
-      let (i1, _) = swt1.struct_with_tuple_p in
+      let* swt1 = new_tuple3 in
+      let (i1, _) = swt1.p in
       if not (i1 = 1)
       then Fail Failure
       else
-        let* swp = new_pair1_fwd in
-        if not (swp.struct_with_pair_p.pair_x = 1)
-        then Fail Failure
-        else Return ()
+        let* swp = new_pair1 in
+        if not (swp.p.x = 1) then Fail Failure else Return ()
 
 (** Unit test for [no_nested_borrows::test_constants] *)
-let _ = assert_norm (test_constants_fwd = Return ())
+let _ = assert_norm (test_constants = Return ())
 
 (** [no_nested_borrows::test_weird_borrows1]: forward function *)
-let test_weird_borrows1_fwd : result unit =
+let test_weird_borrows1 : result unit =
   Return ()
 
 (** Unit test for [no_nested_borrows::test_weird_borrows1] *)
-let _ = assert_norm (test_weird_borrows1_fwd = Return ())
+let _ = assert_norm (test_weird_borrows1 = Return ())
 
 (** [no_nested_borrows::test_mem_replace]: merged forward/backward function
     (there is a single backward function, and the forward function returns ()) *)
-let test_mem_replace_fwd_back (px : u32) : result u32 =
-  let y = mem_replace_fwd u32 px 1 in
+let test_mem_replace (px : u32) : result u32 =
+  let y = core_mem_replace u32 px 1 in
   if not (y = 0) then Fail Failure else Return 2
 
 (** [no_nested_borrows::test_shared_borrow_bool1]: forward function *)
-let test_shared_borrow_bool1_fwd (b : bool) : result u32 =
+let test_shared_borrow_bool1 (b : bool) : result u32 =
   if b then Return 0 else Return 1
 
 (** [no_nested_borrows::test_shared_borrow_bool2]: forward function *)
-let test_shared_borrow_bool2_fwd : result u32 =
+let test_shared_borrow_bool2 : result u32 =
   Return 0
 
 (** [no_nested_borrows::test_shared_borrow_enum1]: forward function *)
-let test_shared_borrow_enum1_fwd (l : list_t u32) : result u32 =
-  begin match l with | ListCons i l0 -> Return 1 | ListNil -> Return 0 end
+let test_shared_borrow_enum1 (l : list_t u32) : result u32 =
+  begin match l with | List_Cons i l0 -> Return 1 | List_Nil -> Return 0 end
 
 (** [no_nested_borrows::test_shared_borrow_enum2]: forward function *)
-let test_shared_borrow_enum2_fwd : result u32 =
+let test_shared_borrow_enum2 : result u32 =
   Return 0
 
diff --git a/tests/fstar/misc/Paper.fst b/tests/fstar/misc/Paper.fst
index e2d692c2..bfb710dc 100644
--- a/tests/fstar/misc/Paper.fst
+++ b/tests/fstar/misc/Paper.fst
@@ -7,19 +7,18 @@ open Primitives
 
 (** [paper::ref_incr]: merged forward/backward function
     (there is a single backward function, and the forward function returns ()) *)
-let ref_incr_fwd_back (x : i32) : result i32 =
+let ref_incr (x : i32) : result i32 =
   i32_add x 1
 
 (** [paper::test_incr]: forward function *)
-let test_incr_fwd : result unit =
-  let* x = ref_incr_fwd_back 0 in
-  if not (x = 1) then Fail Failure else Return ()
+let test_incr : result unit =
+  let* x = ref_incr 0 in if not (x = 1) then Fail Failure else Return ()
 
 (** Unit test for [paper::test_incr] *)
-let _ = assert_norm (test_incr_fwd = Return ())
+let _ = assert_norm (test_incr = Return ())
 
 (** [paper::choose]: forward function *)
-let choose_fwd (t : Type0) (b : bool) (x : t) (y : t) : result t =
+let choose (t : Type0) (b : bool) (x : t) (y : t) : result t =
   if b then Return x else Return y
 
 (** [paper::choose]: backward function 0 *)
@@ -28,8 +27,8 @@ let choose_back
   if b then Return (ret, y) else Return (x, ret)
 
 (** [paper::test_choose]: forward function *)
-let test_choose_fwd : result unit =
-  let* z = choose_fwd i32 true 0 0 in
+let test_choose : result unit =
+  let* z = choose i32 true 0 0 in
   let* z0 = i32_add z 1 in
   if not (z0 = 1)
   then Fail Failure
@@ -40,62 +39,60 @@ let test_choose_fwd : result unit =
     else if not (y = 0) then Fail Failure else Return ()
 
 (** Unit test for [paper::test_choose] *)
-let _ = assert_norm (test_choose_fwd = Return ())
+let _ = assert_norm (test_choose = Return ())
 
 (** [paper::List] *)
 type list_t (t : Type0) =
-| ListCons : t -> list_t t -> list_t t
-| ListNil : list_t t
+| List_Cons : t -> list_t t -> list_t t
+| List_Nil : list_t t
 
 (** [paper::list_nth_mut]: forward function *)
-let rec list_nth_mut_fwd (t : Type0) (l : list_t t) (i : u32) : result t =
+let rec list_nth_mut (t : Type0) (l : list_t t) (i : u32) : result t =
   begin match l with
-  | ListCons x tl ->
-    if i = 0
-    then Return x
-    else let* i0 = u32_sub i 1 in list_nth_mut_fwd t tl i0
-  | ListNil -> Fail Failure
+  | List_Cons x tl ->
+    if i = 0 then Return x else let* i0 = u32_sub i 1 in list_nth_mut t tl i0
+  | List_Nil -> Fail Failure
   end
 
 (** [paper::list_nth_mut]: backward function 0 *)
 let rec list_nth_mut_back
   (t : Type0) (l : list_t t) (i : u32) (ret : t) : result (list_t t) =
   begin match l with
-  | ListCons x tl ->
+  | List_Cons x tl ->
     if i = 0
-    then Return (ListCons ret tl)
+    then Return (List_Cons ret tl)
     else
       let* i0 = u32_sub i 1 in
       let* tl0 = list_nth_mut_back t tl i0 ret in
-      Return (ListCons x tl0)
-  | ListNil -> Fail Failure
+      Return (List_Cons x tl0)
+  | List_Nil -> Fail Failure
   end
 
 (** [paper::sum]: forward function *)
-let rec sum_fwd (l : list_t i32) : result i32 =
+let rec sum (l : list_t i32) : result i32 =
   begin match l with
-  | ListCons x tl -> let* i = sum_fwd tl in i32_add x i
-  | ListNil -> Return 0
+  | List_Cons x tl -> let* i = sum tl in i32_add x i
+  | List_Nil -> Return 0
   end
 
 (** [paper::test_nth]: forward function *)
-let test_nth_fwd : result unit =
-  let l = ListNil in
-  let l0 = ListCons 3 l in
-  let l1 = ListCons 2 l0 in
-  let* x = list_nth_mut_fwd i32 (ListCons 1 l1) 2 in
+let test_nth : result unit =
+  let l = List_Nil in
+  let l0 = List_Cons 3 l in
+  let l1 = List_Cons 2 l0 in
+  let* x = list_nth_mut i32 (List_Cons 1 l1) 2 in
   let* x0 = i32_add x 1 in
-  let* l2 = list_nth_mut_back i32 (ListCons 1 l1) 2 x0 in
-  let* i = sum_fwd l2 in
+  let* l2 = list_nth_mut_back i32 (List_Cons 1 l1) 2 x0 in
+  let* i = sum l2 in
   if not (i = 7) then Fail Failure else Return ()
 
 (** Unit test for [paper::test_nth] *)
-let _ = assert_norm (test_nth_fwd = Return ())
+let _ = assert_norm (test_nth = Return ())
 
 (** [paper::call_choose]: forward function *)
-let call_choose_fwd (p : (u32 & u32)) : result u32 =
+let call_choose (p : (u32 & u32)) : result u32 =
   let (px, py) = p in
-  let* pz = choose_fwd u32 true px py in
+  let* pz = choose u32 true px py in
   let* pz0 = u32_add pz 1 in
   let* (px0, _) = choose_back u32 true px py pz0 in
   Return px0
diff --git a/tests/fstar/misc/PoloniusList.fst b/tests/fstar/misc/PoloniusList.fst
index 79c86606..428c4210 100644
--- a/tests/fstar/misc/PoloniusList.fst
+++ b/tests/fstar/misc/PoloniusList.fst
@@ -7,25 +7,25 @@ open Primitives
 
 (** [polonius_list::List] *)
 type list_t (t : Type0) =
-| ListCons : t -> list_t t -> list_t t
-| ListNil : list_t t
+| List_Cons : t -> list_t t -> list_t t
+| List_Nil : list_t t
 
 (** [polonius_list::get_list_at_x]: forward function *)
-let rec get_list_at_x_fwd (ls : list_t u32) (x : u32) : result (list_t u32) =
+let rec get_list_at_x (ls : list_t u32) (x : u32) : result (list_t u32) =
   begin match ls with
-  | ListCons hd tl ->
-    if hd = x then Return (ListCons hd tl) else get_list_at_x_fwd tl x
-  | ListNil -> Return ListNil
+  | List_Cons hd tl ->
+    if hd = x then Return (List_Cons hd tl) else get_list_at_x tl x
+  | List_Nil -> Return List_Nil
   end
 
 (** [polonius_list::get_list_at_x]: backward function 0 *)
 let rec get_list_at_x_back
   (ls : list_t u32) (x : u32) (ret : list_t u32) : result (list_t u32) =
   begin match ls with
-  | ListCons hd tl ->
+  | List_Cons hd tl ->
     if hd = x
     then Return ret
-    else let* tl0 = get_list_at_x_back tl x ret in Return (ListCons hd tl0)
-  | ListNil -> Return ret
+    else let* tl0 = get_list_at_x_back tl x ret in Return (List_Cons hd tl0)
+  | List_Nil -> Return ret
   end
 
diff --git a/tests/fstar/misc/Primitives.fst b/tests/fstar/misc/Primitives.fst
index 9db82069..3297803c 100644
--- a/tests/fstar/misc/Primitives.fst
+++ b/tests/fstar/misc/Primitives.fst
@@ -55,8 +55,12 @@ type string = string
 let is_zero (n: nat) : bool = n = 0
 let decrease (n: nat{n > 0}) : nat = n - 1
 
-let mem_replace_fwd (a : Type0) (x : a) (y : a) : a = x
-let mem_replace_back (a : Type0) (x : a) (y : a) : a = y
+let core_mem_replace (a : Type0) (x : a) (y : a) : a = x
+let core_mem_replace_back (a : Type0) (x : a) (y : a) : a = y
+
+// We don't really use raw pointers for now
+type mut_raw_ptr (t : Type0) = { v : t }
+type const_raw_ptr (t : Type0) = { v : t }
 
 (*** Scalars *)
 /// Rem.: most of the following code was partially generated
@@ -100,6 +104,11 @@ type scalar_ty =
 | U64
 | U128
 
+let is_unsigned = function
+  | Isize | I8 | I16 | I32 | I64 | I128 -> false
+  | Usize | U8 | U16 | U32 | U64 | U128 -> true
+
+
 let scalar_min (ty : scalar_ty) : int =
   match ty with
   | Isize -> isize_min
@@ -162,6 +171,15 @@ let scalar_sub (#ty : scalar_ty) (x : scalar ty) (y : scalar ty) : result (scala
 let scalar_mul (#ty : scalar_ty) (x : scalar ty) (y : scalar ty) : result (scalar ty) =
   mk_scalar ty (x * y)
 
+let scalar_lxor (#ty : scalar_ty { is_unsigned ty && ty <> Usize })
+    (x : scalar ty) (y : scalar ty) : scalar ty =
+  match ty with
+  | U8 -> FStar.UInt.logxor #8 x y
+  | U16 -> FStar.UInt.logxor #16 x y
+  | U32 -> FStar.UInt.logxor #32 x y
+  | U64 -> FStar.UInt.logxor #64 x y
+  | U128 -> FStar.UInt.logxor #128 x y
+
 (** Cast an integer from a [src_ty] to a [tgt_ty] *)
 // TODO: check the semantics of casts in Rust
 let scalar_cast (src_ty : scalar_ty) (tgt_ty : scalar_ty) (x : scalar src_ty) : result (scalar tgt_ty) =
@@ -169,17 +187,44 @@ let scalar_cast (src_ty : scalar_ty) (tgt_ty : scalar_ty) (x : scalar src_ty) :
 
 /// The scalar types
 type isize : eqtype = scalar Isize
-type i8 : eqtype = scalar I8
-type i16 : eqtype = scalar I16
-type i32 : eqtype = scalar I32
-type i64 : eqtype = scalar I64
-type i128 : eqtype = scalar I128
+type i8    : eqtype = scalar I8
+type i16   : eqtype = scalar I16
+type i32   : eqtype = scalar I32
+type i64   : eqtype = scalar I64
+type i128  : eqtype = scalar I128
 type usize : eqtype = scalar Usize
-type u8 : eqtype = scalar U8
-type u16 : eqtype = scalar U16
-type u32 : eqtype = scalar U32
-type u64 : eqtype = scalar U64
-type u128 : eqtype = scalar U128
+type u8    : eqtype = scalar U8
+type u16   : eqtype = scalar U16
+type u32   : eqtype = scalar U32
+type u64   : eqtype = scalar U64
+type u128  : eqtype = scalar U128
+
+
+let core_isize_min : isize = isize_min
+let core_isize_max : isize = isize_max
+let core_i8_min    : i8 = i8_min
+let core_i8_max    : i8 = i8_max
+let core_i16_min   : i16 = i16_min
+let core_i16_max   : i16 = i16_max
+let core_i32_min   : i32 = i32_min
+let core_i32_max   : i32 = i32_max
+let core_i64_min   : i64 = i64_min
+let core_i64_max   : i64 = i64_max
+let core_i128_min  : i128 = i128_min
+let core_i128_max  : i128 = i128_max
+
+let core_usize_min : usize = usize_min
+let core_usize_max : usize = usize_max
+let core_u8_min    : u8 = u8_min
+let core_u8_max    : u8 = u8_max
+let core_u16_min   : u16 = u16_min
+let core_u16_max   : u16 = u16_max
+let core_u32_min   : u32 = u32_min
+let core_u32_max   : u32 = u32_max
+let core_u64_min   : u64 = u64_min
+let core_u64_max   : u64 = u64_max
+let core_u128_min  : u128 = u128_min
+let core_u128_max  : u128 = u128_max
 
 /// Negation
 let isize_neg = scalar_neg #Isize
@@ -231,7 +276,7 @@ let u32_add = scalar_add #U32
 let u64_add = scalar_add #U64
 let u128_add = scalar_add #U128
 
-/// Substraction
+/// Subtraction
 let isize_sub = scalar_sub #Isize
 let i8_sub = scalar_sub #I8
 let i16_sub = scalar_sub #I16
@@ -259,12 +304,65 @@ let u32_mul = scalar_mul #U32
 let u64_mul = scalar_mul #U64
 let u128_mul = scalar_mul #U128
 
-(*** Range *)
-type range (a : Type0) = {
+/// Logical operators, defined for unsigned types only, so far
+let u8_xor = scalar_lxor #U8
+let u16_xor = scalar_lxor #U16
+let u32_xor = scalar_lxor #U32
+let u64_xor = scalar_lxor #U64
+let u128_xor = scalar_lxor #U128
+
+(*** core::ops *)
+
+// Trait declaration: [core::ops::index::Index]
+noeq type core_ops_index_Index (self idx : Type0) = {
+  output : Type0;
+  index : self → idx → result output
+}
+
+// Trait declaration: [core::ops::index::IndexMut]
+noeq type core_ops_index_IndexMut (self idx : Type0) = {
+  indexInst : core_ops_index_Index self idx;
+  index_mut : self → idx → result indexInst.output;
+  index_mut_back : self → idx → indexInst.output → result self;
+}
+
+// Trait declaration [core::ops::deref::Deref]
+noeq type core_ops_deref_Deref (self : Type0) = {
+  target : Type0;
+  deref : self → result target;
+}
+
+// Trait declaration [core::ops::deref::DerefMut]
+noeq type core_ops_deref_DerefMut (self : Type0) = {
+  derefInst : core_ops_deref_Deref self;
+  deref_mut : self → result derefInst.target;
+  deref_mut_back : self → derefInst.target → result self;
+}
+
+type core_ops_range_Range (a : Type0) = {
   start : a;
   end_ : a;
 }
 
+(*** [alloc] *)
+
+let alloc_boxed_Box_deref (t : Type0) (x : t) : result t = Return x
+let alloc_boxed_Box_deref_mut (t : Type0) (x : t) : result t = Return x
+let alloc_boxed_Box_deref_mut_back (t : Type) (_ : t) (x : t) : result t = Return x
+
+// Trait instance
+let alloc_boxed_Box_coreOpsDerefInst (self : Type0) : core_ops_deref_Deref self = {
+  target = self;
+  deref = alloc_boxed_Box_deref self;
+}
+
+// Trait instance
+let alloc_boxed_Box_coreOpsDerefMutInst (self : Type0) : core_ops_deref_DerefMut self = {
+  derefInst = alloc_boxed_Box_coreOpsDerefInst self;
+  deref_mut = alloc_boxed_Box_deref_mut self;
+  deref_mut_back = alloc_boxed_Box_deref_mut_back self;
+}
+
 (*** Array *)
 type array (a : Type0) (n : usize) = s:list a{length s = n}
 
@@ -278,15 +376,11 @@ let mk_array (a : Type0) (n : usize)
   normalize_term_spec (FStar.List.Tot.length l);
   l
 
-let array_index_shared (a : Type0) (n : usize) (x : array a n) (i : usize) : result a =
-  if i < length x then Return (index x i)
-  else Fail Failure
-
-let array_index_mut_fwd (a : Type0) (n : usize) (x : array a n) (i : usize) : result a =
+let array_index_usize (a : Type0) (n : usize) (x : array a n) (i : usize) : result a =
   if i < length x then Return (index x i)
   else Fail Failure
 
-let array_index_mut_back (a : Type0) (n : usize) (x : array a n) (i : usize) (nx : a) : result (array a n) =
+let array_update_usize (a : Type0) (n : usize) (x : array a n) (i : usize) (nx : a) : result (array a n) =
   if i < length x then Return (list_update x i nx)
   else Fail Failure
 
@@ -295,55 +389,54 @@ type slice (a : Type0) = s:list a{length s <= usize_max}
 
 let slice_len (a : Type0) (s : slice a) : usize = length s
 
-let slice_index_shared (a : Type0) (x : slice a) (i : usize) : result a =
+let slice_index_usize (a : Type0) (x : slice a) (i : usize) : result a =
   if i < length x then Return (index x i)
   else Fail Failure
 
-let slice_index_mut_fwd (a : Type0) (x : slice a) (i : usize) : result a =
-  if i < length x then Return (index x i)
-  else Fail Failure
-
-let slice_index_mut_back (a : Type0) (x : slice a) (i : usize) (nx : a) : result (slice a) =
+let slice_update_usize (a : Type0) (x : slice a) (i : usize) (nx : a) : result (slice a) =
   if i < length x then Return (list_update x i nx)
   else Fail Failure
 
 (*** Subslices *)
 
-let array_to_slice_shared (a : Type0) (n : usize) (x : array a n) : result (slice a) = Return x
-let array_to_slice_mut_fwd (a : Type0) (n : usize) (x : array a n) : result (slice a) = Return x
-let array_to_slice_mut_back (a : Type0) (n : usize) (x : array a n) (s : slice a) : result (array a n) =
+let array_to_slice (a : Type0) (n : usize) (x : array a n) : result (slice a) = Return x
+let array_from_slice (a : Type0) (n : usize) (x : array a n) (s : slice a) : result (array a n) =
   if length s = n then Return s
   else Fail Failure
 
 // TODO: finish the definitions below (there lacks [List.drop] and [List.take] in the standard library *)
-let array_subslice_shared (a : Type0) (n : usize) (x : array a n) (r : range usize) : result (slice a) =
-  admit()
-
-let array_subslice_mut_fwd (a : Type0) (n : usize) (x : array a n) (r : range usize) : result (slice a) =
+let array_subslice (a : Type0) (n : usize) (x : array a n) (r : core_ops_range_Range usize) : result (slice a) =
   admit()
 
-let array_subslice_mut_back (a : Type0) (n : usize) (x : array a n) (r : range usize) (ns : slice a) : result (array a n) =
+let array_update_subslice (a : Type0) (n : usize) (x : array a n) (r : core_ops_range_Range usize) (ns : slice a) : result (array a n) =
   admit()
 
-let slice_subslice_shared (a : Type0) (x : slice a) (r : range usize) : result (slice a) =
+let array_repeat (a : Type0) (n : usize) (x : a) : array a n =
   admit()
 
-let slice_subslice_mut_fwd (a : Type0) (x : slice a) (r : range usize) : result (slice a) =
+let slice_subslice (a : Type0) (x : slice a) (r : core_ops_range_Range usize) : result (slice a) =
   admit()
 
-let slice_subslice_mut_back (a : Type0) (x : slice a) (r : range usize) (ns : slice a) : result (slice a) =
+let slice_update_subslice (a : Type0) (x : slice a) (r : core_ops_range_Range usize) (ns : slice a) : result (slice a) =
   admit()
 
 (*** Vector *)
-type vec (a : Type0) = v:list a{length v <= usize_max}
+type alloc_vec_Vec (a : Type0) = v:list a{length v <= usize_max}
 
-let vec_new (a  : Type0) : vec a = assert_norm(length #a [] == 0); []
-let vec_len (a : Type0) (v : vec a) : usize = length v
+let alloc_vec_Vec_new (a  : Type0) : alloc_vec_Vec a = assert_norm(length #a [] == 0); []
+let alloc_vec_Vec_len (a : Type0) (v : alloc_vec_Vec a) : usize = length v
+
+// Helper
+let alloc_vec_Vec_index_usize (#a : Type0) (v : alloc_vec_Vec a) (i : usize) : result a =
+  if i < length v then Return (index v i) else Fail Failure
+// Helper
+let alloc_vec_Vec_update_usize (#a : Type0) (v : alloc_vec_Vec a) (i : usize) (x : a) : result (alloc_vec_Vec a) =
+  if i < length v then Return (list_update v i x) else Fail Failure
 
 // The **forward** function shouldn't be used
-let vec_push_fwd (a  : Type0) (v : vec a) (x : a) : unit = ()
-let vec_push_back (a  : Type0) (v : vec a) (x : a) :
-  Pure (result (vec a))
+let alloc_vec_Vec_push_fwd (a  : Type0) (v : alloc_vec_Vec a) (x : a) : unit = ()
+let alloc_vec_Vec_push (a  : Type0) (v : alloc_vec_Vec a) (x : a) :
+  Pure (result (alloc_vec_Vec a))
   (requires True)
   (ensures (fun res ->
     match res with
@@ -358,18 +451,279 @@ let vec_push_back (a  : Type0) (v : vec a) (x : a) :
   else Fail Failure
 
 // The **forward** function shouldn't be used
-let vec_insert_fwd (a : Type0) (v : vec a) (i : usize) (x : a) : result unit =
+let alloc_vec_Vec_insert_fwd (a : Type0) (v : alloc_vec_Vec a) (i : usize) (x : a) : result unit =
   if i < length v then Return () else Fail Failure
-let vec_insert_back (a : Type0) (v : vec a) (i : usize) (x : a) : result (vec a) =
+let alloc_vec_Vec_insert (a : Type0) (v : alloc_vec_Vec a) (i : usize) (x : a) : result (alloc_vec_Vec a) =
   if i < length v then Return (list_update v i x) else Fail Failure
 
-// The **backward** function shouldn't be used
-let vec_index_fwd (a : Type0) (v : vec a) (i : usize) : result a =
-  if i < length v then Return (index v i) else Fail Failure
-let vec_index_back (a : Type0) (v : vec a) (i : usize) (x : a) : result unit =
-  if i < length v then Return () else Fail Failure
+// Trait declaration: [core::slice::index::private_slice_index::Sealed]
+type core_slice_index_private_slice_index_Sealed (self : Type0) = unit
+
+// Trait declaration: [core::slice::index::SliceIndex]
+noeq type core_slice_index_SliceIndex (self t : Type0) = {
+  sealedInst : core_slice_index_private_slice_index_Sealed self;
+  output : Type0;
+  get : self → t → result (option output);
+  get_mut : self → t → result (option output);
+  get_mut_back : self → t → option output → result t;
+  get_unchecked : self → const_raw_ptr t → result (const_raw_ptr output);
+  get_unchecked_mut : self → mut_raw_ptr t → result (mut_raw_ptr output);
+  index : self → t → result output;
+  index_mut : self → t → result output;
+  index_mut_back : self → t → output → result t;
+}
 
-let vec_index_mut_fwd (a : Type0) (v : vec a) (i : usize) : result a =
-  if i < length v then Return (index v i) else Fail Failure
-let vec_index_mut_back (a : Type0) (v : vec a) (i : usize) (nx : a) : result (vec a) =
-  if i < length v then Return (list_update v i nx) else Fail Failure
+// [core::slice::index::[T]::index]: forward function
+let core_slice_index_Slice_index
+  (t idx : Type0) (inst : core_slice_index_SliceIndex idx (slice t))
+  (s : slice t) (i : idx) : result inst.output =
+  let* x = inst.get i s in
+  match x with
+  | None -> Fail Failure
+  | Some x -> Return x
+
+// [core::slice::index::Range:::get]: forward function
+let core_slice_index_Range_get (t : Type0) (i : core_ops_range_Range usize) (s : slice t) :
+  result (option (slice t)) =
+  admit () // TODO
+
+// [core::slice::index::Range::get_mut]: forward function
+let core_slice_index_Range_get_mut
+  (t : Type0) : core_ops_range_Range usize → slice t → result (option (slice t)) =
+  admit () // TODO
+
+// [core::slice::index::Range::get_mut]: backward function 0
+let core_slice_index_Range_get_mut_back
+  (t : Type0) :
+  core_ops_range_Range usize → slice t → option (slice t) → result (slice t) =
+  admit () // TODO
+
+// [core::slice::index::Range::get_unchecked]: forward function
+let core_slice_index_Range_get_unchecked
+  (t : Type0) :
+  core_ops_range_Range usize → const_raw_ptr (slice t) → result (const_raw_ptr (slice t)) =
+  // Don't know what the model should be - for now we always fail to make
+  // sure code which uses it fails
+  fun _ _ -> Fail Failure
+
+// [core::slice::index::Range::get_unchecked_mut]: forward function
+let core_slice_index_Range_get_unchecked_mut
+  (t : Type0) :
+  core_ops_range_Range usize → mut_raw_ptr (slice t) → result (mut_raw_ptr (slice t)) =
+  // Don't know what the model should be - for now we always fail to make
+  // sure code which uses it fails
+  fun _ _ -> Fail Failure
+
+// [core::slice::index::Range::index]: forward function
+let core_slice_index_Range_index
+  (t : Type0) : core_ops_range_Range usize → slice t → result (slice t) =
+  admit () // TODO
+
+// [core::slice::index::Range::index_mut]: forward function
+let core_slice_index_Range_index_mut
+  (t : Type0) : core_ops_range_Range usize → slice t → result (slice t) =
+  admit () // TODO
+
+// [core::slice::index::Range::index_mut]: backward function 0
+let core_slice_index_Range_index_mut_back
+  (t : Type0) : core_ops_range_Range usize → slice t → slice t → result (slice t) =
+  admit () // TODO
+
+// [core::slice::index::[T]::index_mut]: forward function
+let core_slice_index_Slice_index_mut
+  (t idx : Type0) (inst : core_slice_index_SliceIndex idx (slice t)) :
+  slice t → idx → result inst.output =
+  admit () // 
+
+// [core::slice::index::[T]::index_mut]: backward function 0
+let core_slice_index_Slice_index_mut_back
+  (t idx : Type0) (inst : core_slice_index_SliceIndex idx (slice t)) :
+  slice t → idx → inst.output → result (slice t) =
+  admit () // TODO
+
+// [core::array::[T; N]::index]: forward function
+let core_array_Array_index
+  (t idx : Type0) (n : usize) (inst : core_ops_index_Index (slice t) idx)
+  (a : array t n) (i : idx) : result inst.output =
+  admit () // TODO
+
+// [core::array::[T; N]::index_mut]: forward function
+let core_array_Array_index_mut
+  (t idx : Type0) (n : usize) (inst : core_ops_index_IndexMut (slice t) idx)
+  (a : array t n) (i : idx) : result inst.indexInst.output =
+  admit () // TODO
+
+// [core::array::[T; N]::index_mut]: backward function 0
+let core_array_Array_index_mut_back
+  (t idx : Type0) (n : usize) (inst : core_ops_index_IndexMut (slice t) idx)
+  (a : array t n) (i : idx) (x : inst.indexInst.output) : result (array t n) =
+  admit () // TODO
+
+// Trait implementation: [core::slice::index::[T]]
+let core_slice_index_Slice_coreopsindexIndexInst (t idx : Type0)
+  (inst : core_slice_index_SliceIndex idx (slice t)) :
+  core_ops_index_Index (slice t) idx = {
+  output = inst.output;
+  index = core_slice_index_Slice_index t idx inst;
+}
+
+// Trait implementation: [core::slice::index::private_slice_index::Range]
+let core_slice_index_private_slice_index_Range_coresliceindexprivate_slice_indexSealedInst
+  : core_slice_index_private_slice_index_Sealed (core_ops_range_Range usize) = ()
+
+// Trait implementation: [core::slice::index::Range]
+let core_slice_index_Range_coresliceindexSliceIndexInst (t : Type0) :
+  core_slice_index_SliceIndex (core_ops_range_Range usize) (slice t) = {
+  sealedInst = core_slice_index_private_slice_index_Range_coresliceindexprivate_slice_indexSealedInst;
+  output = slice t;
+  get = core_slice_index_Range_get t;
+  get_mut = core_slice_index_Range_get_mut t;
+  get_mut_back = core_slice_index_Range_get_mut_back t;
+  get_unchecked = core_slice_index_Range_get_unchecked t;
+  get_unchecked_mut = core_slice_index_Range_get_unchecked_mut t;
+  index = core_slice_index_Range_index t;
+  index_mut = core_slice_index_Range_index_mut t;
+  index_mut_back = core_slice_index_Range_index_mut_back t;
+}
+
+// Trait implementation: [core::slice::index::[T]]
+let core_slice_index_Slice_coreopsindexIndexMutInst (t idx : Type0)
+  (inst : core_slice_index_SliceIndex idx (slice t)) :
+  core_ops_index_IndexMut (slice t) idx = {
+  indexInst = core_slice_index_Slice_coreopsindexIndexInst t idx inst;
+  index_mut = core_slice_index_Slice_index_mut t idx inst;
+  index_mut_back = core_slice_index_Slice_index_mut_back t idx inst;
+}
+
+// Trait implementation: [core::array::[T; N]]
+let core_array_Array_coreopsindexIndexInst (t idx : Type0) (n : usize)
+  (inst : core_ops_index_Index (slice t) idx) :
+  core_ops_index_Index (array t n) idx = {
+  output = inst.output;
+  index = core_array_Array_index t idx n inst;
+}
+
+// Trait implementation: [core::array::[T; N]]
+let core_array_Array_coreopsindexIndexMutInst (t idx : Type0) (n : usize)
+  (inst : core_ops_index_IndexMut (slice t) idx) :
+  core_ops_index_IndexMut (array t n) idx = {
+  indexInst = core_array_Array_coreopsindexIndexInst t idx n inst.indexInst;
+  index_mut = core_array_Array_index_mut t idx n inst;
+  index_mut_back = core_array_Array_index_mut_back t idx n inst;
+}
+
+// [core::slice::index::usize::get]: forward function
+let core_slice_index_usize_get
+  (t : Type0) : usize → slice t → result (option t) =
+  admit () // TODO
+
+// [core::slice::index::usize::get_mut]: forward function
+let core_slice_index_usize_get_mut
+  (t : Type0) : usize → slice t → result (option t) =
+  admit () // TODO
+
+// [core::slice::index::usize::get_mut]: backward function 0
+let core_slice_index_usize_get_mut_back
+  (t : Type0) : usize → slice t → option t → result (slice t) =
+  admit () // TODO
+
+// [core::slice::index::usize::get_unchecked]: forward function
+let core_slice_index_usize_get_unchecked
+  (t : Type0) : usize → const_raw_ptr (slice t) → result (const_raw_ptr t) =
+  admit () // TODO
+
+// [core::slice::index::usize::get_unchecked_mut]: forward function
+let core_slice_index_usize_get_unchecked_mut
+  (t : Type0) : usize → mut_raw_ptr (slice t) → result (mut_raw_ptr t) =
+  admit () // TODO
+
+// [core::slice::index::usize::index]: forward function
+let core_slice_index_usize_index (t : Type0) : usize → slice t → result t =
+  admit () // TODO
+
+// [core::slice::index::usize::index_mut]: forward function
+let core_slice_index_usize_index_mut (t : Type0) : usize → slice t → result t =
+  admit () // TODO
+
+// [core::slice::index::usize::index_mut]: backward function 0
+let core_slice_index_usize_index_mut_back
+  (t : Type0) : usize → slice t → t → result (slice t) =
+  admit () // TODO
+
+// Trait implementation: [core::slice::index::private_slice_index::usize]
+let core_slice_index_private_slice_index_usize_coresliceindexprivate_slice_indexSealedInst
+  : core_slice_index_private_slice_index_Sealed usize = ()
+
+// Trait implementation: [core::slice::index::usize]
+let core_slice_index_usize_coresliceindexSliceIndexInst (t : Type0) :
+  core_slice_index_SliceIndex usize (slice t) = {
+  sealedInst = core_slice_index_private_slice_index_usize_coresliceindexprivate_slice_indexSealedInst;
+  output = t;
+  get = core_slice_index_usize_get t;
+  get_mut = core_slice_index_usize_get_mut t;
+  get_mut_back = core_slice_index_usize_get_mut_back t;
+  get_unchecked = core_slice_index_usize_get_unchecked t;
+  get_unchecked_mut = core_slice_index_usize_get_unchecked_mut t;
+  index = core_slice_index_usize_index t;
+  index_mut = core_slice_index_usize_index_mut t;
+  index_mut_back = core_slice_index_usize_index_mut_back t;
+}
+
+// [alloc::vec::Vec::index]: forward function
+let alloc_vec_Vec_index (t idx : Type0) (inst : core_slice_index_SliceIndex idx (slice t))
+  (self : alloc_vec_Vec t) (i : idx) : result inst.output =
+  admit () // TODO
+
+// [alloc::vec::Vec::index_mut]: forward function
+let alloc_vec_Vec_index_mut (t idx : Type0) (inst : core_slice_index_SliceIndex idx (slice t))
+  (self : alloc_vec_Vec t) (i : idx) : result inst.output =
+  admit () // TODO
+
+// [alloc::vec::Vec::index_mut]: backward function 0
+let alloc_vec_Vec_index_mut_back
+  (t idx : Type0) (inst : core_slice_index_SliceIndex idx (slice t))
+  (self : alloc_vec_Vec t) (i : idx) (x : inst.output) : result (alloc_vec_Vec t) =
+  admit () // TODO
+
+// Trait implementation: [alloc::vec::Vec]
+let alloc_vec_Vec_coreopsindexIndexInst (t idx : Type0)
+  (inst : core_slice_index_SliceIndex idx (slice t)) :
+  core_ops_index_Index (alloc_vec_Vec t) idx = {
+  output = inst.output;
+  index = alloc_vec_Vec_index t idx inst;
+}
+
+// Trait implementation: [alloc::vec::Vec]
+let alloc_vec_Vec_coreopsindexIndexMutInst (t idx : Type0)
+  (inst : core_slice_index_SliceIndex idx (slice t)) :
+  core_ops_index_IndexMut (alloc_vec_Vec t) idx = {
+  indexInst = alloc_vec_Vec_coreopsindexIndexInst t idx inst;
+  index_mut = alloc_vec_Vec_index_mut t idx inst;
+  index_mut_back = alloc_vec_Vec_index_mut_back t idx inst;
+}
+
+(*** Theorems *)
+
+let alloc_vec_Vec_index_eq (#a : Type0) (v : alloc_vec_Vec a) (i : usize) :
+  Lemma (
+    alloc_vec_Vec_index a usize (core_slice_index_usize_coresliceindexSliceIndexInst a) v i ==
+      alloc_vec_Vec_index_usize v i)
+  [SMTPat (alloc_vec_Vec_index a usize (core_slice_index_usize_coresliceindexSliceIndexInst a) v i)]
+  =
+  admit()
+
+let alloc_vec_Vec_index_mut_eq (#a : Type0) (v : alloc_vec_Vec a) (i : usize) :
+  Lemma (
+    alloc_vec_Vec_index_mut a usize (core_slice_index_usize_coresliceindexSliceIndexInst a) v i ==
+      alloc_vec_Vec_index_usize v i)
+  [SMTPat (alloc_vec_Vec_index_mut a usize (core_slice_index_usize_coresliceindexSliceIndexInst a) v i)]
+  =
+  admit()
+
+let alloc_vec_Vec_index_mut_back_eq (#a : Type0) (v : alloc_vec_Vec a) (i : usize) (x : a) :
+  Lemma (
+    alloc_vec_Vec_index_mut_back a usize (core_slice_index_usize_coresliceindexSliceIndexInst a) v i x ==
+      alloc_vec_Vec_update_usize v i x)
+  [SMTPat (alloc_vec_Vec_index_mut_back a usize (core_slice_index_usize_coresliceindexSliceIndexInst a) v i x)]
+  =
+  admit()
diff --git a/tests/fstar/traits/Makefile b/tests/fstar/traits/Makefile
new file mode 100644
index 00000000..fa7d1f36
--- /dev/null
+++ b/tests/fstar/traits/Makefile
@@ -0,0 +1,49 @@
+# This file was automatically generated - modify ../Makefile.template instead
+INCLUDE_DIRS = .
+
+FSTAR_INCLUDES = $(addprefix --include ,$(INCLUDE_DIRS))
+
+FSTAR_HINTS ?= --use_hints --use_hint_hashes --record_hints
+
+FSTAR_OPTIONS = $(FSTAR_HINTS) \
+  --cache_checked_modules $(FSTAR_INCLUDES) --cmi \
+  --warn_error '+241@247+285-274' \
+
+FSTAR_EXE ?= fstar.exe
+FSTAR_NO_FLAGS = $(FSTAR_EXE) --already_cached 'Prims FStar LowStar Steel' --odir obj --cache_dir obj
+
+FSTAR = $(FSTAR_NO_FLAGS) $(FSTAR_OPTIONS)
+
+# The F* roots are used to compute the dependency graph, and generate the .depend file
+FSTAR_ROOTS ?= $(wildcard *.fst *.fsti)
+
+# Build all the files
+all: $(addprefix obj/,$(addsuffix .checked,$(FSTAR_ROOTS)))
+
+# This is the right way to ensure the .depend file always gets re-built.
+ifeq (,$(filter %-in,$(MAKECMDGOALS)))
+ifndef NODEPEND
+ifndef MAKE_RESTARTS
+.depend: .FORCE
+	$(FSTAR_NO_FLAGS) --dep full $(notdir $(FSTAR_ROOTS)) > $@
+
+.PHONY: .FORCE
+.FORCE:
+endif
+endif
+
+include .depend
+endif
+
+# For the interactive mode
+%.fst-in %.fsti-in:
+	@echo $(FSTAR_OPTIONS)
+
+# Generete the .checked files in batch mode
+%.checked:
+	$(FSTAR) $(FSTAR_OPTIONS) $< && \
+	touch -c $@
+
+.PHONY: clean
+clean:
+	rm -f obj/*
diff --git a/tests/fstar/traits/Primitives.fst b/tests/fstar/traits/Primitives.fst
new file mode 100644
index 00000000..3297803c
--- /dev/null
+++ b/tests/fstar/traits/Primitives.fst
@@ -0,0 +1,729 @@
+/// This file lists primitive and assumed functions and types
+module Primitives
+open FStar.Mul
+open FStar.List.Tot
+
+#set-options "--z3rlimit 15 --fuel 0 --ifuel 1"
+
+(*** Utilities *)
+val list_update (#a : Type0) (ls : list a) (i : nat{i < length ls}) (x : a) :
+  ls':list a{
+    length ls' = length ls /\
+    index ls' i == x
+  }
+#push-options "--fuel 1"
+let rec list_update #a ls i x =
+  match ls with
+  | x' :: ls -> if i = 0 then x :: ls else x' :: list_update ls (i-1) x
+#pop-options
+
+(*** Result *)
+type error : Type0 =
+| Failure
+| OutOfFuel
+
+type result (a : Type0) : Type0 =
+| Return : v:a -> result a
+| Fail : e:error -> result a
+
+// Monadic return operator
+unfold let return (#a : Type0) (x : a) : result a = Return x
+
+// Monadic bind operator.
+// Allows to use the notation:
+// ```
+// let* x = y in
+// ...
+// ```
+unfold let (let*) (#a #b : Type0) (m: result a)
+  (f: (x:a) -> Pure (result b) (requires (m == Return x)) (ensures fun _ -> True)) :
+  result b =
+  match m with
+  | Return x -> f x
+  | Fail e   -> Fail e
+
+// Monadic assert(...)
+let massert (b:bool) : result unit = if b then Return () else Fail Failure
+
+// Normalize and unwrap a successful result (used for globals).
+let eval_global (#a : Type0) (x : result a{Return? (normalize_term x)}) : a = Return?.v x
+
+(*** Misc *)
+type char = FStar.Char.char
+type string = string
+
+let is_zero (n: nat) : bool = n = 0
+let decrease (n: nat{n > 0}) : nat = n - 1
+
+let core_mem_replace (a : Type0) (x : a) (y : a) : a = x
+let core_mem_replace_back (a : Type0) (x : a) (y : a) : a = y
+
+// We don't really use raw pointers for now
+type mut_raw_ptr (t : Type0) = { v : t }
+type const_raw_ptr (t : Type0) = { v : t }
+
+(*** Scalars *)
+/// Rem.: most of the following code was partially generated
+
+let isize_min : int = -9223372036854775808 // TODO: should be opaque
+let isize_max : int = 9223372036854775807 // TODO: should be opaque
+let i8_min : int = -128
+let i8_max : int = 127
+let i16_min : int = -32768
+let i16_max : int = 32767
+let i32_min : int = -2147483648
+let i32_max : int = 2147483647
+let i64_min : int = -9223372036854775808
+let i64_max : int = 9223372036854775807
+let i128_min : int = -170141183460469231731687303715884105728
+let i128_max : int = 170141183460469231731687303715884105727
+let usize_min : int = 0
+let usize_max : int = 4294967295 // TODO: should be opaque
+let u8_min : int = 0
+let u8_max : int = 255
+let u16_min : int = 0
+let u16_max : int = 65535
+let u32_min : int = 0
+let u32_max : int = 4294967295
+let u64_min : int = 0
+let u64_max : int = 18446744073709551615
+let u128_min : int = 0
+let u128_max : int = 340282366920938463463374607431768211455
+
+type scalar_ty =
+| Isize
+| I8
+| I16
+| I32
+| I64
+| I128
+| Usize
+| U8
+| U16
+| U32
+| U64
+| U128
+
+let is_unsigned = function
+  | Isize | I8 | I16 | I32 | I64 | I128 -> false
+  | Usize | U8 | U16 | U32 | U64 | U128 -> true
+
+
+let scalar_min (ty : scalar_ty) : int =
+  match ty with
+  | Isize -> isize_min
+  | I8 -> i8_min
+  | I16 -> i16_min
+  | I32 -> i32_min
+  | I64 -> i64_min
+  | I128 -> i128_min
+  | Usize -> usize_min
+  | U8 -> u8_min
+  | U16 -> u16_min
+  | U32 -> u32_min
+  | U64 -> u64_min
+  | U128 -> u128_min
+
+let scalar_max (ty : scalar_ty) : int =
+  match ty with
+  | Isize -> isize_max
+  | I8 -> i8_max
+  | I16 -> i16_max
+  | I32 -> i32_max
+  | I64 -> i64_max
+  | I128 -> i128_max
+  | Usize -> usize_max
+  | U8 -> u8_max
+  | U16 -> u16_max
+  | U32 -> u32_max
+  | U64 -> u64_max
+  | U128 -> u128_max
+
+type scalar (ty : scalar_ty) : eqtype = x:int{scalar_min ty <= x && x <= scalar_max ty}
+
+let mk_scalar (ty : scalar_ty) (x : int) : result (scalar ty) =
+  if scalar_min ty <= x && scalar_max ty >= x then Return x else Fail Failure
+
+let scalar_neg (#ty : scalar_ty) (x : scalar ty) : result (scalar ty) = mk_scalar ty (-x)
+
+let scalar_div (#ty : scalar_ty) (x : scalar ty) (y : scalar ty) : result (scalar ty) =
+  if y <> 0 then mk_scalar ty (x / y) else Fail Failure
+
+/// The remainder operation
+let int_rem (x : int) (y : int{y <> 0}) : int =
+  if x >= 0 then (x % y) else -(x % y)
+
+(* Checking consistency with Rust *)
+let _ = assert_norm(int_rem 1 2 = 1)
+let _ = assert_norm(int_rem (-1) 2 = -1)
+let _ = assert_norm(int_rem 1 (-2) = 1)
+let _ = assert_norm(int_rem (-1) (-2) = -1)
+
+let scalar_rem (#ty : scalar_ty) (x : scalar ty) (y : scalar ty) : result (scalar ty) =
+  if y <> 0 then mk_scalar ty (int_rem x y) else Fail Failure
+
+let scalar_add (#ty : scalar_ty) (x : scalar ty) (y : scalar ty) : result (scalar ty) =
+  mk_scalar ty (x + y)
+
+let scalar_sub (#ty : scalar_ty) (x : scalar ty) (y : scalar ty) : result (scalar ty) =
+  mk_scalar ty (x - y)
+
+let scalar_mul (#ty : scalar_ty) (x : scalar ty) (y : scalar ty) : result (scalar ty) =
+  mk_scalar ty (x * y)
+
+let scalar_lxor (#ty : scalar_ty { is_unsigned ty && ty <> Usize })
+    (x : scalar ty) (y : scalar ty) : scalar ty =
+  match ty with
+  | U8 -> FStar.UInt.logxor #8 x y
+  | U16 -> FStar.UInt.logxor #16 x y
+  | U32 -> FStar.UInt.logxor #32 x y
+  | U64 -> FStar.UInt.logxor #64 x y
+  | U128 -> FStar.UInt.logxor #128 x y
+
+(** Cast an integer from a [src_ty] to a [tgt_ty] *)
+// TODO: check the semantics of casts in Rust
+let scalar_cast (src_ty : scalar_ty) (tgt_ty : scalar_ty) (x : scalar src_ty) : result (scalar tgt_ty) =
+  mk_scalar tgt_ty x
+
+/// The scalar types
+type isize : eqtype = scalar Isize
+type i8    : eqtype = scalar I8
+type i16   : eqtype = scalar I16
+type i32   : eqtype = scalar I32
+type i64   : eqtype = scalar I64
+type i128  : eqtype = scalar I128
+type usize : eqtype = scalar Usize
+type u8    : eqtype = scalar U8
+type u16   : eqtype = scalar U16
+type u32   : eqtype = scalar U32
+type u64   : eqtype = scalar U64
+type u128  : eqtype = scalar U128
+
+
+let core_isize_min : isize = isize_min
+let core_isize_max : isize = isize_max
+let core_i8_min    : i8 = i8_min
+let core_i8_max    : i8 = i8_max
+let core_i16_min   : i16 = i16_min
+let core_i16_max   : i16 = i16_max
+let core_i32_min   : i32 = i32_min
+let core_i32_max   : i32 = i32_max
+let core_i64_min   : i64 = i64_min
+let core_i64_max   : i64 = i64_max
+let core_i128_min  : i128 = i128_min
+let core_i128_max  : i128 = i128_max
+
+let core_usize_min : usize = usize_min
+let core_usize_max : usize = usize_max
+let core_u8_min    : u8 = u8_min
+let core_u8_max    : u8 = u8_max
+let core_u16_min   : u16 = u16_min
+let core_u16_max   : u16 = u16_max
+let core_u32_min   : u32 = u32_min
+let core_u32_max   : u32 = u32_max
+let core_u64_min   : u64 = u64_min
+let core_u64_max   : u64 = u64_max
+let core_u128_min  : u128 = u128_min
+let core_u128_max  : u128 = u128_max
+
+/// Negation
+let isize_neg = scalar_neg #Isize
+let i8_neg = scalar_neg #I8
+let i16_neg = scalar_neg #I16
+let i32_neg = scalar_neg #I32
+let i64_neg = scalar_neg #I64
+let i128_neg = scalar_neg #I128
+
+/// Division
+let isize_div = scalar_div #Isize
+let i8_div = scalar_div #I8
+let i16_div = scalar_div #I16
+let i32_div = scalar_div #I32
+let i64_div = scalar_div #I64
+let i128_div = scalar_div #I128
+let usize_div = scalar_div #Usize
+let u8_div = scalar_div #U8
+let u16_div = scalar_div #U16
+let u32_div = scalar_div #U32
+let u64_div = scalar_div #U64
+let u128_div = scalar_div #U128
+
+/// Remainder
+let isize_rem = scalar_rem #Isize
+let i8_rem = scalar_rem #I8
+let i16_rem = scalar_rem #I16
+let i32_rem = scalar_rem #I32
+let i64_rem = scalar_rem #I64
+let i128_rem = scalar_rem #I128
+let usize_rem = scalar_rem #Usize
+let u8_rem = scalar_rem #U8
+let u16_rem = scalar_rem #U16
+let u32_rem = scalar_rem #U32
+let u64_rem = scalar_rem #U64
+let u128_rem = scalar_rem #U128
+
+/// Addition
+let isize_add = scalar_add #Isize
+let i8_add = scalar_add #I8
+let i16_add = scalar_add #I16
+let i32_add = scalar_add #I32
+let i64_add = scalar_add #I64
+let i128_add = scalar_add #I128
+let usize_add = scalar_add #Usize
+let u8_add = scalar_add #U8
+let u16_add = scalar_add #U16
+let u32_add = scalar_add #U32
+let u64_add = scalar_add #U64
+let u128_add = scalar_add #U128
+
+/// Subtraction
+let isize_sub = scalar_sub #Isize
+let i8_sub = scalar_sub #I8
+let i16_sub = scalar_sub #I16
+let i32_sub = scalar_sub #I32
+let i64_sub = scalar_sub #I64
+let i128_sub = scalar_sub #I128
+let usize_sub = scalar_sub #Usize
+let u8_sub = scalar_sub #U8
+let u16_sub = scalar_sub #U16
+let u32_sub = scalar_sub #U32
+let u64_sub = scalar_sub #U64
+let u128_sub = scalar_sub #U128
+
+/// Multiplication
+let isize_mul = scalar_mul #Isize
+let i8_mul = scalar_mul #I8
+let i16_mul = scalar_mul #I16
+let i32_mul = scalar_mul #I32
+let i64_mul = scalar_mul #I64
+let i128_mul = scalar_mul #I128
+let usize_mul = scalar_mul #Usize
+let u8_mul = scalar_mul #U8
+let u16_mul = scalar_mul #U16
+let u32_mul = scalar_mul #U32
+let u64_mul = scalar_mul #U64
+let u128_mul = scalar_mul #U128
+
+/// Logical operators, defined for unsigned types only, so far
+let u8_xor = scalar_lxor #U8
+let u16_xor = scalar_lxor #U16
+let u32_xor = scalar_lxor #U32
+let u64_xor = scalar_lxor #U64
+let u128_xor = scalar_lxor #U128
+
+(*** core::ops *)
+
+// Trait declaration: [core::ops::index::Index]
+noeq type core_ops_index_Index (self idx : Type0) = {
+  output : Type0;
+  index : self → idx → result output
+}
+
+// Trait declaration: [core::ops::index::IndexMut]
+noeq type core_ops_index_IndexMut (self idx : Type0) = {
+  indexInst : core_ops_index_Index self idx;
+  index_mut : self → idx → result indexInst.output;
+  index_mut_back : self → idx → indexInst.output → result self;
+}
+
+// Trait declaration [core::ops::deref::Deref]
+noeq type core_ops_deref_Deref (self : Type0) = {
+  target : Type0;
+  deref : self → result target;
+}
+
+// Trait declaration [core::ops::deref::DerefMut]
+noeq type core_ops_deref_DerefMut (self : Type0) = {
+  derefInst : core_ops_deref_Deref self;
+  deref_mut : self → result derefInst.target;
+  deref_mut_back : self → derefInst.target → result self;
+}
+
+type core_ops_range_Range (a : Type0) = {
+  start : a;
+  end_ : a;
+}
+
+(*** [alloc] *)
+
+let alloc_boxed_Box_deref (t : Type0) (x : t) : result t = Return x
+let alloc_boxed_Box_deref_mut (t : Type0) (x : t) : result t = Return x
+let alloc_boxed_Box_deref_mut_back (t : Type) (_ : t) (x : t) : result t = Return x
+
+// Trait instance
+let alloc_boxed_Box_coreOpsDerefInst (self : Type0) : core_ops_deref_Deref self = {
+  target = self;
+  deref = alloc_boxed_Box_deref self;
+}
+
+// Trait instance
+let alloc_boxed_Box_coreOpsDerefMutInst (self : Type0) : core_ops_deref_DerefMut self = {
+  derefInst = alloc_boxed_Box_coreOpsDerefInst self;
+  deref_mut = alloc_boxed_Box_deref_mut self;
+  deref_mut_back = alloc_boxed_Box_deref_mut_back self;
+}
+
+(*** Array *)
+type array (a : Type0) (n : usize) = s:list a{length s = n}
+
+// We tried putting the normalize_term condition as a refinement on the list
+// but it didn't work. It works with the requires clause.
+let mk_array (a : Type0) (n : usize)
+  (l : list a) :
+  Pure (array a n)
+  (requires (normalize_term(FStar.List.Tot.length l) = n))
+  (ensures (fun _ -> True)) =
+  normalize_term_spec (FStar.List.Tot.length l);
+  l
+
+let array_index_usize (a : Type0) (n : usize) (x : array a n) (i : usize) : result a =
+  if i < length x then Return (index x i)
+  else Fail Failure
+
+let array_update_usize (a : Type0) (n : usize) (x : array a n) (i : usize) (nx : a) : result (array a n) =
+  if i < length x then Return (list_update x i nx)
+  else Fail Failure
+
+(*** Slice *)
+type slice (a : Type0) = s:list a{length s <= usize_max}
+
+let slice_len (a : Type0) (s : slice a) : usize = length s
+
+let slice_index_usize (a : Type0) (x : slice a) (i : usize) : result a =
+  if i < length x then Return (index x i)
+  else Fail Failure
+
+let slice_update_usize (a : Type0) (x : slice a) (i : usize) (nx : a) : result (slice a) =
+  if i < length x then Return (list_update x i nx)
+  else Fail Failure
+
+(*** Subslices *)
+
+let array_to_slice (a : Type0) (n : usize) (x : array a n) : result (slice a) = Return x
+let array_from_slice (a : Type0) (n : usize) (x : array a n) (s : slice a) : result (array a n) =
+  if length s = n then Return s
+  else Fail Failure
+
+// TODO: finish the definitions below (there lacks [List.drop] and [List.take] in the standard library *)
+let array_subslice (a : Type0) (n : usize) (x : array a n) (r : core_ops_range_Range usize) : result (slice a) =
+  admit()
+
+let array_update_subslice (a : Type0) (n : usize) (x : array a n) (r : core_ops_range_Range usize) (ns : slice a) : result (array a n) =
+  admit()
+
+let array_repeat (a : Type0) (n : usize) (x : a) : array a n =
+  admit()
+
+let slice_subslice (a : Type0) (x : slice a) (r : core_ops_range_Range usize) : result (slice a) =
+  admit()
+
+let slice_update_subslice (a : Type0) (x : slice a) (r : core_ops_range_Range usize) (ns : slice a) : result (slice a) =
+  admit()
+
+(*** Vector *)
+type alloc_vec_Vec (a : Type0) = v:list a{length v <= usize_max}
+
+let alloc_vec_Vec_new (a  : Type0) : alloc_vec_Vec a = assert_norm(length #a [] == 0); []
+let alloc_vec_Vec_len (a : Type0) (v : alloc_vec_Vec a) : usize = length v
+
+// Helper
+let alloc_vec_Vec_index_usize (#a : Type0) (v : alloc_vec_Vec a) (i : usize) : result a =
+  if i < length v then Return (index v i) else Fail Failure
+// Helper
+let alloc_vec_Vec_update_usize (#a : Type0) (v : alloc_vec_Vec a) (i : usize) (x : a) : result (alloc_vec_Vec a) =
+  if i < length v then Return (list_update v i x) else Fail Failure
+
+// The **forward** function shouldn't be used
+let alloc_vec_Vec_push_fwd (a  : Type0) (v : alloc_vec_Vec a) (x : a) : unit = ()
+let alloc_vec_Vec_push (a  : Type0) (v : alloc_vec_Vec a) (x : a) :
+  Pure (result (alloc_vec_Vec a))
+  (requires True)
+  (ensures (fun res ->
+    match res with
+    | Fail e -> e == Failure
+    | Return v' -> length v' = length v + 1)) =
+  if length v < usize_max then begin
+    (**) assert_norm(length [x] == 1);
+    (**) append_length v [x];
+    (**) assert(length (append v [x]) = length v + 1);
+    Return (append v [x])
+    end
+  else Fail Failure
+
+// The **forward** function shouldn't be used
+let alloc_vec_Vec_insert_fwd (a : Type0) (v : alloc_vec_Vec a) (i : usize) (x : a) : result unit =
+  if i < length v then Return () else Fail Failure
+let alloc_vec_Vec_insert (a : Type0) (v : alloc_vec_Vec a) (i : usize) (x : a) : result (alloc_vec_Vec a) =
+  if i < length v then Return (list_update v i x) else Fail Failure
+
+// Trait declaration: [core::slice::index::private_slice_index::Sealed]
+type core_slice_index_private_slice_index_Sealed (self : Type0) = unit
+
+// Trait declaration: [core::slice::index::SliceIndex]
+noeq type core_slice_index_SliceIndex (self t : Type0) = {
+  sealedInst : core_slice_index_private_slice_index_Sealed self;
+  output : Type0;
+  get : self → t → result (option output);
+  get_mut : self → t → result (option output);
+  get_mut_back : self → t → option output → result t;
+  get_unchecked : self → const_raw_ptr t → result (const_raw_ptr output);
+  get_unchecked_mut : self → mut_raw_ptr t → result (mut_raw_ptr output);
+  index : self → t → result output;
+  index_mut : self → t → result output;
+  index_mut_back : self → t → output → result t;
+}
+
+// [core::slice::index::[T]::index]: forward function
+let core_slice_index_Slice_index
+  (t idx : Type0) (inst : core_slice_index_SliceIndex idx (slice t))
+  (s : slice t) (i : idx) : result inst.output =
+  let* x = inst.get i s in
+  match x with
+  | None -> Fail Failure
+  | Some x -> Return x
+
+// [core::slice::index::Range:::get]: forward function
+let core_slice_index_Range_get (t : Type0) (i : core_ops_range_Range usize) (s : slice t) :
+  result (option (slice t)) =
+  admit () // TODO
+
+// [core::slice::index::Range::get_mut]: forward function
+let core_slice_index_Range_get_mut
+  (t : Type0) : core_ops_range_Range usize → slice t → result (option (slice t)) =
+  admit () // TODO
+
+// [core::slice::index::Range::get_mut]: backward function 0
+let core_slice_index_Range_get_mut_back
+  (t : Type0) :
+  core_ops_range_Range usize → slice t → option (slice t) → result (slice t) =
+  admit () // TODO
+
+// [core::slice::index::Range::get_unchecked]: forward function
+let core_slice_index_Range_get_unchecked
+  (t : Type0) :
+  core_ops_range_Range usize → const_raw_ptr (slice t) → result (const_raw_ptr (slice t)) =
+  // Don't know what the model should be - for now we always fail to make
+  // sure code which uses it fails
+  fun _ _ -> Fail Failure
+
+// [core::slice::index::Range::get_unchecked_mut]: forward function
+let core_slice_index_Range_get_unchecked_mut
+  (t : Type0) :
+  core_ops_range_Range usize → mut_raw_ptr (slice t) → result (mut_raw_ptr (slice t)) =
+  // Don't know what the model should be - for now we always fail to make
+  // sure code which uses it fails
+  fun _ _ -> Fail Failure
+
+// [core::slice::index::Range::index]: forward function
+let core_slice_index_Range_index
+  (t : Type0) : core_ops_range_Range usize → slice t → result (slice t) =
+  admit () // TODO
+
+// [core::slice::index::Range::index_mut]: forward function
+let core_slice_index_Range_index_mut
+  (t : Type0) : core_ops_range_Range usize → slice t → result (slice t) =
+  admit () // TODO
+
+// [core::slice::index::Range::index_mut]: backward function 0
+let core_slice_index_Range_index_mut_back
+  (t : Type0) : core_ops_range_Range usize → slice t → slice t → result (slice t) =
+  admit () // TODO
+
+// [core::slice::index::[T]::index_mut]: forward function
+let core_slice_index_Slice_index_mut
+  (t idx : Type0) (inst : core_slice_index_SliceIndex idx (slice t)) :
+  slice t → idx → result inst.output =
+  admit () // 
+
+// [core::slice::index::[T]::index_mut]: backward function 0
+let core_slice_index_Slice_index_mut_back
+  (t idx : Type0) (inst : core_slice_index_SliceIndex idx (slice t)) :
+  slice t → idx → inst.output → result (slice t) =
+  admit () // TODO
+
+// [core::array::[T; N]::index]: forward function
+let core_array_Array_index
+  (t idx : Type0) (n : usize) (inst : core_ops_index_Index (slice t) idx)
+  (a : array t n) (i : idx) : result inst.output =
+  admit () // TODO
+
+// [core::array::[T; N]::index_mut]: forward function
+let core_array_Array_index_mut
+  (t idx : Type0) (n : usize) (inst : core_ops_index_IndexMut (slice t) idx)
+  (a : array t n) (i : idx) : result inst.indexInst.output =
+  admit () // TODO
+
+// [core::array::[T; N]::index_mut]: backward function 0
+let core_array_Array_index_mut_back
+  (t idx : Type0) (n : usize) (inst : core_ops_index_IndexMut (slice t) idx)
+  (a : array t n) (i : idx) (x : inst.indexInst.output) : result (array t n) =
+  admit () // TODO
+
+// Trait implementation: [core::slice::index::[T]]
+let core_slice_index_Slice_coreopsindexIndexInst (t idx : Type0)
+  (inst : core_slice_index_SliceIndex idx (slice t)) :
+  core_ops_index_Index (slice t) idx = {
+  output = inst.output;
+  index = core_slice_index_Slice_index t idx inst;
+}
+
+// Trait implementation: [core::slice::index::private_slice_index::Range]
+let core_slice_index_private_slice_index_Range_coresliceindexprivate_slice_indexSealedInst
+  : core_slice_index_private_slice_index_Sealed (core_ops_range_Range usize) = ()
+
+// Trait implementation: [core::slice::index::Range]
+let core_slice_index_Range_coresliceindexSliceIndexInst (t : Type0) :
+  core_slice_index_SliceIndex (core_ops_range_Range usize) (slice t) = {
+  sealedInst = core_slice_index_private_slice_index_Range_coresliceindexprivate_slice_indexSealedInst;
+  output = slice t;
+  get = core_slice_index_Range_get t;
+  get_mut = core_slice_index_Range_get_mut t;
+  get_mut_back = core_slice_index_Range_get_mut_back t;
+  get_unchecked = core_slice_index_Range_get_unchecked t;
+  get_unchecked_mut = core_slice_index_Range_get_unchecked_mut t;
+  index = core_slice_index_Range_index t;
+  index_mut = core_slice_index_Range_index_mut t;
+  index_mut_back = core_slice_index_Range_index_mut_back t;
+}
+
+// Trait implementation: [core::slice::index::[T]]
+let core_slice_index_Slice_coreopsindexIndexMutInst (t idx : Type0)
+  (inst : core_slice_index_SliceIndex idx (slice t)) :
+  core_ops_index_IndexMut (slice t) idx = {
+  indexInst = core_slice_index_Slice_coreopsindexIndexInst t idx inst;
+  index_mut = core_slice_index_Slice_index_mut t idx inst;
+  index_mut_back = core_slice_index_Slice_index_mut_back t idx inst;
+}
+
+// Trait implementation: [core::array::[T; N]]
+let core_array_Array_coreopsindexIndexInst (t idx : Type0) (n : usize)
+  (inst : core_ops_index_Index (slice t) idx) :
+  core_ops_index_Index (array t n) idx = {
+  output = inst.output;
+  index = core_array_Array_index t idx n inst;
+}
+
+// Trait implementation: [core::array::[T; N]]
+let core_array_Array_coreopsindexIndexMutInst (t idx : Type0) (n : usize)
+  (inst : core_ops_index_IndexMut (slice t) idx) :
+  core_ops_index_IndexMut (array t n) idx = {
+  indexInst = core_array_Array_coreopsindexIndexInst t idx n inst.indexInst;
+  index_mut = core_array_Array_index_mut t idx n inst;
+  index_mut_back = core_array_Array_index_mut_back t idx n inst;
+}
+
+// [core::slice::index::usize::get]: forward function
+let core_slice_index_usize_get
+  (t : Type0) : usize → slice t → result (option t) =
+  admit () // TODO
+
+// [core::slice::index::usize::get_mut]: forward function
+let core_slice_index_usize_get_mut
+  (t : Type0) : usize → slice t → result (option t) =
+  admit () // TODO
+
+// [core::slice::index::usize::get_mut]: backward function 0
+let core_slice_index_usize_get_mut_back
+  (t : Type0) : usize → slice t → option t → result (slice t) =
+  admit () // TODO
+
+// [core::slice::index::usize::get_unchecked]: forward function
+let core_slice_index_usize_get_unchecked
+  (t : Type0) : usize → const_raw_ptr (slice t) → result (const_raw_ptr t) =
+  admit () // TODO
+
+// [core::slice::index::usize::get_unchecked_mut]: forward function
+let core_slice_index_usize_get_unchecked_mut
+  (t : Type0) : usize → mut_raw_ptr (slice t) → result (mut_raw_ptr t) =
+  admit () // TODO
+
+// [core::slice::index::usize::index]: forward function
+let core_slice_index_usize_index (t : Type0) : usize → slice t → result t =
+  admit () // TODO
+
+// [core::slice::index::usize::index_mut]: forward function
+let core_slice_index_usize_index_mut (t : Type0) : usize → slice t → result t =
+  admit () // TODO
+
+// [core::slice::index::usize::index_mut]: backward function 0
+let core_slice_index_usize_index_mut_back
+  (t : Type0) : usize → slice t → t → result (slice t) =
+  admit () // TODO
+
+// Trait implementation: [core::slice::index::private_slice_index::usize]
+let core_slice_index_private_slice_index_usize_coresliceindexprivate_slice_indexSealedInst
+  : core_slice_index_private_slice_index_Sealed usize = ()
+
+// Trait implementation: [core::slice::index::usize]
+let core_slice_index_usize_coresliceindexSliceIndexInst (t : Type0) :
+  core_slice_index_SliceIndex usize (slice t) = {
+  sealedInst = core_slice_index_private_slice_index_usize_coresliceindexprivate_slice_indexSealedInst;
+  output = t;
+  get = core_slice_index_usize_get t;
+  get_mut = core_slice_index_usize_get_mut t;
+  get_mut_back = core_slice_index_usize_get_mut_back t;
+  get_unchecked = core_slice_index_usize_get_unchecked t;
+  get_unchecked_mut = core_slice_index_usize_get_unchecked_mut t;
+  index = core_slice_index_usize_index t;
+  index_mut = core_slice_index_usize_index_mut t;
+  index_mut_back = core_slice_index_usize_index_mut_back t;
+}
+
+// [alloc::vec::Vec::index]: forward function
+let alloc_vec_Vec_index (t idx : Type0) (inst : core_slice_index_SliceIndex idx (slice t))
+  (self : alloc_vec_Vec t) (i : idx) : result inst.output =
+  admit () // TODO
+
+// [alloc::vec::Vec::index_mut]: forward function
+let alloc_vec_Vec_index_mut (t idx : Type0) (inst : core_slice_index_SliceIndex idx (slice t))
+  (self : alloc_vec_Vec t) (i : idx) : result inst.output =
+  admit () // TODO
+
+// [alloc::vec::Vec::index_mut]: backward function 0
+let alloc_vec_Vec_index_mut_back
+  (t idx : Type0) (inst : core_slice_index_SliceIndex idx (slice t))
+  (self : alloc_vec_Vec t) (i : idx) (x : inst.output) : result (alloc_vec_Vec t) =
+  admit () // TODO
+
+// Trait implementation: [alloc::vec::Vec]
+let alloc_vec_Vec_coreopsindexIndexInst (t idx : Type0)
+  (inst : core_slice_index_SliceIndex idx (slice t)) :
+  core_ops_index_Index (alloc_vec_Vec t) idx = {
+  output = inst.output;
+  index = alloc_vec_Vec_index t idx inst;
+}
+
+// Trait implementation: [alloc::vec::Vec]
+let alloc_vec_Vec_coreopsindexIndexMutInst (t idx : Type0)
+  (inst : core_slice_index_SliceIndex idx (slice t)) :
+  core_ops_index_IndexMut (alloc_vec_Vec t) idx = {
+  indexInst = alloc_vec_Vec_coreopsindexIndexInst t idx inst;
+  index_mut = alloc_vec_Vec_index_mut t idx inst;
+  index_mut_back = alloc_vec_Vec_index_mut_back t idx inst;
+}
+
+(*** Theorems *)
+
+let alloc_vec_Vec_index_eq (#a : Type0) (v : alloc_vec_Vec a) (i : usize) :
+  Lemma (
+    alloc_vec_Vec_index a usize (core_slice_index_usize_coresliceindexSliceIndexInst a) v i ==
+      alloc_vec_Vec_index_usize v i)
+  [SMTPat (alloc_vec_Vec_index a usize (core_slice_index_usize_coresliceindexSliceIndexInst a) v i)]
+  =
+  admit()
+
+let alloc_vec_Vec_index_mut_eq (#a : Type0) (v : alloc_vec_Vec a) (i : usize) :
+  Lemma (
+    alloc_vec_Vec_index_mut a usize (core_slice_index_usize_coresliceindexSliceIndexInst a) v i ==
+      alloc_vec_Vec_index_usize v i)
+  [SMTPat (alloc_vec_Vec_index_mut a usize (core_slice_index_usize_coresliceindexSliceIndexInst a) v i)]
+  =
+  admit()
+
+let alloc_vec_Vec_index_mut_back_eq (#a : Type0) (v : alloc_vec_Vec a) (i : usize) (x : a) :
+  Lemma (
+    alloc_vec_Vec_index_mut_back a usize (core_slice_index_usize_coresliceindexSliceIndexInst a) v i x ==
+      alloc_vec_Vec_update_usize v i x)
+  [SMTPat (alloc_vec_Vec_index_mut_back a usize (core_slice_index_usize_coresliceindexSliceIndexInst a) v i x)]
+  =
+  admit()
diff --git a/tests/fstar/traits/Traits.fst b/tests/fstar/traits/Traits.fst
new file mode 100644
index 00000000..318efa2b
--- /dev/null
+++ b/tests/fstar/traits/Traits.fst
@@ -0,0 +1,371 @@
+(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
+(** [traits] *)
+module Traits
+open Primitives
+
+#set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
+
+(** Trait declaration: [traits::BoolTrait] *)
+noeq type boolTrait_t (self : Type0) = { get_bool : self -> result bool; }
+
+(** [traits::Bool::{0}::get_bool]: forward function *)
+let bool_get_bool (self : bool) : result bool =
+  Return self
+
+(** Trait implementation: [traits::Bool::{0}] *)
+let bool_BoolTraitInst : boolTrait_t bool = { get_bool = bool_get_bool; }
+
+(** [traits::BoolTrait::ret_true]: forward function *)
+let boolTrait_ret_true
+  (#self : Type0) (self_clause : boolTrait_t self) (self0 : self) :
+  result bool
+  =
+  Return true
+
+(** [traits::test_bool_trait_bool]: forward function *)
+let test_bool_trait_bool (x : bool) : result bool =
+  let* b = bool_get_bool x in
+  if b then boolTrait_ret_true bool_BoolTraitInst x else Return false
+
+(** [traits::Option::{1}::get_bool]: forward function *)
+let option_get_bool (t : Type0) (self : option t) : result bool =
+  begin match self with | None -> Return false | Some x -> Return true end
+
+(** Trait implementation: [traits::Option::{1}] *)
+let option_BoolTraitInst (t : Type0) : boolTrait_t (option t) = {
+  get_bool = option_get_bool t;
+}
+
+(** [traits::test_bool_trait_option]: forward function *)
+let test_bool_trait_option (t : Type0) (x : option t) : result bool =
+  let* b = option_get_bool t x in
+  if b then boolTrait_ret_true (option_BoolTraitInst t) x else Return false
+
+(** [traits::test_bool_trait]: forward function *)
+let test_bool_trait (t : Type0) (inst : boolTrait_t t) (x : t) : result bool =
+  inst.get_bool x
+
+(** Trait declaration: [traits::ToU64] *)
+noeq type toU64_t (self : Type0) = { to_u64 : self -> result u64; }
+
+(** [traits::u64::{2}::to_u64]: forward function *)
+let u64_to_u64 (self : u64) : result u64 =
+  Return self
+
+(** Trait implementation: [traits::u64::{2}] *)
+let u64_ToU64Inst : toU64_t u64 = { to_u64 = u64_to_u64; }
+
+(** [traits::Tuple2::{3}::to_u64]: forward function *)
+let tuple2_to_u64
+  (a : Type0) (inst : toU64_t a) (self : (a & a)) : result u64 =
+  let (x, x0) = self in
+  let* i = inst.to_u64 x in
+  let* i0 = inst.to_u64 x0 in
+  u64_add i i0
+
+(** Trait implementation: [traits::Tuple2::{3}] *)
+let tuple2_ToU64Inst (a : Type0) (inst : toU64_t a) : toU64_t (a & a) = {
+  to_u64 = tuple2_to_u64 a inst;
+}
+
+(** [traits::f]: forward function *)
+let f (t : Type0) (inst : toU64_t t) (x : (t & t)) : result u64 =
+  tuple2_to_u64 t inst x
+
+(** [traits::g]: forward function *)
+let g (t : Type0) (inst : toU64_t (t & t)) (x : (t & t)) : result u64 =
+  inst.to_u64 x
+
+(** [traits::h0]: forward function *)
+let h0 (x : u64) : result u64 =
+  u64_to_u64 x
+
+(** [traits::Wrapper] *)
+type wrapper_t (t : Type0) = { x : t; }
+
+(** [traits::Wrapper::{4}::to_u64]: forward function *)
+let wrapper_to_u64
+  (t : Type0) (inst : toU64_t t) (self : wrapper_t t) : result u64 =
+  inst.to_u64 self.x
+
+(** Trait implementation: [traits::Wrapper::{4}] *)
+let wrapper_ToU64Inst (t : Type0) (inst : toU64_t t) : toU64_t (wrapper_t t)
+  = {
+  to_u64 = wrapper_to_u64 t inst;
+}
+
+(** [traits::h1]: forward function *)
+let h1 (x : wrapper_t u64) : result u64 =
+  wrapper_to_u64 u64 u64_ToU64Inst x
+
+(** [traits::h2]: forward function *)
+let h2 (t : Type0) (inst : toU64_t t) (x : wrapper_t t) : result u64 =
+  wrapper_to_u64 t inst x
+
+(** Trait declaration: [traits::ToType] *)
+noeq type toType_t (self t : Type0) = { to_type : self -> result t; }
+
+(** [traits::u64::{5}::to_type]: forward function *)
+let u64_to_type (self : u64) : result bool =
+  Return (self > 0)
+
+(** Trait implementation: [traits::u64::{5}] *)
+let u64_ToTypeInst : toType_t u64 bool = { to_type = u64_to_type; }
+
+(** Trait declaration: [traits::OfType] *)
+noeq type ofType_t (self : Type0) = {
+  of_type : (t : Type0) -> (inst : toType_t t self) -> t -> result self;
+}
+
+(** [traits::h3]: forward function *)
+let h3
+  (t1 t2 : Type0) (inst : ofType_t t1) (inst0 : toType_t t2 t1) (y : t2) :
+  result t1
+  =
+  inst.of_type t2 inst0 y
+
+(** Trait declaration: [traits::OfTypeBis] *)
+noeq type ofTypeBis_t (self t : Type0) = {
+  parent_clause_0 : toType_t t self;
+  of_type : t -> result self;
+}
+
+(** [traits::h4]: forward function *)
+let h4
+  (t1 t2 : Type0) (inst : ofTypeBis_t t1 t2) (inst0 : toType_t t2 t1) 
+  (y : t2) :
+  result t1
+  =
+  inst.of_type y
+
+(** [traits::TestType] *)
+type testType_t (t : Type0) = { _0 : t; }
+
+(** [traits::TestType::{6}::test::TestType1] *)
+type testType_test_TestType1_t = { _0 : u64; }
+
+(** Trait declaration: [traits::TestType::{6}::test::TestTrait] *)
+noeq type testType_test_TestTrait_t (self : Type0) = {
+  test : self -> result bool;
+}
+
+(** [traits::TestType::{6}::test::TestType1::{0}::test]: forward function *)
+let testType_test_TestType1_test
+  (self : testType_test_TestType1_t) : result bool =
+  Return (self._0 > 1)
+
+(** Trait implementation: [traits::TestType::{6}::test::TestType1::{0}] *)
+let testType_test_TestType1_TestType_test_TestTraitInst :
+  testType_test_TestTrait_t testType_test_TestType1_t = {
+  test = testType_test_TestType1_test;
+}
+
+(** [traits::TestType::{6}::test]: forward function *)
+let testType_test
+  (t : Type0) (inst : toU64_t t) (self : testType_t t) (x : t) : result bool =
+  let* x0 = inst.to_u64 x in
+  if x0 > 0 then testType_test_TestType1_test { _0 = 0 } else Return false
+
+(** [traits::BoolWrapper] *)
+type boolWrapper_t = { _0 : bool; }
+
+(** [traits::BoolWrapper::{7}::to_type]: forward function *)
+let boolWrapper_to_type
+  (t : Type0) (inst : toType_t bool t) (self : boolWrapper_t) : result t =
+  inst.to_type self._0
+
+(** Trait implementation: [traits::BoolWrapper::{7}] *)
+let boolWrapper_ToTypeInst (t : Type0) (inst : toType_t bool t) : toType_t
+  boolWrapper_t t = {
+  to_type = boolWrapper_to_type t inst;
+}
+
+(** [traits::WithConstTy::LEN2] *)
+let with_const_ty_len2_body : result usize = Return 32
+let with_const_ty_len2_c : usize = eval_global with_const_ty_len2_body
+
+(** Trait declaration: [traits::WithConstTy] *)
+noeq type withConstTy_t (self : Type0) (len : usize) = {
+  cLEN1 : usize;
+  cLEN2 : usize;
+  tV : Type0;
+  tW : Type0;
+  tW_clause_0 : toU64_t tW;
+  f : tW -> array u8 len -> result tW;
+}
+
+(** [traits::Bool::{8}::LEN1] *)
+let bool_len1_body : result usize = Return 12
+let bool_len1_c : usize = eval_global bool_len1_body
+
+(** [traits::Bool::{8}::f]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ()) *)
+let bool_f (i : u64) (a : array u8 32) : result u64 =
+  Return i
+
+(** Trait implementation: [traits::Bool::{8}] *)
+let bool_WithConstTyInst : withConstTy_t bool 32 = {
+  cLEN1 = bool_len1_c;
+  cLEN2 = with_const_ty_len2_c;
+  tV = u8;
+  tW = u64;
+  tW_clause_0 = u64_ToU64Inst;
+  f = bool_f;
+}
+
+(** [traits::use_with_const_ty1]: forward function *)
+let use_with_const_ty1
+  (h : Type0) (len : usize) (inst : withConstTy_t h len) : result usize =
+  let i = inst.cLEN1 in Return i
+
+(** [traits::use_with_const_ty2]: forward function *)
+let use_with_const_ty2
+  (h : Type0) (len : usize) (inst : withConstTy_t h len) (w : inst.tW) :
+  result unit
+  =
+  Return ()
+
+(** [traits::use_with_const_ty3]: forward function *)
+let use_with_const_ty3
+  (h : Type0) (len : usize) (inst : withConstTy_t h len) (x : inst.tW) :
+  result u64
+  =
+  inst.tW_clause_0.to_u64 x
+
+(** [traits::test_where1]: forward function *)
+let test_where1 (t : Type0) (_x : t) : result unit =
+  Return ()
+
+(** [traits::test_where2]: forward function *)
+let test_where2
+  (t : Type0) (inst : withConstTy_t t 32) (_x : u32) : result unit =
+  Return ()
+
+(** [alloc::string::String] *)
+assume type alloc_string_String_t : Type0
+
+(** Trait declaration: [traits::ParentTrait0] *)
+noeq type parentTrait0_t (self : Type0) = {
+  tW : Type0;
+  get_name : self -> result alloc_string_String_t;
+  get_w : self -> result tW;
+}
+
+(** Trait declaration: [traits::ParentTrait1] *)
+type parentTrait1_t (self : Type0) = unit
+
+(** Trait declaration: [traits::ChildTrait] *)
+noeq type childTrait_t (self : Type0) = {
+  parent_clause_0 : parentTrait0_t self;
+  parent_clause_1 : parentTrait1_t self;
+}
+
+(** [traits::test_child_trait1]: forward function *)
+let test_child_trait1
+  (t : Type0) (inst : childTrait_t t) (x : t) : result alloc_string_String_t =
+  inst.parent_clause_0.get_name x
+
+(** [traits::test_child_trait2]: forward function *)
+let test_child_trait2
+  (t : Type0) (inst : childTrait_t t) (x : t) :
+  result inst.parent_clause_0.tW
+  =
+  inst.parent_clause_0.get_w x
+
+(** [traits::order1]: forward function *)
+let order1
+  (t u : Type0) (inst : parentTrait0_t t) (inst0 : parentTrait0_t u) :
+  result unit
+  =
+  Return ()
+
+(** Trait declaration: [traits::ChildTrait1] *)
+noeq type childTrait1_t (self : Type0) = {
+  parent_clause_0 : parentTrait1_t self;
+}
+
+(** Trait implementation: [traits::usize::{9}] *)
+let usize_ParentTrait1Inst : parentTrait1_t usize = ()
+
+(** Trait implementation: [traits::usize::{10}] *)
+let usize_ChildTrait1Inst : childTrait1_t usize = {
+  parent_clause_0 = usize_ParentTrait1Inst;
+}
+
+(** Trait declaration: [traits::Iterator] *)
+noeq type iterator_t (self : Type0) = { tItem : Type0; }
+
+(** Trait declaration: [traits::IntoIterator] *)
+noeq type intoIterator_t (self : Type0) = {
+  tItem : Type0;
+  tIntoIter : Type0;
+  tIntoIter_clause_0 : iterator_t tIntoIter;
+  into_iter : self -> result tIntoIter;
+}
+
+(** Trait declaration: [traits::FromResidual] *)
+type fromResidual_t (self t : Type0) = unit
+
+(** Trait declaration: [traits::Try] *)
+noeq type try_t (self : Type0) = {
+  tResidual : Type0;
+  parent_clause_0 : fromResidual_t self tResidual;
+}
+
+(** Trait declaration: [traits::WithTarget] *)
+noeq type withTarget_t (self : Type0) = { tTarget : Type0; }
+
+(** Trait declaration: [traits::ParentTrait2] *)
+noeq type parentTrait2_t (self : Type0) = {
+  tU : Type0;
+  tU_clause_0 : withTarget_t tU;
+}
+
+(** Trait declaration: [traits::ChildTrait2] *)
+noeq type childTrait2_t (self : Type0) = {
+  parent_clause_0 : parentTrait2_t self;
+  convert : parent_clause_0.tU -> result parent_clause_0.tU_clause_0.tTarget;
+}
+
+(** Trait implementation: [traits::u32::{11}] *)
+let u32_WithTargetInst : withTarget_t u32 = { tTarget = u32; }
+
+(** Trait implementation: [traits::u32::{12}] *)
+let u32_ParentTrait2Inst : parentTrait2_t u32 = {
+  tU = u32;
+  tU_clause_0 = u32_WithTargetInst;
+}
+
+(** [traits::u32::{13}::convert]: forward function *)
+let u32_convert (x : u32) : result u32 =
+  Return x
+
+(** Trait implementation: [traits::u32::{13}] *)
+let u32_ChildTrait2Inst : childTrait2_t u32 = {
+  parent_clause_0 = u32_ParentTrait2Inst;
+  convert = u32_convert;
+}
+
+(** [traits::incr_u32]: forward function *)
+let incr_u32 (x : u32) : result u32 =
+  u32_add x 1
+
+(** Trait declaration: [traits::CFnOnce] *)
+noeq type cFnOnce_t (self args : Type0) = {
+  tOutput : Type0;
+  call_once : self -> args -> result tOutput;
+}
+
+(** Trait declaration: [traits::CFnMut] *)
+noeq type cFnMut_t (self args : Type0) = {
+  parent_clause_0 : cFnOnce_t self args;
+  call_mut : self -> args -> result parent_clause_0.tOutput;
+  call_mut_back : self -> args -> parent_clause_0.tOutput -> result self;
+}
+
+(** Trait declaration: [traits::CFn] *)
+noeq type cFn_t (self args : Type0) = {
+  parent_clause_0 : cFnMut_t self args;
+  call_mut : self -> args -> result parent_clause_0.parent_clause_0.tOutput;
+}
+
diff --git a/tests/hol4/betree/betreeMain_FunsScript.sml b/tests/hol4/betree/betreeMain_FunsScript.sml
index 5e604f8c..bd16c16c 100644
--- a/tests/hol4/betree/betreeMain_FunsScript.sml
+++ b/tests/hol4/betree/betreeMain_FunsScript.sml
@@ -88,14 +88,6 @@ val betree_node_id_counter_fresh_id_back_def = Define ‘
     od
 ’
 
-(** [core::num::u64::{9}::MAX] *)
-Definition core_num_u64_max_body_def:
-  core_num_u64_max_body : u64 result = Return (int_to_u64 18446744073709551615)
-End
-Definition core_num_u64_max_c_def:
-  core_num_u64_max_c : u64 = get_return_value core_num_u64_max_body
-End
-
 val betree_upsert_update_fwd_def = Define ‘
   (** [betree_main::betree::upsert_update]: forward function *)
   betree_upsert_update_fwd
@@ -109,8 +101,8 @@ val betree_upsert_update_fwd_def = Define ‘
       (case st of
       | BetreeUpsertFunStateAdd v =>
         do
-        margin <- u64_sub core_num_u64_max_c prev0;
-        if u64_ge margin v then u64_add prev0 v else Return core_num_u64_max_c
+        margin <- u64_sub core_u64_max prev0;
+        if u64_ge margin v then u64_add prev0 v else Return core_u64_max
         od
       | BetreeUpsertFunStateSub v =>
         if u64_ge prev0 v then u64_sub prev0 v else Return (int_to_u64 0)))
diff --git a/tests/hol4/betree/betreeMain_FunsTheory.sig b/tests/hol4/betree/betreeMain_FunsTheory.sig
index 6c249f70..c922ca9f 100644
--- a/tests/hol4/betree/betreeMain_FunsTheory.sig
+++ b/tests/hol4/betree/betreeMain_FunsTheory.sig
@@ -58,8 +58,6 @@ sig
     val betree_store_internal_node_fwd_def : thm
     val betree_store_leaf_node_fwd_def : thm
     val betree_upsert_update_fwd_def : thm
-    val core_num_u64_max_body_def : thm
-    val core_num_u64_max_c_def : thm
     val main_fwd_def : thm
   
   val betreeMain_Funs_grammars : type_grammar.grammar * term_grammar.grammar
@@ -1215,22 +1213,14 @@ sig
             case st of
               BetreeUpsertFunStateAdd v =>
                 do
-                  margin <- u64_sub core_num_u64_max_c prev0;
+                  margin <- u64_sub core_u64_max prev0;
                   if u64_ge margin v then u64_add prev0 v
-                  else Return core_num_u64_max_c
+                  else Return core_u64_max
                 od
             | BetreeUpsertFunStateSub v' =>
               if u64_ge prev0 v' then u64_sub prev0 v'
               else Return (int_to_u64 0)
    
-   [core_num_u64_max_body_def]  Definition
-      
-      ⊢ core_num_u64_max_body = Return (int_to_u64 18446744073709551615)
-   
-   [core_num_u64_max_c_def]  Definition
-      
-      ⊢ core_num_u64_max_c = get_return_value core_num_u64_max_body
-   
    [main_fwd_def]  Definition
       
       ⊢ main_fwd = Return ()
diff --git a/tests/hol4/hashmap/hashmap_FunsScript.sml b/tests/hol4/hashmap/hashmap_FunsScript.sml
index e3c3d2a5..682c5760 100644
--- a/tests/hol4/hashmap/hashmap_FunsScript.sml
+++ b/tests/hol4/hashmap/hashmap_FunsScript.sml
@@ -170,14 +170,6 @@ val hash_map_insert_no_resize_fwd_back_def = Define ‘
     od
 ’
 
-(** [core::num::u32::{8}::MAX] *)
-Definition core_num_u32_max_body_def:
-  core_num_u32_max_body : u32 result = Return (int_to_u32 4294967295)
-End
-Definition core_num_u32_max_c_def:
-  core_num_u32_max_c : u32 = get_return_value core_num_u32_max_body
-End
-
 val [hash_map_move_elements_from_list_loop_fwd_back_def] = DefineDiv ‘
   (** [hashmap::HashMap::{0}::move_elements_from_list]: loop 0: merged forward/backward function
       (there is a single backward function, and the forward function returns ()) *)
@@ -241,7 +233,7 @@ val hash_map_try_resize_fwd_back_def = Define ‘
       (there is a single backward function, and the forward function returns ()) *)
   hash_map_try_resize_fwd_back (self : 't hash_map_t) : 't hash_map_t result =
     do
-    max_usize <- mk_usize (u32_to_int core_num_u32_max_c);
+    max_usize <- mk_usize (u32_to_int core_u32_max);
     let capacity = vec_len self.hash_map_slots in
     do
     n1 <- usize_div max_usize (int_to_usize 2);
diff --git a/tests/hol4/hashmap/hashmap_FunsTheory.sig b/tests/hol4/hashmap/hashmap_FunsTheory.sig
index 50482547..bb3e192b 100644
--- a/tests/hol4/hashmap/hashmap_FunsTheory.sig
+++ b/tests/hol4/hashmap/hashmap_FunsTheory.sig
@@ -3,8 +3,6 @@ sig
   type thm = Thm.thm
   
   (*  Definitions  *)
-    val core_num_u32_max_body_def : thm
-    val core_num_u32_max_c_def : thm
     val hash_key_fwd_def : thm
     val hash_map_allocate_slots_fwd_def : thm
     val hash_map_allocate_slots_loop_fwd_def : thm
@@ -48,14 +46,6 @@ sig
 (*
    [hashmap_Types] Parent theory of "hashmap_Funs"
    
-   [core_num_u32_max_body_def]  Definition
-      
-      ⊢ core_num_u32_max_body = Return (int_to_u32 4294967295)
-   
-   [core_num_u32_max_c_def]  Definition
-      
-      ⊢ core_num_u32_max_c = get_return_value core_num_u32_max_body
-   
    [hash_key_fwd_def]  Definition
       
       ⊢ ∀k. hash_key_fwd k = Return k
@@ -472,7 +462,7 @@ sig
       ⊢ ∀self.
           hash_map_try_resize_fwd_back self =
           do
-            max_usize <- mk_usize (u32_to_int core_num_u32_max_c);
+            max_usize <- mk_usize (u32_to_int core_u32_max);
             capacity <<- vec_len self.hash_map_slots;
             n1 <- usize_div max_usize (int_to_usize 2);
             (i,i0) <<- self.hash_map_max_load_factor;
diff --git a/tests/hol4/hashmap/hashmap_PropertiesScript.sml b/tests/hol4/hashmap/hashmap_PropertiesScript.sml
index 7259f2f5..8bc12fa5 100644
--- a/tests/hol4/hashmap/hashmap_PropertiesScript.sml
+++ b/tests/hol4/hashmap/hashmap_PropertiesScript.sml
@@ -1296,7 +1296,7 @@ Proof
   rw [hash_map_try_resize_fwd_back_def] >>
   (* “_ <-- mk_usize (u32_to_int core_num_u32_max_c)” *)
   assume_tac usize_u32_bounds >>
-  fs [core_num_u32_max_c_def, core_num_u32_max_body_def, get_return_value_def, u32_max_def] >>
+  fs [core_u32_max_def, u32_max_def] >>
   massage >> fs [mk_usize_def, u32_max_def] >>
   (* / 2 *)
   progress >>
diff --git a/tests/hol4/hashmap_on_disk/hashmapMain_FunsScript.sml b/tests/hol4/hashmap_on_disk/hashmapMain_FunsScript.sml
index b21c4f58..c1e30aa6 100644
--- a/tests/hol4/hashmap_on_disk/hashmapMain_FunsScript.sml
+++ b/tests/hol4/hashmap_on_disk/hashmapMain_FunsScript.sml
@@ -193,14 +193,6 @@ val hashmap_hash_map_insert_no_resize_fwd_back_def = Define ‘
     od
 ’
 
-(** [core::num::u32::{8}::MAX] *)
-Definition core_num_u32_max_body_def:
-  core_num_u32_max_body : u32 result = Return (int_to_u32 4294967295)
-End
-Definition core_num_u32_max_c_def:
-  core_num_u32_max_c : u32 = get_return_value core_num_u32_max_body
-End
-
 val [hashmap_hash_map_move_elements_from_list_loop_fwd_back_def] = DefineDiv ‘
   (** [hashmap_main::hashmap::HashMap::{0}::move_elements_from_list]: loop 0: merged forward/backward function
       (there is a single backward function, and the forward function returns ()) *)
@@ -271,7 +263,7 @@ val hashmap_hash_map_try_resize_fwd_back_def = Define ‘
   hashmap_hash_map_try_resize_fwd_back
     (self : 't hashmap_hash_map_t) : 't hashmap_hash_map_t result =
     do
-    max_usize <- mk_usize (u32_to_int core_num_u32_max_c);
+    max_usize <- mk_usize (u32_to_int core_u32_max);
     let capacity = vec_len self.hashmap_hash_map_slots in
     do
     n1 <- usize_div max_usize (int_to_usize 2);
diff --git a/tests/hol4/hashmap_on_disk/hashmapMain_FunsTheory.sig b/tests/hol4/hashmap_on_disk/hashmapMain_FunsTheory.sig
index 1d24cb26..d4e43d9a 100644
--- a/tests/hol4/hashmap_on_disk/hashmapMain_FunsTheory.sig
+++ b/tests/hol4/hashmap_on_disk/hashmapMain_FunsTheory.sig
@@ -3,8 +3,6 @@ sig
   type thm = Thm.thm
   
   (*  Definitions  *)
-    val core_num_u32_max_body_def : thm
-    val core_num_u32_max_c_def : thm
     val hashmap_hash_key_fwd_def : thm
     val hashmap_hash_map_allocate_slots_fwd_def : thm
     val hashmap_hash_map_allocate_slots_loop_fwd_def : thm
@@ -50,14 +48,6 @@ sig
 (*
    [hashmapMain_Opaque] Parent theory of "hashmapMain_Funs"
    
-   [core_num_u32_max_body_def]  Definition
-      
-      ⊢ core_num_u32_max_body = Return (int_to_u32 4294967295)
-   
-   [core_num_u32_max_c_def]  Definition
-      
-      ⊢ core_num_u32_max_c = get_return_value core_num_u32_max_body
-   
    [hashmap_hash_key_fwd_def]  Definition
       
       ⊢ ∀k. hashmap_hash_key_fwd k = Return k
@@ -506,7 +496,7 @@ sig
       ⊢ ∀self.
           hashmap_hash_map_try_resize_fwd_back self =
           do
-            max_usize <- mk_usize (u32_to_int core_num_u32_max_c);
+            max_usize <- mk_usize (u32_to_int core_u32_max);
             capacity <<- vec_len self.hashmap_hash_map_slots;
             n1 <- usize_div max_usize (int_to_usize 2);
             (i,i0) <<- self.hashmap_hash_map_max_load_factor;
diff --git a/tests/hol4/misc-constants/constantsScript.sml b/tests/hol4/misc-constants/constantsScript.sml
index d589d348..40a319c6 100644
--- a/tests/hol4/misc-constants/constantsScript.sml
+++ b/tests/hol4/misc-constants/constantsScript.sml
@@ -13,17 +13,9 @@ Definition x0_c_def:
   x0_c : u32 = get_return_value x0_body
 End
 
-(** [core::num::u32::{8}::MAX] *)
-Definition core_num_u32_max_body_def:
-  core_num_u32_max_body : u32 result = Return (int_to_u32 4294967295)
-End
-Definition core_num_u32_max_c_def:
-  core_num_u32_max_c : u32 = get_return_value core_num_u32_max_body
-End
-
 (** [constants::X1] *)
 Definition x1_body_def:
-  x1_body : u32 result = Return core_num_u32_max_c
+  x1_body : u32 result = Return core_u32_max
 End
 Definition x1_c_def:
   x1_c : u32 = get_return_value x1_body
diff --git a/tests/hol4/misc-constants/constantsTheory.sig b/tests/hol4/misc-constants/constantsTheory.sig
index 149d7e22..287ad5f5 100644
--- a/tests/hol4/misc-constants/constantsTheory.sig
+++ b/tests/hol4/misc-constants/constantsTheory.sig
@@ -4,8 +4,6 @@ sig
   
   (*  Definitions  *)
     val add_fwd_def : thm
-    val core_num_u32_max_body_def : thm
-    val core_num_u32_max_c_def : thm
     val get_z1_fwd_def : thm
     val get_z1_z1_body_def : thm
     val get_z1_z1_c_def : thm
@@ -110,14 +108,6 @@ sig
       
       ⊢ ∀a b. add_fwd a b = i32_add a b
    
-   [core_num_u32_max_body_def]  Definition
-      
-      ⊢ core_num_u32_max_body = Return (int_to_u32 4294967295)
-   
-   [core_num_u32_max_c_def]  Definition
-      
-      ⊢ core_num_u32_max_c = get_return_value core_num_u32_max_body
-   
    [get_z1_fwd_def]  Definition
       
       ⊢ get_z1_fwd = Return get_z1_z1_c
@@ -321,7 +311,7 @@ sig
    
    [x1_body_def]  Definition
       
-      ⊢ x1_body = Return core_num_u32_max_c
+      ⊢ x1_body = Return core_u32_max
    
    [x1_c_def]  Definition
       
diff --git a/tests/lean/Array.lean b/tests/lean/Array.lean
index 277b63d9..20f02e97 100644
--- a/tests/lean/Array.lean
+++ b/tests/lean/Array.lean
@@ -1 +1,435 @@
-import Array.Funs
+-- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
+-- [array]
+import Base
+open Primitives
+
+namespace array
+
+/- [array::AB] -/
+inductive AB :=
+| A : AB
+| B : AB
+
+/- [array::incr]: merged forward/backward function
+   (there is a single backward function, and the forward function returns ()) -/
+def incr (x : U32) : Result U32 :=
+  x + 1#u32
+
+/- [array::array_to_shared_slice_]: forward function -/
+def array_to_shared_slice_
+  (T : Type) (s : Array T 32#usize) : Result (Slice T) :=
+  Array.to_slice T 32#usize s
+
+/- [array::array_to_mut_slice_]: forward function -/
+def array_to_mut_slice_ (T : Type) (s : Array T 32#usize) : Result (Slice T) :=
+  Array.to_slice T 32#usize s
+
+/- [array::array_to_mut_slice_]: backward function 0 -/
+def array_to_mut_slice__back
+  (T : Type) (s : Array T 32#usize) (ret0 : Slice T) :
+  Result (Array T 32#usize)
+  :=
+  Array.from_slice T 32#usize s ret0
+
+/- [array::array_len]: forward function -/
+def array_len (T : Type) (s : Array T 32#usize) : Result Usize :=
+  do
+    let s0 ← Array.to_slice T 32#usize s
+    let i := Slice.len T s0
+    Result.ret i
+
+/- [array::shared_array_len]: forward function -/
+def shared_array_len (T : Type) (s : Array T 32#usize) : Result Usize :=
+  do
+    let s0 ← Array.to_slice T 32#usize s
+    let i := Slice.len T s0
+    Result.ret i
+
+/- [array::shared_slice_len]: forward function -/
+def shared_slice_len (T : Type) (s : Slice T) : Result Usize :=
+  let i := Slice.len T s
+  Result.ret i
+
+/- [array::index_array_shared]: forward function -/
+def index_array_shared
+  (T : Type) (s : Array T 32#usize) (i : Usize) : Result T :=
+  Array.index_usize T 32#usize s i
+
+/- [array::index_array_u32]: forward function -/
+def index_array_u32 (s : Array U32 32#usize) (i : Usize) : Result U32 :=
+  Array.index_usize U32 32#usize s i
+
+/- [array::index_array_copy]: forward function -/
+def index_array_copy (x : Array U32 32#usize) : Result U32 :=
+  Array.index_usize U32 32#usize x 0#usize
+
+/- [array::index_mut_array]: forward function -/
+def index_mut_array (T : Type) (s : Array T 32#usize) (i : Usize) : Result T :=
+  Array.index_usize T 32#usize s i
+
+/- [array::index_mut_array]: backward function 0 -/
+def index_mut_array_back
+  (T : Type) (s : Array T 32#usize) (i : Usize) (ret0 : T) :
+  Result (Array T 32#usize)
+  :=
+  Array.update_usize T 32#usize s i ret0
+
+/- [array::index_slice]: forward function -/
+def index_slice (T : Type) (s : Slice T) (i : Usize) : Result T :=
+  Slice.index_usize T s i
+
+/- [array::index_mut_slice]: forward function -/
+def index_mut_slice (T : Type) (s : Slice T) (i : Usize) : Result T :=
+  Slice.index_usize T s i
+
+/- [array::index_mut_slice]: backward function 0 -/
+def index_mut_slice_back
+  (T : Type) (s : Slice T) (i : Usize) (ret0 : T) : Result (Slice T) :=
+  Slice.update_usize T s i ret0
+
+/- [array::slice_subslice_shared_]: forward function -/
+def slice_subslice_shared_
+  (x : Slice U32) (y : Usize) (z : Usize) : Result (Slice U32) :=
+  core.slice.index.Slice.index U32 (core.ops.range.Range Usize)
+    (core.slice.index.Range.coresliceindexSliceIndexInst U32) x
+    { start := y, end_ := z }
+
+/- [array::slice_subslice_mut_]: forward function -/
+def slice_subslice_mut_
+  (x : Slice U32) (y : Usize) (z : Usize) : Result (Slice U32) :=
+  core.slice.index.Slice.index_mut U32 (core.ops.range.Range Usize)
+    (core.slice.index.Range.coresliceindexSliceIndexInst U32) x
+    { start := y, end_ := z }
+
+/- [array::slice_subslice_mut_]: backward function 0 -/
+def slice_subslice_mut__back
+  (x : Slice U32) (y : Usize) (z : Usize) (ret0 : Slice U32) :
+  Result (Slice U32)
+  :=
+  core.slice.index.Slice.index_mut_back U32 (core.ops.range.Range Usize)
+    (core.slice.index.Range.coresliceindexSliceIndexInst U32) x
+    { start := y, end_ := z } ret0
+
+/- [array::array_to_slice_shared_]: forward function -/
+def array_to_slice_shared_ (x : Array U32 32#usize) : Result (Slice U32) :=
+  Array.to_slice U32 32#usize x
+
+/- [array::array_to_slice_mut_]: forward function -/
+def array_to_slice_mut_ (x : Array U32 32#usize) : Result (Slice U32) :=
+  Array.to_slice U32 32#usize x
+
+/- [array::array_to_slice_mut_]: backward function 0 -/
+def array_to_slice_mut__back
+  (x : Array U32 32#usize) (ret0 : Slice U32) : Result (Array U32 32#usize) :=
+  Array.from_slice U32 32#usize x ret0
+
+/- [array::array_subslice_shared_]: forward function -/
+def array_subslice_shared_
+  (x : Array U32 32#usize) (y : Usize) (z : Usize) : Result (Slice U32) :=
+  core.array.Array.index U32 (core.ops.range.Range Usize) 32#usize
+    (core.slice.index.Slice.coreopsindexIndexInst U32 (core.ops.range.Range
+    Usize) (core.slice.index.Range.coresliceindexSliceIndexInst U32)) x
+    { start := y, end_ := z }
+
+/- [array::array_subslice_mut_]: forward function -/
+def array_subslice_mut_
+  (x : Array U32 32#usize) (y : Usize) (z : Usize) : Result (Slice U32) :=
+  core.array.Array.index_mut U32 (core.ops.range.Range Usize) 32#usize
+    (core.slice.index.Slice.coreopsindexIndexMutInst U32 (core.ops.range.Range
+    Usize) (core.slice.index.Range.coresliceindexSliceIndexInst U32)) x
+    { start := y, end_ := z }
+
+/- [array::array_subslice_mut_]: backward function 0 -/
+def array_subslice_mut__back
+  (x : Array U32 32#usize) (y : Usize) (z : Usize) (ret0 : Slice U32) :
+  Result (Array U32 32#usize)
+  :=
+  core.array.Array.index_mut_back U32 (core.ops.range.Range Usize) 32#usize
+    (core.slice.index.Slice.coreopsindexIndexMutInst U32 (core.ops.range.Range
+    Usize) (core.slice.index.Range.coresliceindexSliceIndexInst U32)) x
+    { start := y, end_ := z } ret0
+
+/- [array::index_slice_0]: forward function -/
+def index_slice_0 (T : Type) (s : Slice T) : Result T :=
+  Slice.index_usize T s 0#usize
+
+/- [array::index_array_0]: forward function -/
+def index_array_0 (T : Type) (s : Array T 32#usize) : Result T :=
+  Array.index_usize T 32#usize s 0#usize
+
+/- [array::index_index_array]: forward function -/
+def index_index_array
+  (s : Array (Array U32 32#usize) 32#usize) (i : Usize) (j : Usize) :
+  Result U32
+  :=
+  do
+    let a ← Array.index_usize (Array U32 32#usize) 32#usize s i
+    Array.index_usize U32 32#usize a j
+
+/- [array::update_update_array]: forward function -/
+def update_update_array
+  (s : Array (Array U32 32#usize) 32#usize) (i : Usize) (j : Usize) :
+  Result Unit
+  :=
+  do
+    let a ← Array.index_usize (Array U32 32#usize) 32#usize s i
+    let a0 ← Array.update_usize U32 32#usize a j 0#u32
+    let _ ← Array.update_usize (Array U32 32#usize) 32#usize s i a0
+    Result.ret ()
+
+/- [array::array_local_deep_copy]: forward function -/
+def array_local_deep_copy (x : Array U32 32#usize) : Result Unit :=
+  Result.ret ()
+
+/- [array::take_array]: forward function -/
+def take_array (a : Array U32 2#usize) : Result Unit :=
+  Result.ret ()
+
+/- [array::take_array_borrow]: forward function -/
+def take_array_borrow (a : Array U32 2#usize) : Result Unit :=
+  Result.ret ()
+
+/- [array::take_slice]: forward function -/
+def take_slice (s : Slice U32) : Result Unit :=
+  Result.ret ()
+
+/- [array::take_mut_slice]: merged forward/backward function
+   (there is a single backward function, and the forward function returns ()) -/
+def take_mut_slice (s : Slice U32) : Result (Slice U32) :=
+  Result.ret s
+
+/- [array::take_all]: forward function -/
+def take_all : Result Unit :=
+  do
+    let _ ← take_array (Array.make U32 2#usize [ 0#u32, 0#u32 ])
+    let _ ← take_array_borrow (Array.make U32 2#usize [ 0#u32, 0#u32 ])
+    let s ←
+      Array.to_slice U32 2#usize (Array.make U32 2#usize [ 0#u32, 0#u32 ])
+    let _ ← take_slice s
+    let s0 ←
+      Array.to_slice U32 2#usize (Array.make U32 2#usize [ 0#u32, 0#u32 ])
+    let s1 ← take_mut_slice s0
+    let _ ←
+      Array.from_slice U32 2#usize (Array.make U32 2#usize [ 0#u32, 0#u32 ]) s1
+    Result.ret ()
+
+/- [array::index_array]: forward function -/
+def index_array (x : Array U32 2#usize) : Result U32 :=
+  Array.index_usize U32 2#usize x 0#usize
+
+/- [array::index_array_borrow]: forward function -/
+def index_array_borrow (x : Array U32 2#usize) : Result U32 :=
+  Array.index_usize U32 2#usize x 0#usize
+
+/- [array::index_slice_u32_0]: forward function -/
+def index_slice_u32_0 (x : Slice U32) : Result U32 :=
+  Slice.index_usize U32 x 0#usize
+
+/- [array::index_mut_slice_u32_0]: forward function -/
+def index_mut_slice_u32_0 (x : Slice U32) : Result U32 :=
+  Slice.index_usize U32 x 0#usize
+
+/- [array::index_mut_slice_u32_0]: backward function 0 -/
+def index_mut_slice_u32_0_back (x : Slice U32) : Result (Slice U32) :=
+  do
+    let _ ← Slice.index_usize U32 x 0#usize
+    Result.ret x
+
+/- [array::index_all]: forward function -/
+def index_all : Result U32 :=
+  do
+    let i ← index_array (Array.make U32 2#usize [ 0#u32, 0#u32 ])
+    let i0 ← index_array (Array.make U32 2#usize [ 0#u32, 0#u32 ])
+    let i1 ← i + i0
+    let i2 ← index_array_borrow (Array.make U32 2#usize [ 0#u32, 0#u32 ])
+    let i3 ← i1 + i2
+    let s ←
+      Array.to_slice U32 2#usize (Array.make U32 2#usize [ 0#u32, 0#u32 ])
+    let i4 ← index_slice_u32_0 s
+    let i5 ← i3 + i4
+    let s0 ←
+      Array.to_slice U32 2#usize (Array.make U32 2#usize [ 0#u32, 0#u32 ])
+    let i6 ← index_mut_slice_u32_0 s0
+    let i7 ← i5 + i6
+    let s1 ← index_mut_slice_u32_0_back s0
+    let _ ←
+      Array.from_slice U32 2#usize (Array.make U32 2#usize [ 0#u32, 0#u32 ]) s1
+    Result.ret i7
+
+/- [array::update_array]: forward function -/
+def update_array (x : Array U32 2#usize) : Result Unit :=
+  do
+    let _ ← Array.update_usize U32 2#usize x 0#usize 1#u32
+    Result.ret ()
+
+/- [array::update_array_mut_borrow]: merged forward/backward function
+   (there is a single backward function, and the forward function returns ()) -/
+def update_array_mut_borrow
+  (x : Array U32 2#usize) : Result (Array U32 2#usize) :=
+  Array.update_usize U32 2#usize x 0#usize 1#u32
+
+/- [array::update_mut_slice]: merged forward/backward function
+   (there is a single backward function, and the forward function returns ()) -/
+def update_mut_slice (x : Slice U32) : Result (Slice U32) :=
+  Slice.update_usize U32 x 0#usize 1#u32
+
+/- [array::update_all]: forward function -/
+def update_all : Result Unit :=
+  do
+    let _ ← update_array (Array.make U32 2#usize [ 0#u32, 0#u32 ])
+    let x ← update_array_mut_borrow (Array.make U32 2#usize [ 0#u32, 0#u32 ])
+    let s ← Array.to_slice U32 2#usize x
+    let s0 ← update_mut_slice s
+    let _ ← Array.from_slice U32 2#usize x s0
+    Result.ret ()
+
+/- [array::range_all]: forward function -/
+def range_all : Result Unit :=
+  do
+    let s ←
+      core.array.Array.index_mut U32 (core.ops.range.Range Usize) 4#usize
+        (core.slice.index.Slice.coreopsindexIndexMutInst U32
+        (core.ops.range.Range Usize)
+        (core.slice.index.Range.coresliceindexSliceIndexInst U32))
+        (Array.make U32 4#usize [ 0#u32, 0#u32, 0#u32, 0#u32 ])
+        { start := 1#usize, end_ := 3#usize }
+    let s0 ← update_mut_slice s
+    let _ ←
+      core.array.Array.index_mut_back U32 (core.ops.range.Range Usize) 4#usize
+        (core.slice.index.Slice.coreopsindexIndexMutInst U32
+        (core.ops.range.Range Usize)
+        (core.slice.index.Range.coresliceindexSliceIndexInst U32))
+        (Array.make U32 4#usize [ 0#u32, 0#u32, 0#u32, 0#u32 ])
+        { start := 1#usize, end_ := 3#usize } s0
+    Result.ret ()
+
+/- [array::deref_array_borrow]: forward function -/
+def deref_array_borrow (x : Array U32 2#usize) : Result U32 :=
+  Array.index_usize U32 2#usize x 0#usize
+
+/- [array::deref_array_mut_borrow]: forward function -/
+def deref_array_mut_borrow (x : Array U32 2#usize) : Result U32 :=
+  Array.index_usize U32 2#usize x 0#usize
+
+/- [array::deref_array_mut_borrow]: backward function 0 -/
+def deref_array_mut_borrow_back
+  (x : Array U32 2#usize) : Result (Array U32 2#usize) :=
+  do
+    let _ ← Array.index_usize U32 2#usize x 0#usize
+    Result.ret x
+
+/- [array::take_array_t]: forward function -/
+def take_array_t (a : Array AB 2#usize) : Result Unit :=
+  Result.ret ()
+
+/- [array::non_copyable_array]: forward function -/
+def non_copyable_array : Result Unit :=
+  do
+    let _ ← take_array_t (Array.make AB 2#usize [ AB.A, AB.B ])
+    Result.ret ()
+
+/- [array::sum]: loop 0: forward function -/
+divergent def sum_loop (s : Slice U32) (sum0 : U32) (i : Usize) : Result U32 :=
+  let i0 := Slice.len U32 s
+  if i < i0
+  then
+    do
+      let i1 ← Slice.index_usize U32 s i
+      let sum1 ← sum0 + i1
+      let i2 ← i + 1#usize
+      sum_loop s sum1 i2
+  else Result.ret sum0
+
+/- [array::sum]: forward function -/
+def sum (s : Slice U32) : Result U32 :=
+  sum_loop s 0#u32 0#usize
+
+/- [array::sum2]: loop 0: forward function -/
+divergent def sum2_loop
+  (s : Slice U32) (s2 : Slice U32) (sum0 : U32) (i : Usize) : Result U32 :=
+  let i0 := Slice.len U32 s
+  if i < i0
+  then
+    do
+      let i1 ← Slice.index_usize U32 s i
+      let i2 ← Slice.index_usize U32 s2 i
+      let i3 ← i1 + i2
+      let sum1 ← sum0 + i3
+      let i4 ← i + 1#usize
+      sum2_loop s s2 sum1 i4
+  else Result.ret sum0
+
+/- [array::sum2]: forward function -/
+def sum2 (s : Slice U32) (s2 : Slice U32) : Result U32 :=
+  let i := Slice.len U32 s
+  let i0 := Slice.len U32 s2
+  if not (i = i0)
+  then Result.fail Error.panic
+  else sum2_loop s s2 0#u32 0#usize
+
+/- [array::f0]: forward function -/
+def f0 : Result Unit :=
+  do
+    let s ←
+      Array.to_slice U32 2#usize (Array.make U32 2#usize [ 1#u32, 2#u32 ])
+    let s0 ← Slice.update_usize U32 s 0#usize 1#u32
+    let _ ←
+      Array.from_slice U32 2#usize (Array.make U32 2#usize [ 1#u32, 2#u32 ]) s0
+    Result.ret ()
+
+/- [array::f1]: forward function -/
+def f1 : Result Unit :=
+  do
+    let _ ←
+      Array.update_usize U32 2#usize (Array.make U32 2#usize [ 1#u32, 2#u32 ])
+        0#usize 1#u32
+    Result.ret ()
+
+/- [array::f2]: forward function -/
+def f2 (i : U32) : Result Unit :=
+  Result.ret ()
+
+/- [array::f4]: forward function -/
+def f4 (x : Array U32 32#usize) (y : Usize) (z : Usize) : Result (Slice U32) :=
+  core.array.Array.index U32 (core.ops.range.Range Usize) 32#usize
+    (core.slice.index.Slice.coreopsindexIndexInst U32 (core.ops.range.Range
+    Usize) (core.slice.index.Range.coresliceindexSliceIndexInst U32)) x
+    { start := y, end_ := z }
+
+/- [array::f3]: forward function -/
+def f3 : Result U32 :=
+  do
+    let i ←
+      Array.index_usize U32 2#usize (Array.make U32 2#usize [ 1#u32, 2#u32 ])
+        0#usize
+    let _ ← f2 i
+    let b := Array.repeat U32 32#usize 0#u32
+    let s ←
+      Array.to_slice U32 2#usize (Array.make U32 2#usize [ 1#u32, 2#u32 ])
+    let s0 ← f4 b 16#usize 18#usize
+    sum2 s s0
+
+/- [array::SZ] -/
+def sz_body : Result Usize := Result.ret 32#usize
+def sz_c : Usize := eval_global sz_body (by simp)
+
+/- [array::f5]: forward function -/
+def f5 (x : Array U32 32#usize) : Result U32 :=
+  Array.index_usize U32 32#usize x 0#usize
+
+/- [array::ite]: forward function -/
+def ite : Result Unit :=
+  do
+    let s ←
+      Array.to_slice U32 2#usize (Array.make U32 2#usize [ 0#u32, 0#u32 ])
+    let s0 ←
+      Array.to_slice U32 2#usize (Array.make U32 2#usize [ 0#u32, 0#u32 ])
+    let s1 ← index_mut_slice_u32_0_back s0
+    let _ ←
+      Array.from_slice U32 2#usize (Array.make U32 2#usize [ 0#u32, 0#u32 ]) s1
+    let s2 ← index_mut_slice_u32_0_back s
+    let _ ←
+      Array.from_slice U32 2#usize (Array.make U32 2#usize [ 0#u32, 0#u32 ]) s2
+    Result.ret ()
+
+end array
diff --git a/tests/lean/Array/Funs.lean b/tests/lean/Array/Funs.lean
index ad737dca..32ae6248 100644
--- a/tests/lean/Array/Funs.lean
+++ b/tests/lean/Array/Funs.lean
@@ -6,189 +6,183 @@ open Primitives
 
 namespace array
 
+/- [array::incr]: merged forward/backward function
+   (there is a single backward function, and the forward function returns ()) -/
+def incr (x : U32) : Result U32 :=
+  x + 1#u32
+
 /- [array::array_to_shared_slice_]: forward function -/
 def array_to_shared_slice_
-  (T0 : Type) (s : Array T0 (Usize.ofInt 32)) : Result (Slice T0) :=
-  Array.to_slice_shared T0 (Usize.ofInt 32) s
+  (T : Type) (s : Array T 32#usize) : Result (Slice T) :=
+  Array.to_slice T 32#usize s
 
 /- [array::array_to_mut_slice_]: forward function -/
-def array_to_mut_slice_
-  (T0 : Type) (s : Array T0 (Usize.ofInt 32)) : Result (Slice T0) :=
-  Array.to_slice_mut T0 (Usize.ofInt 32) s
+def array_to_mut_slice_ (T : Type) (s : Array T 32#usize) : Result (Slice T) :=
+  Array.to_slice T 32#usize s
 
 /- [array::array_to_mut_slice_]: backward function 0 -/
 def array_to_mut_slice__back
-  (T0 : Type) (s : Array T0 (Usize.ofInt 32)) (ret0 : Slice T0) :
-  Result (Array T0 (Usize.ofInt 32))
+  (T : Type) (s : Array T 32#usize) (ret0 : Slice T) :
+  Result (Array T 32#usize)
   :=
-  Array.to_slice_mut_back T0 (Usize.ofInt 32) s ret0
+  Array.from_slice T 32#usize s ret0
 
 /- [array::array_len]: forward function -/
-def array_len (T0 : Type) (s : Array T0 (Usize.ofInt 32)) : Result Usize :=
+def array_len (T : Type) (s : Array T 32#usize) : Result Usize :=
   do
-    let s0 ← Array.to_slice_shared T0 (Usize.ofInt 32) s
-    let i := Slice.len T0 s0
+    let s0 ← Array.to_slice T 32#usize s
+    let i := Slice.len T s0
     Result.ret i
 
 /- [array::shared_array_len]: forward function -/
-def shared_array_len
-  (T0 : Type) (s : Array T0 (Usize.ofInt 32)) : Result Usize :=
+def shared_array_len (T : Type) (s : Array T 32#usize) : Result Usize :=
   do
-    let s0 ← Array.to_slice_shared T0 (Usize.ofInt 32) s
-    let i := Slice.len T0 s0
+    let s0 ← Array.to_slice T 32#usize s
+    let i := Slice.len T s0
     Result.ret i
 
 /- [array::shared_slice_len]: forward function -/
-def shared_slice_len (T0 : Type) (s : Slice T0) : Result Usize :=
-  let i := Slice.len T0 s
+def shared_slice_len (T : Type) (s : Slice T) : Result Usize :=
+  let i := Slice.len T s
   Result.ret i
 
 /- [array::index_array_shared]: forward function -/
 def index_array_shared
-  (T0 : Type) (s : Array T0 (Usize.ofInt 32)) (i : Usize) : Result T0 :=
-  Array.index_shared T0 (Usize.ofInt 32) s i
+  (T : Type) (s : Array T 32#usize) (i : Usize) : Result T :=
+  Array.index_usize T 32#usize s i
 
 /- [array::index_array_u32]: forward function -/
-def index_array_u32
-  (s : Array U32 (Usize.ofInt 32)) (i : Usize) : Result U32 :=
-  Array.index_shared U32 (Usize.ofInt 32) s i
-
-/- [array::index_array_generic]: forward function -/
-def index_array_generic
-  (N : Usize) (s : Array U32 N) (i : Usize) : Result U32 :=
-  Array.index_shared U32 N s i
-
-/- [array::index_array_generic_call]: forward function -/
-def index_array_generic_call
-  (N : Usize) (s : Array U32 N) (i : Usize) : Result U32 :=
-  index_array_generic N s i
+def index_array_u32 (s : Array U32 32#usize) (i : Usize) : Result U32 :=
+  Array.index_usize U32 32#usize s i
 
 /- [array::index_array_copy]: forward function -/
-def index_array_copy (x : Array U32 (Usize.ofInt 32)) : Result U32 :=
-  Array.index_shared U32 (Usize.ofInt 32) x (Usize.ofInt 0)
+def index_array_copy (x : Array U32 32#usize) : Result U32 :=
+  Array.index_usize U32 32#usize x 0#usize
 
 /- [array::index_mut_array]: forward function -/
-def index_mut_array
-  (T0 : Type) (s : Array T0 (Usize.ofInt 32)) (i : Usize) : Result T0 :=
-  Array.index_mut T0 (Usize.ofInt 32) s i
+def index_mut_array (T : Type) (s : Array T 32#usize) (i : Usize) : Result T :=
+  Array.index_usize T 32#usize s i
 
 /- [array::index_mut_array]: backward function 0 -/
 def index_mut_array_back
-  (T0 : Type) (s : Array T0 (Usize.ofInt 32)) (i : Usize) (ret0 : T0) :
-  Result (Array T0 (Usize.ofInt 32))
+  (T : Type) (s : Array T 32#usize) (i : Usize) (ret0 : T) :
+  Result (Array T 32#usize)
   :=
-  Array.index_mut_back T0 (Usize.ofInt 32) s i ret0
+  Array.update_usize T 32#usize s i ret0
 
 /- [array::index_slice]: forward function -/
-def index_slice (T0 : Type) (s : Slice T0) (i : Usize) : Result T0 :=
-  Slice.index_shared T0 s i
+def index_slice (T : Type) (s : Slice T) (i : Usize) : Result T :=
+  Slice.index_usize T s i
 
 /- [array::index_mut_slice]: forward function -/
-def index_mut_slice (T0 : Type) (s : Slice T0) (i : Usize) : Result T0 :=
-  Slice.index_mut T0 s i
+def index_mut_slice (T : Type) (s : Slice T) (i : Usize) : Result T :=
+  Slice.index_usize T s i
 
 /- [array::index_mut_slice]: backward function 0 -/
 def index_mut_slice_back
-  (T0 : Type) (s : Slice T0) (i : Usize) (ret0 : T0) : Result (Slice T0) :=
-  Slice.index_mut_back T0 s i ret0
+  (T : Type) (s : Slice T) (i : Usize) (ret0 : T) : Result (Slice T) :=
+  Slice.update_usize T s i ret0
 
 /- [array::slice_subslice_shared_]: forward function -/
 def slice_subslice_shared_
   (x : Slice U32) (y : Usize) (z : Usize) : Result (Slice U32) :=
-  Slice.subslice_shared U32 x (Range.mk y z)
+  core.slice.index.Slice.index U32 (core.ops.range.Range Usize)
+    (core.slice.index.Range.coresliceindexSliceIndexInst U32) x
+    { start := y, end_ := z }
 
 /- [array::slice_subslice_mut_]: forward function -/
 def slice_subslice_mut_
   (x : Slice U32) (y : Usize) (z : Usize) : Result (Slice U32) :=
-  Slice.subslice_mut U32 x (Range.mk y z)
+  core.slice.index.Slice.index_mut U32 (core.ops.range.Range Usize)
+    (core.slice.index.Range.coresliceindexSliceIndexInst U32) x
+    { start := y, end_ := z }
 
 /- [array::slice_subslice_mut_]: backward function 0 -/
 def slice_subslice_mut__back
   (x : Slice U32) (y : Usize) (z : Usize) (ret0 : Slice U32) :
   Result (Slice U32)
   :=
-  Slice.subslice_mut_back U32 x (Range.mk y z) ret0
+  core.slice.index.Slice.index_mut_back U32 (core.ops.range.Range Usize)
+    (core.slice.index.Range.coresliceindexSliceIndexInst U32) x
+    { start := y, end_ := z } ret0
 
 /- [array::array_to_slice_shared_]: forward function -/
-def array_to_slice_shared_
-  (x : Array U32 (Usize.ofInt 32)) : Result (Slice U32) :=
-  Array.to_slice_shared U32 (Usize.ofInt 32) x
+def array_to_slice_shared_ (x : Array U32 32#usize) : Result (Slice U32) :=
+  Array.to_slice U32 32#usize x
 
 /- [array::array_to_slice_mut_]: forward function -/
-def array_to_slice_mut_
-  (x : Array U32 (Usize.ofInt 32)) : Result (Slice U32) :=
-  Array.to_slice_mut U32 (Usize.ofInt 32) x
+def array_to_slice_mut_ (x : Array U32 32#usize) : Result (Slice U32) :=
+  Array.to_slice U32 32#usize x
 
 /- [array::array_to_slice_mut_]: backward function 0 -/
 def array_to_slice_mut__back
-  (x : Array U32 (Usize.ofInt 32)) (ret0 : Slice U32) :
-  Result (Array U32 (Usize.ofInt 32))
-  :=
-  Array.to_slice_mut_back U32 (Usize.ofInt 32) x ret0
+  (x : Array U32 32#usize) (ret0 : Slice U32) : Result (Array U32 32#usize) :=
+  Array.from_slice U32 32#usize x ret0
 
 /- [array::array_subslice_shared_]: forward function -/
 def array_subslice_shared_
-  (x : Array U32 (Usize.ofInt 32)) (y : Usize) (z : Usize) :
-  Result (Slice U32)
-  :=
-  Array.subslice_shared U32 (Usize.ofInt 32) x (Range.mk y z)
+  (x : Array U32 32#usize) (y : Usize) (z : Usize) : Result (Slice U32) :=
+  core.array.Array.index U32 (core.ops.range.Range Usize) 32#usize
+    (core.slice.index.Slice.coreopsindexIndexInst U32 (core.ops.range.Range
+    Usize) (core.slice.index.Range.coresliceindexSliceIndexInst U32)) x
+    { start := y, end_ := z }
 
 /- [array::array_subslice_mut_]: forward function -/
 def array_subslice_mut_
-  (x : Array U32 (Usize.ofInt 32)) (y : Usize) (z : Usize) :
-  Result (Slice U32)
-  :=
-  Array.subslice_mut U32 (Usize.ofInt 32) x (Range.mk y z)
+  (x : Array U32 32#usize) (y : Usize) (z : Usize) : Result (Slice U32) :=
+  core.array.Array.index_mut U32 (core.ops.range.Range Usize) 32#usize
+    (core.slice.index.Slice.coreopsindexIndexMutInst U32 (core.ops.range.Range
+    Usize) (core.slice.index.Range.coresliceindexSliceIndexInst U32)) x
+    { start := y, end_ := z }
 
 /- [array::array_subslice_mut_]: backward function 0 -/
 def array_subslice_mut__back
-  (x : Array U32 (Usize.ofInt 32)) (y : Usize) (z : Usize) (ret0 : Slice U32) :
-  Result (Array U32 (Usize.ofInt 32))
+  (x : Array U32 32#usize) (y : Usize) (z : Usize) (ret0 : Slice U32) :
+  Result (Array U32 32#usize)
   :=
-  Array.subslice_mut_back U32 (Usize.ofInt 32) x (Range.mk y z) ret0
+  core.array.Array.index_mut_back U32 (core.ops.range.Range Usize) 32#usize
+    (core.slice.index.Slice.coreopsindexIndexMutInst U32 (core.ops.range.Range
+    Usize) (core.slice.index.Range.coresliceindexSliceIndexInst U32)) x
+    { start := y, end_ := z } ret0
 
 /- [array::index_slice_0]: forward function -/
-def index_slice_0 (T0 : Type) (s : Slice T0) : Result T0 :=
-  Slice.index_shared T0 s (Usize.ofInt 0)
+def index_slice_0 (T : Type) (s : Slice T) : Result T :=
+  Slice.index_usize T s 0#usize
 
 /- [array::index_array_0]: forward function -/
-def index_array_0 (T0 : Type) (s : Array T0 (Usize.ofInt 32)) : Result T0 :=
-  Array.index_shared T0 (Usize.ofInt 32) s (Usize.ofInt 0)
+def index_array_0 (T : Type) (s : Array T 32#usize) : Result T :=
+  Array.index_usize T 32#usize s 0#usize
 
 /- [array::index_index_array]: forward function -/
 def index_index_array
-  (s : Array (Array U32 (Usize.ofInt 32)) (Usize.ofInt 32)) (i : Usize)
-  (j : Usize) :
+  (s : Array (Array U32 32#usize) 32#usize) (i : Usize) (j : Usize) :
   Result U32
   :=
   do
-    let a ←
-      Array.index_shared (Array U32 (Usize.ofInt 32)) (Usize.ofInt 32) s i
-    Array.index_shared U32 (Usize.ofInt 32) a j
+    let a ← Array.index_usize (Array U32 32#usize) 32#usize s i
+    Array.index_usize U32 32#usize a j
 
 /- [array::update_update_array]: forward function -/
 def update_update_array
-  (s : Array (Array U32 (Usize.ofInt 32)) (Usize.ofInt 32)) (i : Usize)
-  (j : Usize) :
+  (s : Array (Array U32 32#usize) 32#usize) (i : Usize) (j : Usize) :
   Result Unit
   :=
   do
-    let a ← Array.index_mut (Array U32 (Usize.ofInt 32)) (Usize.ofInt 32) s i
-    let a0 ← Array.index_mut_back U32 (Usize.ofInt 32) a j (U32.ofInt 0)
-    let _ ←
-      Array.index_mut_back (Array U32 (Usize.ofInt 32)) (Usize.ofInt 32) s i a0
+    let a ← Array.index_usize (Array U32 32#usize) 32#usize s i
+    let a0 ← Array.update_usize U32 32#usize a j 0#u32
+    let _ ← Array.update_usize (Array U32 32#usize) 32#usize s i a0
     Result.ret ()
 
 /- [array::array_local_deep_copy]: forward function -/
-def array_local_deep_copy (x : Array U32 (Usize.ofInt 32)) : Result Unit :=
+def array_local_deep_copy (x : Array U32 32#usize) : Result Unit :=
   Result.ret ()
 
 /- [array::take_array]: forward function -/
-def take_array (a : Array U32 (Usize.ofInt 2)) : Result Unit :=
+def take_array (a : Array U32 2#usize) : Result Unit :=
   Result.ret ()
 
 /- [array::take_array_borrow]: forward function -/
-def take_array_borrow (a : Array U32 (Usize.ofInt 2)) : Result Unit :=
+def take_array_borrow (a : Array U32 2#usize) : Result Unit :=
   Result.ret ()
 
 /- [array::take_slice]: forward function -/
@@ -203,148 +197,131 @@ def take_mut_slice (s : Slice U32) : Result (Slice U32) :=
 /- [array::take_all]: forward function -/
 def take_all : Result Unit :=
   do
-    let _ ←
-      take_array
-        (Array.make U32 (Usize.ofInt 2) [ (U32.ofInt 0), (U32.ofInt 0) ])
-    let _ ←
-      take_array_borrow
-        (Array.make U32 (Usize.ofInt 2) [ (U32.ofInt 0), (U32.ofInt 0) ])
+    let _ ← take_array (Array.make U32 2#usize [ 0#u32, 0#u32 ])
+    let _ ← take_array_borrow (Array.make U32 2#usize [ 0#u32, 0#u32 ])
     let s ←
-      Array.to_slice_shared U32 (Usize.ofInt 2)
-        (Array.make U32 (Usize.ofInt 2) [ (U32.ofInt 0), (U32.ofInt 0) ])
+      Array.to_slice U32 2#usize (Array.make U32 2#usize [ 0#u32, 0#u32 ])
     let _ ← take_slice s
     let s0 ←
-      Array.to_slice_mut U32 (Usize.ofInt 2)
-        (Array.make U32 (Usize.ofInt 2) [ (U32.ofInt 0), (U32.ofInt 0) ])
+      Array.to_slice U32 2#usize (Array.make U32 2#usize [ 0#u32, 0#u32 ])
     let s1 ← take_mut_slice s0
     let _ ←
-      Array.to_slice_mut_back U32 (Usize.ofInt 2)
-        (Array.make U32 (Usize.ofInt 2) [ (U32.ofInt 0), (U32.ofInt 0) ]) s1
+      Array.from_slice U32 2#usize (Array.make U32 2#usize [ 0#u32, 0#u32 ]) s1
     Result.ret ()
 
 /- [array::index_array]: forward function -/
-def index_array (x : Array U32 (Usize.ofInt 2)) : Result U32 :=
-  Array.index_shared U32 (Usize.ofInt 2) x (Usize.ofInt 0)
+def index_array (x : Array U32 2#usize) : Result U32 :=
+  Array.index_usize U32 2#usize x 0#usize
 
 /- [array::index_array_borrow]: forward function -/
-def index_array_borrow (x : Array U32 (Usize.ofInt 2)) : Result U32 :=
-  Array.index_shared U32 (Usize.ofInt 2) x (Usize.ofInt 0)
+def index_array_borrow (x : Array U32 2#usize) : Result U32 :=
+  Array.index_usize U32 2#usize x 0#usize
 
 /- [array::index_slice_u32_0]: forward function -/
 def index_slice_u32_0 (x : Slice U32) : Result U32 :=
-  Slice.index_shared U32 x (Usize.ofInt 0)
+  Slice.index_usize U32 x 0#usize
 
 /- [array::index_mut_slice_u32_0]: forward function -/
 def index_mut_slice_u32_0 (x : Slice U32) : Result U32 :=
-  Slice.index_shared U32 x (Usize.ofInt 0)
+  Slice.index_usize U32 x 0#usize
 
 /- [array::index_mut_slice_u32_0]: backward function 0 -/
 def index_mut_slice_u32_0_back (x : Slice U32) : Result (Slice U32) :=
   do
-    let _ ← Slice.index_shared U32 x (Usize.ofInt 0)
+    let _ ← Slice.index_usize U32 x 0#usize
     Result.ret x
 
 /- [array::index_all]: forward function -/
 def index_all : Result U32 :=
   do
-    let i ←
-      index_array
-        (Array.make U32 (Usize.ofInt 2) [ (U32.ofInt 0), (U32.ofInt 0) ])
-    let i0 ←
-      index_array
-        (Array.make U32 (Usize.ofInt 2) [ (U32.ofInt 0), (U32.ofInt 0) ])
+    let i ← index_array (Array.make U32 2#usize [ 0#u32, 0#u32 ])
+    let i0 ← index_array (Array.make U32 2#usize [ 0#u32, 0#u32 ])
     let i1 ← i + i0
-    let i2 ←
-      index_array_borrow
-        (Array.make U32 (Usize.ofInt 2) [ (U32.ofInt 0), (U32.ofInt 0) ])
+    let i2 ← index_array_borrow (Array.make U32 2#usize [ 0#u32, 0#u32 ])
     let i3 ← i1 + i2
     let s ←
-      Array.to_slice_shared U32 (Usize.ofInt 2)
-        (Array.make U32 (Usize.ofInt 2) [ (U32.ofInt 0), (U32.ofInt 0) ])
+      Array.to_slice U32 2#usize (Array.make U32 2#usize [ 0#u32, 0#u32 ])
     let i4 ← index_slice_u32_0 s
     let i5 ← i3 + i4
     let s0 ←
-      Array.to_slice_mut U32 (Usize.ofInt 2)
-        (Array.make U32 (Usize.ofInt 2) [ (U32.ofInt 0), (U32.ofInt 0) ])
+      Array.to_slice U32 2#usize (Array.make U32 2#usize [ 0#u32, 0#u32 ])
     let i6 ← index_mut_slice_u32_0 s0
     let i7 ← i5 + i6
     let s1 ← index_mut_slice_u32_0_back s0
     let _ ←
-      Array.to_slice_mut_back U32 (Usize.ofInt 2)
-        (Array.make U32 (Usize.ofInt 2) [ (U32.ofInt 0), (U32.ofInt 0) ]) s1
+      Array.from_slice U32 2#usize (Array.make U32 2#usize [ 0#u32, 0#u32 ]) s1
     Result.ret i7
 
 /- [array::update_array]: forward function -/
-def update_array (x : Array U32 (Usize.ofInt 2)) : Result Unit :=
+def update_array (x : Array U32 2#usize) : Result Unit :=
   do
-    let _ ←
-      Array.index_mut_back U32 (Usize.ofInt 2) x (Usize.ofInt 0) (U32.ofInt 1)
+    let _ ← Array.update_usize U32 2#usize x 0#usize 1#u32
     Result.ret ()
 
 /- [array::update_array_mut_borrow]: merged forward/backward function
    (there is a single backward function, and the forward function returns ()) -/
 def update_array_mut_borrow
-  (x : Array U32 (Usize.ofInt 2)) : Result (Array U32 (Usize.ofInt 2)) :=
-  Array.index_mut_back U32 (Usize.ofInt 2) x (Usize.ofInt 0) (U32.ofInt 1)
+  (x : Array U32 2#usize) : Result (Array U32 2#usize) :=
+  Array.update_usize U32 2#usize x 0#usize 1#u32
 
 /- [array::update_mut_slice]: merged forward/backward function
    (there is a single backward function, and the forward function returns ()) -/
 def update_mut_slice (x : Slice U32) : Result (Slice U32) :=
-  Slice.index_mut_back U32 x (Usize.ofInt 0) (U32.ofInt 1)
+  Slice.update_usize U32 x 0#usize 1#u32
 
 /- [array::update_all]: forward function -/
 def update_all : Result Unit :=
   do
-    let _ ←
-      update_array
-        (Array.make U32 (Usize.ofInt 2) [ (U32.ofInt 0), (U32.ofInt 0) ])
-    let x ←
-      update_array_mut_borrow
-        (Array.make U32 (Usize.ofInt 2) [ (U32.ofInt 0), (U32.ofInt 0) ])
-    let s ← Array.to_slice_mut U32 (Usize.ofInt 2) x
+    let _ ← update_array (Array.make U32 2#usize [ 0#u32, 0#u32 ])
+    let x ← update_array_mut_borrow (Array.make U32 2#usize [ 0#u32, 0#u32 ])
+    let s ← Array.to_slice U32 2#usize x
     let s0 ← update_mut_slice s
-    let _ ← Array.to_slice_mut_back U32 (Usize.ofInt 2) x s0
+    let _ ← Array.from_slice U32 2#usize x s0
     Result.ret ()
 
 /- [array::range_all]: forward function -/
 def range_all : Result Unit :=
   do
     let s ←
-      Array.subslice_mut U32 (Usize.ofInt 4)
-        (Array.make U32 (Usize.ofInt 4) [
-          (U32.ofInt 0), (U32.ofInt 0), (U32.ofInt 0), (U32.ofInt 0)
-          ]) (Range.mk (Usize.ofInt 1) (Usize.ofInt 3))
+      core.array.Array.index_mut U32 (core.ops.range.Range Usize) 4#usize
+        (core.slice.index.Slice.coreopsindexIndexMutInst U32
+        (core.ops.range.Range Usize)
+        (core.slice.index.Range.coresliceindexSliceIndexInst U32))
+        (Array.make U32 4#usize [ 0#u32, 0#u32, 0#u32, 0#u32 ])
+        { start := 1#usize, end_ := 3#usize }
     let s0 ← update_mut_slice s
     let _ ←
-      Array.subslice_mut_back U32 (Usize.ofInt 4)
-        (Array.make U32 (Usize.ofInt 4) [
-          (U32.ofInt 0), (U32.ofInt 0), (U32.ofInt 0), (U32.ofInt 0)
-          ]) (Range.mk (Usize.ofInt 1) (Usize.ofInt 3)) s0
+      core.array.Array.index_mut_back U32 (core.ops.range.Range Usize) 4#usize
+        (core.slice.index.Slice.coreopsindexIndexMutInst U32
+        (core.ops.range.Range Usize)
+        (core.slice.index.Range.coresliceindexSliceIndexInst U32))
+        (Array.make U32 4#usize [ 0#u32, 0#u32, 0#u32, 0#u32 ])
+        { start := 1#usize, end_ := 3#usize } s0
     Result.ret ()
 
 /- [array::deref_array_borrow]: forward function -/
-def deref_array_borrow (x : Array U32 (Usize.ofInt 2)) : Result U32 :=
-  Array.index_shared U32 (Usize.ofInt 2) x (Usize.ofInt 0)
+def deref_array_borrow (x : Array U32 2#usize) : Result U32 :=
+  Array.index_usize U32 2#usize x 0#usize
 
 /- [array::deref_array_mut_borrow]: forward function -/
-def deref_array_mut_borrow (x : Array U32 (Usize.ofInt 2)) : Result U32 :=
-  Array.index_shared U32 (Usize.ofInt 2) x (Usize.ofInt 0)
+def deref_array_mut_borrow (x : Array U32 2#usize) : Result U32 :=
+  Array.index_usize U32 2#usize x 0#usize
 
 /- [array::deref_array_mut_borrow]: backward function 0 -/
 def deref_array_mut_borrow_back
-  (x : Array U32 (Usize.ofInt 2)) : Result (Array U32 (Usize.ofInt 2)) :=
+  (x : Array U32 2#usize) : Result (Array U32 2#usize) :=
   do
-    let _ ← Array.index_shared U32 (Usize.ofInt 2) x (Usize.ofInt 0)
+    let _ ← Array.index_usize U32 2#usize x 0#usize
     Result.ret x
 
 /- [array::take_array_t]: forward function -/
-def take_array_t (a : Array T (Usize.ofInt 2)) : Result Unit :=
+def take_array_t (a : Array AB 2#usize) : Result Unit :=
   Result.ret ()
 
 /- [array::non_copyable_array]: forward function -/
 def non_copyable_array : Result Unit :=
   do
-    let _ ← take_array_t (Array.make T (Usize.ofInt 2) [ T.A, T.B ])
+    let _ ← take_array_t (Array.make AB 2#usize [ AB.A, AB.B ])
     Result.ret ()
 
 /- [array::sum]: loop 0: forward function -/
@@ -353,15 +330,15 @@ divergent def sum_loop (s : Slice U32) (sum0 : U32) (i : Usize) : Result U32 :=
   if i < i0
   then
     do
-      let i1 ← Slice.index_shared U32 s i
+      let i1 ← Slice.index_usize U32 s i
       let sum1 ← sum0 + i1
-      let i2 ← i + (Usize.ofInt 1)
+      let i2 ← i + 1#usize
       sum_loop s sum1 i2
   else Result.ret sum0
 
 /- [array::sum]: forward function -/
 def sum (s : Slice U32) : Result U32 :=
-  sum_loop s (U32.ofInt 0) (Usize.ofInt 0)
+  sum_loop s 0#u32 0#usize
 
 /- [array::sum2]: loop 0: forward function -/
 divergent def sum2_loop
@@ -370,11 +347,11 @@ divergent def sum2_loop
   if i < i0
   then
     do
-      let i1 ← Slice.index_shared U32 s i
-      let i2 ← Slice.index_shared U32 s2 i
+      let i1 ← Slice.index_usize U32 s i
+      let i2 ← Slice.index_usize U32 s2 i
       let i3 ← i1 + i2
       let sum1 ← sum0 + i3
-      let i4 ← i + (Usize.ofInt 1)
+      let i4 ← i + 1#usize
       sum2_loop s s2 sum1 i4
   else Result.ret sum0
 
@@ -384,27 +361,24 @@ def sum2 (s : Slice U32) (s2 : Slice U32) : Result U32 :=
   let i0 := Slice.len U32 s2
   if not (i = i0)
   then Result.fail Error.panic
-  else sum2_loop s s2 (U32.ofInt 0) (Usize.ofInt 0)
+  else sum2_loop s s2 0#u32 0#usize
 
 /- [array::f0]: forward function -/
 def f0 : Result Unit :=
   do
     let s ←
-      Array.to_slice_mut U32 (Usize.ofInt 2)
-        (Array.make U32 (Usize.ofInt 2) [ (U32.ofInt 1), (U32.ofInt 2) ])
-    let s0 ← Slice.index_mut_back U32 s (Usize.ofInt 0) (U32.ofInt 1)
+      Array.to_slice U32 2#usize (Array.make U32 2#usize [ 1#u32, 2#u32 ])
+    let s0 ← Slice.update_usize U32 s 0#usize 1#u32
     let _ ←
-      Array.to_slice_mut_back U32 (Usize.ofInt 2)
-        (Array.make U32 (Usize.ofInt 2) [ (U32.ofInt 1), (U32.ofInt 2) ]) s0
+      Array.from_slice U32 2#usize (Array.make U32 2#usize [ 1#u32, 2#u32 ]) s0
     Result.ret ()
 
 /- [array::f1]: forward function -/
 def f1 : Result Unit :=
   do
     let _ ←
-      Array.index_mut_back U32 (Usize.ofInt 2)
-        (Array.make U32 (Usize.ofInt 2) [ (U32.ofInt 1), (U32.ofInt 2) ])
-        (Usize.ofInt 0) (U32.ofInt 1)
+      Array.update_usize U32 2#usize (Array.make U32 2#usize [ 1#u32, 2#u32 ])
+        0#usize 1#u32
     Result.ret ()
 
 /- [array::f2]: forward function -/
@@ -412,54 +386,46 @@ def f2 (i : U32) : Result Unit :=
   Result.ret ()
 
 /- [array::f4]: forward function -/
-def f4
-  (x : Array U32 (Usize.ofInt 32)) (y : Usize) (z : Usize) :
-  Result (Slice U32)
-  :=
-  Array.subslice_shared U32 (Usize.ofInt 32) x (Range.mk y z)
+def f4 (x : Array U32 32#usize) (y : Usize) (z : Usize) : Result (Slice U32) :=
+  core.array.Array.index U32 (core.ops.range.Range Usize) 32#usize
+    (core.slice.index.Slice.coreopsindexIndexInst U32 (core.ops.range.Range
+    Usize) (core.slice.index.Range.coresliceindexSliceIndexInst U32)) x
+    { start := y, end_ := z }
 
 /- [array::f3]: forward function -/
 def f3 : Result U32 :=
   do
     let i ←
-      Array.index_shared U32 (Usize.ofInt 2)
-        (Array.make U32 (Usize.ofInt 2) [ (U32.ofInt 1), (U32.ofInt 2) ])
-        (Usize.ofInt 0)
+      Array.index_usize U32 2#usize (Array.make U32 2#usize [ 1#u32, 2#u32 ])
+        0#usize
     let _ ← f2 i
+    let b := Array.repeat U32 32#usize 0#u32
     let s ←
-      Array.to_slice_shared U32 (Usize.ofInt 2)
-        (Array.make U32 (Usize.ofInt 2) [ (U32.ofInt 1), (U32.ofInt 2) ])
-    let s0 ←
-      f4
-        (Array.make U32 (Usize.ofInt 32) [
-          (U32.ofInt 0), (U32.ofInt 0), (U32.ofInt 0), (U32.ofInt 0),
-          (U32.ofInt 0), (U32.ofInt 0), (U32.ofInt 0), (U32.ofInt 0),
-          (U32.ofInt 0), (U32.ofInt 0), (U32.ofInt 0), (U32.ofInt 0),
-          (U32.ofInt 0), (U32.ofInt 0), (U32.ofInt 0), (U32.ofInt 0),
-          (U32.ofInt 0), (U32.ofInt 0), (U32.ofInt 0), (U32.ofInt 0),
-          (U32.ofInt 0), (U32.ofInt 0), (U32.ofInt 0), (U32.ofInt 0),
-          (U32.ofInt 0), (U32.ofInt 0), (U32.ofInt 0), (U32.ofInt 0),
-          (U32.ofInt 0), (U32.ofInt 0), (U32.ofInt 0), (U32.ofInt 0)
-          ]) (Usize.ofInt 16) (Usize.ofInt 18)
+      Array.to_slice U32 2#usize (Array.make U32 2#usize [ 1#u32, 2#u32 ])
+    let s0 ← f4 b 16#usize 18#usize
     sum2 s s0
 
+/- [array::SZ] -/
+def sz_body : Result Usize := Result.ret 32#usize
+def sz_c : Usize := eval_global sz_body (by simp)
+
+/- [array::f5]: forward function -/
+def f5 (x : Array U32 32#usize) : Result U32 :=
+  Array.index_usize U32 32#usize x 0#usize
+
 /- [array::ite]: forward function -/
 def ite : Result Unit :=
   do
     let s ←
-      Array.to_slice_mut U32 (Usize.ofInt 2)
-        (Array.make U32 (Usize.ofInt 2) [ (U32.ofInt 0), (U32.ofInt 0) ])
+      Array.to_slice U32 2#usize (Array.make U32 2#usize [ 0#u32, 0#u32 ])
     let s0 ←
-      Array.to_slice_mut U32 (Usize.ofInt 2)
-        (Array.make U32 (Usize.ofInt 2) [ (U32.ofInt 0), (U32.ofInt 0) ])
+      Array.to_slice U32 2#usize (Array.make U32 2#usize [ 0#u32, 0#u32 ])
     let s1 ← index_mut_slice_u32_0_back s0
     let _ ←
-      Array.to_slice_mut_back U32 (Usize.ofInt 2)
-        (Array.make U32 (Usize.ofInt 2) [ (U32.ofInt 0), (U32.ofInt 0) ]) s1
+      Array.from_slice U32 2#usize (Array.make U32 2#usize [ 0#u32, 0#u32 ]) s1
     let s2 ← index_mut_slice_u32_0_back s
     let _ ←
-      Array.to_slice_mut_back U32 (Usize.ofInt 2)
-        (Array.make U32 (Usize.ofInt 2) [ (U32.ofInt 0), (U32.ofInt 0) ]) s2
+      Array.from_slice U32 2#usize (Array.make U32 2#usize [ 0#u32, 0#u32 ]) s2
     Result.ret ()
 
 end array
diff --git a/tests/lean/Array/Types.lean b/tests/lean/Array/Types.lean
index 72241276..60fa81ab 100644
--- a/tests/lean/Array/Types.lean
+++ b/tests/lean/Array/Types.lean
@@ -5,9 +5,9 @@ open Primitives
 
 namespace array
 
-/- [array::T] -/
-inductive T :=
-| A : T
-| B : T
+/- [array::AB] -/
+inductive AB :=
+| A : AB
+| B : AB
 
 end array
diff --git a/tests/lean/BetreeMain/Funs.lean b/tests/lean/BetreeMain/Funs.lean
index 07ef08dc..0901d449 100644
--- a/tests/lean/BetreeMain/Funs.lean
+++ b/tests/lean/BetreeMain/Funs.lean
@@ -40,77 +40,71 @@ def betree.store_leaf_node
 /- [betree_main::betree::fresh_node_id]: forward function -/
 def betree.fresh_node_id (counter : U64) : Result U64 :=
   do
-    let _ ← counter + (U64.ofInt 1)
+    let _ ← counter + 1#u64
     Result.ret counter
 
 /- [betree_main::betree::fresh_node_id]: backward function 0 -/
 def betree.fresh_node_id_back (counter : U64) : Result U64 :=
-  counter + (U64.ofInt 1)
+  counter + 1#u64
 
 /- [betree_main::betree::NodeIdCounter::{0}::new]: forward function -/
 def betree.NodeIdCounter.new : Result betree.NodeIdCounter :=
-  Result.ret { next_node_id := (U64.ofInt 0) }
+  Result.ret { next_node_id := 0#u64 }
 
 /- [betree_main::betree::NodeIdCounter::{0}::fresh_id]: forward function -/
 def betree.NodeIdCounter.fresh_id (self : betree.NodeIdCounter) : Result U64 :=
   do
-    let _ ← self.next_node_id + (U64.ofInt 1)
+    let _ ← self.next_node_id + 1#u64
     Result.ret self.next_node_id
 
 /- [betree_main::betree::NodeIdCounter::{0}::fresh_id]: backward function 0 -/
 def betree.NodeIdCounter.fresh_id_back
   (self : betree.NodeIdCounter) : Result betree.NodeIdCounter :=
   do
-    let i ← self.next_node_id + (U64.ofInt 1)
+    let i ← self.next_node_id + 1#u64
     Result.ret { next_node_id := i }
 
-/- [core::num::u64::{9}::MAX] -/
-def core_num_u64_max_body : Result U64 :=
-  Result.ret (U64.ofInt 18446744073709551615)
-def core_num_u64_max_c : U64 := eval_global core_num_u64_max_body (by simp)
-
 /- [betree_main::betree::upsert_update]: forward function -/
 def betree.upsert_update
   (prev : Option U64) (st : betree.UpsertFunState) : Result U64 :=
   match prev with
-  | Option.none =>
+  | none =>
     match st with
     | betree.UpsertFunState.Add v => Result.ret v
-    | betree.UpsertFunState.Sub i => Result.ret (U64.ofInt 0)
-  | Option.some prev0 =>
+    | betree.UpsertFunState.Sub i => Result.ret 0#u64
+  | some prev0 =>
     match st with
     | betree.UpsertFunState.Add v =>
       do
-        let margin ← core_num_u64_max_c - prev0
+        let margin ← core_u64_max - prev0
         if margin >= v
         then prev0 + v
-        else Result.ret core_num_u64_max_c
+        else Result.ret core_u64_max
     | betree.UpsertFunState.Sub v =>
       if prev0 >= v
       then prev0 - v
-      else Result.ret (U64.ofInt 0)
+      else Result.ret 0#u64
 
 /- [betree_main::betree::List::{1}::len]: forward function -/
 divergent def betree.List.len (T : Type) (self : betree.List T) : Result U64 :=
   match self with
-  | betree.List.Cons t tl =>
-    do
-      let i ← betree.List.len T tl
-      (U64.ofInt 1) + i
-  | betree.List.Nil => Result.ret (U64.ofInt 0)
+  | betree.List.Cons t tl => do
+                               let i ← betree.List.len T tl
+                               1#u64 + i
+  | betree.List.Nil => Result.ret 0#u64
 
 /- [betree_main::betree::List::{1}::split_at]: forward function -/
 divergent def betree.List.split_at
   (T : Type) (self : betree.List T) (n : U64) :
   Result ((betree.List T) × (betree.List T))
   :=
-  if n = (U64.ofInt 0)
+  if n = 0#u64
   then Result.ret (betree.List.Nil, self)
   else
     match self with
     | betree.List.Cons hd tl =>
       do
-        let i ← n - (U64.ofInt 1)
+        let i ← n - 1#u64
         let p ← betree.List.split_at T tl i
         let (ls0, ls1) := p
         let l := ls0
@@ -121,13 +115,13 @@ divergent def betree.List.split_at
    (there is a single backward function, and the forward function returns ()) -/
 def betree.List.push_front
   (T : Type) (self : betree.List T) (x : T) : Result (betree.List T) :=
-  let tl := mem.replace (betree.List T) self betree.List.Nil
+  let tl := core.mem.replace (betree.List T) self betree.List.Nil
   let l := tl
   Result.ret (betree.List.Cons x l)
 
 /- [betree_main::betree::List::{1}::pop_front]: forward function -/
 def betree.List.pop_front (T : Type) (self : betree.List T) : Result T :=
-  let ls := mem.replace (betree.List T) self betree.List.Nil
+  let ls := core.mem.replace (betree.List T) self betree.List.Nil
   match ls with
   | betree.List.Cons x tl => Result.ret x
   | betree.List.Nil => Result.fail Error.panic
@@ -135,7 +129,7 @@ def betree.List.pop_front (T : Type) (self : betree.List T) : Result T :=
 /- [betree_main::betree::List::{1}::pop_front]: backward function 0 -/
 def betree.List.pop_front_back
   (T : Type) (self : betree.List T) : Result (betree.List T) :=
-  let ls := mem.replace (betree.List T) self betree.List.Nil
+  let ls := core.mem.replace (betree.List T) self betree.List.Nil
   match ls with
   | betree.List.Cons x tl => Result.ret tl
   | betree.List.Nil => Result.fail Error.panic
@@ -261,7 +255,7 @@ divergent def betree.Node.apply_upserts
             let v ← betree.upsert_update prev s
             let msgs0 ←
               betree.List.pop_front_back (U64 × betree.Message) msgs
-            betree.Node.apply_upserts msgs0 (Option.some v) key st
+            betree.Node.apply_upserts msgs0 (some v) key st
     else
       do
         let (st0, v) ← core.option.Option.unwrap U64 prev st
@@ -291,7 +285,7 @@ divergent def betree.Node.apply_upserts_back
             let v ← betree.upsert_update prev s
             let msgs0 ←
               betree.List.pop_front_back (U64 × betree.Message) msgs
-            betree.Node.apply_upserts_back msgs0 (Option.some v) key st
+            betree.Node.apply_upserts_back msgs0 (some v) key st
     else
       do
         let (_, v) ← core.option.Option.unwrap U64 prev st
@@ -305,12 +299,12 @@ divergent def betree.Node.lookup_in_bindings
   | betree.List.Cons hd tl =>
     let (i, i0) := hd
     if i = key
-    then Result.ret (Option.some i0)
+    then Result.ret (some i0)
     else
       if i > key
-      then Result.ret Option.none
+      then Result.ret none
       else betree.Node.lookup_in_bindings key tl
-  | betree.List.Nil => Result.ret Option.none
+  | betree.List.Nil => Result.ret none
 
 /- [betree_main::betree::Internal::{4}::lookup_in_children]: forward function -/
 mutual divergent def betree.Internal.lookup_in_children
@@ -353,13 +347,13 @@ divergent def betree.Node.lookup
         if k != key
         then
           do
-            let (st1, opt) ←
+            let (st1, o) ←
               betree.Internal.lookup_in_children (betree.Internal.mk i i0 n n0)
                 key st0
             let _ ←
               betree.Node.lookup_first_message_for_key_back key msgs
                 (betree.List.Cons (k, msg) l)
-            Result.ret (st1, opt)
+            Result.ret (st1, o)
         else
           match msg with
           | betree.Message.Insert v =>
@@ -367,13 +361,13 @@ divergent def betree.Node.lookup
               let _ ←
                 betree.Node.lookup_first_message_for_key_back key msgs
                   (betree.List.Cons (k, betree.Message.Insert v) l)
-              Result.ret (st0, Option.some v)
+              Result.ret (st0, some v)
           | betree.Message.Delete =>
             do
               let _ ←
                 betree.Node.lookup_first_message_for_key_back key msgs
                   (betree.List.Cons (k, betree.Message.Delete) l)
-              Result.ret (st0, Option.none)
+              Result.ret (st0, none)
           | betree.Message.Upsert ufs =>
             do
               let (st1, v) ←
@@ -392,21 +386,21 @@ divergent def betree.Node.lookup
               let msgs0 ←
                 betree.Node.lookup_first_message_for_key_back key msgs pending0
               let (st3, _) ← betree.store_internal_node i1 msgs0 st2
-              Result.ret (st3, Option.some v0)
+              Result.ret (st3, some v0)
       | betree.List.Nil =>
         do
-          let (st1, opt) ←
+          let (st1, o) ←
             betree.Internal.lookup_in_children (betree.Internal.mk i i0 n n0)
               key st0
           let _ ←
             betree.Node.lookup_first_message_for_key_back key msgs
               betree.List.Nil
-          Result.ret (st1, opt)
+          Result.ret (st1, o)
   | betree.Node.Leaf node =>
     do
       let (st0, bindings) ← betree.load_leaf_node node.id st
-      let opt ← betree.Node.lookup_in_bindings key bindings
-      Result.ret (st0, opt)
+      let o ← betree.Node.lookup_in_bindings key bindings
+      Result.ret (st0, o)
 
 /- [betree_main::betree::Node::{5}::lookup]: backward function 0 -/
 divergent def betree.Node.lookup_back
@@ -565,7 +559,7 @@ def betree.Node.apply_to_internal
           match m with
           | betree.Message.Insert prev =>
             do
-              let v ← betree.upsert_update (Option.some prev) s
+              let v ← betree.upsert_update (some prev) s
               let msgs1 ←
                 betree.List.pop_front_back (U64 × betree.Message) msgs0
               let msgs2 ←
@@ -574,7 +568,7 @@ def betree.Node.apply_to_internal
               betree.Node.lookup_first_message_for_key_back key msgs msgs2
           | betree.Message.Delete =>
             do
-              let v ← betree.upsert_update Option.none s
+              let v ← betree.upsert_update none s
               let msgs1 ←
                 betree.List.pop_front_back (U64 × betree.Message) msgs0
               let msgs2 ←
@@ -670,7 +664,7 @@ def betree.Node.apply_to_leaf
         | betree.Message.Upsert s =>
           do
             let (_, i) := hd
-            let v ← betree.upsert_update (Option.some i) s
+            let v ← betree.upsert_update (some i) s
             let bindings1 ← betree.List.pop_front_back (U64 × U64) bindings0
             let bindings2 ←
               betree.List.push_front (U64 × U64) bindings1 (key, v)
@@ -686,7 +680,7 @@ def betree.Node.apply_to_leaf
         betree.Node.lookup_mut_in_bindings_back key bindings bindings0
       | betree.Message.Upsert s =>
         do
-          let v ← betree.upsert_update Option.none s
+          let v ← betree.upsert_update none s
           let bindings1 ←
             betree.List.push_front (U64 × U64) bindings0 (key, v)
           betree.Node.lookup_mut_in_bindings_back key bindings bindings1
@@ -813,7 +807,7 @@ divergent def betree.Node.apply_messages
       let (st0, content) ← betree.load_leaf_node node.id st
       let content0 ← betree.Node.apply_messages_to_leaf content msgs
       let len ← betree.List.len (U64 × U64) content0
-      let i ← (U64.ofInt 2) * params.split_size
+      let i ← 2#u64 * params.split_size
       if len >= i
       then
         do
@@ -863,7 +857,7 @@ divergent def betree.Node.apply_messages_back
       let (st0, content) ← betree.load_leaf_node node.id st
       let content0 ← betree.Node.apply_messages_to_leaf content msgs
       let len ← betree.List.len (U64 × U64) content0
-      let i ← (U64.ofInt 2) * params.split_size
+      let i ← 2#u64 * params.split_size
       if len >= i
       then
         do
@@ -923,7 +917,7 @@ def betree.BeTree.new
         params :=
           { min_flush_size := min_flush_size, split_size := split_size },
         node_id_cnt := node_id_cnt0,
-        root := (betree.Node.Leaf { id := id, size := (U64.ofInt 0) })
+        root := (betree.Node.Leaf { id := id, size := 0#u64 })
       })
 
 /- [betree_main::betree::BeTree::{6}::apply]: forward function -/
diff --git a/tests/lean/Constants.lean b/tests/lean/Constants.lean
index 51b415d6..bd3a07b7 100644
--- a/tests/lean/Constants.lean
+++ b/tests/lean/Constants.lean
@@ -6,27 +6,23 @@ open Primitives
 namespace constants
 
 /- [constants::X0] -/
-def x0_body : Result U32 := Result.ret (U32.ofInt 0)
+def x0_body : Result U32 := Result.ret 0#u32
 def x0_c : U32 := eval_global x0_body (by simp)
 
-/- [core::num::u32::{8}::MAX] -/
-def core_num_u32_max_body : Result U32 := Result.ret (U32.ofInt 4294967295)
-def core_num_u32_max_c : U32 := eval_global core_num_u32_max_body (by simp)
-
 /- [constants::X1] -/
-def x1_body : Result U32 := Result.ret core_num_u32_max_c
+def x1_body : Result U32 := Result.ret core_u32_max
 def x1_c : U32 := eval_global x1_body (by simp)
 
 /- [constants::X2] -/
-def x2_body : Result U32 := Result.ret (U32.ofInt 3)
+def x2_body : Result U32 := Result.ret 3#u32
 def x2_c : U32 := eval_global x2_body (by simp)
 
 /- [constants::incr]: forward function -/
 def incr (n : U32) : Result U32 :=
-  n + (U32.ofInt 1)
+  n + 1#u32
 
 /- [constants::X3] -/
-def x3_body : Result U32 := incr (U32.ofInt 32)
+def x3_body : Result U32 := incr 32#u32
 def x3_c : U32 := eval_global x3_body (by simp)
 
 /- [constants::mk_pair0]: forward function -/
@@ -43,44 +39,43 @@ def mk_pair1 (x : U32) (y : U32) : Result (Pair U32 U32) :=
   Result.ret { x := x, y := y }
 
 /- [constants::P0] -/
-def p0_body : Result (U32 × U32) := mk_pair0 (U32.ofInt 0) (U32.ofInt 1)
+def p0_body : Result (U32 × U32) := mk_pair0 0#u32 1#u32
 def p0_c : (U32 × U32) := eval_global p0_body (by simp)
 
 /- [constants::P1] -/
-def p1_body : Result (Pair U32 U32) := mk_pair1 (U32.ofInt 0) (U32.ofInt 1)
+def p1_body : Result (Pair U32 U32) := mk_pair1 0#u32 1#u32
 def p1_c : Pair U32 U32 := eval_global p1_body (by simp)
 
 /- [constants::P2] -/
-def p2_body : Result (U32 × U32) := Result.ret ((U32.ofInt 0), (U32.ofInt 1))
+def p2_body : Result (U32 × U32) := Result.ret (0#u32, 1#u32)
 def p2_c : (U32 × U32) := eval_global p2_body (by simp)
 
 /- [constants::P3] -/
-def p3_body : Result (Pair U32 U32) :=
-  Result.ret { x := (U32.ofInt 0), y := (U32.ofInt 1) }
+def p3_body : Result (Pair U32 U32) := Result.ret { x := 0#u32, y := 1#u32 }
 def p3_c : Pair U32 U32 := eval_global p3_body (by simp)
 
 /- [constants::Wrap] -/
 structure Wrap (T : Type) where
-  val : T
+  value : T
 
 /- [constants::Wrap::{0}::new]: forward function -/
-def Wrap.new (T : Type) (val : T) : Result (Wrap T) :=
-  Result.ret { val := val }
+def Wrap.new (T : Type) (value : T) : Result (Wrap T) :=
+  Result.ret { value := value }
 
 /- [constants::Y] -/
-def y_body : Result (Wrap I32) := Wrap.new I32 (I32.ofInt 2)
+def y_body : Result (Wrap I32) := Wrap.new I32 2#i32
 def y_c : Wrap I32 := eval_global y_body (by simp)
 
 /- [constants::unwrap_y]: forward function -/
 def unwrap_y : Result I32 :=
-  Result.ret y_c.val
+  Result.ret y_c.value
 
 /- [constants::YVAL] -/
 def yval_body : Result I32 := unwrap_y
 def yval_c : I32 := eval_global yval_body (by simp)
 
 /- [constants::get_z1::Z1] -/
-def get_z1_z1_body : Result I32 := Result.ret (I32.ofInt 3)
+def get_z1_z1_body : Result I32 := Result.ret 3#i32
 def get_z1_z1_c : I32 := eval_global get_z1_z1_body (by simp)
 
 /- [constants::get_z1]: forward function -/
@@ -92,7 +87,7 @@ def add (a : I32) (b : I32) : Result I32 :=
   a + b
 
 /- [constants::Q1] -/
-def q1_body : Result I32 := Result.ret (I32.ofInt 5)
+def q1_body : Result I32 := Result.ret 5#i32
 def q1_c : I32 := eval_global q1_body (by simp)
 
 /- [constants::Q2] -/
@@ -100,7 +95,7 @@ def q2_body : Result I32 := Result.ret q1_c
 def q2_c : I32 := eval_global q2_body (by simp)
 
 /- [constants::Q3] -/
-def q3_body : Result I32 := add q2_c (I32.ofInt 3)
+def q3_body : Result I32 := add q2_c 3#i32
 def q3_c : I32 := eval_global q3_body (by simp)
 
 /- [constants::get_z2]: forward function -/
@@ -111,7 +106,7 @@ def get_z2 : Result I32 :=
     add q1_c i0
 
 /- [constants::S1] -/
-def s1_body : Result U32 := Result.ret (U32.ofInt 6)
+def s1_body : Result U32 := Result.ret 6#u32
 def s1_c : U32 := eval_global s1_body (by simp)
 
 /- [constants::S2] -/
@@ -123,7 +118,7 @@ def s3_body : Result (Pair U32 U32) := Result.ret p3_c
 def s3_c : Pair U32 U32 := eval_global s3_body (by simp)
 
 /- [constants::S4] -/
-def s4_body : Result (Pair U32 U32) := mk_pair1 (U32.ofInt 7) (U32.ofInt 8)
+def s4_body : Result (Pair U32 U32) := mk_pair1 7#u32 8#u32
 def s4_c : Pair U32 U32 := eval_global s4_body (by simp)
 
 end constants
diff --git a/tests/lean/External/Funs.lean b/tests/lean/External/Funs.lean
index 055d7860..55fb07be 100644
--- a/tests/lean/External/Funs.lean
+++ b/tests/lean/External/Funs.lean
@@ -30,14 +30,14 @@ def swap_back
 def test_new_non_zero_u32
   (x : U32) (st : State) : Result (State × core.num.nonzero.NonZeroU32) :=
   do
-    let (st0, opt) ← core.num.nonzero.NonZeroU32.new x st
-    core.option.Option.unwrap core.num.nonzero.NonZeroU32 opt st0
+    let (st0, o) ← core.num.nonzero.NonZeroU32.new x st
+    core.option.Option.unwrap core.num.nonzero.NonZeroU32 o st0
 
 /- [external::test_vec]: forward function -/
 def test_vec : Result Unit :=
   do
-    let v := Vec.new U32
-    let _ ← Vec.push U32 v (U32.ofInt 0)
+    let v := alloc.vec.Vec.new U32
+    let _ ← alloc.vec.Vec.push U32 v 0#u32
     Result.ret ()
 
 /- Unit test for [external::test_vec] -/
@@ -75,14 +75,14 @@ def test_custom_swap_back
   (x : U32) (y : U32) (st : State) (st0 : State) :
   Result (State × (U32 × U32))
   :=
-  custom_swap_back U32 x y st (U32.ofInt 1) st0
+  custom_swap_back U32 x y st 1#u32 st0
 
 /- [external::test_swap_non_zero]: forward function -/
 def test_swap_non_zero (x : U32) (st : State) : Result (State × U32) :=
   do
-    let (st0, _) ← swap U32 x (U32.ofInt 0) st
-    let (st1, (x0, _)) ← swap_back U32 x (U32.ofInt 0) st st0
-    if x0 = (U32.ofInt 0)
+    let (st0, _) ← swap U32 x 0#u32 st
+    let (st1, (x0, _)) ← swap_back U32 x 0#u32 st st0
+    if x0 = 0#u32
     then Result.fail Error.panic
     else Result.ret (st1, x0)
 
diff --git a/tests/lean/Hashmap/Funs.lean b/tests/lean/Hashmap/Funs.lean
index 30b30e0b..8464c432 100644
--- a/tests/lean/Hashmap/Funs.lean
+++ b/tests/lean/Hashmap/Funs.lean
@@ -12,18 +12,22 @@ def hash_key (k : Usize) : Result Usize :=
 
 /- [hashmap::HashMap::{0}::allocate_slots]: loop 0: forward function -/
 divergent def HashMap.allocate_slots_loop
-  (T : Type) (slots : Vec (List T)) (n : Usize) : Result (Vec (List T)) :=
-  if n > (Usize.ofInt 0)
+  (T : Type) (slots : alloc.vec.Vec (List T)) (n : Usize) :
+  Result (alloc.vec.Vec (List T))
+  :=
+  if n > 0#usize
   then
     do
-      let slots0 ← Vec.push (List T) slots List.Nil
-      let n0 ← n - (Usize.ofInt 1)
+      let slots0 ← alloc.vec.Vec.push (List T) slots List.Nil
+      let n0 ← n - 1#usize
       HashMap.allocate_slots_loop T slots0 n0
   else Result.ret slots
 
 /- [hashmap::HashMap::{0}::allocate_slots]: forward function -/
 def HashMap.allocate_slots
-  (T : Type) (slots : Vec (List T)) (n : Usize) : Result (Vec (List T)) :=
+  (T : Type) (slots : alloc.vec.Vec (List T)) (n : Usize) :
+  Result (alloc.vec.Vec (List T))
+  :=
   HashMap.allocate_slots_loop T slots n
 
 /- [hashmap::HashMap::{0}::new_with_capacity]: forward function -/
@@ -33,13 +37,13 @@ def HashMap.new_with_capacity
   Result (HashMap T)
   :=
   do
-    let v := Vec.new (List T)
+    let v := alloc.vec.Vec.new (List T)
     let slots ← HashMap.allocate_slots T v capacity
     let i ← capacity * max_load_dividend
     let i0 ← i / max_load_divisor
     Result.ret
       {
-        num_entries := (Usize.ofInt 0),
+        num_entries := 0#usize,
         max_load_factor := (max_load_dividend, max_load_divisor),
         max_load := i0,
         slots := slots
@@ -47,18 +51,23 @@ def HashMap.new_with_capacity
 
 /- [hashmap::HashMap::{0}::new]: forward function -/
 def HashMap.new (T : Type) : Result (HashMap T) :=
-  HashMap.new_with_capacity T (Usize.ofInt 32) (Usize.ofInt 4) (Usize.ofInt 5)
+  HashMap.new_with_capacity T 32#usize 4#usize 5#usize
 
 /- [hashmap::HashMap::{0}::clear]: loop 0: merged forward/backward function
    (there is a single backward function, and the forward function returns ()) -/
 divergent def HashMap.clear_loop
-  (T : Type) (slots : Vec (List T)) (i : Usize) : Result (Vec (List T)) :=
-  let i0 := Vec.len (List T) slots
+  (T : Type) (slots : alloc.vec.Vec (List T)) (i : Usize) :
+  Result (alloc.vec.Vec (List T))
+  :=
+  let i0 := alloc.vec.Vec.len (List T) slots
   if i < i0
   then
     do
-      let i1 ← i + (Usize.ofInt 1)
-      let slots0 ← Vec.index_mut_back (List T) slots i List.Nil
+      let i1 ← i + 1#usize
+      let slots0 ←
+        alloc.vec.Vec.index_mut_back (List T) Usize
+          (core.slice.index.usize.coresliceindexSliceIndexInst (List T)) slots
+          i List.Nil
       HashMap.clear_loop T slots0 i1
   else Result.ret slots
 
@@ -66,8 +75,8 @@ divergent def HashMap.clear_loop
    (there is a single backward function, and the forward function returns ()) -/
 def HashMap.clear (T : Type) (self : HashMap T) : Result (HashMap T) :=
   do
-    let v ← HashMap.clear_loop T self.slots (Usize.ofInt 0)
-    Result.ret { self with num_entries := (Usize.ofInt 0), slots := v }
+    let v ← HashMap.clear_loop T self.slots 0#usize
+    Result.ret { self with num_entries := 0#usize, slots := v }
 
 /- [hashmap::HashMap::{0}::len]: forward function -/
 def HashMap.len (T : Type) (self : HashMap T) : Result Usize :=
@@ -115,27 +124,32 @@ def HashMap.insert_no_resize
   :=
   do
     let hash ← hash_key key
-    let i := Vec.len (List T) self.slots
+    let i := alloc.vec.Vec.len (List T) self.slots
     let hash_mod ← hash % i
-    let l ← Vec.index_mut (List T) self.slots hash_mod
+    let l ←
+      alloc.vec.Vec.index_mut (List T) Usize
+        (core.slice.index.usize.coresliceindexSliceIndexInst (List T))
+        self.slots hash_mod
     let inserted ← HashMap.insert_in_list T key value l
     if inserted
     then
       do
-        let i0 ← self.num_entries + (Usize.ofInt 1)
+        let i0 ← self.num_entries + 1#usize
         let l0 ← HashMap.insert_in_list_back T key value l
-        let v ← Vec.index_mut_back (List T) self.slots hash_mod l0
+        let v ←
+          alloc.vec.Vec.index_mut_back (List T) Usize
+            (core.slice.index.usize.coresliceindexSliceIndexInst (List T))
+            self.slots hash_mod l0
         Result.ret { self with num_entries := i0, slots := v }
     else
       do
         let l0 ← HashMap.insert_in_list_back T key value l
-        let v ← Vec.index_mut_back (List T) self.slots hash_mod l0
+        let v ←
+          alloc.vec.Vec.index_mut_back (List T) Usize
+            (core.slice.index.usize.coresliceindexSliceIndexInst (List T))
+            self.slots hash_mod l0
         Result.ret { self with slots := v }
 
-/- [core::num::u32::{8}::MAX] -/
-def core_num_u32_max_body : Result U32 := Result.ret (U32.ofInt 4294967295)
-def core_num_u32_max_c : U32 := eval_global core_num_u32_max_body (by simp)
-
 /- [hashmap::HashMap::{0}::move_elements_from_list]: loop 0: merged forward/backward function
    (there is a single backward function, and the forward function returns ()) -/
 divergent def HashMap.move_elements_from_list_loop
@@ -156,27 +170,35 @@ def HashMap.move_elements_from_list
 /- [hashmap::HashMap::{0}::move_elements]: loop 0: merged forward/backward function
    (there is a single backward function, and the forward function returns ()) -/
 divergent def HashMap.move_elements_loop
-  (T : Type) (ntable : HashMap T) (slots : Vec (List T)) (i : Usize) :
-  Result ((HashMap T) × (Vec (List T)))
+  (T : Type) (ntable : HashMap T) (slots : alloc.vec.Vec (List T)) (i : Usize)
+  :
+  Result ((HashMap T) × (alloc.vec.Vec (List T)))
   :=
-  let i0 := Vec.len (List T) slots
+  let i0 := alloc.vec.Vec.len (List T) slots
   if i < i0
   then
     do
-      let l ← Vec.index_mut (List T) slots i
-      let ls := mem.replace (List T) l List.Nil
+      let l ←
+        alloc.vec.Vec.index_mut (List T) Usize
+          (core.slice.index.usize.coresliceindexSliceIndexInst (List T)) slots
+          i
+      let ls := core.mem.replace (List T) l List.Nil
       let ntable0 ← HashMap.move_elements_from_list T ntable ls
-      let i1 ← i + (Usize.ofInt 1)
-      let l0 := mem.replace_back (List T) l List.Nil
-      let slots0 ← Vec.index_mut_back (List T) slots i l0
+      let i1 ← i + 1#usize
+      let l0 := core.mem.replace_back (List T) l List.Nil
+      let slots0 ←
+        alloc.vec.Vec.index_mut_back (List T) Usize
+          (core.slice.index.usize.coresliceindexSliceIndexInst (List T)) slots
+          i l0
       HashMap.move_elements_loop T ntable0 slots0 i1
   else Result.ret (ntable, slots)
 
 /- [hashmap::HashMap::{0}::move_elements]: merged forward/backward function
    (there is a single backward function, and the forward function returns ()) -/
 def HashMap.move_elements
-  (T : Type) (ntable : HashMap T) (slots : Vec (List T)) (i : Usize) :
-  Result ((HashMap T) × (Vec (List T)))
+  (T : Type) (ntable : HashMap T) (slots : alloc.vec.Vec (List T)) (i : Usize)
+  :
+  Result ((HashMap T) × (alloc.vec.Vec (List T)))
   :=
   HashMap.move_elements_loop T ntable slots i
 
@@ -184,18 +206,17 @@ def HashMap.move_elements
    (there is a single backward function, and the forward function returns ()) -/
 def HashMap.try_resize (T : Type) (self : HashMap T) : Result (HashMap T) :=
   do
-    let max_usize ← Scalar.cast .Usize core_num_u32_max_c
-    let capacity := Vec.len (List T) self.slots
-    let n1 ← max_usize / (Usize.ofInt 2)
+    let max_usize ← Scalar.cast .Usize core_u32_max
+    let capacity := alloc.vec.Vec.len (List T) self.slots
+    let n1 ← max_usize / 2#usize
     let (i, i0) := self.max_load_factor
     let i1 ← n1 / i
     if capacity <= i1
     then
       do
-        let i2 ← capacity * (Usize.ofInt 2)
+        let i2 ← capacity * 2#usize
         let ntable ← HashMap.new_with_capacity T i2 i i0
-        let (ntable0, _) ←
-          HashMap.move_elements T ntable self.slots (Usize.ofInt 0)
+        let (ntable0, _) ← HashMap.move_elements T ntable self.slots 0#usize
         Result.ret
           {
             ntable0
@@ -237,9 +258,12 @@ def HashMap.contains_key
   (T : Type) (self : HashMap T) (key : Usize) : Result Bool :=
   do
     let hash ← hash_key key
-    let i := Vec.len (List T) self.slots
+    let i := alloc.vec.Vec.len (List T) self.slots
     let hash_mod ← hash % i
-    let l ← Vec.index_shared (List T) self.slots hash_mod
+    let l ←
+      alloc.vec.Vec.index (List T) Usize
+        (core.slice.index.usize.coresliceindexSliceIndexInst (List T))
+        self.slots hash_mod
     HashMap.contains_key_in_list T key l
 
 /- [hashmap::HashMap::{0}::get_in_list]: loop 0: forward function -/
@@ -260,9 +284,12 @@ def HashMap.get_in_list (T : Type) (key : Usize) (ls : List T) : Result T :=
 def HashMap.get (T : Type) (self : HashMap T) (key : Usize) : Result T :=
   do
     let hash ← hash_key key
-    let i := Vec.len (List T) self.slots
+    let i := alloc.vec.Vec.len (List T) self.slots
     let hash_mod ← hash % i
-    let l ← Vec.index_shared (List T) self.slots hash_mod
+    let l ←
+      alloc.vec.Vec.index (List T) Usize
+        (core.slice.index.usize.coresliceindexSliceIndexInst (List T))
+        self.slots hash_mod
     HashMap.get_in_list T key l
 
 /- [hashmap::HashMap::{0}::get_mut_in_list]: loop 0: forward function -/
@@ -302,9 +329,12 @@ def HashMap.get_mut_in_list_back
 def HashMap.get_mut (T : Type) (self : HashMap T) (key : Usize) : Result T :=
   do
     let hash ← hash_key key
-    let i := Vec.len (List T) self.slots
+    let i := alloc.vec.Vec.len (List T) self.slots
     let hash_mod ← hash % i
-    let l ← Vec.index_mut (List T) self.slots hash_mod
+    let l ←
+      alloc.vec.Vec.index_mut (List T) Usize
+        (core.slice.index.usize.coresliceindexSliceIndexInst (List T))
+        self.slots hash_mod
     HashMap.get_mut_in_list T l key
 
 /- [hashmap::HashMap::{0}::get_mut]: backward function 0 -/
@@ -314,11 +344,17 @@ def HashMap.get_mut_back
   :=
   do
     let hash ← hash_key key
-    let i := Vec.len (List T) self.slots
+    let i := alloc.vec.Vec.len (List T) self.slots
     let hash_mod ← hash % i
-    let l ← Vec.index_mut (List T) self.slots hash_mod
+    let l ←
+      alloc.vec.Vec.index_mut (List T) Usize
+        (core.slice.index.usize.coresliceindexSliceIndexInst (List T))
+        self.slots hash_mod
     let l0 ← HashMap.get_mut_in_list_back T l key ret0
-    let v ← Vec.index_mut_back (List T) self.slots hash_mod l0
+    let v ←
+      alloc.vec.Vec.index_mut_back (List T) Usize
+        (core.slice.index.usize.coresliceindexSliceIndexInst (List T))
+        self.slots hash_mod l0
     Result.ret { self with slots := v }
 
 /- [hashmap::HashMap::{0}::remove_from_list]: loop 0: forward function -/
@@ -328,12 +364,12 @@ divergent def HashMap.remove_from_list_loop
   | List.Cons ckey t tl =>
     if ckey = key
     then
-      let mv_ls := mem.replace (List T) (List.Cons ckey t tl) List.Nil
+      let mv_ls := core.mem.replace (List T) (List.Cons ckey t tl) List.Nil
       match mv_ls with
-      | List.Cons i cvalue tl0 => Result.ret (Option.some cvalue)
+      | List.Cons i cvalue tl0 => Result.ret (some cvalue)
       | List.Nil => Result.fail Error.panic
     else HashMap.remove_from_list_loop T key tl
-  | List.Nil => Result.ret Option.none
+  | List.Nil => Result.ret none
 
 /- [hashmap::HashMap::{0}::remove_from_list]: forward function -/
 def HashMap.remove_from_list
@@ -347,7 +383,7 @@ divergent def HashMap.remove_from_list_loop_back
   | List.Cons ckey t tl =>
     if ckey = key
     then
-      let mv_ls := mem.replace (List T) (List.Cons ckey t tl) List.Nil
+      let mv_ls := core.mem.replace (List T) (List.Cons ckey t tl) List.Nil
       match mv_ls with
       | List.Cons i cvalue tl0 => Result.ret tl0
       | List.Nil => Result.fail Error.panic
@@ -367,84 +403,91 @@ def HashMap.remove
   (T : Type) (self : HashMap T) (key : Usize) : Result (Option T) :=
   do
     let hash ← hash_key key
-    let i := Vec.len (List T) self.slots
+    let i := alloc.vec.Vec.len (List T) self.slots
     let hash_mod ← hash % i
-    let l ← Vec.index_mut (List T) self.slots hash_mod
+    let l ←
+      alloc.vec.Vec.index_mut (List T) Usize
+        (core.slice.index.usize.coresliceindexSliceIndexInst (List T))
+        self.slots hash_mod
     let x ← HashMap.remove_from_list T key l
     match x with
-    | Option.none => Result.ret Option.none
-    | Option.some x0 =>
-      do
-        let _ ← self.num_entries - (Usize.ofInt 1)
-        Result.ret (Option.some x0)
+    | none => Result.ret none
+    | some x0 => do
+                   let _ ← self.num_entries - 1#usize
+                   Result.ret (some x0)
 
 /- [hashmap::HashMap::{0}::remove]: backward function 0 -/
 def HashMap.remove_back
   (T : Type) (self : HashMap T) (key : Usize) : Result (HashMap T) :=
   do
     let hash ← hash_key key
-    let i := Vec.len (List T) self.slots
+    let i := alloc.vec.Vec.len (List T) self.slots
     let hash_mod ← hash % i
-    let l ← Vec.index_mut (List T) self.slots hash_mod
+    let l ←
+      alloc.vec.Vec.index_mut (List T) Usize
+        (core.slice.index.usize.coresliceindexSliceIndexInst (List T))
+        self.slots hash_mod
     let x ← HashMap.remove_from_list T key l
     match x with
-    | Option.none =>
+    | none =>
       do
         let l0 ← HashMap.remove_from_list_back T key l
-        let v ← Vec.index_mut_back (List T) self.slots hash_mod l0
+        let v ←
+          alloc.vec.Vec.index_mut_back (List T) Usize
+            (core.slice.index.usize.coresliceindexSliceIndexInst (List T))
+            self.slots hash_mod l0
         Result.ret { self with slots := v }
-    | Option.some x0 =>
+    | some x0 =>
       do
-        let i0 ← self.num_entries - (Usize.ofInt 1)
+        let i0 ← self.num_entries - 1#usize
         let l0 ← HashMap.remove_from_list_back T key l
-        let v ← Vec.index_mut_back (List T) self.slots hash_mod l0
+        let v ←
+          alloc.vec.Vec.index_mut_back (List T) Usize
+            (core.slice.index.usize.coresliceindexSliceIndexInst (List T))
+            self.slots hash_mod l0
         Result.ret { self with num_entries := i0, slots := v }
 
 /- [hashmap::test1]: forward function -/
 def test1 : Result Unit :=
   do
     let hm ← HashMap.new U64
-    let hm0 ← HashMap.insert U64 hm (Usize.ofInt 0) (U64.ofInt 42)
-    let hm1 ← HashMap.insert U64 hm0 (Usize.ofInt 128) (U64.ofInt 18)
-    let hm2 ← HashMap.insert U64 hm1 (Usize.ofInt 1024) (U64.ofInt 138)
-    let hm3 ← HashMap.insert U64 hm2 (Usize.ofInt 1056) (U64.ofInt 256)
-    let i ← HashMap.get U64 hm3 (Usize.ofInt 128)
-    if not (i = (U64.ofInt 18))
+    let hm0 ← HashMap.insert U64 hm 0#usize 42#u64
+    let hm1 ← HashMap.insert U64 hm0 128#usize 18#u64
+    let hm2 ← HashMap.insert U64 hm1 1024#usize 138#u64
+    let hm3 ← HashMap.insert U64 hm2 1056#usize 256#u64
+    let i ← HashMap.get U64 hm3 128#usize
+    if not (i = 18#u64)
     then Result.fail Error.panic
     else
       do
-        let hm4 ←
-          HashMap.get_mut_back U64 hm3 (Usize.ofInt 1024) (U64.ofInt 56)
-        let i0 ← HashMap.get U64 hm4 (Usize.ofInt 1024)
-        if not (i0 = (U64.ofInt 56))
+        let hm4 ← HashMap.get_mut_back U64 hm3 1024#usize 56#u64
+        let i0 ← HashMap.get U64 hm4 1024#usize
+        if not (i0 = 56#u64)
         then Result.fail Error.panic
         else
           do
-            let x ← HashMap.remove U64 hm4 (Usize.ofInt 1024)
+            let x ← HashMap.remove U64 hm4 1024#usize
             match x with
-            | Option.none => Result.fail Error.panic
-            | Option.some x0 =>
-              if not (x0 = (U64.ofInt 56))
+            | none => Result.fail Error.panic
+            | some x0 =>
+              if not (x0 = 56#u64)
               then Result.fail Error.panic
               else
                 do
-                  let hm5 ← HashMap.remove_back U64 hm4 (Usize.ofInt 1024)
-                  let i1 ← HashMap.get U64 hm5 (Usize.ofInt 0)
-                  if not (i1 = (U64.ofInt 42))
+                  let hm5 ← HashMap.remove_back U64 hm4 1024#usize
+                  let i1 ← HashMap.get U64 hm5 0#usize
+                  if not (i1 = 42#u64)
                   then Result.fail Error.panic
                   else
                     do
-                      let i2 ← HashMap.get U64 hm5 (Usize.ofInt 128)
-                      if not (i2 = (U64.ofInt 18))
+                      let i2 ← HashMap.get U64 hm5 128#usize
+                      if not (i2 = 18#u64)
                       then Result.fail Error.panic
                       else
                         do
-                          let i3 ← HashMap.get U64 hm5 (Usize.ofInt 1056)
-                          if not (i3 = (U64.ofInt 256))
+                          let i3 ← HashMap.get U64 hm5 1056#usize
+                          if not (i3 = 256#u64)
                           then Result.fail Error.panic
                           else Result.ret ()
 
-/- Unit test for [hashmap::test1] -/
-#assert (test1 == .ret ())
-
 end hashmap
diff --git a/tests/lean/Hashmap/Properties.lean b/tests/lean/Hashmap/Properties.lean
index fe00ab14..e79c422d 100644
--- a/tests/lean/Hashmap/Properties.lean
+++ b/tests/lean/Hashmap/Properties.lean
@@ -157,7 +157,7 @@ instance : Inhabited (List α) where
 def slots_s_inv (s : Core.List (List α)) : Prop :=
   ∀ (i : Int), 0 ≤ i → i < s.len → slot_t_inv s.len i (s.index i)
 
-def slots_t_inv (s : Vec (List α)) : Prop :=
+def slots_t_inv (s : alloc.vec.Vec (List α)) : Prop :=
   slots_s_inv s.v
 
 @[simp]
@@ -302,20 +302,19 @@ theorem insert_no_resize_spec {α : Type} (hm : HashMap α) (key : Usize) (value
    | none => nhm.len_s = hm.len_s + 1
    | some _ => nhm.len_s = hm.len_s) := by
   rw [insert_no_resize]
-  simp only [hash_key, bind_tc_ret] -- TODO: annoying
-  have _ : (Vec.len (List α) hm.slots).val ≠ 0 := by checkpoint
+  -- Simplify. Note that this also simplifies some function calls, like array index
+  simp [hash_key, bind_tc_ret]
+  have _ : (alloc.vec.Vec.len (List α) hm.slots).val ≠ 0 := by
    intro
    simp_all [inv]
-  progress keep _ as ⟨ hash_mod, hhm ⟩
-  have _ : 0 ≤ hash_mod.val := by checkpoint scalar_tac
-  have _ : hash_mod.val < Vec.length hm.slots := by
+  progress as ⟨ hash_mod, hhm ⟩
+  have _ : 0 ≤ hash_mod.val := by scalar_tac
+  have _ : hash_mod.val < alloc.vec.Vec.length hm.slots := by
     have : 0 < hm.slots.val.len := by
       simp [inv] at hinv
       simp [hinv]
     -- TODO: we want to automate that
     simp [*, Int.emod_lt_of_pos]
-  -- TODO: change the spec of Vec.index_mut to introduce a let-binding.
-  -- or: make progress introduce the let-binding by itself (this is clearer)
   progress as ⟨ l, h_leq ⟩
   -- TODO: make progress use the names written in the goal
   progress as ⟨ inserted ⟩
@@ -376,7 +375,7 @@ theorem insert_no_resize_spec {α : Type} (hm : HashMap α) (key : Usize) (value
       -- TODO: we want to automate this
       simp
       apply Int.emod_nonneg k.val hvnz
-    have _ : k_hash_mod < Vec.length hm.slots := by
+    have _ : k_hash_mod < alloc.vec.Vec.length hm.slots := by
       -- TODO: we want to automate this
       simp
       have h := Int.emod_lt_of_pos k.val hvpos
diff --git a/tests/lean/Hashmap/Types.lean b/tests/lean/Hashmap/Types.lean
index 6455798d..e007bce0 100644
--- a/tests/lean/Hashmap/Types.lean
+++ b/tests/lean/Hashmap/Types.lean
@@ -15,6 +15,6 @@ structure HashMap (T : Type) where
   num_entries : Usize
   max_load_factor : (Usize × Usize)
   max_load : Usize
-  slots : Vec (List T)
+  slots : alloc.vec.Vec (List T)
 
 end hashmap
diff --git a/tests/lean/HashmapMain/Funs.lean b/tests/lean/HashmapMain/Funs.lean
index aec957ec..74fa8653 100644
--- a/tests/lean/HashmapMain/Funs.lean
+++ b/tests/lean/HashmapMain/Funs.lean
@@ -13,21 +13,21 @@ def hashmap.hash_key (k : Usize) : Result Usize :=
 
 /- [hashmap_main::hashmap::HashMap::{0}::allocate_slots]: loop 0: forward function -/
 divergent def hashmap.HashMap.allocate_slots_loop
-  (T : Type) (slots : Vec (hashmap.List T)) (n : Usize) :
-  Result (Vec (hashmap.List T))
+  (T : Type) (slots : alloc.vec.Vec (hashmap.List T)) (n : Usize) :
+  Result (alloc.vec.Vec (hashmap.List T))
   :=
-  if n > (Usize.ofInt 0)
+  if n > 0#usize
   then
     do
-      let slots0 ← Vec.push (hashmap.List T) slots hashmap.List.Nil
-      let n0 ← n - (Usize.ofInt 1)
+      let slots0 ← alloc.vec.Vec.push (hashmap.List T) slots hashmap.List.Nil
+      let n0 ← n - 1#usize
       hashmap.HashMap.allocate_slots_loop T slots0 n0
   else Result.ret slots
 
 /- [hashmap_main::hashmap::HashMap::{0}::allocate_slots]: forward function -/
 def hashmap.HashMap.allocate_slots
-  (T : Type) (slots : Vec (hashmap.List T)) (n : Usize) :
-  Result (Vec (hashmap.List T))
+  (T : Type) (slots : alloc.vec.Vec (hashmap.List T)) (n : Usize) :
+  Result (alloc.vec.Vec (hashmap.List T))
   :=
   hashmap.HashMap.allocate_slots_loop T slots n
 
@@ -38,13 +38,13 @@ def hashmap.HashMap.new_with_capacity
   Result (hashmap.HashMap T)
   :=
   do
-    let v := Vec.new (hashmap.List T)
+    let v := alloc.vec.Vec.new (hashmap.List T)
     let slots ← hashmap.HashMap.allocate_slots T v capacity
     let i ← capacity * max_load_dividend
     let i0 ← i / max_load_divisor
     Result.ret
       {
-        num_entries := (Usize.ofInt 0),
+        num_entries := 0#usize,
         max_load_factor := (max_load_dividend, max_load_divisor),
         max_load := i0,
         slots := slots
@@ -52,22 +52,23 @@ def hashmap.HashMap.new_with_capacity
 
 /- [hashmap_main::hashmap::HashMap::{0}::new]: forward function -/
 def hashmap.HashMap.new (T : Type) : Result (hashmap.HashMap T) :=
-  hashmap.HashMap.new_with_capacity T (Usize.ofInt 32) (Usize.ofInt 4)
-    (Usize.ofInt 5)
+  hashmap.HashMap.new_with_capacity T 32#usize 4#usize 5#usize
 
 /- [hashmap_main::hashmap::HashMap::{0}::clear]: loop 0: merged forward/backward function
    (there is a single backward function, and the forward function returns ()) -/
 divergent def hashmap.HashMap.clear_loop
-  (T : Type) (slots : Vec (hashmap.List T)) (i : Usize) :
-  Result (Vec (hashmap.List T))
+  (T : Type) (slots : alloc.vec.Vec (hashmap.List T)) (i : Usize) :
+  Result (alloc.vec.Vec (hashmap.List T))
   :=
-  let i0 := Vec.len (hashmap.List T) slots
+  let i0 := alloc.vec.Vec.len (hashmap.List T) slots
   if i < i0
   then
     do
-      let i1 ← i + (Usize.ofInt 1)
+      let i1 ← i + 1#usize
       let slots0 ←
-        Vec.index_mut_back (hashmap.List T) slots i hashmap.List.Nil
+        alloc.vec.Vec.index_mut_back (hashmap.List T) Usize
+          (core.slice.index.usize.coresliceindexSliceIndexInst (hashmap.List
+          T)) slots i hashmap.List.Nil
       hashmap.HashMap.clear_loop T slots0 i1
   else Result.ret slots
 
@@ -76,8 +77,8 @@ divergent def hashmap.HashMap.clear_loop
 def hashmap.HashMap.clear
   (T : Type) (self : hashmap.HashMap T) : Result (hashmap.HashMap T) :=
   do
-    let v ← hashmap.HashMap.clear_loop T self.slots (Usize.ofInt 0)
-    Result.ret { self with num_entries := (Usize.ofInt 0), slots := v }
+    let v ← hashmap.HashMap.clear_loop T self.slots 0#usize
+    Result.ret { self with num_entries := 0#usize, slots := v }
 
 /- [hashmap_main::hashmap::HashMap::{0}::len]: forward function -/
 def hashmap.HashMap.len (T : Type) (self : hashmap.HashMap T) : Result Usize :=
@@ -130,27 +131,32 @@ def hashmap.HashMap.insert_no_resize
   :=
   do
     let hash ← hashmap.hash_key key
-    let i := Vec.len (hashmap.List T) self.slots
+    let i := alloc.vec.Vec.len (hashmap.List T) self.slots
     let hash_mod ← hash % i
-    let l ← Vec.index_mut (hashmap.List T) self.slots hash_mod
+    let l ←
+      alloc.vec.Vec.index_mut (hashmap.List T) Usize
+        (core.slice.index.usize.coresliceindexSliceIndexInst (hashmap.List T))
+        self.slots hash_mod
     let inserted ← hashmap.HashMap.insert_in_list T key value l
     if inserted
     then
       do
-        let i0 ← self.num_entries + (Usize.ofInt 1)
+        let i0 ← self.num_entries + 1#usize
         let l0 ← hashmap.HashMap.insert_in_list_back T key value l
-        let v ← Vec.index_mut_back (hashmap.List T) self.slots hash_mod l0
+        let v ←
+          alloc.vec.Vec.index_mut_back (hashmap.List T) Usize
+            (core.slice.index.usize.coresliceindexSliceIndexInst (hashmap.List
+            T)) self.slots hash_mod l0
         Result.ret { self with num_entries := i0, slots := v }
     else
       do
         let l0 ← hashmap.HashMap.insert_in_list_back T key value l
-        let v ← Vec.index_mut_back (hashmap.List T) self.slots hash_mod l0
+        let v ←
+          alloc.vec.Vec.index_mut_back (hashmap.List T) Usize
+            (core.slice.index.usize.coresliceindexSliceIndexInst (hashmap.List
+            T)) self.slots hash_mod l0
         Result.ret { self with slots := v }
 
-/- [core::num::u32::{8}::MAX] -/
-def core_num_u32_max_body : Result U32 := Result.ret (U32.ofInt 4294967295)
-def core_num_u32_max_c : U32 := eval_global core_num_u32_max_body (by simp)
-
 /- [hashmap_main::hashmap::HashMap::{0}::move_elements_from_list]: loop 0: merged forward/backward function
    (there is a single backward function, and the forward function returns ()) -/
 divergent def hashmap.HashMap.move_elements_from_list_loop
@@ -175,29 +181,35 @@ def hashmap.HashMap.move_elements_from_list
 /- [hashmap_main::hashmap::HashMap::{0}::move_elements]: loop 0: merged forward/backward function
    (there is a single backward function, and the forward function returns ()) -/
 divergent def hashmap.HashMap.move_elements_loop
-  (T : Type) (ntable : hashmap.HashMap T) (slots : Vec (hashmap.List T))
-  (i : Usize) :
-  Result ((hashmap.HashMap T) × (Vec (hashmap.List T)))
+  (T : Type) (ntable : hashmap.HashMap T)
+  (slots : alloc.vec.Vec (hashmap.List T)) (i : Usize) :
+  Result ((hashmap.HashMap T) × (alloc.vec.Vec (hashmap.List T)))
   :=
-  let i0 := Vec.len (hashmap.List T) slots
+  let i0 := alloc.vec.Vec.len (hashmap.List T) slots
   if i < i0
   then
     do
-      let l ← Vec.index_mut (hashmap.List T) slots i
-      let ls := mem.replace (hashmap.List T) l hashmap.List.Nil
+      let l ←
+        alloc.vec.Vec.index_mut (hashmap.List T) Usize
+          (core.slice.index.usize.coresliceindexSliceIndexInst (hashmap.List
+          T)) slots i
+      let ls := core.mem.replace (hashmap.List T) l hashmap.List.Nil
       let ntable0 ← hashmap.HashMap.move_elements_from_list T ntable ls
-      let i1 ← i + (Usize.ofInt 1)
-      let l0 := mem.replace_back (hashmap.List T) l hashmap.List.Nil
-      let slots0 ← Vec.index_mut_back (hashmap.List T) slots i l0
+      let i1 ← i + 1#usize
+      let l0 := core.mem.replace_back (hashmap.List T) l hashmap.List.Nil
+      let slots0 ←
+        alloc.vec.Vec.index_mut_back (hashmap.List T) Usize
+          (core.slice.index.usize.coresliceindexSliceIndexInst (hashmap.List
+          T)) slots i l0
       hashmap.HashMap.move_elements_loop T ntable0 slots0 i1
   else Result.ret (ntable, slots)
 
 /- [hashmap_main::hashmap::HashMap::{0}::move_elements]: merged forward/backward function
    (there is a single backward function, and the forward function returns ()) -/
 def hashmap.HashMap.move_elements
-  (T : Type) (ntable : hashmap.HashMap T) (slots : Vec (hashmap.List T))
-  (i : Usize) :
-  Result ((hashmap.HashMap T) × (Vec (hashmap.List T)))
+  (T : Type) (ntable : hashmap.HashMap T)
+  (slots : alloc.vec.Vec (hashmap.List T)) (i : Usize) :
+  Result ((hashmap.HashMap T) × (alloc.vec.Vec (hashmap.List T)))
   :=
   hashmap.HashMap.move_elements_loop T ntable slots i
 
@@ -206,18 +218,18 @@ def hashmap.HashMap.move_elements
 def hashmap.HashMap.try_resize
   (T : Type) (self : hashmap.HashMap T) : Result (hashmap.HashMap T) :=
   do
-    let max_usize ← Scalar.cast .Usize core_num_u32_max_c
-    let capacity := Vec.len (hashmap.List T) self.slots
-    let n1 ← max_usize / (Usize.ofInt 2)
+    let max_usize ← Scalar.cast .Usize core_u32_max
+    let capacity := alloc.vec.Vec.len (hashmap.List T) self.slots
+    let n1 ← max_usize / 2#usize
     let (i, i0) := self.max_load_factor
     let i1 ← n1 / i
     if capacity <= i1
     then
       do
-        let i2 ← capacity * (Usize.ofInt 2)
+        let i2 ← capacity * 2#usize
         let ntable ← hashmap.HashMap.new_with_capacity T i2 i i0
         let (ntable0, _) ←
-          hashmap.HashMap.move_elements T ntable self.slots (Usize.ofInt 0)
+          hashmap.HashMap.move_elements T ntable self.slots 0#usize
         Result.ret
           {
             ntable0
@@ -259,9 +271,12 @@ def hashmap.HashMap.contains_key
   (T : Type) (self : hashmap.HashMap T) (key : Usize) : Result Bool :=
   do
     let hash ← hashmap.hash_key key
-    let i := Vec.len (hashmap.List T) self.slots
+    let i := alloc.vec.Vec.len (hashmap.List T) self.slots
     let hash_mod ← hash % i
-    let l ← Vec.index_shared (hashmap.List T) self.slots hash_mod
+    let l ←
+      alloc.vec.Vec.index (hashmap.List T) Usize
+        (core.slice.index.usize.coresliceindexSliceIndexInst (hashmap.List T))
+        self.slots hash_mod
     hashmap.HashMap.contains_key_in_list T key l
 
 /- [hashmap_main::hashmap::HashMap::{0}::get_in_list]: loop 0: forward function -/
@@ -284,9 +299,12 @@ def hashmap.HashMap.get
   (T : Type) (self : hashmap.HashMap T) (key : Usize) : Result T :=
   do
     let hash ← hashmap.hash_key key
-    let i := Vec.len (hashmap.List T) self.slots
+    let i := alloc.vec.Vec.len (hashmap.List T) self.slots
     let hash_mod ← hash % i
-    let l ← Vec.index_shared (hashmap.List T) self.slots hash_mod
+    let l ←
+      alloc.vec.Vec.index (hashmap.List T) Usize
+        (core.slice.index.usize.coresliceindexSliceIndexInst (hashmap.List T))
+        self.slots hash_mod
     hashmap.HashMap.get_in_list T key l
 
 /- [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list]: loop 0: forward function -/
@@ -331,9 +349,12 @@ def hashmap.HashMap.get_mut
   (T : Type) (self : hashmap.HashMap T) (key : Usize) : Result T :=
   do
     let hash ← hashmap.hash_key key
-    let i := Vec.len (hashmap.List T) self.slots
+    let i := alloc.vec.Vec.len (hashmap.List T) self.slots
     let hash_mod ← hash % i
-    let l ← Vec.index_mut (hashmap.List T) self.slots hash_mod
+    let l ←
+      alloc.vec.Vec.index_mut (hashmap.List T) Usize
+        (core.slice.index.usize.coresliceindexSliceIndexInst (hashmap.List T))
+        self.slots hash_mod
     hashmap.HashMap.get_mut_in_list T l key
 
 /- [hashmap_main::hashmap::HashMap::{0}::get_mut]: backward function 0 -/
@@ -343,11 +364,17 @@ def hashmap.HashMap.get_mut_back
   :=
   do
     let hash ← hashmap.hash_key key
-    let i := Vec.len (hashmap.List T) self.slots
+    let i := alloc.vec.Vec.len (hashmap.List T) self.slots
     let hash_mod ← hash % i
-    let l ← Vec.index_mut (hashmap.List T) self.slots hash_mod
+    let l ←
+      alloc.vec.Vec.index_mut (hashmap.List T) Usize
+        (core.slice.index.usize.coresliceindexSliceIndexInst (hashmap.List T))
+        self.slots hash_mod
     let l0 ← hashmap.HashMap.get_mut_in_list_back T l key ret0
-    let v ← Vec.index_mut_back (hashmap.List T) self.slots hash_mod l0
+    let v ←
+      alloc.vec.Vec.index_mut_back (hashmap.List T) Usize
+        (core.slice.index.usize.coresliceindexSliceIndexInst (hashmap.List T))
+        self.slots hash_mod l0
     Result.ret { self with slots := v }
 
 /- [hashmap_main::hashmap::HashMap::{0}::remove_from_list]: loop 0: forward function -/
@@ -358,13 +385,13 @@ divergent def hashmap.HashMap.remove_from_list_loop
     if ckey = key
     then
       let mv_ls :=
-        mem.replace (hashmap.List T) (hashmap.List.Cons ckey t tl)
+        core.mem.replace (hashmap.List T) (hashmap.List.Cons ckey t tl)
           hashmap.List.Nil
       match mv_ls with
-      | hashmap.List.Cons i cvalue tl0 => Result.ret (Option.some cvalue)
+      | hashmap.List.Cons i cvalue tl0 => Result.ret (some cvalue)
       | hashmap.List.Nil => Result.fail Error.panic
     else hashmap.HashMap.remove_from_list_loop T key tl
-  | hashmap.List.Nil => Result.ret Option.none
+  | hashmap.List.Nil => Result.ret none
 
 /- [hashmap_main::hashmap::HashMap::{0}::remove_from_list]: forward function -/
 def hashmap.HashMap.remove_from_list
@@ -379,7 +406,7 @@ divergent def hashmap.HashMap.remove_from_list_loop_back
     if ckey = key
     then
       let mv_ls :=
-        mem.replace (hashmap.List T) (hashmap.List.Cons ckey t tl)
+        core.mem.replace (hashmap.List T) (hashmap.List.Cons ckey t tl)
           hashmap.List.Nil
       match mv_ls with
       | hashmap.List.Cons i cvalue tl0 => Result.ret tl0
@@ -400,16 +427,18 @@ def hashmap.HashMap.remove
   (T : Type) (self : hashmap.HashMap T) (key : Usize) : Result (Option T) :=
   do
     let hash ← hashmap.hash_key key
-    let i := Vec.len (hashmap.List T) self.slots
+    let i := alloc.vec.Vec.len (hashmap.List T) self.slots
     let hash_mod ← hash % i
-    let l ← Vec.index_mut (hashmap.List T) self.slots hash_mod
+    let l ←
+      alloc.vec.Vec.index_mut (hashmap.List T) Usize
+        (core.slice.index.usize.coresliceindexSliceIndexInst (hashmap.List T))
+        self.slots hash_mod
     let x ← hashmap.HashMap.remove_from_list T key l
     match x with
-    | Option.none => Result.ret Option.none
-    | Option.some x0 =>
-      do
-        let _ ← self.num_entries - (Usize.ofInt 1)
-        Result.ret (Option.some x0)
+    | none => Result.ret none
+    | some x0 => do
+                   let _ ← self.num_entries - 1#usize
+                   Result.ret (some x0)
 
 /- [hashmap_main::hashmap::HashMap::{0}::remove]: backward function 0 -/
 def hashmap.HashMap.remove_back
@@ -418,75 +447,75 @@ def hashmap.HashMap.remove_back
   :=
   do
     let hash ← hashmap.hash_key key
-    let i := Vec.len (hashmap.List T) self.slots
+    let i := alloc.vec.Vec.len (hashmap.List T) self.slots
     let hash_mod ← hash % i
-    let l ← Vec.index_mut (hashmap.List T) self.slots hash_mod
+    let l ←
+      alloc.vec.Vec.index_mut (hashmap.List T) Usize
+        (core.slice.index.usize.coresliceindexSliceIndexInst (hashmap.List T))
+        self.slots hash_mod
     let x ← hashmap.HashMap.remove_from_list T key l
     match x with
-    | Option.none =>
+    | none =>
       do
         let l0 ← hashmap.HashMap.remove_from_list_back T key l
-        let v ← Vec.index_mut_back (hashmap.List T) self.slots hash_mod l0
+        let v ←
+          alloc.vec.Vec.index_mut_back (hashmap.List T) Usize
+            (core.slice.index.usize.coresliceindexSliceIndexInst (hashmap.List
+            T)) self.slots hash_mod l0
         Result.ret { self with slots := v }
-    | Option.some x0 =>
+    | some x0 =>
       do
-        let i0 ← self.num_entries - (Usize.ofInt 1)
+        let i0 ← self.num_entries - 1#usize
         let l0 ← hashmap.HashMap.remove_from_list_back T key l
-        let v ← Vec.index_mut_back (hashmap.List T) self.slots hash_mod l0
+        let v ←
+          alloc.vec.Vec.index_mut_back (hashmap.List T) Usize
+            (core.slice.index.usize.coresliceindexSliceIndexInst (hashmap.List
+            T)) self.slots hash_mod l0
         Result.ret { self with num_entries := i0, slots := v }
 
 /- [hashmap_main::hashmap::test1]: forward function -/
 def hashmap.test1 : Result Unit :=
   do
     let hm ← hashmap.HashMap.new U64
-    let hm0 ← hashmap.HashMap.insert U64 hm (Usize.ofInt 0) (U64.ofInt 42)
-    let hm1 ← hashmap.HashMap.insert U64 hm0 (Usize.ofInt 128) (U64.ofInt 18)
-    let hm2 ←
-      hashmap.HashMap.insert U64 hm1 (Usize.ofInt 1024) (U64.ofInt 138)
-    let hm3 ←
-      hashmap.HashMap.insert U64 hm2 (Usize.ofInt 1056) (U64.ofInt 256)
-    let i ← hashmap.HashMap.get U64 hm3 (Usize.ofInt 128)
-    if not (i = (U64.ofInt 18))
+    let hm0 ← hashmap.HashMap.insert U64 hm 0#usize 42#u64
+    let hm1 ← hashmap.HashMap.insert U64 hm0 128#usize 18#u64
+    let hm2 ← hashmap.HashMap.insert U64 hm1 1024#usize 138#u64
+    let hm3 ← hashmap.HashMap.insert U64 hm2 1056#usize 256#u64
+    let i ← hashmap.HashMap.get U64 hm3 128#usize
+    if not (i = 18#u64)
     then Result.fail Error.panic
     else
       do
-        let hm4 ←
-          hashmap.HashMap.get_mut_back U64 hm3 (Usize.ofInt 1024)
-            (U64.ofInt 56)
-        let i0 ← hashmap.HashMap.get U64 hm4 (Usize.ofInt 1024)
-        if not (i0 = (U64.ofInt 56))
+        let hm4 ← hashmap.HashMap.get_mut_back U64 hm3 1024#usize 56#u64
+        let i0 ← hashmap.HashMap.get U64 hm4 1024#usize
+        if not (i0 = 56#u64)
         then Result.fail Error.panic
         else
           do
-            let x ← hashmap.HashMap.remove U64 hm4 (Usize.ofInt 1024)
+            let x ← hashmap.HashMap.remove U64 hm4 1024#usize
             match x with
-            | Option.none => Result.fail Error.panic
-            | Option.some x0 =>
-              if not (x0 = (U64.ofInt 56))
+            | none => Result.fail Error.panic
+            | some x0 =>
+              if not (x0 = 56#u64)
               then Result.fail Error.panic
               else
                 do
-                  let hm5 ←
-                    hashmap.HashMap.remove_back U64 hm4 (Usize.ofInt 1024)
-                  let i1 ← hashmap.HashMap.get U64 hm5 (Usize.ofInt 0)
-                  if not (i1 = (U64.ofInt 42))
+                  let hm5 ← hashmap.HashMap.remove_back U64 hm4 1024#usize
+                  let i1 ← hashmap.HashMap.get U64 hm5 0#usize
+                  if not (i1 = 42#u64)
                   then Result.fail Error.panic
                   else
                     do
-                      let i2 ← hashmap.HashMap.get U64 hm5 (Usize.ofInt 128)
-                      if not (i2 = (U64.ofInt 18))
+                      let i2 ← hashmap.HashMap.get U64 hm5 128#usize
+                      if not (i2 = 18#u64)
                       then Result.fail Error.panic
                       else
                         do
-                          let i3 ←
-                            hashmap.HashMap.get U64 hm5 (Usize.ofInt 1056)
-                          if not (i3 = (U64.ofInt 256))
+                          let i3 ← hashmap.HashMap.get U64 hm5 1056#usize
+                          if not (i3 = 256#u64)
                           then Result.fail Error.panic
                           else Result.ret ()
 
-/- Unit test for [hashmap_main::hashmap::test1] -/
-#assert (hashmap.test1 == .ret ())
-
 /- [hashmap_main::insert_on_disk]: forward function -/
 def insert_on_disk
   (key : Usize) (value : U64) (st : State) : Result (State × Unit) :=
@@ -500,7 +529,4 @@ def insert_on_disk
 def main : Result Unit :=
   Result.ret ()
 
-/- Unit test for [hashmap_main::main] -/
-#assert (main == .ret ())
-
 end hashmap_main
diff --git a/tests/lean/HashmapMain/Types.lean b/tests/lean/HashmapMain/Types.lean
index 2b5cbd6c..065c109b 100644
--- a/tests/lean/HashmapMain/Types.lean
+++ b/tests/lean/HashmapMain/Types.lean
@@ -15,7 +15,7 @@ structure hashmap.HashMap (T : Type) where
   num_entries : Usize
   max_load_factor : (Usize × Usize)
   max_load : Usize
-  slots : Vec (hashmap.List T)
+  slots : alloc.vec.Vec (hashmap.List T)
 
 /- The state type used in the state-error monad -/
 axiom State : Type
diff --git a/tests/lean/Loops.lean b/tests/lean/Loops.lean
index 60c73776..c6360338 100644
--- a/tests/lean/Loops.lean
+++ b/tests/lean/Loops.lean
@@ -1 +1,629 @@
-import Loops.Funs
+-- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
+-- [loops]
+import Base
+open Primitives
+
+namespace loops
+
+/- [loops::sum]: loop 0: forward function -/
+divergent def sum_loop (max : U32) (i : U32) (s : U32) : Result U32 :=
+  if i < max
+  then do
+         let s0 ← s + i
+         let i0 ← i + 1#u32
+         sum_loop max i0 s0
+  else s * 2#u32
+
+/- [loops::sum]: forward function -/
+def sum (max : U32) : Result U32 :=
+  sum_loop max 0#u32 0#u32
+
+/- [loops::sum_with_mut_borrows]: loop 0: forward function -/
+divergent def sum_with_mut_borrows_loop
+  (max : U32) (mi : U32) (ms : U32) : Result U32 :=
+  if mi < max
+  then
+    do
+      let ms0 ← ms + mi
+      let mi0 ← mi + 1#u32
+      sum_with_mut_borrows_loop max mi0 ms0
+  else ms * 2#u32
+
+/- [loops::sum_with_mut_borrows]: forward function -/
+def sum_with_mut_borrows (max : U32) : Result U32 :=
+  sum_with_mut_borrows_loop max 0#u32 0#u32
+
+/- [loops::sum_with_shared_borrows]: loop 0: forward function -/
+divergent def sum_with_shared_borrows_loop
+  (max : U32) (i : U32) (s : U32) : Result U32 :=
+  if i < max
+  then
+    do
+      let i0 ← i + 1#u32
+      let s0 ← s + i0
+      sum_with_shared_borrows_loop max i0 s0
+  else s * 2#u32
+
+/- [loops::sum_with_shared_borrows]: forward function -/
+def sum_with_shared_borrows (max : U32) : Result U32 :=
+  sum_with_shared_borrows_loop max 0#u32 0#u32
+
+/- [loops::clear]: loop 0: merged forward/backward function
+   (there is a single backward function, and the forward function returns ()) -/
+divergent def clear_loop
+  (v : alloc.vec.Vec U32) (i : Usize) : Result (alloc.vec.Vec U32) :=
+  let i0 := alloc.vec.Vec.len U32 v
+  if i < i0
+  then
+    do
+      let i1 ← i + 1#usize
+      let v0 ←
+        alloc.vec.Vec.index_mut_back U32 Usize
+          (core.slice.index.usize.coresliceindexSliceIndexInst U32) v i 0#u32
+      clear_loop v0 i1
+  else Result.ret v
+
+/- [loops::clear]: merged forward/backward function
+   (there is a single backward function, and the forward function returns ()) -/
+def clear (v : alloc.vec.Vec U32) : Result (alloc.vec.Vec U32) :=
+  clear_loop v 0#usize
+
+/- [loops::List] -/
+inductive List (T : Type) :=
+| Cons : T → List T → List T
+| Nil : List T
+
+/- [loops::list_mem]: loop 0: forward function -/
+divergent def list_mem_loop (x : U32) (ls : List U32) : Result Bool :=
+  match ls with
+  | List.Cons y tl => if y = x
+                      then Result.ret true
+                      else list_mem_loop x tl
+  | List.Nil => Result.ret false
+
+/- [loops::list_mem]: forward function -/
+def list_mem (x : U32) (ls : List U32) : Result Bool :=
+  list_mem_loop x ls
+
+/- [loops::list_nth_mut_loop]: loop 0: forward function -/
+divergent def list_nth_mut_loop_loop
+  (T : Type) (ls : List T) (i : U32) : Result T :=
+  match ls with
+  | List.Cons x tl =>
+    if i = 0#u32
+    then Result.ret x
+    else do
+           let i0 ← i - 1#u32
+           list_nth_mut_loop_loop T tl i0
+  | List.Nil => Result.fail Error.panic
+
+/- [loops::list_nth_mut_loop]: forward function -/
+def list_nth_mut_loop (T : Type) (ls : List T) (i : U32) : Result T :=
+  list_nth_mut_loop_loop T ls i
+
+/- [loops::list_nth_mut_loop]: loop 0: backward function 0 -/
+divergent def list_nth_mut_loop_loop_back
+  (T : Type) (ls : List T) (i : U32) (ret0 : T) : Result (List T) :=
+  match ls with
+  | List.Cons x tl =>
+    if i = 0#u32
+    then Result.ret (List.Cons ret0 tl)
+    else
+      do
+        let i0 ← i - 1#u32
+        let tl0 ← list_nth_mut_loop_loop_back T tl i0 ret0
+        Result.ret (List.Cons x tl0)
+  | List.Nil => Result.fail Error.panic
+
+/- [loops::list_nth_mut_loop]: backward function 0 -/
+def list_nth_mut_loop_back
+  (T : Type) (ls : List T) (i : U32) (ret0 : T) : Result (List T) :=
+  list_nth_mut_loop_loop_back T ls i ret0
+
+/- [loops::list_nth_shared_loop]: loop 0: forward function -/
+divergent def list_nth_shared_loop_loop
+  (T : Type) (ls : List T) (i : U32) : Result T :=
+  match ls with
+  | List.Cons x tl =>
+    if i = 0#u32
+    then Result.ret x
+    else do
+           let i0 ← i - 1#u32
+           list_nth_shared_loop_loop T tl i0
+  | List.Nil => Result.fail Error.panic
+
+/- [loops::list_nth_shared_loop]: forward function -/
+def list_nth_shared_loop (T : Type) (ls : List T) (i : U32) : Result T :=
+  list_nth_shared_loop_loop T ls i
+
+/- [loops::get_elem_mut]: loop 0: forward function -/
+divergent def get_elem_mut_loop (x : Usize) (ls : List Usize) : Result Usize :=
+  match ls with
+  | List.Cons y tl => if y = x
+                      then Result.ret y
+                      else get_elem_mut_loop x tl
+  | List.Nil => Result.fail Error.panic
+
+/- [loops::get_elem_mut]: forward function -/
+def get_elem_mut
+  (slots : alloc.vec.Vec (List Usize)) (x : Usize) : Result Usize :=
+  do
+    let l ←
+      alloc.vec.Vec.index_mut (List Usize) Usize
+        (core.slice.index.usize.coresliceindexSliceIndexInst (List Usize))
+        slots 0#usize
+    get_elem_mut_loop x l
+
+/- [loops::get_elem_mut]: loop 0: backward function 0 -/
+divergent def get_elem_mut_loop_back
+  (x : Usize) (ls : List Usize) (ret0 : Usize) : Result (List Usize) :=
+  match ls with
+  | List.Cons y tl =>
+    if y = x
+    then Result.ret (List.Cons ret0 tl)
+    else
+      do
+        let tl0 ← get_elem_mut_loop_back x tl ret0
+        Result.ret (List.Cons y tl0)
+  | List.Nil => Result.fail Error.panic
+
+/- [loops::get_elem_mut]: backward function 0 -/
+def get_elem_mut_back
+  (slots : alloc.vec.Vec (List Usize)) (x : Usize) (ret0 : Usize) :
+  Result (alloc.vec.Vec (List Usize))
+  :=
+  do
+    let l ←
+      alloc.vec.Vec.index_mut (List Usize) Usize
+        (core.slice.index.usize.coresliceindexSliceIndexInst (List Usize))
+        slots 0#usize
+    let l0 ← get_elem_mut_loop_back x l ret0
+    alloc.vec.Vec.index_mut_back (List Usize) Usize
+      (core.slice.index.usize.coresliceindexSliceIndexInst (List Usize)) slots
+      0#usize l0
+
+/- [loops::get_elem_shared]: loop 0: forward function -/
+divergent def get_elem_shared_loop
+  (x : Usize) (ls : List Usize) : Result Usize :=
+  match ls with
+  | List.Cons y tl => if y = x
+                      then Result.ret y
+                      else get_elem_shared_loop x tl
+  | List.Nil => Result.fail Error.panic
+
+/- [loops::get_elem_shared]: forward function -/
+def get_elem_shared
+  (slots : alloc.vec.Vec (List Usize)) (x : Usize) : Result Usize :=
+  do
+    let l ←
+      alloc.vec.Vec.index (List Usize) Usize
+        (core.slice.index.usize.coresliceindexSliceIndexInst (List Usize))
+        slots 0#usize
+    get_elem_shared_loop x l
+
+/- [loops::id_mut]: forward function -/
+def id_mut (T : Type) (ls : List T) : Result (List T) :=
+  Result.ret ls
+
+/- [loops::id_mut]: backward function 0 -/
+def id_mut_back (T : Type) (ls : List T) (ret0 : List T) : Result (List T) :=
+  Result.ret ret0
+
+/- [loops::id_shared]: forward function -/
+def id_shared (T : Type) (ls : List T) : Result (List T) :=
+  Result.ret ls
+
+/- [loops::list_nth_mut_loop_with_id]: loop 0: forward function -/
+divergent def list_nth_mut_loop_with_id_loop
+  (T : Type) (i : U32) (ls : List T) : Result T :=
+  match ls with
+  | List.Cons x tl =>
+    if i = 0#u32
+    then Result.ret x
+    else do
+           let i0 ← i - 1#u32
+           list_nth_mut_loop_with_id_loop T i0 tl
+  | List.Nil => Result.fail Error.panic
+
+/- [loops::list_nth_mut_loop_with_id]: forward function -/
+def list_nth_mut_loop_with_id (T : Type) (ls : List T) (i : U32) : Result T :=
+  do
+    let ls0 ← id_mut T ls
+    list_nth_mut_loop_with_id_loop T i ls0
+
+/- [loops::list_nth_mut_loop_with_id]: loop 0: backward function 0 -/
+divergent def list_nth_mut_loop_with_id_loop_back
+  (T : Type) (i : U32) (ls : List T) (ret0 : T) : Result (List T) :=
+  match ls with
+  | List.Cons x tl =>
+    if i = 0#u32
+    then Result.ret (List.Cons ret0 tl)
+    else
+      do
+        let i0 ← i - 1#u32
+        let tl0 ← list_nth_mut_loop_with_id_loop_back T i0 tl ret0
+        Result.ret (List.Cons x tl0)
+  | List.Nil => Result.fail Error.panic
+
+/- [loops::list_nth_mut_loop_with_id]: backward function 0 -/
+def list_nth_mut_loop_with_id_back
+  (T : Type) (ls : List T) (i : U32) (ret0 : T) : Result (List T) :=
+  do
+    let ls0 ← id_mut T ls
+    let l ← list_nth_mut_loop_with_id_loop_back T i ls0 ret0
+    id_mut_back T ls l
+
+/- [loops::list_nth_shared_loop_with_id]: loop 0: forward function -/
+divergent def list_nth_shared_loop_with_id_loop
+  (T : Type) (i : U32) (ls : List T) : Result T :=
+  match ls with
+  | List.Cons x tl =>
+    if i = 0#u32
+    then Result.ret x
+    else do
+           let i0 ← i - 1#u32
+           list_nth_shared_loop_with_id_loop T i0 tl
+  | List.Nil => Result.fail Error.panic
+
+/- [loops::list_nth_shared_loop_with_id]: forward function -/
+def list_nth_shared_loop_with_id
+  (T : Type) (ls : List T) (i : U32) : Result T :=
+  do
+    let ls0 ← id_shared T ls
+    list_nth_shared_loop_with_id_loop T i ls0
+
+/- [loops::list_nth_mut_loop_pair]: loop 0: forward function -/
+divergent def list_nth_mut_loop_pair_loop
+  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
+  match ls0 with
+  | List.Cons x0 tl0 =>
+    match ls1 with
+    | List.Cons x1 tl1 =>
+      if i = 0#u32
+      then Result.ret (x0, x1)
+      else do
+             let i0 ← i - 1#u32
+             list_nth_mut_loop_pair_loop T tl0 tl1 i0
+    | List.Nil => Result.fail Error.panic
+  | List.Nil => Result.fail Error.panic
+
+/- [loops::list_nth_mut_loop_pair]: forward function -/
+def list_nth_mut_loop_pair
+  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
+  list_nth_mut_loop_pair_loop T ls0 ls1 i
+
+/- [loops::list_nth_mut_loop_pair]: loop 0: backward function 0 -/
+divergent def list_nth_mut_loop_pair_loop_back'a
+  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret0 : T) :
+  Result (List T)
+  :=
+  match ls0 with
+  | List.Cons x0 tl0 =>
+    match ls1 with
+    | List.Cons x1 tl1 =>
+      if i = 0#u32
+      then Result.ret (List.Cons ret0 tl0)
+      else
+        do
+          let i0 ← i - 1#u32
+          let tl00 ← list_nth_mut_loop_pair_loop_back'a T tl0 tl1 i0 ret0
+          Result.ret (List.Cons x0 tl00)
+    | List.Nil => Result.fail Error.panic
+  | List.Nil => Result.fail Error.panic
+
+/- [loops::list_nth_mut_loop_pair]: backward function 0 -/
+def list_nth_mut_loop_pair_back'a
+  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret0 : T) :
+  Result (List T)
+  :=
+  list_nth_mut_loop_pair_loop_back'a T ls0 ls1 i ret0
+
+/- [loops::list_nth_mut_loop_pair]: loop 0: backward function 1 -/
+divergent def list_nth_mut_loop_pair_loop_back'b
+  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret0 : T) :
+  Result (List T)
+  :=
+  match ls0 with
+  | List.Cons x0 tl0 =>
+    match ls1 with
+    | List.Cons x1 tl1 =>
+      if i = 0#u32
+      then Result.ret (List.Cons ret0 tl1)
+      else
+        do
+          let i0 ← i - 1#u32
+          let tl10 ← list_nth_mut_loop_pair_loop_back'b T tl0 tl1 i0 ret0
+          Result.ret (List.Cons x1 tl10)
+    | List.Nil => Result.fail Error.panic
+  | List.Nil => Result.fail Error.panic
+
+/- [loops::list_nth_mut_loop_pair]: backward function 1 -/
+def list_nth_mut_loop_pair_back'b
+  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret0 : T) :
+  Result (List T)
+  :=
+  list_nth_mut_loop_pair_loop_back'b T ls0 ls1 i ret0
+
+/- [loops::list_nth_shared_loop_pair]: loop 0: forward function -/
+divergent def list_nth_shared_loop_pair_loop
+  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
+  match ls0 with
+  | List.Cons x0 tl0 =>
+    match ls1 with
+    | List.Cons x1 tl1 =>
+      if i = 0#u32
+      then Result.ret (x0, x1)
+      else do
+             let i0 ← i - 1#u32
+             list_nth_shared_loop_pair_loop T tl0 tl1 i0
+    | List.Nil => Result.fail Error.panic
+  | List.Nil => Result.fail Error.panic
+
+/- [loops::list_nth_shared_loop_pair]: forward function -/
+def list_nth_shared_loop_pair
+  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
+  list_nth_shared_loop_pair_loop T ls0 ls1 i
+
+/- [loops::list_nth_mut_loop_pair_merge]: loop 0: forward function -/
+divergent def list_nth_mut_loop_pair_merge_loop
+  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
+  match ls0 with
+  | List.Cons x0 tl0 =>
+    match ls1 with
+    | List.Cons x1 tl1 =>
+      if i = 0#u32
+      then Result.ret (x0, x1)
+      else
+        do
+          let i0 ← i - 1#u32
+          list_nth_mut_loop_pair_merge_loop T tl0 tl1 i0
+    | List.Nil => Result.fail Error.panic
+  | List.Nil => Result.fail Error.panic
+
+/- [loops::list_nth_mut_loop_pair_merge]: forward function -/
+def list_nth_mut_loop_pair_merge
+  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
+  list_nth_mut_loop_pair_merge_loop T ls0 ls1 i
+
+/- [loops::list_nth_mut_loop_pair_merge]: loop 0: backward function 0 -/
+divergent def list_nth_mut_loop_pair_merge_loop_back
+  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret0 : (T × T)) :
+  Result ((List T) × (List T))
+  :=
+  match ls0 with
+  | List.Cons x0 tl0 =>
+    match ls1 with
+    | List.Cons x1 tl1 =>
+      if i = 0#u32
+      then let (t, t0) := ret0
+           Result.ret (List.Cons t tl0, List.Cons t0 tl1)
+      else
+        do
+          let i0 ← i - 1#u32
+          let (tl00, tl10) ←
+            list_nth_mut_loop_pair_merge_loop_back T tl0 tl1 i0 ret0
+          Result.ret (List.Cons x0 tl00, List.Cons x1 tl10)
+    | List.Nil => Result.fail Error.panic
+  | List.Nil => Result.fail Error.panic
+
+/- [loops::list_nth_mut_loop_pair_merge]: backward function 0 -/
+def list_nth_mut_loop_pair_merge_back
+  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret0 : (T × T)) :
+  Result ((List T) × (List T))
+  :=
+  list_nth_mut_loop_pair_merge_loop_back T ls0 ls1 i ret0
+
+/- [loops::list_nth_shared_loop_pair_merge]: loop 0: forward function -/
+divergent def list_nth_shared_loop_pair_merge_loop
+  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
+  match ls0 with
+  | List.Cons x0 tl0 =>
+    match ls1 with
+    | List.Cons x1 tl1 =>
+      if i = 0#u32
+      then Result.ret (x0, x1)
+      else
+        do
+          let i0 ← i - 1#u32
+          list_nth_shared_loop_pair_merge_loop T tl0 tl1 i0
+    | List.Nil => Result.fail Error.panic
+  | List.Nil => Result.fail Error.panic
+
+/- [loops::list_nth_shared_loop_pair_merge]: forward function -/
+def list_nth_shared_loop_pair_merge
+  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
+  list_nth_shared_loop_pair_merge_loop T ls0 ls1 i
+
+/- [loops::list_nth_mut_shared_loop_pair]: loop 0: forward function -/
+divergent def list_nth_mut_shared_loop_pair_loop
+  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
+  match ls0 with
+  | List.Cons x0 tl0 =>
+    match ls1 with
+    | List.Cons x1 tl1 =>
+      if i = 0#u32
+      then Result.ret (x0, x1)
+      else
+        do
+          let i0 ← i - 1#u32
+          list_nth_mut_shared_loop_pair_loop T tl0 tl1 i0
+    | List.Nil => Result.fail Error.panic
+  | List.Nil => Result.fail Error.panic
+
+/- [loops::list_nth_mut_shared_loop_pair]: forward function -/
+def list_nth_mut_shared_loop_pair
+  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
+  list_nth_mut_shared_loop_pair_loop T ls0 ls1 i
+
+/- [loops::list_nth_mut_shared_loop_pair]: loop 0: backward function 0 -/
+divergent def list_nth_mut_shared_loop_pair_loop_back
+  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret0 : T) :
+  Result (List T)
+  :=
+  match ls0 with
+  | List.Cons x0 tl0 =>
+    match ls1 with
+    | List.Cons x1 tl1 =>
+      if i = 0#u32
+      then Result.ret (List.Cons ret0 tl0)
+      else
+        do
+          let i0 ← i - 1#u32
+          let tl00 ←
+            list_nth_mut_shared_loop_pair_loop_back T tl0 tl1 i0 ret0
+          Result.ret (List.Cons x0 tl00)
+    | List.Nil => Result.fail Error.panic
+  | List.Nil => Result.fail Error.panic
+
+/- [loops::list_nth_mut_shared_loop_pair]: backward function 0 -/
+def list_nth_mut_shared_loop_pair_back
+  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret0 : T) :
+  Result (List T)
+  :=
+  list_nth_mut_shared_loop_pair_loop_back T ls0 ls1 i ret0
+
+/- [loops::list_nth_mut_shared_loop_pair_merge]: loop 0: forward function -/
+divergent def list_nth_mut_shared_loop_pair_merge_loop
+  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
+  match ls0 with
+  | List.Cons x0 tl0 =>
+    match ls1 with
+    | List.Cons x1 tl1 =>
+      if i = 0#u32
+      then Result.ret (x0, x1)
+      else
+        do
+          let i0 ← i - 1#u32
+          list_nth_mut_shared_loop_pair_merge_loop T tl0 tl1 i0
+    | List.Nil => Result.fail Error.panic
+  | List.Nil => Result.fail Error.panic
+
+/- [loops::list_nth_mut_shared_loop_pair_merge]: forward function -/
+def list_nth_mut_shared_loop_pair_merge
+  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
+  list_nth_mut_shared_loop_pair_merge_loop T ls0 ls1 i
+
+/- [loops::list_nth_mut_shared_loop_pair_merge]: loop 0: backward function 0 -/
+divergent def list_nth_mut_shared_loop_pair_merge_loop_back
+  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret0 : T) :
+  Result (List T)
+  :=
+  match ls0 with
+  | List.Cons x0 tl0 =>
+    match ls1 with
+    | List.Cons x1 tl1 =>
+      if i = 0#u32
+      then Result.ret (List.Cons ret0 tl0)
+      else
+        do
+          let i0 ← i - 1#u32
+          let tl00 ←
+            list_nth_mut_shared_loop_pair_merge_loop_back T tl0 tl1 i0 ret0
+          Result.ret (List.Cons x0 tl00)
+    | List.Nil => Result.fail Error.panic
+  | List.Nil => Result.fail Error.panic
+
+/- [loops::list_nth_mut_shared_loop_pair_merge]: backward function 0 -/
+def list_nth_mut_shared_loop_pair_merge_back
+  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret0 : T) :
+  Result (List T)
+  :=
+  list_nth_mut_shared_loop_pair_merge_loop_back T ls0 ls1 i ret0
+
+/- [loops::list_nth_shared_mut_loop_pair]: loop 0: forward function -/
+divergent def list_nth_shared_mut_loop_pair_loop
+  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
+  match ls0 with
+  | List.Cons x0 tl0 =>
+    match ls1 with
+    | List.Cons x1 tl1 =>
+      if i = 0#u32
+      then Result.ret (x0, x1)
+      else
+        do
+          let i0 ← i - 1#u32
+          list_nth_shared_mut_loop_pair_loop T tl0 tl1 i0
+    | List.Nil => Result.fail Error.panic
+  | List.Nil => Result.fail Error.panic
+
+/- [loops::list_nth_shared_mut_loop_pair]: forward function -/
+def list_nth_shared_mut_loop_pair
+  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
+  list_nth_shared_mut_loop_pair_loop T ls0 ls1 i
+
+/- [loops::list_nth_shared_mut_loop_pair]: loop 0: backward function 1 -/
+divergent def list_nth_shared_mut_loop_pair_loop_back
+  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret0 : T) :
+  Result (List T)
+  :=
+  match ls0 with
+  | List.Cons x0 tl0 =>
+    match ls1 with
+    | List.Cons x1 tl1 =>
+      if i = 0#u32
+      then Result.ret (List.Cons ret0 tl1)
+      else
+        do
+          let i0 ← i - 1#u32
+          let tl10 ←
+            list_nth_shared_mut_loop_pair_loop_back T tl0 tl1 i0 ret0
+          Result.ret (List.Cons x1 tl10)
+    | List.Nil => Result.fail Error.panic
+  | List.Nil => Result.fail Error.panic
+
+/- [loops::list_nth_shared_mut_loop_pair]: backward function 1 -/
+def list_nth_shared_mut_loop_pair_back
+  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret0 : T) :
+  Result (List T)
+  :=
+  list_nth_shared_mut_loop_pair_loop_back T ls0 ls1 i ret0
+
+/- [loops::list_nth_shared_mut_loop_pair_merge]: loop 0: forward function -/
+divergent def list_nth_shared_mut_loop_pair_merge_loop
+  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
+  match ls0 with
+  | List.Cons x0 tl0 =>
+    match ls1 with
+    | List.Cons x1 tl1 =>
+      if i = 0#u32
+      then Result.ret (x0, x1)
+      else
+        do
+          let i0 ← i - 1#u32
+          list_nth_shared_mut_loop_pair_merge_loop T tl0 tl1 i0
+    | List.Nil => Result.fail Error.panic
+  | List.Nil => Result.fail Error.panic
+
+/- [loops::list_nth_shared_mut_loop_pair_merge]: forward function -/
+def list_nth_shared_mut_loop_pair_merge
+  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
+  list_nth_shared_mut_loop_pair_merge_loop T ls0 ls1 i
+
+/- [loops::list_nth_shared_mut_loop_pair_merge]: loop 0: backward function 0 -/
+divergent def list_nth_shared_mut_loop_pair_merge_loop_back
+  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret0 : T) :
+  Result (List T)
+  :=
+  match ls0 with
+  | List.Cons x0 tl0 =>
+    match ls1 with
+    | List.Cons x1 tl1 =>
+      if i = 0#u32
+      then Result.ret (List.Cons ret0 tl1)
+      else
+        do
+          let i0 ← i - 1#u32
+          let tl10 ←
+            list_nth_shared_mut_loop_pair_merge_loop_back T tl0 tl1 i0 ret0
+          Result.ret (List.Cons x1 tl10)
+    | List.Nil => Result.fail Error.panic
+  | List.Nil => Result.fail Error.panic
+
+/- [loops::list_nth_shared_mut_loop_pair_merge]: backward function 0 -/
+def list_nth_shared_mut_loop_pair_merge_back
+  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret0 : T) :
+  Result (List T)
+  :=
+  list_nth_shared_mut_loop_pair_merge_loop_back T ls0 ls1 i ret0
+
+end loops
diff --git a/tests/lean/Loops/Funs.lean b/tests/lean/Loops/Funs.lean
deleted file mode 100644
index 5fbe200f..00000000
--- a/tests/lean/Loops/Funs.lean
+++ /dev/null
@@ -1,612 +0,0 @@
--- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
--- [loops]: function definitions
-import Base
-import Loops.Types
-open Primitives
-
-namespace loops
-
-/- [loops::sum]: loop 0: forward function -/
-divergent def sum_loop (max : U32) (i : U32) (s : U32) : Result U32 :=
-  if i < max
-  then do
-         let s0 ← s + i
-         let i0 ← i + (U32.ofInt 1)
-         sum_loop max i0 s0
-  else s * (U32.ofInt 2)
-
-/- [loops::sum]: forward function -/
-def sum (max : U32) : Result U32 :=
-  sum_loop max (U32.ofInt 0) (U32.ofInt 0)
-
-/- [loops::sum_with_mut_borrows]: loop 0: forward function -/
-divergent def sum_with_mut_borrows_loop
-  (max : U32) (mi : U32) (ms : U32) : Result U32 :=
-  if mi < max
-  then
-    do
-      let ms0 ← ms + mi
-      let mi0 ← mi + (U32.ofInt 1)
-      sum_with_mut_borrows_loop max mi0 ms0
-  else ms * (U32.ofInt 2)
-
-/- [loops::sum_with_mut_borrows]: forward function -/
-def sum_with_mut_borrows (max : U32) : Result U32 :=
-  sum_with_mut_borrows_loop max (U32.ofInt 0) (U32.ofInt 0)
-
-/- [loops::sum_with_shared_borrows]: loop 0: forward function -/
-divergent def sum_with_shared_borrows_loop
-  (max : U32) (i : U32) (s : U32) : Result U32 :=
-  if i < max
-  then
-    do
-      let i0 ← i + (U32.ofInt 1)
-      let s0 ← s + i0
-      sum_with_shared_borrows_loop max i0 s0
-  else s * (U32.ofInt 2)
-
-/- [loops::sum_with_shared_borrows]: forward function -/
-def sum_with_shared_borrows (max : U32) : Result U32 :=
-  sum_with_shared_borrows_loop max (U32.ofInt 0) (U32.ofInt 0)
-
-/- [loops::clear]: loop 0: merged forward/backward function
-   (there is a single backward function, and the forward function returns ()) -/
-divergent def clear_loop (v : Vec U32) (i : Usize) : Result (Vec U32) :=
-  let i0 := Vec.len U32 v
-  if i < i0
-  then
-    do
-      let i1 ← i + (Usize.ofInt 1)
-      let v0 ← Vec.index_mut_back U32 v i (U32.ofInt 0)
-      clear_loop v0 i1
-  else Result.ret v
-
-/- [loops::clear]: merged forward/backward function
-   (there is a single backward function, and the forward function returns ()) -/
-def clear (v : Vec U32) : Result (Vec U32) :=
-  clear_loop v (Usize.ofInt 0)
-
-/- [loops::list_mem]: loop 0: forward function -/
-divergent def list_mem_loop (x : U32) (ls : List U32) : Result Bool :=
-  match ls with
-  | List.Cons y tl => if y = x
-                      then Result.ret true
-                      else list_mem_loop x tl
-  | List.Nil => Result.ret false
-
-/- [loops::list_mem]: forward function -/
-def list_mem (x : U32) (ls : List U32) : Result Bool :=
-  list_mem_loop x ls
-
-/- [loops::list_nth_mut_loop]: loop 0: forward function -/
-divergent def list_nth_mut_loop_loop
-  (T : Type) (ls : List T) (i : U32) : Result T :=
-  match ls with
-  | List.Cons x tl =>
-    if i = (U32.ofInt 0)
-    then Result.ret x
-    else do
-           let i0 ← i - (U32.ofInt 1)
-           list_nth_mut_loop_loop T tl i0
-  | List.Nil => Result.fail Error.panic
-
-/- [loops::list_nth_mut_loop]: forward function -/
-def list_nth_mut_loop (T : Type) (ls : List T) (i : U32) : Result T :=
-  list_nth_mut_loop_loop T ls i
-
-/- [loops::list_nth_mut_loop]: loop 0: backward function 0 -/
-divergent def list_nth_mut_loop_loop_back
-  (T : Type) (ls : List T) (i : U32) (ret0 : T) : Result (List T) :=
-  match ls with
-  | List.Cons x tl =>
-    if i = (U32.ofInt 0)
-    then Result.ret (List.Cons ret0 tl)
-    else
-      do
-        let i0 ← i - (U32.ofInt 1)
-        let tl0 ← list_nth_mut_loop_loop_back T tl i0 ret0
-        Result.ret (List.Cons x tl0)
-  | List.Nil => Result.fail Error.panic
-
-/- [loops::list_nth_mut_loop]: backward function 0 -/
-def list_nth_mut_loop_back
-  (T : Type) (ls : List T) (i : U32) (ret0 : T) : Result (List T) :=
-  list_nth_mut_loop_loop_back T ls i ret0
-
-/- [loops::list_nth_shared_loop]: loop 0: forward function -/
-divergent def list_nth_shared_loop_loop
-  (T : Type) (ls : List T) (i : U32) : Result T :=
-  match ls with
-  | List.Cons x tl =>
-    if i = (U32.ofInt 0)
-    then Result.ret x
-    else do
-           let i0 ← i - (U32.ofInt 1)
-           list_nth_shared_loop_loop T tl i0
-  | List.Nil => Result.fail Error.panic
-
-/- [loops::list_nth_shared_loop]: forward function -/
-def list_nth_shared_loop (T : Type) (ls : List T) (i : U32) : Result T :=
-  list_nth_shared_loop_loop T ls i
-
-/- [loops::get_elem_mut]: loop 0: forward function -/
-divergent def get_elem_mut_loop (x : Usize) (ls : List Usize) : Result Usize :=
-  match ls with
-  | List.Cons y tl => if y = x
-                      then Result.ret y
-                      else get_elem_mut_loop x tl
-  | List.Nil => Result.fail Error.panic
-
-/- [loops::get_elem_mut]: forward function -/
-def get_elem_mut (slots : Vec (List Usize)) (x : Usize) : Result Usize :=
-  do
-    let l ← Vec.index_mut (List Usize) slots (Usize.ofInt 0)
-    get_elem_mut_loop x l
-
-/- [loops::get_elem_mut]: loop 0: backward function 0 -/
-divergent def get_elem_mut_loop_back
-  (x : Usize) (ls : List Usize) (ret0 : Usize) : Result (List Usize) :=
-  match ls with
-  | List.Cons y tl =>
-    if y = x
-    then Result.ret (List.Cons ret0 tl)
-    else
-      do
-        let tl0 ← get_elem_mut_loop_back x tl ret0
-        Result.ret (List.Cons y tl0)
-  | List.Nil => Result.fail Error.panic
-
-/- [loops::get_elem_mut]: backward function 0 -/
-def get_elem_mut_back
-  (slots : Vec (List Usize)) (x : Usize) (ret0 : Usize) :
-  Result (Vec (List Usize))
-  :=
-  do
-    let l ← Vec.index_mut (List Usize) slots (Usize.ofInt 0)
-    let l0 ← get_elem_mut_loop_back x l ret0
-    Vec.index_mut_back (List Usize) slots (Usize.ofInt 0) l0
-
-/- [loops::get_elem_shared]: loop 0: forward function -/
-divergent def get_elem_shared_loop
-  (x : Usize) (ls : List Usize) : Result Usize :=
-  match ls with
-  | List.Cons y tl => if y = x
-                      then Result.ret y
-                      else get_elem_shared_loop x tl
-  | List.Nil => Result.fail Error.panic
-
-/- [loops::get_elem_shared]: forward function -/
-def get_elem_shared (slots : Vec (List Usize)) (x : Usize) : Result Usize :=
-  do
-    let l ← Vec.index_shared (List Usize) slots (Usize.ofInt 0)
-    get_elem_shared_loop x l
-
-/- [loops::id_mut]: forward function -/
-def id_mut (T : Type) (ls : List T) : Result (List T) :=
-  Result.ret ls
-
-/- [loops::id_mut]: backward function 0 -/
-def id_mut_back (T : Type) (ls : List T) (ret0 : List T) : Result (List T) :=
-  Result.ret ret0
-
-/- [loops::id_shared]: forward function -/
-def id_shared (T : Type) (ls : List T) : Result (List T) :=
-  Result.ret ls
-
-/- [loops::list_nth_mut_loop_with_id]: loop 0: forward function -/
-divergent def list_nth_mut_loop_with_id_loop
-  (T : Type) (i : U32) (ls : List T) : Result T :=
-  match ls with
-  | List.Cons x tl =>
-    if i = (U32.ofInt 0)
-    then Result.ret x
-    else do
-           let i0 ← i - (U32.ofInt 1)
-           list_nth_mut_loop_with_id_loop T i0 tl
-  | List.Nil => Result.fail Error.panic
-
-/- [loops::list_nth_mut_loop_with_id]: forward function -/
-def list_nth_mut_loop_with_id (T : Type) (ls : List T) (i : U32) : Result T :=
-  do
-    let ls0 ← id_mut T ls
-    list_nth_mut_loop_with_id_loop T i ls0
-
-/- [loops::list_nth_mut_loop_with_id]: loop 0: backward function 0 -/
-divergent def list_nth_mut_loop_with_id_loop_back
-  (T : Type) (i : U32) (ls : List T) (ret0 : T) : Result (List T) :=
-  match ls with
-  | List.Cons x tl =>
-    if i = (U32.ofInt 0)
-    then Result.ret (List.Cons ret0 tl)
-    else
-      do
-        let i0 ← i - (U32.ofInt 1)
-        let tl0 ← list_nth_mut_loop_with_id_loop_back T i0 tl ret0
-        Result.ret (List.Cons x tl0)
-  | List.Nil => Result.fail Error.panic
-
-/- [loops::list_nth_mut_loop_with_id]: backward function 0 -/
-def list_nth_mut_loop_with_id_back
-  (T : Type) (ls : List T) (i : U32) (ret0 : T) : Result (List T) :=
-  do
-    let ls0 ← id_mut T ls
-    let l ← list_nth_mut_loop_with_id_loop_back T i ls0 ret0
-    id_mut_back T ls l
-
-/- [loops::list_nth_shared_loop_with_id]: loop 0: forward function -/
-divergent def list_nth_shared_loop_with_id_loop
-  (T : Type) (i : U32) (ls : List T) : Result T :=
-  match ls with
-  | List.Cons x tl =>
-    if i = (U32.ofInt 0)
-    then Result.ret x
-    else
-      do
-        let i0 ← i - (U32.ofInt 1)
-        list_nth_shared_loop_with_id_loop T i0 tl
-  | List.Nil => Result.fail Error.panic
-
-/- [loops::list_nth_shared_loop_with_id]: forward function -/
-def list_nth_shared_loop_with_id
-  (T : Type) (ls : List T) (i : U32) : Result T :=
-  do
-    let ls0 ← id_shared T ls
-    list_nth_shared_loop_with_id_loop T i ls0
-
-/- [loops::list_nth_mut_loop_pair]: loop 0: forward function -/
-divergent def list_nth_mut_loop_pair_loop
-  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
-  match ls0 with
-  | List.Cons x0 tl0 =>
-    match ls1 with
-    | List.Cons x1 tl1 =>
-      if i = (U32.ofInt 0)
-      then Result.ret (x0, x1)
-      else
-        do
-          let i0 ← i - (U32.ofInt 1)
-          list_nth_mut_loop_pair_loop T tl0 tl1 i0
-    | List.Nil => Result.fail Error.panic
-  | List.Nil => Result.fail Error.panic
-
-/- [loops::list_nth_mut_loop_pair]: forward function -/
-def list_nth_mut_loop_pair
-  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
-  list_nth_mut_loop_pair_loop T ls0 ls1 i
-
-/- [loops::list_nth_mut_loop_pair]: loop 0: backward function 0 -/
-divergent def list_nth_mut_loop_pair_loop_back'a
-  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret0 : T) :
-  Result (List T)
-  :=
-  match ls0 with
-  | List.Cons x0 tl0 =>
-    match ls1 with
-    | List.Cons x1 tl1 =>
-      if i = (U32.ofInt 0)
-      then Result.ret (List.Cons ret0 tl0)
-      else
-        do
-          let i0 ← i - (U32.ofInt 1)
-          let tl00 ← list_nth_mut_loop_pair_loop_back'a T tl0 tl1 i0 ret0
-          Result.ret (List.Cons x0 tl00)
-    | List.Nil => Result.fail Error.panic
-  | List.Nil => Result.fail Error.panic
-
-/- [loops::list_nth_mut_loop_pair]: backward function 0 -/
-def list_nth_mut_loop_pair_back'a
-  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret0 : T) :
-  Result (List T)
-  :=
-  list_nth_mut_loop_pair_loop_back'a T ls0 ls1 i ret0
-
-/- [loops::list_nth_mut_loop_pair]: loop 0: backward function 1 -/
-divergent def list_nth_mut_loop_pair_loop_back'b
-  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret0 : T) :
-  Result (List T)
-  :=
-  match ls0 with
-  | List.Cons x0 tl0 =>
-    match ls1 with
-    | List.Cons x1 tl1 =>
-      if i = (U32.ofInt 0)
-      then Result.ret (List.Cons ret0 tl1)
-      else
-        do
-          let i0 ← i - (U32.ofInt 1)
-          let tl10 ← list_nth_mut_loop_pair_loop_back'b T tl0 tl1 i0 ret0
-          Result.ret (List.Cons x1 tl10)
-    | List.Nil => Result.fail Error.panic
-  | List.Nil => Result.fail Error.panic
-
-/- [loops::list_nth_mut_loop_pair]: backward function 1 -/
-def list_nth_mut_loop_pair_back'b
-  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret0 : T) :
-  Result (List T)
-  :=
-  list_nth_mut_loop_pair_loop_back'b T ls0 ls1 i ret0
-
-/- [loops::list_nth_shared_loop_pair]: loop 0: forward function -/
-divergent def list_nth_shared_loop_pair_loop
-  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
-  match ls0 with
-  | List.Cons x0 tl0 =>
-    match ls1 with
-    | List.Cons x1 tl1 =>
-      if i = (U32.ofInt 0)
-      then Result.ret (x0, x1)
-      else
-        do
-          let i0 ← i - (U32.ofInt 1)
-          list_nth_shared_loop_pair_loop T tl0 tl1 i0
-    | List.Nil => Result.fail Error.panic
-  | List.Nil => Result.fail Error.panic
-
-/- [loops::list_nth_shared_loop_pair]: forward function -/
-def list_nth_shared_loop_pair
-  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
-  list_nth_shared_loop_pair_loop T ls0 ls1 i
-
-/- [loops::list_nth_mut_loop_pair_merge]: loop 0: forward function -/
-divergent def list_nth_mut_loop_pair_merge_loop
-  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
-  match ls0 with
-  | List.Cons x0 tl0 =>
-    match ls1 with
-    | List.Cons x1 tl1 =>
-      if i = (U32.ofInt 0)
-      then Result.ret (x0, x1)
-      else
-        do
-          let i0 ← i - (U32.ofInt 1)
-          list_nth_mut_loop_pair_merge_loop T tl0 tl1 i0
-    | List.Nil => Result.fail Error.panic
-  | List.Nil => Result.fail Error.panic
-
-/- [loops::list_nth_mut_loop_pair_merge]: forward function -/
-def list_nth_mut_loop_pair_merge
-  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
-  list_nth_mut_loop_pair_merge_loop T ls0 ls1 i
-
-/- [loops::list_nth_mut_loop_pair_merge]: loop 0: backward function 0 -/
-divergent def list_nth_mut_loop_pair_merge_loop_back
-  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret0 : (T × T)) :
-  Result ((List T) × (List T))
-  :=
-  match ls0 with
-  | List.Cons x0 tl0 =>
-    match ls1 with
-    | List.Cons x1 tl1 =>
-      if i = (U32.ofInt 0)
-      then let (t, t0) := ret0
-           Result.ret (List.Cons t tl0, List.Cons t0 tl1)
-      else
-        do
-          let i0 ← i - (U32.ofInt 1)
-          let (tl00, tl10) ←
-            list_nth_mut_loop_pair_merge_loop_back T tl0 tl1 i0 ret0
-          Result.ret (List.Cons x0 tl00, List.Cons x1 tl10)
-    | List.Nil => Result.fail Error.panic
-  | List.Nil => Result.fail Error.panic
-
-/- [loops::list_nth_mut_loop_pair_merge]: backward function 0 -/
-def list_nth_mut_loop_pair_merge_back
-  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret0 : (T × T)) :
-  Result ((List T) × (List T))
-  :=
-  list_nth_mut_loop_pair_merge_loop_back T ls0 ls1 i ret0
-
-/- [loops::list_nth_shared_loop_pair_merge]: loop 0: forward function -/
-divergent def list_nth_shared_loop_pair_merge_loop
-  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
-  match ls0 with
-  | List.Cons x0 tl0 =>
-    match ls1 with
-    | List.Cons x1 tl1 =>
-      if i = (U32.ofInt 0)
-      then Result.ret (x0, x1)
-      else
-        do
-          let i0 ← i - (U32.ofInt 1)
-          list_nth_shared_loop_pair_merge_loop T tl0 tl1 i0
-    | List.Nil => Result.fail Error.panic
-  | List.Nil => Result.fail Error.panic
-
-/- [loops::list_nth_shared_loop_pair_merge]: forward function -/
-def list_nth_shared_loop_pair_merge
-  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
-  list_nth_shared_loop_pair_merge_loop T ls0 ls1 i
-
-/- [loops::list_nth_mut_shared_loop_pair]: loop 0: forward function -/
-divergent def list_nth_mut_shared_loop_pair_loop
-  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
-  match ls0 with
-  | List.Cons x0 tl0 =>
-    match ls1 with
-    | List.Cons x1 tl1 =>
-      if i = (U32.ofInt 0)
-      then Result.ret (x0, x1)
-      else
-        do
-          let i0 ← i - (U32.ofInt 1)
-          list_nth_mut_shared_loop_pair_loop T tl0 tl1 i0
-    | List.Nil => Result.fail Error.panic
-  | List.Nil => Result.fail Error.panic
-
-/- [loops::list_nth_mut_shared_loop_pair]: forward function -/
-def list_nth_mut_shared_loop_pair
-  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
-  list_nth_mut_shared_loop_pair_loop T ls0 ls1 i
-
-/- [loops::list_nth_mut_shared_loop_pair]: loop 0: backward function 0 -/
-divergent def list_nth_mut_shared_loop_pair_loop_back
-  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret0 : T) :
-  Result (List T)
-  :=
-  match ls0 with
-  | List.Cons x0 tl0 =>
-    match ls1 with
-    | List.Cons x1 tl1 =>
-      if i = (U32.ofInt 0)
-      then Result.ret (List.Cons ret0 tl0)
-      else
-        do
-          let i0 ← i - (U32.ofInt 1)
-          let tl00 ←
-            list_nth_mut_shared_loop_pair_loop_back T tl0 tl1 i0 ret0
-          Result.ret (List.Cons x0 tl00)
-    | List.Nil => Result.fail Error.panic
-  | List.Nil => Result.fail Error.panic
-
-/- [loops::list_nth_mut_shared_loop_pair]: backward function 0 -/
-def list_nth_mut_shared_loop_pair_back
-  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret0 : T) :
-  Result (List T)
-  :=
-  list_nth_mut_shared_loop_pair_loop_back T ls0 ls1 i ret0
-
-/- [loops::list_nth_mut_shared_loop_pair_merge]: loop 0: forward function -/
-divergent def list_nth_mut_shared_loop_pair_merge_loop
-  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
-  match ls0 with
-  | List.Cons x0 tl0 =>
-    match ls1 with
-    | List.Cons x1 tl1 =>
-      if i = (U32.ofInt 0)
-      then Result.ret (x0, x1)
-      else
-        do
-          let i0 ← i - (U32.ofInt 1)
-          list_nth_mut_shared_loop_pair_merge_loop T tl0 tl1 i0
-    | List.Nil => Result.fail Error.panic
-  | List.Nil => Result.fail Error.panic
-
-/- [loops::list_nth_mut_shared_loop_pair_merge]: forward function -/
-def list_nth_mut_shared_loop_pair_merge
-  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
-  list_nth_mut_shared_loop_pair_merge_loop T ls0 ls1 i
-
-/- [loops::list_nth_mut_shared_loop_pair_merge]: loop 0: backward function 0 -/
-divergent def list_nth_mut_shared_loop_pair_merge_loop_back
-  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret0 : T) :
-  Result (List T)
-  :=
-  match ls0 with
-  | List.Cons x0 tl0 =>
-    match ls1 with
-    | List.Cons x1 tl1 =>
-      if i = (U32.ofInt 0)
-      then Result.ret (List.Cons ret0 tl0)
-      else
-        do
-          let i0 ← i - (U32.ofInt 1)
-          let tl00 ←
-            list_nth_mut_shared_loop_pair_merge_loop_back T tl0 tl1 i0 ret0
-          Result.ret (List.Cons x0 tl00)
-    | List.Nil => Result.fail Error.panic
-  | List.Nil => Result.fail Error.panic
-
-/- [loops::list_nth_mut_shared_loop_pair_merge]: backward function 0 -/
-def list_nth_mut_shared_loop_pair_merge_back
-  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret0 : T) :
-  Result (List T)
-  :=
-  list_nth_mut_shared_loop_pair_merge_loop_back T ls0 ls1 i ret0
-
-/- [loops::list_nth_shared_mut_loop_pair]: loop 0: forward function -/
-divergent def list_nth_shared_mut_loop_pair_loop
-  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
-  match ls0 with
-  | List.Cons x0 tl0 =>
-    match ls1 with
-    | List.Cons x1 tl1 =>
-      if i = (U32.ofInt 0)
-      then Result.ret (x0, x1)
-      else
-        do
-          let i0 ← i - (U32.ofInt 1)
-          list_nth_shared_mut_loop_pair_loop T tl0 tl1 i0
-    | List.Nil => Result.fail Error.panic
-  | List.Nil => Result.fail Error.panic
-
-/- [loops::list_nth_shared_mut_loop_pair]: forward function -/
-def list_nth_shared_mut_loop_pair
-  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
-  list_nth_shared_mut_loop_pair_loop T ls0 ls1 i
-
-/- [loops::list_nth_shared_mut_loop_pair]: loop 0: backward function 1 -/
-divergent def list_nth_shared_mut_loop_pair_loop_back
-  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret0 : T) :
-  Result (List T)
-  :=
-  match ls0 with
-  | List.Cons x0 tl0 =>
-    match ls1 with
-    | List.Cons x1 tl1 =>
-      if i = (U32.ofInt 0)
-      then Result.ret (List.Cons ret0 tl1)
-      else
-        do
-          let i0 ← i - (U32.ofInt 1)
-          let tl10 ←
-            list_nth_shared_mut_loop_pair_loop_back T tl0 tl1 i0 ret0
-          Result.ret (List.Cons x1 tl10)
-    | List.Nil => Result.fail Error.panic
-  | List.Nil => Result.fail Error.panic
-
-/- [loops::list_nth_shared_mut_loop_pair]: backward function 1 -/
-def list_nth_shared_mut_loop_pair_back
-  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret0 : T) :
-  Result (List T)
-  :=
-  list_nth_shared_mut_loop_pair_loop_back T ls0 ls1 i ret0
-
-/- [loops::list_nth_shared_mut_loop_pair_merge]: loop 0: forward function -/
-divergent def list_nth_shared_mut_loop_pair_merge_loop
-  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
-  match ls0 with
-  | List.Cons x0 tl0 =>
-    match ls1 with
-    | List.Cons x1 tl1 =>
-      if i = (U32.ofInt 0)
-      then Result.ret (x0, x1)
-      else
-        do
-          let i0 ← i - (U32.ofInt 1)
-          list_nth_shared_mut_loop_pair_merge_loop T tl0 tl1 i0
-    | List.Nil => Result.fail Error.panic
-  | List.Nil => Result.fail Error.panic
-
-/- [loops::list_nth_shared_mut_loop_pair_merge]: forward function -/
-def list_nth_shared_mut_loop_pair_merge
-  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
-  list_nth_shared_mut_loop_pair_merge_loop T ls0 ls1 i
-
-/- [loops::list_nth_shared_mut_loop_pair_merge]: loop 0: backward function 0 -/
-divergent def list_nth_shared_mut_loop_pair_merge_loop_back
-  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret0 : T) :
-  Result (List T)
-  :=
-  match ls0 with
-  | List.Cons x0 tl0 =>
-    match ls1 with
-    | List.Cons x1 tl1 =>
-      if i = (U32.ofInt 0)
-      then Result.ret (List.Cons ret0 tl1)
-      else
-        do
-          let i0 ← i - (U32.ofInt 1)
-          let tl10 ←
-            list_nth_shared_mut_loop_pair_merge_loop_back T tl0 tl1 i0 ret0
-          Result.ret (List.Cons x1 tl10)
-    | List.Nil => Result.fail Error.panic
-  | List.Nil => Result.fail Error.panic
-
-/- [loops::list_nth_shared_mut_loop_pair_merge]: backward function 0 -/
-def list_nth_shared_mut_loop_pair_merge_back
-  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret0 : T) :
-  Result (List T)
-  :=
-  list_nth_shared_mut_loop_pair_merge_loop_back T ls0 ls1 i ret0
-
-end loops
diff --git a/tests/lean/Loops/Types.lean b/tests/lean/Loops/Types.lean
deleted file mode 100644
index 018af901..00000000
--- a/tests/lean/Loops/Types.lean
+++ /dev/null
@@ -1,13 +0,0 @@
--- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
--- [loops]: type definitions
-import Base
-open Primitives
-
-namespace loops
-
-/- [loops::List] -/
-inductive List (T : Type) :=
-| Cons : T → List T → List T
-| Nil : List T
-
-end loops
diff --git a/tests/lean/NoNestedBorrows.lean b/tests/lean/NoNestedBorrows.lean
index 884e62c4..c4a6a265 100644
--- a/tests/lean/NoNestedBorrows.lean
+++ b/tests/lean/NoNestedBorrows.lean
@@ -54,12 +54,24 @@ def div_test (x : U32) (y : U32) : Result U32 :=
 
 /- [no_nested_borrows::div_test1]: forward function -/
 def div_test1 (x : U32) : Result U32 :=
-  x / (U32.ofInt 2)
+  x / 2#u32
 
 /- [no_nested_borrows::rem_test]: forward function -/
 def rem_test (x : U32) (y : U32) : Result U32 :=
   x % y
 
+/- [no_nested_borrows::mul_test]: forward function -/
+def mul_test (x : U32) (y : U32) : Result U32 :=
+  x * y
+
+/- [no_nested_borrows::CONST0] -/
+def const0_body : Result Usize := 1#usize + 1#usize
+def const0_c : Usize := eval_global const0_body (by simp)
+
+/- [no_nested_borrows::CONST1] -/
+def const1_body : Result Usize := 2#usize * 2#usize
+def const1_c : Usize := eval_global const1_body (by simp)
+
 /- [no_nested_borrows::cast_test]: forward function -/
 def cast_test (x : U32) : Result I32 :=
   Scalar.cast .I32 x
@@ -67,7 +79,7 @@ def cast_test (x : U32) : Result I32 :=
 /- [no_nested_borrows::test2]: forward function -/
 def test2 : Result Unit :=
   do
-    let _ ← (U32.ofInt 23) + (U32.ofInt 44)
+    let _ ← 23#u32 + 44#u32
     Result.ret ()
 
 /- Unit test for [no_nested_borrows::test2] -/
@@ -82,10 +94,10 @@ def get_max (x : U32) (y : U32) : Result U32 :=
 /- [no_nested_borrows::test3]: forward function -/
 def test3 : Result Unit :=
   do
-    let x ← get_max (U32.ofInt 4) (U32.ofInt 3)
-    let y ← get_max (U32.ofInt 10) (U32.ofInt 11)
+    let x ← get_max 4#u32 3#u32
+    let y ← get_max 10#u32 11#u32
     let z ← x + y
-    if not (z = (U32.ofInt 15))
+    if not (z = 15#u32)
     then Result.fail Error.panic
     else Result.ret ()
 
@@ -95,8 +107,8 @@ def test3 : Result Unit :=
 /- [no_nested_borrows::test_neg1]: forward function -/
 def test_neg1 : Result Unit :=
   do
-    let y ← - (I32.ofInt 3)
-    if not (y = (I32.ofInt (-(3:Int))))
+    let y ← - 3#i32
+    if not (y = (-(3:Int))#i32)
     then Result.fail Error.panic
     else Result.ret ()
 
@@ -105,7 +117,7 @@ def test_neg1 : Result Unit :=
 
 /- [no_nested_borrows::refs_test1]: forward function -/
 def refs_test1 : Result Unit :=
-  if not ((I32.ofInt 1) = (I32.ofInt 1))
+  if not (1#i32 = 1#i32)
   then Result.fail Error.panic
   else Result.ret ()
 
@@ -114,16 +126,16 @@ def refs_test1 : Result Unit :=
 
 /- [no_nested_borrows::refs_test2]: forward function -/
 def refs_test2 : Result Unit :=
-  if not ((I32.ofInt 2) = (I32.ofInt 2))
+  if not (2#i32 = 2#i32)
   then Result.fail Error.panic
   else
-    if not ((I32.ofInt 0) = (I32.ofInt 0))
+    if not (0#i32 = 0#i32)
     then Result.fail Error.panic
     else
-      if not ((I32.ofInt 2) = (I32.ofInt 2))
+      if not (2#i32 = 2#i32)
       then Result.fail Error.panic
       else
-        if not ((I32.ofInt 2) = (I32.ofInt 2))
+        if not (2#i32 = 2#i32)
         then Result.fail Error.panic
         else Result.ret ()
 
@@ -139,9 +151,9 @@ def test_list1 : Result Unit :=
 
 /- [no_nested_borrows::test_box1]: forward function -/
 def test_box1 : Result Unit :=
-  let b := (I32.ofInt 1)
+  let b := 1#i32
   let x := b
-  if not (x = (I32.ofInt 1))
+  if not (x = 1#i32)
   then Result.fail Error.panic
   else Result.ret ()
 
@@ -167,8 +179,8 @@ def test_panic (b : Bool) : Result Unit :=
 /- [no_nested_borrows::test_copy_int]: forward function -/
 def test_copy_int : Result Unit :=
   do
-    let y ← copy_int (I32.ofInt 0)
-    if not ((I32.ofInt 0) = y)
+    let y ← copy_int 0#i32
+    if not (0#i32 = y)
     then Result.fail Error.panic
     else Result.ret ()
 
@@ -185,7 +197,7 @@ def is_cons (T : Type) (l : List T) : Result Bool :=
 def test_is_cons : Result Unit :=
   do
     let l := List.Nil
-    let b ← is_cons I32 (List.Cons (I32.ofInt 0) l)
+    let b ← is_cons I32 (List.Cons 0#i32 l)
     if not b
     then Result.fail Error.panic
     else Result.ret ()
@@ -203,9 +215,9 @@ def split_list (T : Type) (l : List T) : Result (T × (List T)) :=
 def test_split_list : Result Unit :=
   do
     let l := List.Nil
-    let p ← split_list I32 (List.Cons (I32.ofInt 0) l)
+    let p ← split_list I32 (List.Cons 0#i32 l)
     let (hd, _) := p
-    if not (hd = (I32.ofInt 0))
+    if not (hd = 0#i32)
     then Result.fail Error.panic
     else Result.ret ()
 
@@ -228,19 +240,18 @@ def choose_back
 /- [no_nested_borrows::choose_test]: forward function -/
 def choose_test : Result Unit :=
   do
-    let z ← choose I32 true (I32.ofInt 0) (I32.ofInt 0)
-    let z0 ← z + (I32.ofInt 1)
-    if not (z0 = (I32.ofInt 1))
+    let z ← choose I32 true 0#i32 0#i32
+    let z0 ← z + 1#i32
+    if not (z0 = 1#i32)
     then Result.fail Error.panic
     else
       do
-        let (x, y) ← choose_back I32 true (I32.ofInt 0) (I32.ofInt 0) z0
-        if not (x = (I32.ofInt 1))
+        let (x, y) ← choose_back I32 true 0#i32 0#i32 z0
+        if not (x = 1#i32)
         then Result.fail Error.panic
-        else
-          if not (y = (I32.ofInt 0))
-          then Result.fail Error.panic
-          else Result.ret ()
+        else if not (y = 0#i32)
+             then Result.fail Error.panic
+             else Result.ret ()
 
 /- Unit test for [no_nested_borrows::choose_test] -/
 #assert (choose_test == .ret ())
@@ -268,17 +279,17 @@ divergent def list_length (T : Type) (l : List T) : Result U32 :=
   match l with
   | List.Cons t l1 => do
                         let i ← list_length T l1
-                        (U32.ofInt 1) + i
-  | List.Nil => Result.ret (U32.ofInt 0)
+                        1#u32 + i
+  | List.Nil => Result.ret 0#u32
 
 /- [no_nested_borrows::list_nth_shared]: forward function -/
 divergent def list_nth_shared (T : Type) (l : List T) (i : U32) : Result T :=
   match l with
   | List.Cons x tl =>
-    if i = (U32.ofInt 0)
+    if i = 0#u32
     then Result.ret x
     else do
-           let i0 ← i - (U32.ofInt 1)
+           let i0 ← i - 1#u32
            list_nth_shared T tl i0
   | List.Nil => Result.fail Error.panic
 
@@ -286,10 +297,10 @@ divergent def list_nth_shared (T : Type) (l : List T) (i : U32) : Result T :=
 divergent def list_nth_mut (T : Type) (l : List T) (i : U32) : Result T :=
   match l with
   | List.Cons x tl =>
-    if i = (U32.ofInt 0)
+    if i = 0#u32
     then Result.ret x
     else do
-           let i0 ← i - (U32.ofInt 1)
+           let i0 ← i - 1#u32
            list_nth_mut T tl i0
   | List.Nil => Result.fail Error.panic
 
@@ -298,11 +309,11 @@ divergent def list_nth_mut_back
   (T : Type) (l : List T) (i : U32) (ret0 : T) : Result (List T) :=
   match l with
   | List.Cons x tl =>
-    if i = (U32.ofInt 0)
+    if i = 0#u32
     then Result.ret (List.Cons ret0 tl)
     else
       do
-        let i0 ← i - (U32.ofInt 1)
+        let i0 ← i - 1#u32
         let tl0 ← list_nth_mut_back T tl i0 ret0
         Result.ret (List.Cons x tl0)
   | List.Nil => Result.fail Error.panic
@@ -317,54 +328,49 @@ divergent def list_rev_aux
 /- [no_nested_borrows::list_rev]: merged forward/backward function
    (there is a single backward function, and the forward function returns ()) -/
 def list_rev (T : Type) (l : List T) : Result (List T) :=
-  let li := mem.replace (List T) l List.Nil
+  let li := core.mem.replace (List T) l List.Nil
   list_rev_aux T li List.Nil
 
 /- [no_nested_borrows::test_list_functions]: forward function -/
 def test_list_functions : Result Unit :=
   do
     let l := List.Nil
-    let l0 := List.Cons (I32.ofInt 2) l
-    let l1 := List.Cons (I32.ofInt 1) l0
-    let i ← list_length I32 (List.Cons (I32.ofInt 0) l1)
-    if not (i = (U32.ofInt 3))
+    let l0 := List.Cons 2#i32 l
+    let l1 := List.Cons 1#i32 l0
+    let i ← list_length I32 (List.Cons 0#i32 l1)
+    if not (i = 3#u32)
     then Result.fail Error.panic
     else
       do
-        let i0 ←
-          list_nth_shared I32 (List.Cons (I32.ofInt 0) l1) (U32.ofInt 0)
-        if not (i0 = (I32.ofInt 0))
+        let i0 ← list_nth_shared I32 (List.Cons 0#i32 l1) 0#u32
+        if not (i0 = 0#i32)
         then Result.fail Error.panic
         else
           do
-            let i1 ←
-              list_nth_shared I32 (List.Cons (I32.ofInt 0) l1) (U32.ofInt 1)
-            if not (i1 = (I32.ofInt 1))
+            let i1 ← list_nth_shared I32 (List.Cons 0#i32 l1) 1#u32
+            if not (i1 = 1#i32)
             then Result.fail Error.panic
             else
               do
-                let i2 ←
-                  list_nth_shared I32 (List.Cons (I32.ofInt 0) l1)
-                    (U32.ofInt 2)
-                if not (i2 = (I32.ofInt 2))
+                let i2 ← list_nth_shared I32 (List.Cons 0#i32 l1) 2#u32
+                if not (i2 = 2#i32)
                 then Result.fail Error.panic
                 else
                   do
                     let ls ←
-                      list_nth_mut_back I32 (List.Cons (I32.ofInt 0) l1)
-                        (U32.ofInt 1) (I32.ofInt 3)
-                    let i3 ← list_nth_shared I32 ls (U32.ofInt 0)
-                    if not (i3 = (I32.ofInt 0))
+                      list_nth_mut_back I32 (List.Cons 0#i32 l1) 1#u32 3#i32
+                    let i3 ← list_nth_shared I32 ls 0#u32
+                    if not (i3 = 0#i32)
                     then Result.fail Error.panic
                     else
                       do
-                        let i4 ← list_nth_shared I32 ls (U32.ofInt 1)
-                        if not (i4 = (I32.ofInt 3))
+                        let i4 ← list_nth_shared I32 ls 1#u32
+                        if not (i4 = 3#i32)
                         then Result.fail Error.panic
                         else
                           do
-                            let i5 ← list_nth_shared I32 ls (U32.ofInt 2)
-                            if not (i5 = (I32.ofInt 2))
+                            let i5 ← list_nth_shared I32 ls 2#u32
+                            if not (i5 = 2#i32)
                             then Result.fail Error.panic
                             else Result.ret ()
 
@@ -427,15 +433,15 @@ structure StructWithTuple (T1 T2 : Type) where
 
 /- [no_nested_borrows::new_tuple1]: forward function -/
 def new_tuple1 : Result (StructWithTuple U32 U32) :=
-  Result.ret { p := ((U32.ofInt 1), (U32.ofInt 2)) }
+  Result.ret { p := (1#u32, 2#u32) }
 
 /- [no_nested_borrows::new_tuple2]: forward function -/
 def new_tuple2 : Result (StructWithTuple I16 I16) :=
-  Result.ret { p := ((I16.ofInt 1), (I16.ofInt 2)) }
+  Result.ret { p := (1#i16, 2#i16) }
 
 /- [no_nested_borrows::new_tuple3]: forward function -/
 def new_tuple3 : Result (StructWithTuple U64 I64) :=
-  Result.ret { p := ((U64.ofInt 1), (I64.ofInt 2)) }
+  Result.ret { p := (1#u64, 2#i64) }
 
 /- [no_nested_borrows::StructWithPair] -/
 structure StructWithPair (T1 T2 : Type) where
@@ -443,31 +449,31 @@ structure StructWithPair (T1 T2 : Type) where
 
 /- [no_nested_borrows::new_pair1]: forward function -/
 def new_pair1 : Result (StructWithPair U32 U32) :=
-  Result.ret { p := { x := (U32.ofInt 1), y := (U32.ofInt 2) } }
+  Result.ret { p := { x := 1#u32, y := 2#u32 } }
 
 /- [no_nested_borrows::test_constants]: forward function -/
 def test_constants : Result Unit :=
   do
     let swt ← new_tuple1
     let (i, _) := swt.p
-    if not (i = (U32.ofInt 1))
+    if not (i = 1#u32)
     then Result.fail Error.panic
     else
       do
         let swt0 ← new_tuple2
         let (i0, _) := swt0.p
-        if not (i0 = (I16.ofInt 1))
+        if not (i0 = 1#i16)
         then Result.fail Error.panic
         else
           do
             let swt1 ← new_tuple3
             let (i1, _) := swt1.p
-            if not (i1 = (U64.ofInt 1))
+            if not (i1 = 1#u64)
             then Result.fail Error.panic
             else
               do
                 let swp ← new_pair1
-                if not (swp.p.x = (U32.ofInt 1))
+                if not (swp.p.x = 1#u32)
                 then Result.fail Error.panic
                 else Result.ret ()
 
@@ -484,29 +490,29 @@ def test_weird_borrows1 : Result Unit :=
 /- [no_nested_borrows::test_mem_replace]: merged forward/backward function
    (there is a single backward function, and the forward function returns ()) -/
 def test_mem_replace (px : U32) : Result U32 :=
-  let y := mem.replace U32 px (U32.ofInt 1)
-  if not (y = (U32.ofInt 0))
+  let y := core.mem.replace U32 px 1#u32
+  if not (y = 0#u32)
   then Result.fail Error.panic
-  else Result.ret (U32.ofInt 2)
+  else Result.ret 2#u32
 
 /- [no_nested_borrows::test_shared_borrow_bool1]: forward function -/
 def test_shared_borrow_bool1 (b : Bool) : Result U32 :=
   if b
-  then Result.ret (U32.ofInt 0)
-  else Result.ret (U32.ofInt 1)
+  then Result.ret 0#u32
+  else Result.ret 1#u32
 
 /- [no_nested_borrows::test_shared_borrow_bool2]: forward function -/
 def test_shared_borrow_bool2 : Result U32 :=
-  Result.ret (U32.ofInt 0)
+  Result.ret 0#u32
 
 /- [no_nested_borrows::test_shared_borrow_enum1]: forward function -/
 def test_shared_borrow_enum1 (l : List U32) : Result U32 :=
   match l with
-  | List.Cons i l0 => Result.ret (U32.ofInt 1)
-  | List.Nil => Result.ret (U32.ofInt 0)
+  | List.Cons i l0 => Result.ret 1#u32
+  | List.Nil => Result.ret 0#u32
 
 /- [no_nested_borrows::test_shared_borrow_enum2]: forward function -/
 def test_shared_borrow_enum2 : Result U32 :=
-  Result.ret (U32.ofInt 0)
+  Result.ret 0#u32
 
 end no_nested_borrows
diff --git a/tests/lean/Paper.lean b/tests/lean/Paper.lean
index c15c5e4b..ae4dd243 100644
--- a/tests/lean/Paper.lean
+++ b/tests/lean/Paper.lean
@@ -8,13 +8,13 @@ namespace paper
 /- [paper::ref_incr]: merged forward/backward function
    (there is a single backward function, and the forward function returns ()) -/
 def ref_incr (x : I32) : Result I32 :=
-  x + (I32.ofInt 1)
+  x + 1#i32
 
 /- [paper::test_incr]: forward function -/
 def test_incr : Result Unit :=
   do
-    let x ← ref_incr (I32.ofInt 0)
-    if not (x = (I32.ofInt 1))
+    let x ← ref_incr 0#i32
+    if not (x = 1#i32)
     then Result.fail Error.panic
     else Result.ret ()
 
@@ -37,19 +37,18 @@ def choose_back
 /- [paper::test_choose]: forward function -/
 def test_choose : Result Unit :=
   do
-    let z ← choose I32 true (I32.ofInt 0) (I32.ofInt 0)
-    let z0 ← z + (I32.ofInt 1)
-    if not (z0 = (I32.ofInt 1))
+    let z ← choose I32 true 0#i32 0#i32
+    let z0 ← z + 1#i32
+    if not (z0 = 1#i32)
     then Result.fail Error.panic
     else
       do
-        let (x, y) ← choose_back I32 true (I32.ofInt 0) (I32.ofInt 0) z0
-        if not (x = (I32.ofInt 1))
+        let (x, y) ← choose_back I32 true 0#i32 0#i32 z0
+        if not (x = 1#i32)
         then Result.fail Error.panic
-        else
-          if not (y = (I32.ofInt 0))
-          then Result.fail Error.panic
-          else Result.ret ()
+        else if not (y = 0#i32)
+             then Result.fail Error.panic
+             else Result.ret ()
 
 /- Unit test for [paper::test_choose] -/
 #assert (test_choose == .ret ())
@@ -63,10 +62,10 @@ inductive List (T : Type) :=
 divergent def list_nth_mut (T : Type) (l : List T) (i : U32) : Result T :=
   match l with
   | List.Cons x tl =>
-    if i = (U32.ofInt 0)
+    if i = 0#u32
     then Result.ret x
     else do
-           let i0 ← i - (U32.ofInt 1)
+           let i0 ← i - 1#u32
            list_nth_mut T tl i0
   | List.Nil => Result.fail Error.panic
 
@@ -75,11 +74,11 @@ divergent def list_nth_mut_back
   (T : Type) (l : List T) (i : U32) (ret0 : T) : Result (List T) :=
   match l with
   | List.Cons x tl =>
-    if i = (U32.ofInt 0)
+    if i = 0#u32
     then Result.ret (List.Cons ret0 tl)
     else
       do
-        let i0 ← i - (U32.ofInt 1)
+        let i0 ← i - 1#u32
         let tl0 ← list_nth_mut_back T tl i0 ret0
         Result.ret (List.Cons x tl0)
   | List.Nil => Result.fail Error.panic
@@ -90,20 +89,19 @@ divergent def sum (l : List I32) : Result I32 :=
   | List.Cons x tl => do
                         let i ← sum tl
                         x + i
-  | List.Nil => Result.ret (I32.ofInt 0)
+  | List.Nil => Result.ret 0#i32
 
 /- [paper::test_nth]: forward function -/
 def test_nth : Result Unit :=
   do
     let l := List.Nil
-    let l0 := List.Cons (I32.ofInt 3) l
-    let l1 := List.Cons (I32.ofInt 2) l0
-    let x ← list_nth_mut I32 (List.Cons (I32.ofInt 1) l1) (U32.ofInt 2)
-    let x0 ← x + (I32.ofInt 1)
-    let l2 ←
-      list_nth_mut_back I32 (List.Cons (I32.ofInt 1) l1) (U32.ofInt 2) x0
+    let l0 := List.Cons 3#i32 l
+    let l1 := List.Cons 2#i32 l0
+    let x ← list_nth_mut I32 (List.Cons 1#i32 l1) 2#u32
+    let x0 ← x + 1#i32
+    let l2 ← list_nth_mut_back I32 (List.Cons 1#i32 l1) 2#u32 x0
     let i ← sum l2
-    if not (i = (I32.ofInt 7))
+    if not (i = 7#i32)
     then Result.fail Error.panic
     else Result.ret ()
 
@@ -115,7 +113,7 @@ def call_choose (p : (U32 × U32)) : Result U32 :=
   do
     let (px, py) := p
     let pz ← choose U32 true px py
-    let pz0 ← pz + (U32.ofInt 1)
+    let pz0 ← pz + 1#u32
     let (px0, _) ← choose_back U32 true px py pz0
     Result.ret px0
 
diff --git a/tests/lean/Traits.lean b/tests/lean/Traits.lean
new file mode 100644
index 00000000..12e7eafa
--- /dev/null
+++ b/tests/lean/Traits.lean
@@ -0,0 +1,383 @@
+-- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
+-- [traits]
+import Base
+open Primitives
+
+namespace traits
+
+/- Trait declaration: [traits::BoolTrait] -/
+structure BoolTrait (Self : Type) where
+  get_bool : Self → Result Bool
+
+/- [traits::Bool::{0}::get_bool]: forward function -/
+def Bool.get_bool (self : Bool) : Result Bool :=
+  Result.ret self
+
+/- Trait implementation: [traits::Bool::{0}] -/
+def Bool.BoolTraitInst : BoolTrait Bool := {
+  get_bool := Bool.get_bool
+}
+
+/- [traits::BoolTrait::ret_true]: forward function -/
+def BoolTrait.ret_true
+  {Self : Type} (self_clause : BoolTrait Self) (self : Self) : Result Bool :=
+  Result.ret true
+
+/- [traits::test_bool_trait_bool]: forward function -/
+def test_bool_trait_bool (x : Bool) : Result Bool :=
+  do
+    let b ← Bool.get_bool x
+    if b
+    then BoolTrait.ret_true Bool.BoolTraitInst x
+    else Result.ret false
+
+/- [traits::Option::{1}::get_bool]: forward function -/
+def Option.get_bool (T : Type) (self : Option T) : Result Bool :=
+  match self with
+  | none => Result.ret false
+  | some t => Result.ret true
+
+/- Trait implementation: [traits::Option::{1}] -/
+def Option.BoolTraitInst (T : Type) : BoolTrait (Option T) := {
+  get_bool := Option.get_bool T
+}
+
+/- [traits::test_bool_trait_option]: forward function -/
+def test_bool_trait_option (T : Type) (x : Option T) : Result Bool :=
+  do
+    let b ← Option.get_bool T x
+    if b
+    then BoolTrait.ret_true (Option.BoolTraitInst T) x
+    else Result.ret false
+
+/- [traits::test_bool_trait]: forward function -/
+def test_bool_trait (T : Type) (inst : BoolTrait T) (x : T) : Result Bool :=
+  inst.get_bool x
+
+/- Trait declaration: [traits::ToU64] -/
+structure ToU64 (Self : Type) where
+  to_u64 : Self → Result U64
+
+/- [traits::u64::{2}::to_u64]: forward function -/
+def u64.to_u64 (self : U64) : Result U64 :=
+  Result.ret self
+
+/- Trait implementation: [traits::u64::{2}] -/
+def u64.ToU64Inst : ToU64 U64 := {
+  to_u64 := u64.to_u64
+}
+
+/- [traits::Tuple2::{3}::to_u64]: forward function -/
+def Tuple2.to_u64 (A : Type) (inst : ToU64 A) (self : (A × A)) : Result U64 :=
+  do
+    let (t, t0) := self
+    let i ← inst.to_u64 t
+    let i0 ← inst.to_u64 t0
+    i + i0
+
+/- Trait implementation: [traits::Tuple2::{3}] -/
+def Tuple2.ToU64Inst (A : Type) (inst : ToU64 A) : ToU64 (A × A) := {
+  to_u64 := Tuple2.to_u64 A inst
+}
+
+/- [traits::f]: forward function -/
+def f (T : Type) (inst : ToU64 T) (x : (T × T)) : Result U64 :=
+  Tuple2.to_u64 T inst x
+
+/- [traits::g]: forward function -/
+def g (T : Type) (inst : ToU64 (T × T)) (x : (T × T)) : Result U64 :=
+  inst.to_u64 x
+
+/- [traits::h0]: forward function -/
+def h0 (x : U64) : Result U64 :=
+  u64.to_u64 x
+
+/- [traits::Wrapper] -/
+structure Wrapper (T : Type) where
+  x : T
+
+/- [traits::Wrapper::{4}::to_u64]: forward function -/
+def Wrapper.to_u64
+  (T : Type) (inst : ToU64 T) (self : Wrapper T) : Result U64 :=
+  inst.to_u64 self.x
+
+/- Trait implementation: [traits::Wrapper::{4}] -/
+def Wrapper.ToU64Inst (T : Type) (inst : ToU64 T) : ToU64 (Wrapper T) := {
+  to_u64 := Wrapper.to_u64 T inst
+}
+
+/- [traits::h1]: forward function -/
+def h1 (x : Wrapper U64) : Result U64 :=
+  Wrapper.to_u64 U64 u64.ToU64Inst x
+
+/- [traits::h2]: forward function -/
+def h2 (T : Type) (inst : ToU64 T) (x : Wrapper T) : Result U64 :=
+  Wrapper.to_u64 T inst x
+
+/- Trait declaration: [traits::ToType] -/
+structure ToType (Self T : Type) where
+  to_type : Self → Result T
+
+/- [traits::u64::{5}::to_type]: forward function -/
+def u64.to_type (self : U64) : Result Bool :=
+  Result.ret (self > 0#u64)
+
+/- Trait implementation: [traits::u64::{5}] -/
+def u64.ToTypeInst : ToType U64 Bool := {
+  to_type := u64.to_type
+}
+
+/- Trait declaration: [traits::OfType] -/
+structure OfType (Self : Type) where
+  of_type : forall (T : Type) (inst : ToType T Self), T → Result Self
+
+/- [traits::h3]: forward function -/
+def h3
+  (T1 T2 : Type) (inst : OfType T1) (inst0 : ToType T2 T1) (y : T2) :
+  Result T1
+  :=
+  inst.of_type T2 inst0 y
+
+/- Trait declaration: [traits::OfTypeBis] -/
+structure OfTypeBis (Self T : Type) where
+  parent_clause_0 : ToType T Self
+  of_type : T → Result Self
+
+/- [traits::h4]: forward function -/
+def h4
+  (T1 T2 : Type) (inst : OfTypeBis T1 T2) (inst0 : ToType T2 T1) (y : T2) :
+  Result T1
+  :=
+  inst.of_type y
+
+/- [traits::TestType] -/
+structure TestType (T : Type) where
+  _0 : T
+
+/- [traits::TestType::{6}::test::TestType1] -/
+structure TestType.test.TestType1 where
+  _0 : U64
+
+/- Trait declaration: [traits::TestType::{6}::test::TestTrait] -/
+structure TestType.test.TestTrait (Self : Type) where
+  test : Self → Result Bool
+
+/- [traits::TestType::{6}::test::TestType1::{0}::test]: forward function -/
+def TestType.test.TestType1.test
+  (self : TestType.test.TestType1) : Result Bool :=
+  Result.ret (self._0 > 1#u64)
+
+/- Trait implementation: [traits::TestType::{6}::test::TestType1::{0}] -/
+def TestType.test.TestType1.TestTypetestTestTraitInst : TestType.test.TestTrait
+  TestType.test.TestType1 := {
+  test := TestType.test.TestType1.test
+}
+
+/- [traits::TestType::{6}::test]: forward function -/
+def TestType.test
+  (T : Type) (inst : ToU64 T) (self : TestType T) (x : T) : Result Bool :=
+  do
+    let x0 ← inst.to_u64 x
+    if x0 > 0#u64
+    then TestType.test.TestType1.test { _0 := 0#u64 }
+    else Result.ret false
+
+/- [traits::BoolWrapper] -/
+structure BoolWrapper where
+  _0 : Bool
+
+/- [traits::BoolWrapper::{7}::to_type]: forward function -/
+def BoolWrapper.to_type
+  (T : Type) (inst : ToType Bool T) (self : BoolWrapper) : Result T :=
+  inst.to_type self._0
+
+/- Trait implementation: [traits::BoolWrapper::{7}] -/
+def BoolWrapper.ToTypeInst (T : Type) (inst : ToType Bool T) : ToType
+  BoolWrapper T := {
+  to_type := BoolWrapper.to_type T inst
+}
+
+/- [traits::WithConstTy::LEN2] -/
+def with_const_ty_len2_body : Result Usize := Result.ret 32#usize
+def with_const_ty_len2_c : Usize :=
+  eval_global with_const_ty_len2_body (by simp)
+
+/- Trait declaration: [traits::WithConstTy] -/
+structure WithConstTy (Self : Type) (LEN : Usize) where
+  LEN1 : Usize
+  LEN2 : Usize
+  V : Type
+  W : Type
+  W_clause_0 : ToU64 W
+  f : W → Array U8 LEN → Result W
+
+/- [traits::Bool::{8}::LEN1] -/
+def bool_len1_body : Result Usize := Result.ret 12#usize
+def bool_len1_c : Usize := eval_global bool_len1_body (by simp)
+
+/- [traits::Bool::{8}::f]: merged forward/backward function
+   (there is a single backward function, and the forward function returns ()) -/
+def Bool.f (i : U64) (a : Array U8 32#usize) : Result U64 :=
+  Result.ret i
+
+/- Trait implementation: [traits::Bool::{8}] -/
+def Bool.WithConstTyInst : WithConstTy Bool 32#usize := {
+  LEN1 := bool_len1_c
+  LEN2 := with_const_ty_len2_c
+  V := U8
+  W := U64
+  W_clause_0 := u64.ToU64Inst
+  f := Bool.f
+}
+
+/- [traits::use_with_const_ty1]: forward function -/
+def use_with_const_ty1
+  (H : Type) (LEN : Usize) (inst : WithConstTy H LEN) : Result Usize :=
+  let i := inst.LEN1
+  Result.ret i
+
+/- [traits::use_with_const_ty2]: forward function -/
+def use_with_const_ty2
+  (H : Type) (LEN : Usize) (inst : WithConstTy H LEN) (w : inst.W) :
+  Result Unit
+  :=
+  Result.ret ()
+
+/- [traits::use_with_const_ty3]: forward function -/
+def use_with_const_ty3
+  (H : Type) (LEN : Usize) (inst : WithConstTy H LEN) (x : inst.W) :
+  Result U64
+  :=
+  inst.W_clause_0.to_u64 x
+
+/- [traits::test_where1]: forward function -/
+def test_where1 (T : Type) (_x : T) : Result Unit :=
+  Result.ret ()
+
+/- [traits::test_where2]: forward function -/
+def test_where2
+  (T : Type) (inst : WithConstTy T 32#usize) (_x : U32) : Result Unit :=
+  Result.ret ()
+
+/- [alloc::string::String] -/
+axiom alloc.string.String : Type
+
+/- Trait declaration: [traits::ParentTrait0] -/
+structure ParentTrait0 (Self : Type) where
+  W : Type
+  get_name : Self → Result alloc.string.String
+  get_w : Self → Result W
+
+/- Trait declaration: [traits::ParentTrait1] -/
+structure ParentTrait1 (Self : Type) where
+
+/- Trait declaration: [traits::ChildTrait] -/
+structure ChildTrait (Self : Type) where
+  parent_clause_0 : ParentTrait0 Self
+  parent_clause_1 : ParentTrait1 Self
+
+/- [traits::test_child_trait1]: forward function -/
+def test_child_trait1
+  (T : Type) (inst : ChildTrait T) (x : T) : Result alloc.string.String :=
+  inst.parent_clause_0.get_name x
+
+/- [traits::test_child_trait2]: forward function -/
+def test_child_trait2
+  (T : Type) (inst : ChildTrait T) (x : T) : Result inst.parent_clause_0.W :=
+  inst.parent_clause_0.get_w x
+
+/- [traits::order1]: forward function -/
+def order1
+  (T U : Type) (inst : ParentTrait0 T) (inst0 : ParentTrait0 U) :
+  Result Unit
+  :=
+  Result.ret ()
+
+/- Trait declaration: [traits::ChildTrait1] -/
+structure ChildTrait1 (Self : Type) where
+  parent_clause_0 : ParentTrait1 Self
+
+/- Trait implementation: [traits::usize::{9}] -/
+def usize.ParentTrait1Inst : ParentTrait1 Usize := {
+}
+
+/- Trait implementation: [traits::usize::{10}] -/
+def usize.ChildTrait1Inst : ChildTrait1 Usize := {
+  parent_clause_0 := usize.ParentTrait1Inst
+}
+
+/- Trait declaration: [traits::Iterator] -/
+structure Iterator (Self : Type) where
+  Item : Type
+
+/- Trait declaration: [traits::IntoIterator] -/
+structure IntoIterator (Self : Type) where
+  Item : Type
+  IntoIter : Type
+  IntoIter_clause_0 : Iterator IntoIter
+  into_iter : Self → Result IntoIter
+
+/- Trait declaration: [traits::FromResidual] -/
+structure FromResidual (Self T : Type) where
+
+/- Trait declaration: [traits::Try] -/
+structure Try (Self : Type) where
+  Residual : Type
+  parent_clause_0 : FromResidual Self Residual
+
+/- Trait declaration: [traits::WithTarget] -/
+structure WithTarget (Self : Type) where
+  Target : Type
+
+/- Trait declaration: [traits::ParentTrait2] -/
+structure ParentTrait2 (Self : Type) where
+  U : Type
+  U_clause_0 : WithTarget U
+
+/- Trait declaration: [traits::ChildTrait2] -/
+structure ChildTrait2 (Self : Type) where
+  parent_clause_0 : ParentTrait2 Self
+  convert : parent_clause_0.U → Result parent_clause_0.U_clause_0.Target
+
+/- Trait implementation: [traits::u32::{11}] -/
+def u32.WithTargetInst : WithTarget U32 := {
+  Target := U32
+}
+
+/- Trait implementation: [traits::u32::{12}] -/
+def u32.ParentTrait2Inst : ParentTrait2 U32 := {
+  U := U32
+  U_clause_0 := u32.WithTargetInst
+}
+
+/- [traits::u32::{13}::convert]: forward function -/
+def u32.convert (x : U32) : Result U32 :=
+  Result.ret x
+
+/- Trait implementation: [traits::u32::{13}] -/
+def u32.ChildTrait2Inst : ChildTrait2 U32 := {
+  parent_clause_0 := u32.ParentTrait2Inst
+  convert := u32.convert
+}
+
+/- [traits::incr_u32]: forward function -/
+def incr_u32 (x : U32) : Result U32 :=
+  x + 1#u32
+
+/- Trait declaration: [traits::CFnOnce] -/
+structure CFnOnce (Self Args : Type) where
+  Output : Type
+  call_once : Self → Args → Result Output
+
+/- Trait declaration: [traits::CFnMut] -/
+structure CFnMut (Self Args : Type) where
+  parent_clause_0 : CFnOnce Self Args
+  call_mut : Self → Args → Result parent_clause_0.Output
+  call_mut_back : Self → Args → parent_clause_0.Output → Result Self
+
+/- Trait declaration: [traits::CFn] -/
+structure CFn (Self Args : Type) where
+  parent_clause_0 : CFnMut Self Args
+  call_mut : Self → Args → Result parent_clause_0.parent_clause_0.Output
+
+end traits
diff --git a/tests/lean/lakefile.lean b/tests/lean/lakefile.lean
index 8acf6973..fef94971 100644
--- a/tests/lean/lakefile.lean
+++ b/tests/lean/lakefile.lean
@@ -19,3 +19,4 @@ package «tests» {}
 @[default_target] lean_lib paper
 @[default_target] lean_lib poloniusList
 @[default_target] lean_lib array
+@[default_target] lean_lib traits