Merge pull request #64 from AeneasVerif/son/merge_back

Merge the forward/backward functions

162 files changed, 20870 insertions, 10694 deletions

diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml
index 6b5aacf0..2039e65d 100644
--- a/.github/workflows/ci.yml
+++ b/.github/workflows/ci.yml
@@ -14,6 +14,7 @@ jobs:
       - run: nix build -L .#aeneas
       - 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-fstar-split
       - run: nix build -L .#checks.x86_64-linux.aeneas-verify-coq
       - run: nix build -L .#checks.x86_64-linux.aeneas-verify-hol4
       # Lean doesn't work with Nix
diff --git a/Makefile b/Makefile
index 2cce30d9..8d49a200 100644
--- a/Makefile
+++ b/Makefile
@@ -70,9 +70,11 @@ build-bin-dir: build-bin build-lib
 	mkdir -p bin
 	cp -f compiler/_build/default/main.exe bin/aeneas
 	cp -f compiler/_build/default/main.exe bin/aeneas.cmxs
-	mkdir -p bin/backends/fstar
+	mkdir -p bin/backends/fstar/split
+	mkdir -p bin/backends/fstar/merge
 	mkdir -p bin/backends/coq
-	cp -rf backends/fstar/*.fst* bin/backends/fstar/
+	cp -rf backends/fstar/split/*.fst* bin/backends/fstar/split/
+	cp -rf backends/fstar/merge/*.fst* bin/backends/fstar/merge/
 	cp -rf backends/coq/*.v bin/backends/coq/
 
 .PHONY: doc
@@ -254,14 +256,29 @@ testp-%: gen-llbcp-% tfstarp-% tcoqp-% tleanp-% thol4p-%
 .PHONY: tfstar-%
 tfstar-%: OPTIONS += -backend fstar
 tfstar-%: BACKEND_SUBDIR := fstar
-tfstar-%:
+tfstar-%: tsplit-fstar-%
 	$(AENEAS_CMD)
 
 # "p" stands for "Polonius"
 .PHONY: tfstarp-%
 tfstarp-%: OPTIONS += -backend fstar
 tfstarp-%: BACKEND_SUBDIR := fstar
-tfstarp-%:
+tfstarp-%: tsplit-fstarp-%
+	$(AENEAS_CMD)
+
+# Test where we split the forward/backward functions
+.PHONY: tsplit-fstar-%
+tsplit-fstar-%: OPTIONS += -backend fstar -split-fwd-back
+tsplit-fstar-%: BACKEND_SUBDIR := fstar-split
+tsplit-fstar-%:
+	$(AENEAS_CMD)
+
+# Test where we split the forward/backward functions
+# "p" stands for "Polonius"
+.PHONY: tsplit-fstarp-%
+tsplit-fstarp-%: OPTIONS += -backend fstar -split-fwd-back
+tsplit-fstarp-%: BACKEND_SUBDIR := fstar-split
+tsplit-fstarp-%:
 	$(AENEAS_CMD)
 
 .PHONY: tcoq-%
@@ -313,7 +330,8 @@ thol4p-%:
 
 # Nix - TODO: add the lean tests
 .PHONY: nix
-nix: nix-aeneas-tests nix-aeneas-verify-fstar nix-aeneas-verify-coq nix-aeneas-verify-hol4
+nix:
+	nix build && nix flake check
 
 .PHONY: nix-aeneas-tests
 nix-aeneas-tests:
@@ -323,6 +341,10 @@ nix-aeneas-tests:
 nix-aeneas-verify-fstar:
 	nix build .#checks.x86_64-linux.aeneas-verify-fstar --show-trace -L
 
+.PHONY: nix-aeneas-verify-fstar-split
+nix-aeneas-verify-fstar-split:
+	nix build .#checks.x86_64-linux.aeneas-verify-fstar-split --show-trace -L
+
 .PHONY: nix-aeneas-verify-coq
 nix-aeneas-verify-coq:
 	nix build .#checks.x86_64-linux.aeneas-verify-coq --show-trace -L
diff --git a/README.md b/README.md
index c0a09ebe..64100410 100644
--- a/README.md
+++ b/README.md
@@ -48,7 +48,8 @@ Moreover, Aeneas requires the Charon ML library, defined in the
 [Charon](https://github.com/AeneasVerif/charon) project.
 The simplest way is to clone Charon, then go to [`compiler`](./compiler) and
 create a symbolic link to the Charon library:
-`ln -s PATH_TO_CHARON_REPO/charon-ml charon`
+`cd AENEAS_REPO/compiler && ln -s PATH_TO_CHARON_REPO/charon-ml charon`
+(the symbolic link should be placed inside the `aeneas/compiler/` folder).
 
 **Remark:** if you want to test if the symbolic link is valid, copy-paste the
 following script in your terminal (from the `compiler` directory):
diff --git a/backends/coq/Primitives.v b/backends/coq/Primitives.v
index 84280b96..990e27e4 100644
--- a/backends/coq/Primitives.v
+++ b/backends/coq/Primitives.v
@@ -67,8 +67,7 @@ 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 .
+Definition core_mem_replace (a : Type) (x : a) (y : a) : a * a := (x, x) .
 
 Record mut_raw_ptr (T : Type) := { mut_raw_ptr_v : T }.
 Record const_raw_ptr (T : Type) := { const_raw_ptr_v : T }.
@@ -504,13 +503,15 @@ 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;
+  core_ops_index_IndexMut_index_mut :
+    Self ->
+    Idx ->
+    result (core_ops_index_IndexMut_indexInst.(core_ops_index_Index_Output) *
+            (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 {
@@ -524,13 +525,14 @@ 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;
+  core_ops_deref_DerefMut_deref_mut :
+    Self ->
+    result (core_ops_deref_DerefMut_derefInst.(core_ops_deref_Deref_target) *
+            (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;
@@ -543,8 +545,8 @@ 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.
+Definition alloc_boxed_Box_deref_mut (T : Type) (x : T) : result (T * (T -> result T)) :=
+  Return (x, fun x => Return x).
 
 (* Trait instance *)
 Definition alloc_boxed_Box_coreopsDerefInst (Self : Type) : core_ops_deref_Deref Self := {|
@@ -556,7 +558,6 @@ Definition alloc_boxed_Box_coreopsDerefInst (Self : Type) : core_ops_deref_Deref
 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;
 |}.
 
 
@@ -584,6 +585,13 @@ 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).
 
+Definition array_index_mut_usize (T : Type) (n : usize) (a : array T n) (i : usize) :
+  result (T * (T -> result (array T n))) :=
+  match array_index_usize T n a i with
+  | Fail_ e => Fail_ e
+  | Return x => Return (x, array_update_usize T n a i)
+  end.
+
 (*** Slice *)
 Definition slice T := { l: list T | Z.of_nat (length l) <= usize_max}.
 
@@ -591,11 +599,25 @@ 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).
 
+Definition slice_index_mut_usize (T : Type) (s : slice T) (i : usize) :
+  result (T * (T -> result (slice T))) :=
+  match slice_index_usize T s i with
+  | Fail_ e => Fail_ e
+  | Return x => Return (x, slice_update_usize T s i)
+  end.
+
 (*** 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).
 
+Definition array_to_slice_mut (T : Type) (n : usize) (a : array T n) :
+  result (slice T * (slice T -> result (array T n))) :=
+  match array_to_slice T n a with
+  | Fail_ e => Fail_ e
+  | Return x => Return (x, array_from_slice T n a)
+  end.
+
 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).
 
@@ -639,16 +661,9 @@ Definition alloc_vec_Vec_bind {A B} (v: alloc_vec_Vec A) (f: list A -> result (l
   | 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)
@@ -661,6 +676,14 @@ Axiom alloc_vec_Vec_index_usize : forall {T : Type} (v : alloc_vec_Vec T) (i : u
 (* Helper *)
 Axiom alloc_vec_Vec_update_usize : forall {T : Type} (v : alloc_vec_Vec T) (i : usize) (x : T), result (alloc_vec_Vec T).
 
+Definition alloc_vec_Vec_index_mut_usize {T : Type} (v: alloc_vec_Vec T) (i: usize) :
+  result (T * (T -> result (alloc_vec_Vec T))) :=
+  match alloc_vec_Vec_index_usize v i with
+  | Return x =>
+    Return (x, alloc_vec_Vec_update_usize v i)
+  | Fail_ e => Fail_ e
+  end.
+
 (* Trait declaration: [core::slice::index::private_slice_index::Sealed] *)
 Definition core_slice_index_private_slice_index_Sealed (self : Type) := unit.
 
@@ -669,25 +692,23 @@ Record core_slice_index_SliceIndex (Self T : Type) := mk_core_slice_index_SliceI
   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_mut :
+    Self -> T -> result (option core_slice_index_SliceIndex_Output * (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;
+  core_slice_index_SliceIndex_index_mut :
+    Self -> T -> result (core_slice_index_SliceIndex_Output * (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
@@ -704,11 +725,9 @@ Axiom core_slice_index_RangeUsize_get : forall (T : Type) (i : core_ops_range_Ra
 
 (* [core::slice::index::Range::get_mut]: forward function *)
 Axiom core_slice_index_RangeUsize_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_RangeUsize_get_mut_back :
-  forall (T : Type), core_ops_range_Range usize -> slice T -> option (slice T) -> result (slice T).
+  forall (T : Type),
+    core_ops_range_Range usize -> slice T ->
+    result (option (slice T) * (option (slice T) -> result (slice T))).
 
 (* [core::slice::index::Range::get_unchecked]: forward function *)
 Definition core_slice_index_RangeUsize_get_unchecked
@@ -732,21 +751,14 @@ Axiom core_slice_index_RangeUsize_index :
 
 (* [core::slice::index::Range::index_mut]: forward function *)
 Axiom core_slice_index_RangeUsize_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_RangeUsize_index_mut_back :
-  forall (T : Type), core_ops_range_Range usize -> slice T -> slice T -> result (slice T).
+  forall (T : Type), core_ops_range_Range usize -> slice T -> result (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).
+  slice T -> Idx ->
+  result (inst.(core_slice_index_SliceIndex_Output) *
+          (inst.(core_slice_index_SliceIndex_Output) -> result (slice T))).
 
 (* [core::array::[T; N]::index]: forward function *)
 Axiom core_array_Array_index :
@@ -756,12 +768,9 @@ Axiom core_array_Array_index :
 (* [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).
+  (a : array T N) (i : Idx),
+  result (inst.(core_ops_index_IndexMut_indexInst).(core_ops_index_Index_Output) *
+          (inst.(core_ops_index_IndexMut_indexInst).(core_ops_index_Index_Output) -> result (array T N))).
 
 (* Trait implementation: [core::slice::index::private_slice_index::Range] *)
 Definition core_slice_index_private_slice_index_SealedRangeUsizeInst
@@ -774,12 +783,10 @@ Definition core_slice_index_SliceIndexRangeUsizeSliceTInst (T : Type) :
   core_slice_index_SliceIndex_Output := slice T;
   core_slice_index_SliceIndex_get := core_slice_index_RangeUsize_get T;
   core_slice_index_SliceIndex_get_mut := core_slice_index_RangeUsize_get_mut T;
-  core_slice_index_SliceIndex_get_mut_back := core_slice_index_RangeUsize_get_mut_back T;
   core_slice_index_SliceIndex_get_unchecked := core_slice_index_RangeUsize_get_unchecked T;
   core_slice_index_SliceIndex_get_unchecked_mut := core_slice_index_RangeUsize_get_unchecked_mut T;
   core_slice_index_SliceIndex_index := core_slice_index_RangeUsize_index T;
   core_slice_index_SliceIndex_index_mut := core_slice_index_RangeUsize_index_mut T;
-  core_slice_index_SliceIndex_index_mut_back := core_slice_index_RangeUsize_index_mut_back T;
 |}.
 
 (* Trait implementation: [core::slice::index::[T]] *)
@@ -796,7 +803,6 @@ Definition core_ops_index_IndexMutSliceTIInst (T Idx : Type)
   core_ops_index_IndexMut (slice T) Idx := {|
   core_ops_index_IndexMut_indexInst := core_ops_index_IndexSliceTIInst 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]] *)
@@ -813,18 +819,14 @@ Definition core_ops_index_IndexMutArrayInst (T Idx : Type) (N : usize)
   core_ops_index_IndexMut (array T N) Idx := {|
   core_ops_index_IndexMut_indexInst := core_ops_index_IndexArrayInst 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).
+Axiom core_slice_index_usize_get_mut :
+  forall (T : Type), usize -> slice T -> result (option T * (option T -> result (slice T))).
 
 (* [core::slice::index::usize::get_unchecked]: forward function *)
 Axiom core_slice_index_usize_get_unchecked :
@@ -838,11 +840,8 @@ Axiom core_slice_index_usize_get_unchecked_mut :
 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).
+Axiom core_slice_index_usize_index_mut :
+  forall (T : Type), usize -> slice T -> result (T * (T -> result (slice T))).
 
 (* Trait implementation: [core::slice::index::private_slice_index::usize] *)
 Definition core_slice_index_private_slice_index_SealedUsizeInst
@@ -855,12 +854,10 @@ Definition core_slice_index_SliceIndexUsizeSliceTInst (T : Type) :
   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 *)
@@ -869,12 +866,9 @@ Axiom alloc_vec_Vec_index : forall (T Idx : Type) (inst : core_slice_index_Slice
 
 (* [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).
+  (Self : alloc_vec_Vec T) (i : Idx),
+  result (inst.(core_slice_index_SliceIndex_Output) *
+          (inst.(core_slice_index_SliceIndex_Output) -> result (alloc_vec_Vec T))).
 
 (* Trait implementation: [alloc::vec::Vec] *)
 Definition alloc_vec_Vec_coreopsindexIndexInst (T Idx : Type)
@@ -890,7 +884,6 @@ Definition alloc_vec_Vec_coreopsindexIndexMutInst (T Idx : Type)
   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 *)
@@ -901,10 +894,6 @@ Axiom alloc_vec_Vec_index_eq : forall {a : Type} (v : alloc_vec_Vec a) (i : usiz
 
 Axiom alloc_vec_Vec_index_mut_eq : forall {a : Type} (v : alloc_vec_Vec a) (i : usize) (x : a),
   alloc_vec_Vec_index_mut a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i =
-    alloc_vec_Vec_index_usize v i.
-
-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_SliceIndexUsizeSliceTInst a) v i x =
-    alloc_vec_Vec_update_usize v i x.
+    alloc_vec_Vec_index_mut_usize v i.
 
 End Primitives.
diff --git a/backends/fstar/Makefile b/backends/fstar/merge/Makefile
index a16b0edb..a16b0edb 100644
--- a/backends/fstar/Makefile
+++ b/backends/fstar/merge/Makefile
diff --git a/backends/fstar/merge/Primitives.fst b/backends/fstar/merge/Primitives.fst
new file mode 100644
index 00000000..fca80829
--- /dev/null
+++ b/backends/fstar/merge/Primitives.fst
@@ -0,0 +1,848 @@
+/// 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 & a = (x, x)
+
+// 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
+
+assume val size_numbits : pos
+
+// TODO: we could use FStar.Int.int_t and FStar.UInt.int_t
+
+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_xor (#ty : scalar_ty)
+    (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
+  | Usize -> admit() // TODO
+  | I8 ->
+    // Encoding issues...
+    normalize_spec (FStar.Int.int_t 8);
+    normalize_spec (scalar I8);
+    FStar.Int.logxor #8 x y
+  | I16 ->
+    // Encoding issues...
+    normalize_spec (FStar.Int.int_t 16);
+    normalize_spec (scalar I16);
+    FStar.Int.logxor #16 x y
+  | I32 -> FStar.Int.logxor #32 x y
+  | I64 -> FStar.Int.logxor #64 x y
+  | I128 ->
+    // Encoding issues...
+    normalize_spec (FStar.Int.int_t 128);
+    normalize_spec (scalar I128);
+    FStar.Int.logxor #128 x y
+  | Isize -> admit() // TODO
+
+let scalar_or (#ty : scalar_ty)
+    (x : scalar ty) (y : scalar ty) : scalar ty =
+  match ty with
+  | U8 -> FStar.UInt.logor #8 x y
+  | U16 -> FStar.UInt.logor #16 x y
+  | U32 -> FStar.UInt.logor #32 x y
+  | U64 -> FStar.UInt.logor #64 x y
+  | U128 -> FStar.UInt.logor #128 x y
+  | Usize -> admit() // TODO
+  | I8 ->
+    // Encoding issues...
+    normalize_spec (FStar.Int.int_t 8);
+    normalize_spec (scalar I8);
+    FStar.Int.logor #8 x y
+  | I16 ->
+    // Encoding issues...
+    normalize_spec (FStar.Int.int_t 16);
+    normalize_spec (scalar I16);
+    FStar.Int.logor #16 x y
+  | I32 -> FStar.Int.logor #32 x y
+  | I64 -> FStar.Int.logor #64 x y
+  | I128 ->
+    // Encoding issues...
+    normalize_spec (FStar.Int.int_t 128);
+    normalize_spec (scalar I128);
+    FStar.Int.logor #128 x y
+  | Isize -> admit() // TODO
+
+let scalar_and (#ty : scalar_ty)
+    (x : scalar ty) (y : scalar ty) : scalar ty =
+  match ty with
+  | U8 -> FStar.UInt.logand #8 x y
+  | U16 -> FStar.UInt.logand #16 x y
+  | U32 -> FStar.UInt.logand #32 x y
+  | U64 -> FStar.UInt.logand #64 x y
+  | U128 -> FStar.UInt.logand #128 x y
+  | Usize -> admit() // TODO
+  | I8 ->
+    // Encoding issues...
+    normalize_spec (FStar.Int.int_t 8);
+    normalize_spec (scalar I8);
+    FStar.Int.logand #8 x y
+  | I16 ->
+    // Encoding issues...
+    normalize_spec (FStar.Int.int_t 16);
+    normalize_spec (scalar I16);
+    FStar.Int.logand #16 x y
+  | I32 -> FStar.Int.logand #32 x y
+  | I64 -> FStar.Int.logand #64 x y
+  | I128 ->
+    // Encoding issues...
+    normalize_spec (FStar.Int.int_t 128);
+    normalize_spec (scalar I128);
+    FStar.Int.logand #128 x y
+  | Isize -> admit() // TODO
+
+// Shift left
+let scalar_shl (#ty0 #ty1 : scalar_ty)
+    (x : scalar ty0) (y : scalar ty1) : result (scalar ty0) =
+  admit()
+
+// Shift right
+let scalar_shr (#ty0 #ty1 : scalar_ty)
+    (x : scalar ty0) (y : scalar ty1) : result (scalar ty0) =
+  admit()
+
+(** 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
+
+// This can't fail, but for now we make all casts faillible (easier for the translation)
+let scalar_cast_bool (tgt_ty : scalar_ty) (x : bool) : result (scalar tgt_ty) =
+  mk_scalar tgt_ty (if x then 1 else 0)
+
+/// 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
+
+/// Xor
+let u8_xor = scalar_xor #U8
+let u16_xor = scalar_xor #U16
+let u32_xor = scalar_xor #U32
+let u64_xor = scalar_xor #U64
+let u128_xor = scalar_xor #U128
+let usize_xor = scalar_xor #Usize
+let i8_xor = scalar_xor #I8
+let i16_xor = scalar_xor #I16
+let i32_xor = scalar_xor #I32
+let i64_xor = scalar_xor #I64
+let i128_xor = scalar_xor #I128
+let isize_xor = scalar_xor #Isize
+
+/// Or
+let u8_or = scalar_or #U8
+let u16_or = scalar_or #U16
+let u32_or = scalar_or #U32
+let u64_or = scalar_or #U64
+let u128_or = scalar_or #U128
+let usize_or = scalar_or #Usize
+let i8_or = scalar_or #I8
+let i16_or = scalar_or #I16
+let i32_or = scalar_or #I32
+let i64_or = scalar_or #I64
+let i128_or = scalar_or #I128
+let isize_or = scalar_or #Isize
+
+/// And
+let u8_and = scalar_and #U8
+let u16_and = scalar_and #U16
+let u32_and = scalar_and #U32
+let u64_and = scalar_and #U64
+let u128_and = scalar_and #U128
+let usize_and = scalar_and #Usize
+let i8_and = scalar_and #I8
+let i16_and = scalar_and #I16
+let i32_and = scalar_and #I32
+let i64_and = scalar_and #I64
+let i128_and = scalar_and #I128
+let isize_and = scalar_and #Isize
+
+/// Shift left
+let u8_shl #ty = scalar_shl #U8 #ty
+let u16_shl #ty = scalar_shl #U16 #ty
+let u32_shl #ty = scalar_shl #U32 #ty
+let u64_shl #ty = scalar_shl #U64 #ty
+let u128_shl #ty = scalar_shl #U128 #ty
+let usize_shl #ty = scalar_shl #Usize #ty
+let i8_shl #ty = scalar_shl #I8 #ty
+let i16_shl #ty = scalar_shl #I16 #ty
+let i32_shl #ty = scalar_shl #I32 #ty
+let i64_shl #ty = scalar_shl #I64 #ty
+let i128_shl #ty = scalar_shl #I128 #ty
+let isize_shl #ty = scalar_shl #Isize #ty
+
+/// Shift right
+let u8_shr #ty = scalar_shr #U8 #ty
+let u16_shr #ty = scalar_shr #U16 #ty
+let u32_shr #ty = scalar_shr #U32 #ty
+let u64_shr #ty = scalar_shr #U64 #ty
+let u128_shr #ty = scalar_shr #U128 #ty
+let usize_shr #ty = scalar_shr #Usize #ty
+let i8_shr #ty = scalar_shr #I8 #ty
+let i16_shr #ty = scalar_shr #I16 #ty
+let i32_shr #ty = scalar_shr #I32 #ty
+let i64_shr #ty = scalar_shr #I64 #ty
+let i128_shr #ty = scalar_shr #I128 #ty
+let isize_shr #ty = scalar_shr #Isize #ty
+
+(*** 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 & (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 & (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 & (t -> result t)) =
+  Return (x, (fun x -> 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;
+}
+
+(*** 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
+
+let array_index_mut_usize (a : Type0) (n : usize) (x : array a n) (i : usize) :
+  result (a & (a -> result (array a n))) =
+  match array_index_usize a n x i with
+  | Fail e -> Fail e
+  | Return v ->
+    Return (v, array_update_usize a n x i)
+
+(*** 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
+
+let slice_index_mut_usize (a : Type0) (s : slice a) (i : usize) :
+  result (a & (a -> result (slice a))) =
+  match slice_index_usize a s i with
+  | Fail e -> Fail e
+  | Return x ->
+    Return (x, slice_update_usize a s i)
+
+(*** 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
+
+let array_to_slice_mut (a : Type0) (n : usize) (x : array a n) :
+  result (slice a & (slice a -> result (array a n))) =
+  Return (x, array_from_slice a n x)
+
+// 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
+
+let alloc_vec_Vec_index_mut_usize (#a : Type0) (v: alloc_vec_Vec a) (i: usize) :
+  result (a & (a → result (alloc_vec_Vec a))) =
+  match alloc_vec_Vec_index_usize v i with
+  | Return x ->
+    Return (x, alloc_vec_Vec_update_usize v i)
+  | Fail e -> Fail e
+
+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
+
+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 & (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 & (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_RangeUsize_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_RangeUsize_get_mut (t : Type0) :
+  core_ops_range_Range usize → slice t → result (option (slice t) & (option (slice t) -> result (slice t))) =
+  admit () // TODO
+
+// [core::slice::index::Range::get_unchecked]: forward function
+let core_slice_index_RangeUsize_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_RangeUsize_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_RangeUsize_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_RangeUsize_index_mut (t : Type0) :
+  core_ops_range_Range usize → slice t → result (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 & (inst.output -> result (slice t))) =
+  admit () // 
+
+// [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 & (inst.indexInst.output -> result (array t n))) =
+  admit () // TODO
+
+// Trait implementation: [core::slice::index::private_slice_index::Range]
+let core_slice_index_private_slice_index_SealedRangeUsizeInst
+  : core_slice_index_private_slice_index_Sealed (core_ops_range_Range usize) = ()
+
+// Trait implementation: [core::slice::index::Range]
+let core_slice_index_SliceIndexRangeUsizeSliceTInst (t : Type0) :
+  core_slice_index_SliceIndex (core_ops_range_Range usize) (slice t) = {
+  sealedInst = core_slice_index_private_slice_index_SealedRangeUsizeInst;
+  output = slice t;
+  get = core_slice_index_RangeUsize_get t;
+  get_mut = core_slice_index_RangeUsize_get_mut t;
+  get_unchecked = core_slice_index_RangeUsize_get_unchecked t;
+  get_unchecked_mut = core_slice_index_RangeUsize_get_unchecked_mut t;
+  index = core_slice_index_RangeUsize_index t;
+  index_mut = core_slice_index_RangeUsize_index_mut t;
+}
+
+// Trait implementation: [core::slice::index::[T]]
+let core_ops_index_IndexSliceTIInst (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::[T]]
+let core_ops_index_IndexMutSliceTIInst (t idx : Type0)
+  (inst : core_slice_index_SliceIndex idx (slice t)) :
+  core_ops_index_IndexMut (slice t) idx = {
+  indexInst = core_ops_index_IndexSliceTIInst t idx inst;
+  index_mut = core_slice_index_Slice_index_mut t idx inst;
+}
+
+// Trait implementation: [core::array::[T; N]]
+let core_ops_index_IndexArrayInst (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_ops_index_IndexMutArrayIInst (t idx : Type0) (n : usize)
+  (inst : core_ops_index_IndexMut (slice t) idx) :
+  core_ops_index_IndexMut (array t n) idx = {
+  indexInst = core_ops_index_IndexArrayInst t idx n inst.indexInst;
+  index_mut = core_array_Array_index_mut 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 & (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 & (t -> result (slice t))) =
+  admit () // TODO
+
+// Trait implementation: [core::slice::index::private_slice_index::usize]
+let core_slice_index_private_slice_index_SealedUsizeInst
+  : core_slice_index_private_slice_index_Sealed usize = ()
+
+// Trait implementation: [core::slice::index::usize]
+let core_slice_index_SliceIndexUsizeSliceTInst (t : Type0) :
+  core_slice_index_SliceIndex usize (slice t) = {
+  sealedInst = core_slice_index_private_slice_index_SealedUsizeInst;
+  output = t;
+  get = core_slice_index_usize_get t;
+  get_mut = core_slice_index_usize_get_mut 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;
+}
+
+// [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 & (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;
+}
+
+(*** 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_SliceIndexUsizeSliceTInst a) v i ==
+      alloc_vec_Vec_index_usize v i)
+  [SMTPat (alloc_vec_Vec_index a usize (core_slice_index_SliceIndexUsizeSliceTInst 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_SliceIndexUsizeSliceTInst a) v i ==
+      alloc_vec_Vec_index_mut_usize v i)
+  [SMTPat (alloc_vec_Vec_index_mut a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i)]
+  =
+  admit()
diff --git a/backends/fstar/split/Makefile b/backends/fstar/split/Makefile
new file mode 100644
index 00000000..a16b0edb
--- /dev/null
+++ b/backends/fstar/split/Makefile
@@ -0,0 +1,47 @@
+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_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/backends/fstar/Primitives.fst b/backends/fstar/split/Primitives.fst
index a3ffbde4..a3ffbde4 100644
--- a/backends/fstar/Primitives.fst
+++ b/backends/fstar/split/Primitives.fst
diff --git a/backends/lean/Base/Primitives/Alloc.lean b/backends/lean/Base/Primitives/Alloc.lean
index 6c89c6bb..1f470fe1 100644
--- a/backends/lean/Base/Primitives/Alloc.lean
+++ b/backends/lean/Base/Primitives/Alloc.lean
@@ -12,8 +12,7 @@ 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
+def deref_mut (T : Type) (x : T) : Result (T × (T → Result T)) := ret (x, λ x => ret x)
 
 /-- Trait instance -/
 def coreopsDerefInst (Self : Type) :
@@ -27,7 +26,6 @@ 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
diff --git a/backends/lean/Base/Primitives/ArraySlice.lean b/backends/lean/Base/Primitives/ArraySlice.lean
index f68c0846..5057fb01 100644
--- a/backends/lean/Base/Primitives/ArraySlice.lean
+++ b/backends/lean/Base/Primitives/ArraySlice.lean
@@ -93,6 +93,21 @@ theorem Array.update_usize_spec {α : Type u} {n : Usize} (v: Array α n) (i: Us
   . simp_all [length]; cases h <;> scalar_tac
   . simp_all
 
+def Array.index_mut_usize (α : Type u) (n : Usize) (v: Array α n) (i: Usize) :
+  Result (α × (α -> Result (Array α n))) := do
+  let x ← index_usize α n v i
+  ret (x, update_usize α n v i)
+
+@[pspec]
+theorem Array.index_mut_usize_spec {α : Type u} {n : Usize} [Inhabited α] (v: Array α n) (i: Usize)
+  (hbound : i.val < v.length) :
+  ∃ x back, v.index_mut_usize α n i = ret (x, back) ∧
+  x = v.val.index i.val ∧
+  back = update_usize α n v i := by
+  simp only [index_mut_usize, Bind.bind, bind]
+  have ⟨ x, h ⟩ := index_usize_spec v i hbound
+  simp [h]
+
 def Slice (α : Type u) := { l : List α // l.length ≤ Usize.max }
 
 instance (a : Type u) : Arith.HasIntProp (Slice a) where
@@ -149,13 +164,6 @@ theorem Slice.index_usize_spec {α : Type u} [Inhabited α] (v: Slice α) (i: Us
   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
@@ -174,6 +182,21 @@ theorem Slice.update_usize_spec {α : Type u} (v: Slice α) (i: Usize) (x : α)
   . simp_all [length]; cases h <;> scalar_tac
   . simp_all
 
+def Slice.index_mut_usize (α : Type u) (v: Slice α) (i: Usize) :
+  Result (α × (α → Result (Slice α))) := do
+  let x ← Slice.index_usize α v i
+  ret (x, Slice.update_usize α v i)
+
+@[pspec]
+theorem Slice.index_mut_usize_spec {α : Type u} [Inhabited α] (v: Slice α) (i: Usize)
+  (hbound : i.val < v.length) :
+  ∃ x back, v.index_mut_usize α i = ret (x, back) ∧
+  x = v.val.index i.val ∧
+  back = Slice.update_usize α v i := by
+  simp only [index_mut_usize, Bind.bind, bind]
+  have ⟨ x, h ⟩ := Slice.index_usize_spec v i hbound
+  simp [h]
+
 /- Array to slice/subslices -/
 
 /- We could make this function not use the `Result` type. By making it monadic, we
@@ -197,6 +220,18 @@ theorem Array.from_slice_spec {α : Type u} {n : Usize} (a : Array α n) (ns : S
   ∃ na, from_slice α n a ns = ret na ∧ na.val = ns.val
   := by simp [from_slice, *]
 
+def Array.to_slice_mut (α : Type u) (n : Usize) (a : Array α n) :
+  Result (Slice α × (Slice α → Result (Array α n))) := do
+  let s ← Array.to_slice α n a
+  ret (s, Array.from_slice α n a)
+
+@[pspec]
+theorem Array.to_slice_mut_spec {α : Type u} {n : Usize} (v : Array α n) :
+  ∃ s back, to_slice_mut α n v = ret (s, back) ∧
+  v.val = s.val ∧
+  back = Array.from_slice α n v
+  := by simp [to_slice_mut, to_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
@@ -243,7 +278,7 @@ def Array.update_subslice (α : Type u) (n : Usize) (a : Array α n) (r : Range
 -- 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).
+-- (the user 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) :
@@ -345,13 +380,11 @@ 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_mut : Self → T → Result (Option Output × (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
+  index_mut : Self → T → Result (Output × (Output → Result T))
 
 /- [core::slice::index::[T]::index]: forward function -/
 def core.slice.index.Slice.index
@@ -369,13 +402,7 @@ def core.slice.index.RangeUsize.get (T : Type) (i : Range Usize) (slice : Slice
 
 /- [core::slice::index::Range::get_mut]: forward function -/
 def core.slice.index.RangeUsize.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.RangeUsize.get_mut_back
-  (T : Type) :
-  Range Usize → Slice T → Option (Slice T) → Result (Slice T) :=
+  (T : Type) : Range Usize → Slice T → Result (Option (Slice T) × (Option (Slice T) → Result (Slice T))) :=
   sorry -- TODO
 
 /- [core::slice::index::Range::get_unchecked]: forward function -/
@@ -401,24 +428,13 @@ def core.slice.index.RangeUsize.index
 
 /- [core::slice::index::Range::index_mut]: forward function -/
 def core.slice.index.RangeUsize.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.RangeUsize.index_mut_back
-  (T : Type) : Range Usize → Slice T → Slice T → Result (Slice T) :=
+  (T : Type) : Range Usize → Slice T → Result (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) :=
+  Slice T → I → Result (inst.Output × (inst.Output → Result (Slice T))) :=
   sorry -- TODO
 
 /- [core::array::[T; N]::index]: forward function -/
@@ -430,13 +446,8 @@ def core.array.Array.index
 /- [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) :=
+  (a : Array T N) (i : I) :
+  Result (inst.indexInst.Output × (inst.indexInst.Output → Result (Array T N))) :=
   sorry -- TODO
 
 /- Trait implementation: [core::slice::index::private_slice_index::Range] -/
@@ -450,12 +461,10 @@ def core.slice.index.SliceIndexRangeUsizeSliceTInst (T : Type) :
   Output := Slice T
   get := core.slice.index.RangeUsize.get T
   get_mut := core.slice.index.RangeUsize.get_mut T
-  get_mut_back := core.slice.index.RangeUsize.get_mut_back T
   get_unchecked := core.slice.index.RangeUsize.get_unchecked T
   get_unchecked_mut := core.slice.index.RangeUsize.get_unchecked_mut T
   index := core.slice.index.RangeUsize.index T
   index_mut := core.slice.index.RangeUsize.index_mut T
-  index_mut_back := core.slice.index.RangeUsize.index_mut_back T
 }
 
 /- Trait implementation: [core::slice::index::[T]] -/
@@ -472,7 +481,6 @@ def core.ops.index.IndexMutSliceTIInst (T I : Type)
   core.ops.index.IndexMut (Slice T) I := {
   indexInst := core.ops.index.IndexSliceTIInst 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]] -/
@@ -489,7 +497,6 @@ def core.ops.index.IndexMutArrayIInst (T I : Type) (N : Usize)
   core.ops.index.IndexMut (Array T N) I := {
   indexInst := core.ops.index.IndexArrayIInst 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 -/
@@ -499,12 +506,7 @@ def core.slice.index.Usize.get
 
 /- [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) :=
+  (T : Type) : Usize → Slice T → Result (Option T × (Option T → Result (Slice T))) :=
   sorry -- TODO
 
 /- [core::slice::index::usize::get_unchecked]: forward function -/
@@ -522,12 +524,8 @@ 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) :=
+def core.slice.index.Usize.index_mut (T : Type) :
+  Usize → Slice T → Result (T × (T → Result (Slice T))) :=
   sorry -- TODO
 
 /- Trait implementation: [core::slice::index::private_slice_index::usize] -/
@@ -541,12 +539,10 @@ def core.slice.index.SliceIndexUsizeSliceTInst (T : Type) :
   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 7fc33251..3d70c84a 100644
--- a/backends/lean/Base/Primitives/Base.lean
+++ b/backends/lean/Base/Primitives/Base.lean
@@ -120,8 +120,7 @@ def Result.attach {α: Type} (o : Result α): Result { x : α // o = ret x } :=
 -- MISC --
 ----------
 
-@[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
+@[simp] def core.mem.replace (a : Type) (x : a) (_ : a) : a × a := (x, x)
 
 /-- Aeneas-translated function -- useful to reduce non-recursive definitions.
  Use with `simp [ aeneas ]` -/
diff --git a/backends/lean/Base/Primitives/CoreOps.lean b/backends/lean/Base/Primitives/CoreOps.lean
index da458f66..1736bfa6 100644
--- a/backends/lean/Base/Primitives/CoreOps.lean
+++ b/backends/lean/Base/Primitives/CoreOps.lean
@@ -16,8 +16,7 @@ structure Index (Self Idx : Type) where
 /- 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
+  index_mut : Self → Idx → Result (indexInst.Output × (indexInst.Output → Result Self))
 
 end index -- core.ops.index
 
@@ -29,8 +28,7 @@ structure Deref (Self : Type) where
 
 structure DerefMut (Self : Type) where
   derefInst : Deref Self
-  deref_mut : Self → Result derefInst.Target
-  deref_mut_back : Self → derefInst.Target → Result Self
+  deref_mut : Self → Result (derefInst.Target × (Self → Result Self))
 
 end deref -- core.ops.deref
 
diff --git a/backends/lean/Base/Primitives/Vec.lean b/backends/lean/Base/Primitives/Vec.lean
index 2c3fce91..12733a34 100644
--- a/backends/lean/Base/Primitives/Vec.lean
+++ b/backends/lean/Base/Primitives/Vec.lean
@@ -122,6 +122,26 @@ theorem Vec.update_usize_spec {α : Type u} (v: Vec α) (i: Usize) (x : α)
   . simp_all [length]; cases h <;> scalar_tac
   . simp_all
 
+def Vec.index_mut_usize {α : Type u} (v: Vec α) (i: Usize) :
+  Result (α × (α → Result (Vec α))) :=
+  match Vec.index_usize v i with
+  | ret x =>
+    ret (x, Vec.update_usize v i)
+  | fail e => fail e
+  | div => div
+
+@[pspec]
+theorem Vec.index_mut_usize_spec {α : Type u} [Inhabited α] (v: Vec α) (i: Usize)
+  (hbound : i.val < v.length) :
+  ∃ x back, v.index_mut_usize i = ret (x, back) ∧
+  x = v.val.index i.val ∧
+  -- Backward function
+  back = v.update_usize i
+  := by
+  simp only [index_mut_usize]
+  have ⟨ x, h ⟩ := index_usize_spec v i hbound
+  simp [h]
+
 /- [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 :=
@@ -129,13 +149,8 @@ def Vec.index (T I : Type) (inst : core.slice.index.SliceIndex I (Slice T))
 
 /- [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) :=
+  (self : Vec T) (i : I) :
+  Result (inst.Output × (inst.Output → Result (Vec T))) :=
   sorry -- TODO
 
 /- Trait implementation: [alloc::vec::Vec] -/
@@ -152,7 +167,6 @@ def Vec.coreopsindexIndexMutInst (T I : Type)
   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]
@@ -164,13 +178,7 @@ theorem Vec.index_slice_index {α : Type} (v : Vec α) (i : Usize) :
 @[simp]
 theorem Vec.index_mut_slice_index {α : Type} (v : Vec α) (i : Usize) :
   Vec.index_mut α Usize (core.slice.index.SliceIndexUsizeSliceTInst 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.SliceIndexUsizeSliceTInst α) v i x =
-  Vec.update_usize v i x :=
+  index_mut_usize v i :=
   sorry
 
 end alloc.vec
diff --git a/compiler/AssociatedTypes.ml b/compiler/AssociatedTypes.ml
index e2f687e8..054c8169 100644
--- a/compiler/AssociatedTypes.ml
+++ b/compiler/AssociatedTypes.ml
@@ -493,11 +493,11 @@ let norm_ctx_normalize_trait_type_constraint (ctx : norm_ctx)
 let mk_norm_ctx (ctx : eval_ctx) : norm_ctx =
   {
     norm_trait_types = ctx.norm_trait_types;
-    type_decls = ctx.type_context.type_decls;
-    fun_decls = ctx.fun_context.fun_decls;
-    global_decls = ctx.global_context.global_decls;
-    trait_decls = ctx.trait_decls_context.trait_decls;
-    trait_impls = ctx.trait_impls_context.trait_impls;
+    type_decls = ctx.type_ctx.type_decls;
+    fun_decls = ctx.fun_ctx.fun_decls;
+    global_decls = ctx.global_ctx.global_decls;
+    trait_decls = ctx.trait_decls_ctx.trait_decls;
+    trait_impls = ctx.trait_impls_ctx.trait_impls;
     type_vars = ctx.type_vars;
     const_generic_vars = ctx.const_generic_vars;
   }
diff --git a/compiler/Config.ml b/compiler/Config.ml
index b09544ba..2bb1ca34 100644
--- a/compiler/Config.ml
+++ b/compiler/Config.ml
@@ -92,6 +92,69 @@ let loop_fixed_point_max_num_iters = 2
 
 (** {1 Translation} *)
 
+(** If true, do not define separate forward/backward functions, but make the
+    forward functions return the backward function.
+
+    Example:
+    {[
+      (* Rust *)
+      pub fn list_nth<'a, T>(l: &'a mut List<T>, i: u32) -> &'a mut T {
+          match l {
+              List::Nil => {
+                  panic!()
+              }
+              List::Cons(x, tl) => {
+                  if i == 0 {
+                      x
+                  } else {
+                      list_nth(tl, i - 1)
+                  }
+              }
+          }
+      }
+
+      (* Translation, if return_back_funs = false *)
+      def list_nth (T : Type) (l : List T) (i : U32) : Result T :=
+        match l with
+        | List.Cons x tl =>
+          if i = 0#u32
+          then Result.ret x
+          else do
+                 let i0 ← i - 1#u32
+                 list_nth T tl i0
+        | List.Nil => Result.fail .panic
+
+      def list_nth_back
+        (T : Type) (l : List T) (i : U32) (ret : T) : Result (List T) :=
+        match l with
+        | List.Cons x tl =>
+          if i = 0#u32
+          then Result.ret (List.Cons ret tl)
+          else
+            do
+              let i0 ← i - 1#u32
+              let tl0 ← list_nth_back T tl i0 ret
+              Result.ret (List.Cons x tl0)
+        | List.Nil => Result.fail .panic
+
+      (* Translation, if return_back_funs = true *)
+      def list_nth (T: Type) (ls : List T) (i : U32) :
+        Result (T × (T → Result (List T))) :=
+        match ls with
+        | List.Cons x tl =>
+          if i = 0#u32
+          then Result.ret (x, (λ ret => return (ret :: ls)))
+          else do
+            let i0 ← i - 1#u32
+            let (x, back) ← list_nth ls i0
+            Return.ret (x,
+              (λ ret => do
+               let ls ← back ret
+               return (x :: ls)))
+    ]}
+ *)
+let return_back_funs = ref true
+
 (** Forbids using field projectors for structures.
 
     If we don't use field projectors, whenever we symbolically expand a structure
@@ -307,6 +370,32 @@ let filter_useless_monadic_calls = ref true
  *)
 let filter_useless_functions = ref true
 
+(** Simplify the forward/backward functions, in case we merge them
+    (i.e., the forward functions return the backward functions).
+
+    The simplification occurs as follows:
+    - if a forward function returns the unit type and has non-trivial backward
+      functions, then we remove the returned output.
+    - if a backward function doesn't have inputs, we evaluate it inside the
+      forward function and don't wrap it in a result.
+
+    Example:
+    {[
+      // LLBC:
+      fn incr(x: &mut u32) { *x += 1 }
+
+      // Translation without simplification:
+      let incr (x : u32) : result (unit * result u32) = ...
+                                   ^^^^   ^^^^^^
+                                    |     remove this result
+                                remove the unit
+
+      // Translation with simplification:
+      let incr (x : u32) : result u32 = ...
+    ]}
+ *)
+let simplify_merged_fwd_backs = ref true
+
 (** Use short names for the record fields.
 
     Some backends can't disambiguate records when their field names have collisions.
diff --git a/compiler/Contexts.ml b/compiler/Contexts.ml
index a30ed0f1..5d646a61 100644
--- a/compiler/Contexts.ml
+++ b/compiler/Contexts.ml
@@ -180,35 +180,35 @@ type config = {
 
 let mk_config (mode : interpreter_mode) : config = { mode }
 
-type type_context = {
+type type_ctx = {
   type_decls_groups : type_declaration_group TypeDeclId.Map.t;
   type_decls : type_decl TypeDeclId.Map.t;
   type_infos : TypesAnalysis.type_infos;
 }
 [@@deriving show]
 
-type fun_context = {
+type fun_ctx = {
   fun_decls : fun_decl FunDeclId.Map.t;
   fun_infos : FunsAnalysis.fun_info FunDeclId.Map.t;
   regions_hierarchies : region_var_groups FunIdMap.t;
 }
 [@@deriving show]
 
-type global_context = { global_decls : global_decl GlobalDeclId.Map.t }
+type global_ctx = { global_decls : global_decl GlobalDeclId.Map.t }
 [@@deriving show]
 
-type trait_decls_context = { trait_decls : trait_decl TraitDeclId.Map.t }
+type trait_decls_ctx = { trait_decls : trait_decl TraitDeclId.Map.t }
 [@@deriving show]
 
-type trait_impls_context = { trait_impls : trait_impl TraitImplId.Map.t }
+type trait_impls_ctx = { 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;
+  type_ctx : type_ctx;
+  fun_ctx : fun_ctx;
+  global_ctx : global_ctx;
+  trait_decls_ctx : trait_decls_ctx;
+  trait_impls_ctx : trait_impls_ctx;
 }
 [@@deriving show]
 
@@ -230,11 +230,11 @@ module TraitTypeRefMap = Collections.MakeMap (TraitTypeRefOrd)
 
 (** 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;
+  type_ctx : type_ctx;
+  fun_ctx : fun_ctx;
+  global_ctx : global_ctx;
+  trait_decls_ctx : trait_decls_ctx;
+  trait_impls_ctx : trait_impls_ctx;
   region_groups : RegionGroupId.id list;
   type_vars : type_var list;
   const_generic_vars : const_generic_var list;
@@ -290,20 +290,20 @@ let ctx_lookup_var_binder (ctx : eval_ctx) (vid : VarId.id) : var_binder =
   fst (env_lookup_var ctx.env vid)
 
 let ctx_lookup_type_decl (ctx : eval_ctx) (tid : TypeDeclId.id) : type_decl =
-  TypeDeclId.Map.find tid ctx.type_context.type_decls
+  TypeDeclId.Map.find tid ctx.type_ctx.type_decls
 
 let ctx_lookup_fun_decl (ctx : eval_ctx) (fid : FunDeclId.id) : fun_decl =
-  FunDeclId.Map.find fid ctx.fun_context.fun_decls
+  FunDeclId.Map.find fid ctx.fun_ctx.fun_decls
 
 let ctx_lookup_global_decl (ctx : eval_ctx) (gid : GlobalDeclId.id) :
     global_decl =
-  GlobalDeclId.Map.find gid ctx.global_context.global_decls
+  GlobalDeclId.Map.find gid ctx.global_ctx.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
+  TraitDeclId.Map.find id ctx.trait_decls_ctx.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
+  TraitImplId.Map.find id ctx.trait_impls_ctx.trait_impls
 
 (** Retrieve a variable's value in the current frame *)
 let env_lookup_var_value (env : env) (vid : VarId.id) : typed_value =
@@ -528,7 +528,7 @@ let ctx_set_abs_can_end (ctx : eval_ctx) (abs_id : AbstractionId.id)
   fst (ctx_subst_abs ctx abs_id abs)
 
 let ctx_type_decl_is_rec (ctx : eval_ctx) (id : TypeDeclId.id) : bool =
-  let decl_group = TypeDeclId.Map.find id ctx.type_context.type_decls_groups in
+  let decl_group = TypeDeclId.Map.find id ctx.type_ctx.type_decls_groups in
   match decl_group with RecGroup _ -> true | NonRecGroup _ -> false
 
 (** Visitor to iterate over the values in the *current* frame *)
diff --git a/compiler/Extract.ml b/compiler/Extract.ml
index 20cdb20b..87dcb1fd 100644
--- a/compiler/Extract.ml
+++ b/compiler/Extract.ml
@@ -43,8 +43,12 @@ let extract_fun_decl_register_names (ctx : extraction_ctx)
                 }
             | _ -> 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
+          let funs =
+            if !Config.return_back_funs then [ def.fwd.f ]
+            else
+              let backs = List.map (fun f -> f.f) def.backs in
+              if def.keep_fwd then def.fwd.f :: backs else backs
+          in
           List.fold_left
             (fun ctx (f : fun_decl) ->
               let open ExtractBuiltin in
@@ -128,9 +132,15 @@ let extract_adt_g_value
       F.pp_print_string fmt "tt";
       ctx)
     else
-      (* If there is exactly one value, we don't print the parentheses *)
+      (* If there is exactly one value, we don't print the parentheses.
+         Also, for Coq, we need the special syntax ['(...)] if we destruct
+         a tuple pattern in a let-binding and the tuple has > 2 values.
+      *)
       let lb, rb =
-        if List.length field_values = 1 then ("", "") else ("(", ")")
+        if List.length field_values = 1 then ("", "")
+        else if !backend = Coq && is_single_pat && List.length field_values > 2
+        then ("'(", ")")
+        else ("(", ")")
       in
       F.pp_print_string fmt lb;
       let ctx =
@@ -237,30 +247,60 @@ let fun_builtin_filter_types (id : FunDeclId.id) (types : 'a list)
         Result.Ok types
 
 (** [inside]: see {!extract_ty}.
+    [with_type]: do we also generate a type annotation? This is necessary for
+    backends like Coq when we write lambdas (Coq is not powerful enough to
+    infer the type).
 
     As a pattern can introduce new variables, we return an extraction context
     updated with new bindings.
  *)
 let rec extract_typed_pattern (ctx : extraction_ctx) (fmt : F.formatter)
-    (is_let : bool) (inside : bool) (v : typed_pattern) : extraction_ctx =
-  match v.value with
-  | PatConstant cv ->
-      extract_literal fmt inside cv;
-      ctx
-  | PatVar (v, _) ->
-      let vname = ctx_compute_var_basename ctx v.basename v.ty in
-      let ctx, vname = ctx_add_var vname v.id ctx in
-      F.pp_print_string fmt vname;
-      ctx
-  | PatDummy ->
-      F.pp_print_string fmt "_";
-      ctx
-  | PatAdt av ->
-      let extract_value ctx inside v =
-        extract_typed_pattern ctx fmt is_let inside v
-      in
-      extract_adt_g_value extract_value fmt ctx is_let inside av.variant_id
-        av.field_values v.ty
+    (is_let : bool) (inside : bool) ?(with_type = false) (v : typed_pattern) :
+    extraction_ctx =
+  if with_type then F.pp_print_string fmt "(";
+  let inside = inside && not with_type in
+  let ctx =
+    match v.value with
+    | PatConstant cv ->
+        extract_literal fmt inside cv;
+        ctx
+    | PatVar (v, _) ->
+        let vname = ctx_compute_var_basename ctx v.basename v.ty in
+        let ctx, vname = ctx_add_var vname v.id ctx in
+        F.pp_print_string fmt vname;
+        ctx
+    | PatDummy ->
+        F.pp_print_string fmt "_";
+        ctx
+    | PatAdt av ->
+        let extract_value ctx inside v =
+          extract_typed_pattern ctx fmt is_let inside v
+        in
+        extract_adt_g_value extract_value fmt ctx is_let inside av.variant_id
+          av.field_values v.ty
+  in
+  if with_type then (
+    F.pp_print_space fmt ();
+    F.pp_print_string fmt ":";
+    F.pp_print_space fmt ();
+    extract_ty ctx fmt TypeDeclId.Set.empty false v.ty;
+    F.pp_print_string fmt ")");
+  ctx
+
+(** Return true if we need to wrap a succession of let-bindings in a [do ...]
+    block (because some of them are monadic) *)
+let lets_require_wrap_in_do (lets : (bool * typed_pattern * texpression) list) :
+    bool =
+  match !backend with
+  | Lean ->
+      (* For Lean, we wrap in a block iff at least one of the let-bindings is monadic *)
+      List.exists (fun (m, _, _) -> m) lets
+  | HOL4 ->
+      (* HOL4 is similar to HOL4, but we add a sanity check *)
+      let wrap_in_do = List.exists (fun (m, _, _) -> m) lets in
+      if wrap_in_do then assert (List.for_all (fun (m, _, _) -> m) lets);
+      wrap_in_do
+  | FStar | Coq -> false
 
 (** [inside]: controls the introduction of parentheses. See [extract_ty]
 
@@ -285,9 +325,9 @@ let rec extract_texpression (ctx : extraction_ctx) (fmt : F.formatter)
   | App _ ->
       let app, args = destruct_apps e in
       extract_App ctx fmt inside app args
-  | Abs _ ->
-      let xl, e = destruct_abs_list e in
-      extract_Abs ctx fmt inside xl e
+  | Lambda _ ->
+      let xl, e = destruct_lambdas e in
+      extract_Lambda ctx fmt inside xl e
   | Qualif _ ->
       (* We use the app case *)
       extract_App ctx fmt inside e []
@@ -574,7 +614,7 @@ and extract_field_projector (ctx : extraction_ctx) (fmt : F.formatter)
       (* No argument: shouldn't happen *)
       raise (Failure "Unreachable")
 
-and extract_Abs (ctx : extraction_ctx) (fmt : F.formatter) (inside : bool)
+and extract_Lambda (ctx : extraction_ctx) (fmt : F.formatter) (inside : bool)
     (xl : typed_pattern list) (e : texpression) : unit =
   (* Open a box for the abs expression *)
   F.pp_open_hovbox fmt ctx.indent_incr;
@@ -583,15 +623,16 @@ and extract_Abs (ctx : extraction_ctx) (fmt : F.formatter) (inside : bool)
   (* Print the lambda - note that there should always be at least one variable *)
   assert (xl <> []);
   F.pp_print_string fmt "fun";
+  let with_type = !backend = Coq in
   let ctx =
     List.fold_left
       (fun ctx x ->
         F.pp_print_space fmt ();
-        extract_typed_pattern ctx fmt true true x)
+        extract_typed_pattern ctx fmt true true ~with_type x)
       ctx xl
   in
   F.pp_print_space fmt ();
-  if !backend = Lean then F.pp_print_string fmt "=>"
+  if !backend = Lean || !backend = Coq then F.pp_print_string fmt "=>"
   else F.pp_print_string fmt "->";
   F.pp_print_space fmt ();
   (* Print the body *)
@@ -630,15 +671,6 @@ and extract_lets (ctx : extraction_ctx) (fmt : F.formatter) (inside : bool)
     | HOL4 -> destruct_lets_no_interleave e
     | FStar | Coq | Lean -> destruct_lets e
   in
-  (* Open a box for the whole expression.
-
-     In the case of Lean, we use a vbox so that line breaks are inserted
-     at the end of every let-binding: let-bindings are indeed not ended
-     with an "in" keyword.
-  *)
-  if !Config.backend = Lean then F.pp_open_vbox fmt 0 else F.pp_open_hvbox fmt 0;
-  (* Open parentheses *)
-  if inside && !backend <> Lean then F.pp_print_string fmt "(";
   (* Extract the let-bindings *)
   let extract_let (ctx : extraction_ctx) (monadic : bool) (lv : typed_pattern)
       (re : texpression) : extraction_ctx =
@@ -711,22 +743,19 @@ and extract_lets (ctx : extraction_ctx) (fmt : F.formatter) (inside : bool)
     (* Return *)
     ctx
   in
+  (* Open a box for the whole expression.
+
+     In the case of Lean, we use a vbox so that line breaks are inserted
+     at the end of every let-binding: let-bindings are indeed not ended
+     with an "in" keyword.
+  *)
+  if !Config.backend = Lean then F.pp_open_vbox fmt 0 else F.pp_open_hvbox fmt 0;
+  (* Open parentheses *)
+  if inside && !backend <> Lean then F.pp_print_string fmt "(";
   (* If Lean and HOL4, we rely on monadic blocks, so we insert a do and open a new box
      immediately *)
-  let wrap_in_do_od =
-    match !backend with
-    | Lean ->
-        (* For Lean, we wrap in a block iff at least one of the let-bindings is monadic *)
-        List.exists (fun (m, _, _) -> m) lets
-    | HOL4 ->
-        (* HOL4 is similar to HOL4, but we add a sanity check *)
-        let wrap_in_do = List.exists (fun (m, _, _) -> m) lets in
-        if wrap_in_do then assert (List.for_all (fun (m, _, _) -> m) lets);
-        wrap_in_do
-    | FStar | Coq -> false
-  in
+  let wrap_in_do_od = lets_require_wrap_in_do lets in
   if wrap_in_do_od then (
-    F.pp_open_vbox fmt (if !backend = Lean then ctx.indent_incr else 0);
     F.pp_print_string fmt "do";
     F.pp_print_space fmt ());
   let ctx =
@@ -742,11 +771,10 @@ and extract_lets (ctx : extraction_ctx) (fmt : F.formatter) (inside : bool)
   F.pp_close_box fmt ();
 
   (* do-box (Lean and HOL4 only) *)
-  if wrap_in_do_od then (
+  if wrap_in_do_od then
     if !backend = HOL4 then (
       F.pp_print_space fmt ();
       F.pp_print_string fmt "od");
-    F.pp_close_box fmt ());
   (* Close parentheses *)
   if inside && !backend <> Lean then F.pp_print_string fmt ")";
   (* Close the box for the whole expression *)
@@ -1319,16 +1347,16 @@ let extract_fun_comment (ctx : extraction_ctx) (fmt : F.formatter)
       (Pure.FunId (FRegular def.def_id), def.loop_id, def.back_id)
       ctx.fun_name_info
   in
-  let comment_pre = "[" ^ name_to_string ctx def.llbc_name ^ "]: " in
+  let comment_pre = "[" ^ name_to_string ctx def.llbc_name ^ "]:" in
   let comment =
     let loop_comment =
       match def.loop_id with
       | None -> ""
-      | Some id -> "loop " ^ LoopId.to_string id ^ ": "
+      | Some id -> " loop " ^ LoopId.to_string id ^ ":"
     in
     let fwd_back_comment =
       match def.back_id with
-      | None -> [ "forward function" ]
+      | None -> if !Config.return_back_funs then [] else [ "forward function" ]
       | Some id ->
           (* Check if there is only one backward function, and no forward function *)
           if (not keep_fwd) && num_backs = 1 then
@@ -1340,9 +1368,9 @@ let extract_fun_comment (ctx : extraction_ctx) (fmt : F.formatter)
           else [ "backward function " ^ T.RegionGroupId.to_string id ]
     in
     match fwd_back_comment with
-    | [] -> raise (Failure "Unreachable")
-    | [ s ] -> [ comment_pre ^ loop_comment ^ s ]
-    | s :: sl -> (comment_pre ^ loop_comment ^ s) :: sl
+    | [] -> [ comment_pre ^ loop_comment ]
+    | [ s ] -> [ comment_pre ^ loop_comment ^ " " ^ s ]
+    | s :: sl -> (comment_pre ^ loop_comment ^ " " ^ s) :: sl
   in
   extract_comment_with_span fmt comment def.meta.span
 
@@ -1470,7 +1498,7 @@ let extract_fun_decl_gen (ctx : extraction_ctx) (fmt : F.formatter)
       let inputs_lvs =
         let all_inputs = (Option.get def.body).inputs_lvs in
         let num_fwd_inputs =
-          def.signature.info.num_fwd_inputs_with_fuel_with_state
+          def.signature.fwd_info.fwd_info.num_inputs_with_fuel_with_state
         in
         Collections.List.prefix num_fwd_inputs all_inputs
       in
@@ -1516,7 +1544,7 @@ let extract_fun_decl_gen (ctx : extraction_ctx) (fmt : F.formatter)
     let def_body = Option.get def.body in
     let all_vars = List.map (fun (v : var) -> v.id) def_body.inputs in
     let num_fwd_inputs =
-      def.signature.info.num_fwd_inputs_with_fuel_with_state
+      def.signature.fwd_info.fwd_info.num_inputs_with_fuel_with_state
     in
     let vars = Collections.List.prefix num_fwd_inputs all_vars in
 
@@ -1794,7 +1822,6 @@ let extract_global_decl (ctx : extraction_ctx) (fmt : F.formatter)
   assert body.is_global_decl_body;
   assert (Option.is_none body.back_id);
   assert (body.signature.inputs = []);
-  assert (List.length body.signature.doutputs = 1);
   assert (body.signature.generics = empty_generic_params);
 
   (* Add a break then the name of the corresponding LLBC declaration *)
@@ -1813,7 +1840,8 @@ let extract_global_decl (ctx : extraction_ctx) (fmt : F.formatter)
 
   let decl_ty, body_ty =
     let ty = body.signature.output in
-    if body.signature.info.effect_info.can_fail then (unwrap_result_ty ty, ty)
+    if body.signature.fwd_info.effect_info.can_fail then
+      (unwrap_result_ty ty, ty)
     else (ty, mk_result_ty ty)
   in
   match body.body with
@@ -1984,7 +2012,8 @@ let extract_trait_decl_method_names (ctx : extraction_ctx)
     (* 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)
+      if !Config.return_back_funs then [ trans.fwd.f ]
+      else List.map (fun f -> f.f) (trans.fwd :: trans.backs)
     in
     match builtin_info with
     | None ->
diff --git a/compiler/ExtractBase.ml b/compiler/ExtractBase.ml
index eb2a2ec9..db887539 100644
--- a/compiler/ExtractBase.ml
+++ b/compiler/ExtractBase.ml
@@ -351,7 +351,7 @@ let basename_to_unique (names_set : StringSet.t)
     let s = append basename i in
     if StringSet.mem s names_set then gen (i + 1) else s
   in
-  if StringSet.mem basename names_set then gen 0 else basename
+  if StringSet.mem basename names_set then gen 1 else basename
 
 type fun_name_info = { keep_fwd : bool; num_backs : int }
 
@@ -1051,33 +1051,60 @@ let assumed_variants () : (assumed_ty * VariantId.id * string) list =
 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");
-      ]
-  | 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");
-      ]
+  let regular : (A.assumed_fun_id * T.RegionGroupId.id option * string) list =
+    match !backend with
+    | FStar | Coq | HOL4 ->
+        [
+          (ArrayIndexShared, None, "array_index_usize");
+          (ArrayToSliceShared, None, "array_to_slice");
+          (ArrayRepeat, None, "array_repeat");
+          (SliceIndexShared, None, "slice_index_usize");
+        ]
+    | Lean ->
+        [
+          (ArrayIndexShared, None, "Array.index_usize");
+          (ArrayToSliceShared, None, "Array.to_slice");
+          (ArrayRepeat, None, "Array.repeat");
+          (SliceIndexShared, None, "Slice.index_usize");
+        ]
+  in
+  let mut_funs : (A.assumed_fun_id * T.RegionGroupId.id option * string) list =
+    if !Config.return_back_funs then
+      match !backend with
+      | FStar | Coq | HOL4 ->
+          [
+            (ArrayIndexMut, None, "array_index_mut_usize");
+            (ArrayToSliceMut, None, "array_to_slice_mut");
+            (SliceIndexMut, None, "slice_index_mut_usize");
+          ]
+      | Lean ->
+          [
+            (ArrayIndexMut, None, "Array.index_mut_usize");
+            (ArrayToSliceMut, None, "Array.to_slice_mut");
+            (SliceIndexMut, None, "Slice.index_mut_usize");
+          ]
+    else
+      match !backend with
+      | FStar | Coq | HOL4 ->
+          [
+            (ArrayIndexMut, None, "array_index_usize");
+            (ArrayIndexMut, rg0, "array_update_usize");
+            (ArrayToSliceMut, None, "array_to_slice");
+            (ArrayToSliceMut, rg0, "array_from_slice");
+            (SliceIndexMut, None, "slice_index_usize");
+            (SliceIndexMut, rg0, "slice_update_usize");
+          ]
+      | Lean ->
+          [
+            (ArrayIndexMut, None, "Array.index_usize");
+            (ArrayIndexMut, rg0, "Array.update_usize");
+            (ArrayToSliceMut, None, "Array.to_slice");
+            (ArrayToSliceMut, rg0, "Array.from_slice");
+            (SliceIndexMut, None, "Slice.index_usize");
+            (SliceIndexMut, rg0, "Slice.update_usize");
+          ]
+  in
+  regular @ mut_funs
 
 let assumed_pure_functions () : (pure_assumed_fun_id * string) list =
   match !backend with
diff --git a/compiler/ExtractBuiltin.ml b/compiler/ExtractBuiltin.ml
index 24d16dca..ee8d4831 100644
--- a/compiler/ExtractBuiltin.ml
+++ b/compiler/ExtractBuiltin.ml
@@ -232,6 +232,14 @@ let builtin_funs () : (pattern * bool list option * builtin_fun_info list) list
   let mk_fun (rust_name : string) (extract_name : string option)
       (filter : bool list option) (with_back : bool) (back_no_suffix : bool) :
       pattern * bool list option * builtin_fun_info list =
+    (* [back_no_suffix] is used to control whether the backward function should
+       have the suffix "_back" or not (if not, then the forward function has the
+       prefix "_fwd", and is filtered anyway). This is pertinent only if we split
+       the fwd/back functions. *)
+    let back_no_suffix = back_no_suffix && not !Config.return_back_funs in
+    (* Same for the [with_back] option: this is pertinent only if we split
+       the fwd/back functions *)
+    let with_back = with_back && not !Config.return_back_funs in
     let rust_name =
       try parse_pattern rust_name
       with Failure _ ->
diff --git a/compiler/Interpreter.ml b/compiler/Interpreter.ml
index 76432faa..22d176c9 100644
--- a/compiler/Interpreter.ml
+++ b/compiler/Interpreter.ml
@@ -195,7 +195,7 @@ let initialize_symbolic_context_for_fun (ctx : decls_ctx) (fdef : fun_decl) :
     List.map (fun (g : region_var_group) -> g.id) regions_hierarchy
   in
   let ctx =
-    initialize_eval_context ctx region_groups sg.generics.types
+    initialize_eval_ctx ctx region_groups sg.generics.types
       sg.generics.const_generics
   in
   (* Instantiate the signature. This updates the context because we compute
@@ -277,7 +277,7 @@ let evaluate_function_symbolic_synthesize_backward_from_return (config : config)
    * an instantiation of the signature, so that we use fresh
    * region ids for the return abstractions. *)
   let regions_hierarchy =
-    FunIdMap.find (FRegular fdef.def_id) ctx.fun_context.regions_hierarchies
+    FunIdMap.find (FRegular fdef.def_id) ctx.fun_ctx.regions_hierarchies
   in
   let _, ret_inst_sg =
     symbolic_instantiate_fun_sig ctx fdef.signature regions_hierarchy fdef.kind
@@ -466,7 +466,7 @@ let evaluate_function_symbolic (synthesize : bool) (ctx : decls_ctx)
   let ctx, input_svs, inst_sg = initialize_symbolic_context_for_fun ctx fdef in
 
   let regions_hierarchy =
-    FunIdMap.find (FRegular fdef.def_id) ctx.fun_context.regions_hierarchies
+    FunIdMap.find (FRegular fdef.def_id) ctx.fun_ctx.regions_hierarchies
   in
 
   (* Create the continuation to finish the evaluation *)
@@ -615,7 +615,7 @@ module Test = struct
     assert (body.arg_count = 0);
 
     (* Create the evaluation context *)
-    let ctx = initialize_eval_context decls_ctx [] [] [] in
+    let ctx = initialize_eval_ctx decls_ctx [] [] [] in
 
     (* Insert the (uninitialized) local variables *)
     let ctx = ctx_push_uninitialized_vars ctx body.locals in
diff --git a/compiler/InterpreterBorrows.ml b/compiler/InterpreterBorrows.ml
index e56919fa..a2eb2545 100644
--- a/compiler/InterpreterBorrows.ml
+++ b/compiler/InterpreterBorrows.ml
@@ -1628,7 +1628,7 @@ let destructure_abs (abs_kind : abs_kind) (can_end : bool)
             push { value; ty }
         | AIgnoredMutLoan (opt_bid, child_av) ->
             (* We don't support nested borrows for now *)
-            assert (not (ty_has_borrows ctx.type_context.type_infos child_av.ty));
+            assert (not (ty_has_borrows ctx.type_ctx.type_infos child_av.ty));
             assert (opt_bid = None);
             (* Simply explore the child *)
             list_avalues false push_fail child_av
@@ -1639,7 +1639,7 @@ let destructure_abs (abs_kind : abs_kind) (can_end : bool)
             { child = child_av; given_back = _; given_back_meta = _ }
         | AIgnoredSharedLoan child_av ->
             (* We don't support nested borrows for now *)
-            assert (not (ty_has_borrows ctx.type_context.type_infos child_av.ty));
+            assert (not (ty_has_borrows ctx.type_ctx.type_infos child_av.ty));
             (* Simply explore the child *)
             list_avalues false push_fail child_av)
     | ABorrow bc -> (
@@ -1659,14 +1659,14 @@ let destructure_abs (abs_kind : abs_kind) (can_end : bool)
             push av
         | AIgnoredMutBorrow (opt_bid, child_av) ->
             (* We don't support nested borrows for now *)
-            assert (not (ty_has_borrows ctx.type_context.type_infos child_av.ty));
+            assert (not (ty_has_borrows ctx.type_ctx.type_infos child_av.ty));
             assert (opt_bid = None);
             (* Just explore the child *)
             list_avalues false push_fail child_av
         | AEndedIgnoredMutBorrow
             { child = child_av; given_back = _; given_back_meta = _ } ->
             (* We don't support nested borrows for now *)
-            assert (not (ty_has_borrows ctx.type_context.type_infos child_av.ty));
+            assert (not (ty_has_borrows ctx.type_ctx.type_infos child_av.ty));
             (* Just explore the child *)
             list_avalues false push_fail child_av
         | AProjSharedBorrow asb ->
@@ -1683,7 +1683,7 @@ let destructure_abs (abs_kind : abs_kind) (can_end : bool)
     | ASymbolic _ ->
         (* For now, we fore all symbolic values containing borrows to be eagerly
            expanded *)
-        assert (not (ty_has_borrows ctx.type_context.type_infos ty))
+        assert (not (ty_has_borrows ctx.type_ctx.type_infos ty))
   and list_values (v : typed_value) : typed_avalue list * typed_value =
     let ty = v.ty in
     match v.value with
@@ -1732,7 +1732,7 @@ let destructure_abs (abs_kind : abs_kind) (can_end : bool)
     | VSymbolic _ ->
         (* For now, we fore all symbolic values containing borrows to be eagerly
            expanded *)
-        assert (not (ty_has_borrows ctx.type_context.type_infos ty));
+        assert (not (ty_has_borrows ctx.type_ctx.type_infos ty));
         ([], v)
   in
 
diff --git a/compiler/InterpreterExpansion.ml b/compiler/InterpreterExpansion.ml
index bbf4d9d5..e489ddc3 100644
--- a/compiler/InterpreterExpansion.ml
+++ b/compiler/InterpreterExpansion.ml
@@ -627,7 +627,7 @@ let greedy_expand_symbolics_with_borrows (config : config) : cm_fun =
       inherit [_] iter_eval_ctx
 
       method! visit_VSymbolic _ sv =
-        if ty_has_borrows ctx.type_context.type_infos sv.sv_ty then
+        if ty_has_borrows ctx.type_ctx.type_infos sv.sv_ty then
           raise (FoundSymbolicValue sv)
         else ()
 
diff --git a/compiler/InterpreterExpressions.ml b/compiler/InterpreterExpressions.ml
index 1b5b79dd..8536b4ab 100644
--- a/compiler/InterpreterExpressions.ml
+++ b/compiler/InterpreterExpressions.ml
@@ -32,8 +32,7 @@ let expand_primitively_copyable_at_place (config : config)
    fun cf ctx ->
     let v = read_place access p ctx in
     match
-      find_first_primitively_copyable_sv_with_borrows
-        ctx.type_context.type_infos v
+      find_first_primitively_copyable_sv_with_borrows ctx.type_ctx.type_infos v
     with
     | None -> cf ctx
     | Some sv ->
@@ -351,7 +350,7 @@ let eval_operand_no_reorganize (config : config) (op : operand)
         assert (
           Option.is_none
             (find_first_primitively_copyable_sv_with_borrows
-               ctx.type_context.type_infos v));
+               ctx.type_ctx.type_infos v));
         (* Actually perform the copy *)
         let allow_adt_copy = false in
         let ctx, v = copy_value allow_adt_copy config ctx v in
diff --git a/compiler/InterpreterExpressions.mli b/compiler/InterpreterExpressions.mli
index f8d979f4..b975371c 100644
--- a/compiler/InterpreterExpressions.mli
+++ b/compiler/InterpreterExpressions.mli
@@ -52,7 +52,7 @@ val eval_operands :
 
     Transmits the computed rvalue to the received continuation.
 
-    Note that this function fails on {!constructor:Aeneas.Expressions.rvalue.Discriminant}: discriminant
+    Note that this function fails on {!Aeneas.Expressions.rvalue.Discriminant}: discriminant
     reads should have been eliminated from the AST.
  *)
 val eval_rvalue_not_global :
diff --git a/compiler/InterpreterLoopsFixedPoint.ml b/compiler/InterpreterLoopsFixedPoint.ml
index c4e180fa..4dabe974 100644
--- a/compiler/InterpreterLoopsFixedPoint.ml
+++ b/compiler/InterpreterLoopsFixedPoint.ml
@@ -300,7 +300,7 @@ let prepare_ashared_loans (loop_id : LoopId.id option) : cm_fun =
   let env = List.append fresh_absl env in
   let ctx = { ctx with env } in
 
-  let _, new_ctx_ids_map = compute_context_ids ctx in
+  let _, new_ctx_ids_map = compute_ctx_ids ctx in
 
   (* Synthesize *)
   match cf ctx with
@@ -385,8 +385,8 @@ let compute_loop_entry_fixed_point (config : config) (loop_id : LoopId.id)
       match !fixed_ids with
       | Some _ -> ctx1
       | None ->
-          let old_ids, _ = compute_context_ids ctx1 in
-          let new_ids, _ = compute_contexts_ids !ctxs in
+          let old_ids, _ = compute_ctx_ids ctx1 in
+          let new_ids, _ = compute_ctxs_ids !ctxs in
           let blids = BorrowId.Set.diff old_ids.blids new_ids.blids in
           let aids = AbstractionId.Set.diff old_ids.aids new_ids.aids in
           (* End those borrows and abstractions *)
@@ -409,7 +409,7 @@ let compute_loop_entry_fixed_point (config : config) (loop_id : LoopId.id)
           ctxs := List.map (end_borrows_abs blids aids) !ctxs;
           (* Note that the fixed ids are given by the original context, from *before*
              we introduce fresh abstractions/reborrows for the shared values *)
-          fixed_ids := Some (fst (compute_context_ids ctx0));
+          fixed_ids := Some (fst (compute_ctx_ids ctx0));
           ctx1
     in
 
@@ -424,12 +424,12 @@ let compute_loop_entry_fixed_point (config : config) (loop_id : LoopId.id)
      intersection of ids between the original environment and the list
      of new environments *)
   let compute_fixed_ids (ctxl : eval_ctx list) : ids_sets =
-    let fixed_ids, _ = compute_context_ids ctx0 in
+    let fixed_ids, _ = compute_ctx_ids ctx0 in
     let { aids; blids; borrow_ids; loan_ids; dids; rids; sids } = fixed_ids in
     let sids = ref sids in
     List.iter
       (fun ctx ->
-        let fixed_ids, _ = compute_context_ids ctx in
+        let fixed_ids, _ = compute_ctx_ids ctx in
         sids := SymbolicValueId.Set.inter !sids fixed_ids.sids)
       ctxl;
     let sids = !sids in
@@ -568,7 +568,7 @@ let compute_loop_entry_fixed_point (config : config) (loop_id : LoopId.id)
                   InterpreterBorrows.end_abstraction_no_synth config abs_id ctx
                 in
                 (* Explore the context, and check which abstractions are not there anymore *)
-                let ids, _ = compute_context_ids ctx in
+                let ids, _ = compute_ctx_ids ctx in
                 let ended_ids = AbstractionId.Set.diff !fp_aids ids.aids in
                 add_ended_aids rg_id ended_ids)
               ctx.region_groups
@@ -840,8 +840,8 @@ let compute_fixed_point_id_correspondance (fixed_ids : ids_sets)
 
 let compute_fp_ctx_symbolic_values (ctx : eval_ctx) (fp_ctx : eval_ctx) :
     SymbolicValueId.Set.t * symbolic_value list =
-  let old_ids, _ = compute_context_ids ctx in
-  let fp_ids, fp_ids_maps = compute_context_ids fp_ctx in
+  let old_ids, _ = compute_ctx_ids ctx in
+  let fp_ids, fp_ids_maps = compute_ctx_ids fp_ctx in
   let fresh_sids = SymbolicValueId.Set.diff fp_ids.sids old_ids.sids in
 
   (* Compute the set of symbolic values which appear in shared values inside
diff --git a/compiler/InterpreterLoopsJoinCtxs.ml b/compiler/InterpreterLoopsJoinCtxs.ml
index 8d485483..445e5abf 100644
--- a/compiler/InterpreterLoopsJoinCtxs.ml
+++ b/compiler/InterpreterLoopsJoinCtxs.ml
@@ -326,8 +326,8 @@ let mk_collapse_ctx_merge_duplicate_funs (loop_id : LoopId.id) (ctx : eval_ctx)
     let _ =
       let _, ty0, _ = ty_as_ref ty0 in
       let _, ty1, _ = ty_as_ref ty1 in
-      assert (not (ty_has_borrows ctx.type_context.type_infos ty0));
-      assert (not (ty_has_borrows ctx.type_context.type_infos ty1))
+      assert (not (ty_has_borrows ctx.type_ctx.type_infos ty0));
+      assert (not (ty_has_borrows ctx.type_ctx.type_infos ty1))
     in
 
     (* Same remarks as for [merge_amut_borrows] *)
@@ -543,11 +543,11 @@ let join_ctxs (loop_id : LoopId.id) (fixed_ids : ids_sets) (ctx0 : eval_ctx)
     (* Construct the joined context - of course, the type, fun, etc. contexts
      * should be the same in the two contexts *)
     let {
-      type_context;
-      fun_context;
-      global_context;
-      trait_decls_context;
-      trait_impls_context;
+      type_ctx;
+      fun_ctx;
+      global_ctx;
+      trait_decls_ctx;
+      trait_impls_ctx;
       region_groups;
       type_vars;
       const_generic_vars;
@@ -559,11 +559,11 @@ let join_ctxs (loop_id : LoopId.id) (fixed_ids : ids_sets) (ctx0 : eval_ctx)
       ctx0
     in
     let {
-      type_context = _;
-      fun_context = _;
-      global_context = _;
-      trait_decls_context = _;
-      trait_impls_context = _;
+      type_ctx = _;
+      fun_ctx = _;
+      global_ctx = _;
+      trait_decls_ctx = _;
+      trait_impls_ctx = _;
       region_groups = _;
       type_vars = _;
       const_generic_vars = _;
@@ -577,11 +577,11 @@ let join_ctxs (loop_id : LoopId.id) (fixed_ids : ids_sets) (ctx0 : eval_ctx)
     let ended_regions = RegionId.Set.union ended_regions0 ended_regions1 in
     Ok
       {
-        type_context;
-        fun_context;
-        global_context;
-        trait_decls_context;
-        trait_impls_context;
+        type_ctx;
+        fun_ctx;
+        global_ctx;
+        trait_decls_ctx;
+        trait_impls_ctx;
         region_groups;
         type_vars;
         const_generic_vars;
@@ -621,7 +621,7 @@ let destructure_new_abs (loop_id : LoopId.id)
     contexts we join don't have non-fixed abstractions with the same ids.
   *)
 let refresh_abs (old_abs : AbstractionId.Set.t) (ctx : eval_ctx) : eval_ctx =
-  let ids, _ = compute_context_ids ctx in
+  let ids, _ = compute_ctx_ids ctx in
   let abs_to_refresh = AbstractionId.Set.diff ids.aids old_abs in
   let aids_subst =
     List.map
diff --git a/compiler/InterpreterLoopsMatchCtxs.ml b/compiler/InterpreterLoopsMatchCtxs.ml
index 90559c29..2a688fa7 100644
--- a/compiler/InterpreterLoopsMatchCtxs.ml
+++ b/compiler/InterpreterLoopsMatchCtxs.ml
@@ -658,7 +658,7 @@ module MakeJoinMatcher (S : MatchJoinState) : PrimMatcher = struct
     else (
       (* The caller should have checked that the symbolic values don't contain
          borrows *)
-      assert (not (ty_has_borrows S.ctx.type_context.type_infos sv0.sv_ty));
+      assert (not (ty_has_borrows S.ctx.type_ctx.type_infos sv0.sv_ty));
       (* We simply introduce a fresh symbolic value *)
       mk_fresh_symbolic_value sv0.sv_ty)
 
@@ -669,7 +669,7 @@ module MakeJoinMatcher (S : MatchJoinState) : PrimMatcher = struct
        - there are no borrows in the "regular" value
        If there are loans in the regular value, raise an exception.
     *)
-    assert (not (ty_has_borrows S.ctx.type_context.type_infos sv.sv_ty));
+    assert (not (ty_has_borrows S.ctx.type_ctx.type_infos sv.sv_ty));
     assert (not (value_has_borrows S.ctx v.value));
     let value_is_left = not left in
     (match InterpreterBorrowsCore.get_first_loan_in_value v with
diff --git a/compiler/InterpreterStatements.ml b/compiler/InterpreterStatements.ml
index 30b7b333..97c8bcd6 100644
--- a/compiler/InterpreterStatements.ml
+++ b/compiler/InterpreterStatements.ml
@@ -728,7 +728,13 @@ let create_push_abstractions_from_abs_region_groups
     to a trait clause but directly to the method provided in the trait declaration.
  *)
 let eval_transparent_function_call_symbolic_inst (call : call) (ctx : eval_ctx)
-    : fun_id_or_trait_method_ref * generic_args * fun_decl * inst_fun_sig =
+    :
+    fun_id_or_trait_method_ref
+    * generic_args
+    * (generic_args * trait_instance_id) option
+    * fun_decl
+    * region_var_groups
+    * inst_fun_sig =
   match call.func with
   | FnOpMove _ ->
       (* Closure case: TODO *)
@@ -747,13 +753,13 @@ let eval_transparent_function_call_symbolic_inst (call : call) (ctx : eval_ctx)
           let tr_self = UnknownTrait __FUNCTION__ in
           let regions_hierarchy =
             LlbcAstUtils.FunIdMap.find (FRegular fid)
-              ctx.fun_context.regions_hierarchies
+              ctx.fun_ctx.regions_hierarchies
           in
           let inst_sg =
             instantiate_fun_sig ctx func.generics tr_self def.signature
               regions_hierarchy
           in
-          (func.func, func.generics, def, inst_sg)
+          (func.func, func.generics, None, def, regions_hierarchy, inst_sg)
       | FunId (FAssumed _) ->
           (* Unreachable: must be a transparent function *)
           raise (Failure "Unreachable")
@@ -793,7 +799,7 @@ let eval_transparent_function_call_symbolic_inst (call : call) (ctx : eval_ctx)
                   let fid : fun_id = FRegular id in
                   let regions_hierarchy =
                     LlbcAstUtils.FunIdMap.find fid
-                      ctx.fun_context.regions_hierarchies
+                      ctx.fun_ctx.regions_hierarchies
                   in
                   let inst_sg =
                     instantiate_fun_sig ctx generics tr_self
@@ -806,7 +812,12 @@ let eval_transparent_function_call_symbolic_inst (call : call) (ctx : eval_ctx)
                      we also need to update the generics.
                   *)
                   let func = FunId fid in
-                  (func, generics, method_def, inst_sg)
+                  ( func,
+                    generics,
+                    Some (generics, tr_self),
+                    method_def,
+                    regions_hierarchy,
+                    inst_sg )
               | None ->
                   (* If not found, lookup the methods provided by the trait *declaration*
                      (remember: for now, we forbid overriding provided methods) *)
@@ -853,14 +864,19 @@ let eval_transparent_function_call_symbolic_inst (call : call) (ctx : eval_ctx)
                           method_def.signature.parent_params_info));
                   let regions_hierarchy =
                     LlbcAstUtils.FunIdMap.find (FRegular method_id)
-                      ctx.fun_context.regions_hierarchies
+                      ctx.fun_ctx.regions_hierarchies
                   in
                   let tr_self = TraitRef trait_ref in
                   let inst_sg =
                     instantiate_fun_sig ctx all_generics tr_self
                       method_def.signature regions_hierarchy
                   in
-                  (func.func, func.generics, method_def, inst_sg))
+                  ( func.func,
+                    func.generics,
+                    Some (all_generics, tr_self),
+                    method_def,
+                    regions_hierarchy,
+                    inst_sg ))
           | _ ->
               (* We are using a local clause - we lookup the trait decl *)
               let trait_decl =
@@ -884,14 +900,19 @@ let eval_transparent_function_call_symbolic_inst (call : call) (ctx : eval_ctx)
               (* Instantiate *)
               let regions_hierarchy =
                 LlbcAstUtils.FunIdMap.find (FRegular method_id)
-                  ctx.fun_context.regions_hierarchies
+                  ctx.fun_ctx.regions_hierarchies
               in
               let tr_self = TraitRef trait_ref in
               let inst_sg =
                 instantiate_fun_sig ctx generics tr_self method_def.signature
                   regions_hierarchy
               in
-              (func.func, func.generics, method_def, inst_sg)))
+              ( func.func,
+                func.generics,
+                Some (generics, tr_self),
+                method_def,
+                regions_hierarchy,
+                inst_sg )))
 
 (** Evaluate a statement *)
 let rec eval_statement (config : config) (st : statement) : st_cm_fun =
@@ -1277,14 +1298,15 @@ and eval_transparent_function_call_concrete (config : config)
 and eval_transparent_function_call_symbolic (config : config) (call : call) :
     st_cm_fun =
  fun cf ctx ->
-  let func, generics, def, inst_sg =
+  let func, generics, trait_method_generics, def, regions_hierarchy, inst_sg =
     eval_transparent_function_call_symbolic_inst call ctx
   in
   (* Sanity check *)
   assert (List.length call.args = List.length def.signature.inputs);
   (* Evaluate the function call *)
-  eval_function_call_symbolic_from_inst_sig config func inst_sg generics
-    call.args call.dest cf ctx
+  eval_function_call_symbolic_from_inst_sig config func def.signature
+    regions_hierarchy inst_sg generics trait_method_generics call.args call.dest
+    cf ctx
 
 (** Evaluate a function call in symbolic mode by using the function signature.
 
@@ -1298,8 +1320,11 @@ and eval_transparent_function_call_symbolic (config : config) (call : call) :
     trait ref as input.
  *)
 and eval_function_call_symbolic_from_inst_sig (config : config)
-    (fid : fun_id_or_trait_method_ref) (inst_sg : inst_fun_sig)
-    (generics : generic_args) (args : operand list) (dest : place) : st_cm_fun =
+    (fid : fun_id_or_trait_method_ref) (sg : fun_sig)
+    (regions_hierarchy : region_var_groups) (inst_sg : inst_fun_sig)
+    (generics : generic_args)
+    (trait_method_generics : (generic_args * trait_instance_id) option)
+    (args : operand list) (dest : place) : st_cm_fun =
  fun cf ctx ->
   log#ldebug
     (lazy
@@ -1378,8 +1403,9 @@ and eval_function_call_symbolic_from_inst_sig (config : config)
     let expr = cf ctx in
 
     (* Synthesize the symbolic AST *)
-    S.synthesize_regular_function_call fid call_id ctx abs_ids generics args
-      args_places ret_spc dest_place expr
+    S.synthesize_regular_function_call fid call_id ctx sg regions_hierarchy
+      abs_ids generics trait_method_generics args args_places ret_spc dest_place
+      expr
   in
   let cc = comp cc cf_call in
 
@@ -1450,7 +1476,7 @@ and eval_assumed_function_call_symbolic (config : config) (fid : assumed_fun_id)
    * this is a current limitation of our synthesis *)
   assert (
     List.for_all
-      (fun ty -> not (ty_has_borrows ctx.type_context.type_infos ty))
+      (fun ty -> not (ty_has_borrows ctx.type_ctx.type_infos ty))
       generics.types);
 
   (* There are two cases (and this is extremely annoying):
@@ -1468,7 +1494,7 @@ and eval_assumed_function_call_symbolic (config : config) (fid : assumed_fun_id)
       (* In symbolic mode, the behaviour of a function call is completely defined
        * by the signature of the function: we thus simply generate correctly
        * instantiated signatures, and delegate the work to an auxiliary function *)
-      let inst_sig =
+      let sg, regions_hierarchy, inst_sig =
         match fid with
         | BoxFree ->
             (* Should have been treated above *)
@@ -1476,18 +1502,20 @@ and eval_assumed_function_call_symbolic (config : config) (fid : assumed_fun_id)
         | _ ->
             let regions_hierarchy =
               LlbcAstUtils.FunIdMap.find (FAssumed fid)
-                ctx.fun_context.regions_hierarchies
+                ctx.fun_ctx.regions_hierarchies
             in
             (* There shouldn't be any reference to Self *)
             let tr_self = UnknownTrait __FUNCTION__ in
-            instantiate_fun_sig ctx generics tr_self
-              (Assumed.get_assumed_fun_sig fid)
-              regions_hierarchy
+            let sg = Assumed.get_assumed_fun_sig fid in
+            let inst_sg =
+              instantiate_fun_sig ctx generics tr_self sg regions_hierarchy
+            in
+            (sg, regions_hierarchy, inst_sg)
       in
 
       (* Evaluate the function call *)
-      eval_function_call_symbolic_from_inst_sig config (FunId (FAssumed fid))
-        inst_sig generics args dest cf ctx
+      eval_function_call_symbolic_from_inst_sig config (FunId (FAssumed fid)) sg
+        regions_hierarchy inst_sig generics None args dest cf ctx
 
 (** Evaluate a statement seen as a function body *)
 and eval_function_body (config : config) (body : statement) : st_cm_fun =
diff --git a/compiler/InterpreterUtils.ml b/compiler/InterpreterUtils.ml
index e04a6b90..a1a06ee5 100644
--- a/compiler/InterpreterUtils.ml
+++ b/compiler/InterpreterUtils.ml
@@ -265,7 +265,7 @@ let value_has_ret_symbolic_value_with_borrow_under_mut (ctx : eval_ctx)
       inherit [_] iter_typed_value
 
       method! visit_symbolic_value _ s =
-        if ty_has_borrow_under_mut ctx.type_context.type_infos s.sv_ty then
+        if ty_has_borrow_under_mut ctx.type_ctx.type_infos s.sv_ty then
           raise Found
         else ()
     end
@@ -288,15 +288,15 @@ let rvalue_get_place (rv : rvalue) : place option =
 
 (** See {!ValuesUtils.symbolic_value_has_borrows} *)
 let symbolic_value_has_borrows (ctx : eval_ctx) (sv : symbolic_value) : bool =
-  ValuesUtils.symbolic_value_has_borrows ctx.type_context.type_infos sv
+  ValuesUtils.symbolic_value_has_borrows ctx.type_ctx.type_infos sv
 
 (** See {!ValuesUtils.value_has_borrows}. *)
 let value_has_borrows (ctx : eval_ctx) (v : value) : bool =
-  ValuesUtils.value_has_borrows ctx.type_context.type_infos v
+  ValuesUtils.value_has_borrows ctx.type_ctx.type_infos v
 
 (** See {!ValuesUtils.value_has_loans_or_borrows}. *)
 let value_has_loans_or_borrows (ctx : eval_ctx) (v : value) : bool =
-  ValuesUtils.value_has_loans_or_borrows ctx.type_context.type_infos v
+  ValuesUtils.value_has_loans_or_borrows ctx.type_ctx.type_infos v
 
 (** See {!ValuesUtils.value_has_loans}. *)
 let value_has_loans (v : value) : bool = ValuesUtils.value_has_loans v
@@ -401,19 +401,19 @@ let compute_env_elem_ids (x : env_elem) : ids_sets * ids_to_values =
   compute_env_ids [ x ]
 
 (** Compute the sets of ids found in a list of contexts. *)
-let compute_contexts_ids (ctxl : eval_ctx list) : ids_sets * ids_to_values =
+let compute_ctxs_ids (ctxl : eval_ctx list) : ids_sets * ids_to_values =
   let compute, get_ids, get_ids_to_values = compute_ids () in
   List.iter (compute#visit_eval_ctx ()) ctxl;
   (get_ids (), get_ids_to_values ())
 
 (** Compute the sets of ids found in a context. *)
-let compute_context_ids (ctx : eval_ctx) : ids_sets * ids_to_values =
-  compute_contexts_ids [ ctx ]
+let compute_ctx_ids (ctx : eval_ctx) : ids_sets * ids_to_values =
+  compute_ctxs_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 : decls_ctx)
+let initialize_eval_ctx (ctx : decls_ctx)
     (region_groups : RegionGroupId.id list) (type_vars : type_var list)
     (const_generic_vars : const_generic_var list) : eval_ctx =
   reset_global_counters ();
@@ -427,11 +427,11 @@ let initialize_eval_context (ctx : decls_ctx)
          const_generic_vars)
   in
   {
-    type_context = ctx.type_ctx;
-    fun_context = ctx.fun_ctx;
-    global_context = ctx.global_ctx;
-    trait_decls_context = ctx.trait_decls_ctx;
-    trait_impls_context = ctx.trait_impls_ctx;
+    type_ctx = ctx.type_ctx;
+    fun_ctx = ctx.fun_ctx;
+    global_ctx = ctx.global_ctx;
+    trait_decls_ctx = ctx.trait_decls_ctx;
+    trait_impls_ctx = ctx.trait_impls_ctx;
     region_groups;
     type_vars;
     const_generic_vars;
diff --git a/compiler/Invariants.ml b/compiler/Invariants.ml
index fa0d7436..b87cdff7 100644
--- a/compiler/Invariants.ml
+++ b/compiler/Invariants.ml
@@ -768,7 +768,7 @@ let check_symbolic_values (ctx : eval_ctx) : unit =
     assert (info.env_count = 0 || info.aproj_borrows = []);
     (* A symbolic value containing borrows can't be duplicated (i.e., copied):
      * it must be expanded first *)
-    if ty_has_borrows ctx.type_context.type_infos info.ty then
+    if ty_has_borrows ctx.type_ctx.type_infos info.ty then
       assert (info.env_count <= 1);
     (* A duplicated symbolic value is necessarily primitively copyable *)
     assert (info.env_count <= 1 || ty_is_primitively_copyable info.ty);
diff --git a/compiler/Main.ml b/compiler/Main.ml
index 835b9088..0b8ec439 100644
--- a/compiler/Main.ml
+++ b/compiler/Main.ml
@@ -120,6 +120,9 @@ let () =
         " 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");
+      ( "-split-fwd-back",
+        Arg.Clear return_back_funs,
+        " Split the forward and backward functions." );
     ]
   in
 
@@ -193,9 +196,6 @@ let () =
   let _ =
     match !backend with
     | FStar ->
-        (* Some patterns are not supported *)
-        decompose_monadic_let_bindings := false;
-        decompose_nested_let_patterns := false;
         (* F* can disambiguate the field names *)
         record_fields_short_names := true
     | Coq ->
diff --git a/compiler/Print.ml b/compiler/Print.ml
index 0e2ec1fc..8999c77d 100644
--- a/compiler/Print.ml
+++ b/compiler/Print.ml
@@ -409,11 +409,11 @@ module Contexts = struct
     }
 
   let eval_ctx_to_fmt_env (ctx : eval_ctx) : fmt_env =
-    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 trait_decls = ctx.trait_decls_context.trait_decls in
-    let trait_impls = ctx.trait_impls_context.trait_impls in
+    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
     (* Below: it is always safe to omit fields - if an id can't be found at
        printing time, we print the id (in raw form) instead of the name it
        designates. *)
diff --git a/compiler/PrintPure.ml b/compiler/PrintPure.ml
index 2fe5843e..66475d02 100644
--- a/compiler/PrintPure.ml
+++ b/compiler/PrintPure.ml
@@ -103,10 +103,13 @@ let adt_field_names (env : fmt_env) =
   Print.Types.adt_field_names (fmt_env_to_llbc_fmt_env env)
 
 let option_to_string = Print.option_to_string
-let type_var_to_string = Print.Types.type_var_to_string
-let const_generic_var_to_string = Print.Types.const_generic_var_to_string
-let integer_type_to_string = Print.Values.integer_type_to_string
 let literal_type_to_string = Print.Values.literal_type_to_string
+let type_var_to_string (v : type_var) = "(" ^ v.name ^ ": Type)"
+
+let const_generic_var_to_string (v : const_generic_var) =
+  "(" ^ v.name ^ " : " ^ literal_type_to_string v.ty ^ ")"
+
+let integer_type_to_string = Print.Values.integer_type_to_string
 let scalar_value_to_string = Print.Values.scalar_value_to_string
 let literal_to_string = Print.Values.literal_to_string
 
@@ -203,13 +206,12 @@ and trait_instance_id_to_string (env : fmt_env) (inside : bool)
   | UnknownTrait msg -> "UNKNOWN(" ^ msg ^ ")"
 
 let trait_clause_to_string (env : fmt_env) (clause : trait_clause) : string =
-  let clause_id = trait_clause_id_to_string env clause.clause_id in
   let trait_id = trait_decl_id_to_string env clause.trait_id in
   let generics = generic_args_to_strings env true clause.generics in
   let generics =
     if generics = [] then "" else " " ^ String.concat " " generics
   in
-  "[" ^ clause_id ^ "]: " ^ trait_id ^ generics
+  trait_id ^ generics
 
 let generic_params_to_strings (env : fmt_env) (generics : generic_params) :
     string list =
@@ -543,9 +545,9 @@ let rec texpression_to_string (env : fmt_env) (inside : bool) (indent : string)
       let app, args = destruct_apps e in
       (* Convert to string *)
       app_to_string env inside indent indent_incr app args
-  | Abs _ ->
-      let xl, e = destruct_abs_list e in
-      let e = abs_to_string env indent indent_incr xl e in
+  | Lambda _ ->
+      let xl, e = destruct_lambdas e in
+      let e = lambda_to_string env indent indent_incr xl e in
       if inside then "(" ^ e ^ ")" else e
   | Qualif _ ->
       (* Qualifier without arguments *)
@@ -609,35 +611,36 @@ and app_to_string (env : fmt_env) (inside : bool) (indent : string)
    * expression *)
   let app, generics =
     match app.e with
-    | Qualif qualif ->
+    | Qualif qualif -> (
         (* Qualifier case *)
-        (* Convert the qualifier identifier *)
-        let qualif_s =
-          match qualif.id with
-          | FunOrOp fun_id -> fun_or_op_id_to_string env fun_id
-          | Global global_id -> global_decl_id_to_string env global_id
-          | AdtCons adt_cons_id ->
-              let variant_s =
-                adt_variant_to_string env adt_cons_id.adt_id
-                  adt_cons_id.variant_id
-              in
-              ConstStrings.constructor_prefix ^ variant_s
-          | Proj { adt_id; field_id } ->
-              let adt_s = adt_variant_to_string env adt_id None in
-              let field_s = adt_field_to_string env 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 env true trait_ref in
-              let generics_s = generic_args_to_string env generics in
+        match qualif.id with
+        | FunOrOp fun_id ->
+            let generics = generic_args_to_strings env true qualif.generics in
+            let qualif_s = fun_or_op_id_to_string env fun_id in
+            (qualif_s, generics)
+        | Global global_id ->
+            let generics = generic_args_to_strings env true qualif.generics in
+            (global_decl_id_to_string env global_id, generics)
+        | AdtCons adt_cons_id ->
+            let variant_s =
+              adt_variant_to_string env adt_cons_id.adt_id
+                adt_cons_id.variant_id
+            in
+            (ConstStrings.constructor_prefix ^ variant_s, [])
+        | Proj { adt_id; field_id } ->
+            let adt_s = adt_variant_to_string env adt_id None in
+            let field_s = adt_field_to_string env 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 env true trait_ref in
+            let generics_s = generic_args_to_string env generics in
+            let qualif =
               if generics <> empty_generic_args then
                 "(" ^ trait_ref ^ generics_s ^ ")." ^ const_name
               else trait_ref ^ "." ^ const_name
-        in
-        (* Convert the type instantiation *)
-        let generics = generic_args_to_strings env true qualif.generics in
-        (* *)
-        (qualif_s, generics)
+            in
+            (qualif, []))
     | _ ->
         (* "Regular" expression case *)
         let inside = args <> [] || (args = [] && inside) in
@@ -660,7 +663,7 @@ and app_to_string (env : fmt_env) (inside : bool) (indent : string)
   (* Add parentheses *)
   if all_args <> [] && inside then "(" ^ e ^ ")" else e
 
-and abs_to_string (env : fmt_env) (indent : string) (indent_incr : string)
+and lambda_to_string (env : fmt_env) (indent : string) (indent_incr : string)
     (xl : typed_pattern list) (e : texpression) : string =
   let xl = List.map (typed_pattern_to_string env) xl in
   let e = texpression_to_string env false indent indent_incr e in
@@ -708,21 +711,14 @@ and loop_to_string (env : fmt_env) (indent : string) (indent_incr : string)
     ^ String.concat "; " (List.map (var_to_string env) loop.inputs)
     ^ "]"
   in
-  let back_output_tys =
-    let tys =
-      match loop.back_output_tys with
-      | None -> ""
-      | Some tys -> String.concat "; " (List.map (ty_to_string env false) tys)
-    in
-    "back_output_tys: [" ^ tys ^ "]"
-  in
+  let output_ty = "output_ty: " ^ ty_to_string env false loop.output_ty in
   let fun_end =
     texpression_to_string env false indent2 indent_incr loop.fun_end
   in
   let loop_body =
     texpression_to_string env false indent2 indent_incr loop.loop_body
   in
-  "loop {\n" ^ indent1 ^ loop_inputs ^ "\n" ^ indent1 ^ back_output_tys ^ "\n"
+  "loop {\n" ^ indent1 ^ loop_inputs ^ "\n" ^ indent1 ^ output_ty ^ "\n"
   ^ indent1 ^ "fun_end: {\n" ^ indent2 ^ fun_end ^ "\n" ^ indent1 ^ "}\n"
   ^ indent1 ^ "loop_body: {\n" ^ indent2 ^ loop_body ^ "\n" ^ indent1 ^ "}\n"
   ^ indent ^ "}"
diff --git a/compiler/Pure.ml b/compiler/Pure.ml
index 8d39cc69..a879ba37 100644
--- a/compiler/Pure.ml
+++ b/compiler/Pure.ml
@@ -561,7 +561,7 @@ type fun_id_or_trait_method_ref =
 
 (** A function id for a non-assumed function *)
 type regular_fun_id =
-  fun_id_or_trait_method_ref * LoopId.id option * T.RegionGroupId.id option
+  fun_id_or_trait_method_ref * LoopId.id option * RegionGroupId.id option
 [@@deriving show, ord]
 
 (** A function identifier *)
@@ -684,7 +684,7 @@ type expression =
           field accesses with calls to projectors over fields (when there
           are clashes of field names, some provers like F* get pretty bad...)
        *)
-  | Abs of typed_pattern * texpression  (** Lambda abstraction: [fun x -> e] *)
+  | Lambda of typed_pattern * texpression  (** Lambda abstraction: [λ x => e] *)
   | Qualif of qualif  (** A top-level qualifier *)
   | Let of bool * typed_pattern * texpression * texpression
       (** Let binding.
@@ -754,9 +754,7 @@ and loop = {
   inputs : var list;
   inputs_lvs : typed_pattern list;
       (** The inputs seen as patterns. See {!fun_body}. *)
-  back_output_tys : ty list option;
-      (** The types of the given back values, if we ar esynthesizing a backward
-          function *)
+  output_ty : ty;  (** The output type of the loop *)
   loop_body : texpression;
 }
 
@@ -860,8 +858,8 @@ type fun_effect_info = {
           the set [{ forward function } U { backward functions }].
 
           We need this because of the option {!val:Config.backward_no_state_update}:
-          if it is [true], then in case of a backward function {!stateful} is [false],
-          but we might need to know whether the corresponding forward function
+          if it is [true], then in case of a backward function {!stateful} might be
+          [false], but we might need to know whether the corresponding forward function
           is stateful or not.
        *)
   stateful : bool;  (** [true] if the function is stateful (updates a state) *)
@@ -873,22 +871,108 @@ type fun_effect_info = {
 }
 [@@deriving show]
 
-(** Meta information about a function signature *)
-type fun_sig_info = {
+type inputs_info = {
   has_fuel : bool;
-  (* TODO: add [num_fwd_inputs_no_fuel_no_state] *)
-  num_fwd_inputs_with_fuel_no_state : int;
-      (** The number of input types for forward computation, with the fuel (if used)
+  num_inputs_no_fuel_no_state : int;
+      (** The number of input types ignoring the fuel (if used)
+          and ignoring the state (if used) *)
+  num_inputs_with_fuel_no_state : int;
+      (** The number of input types, with the fuel (if used)
           and ignoring the state (if used) *)
-  num_fwd_inputs_with_fuel_with_state : int;
-      (** The number of input types for forward computation, with fuel and state (if used) *)
-  num_back_inputs_no_state : int option;
-      (** The number of additional inputs for the backward computation (if pertinent),
-          ignoring the state (if there is one) *)
-  num_back_inputs_with_state : int option;
-      (** The number of additional inputs for the backward computation (if pertinent),
-          with the state (if there is one) *)
+  num_inputs_with_fuel_with_state : int;
+      (** The number of input types, with fuel and state (if used) *)
+}
+[@@deriving show]
+
+(** Meta information about a function signature *)
+type fun_sig_info = {
+  fwd_info : inputs_info;
+      (** Information about the inputs of the forward function *)
   effect_info : fun_effect_info;
+  ignore_output : bool;
+      (** In case we merge the forward/backward functions: should we ignore
+          the output (happens for forward functions if the output type is
+          [unit] and there are non-filtered backward functions)?
+       *)
+}
+[@@deriving show]
+
+type back_sg_info = {
+  inputs : (string option * ty) list;
+      (** The additional inputs of the backward function *)
+  inputs_no_state : (string option * ty) list;
+  outputs : ty list;
+      (** The "decomposed" list of outputs.
+
+          The list contains all the types of
+          all the given back values (there is at most one type per forward
+          input argument).
+
+          Ex.:
+          {[
+            fn choose<'a, T>(b : bool, x : &'a mut T, y : &'a mut T) -> &'a mut T;
+          ]}
+          Decomposed outputs:
+          - forward function:  [[T]]
+          - backward function: [[T; T]] (for "x" and "y")
+
+          Non-decomposed ouputs (if the function can fail, but is not stateful):
+          - [result T]
+          - [[result (T * T)]]
+       *)
+  output_names : string option list;
+      (** The optional names for the backward outputs.
+          We derive those from the names of the inputs of the original LLBC
+          function. *)
+  effect_info : fun_effect_info;
+  filter : bool;  (** Should we filter this backward function? *)
+}
+[@@deriving show]
+
+(** A *decomposed* function signature. *)
+type decomposed_fun_sig = {
+  generics : generic_params;
+      (** TODO: we should analyse the signature to make the type parameters implicit whenever possible *)
+  llbc_generics : Types.generic_params;
+      (** We use the LLBC generics to generate "pretty" names, for instance
+          for the variables we introduce for the trait clauses: we derive
+          those names from the types, and when doing so it is more meaningful
+          to derive them from the original LLBC types from before the
+          simplification of types like boxes and references. *)
+  preds : predicates;
+  fwd_inputs : ty list;
+      (** The types of the inputs of the forward function.
+
+          Note that those input types take include the [fuel] parameter,
+          if the function uses fuel for termination, and the [state] parameter,
+          if the function is stateful.
+
+          For instance, if we have the following Rust function:
+          {[
+            fn f(x : int);
+          ]}
+
+          If we translate it to a stateful function which uses fuel we get:
+          {[
+            val f : nat -> int -> state -> result (state * unit);
+          ]}
+
+          In particular, the list of input types is: [[nat; int; state]].
+       *)
+  fwd_output : ty;
+      (** The "pure" output type of the forward function.
+
+          Note that this type doesn't contain the "effect" of the function (i.e.,
+          we haven't added the [state] if it is a stateful function and haven't
+          wrapped the type in a [result]). Also, this output type is only about
+          the forward function (it doesn't contain the type of the closures we
+          return for the backward functions, in case we merge the forward and
+          backward functions).
+       *)
+  back_sg : back_sg_info RegionGroupId.Map.t;
+      (** Information about the backward functions *)
+  fwd_info : fun_sig_info;
+      (** Additional information about the forward function *)
 }
 [@@deriving show]
 
@@ -906,15 +990,15 @@ type fun_sig_info = {
       [in_ty0 -> ... -> in_tyn -> state -> back_in0 -> ... back_inm -> state ->
        result (state & (back_out0 & ... & back_outp))] (* state-error *)
 
-       Note that a stateful backward function may take two states as inputs: the
-       state received by the associated forward function, and the state at which
-       the backward is called. This leads to code of the following shape:
+      Note that a stateful backward function may take two states as inputs: the
+      state received by the associated forward function, and the state at which
+      the backward is called. This leads to code of the following shape:
 
-       {[
-         (st1, y)  <-- f_fwd x st0; // st0 is the state upon calling f_fwd
-         ... // the state may be updated
-         (st3, x') <-- f_back x st0 y' st2; // st2 is the state upon calling f_back
-       ]}
+      {[
+        (st1, y)  <-- f_fwd x st0; // st0 is the state upon calling f_fwd
+        ... // the state may be updated
+        (st3, x') <-- f_back x st0 y' st2; // st2 is the state upon calling f_back
+      ]}
 
     The function's type should be given by [mk_arrows sig.inputs sig.output].
     We provide additional meta-information with {!fun_sig.info}:
@@ -962,40 +1046,14 @@ type fun_sig = {
           be a tuple with a [state] if the function is stateful, and will be wrapped
           in a [result] if the function can fail.
        *)
-  doutputs : ty list;
-      (** The "decomposed" list of outputs.
-
-          In case of a forward function, the list has length = 1, for the
-          type of the returned value.
-
-          In case of backward function, the list contains all the types of
-          all the given back values (there is at most one type per forward
-          input argument).
-
-          Ex.:
-          {[
-            fn choose<'a, T>(b : bool, x : &'a mut T, y : &'a mut T) -> &'a mut T;
-          ]}
-          Decomposed outputs:
-          - forward function:  [[T]]
-          - backward function: [[T; T]] (for "x" and "y")
-
-          Non-decomposed ouputs (if the function can fail, but is not stateful):
-          - [result T]
-          - [[result (T * T)]]
-       *)
-  info : fun_sig_info;  (** Additional information *)
+  fwd_info : fun_sig_info;
+      (** Additional information about the forward function. *)
+  back_effect_info : fun_effect_info RegionGroupId.Map.t;
 }
 [@@deriving show]
 
 (** An instantiated function signature. See {!fun_sig} *)
-type inst_fun_sig = {
-  inputs : ty list;
-  output : ty;
-  doutputs : ty list;
-  info : fun_sig_info;
-}
-[@@deriving show]
+type inst_fun_sig = { inputs : ty list; output : ty } [@@deriving show]
 
 type fun_body = {
   inputs : var list;
@@ -1020,7 +1078,7 @@ type fun_decl = {
        *)
   loop_id : LoopId.id option;
       (** [Some] if this definition was generated for a loop *)
-  back_id : T.RegionGroupId.id option;
+  back_id : RegionGroupId.id option;
   llbc_name : llbc_name;  (** The original LLBC name. *)
   name : string;
       (** We use the name only for printing purposes (for debugging):
diff --git a/compiler/PureMicroPasses.ml b/compiler/PureMicroPasses.ml
index 959ec1c8..ec64df21 100644
--- a/compiler/PureMicroPasses.ml
+++ b/compiler/PureMicroPasses.ml
@@ -11,6 +11,10 @@ let fun_decl_to_string (ctx : trans_ctx) (def : Pure.fun_decl) : string =
   let fmt = trans_ctx_to_pure_fmt_env ctx in
   PrintPure.fun_decl_to_string fmt def
 
+let fun_sig_to_string (ctx : trans_ctx) (sg : Pure.fun_sig) : string =
+  let fmt = trans_ctx_to_pure_fmt_env ctx in
+  PrintPure.fun_sig_to_string fmt sg
+
 (** Small utility.
 
     We sometimes have to insert new fresh variables in a function body, in which
@@ -385,17 +389,17 @@ let compute_pretty_names (def : fun_decl) : fun_decl =
           let ctx, arg = update_texpression arg ctx in
           let e = App (app, arg) in
           (ctx, e)
-      | Abs (x, e) -> update_abs x e ctx
       | Qualif _ -> (* nothing to do *) (ctx, e.e)
       | Let (monadic, lb, re, e) -> update_let monadic lb re e ctx
       | Switch (scrut, body) -> update_switch_body scrut body ctx
       | Loop loop -> update_loop loop ctx
       | StructUpdate supd -> update_struct_update supd ctx
+      | Lambda (lb, e) -> update_lambda lb e ctx
       | Meta (meta, e) -> update_emeta meta e ctx
     in
     (ctx, { e; ty })
   (* *)
-  and update_abs (x : typed_pattern) (e : texpression) (ctx : pn_ctx) :
+  and update_lambda (x : typed_pattern) (e : texpression) (ctx : pn_ctx) :
       pn_ctx * expression =
     (* We first add the left-constraint *)
     let ctx = add_left_constraint x ctx in
@@ -404,7 +408,7 @@ let compute_pretty_names (def : fun_decl) : fun_decl =
     (* Update the abstracted value *)
     let x = update_typed_pattern ctx x in
     (* Put together *)
-    (ctx, Abs (x, e))
+    (ctx, Lambda (x, e))
   (* *)
   and update_let (monadic : bool) (lv : typed_pattern) (re : texpression)
       (e : texpression) (ctx : pn_ctx) : pn_ctx * expression =
@@ -455,7 +459,7 @@ let compute_pretty_names (def : fun_decl) : fun_decl =
       input_state;
       inputs;
       inputs_lvs;
-      back_output_tys;
+      output_ty;
       loop_body;
     } =
       loop
@@ -474,7 +478,7 @@ let compute_pretty_names (def : fun_decl) : fun_decl =
         input_state;
         inputs;
         inputs_lvs;
-        back_output_tys;
+        output_ty;
         loop_body;
       }
     in
@@ -641,6 +645,135 @@ let intro_struct_updates (ctx : trans_ctx) (def : fun_decl) : fun_decl =
       let body = { body with body = obj#visit_texpression () body.body } in
       { def with body = Some body }
 
+(** Simplify the let-bindings by performing the following rewritings:
+
+    Move inner let-bindings outside. This is especially useful to simplify
+    the backward expressions, when we merge the forward/backward functions.
+    Note that the rule is also applied with monadic let-bindings.
+    {[
+      let x :=
+        let y := ... in
+        e
+
+        ~~>
+
+      let y := ... in
+      let x := e
+    ]}
+
+    Simplify panics and returns:
+    {[
+      let x ← fail
+      ...
+        ~~>
+      fail
+
+      let x ← return y
+      ...
+        ~~>
+      let x := y
+      ...
+    ]}
+
+    Simplify tuples:
+    {[
+      let (y0, y1) := (x0, x1) in
+      ...
+        ~~>
+      let y0 = x0 in
+      let y1 = x1 in
+      ...
+    ]}
+
+    Simplify arrows:
+    {[
+      let f := fun x => g x in
+      ...
+        ~~>
+      let f := g in
+      ...
+    ]}
+ *)
+let simplify_let_bindings (_ctx : trans_ctx) (def : fun_decl) : fun_decl =
+  let obj =
+    object (self)
+      inherit [_] map_expression as super
+
+      method! visit_Let env monadic lv rv next =
+        match rv.e with
+        | Let (rmonadic, rlv, rrv, rnext) ->
+            (* Case 1: move the inner let outside then re-visit *)
+            let rnext1 = Let (monadic, lv, rnext, next) in
+            let rnext1 = { ty = next.ty; e = rnext1 } in
+            self#visit_Let env rmonadic rlv rrv rnext1
+        | App
+            ( {
+                e =
+                  Qualif
+                    {
+                      id =
+                        AdtCons
+                          {
+                            adt_id = TAssumed TResult;
+                            variant_id = Some variant_id;
+                          };
+                      generics = _;
+                    };
+                ty = _;
+              },
+              x ) ->
+            (* return/fail case *)
+            if variant_id = result_return_id then
+              (* Return case - note that the simplification we just perform
+                 might have unlocked the tuple simplification below *)
+              self#visit_Let env false lv x next
+            else if variant_id = result_fail_id then
+              (* Fail case *)
+              self#visit_expression env rv.e
+            else raise (Failure "Unexpected")
+        | App _ ->
+            (* This might be the tuple case *)
+            if not monadic then
+              match
+                (opt_dest_struct_pattern lv, opt_dest_tuple_texpression rv)
+              with
+              | Some pats, Some vals ->
+                  (* Tuple case *)
+                  let pat_vals = List.combine pats vals in
+                  let e =
+                    List.fold_right
+                      (fun (pat, v) next -> mk_let false pat v next)
+                      pat_vals next
+                  in
+                  super#visit_expression env e.e
+              | _ -> super#visit_Let env monadic lv rv next
+            else super#visit_Let env monadic lv rv next
+        | Lambda _ ->
+            if not monadic then
+              (* Arrow case *)
+              let pats, e = destruct_lambdas rv in
+              let g, args = destruct_apps e in
+              if List.length pats = List.length args then
+                (* Check if the arguments are exactly the lambdas *)
+                let check_pat_arg ((pat, arg) : typed_pattern * texpression) =
+                  match (pat.value, arg.e) with
+                  | PatVar (v, _), Var vid -> v.id = vid
+                  | _ -> false
+                in
+                if List.for_all check_pat_arg (List.combine pats args) then
+                  self#visit_Let env monadic lv g next
+                else super#visit_Let env monadic lv rv next
+              else super#visit_Let env monadic lv rv next
+            else super#visit_Let env monadic lv rv next
+        | _ -> super#visit_Let env monadic lv rv next
+    end
+  in
+  match def.body with
+  | None -> def
+  | Some body ->
+      let body = { body with body = obj#visit_texpression () body.body } in
+      { def with body = Some body }
+
 (** Inline the useless variable (re-)assignments:
 
     A lot of intermediate variable assignments are introduced through the
@@ -667,8 +800,8 @@ let intro_struct_updates (ctx : trans_ctx) (def : fun_decl) : fun_decl =
     leave the let-bindings where they are, and eliminated them in a subsequent
     pass (if they are useless).
  *)
-let inline_useless_var_reassignments (ctx : trans_ctx) (inline_named : bool)
-    (inline_pure : bool) (def : fun_decl) : fun_decl =
+let inline_useless_var_reassignments (ctx : trans_ctx) ~(inline_named : bool)
+    ~(inline_const : bool) ~(inline_pure : bool) (def : fun_decl) : fun_decl =
   let obj =
     object (self)
       inherit [_] map_expression as super
@@ -693,15 +826,31 @@ let inline_useless_var_reassignments (ctx : trans_ctx) (inline_named : bool)
               | _ -> false
             in
             (* And either:
-             * 2.1 the right-expression is a variable, a global or a const generic var *)
+               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
-             *     [inline_pure] is set *)
+               2.2 the right-expression is a constant-value and we inline constant values,
+                   *or* it is a qualif with no arguments (we consider this as a const) *)
+            let const_re =
+              inline_const
+              &&
+              let is_const_adt =
+                let app, args = destruct_apps re in
+                if args = [] then
+                  match app.e with
+                  | Qualif _ -> true
+                  | StructUpdate upd -> upd.updates = []
+                  | _ -> false
+                else false
+              in
+              is_const re || is_const_adt
+            in
+            (* Or:
+               2.3 the right-expression is an ADT value, a projection or a
+                   primitive function call *and* the flag [inline_pure] is set *)
             let pure_re =
-              is_const re
-              ||
+              inline_pure
+              &&
               let app, _ = destruct_apps re in
               match app.e with
               | Qualif qualif -> (
@@ -716,7 +865,7 @@ let inline_useless_var_reassignments (ctx : trans_ctx) (inline_named : bool)
               | _ -> false
             in
             let filter =
-              filter_left && (var_or_global || (inline_pure && pure_re))
+              filter_left && (var_or_global || const_re || pure_re)
             in
 
             (* Update the rhs (we may perform substitutions inside, and it is
@@ -776,9 +925,11 @@ let inline_useless_var_reassignments (ctx : trans_ctx) (inline_named : bool)
       in
       { def with body = Some body }
 
-(** Given a forward or backward function call, is there, for every execution
+(** For the cases where we split the forward/backward functions.
+
+    Given a forward or backward function call, is there, for every execution
     path, a child backward function called later with exactly the same input
-    list prefix? We use this to filter useless function calls: if there are
+    list prefix. We use this to filter useless function calls: if there are
     such child calls, we can remove this one (in case its outputs are not
     used).
     We do this check because we can't simply remove function calls whose
@@ -890,12 +1041,12 @@ let expression_contains_child_call_in_all_paths (ctx : trans_ctx)
                 let call_is_child = check_call func1 generics1 args1 in
                 if call_is_child then fun () -> true
                 else fun () -> self#visit_texpression env e ())
+        | Lambda (_, e) -> self#visit_texpression env e
         | App _ -> (
             fun () ->
               match opt_destruct_function_call e with
               | Some (func1, tys1, args1) -> check_call func1 tys1 args1
               | None -> false)
-        | Abs (_, e) -> self#visit_texpression env e
         | Qualif _ ->
             (* Note that this case includes functions without arguments *)
             fun () -> false
@@ -973,10 +1124,23 @@ let filter_useless (filter_monadic_calls : bool) (ctx : trans_ctx)
       method! visit_expression env e =
         match e with
         | Var _ | CVar _ | Const _ | App _ | Qualif _
-        | Switch (_, _)
         | Meta (_, _)
-        | StructUpdate _ | Abs _ ->
+        | StructUpdate _ | Lambda _ ->
             super#visit_expression env e
+        | Switch (scrut, switch) -> (
+            match switch with
+            | If (_, _) -> super#visit_expression env e
+            | Match branches ->
+                (* Simplify the branches *)
+                let simplify_branch (br : match_branch) =
+                  (* Compute the set of values used inside the branch *)
+                  let branch, used = self#visit_texpression env br.branch in
+                  (* Simplify the pattern *)
+                  let pat, _ = filter_typed_pattern (used ()) br.pat in
+                  { pat; branch }
+                in
+                super#visit_expression env
+                  (Switch (scrut, Match (List.map simplify_branch branches))))
         | Let (monadic, lv, re, e) ->
             (* Compute the set of values used in the next expression *)
             let e, used = self#visit_texpression env e in
@@ -1008,17 +1172,21 @@ let filter_useless (filter_monadic_calls : bool) (ctx : trans_ctx)
                  * under some conditions. *)
                 match (filter_monadic_calls, opt_destruct_function_call re) with
                 | true, Some (Fun (FromLlbc (fid, lp_id, rg_id)), tys, args) ->
-                    (* We need to check if there is a child call - see
-                     * the comments for:
-                     * [expression_contains_child_call_in_all_paths] *)
-                    let has_child_call =
-                      expression_contains_child_call_in_all_paths ctx fid lp_id
-                        rg_id tys args e
-                    in
-                    if has_child_call then (* Filter *)
-                      (e.e, fun _ -> used)
-                    else (* No child call: don't filter *)
-                      dont_filter ()
+                    (* If we split the forward/backward functions.
+
+                       We need to check if there is a child call - see
+                       the comments for:
+                       [expression_contains_child_call_in_all_paths] *)
+                    if not !Config.return_back_funs then
+                      let has_child_call =
+                        expression_contains_child_call_in_all_paths ctx fid
+                          lp_id rg_id tys args e
+                      in
+                      if has_child_call then (* Filter *)
+                        (e.e, fun _ -> used)
+                      else (* No child call: don't filter *)
+                        dont_filter ()
+                    else dont_filter ()
                 | _ ->
                     (* Not an LLBC function call or not allowed to filter: we can't filter *)
                     dont_filter ()
@@ -1297,7 +1465,8 @@ let filter_if_backward_with_no_outputs (def : fun_decl) : fun_decl option =
     those function bodies into independent definitions while removing
     occurrences of the {!Pure.Loop} node.
  *)
-let decompose_loops (def : fun_decl) : fun_decl * fun_decl list =
+let decompose_loops (_ctx : trans_ctx) (def : fun_decl) :
+    fun_decl * fun_decl list =
   match def.body with
   | None -> (def, [])
   | Some body ->
@@ -1323,77 +1492,55 @@ let decompose_loops (def : fun_decl) : fun_decl * fun_decl list =
 
           method! visit_Loop env loop =
             let fun_sig = def.signature in
-            let fun_sig_info = fun_sig.info in
-            let fun_effect_info = fun_sig_info.effect_info in
+            let fwd_info = fun_sig.fwd_info in
+            let fwd_effect_info = fwd_info.effect_info in
+            let ignore_output = fwd_info.ignore_output in
 
             (* Generate the loop definition *)
-            let loop_effect_info =
-              {
-                stateful_group = fun_effect_info.stateful_group;
-                stateful = fun_effect_info.stateful;
-                can_fail = fun_effect_info.can_fail;
-                can_diverge = fun_effect_info.can_diverge;
-                is_rec = fun_effect_info.is_rec;
-              }
-            in
+            let loop_fwd_effect_info = fwd_effect_info in
 
-            let loop_sig_info =
+            let loop_fwd_sig_info : fun_sig_info =
               let fuel = if !Config.use_fuel then 1 else 0 in
               let num_inputs = List.length loop.inputs in
-              let num_fwd_inputs_with_fuel_no_state = fuel + num_inputs in
-              let fwd_state =
-                fun_sig_info.num_fwd_inputs_with_fuel_with_state
-                - fun_sig_info.num_fwd_inputs_with_fuel_no_state
-              in
-              let num_fwd_inputs_with_fuel_with_state =
-                num_fwd_inputs_with_fuel_no_state + fwd_state
+              let fwd_info : inputs_info =
+                let info = fwd_info.fwd_info in
+                let fwd_state =
+                  info.num_inputs_with_fuel_with_state
+                  - info.num_inputs_with_fuel_no_state
+                in
+                {
+                  has_fuel = !Config.use_fuel;
+                  num_inputs_no_fuel_no_state = num_inputs;
+                  num_inputs_with_fuel_no_state = num_inputs + fuel;
+                  num_inputs_with_fuel_with_state =
+                    num_inputs + fuel + fwd_state;
+                }
               in
-              {
-                has_fuel = !Config.use_fuel;
-                num_fwd_inputs_with_fuel_no_state;
-                num_fwd_inputs_with_fuel_with_state;
-                num_back_inputs_no_state = fun_sig_info.num_back_inputs_no_state;
-                num_back_inputs_with_state =
-                  fun_sig_info.num_back_inputs_with_state;
-                effect_info = loop_effect_info;
-              }
+
+              { fwd_info; effect_info = loop_fwd_effect_info; ignore_output }
             in
+            assert (fun_sig_info_is_wf loop_fwd_sig_info);
 
             let inputs_tys =
               let fuel = if !Config.use_fuel then [ mk_fuel_ty ] else [] in
               let fwd_inputs = List.map (fun (v : var) -> v.ty) loop.inputs in
-              let state =
+              let info = fwd_info.fwd_info in
+              let fwd_state =
                 Collections.List.subslice fun_sig.inputs
-                  fun_sig_info.num_fwd_inputs_with_fuel_no_state
-                  fun_sig_info.num_fwd_inputs_with_fuel_with_state
+                  info.num_inputs_with_fuel_no_state
+                  info.num_inputs_with_fuel_with_state
               in
-              let _, back_inputs =
-                Collections.List.split_at fun_sig.inputs
-                  fun_sig_info.num_fwd_inputs_with_fuel_with_state
+              let back_inputs =
+                if !Config.return_back_funs then []
+                else
+                  snd
+                    (Collections.List.split_at fun_sig.inputs
+                       info.num_inputs_with_fuel_with_state)
               in
-              List.concat [ fuel; fwd_inputs; state; back_inputs ]
+              List.concat [ fuel; fwd_inputs; fwd_state; back_inputs ]
             in
 
-            let output, doutputs =
-              match loop.back_output_tys with
-              | None ->
-                  (* Forward function: the return type is the same as the
-                     parent function *)
-                  (fun_sig.output, fun_sig.doutputs)
-              | Some doutputs ->
-                  (* Backward function: custom return type *)
-                  let output = mk_simpl_tuple_ty doutputs in
-                  let output =
-                    if loop_effect_info.stateful then
-                      mk_simpl_tuple_ty [ mk_state_ty; output ]
-                    else output
-                  in
-                  let output =
-                    if loop_effect_info.can_fail then mk_result_ty output
-                    else output
-                  in
-                  (output, doutputs)
-            in
+            let output = loop.output_ty in
 
             let loop_sig =
               {
@@ -1402,8 +1549,8 @@ let decompose_loops (def : fun_decl) : fun_decl * fun_decl list =
                 preds = fun_sig.preds;
                 inputs = inputs_tys;
                 output;
-                doutputs;
-                info = loop_sig_info;
+                fwd_info = loop_fwd_sig_info;
+                back_effect_info = fun_sig.back_effect_info;
               }
             in
 
@@ -1420,7 +1567,8 @@ let decompose_loops (def : fun_decl) : fun_decl * fun_decl list =
               (* Introduce the forward input state *)
               let fwd_state_var, fwd_state_lvs =
                 assert (
-                  loop_effect_info.stateful = Option.is_some loop.input_state);
+                  loop_fwd_effect_info.stateful
+                  = Option.is_some loop.input_state);
                 match loop.input_state with
                 | None -> ([], [])
                 | Some input_state ->
@@ -1429,15 +1577,16 @@ let decompose_loops (def : fun_decl) : fun_decl * fun_decl list =
                     ([ state_var ], [ state_lvs ])
               in
 
-              (* Introduce the additional backward inputs *)
+              (* Introduce the additional backward inputs, if necessary *)
               let fun_body = Option.get def.body in
+              let info = fwd_info.fwd_info in
               let _, back_inputs =
                 Collections.List.split_at fun_body.inputs
-                  fun_sig_info.num_fwd_inputs_with_fuel_with_state
+                  info.num_inputs_with_fuel_with_state
               in
               let _, back_inputs_lvs =
                 Collections.List.split_at fun_body.inputs_lvs
-                  fun_sig_info.num_fwd_inputs_with_fuel_with_state
+                  info.num_inputs_with_fuel_with_state
               in
 
               let inputs =
@@ -1508,9 +1657,12 @@ let decompose_loops (def : fun_decl) : fun_decl * fun_decl list =
     altogether.
   *)
 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
+  (* The question of filtering the forward functions arises only if we split
+     the forward/backward functions *)
+  if !Config.return_back_funs then true
+  else if
+    (* Note that at this point, the output types are no longer seen as tuples:
+     * they should be lists of length 1. *)
     !Config.filter_useless_functions
     && fwd.f.signature.output = mk_result_ty mk_unit_ty
     && backs <> []
@@ -1816,11 +1968,15 @@ let apply_end_passes_to_def (ctx : trans_ctx) (def : fun_decl) : fun_decl =
   log#ldebug
     (lazy ("intro_struct_updates:\n\n" ^ fun_decl_to_string ctx def ^ "\n"));
 
+  (* Simplify the let-bindings *)
+  let def = simplify_let_bindings ctx def in
+  log#ldebug
+    (lazy ("simplify_let_bindings:\n\n" ^ fun_decl_to_string ctx def ^ "\n"));
+
   (* Inline the useless variable reassignments *)
-  let inline_named_vars = true in
-  let inline_pure = true in
   let def =
-    inline_useless_var_reassignments ctx inline_named_vars inline_pure def
+    inline_useless_var_reassignments ctx ~inline_named:true ~inline_const:true
+      ~inline_pure:true def
   in
   log#ldebug
     (lazy
@@ -1867,6 +2023,23 @@ let apply_end_passes_to_def (ctx : trans_ctx) (def : fun_decl) : fun_decl =
   log#ldebug
     (lazy ("simplify_aggregates:\n\n" ^ fun_decl_to_string ctx def ^ "\n"));
 
+  (* Simplify the let-bindings - some simplifications may have been unlocked by
+     the pass above (for instance, the lambda simplification) *)
+  let def = simplify_let_bindings ctx def in
+  log#ldebug
+    (lazy
+      ("simplify_let_bindings (pass 2):\n\n" ^ fun_decl_to_string ctx def ^ "\n"));
+
+  (* Inline the useless vars again *)
+  let def =
+    inline_useless_var_reassignments ctx ~inline_named:true ~inline_const:true
+      ~inline_pure:false def
+  in
+  log#ldebug
+    (lazy
+      ("inline_useless_var_assignments (pass 2):\n\n"
+     ^ fun_decl_to_string ctx def ^ "\n"));
+
   (* Decompose the monadic let-bindings - used by Coq *)
   let def =
     if !Config.decompose_monadic_let_bindings then (
@@ -1917,67 +2090,6 @@ let apply_end_passes_to_def (ctx : trans_ctx) (def : fun_decl) : fun_decl =
   (* We are done *)
   def
 
-(** Apply all the micro-passes to a function.
-
-    As loops are initially directly integrated into the function definition,
-    {!apply_passes_to_def} extracts those loops definitions from the body;
-    it thus returns the pair: (function def, loop defs). See {!decompose_loops}
-    for more information.
-
-    Will return [None] if the function is a backward function with no outputs.
-
-    [ctx]: used only for printing.
- *)
-let apply_passes_to_def (ctx : trans_ctx) (def : fun_decl) :
-    fun_and_loops option =
-  (* Debug *)
-  log#ldebug
-    (lazy
-      ("PureMicroPasses.apply_passes_to_def: " ^ def.name ^ " ("
-      ^ Print.option_to_string T.RegionGroupId.to_string def.back_id
-      ^ ")"));
-
-  log#ldebug (lazy ("original decl:\n\n" ^ fun_decl_to_string ctx def ^ "\n"));
-
-  (* First, find names for the variables which are unnamed *)
-  let def = compute_pretty_names def in
-  log#ldebug
-    (lazy ("compute_pretty_name:\n\n" ^ fun_decl_to_string ctx def ^ "\n"));
-
-  (* TODO: we might want to leverage more the assignment meta-data, for
-   * aggregates for instance. *)
-
-  (* TODO: reorder the branches of the matches/switches *)
-
-  (* The meta-information is now useless: remove it.
-   * Rk.: some passes below use the fact that we removed the meta-data
-   * (otherwise we would have to "unmeta" expressions before matching) *)
-  let def = remove_meta def in
-  log#ldebug (lazy ("remove_meta:\n\n" ^ fun_decl_to_string ctx def ^ "\n"));
-
-  (* Remove the backward functions with no outputs.
-   * Note that the calls to those functions should already have been removed,
-   * when translating from symbolic to pure. Here, we remove the definitions
-   * altogether, because they are now useless *)
-  let name = def.name ^ PrintPure.fun_suffix def.loop_id def.back_id in
-  let opt_def = filter_if_backward_with_no_outputs def in
-
-  match opt_def with
-  | None ->
-      log#ldebug (lazy ("filtered (backward with no outputs): " ^ name ^ "\n"));
-      None
-  | Some def ->
-      log#ldebug
-        (lazy ("not filtered (not backward with no outputs): " ^ name ^ "\n"));
-
-      (* Extract the loop definitions by removing the {!Loop} node *)
-      let def, loops = decompose_loops def in
-
-      (* Apply the remaining passes *)
-      let f = apply_end_passes_to_def ctx def in
-      let loops = List.map (apply_end_passes_to_def ctx) loops in
-      Some { f; loops }
-
 (** Small utility for {!filter_loop_inputs} *)
 let filter_prefix (keep : bool list) (ls : 'a list) : 'a list =
   let ls0, ls1 = Collections.List.split_at ls (List.length keep) in
@@ -2058,7 +2170,7 @@ let filter_loop_inputs (transl : pure_fun_translation list) :
     (* We only look at the forward inputs, without the state *)
     let inputs_prefix, _ =
       Collections.List.split_at body.inputs
-        decl.signature.info.num_fwd_inputs_with_fuel_no_state
+        decl.signature.fwd_info.fwd_info.num_inputs_with_fuel_no_state
     in
     let used = ref (List.map (fun v -> (var_get_id v, false)) inputs_prefix) in
     let inputs_prefix_length = List.length inputs_prefix in
@@ -2077,8 +2189,9 @@ let filter_loop_inputs (transl : pure_fun_translation list) :
     in
 
     (* Set the fuel as used *)
-    let sg_info = decl.signature.info in
-    if sg_info.has_fuel then set_used (fst (Collections.List.nth inputs 0));
+    let sg_info = decl.signature.fwd_info in
+    if sg_info.fwd_info.has_fuel then
+      set_used (fst (Collections.List.nth inputs 0));
 
     let visitor =
       object (self : 'self)
@@ -2162,37 +2275,54 @@ let filter_loop_inputs (transl : pure_fun_translation list) :
           let num_filtered =
             List.length (List.filter (fun b -> not b) used_info)
           in
-          let { generics; llbc_generics; preds; inputs; output; doutputs; info }
-              =
+          let {
+            generics;
+            llbc_generics;
+            preds;
+            inputs;
+            output;
+            fwd_info;
+            back_effect_info;
+          } =
             decl.signature
           in
+          let { fwd_info; effect_info; ignore_output } = fwd_info in
+
           let {
             has_fuel;
-            num_fwd_inputs_with_fuel_no_state;
-            num_fwd_inputs_with_fuel_with_state;
-            num_back_inputs_no_state;
-            num_back_inputs_with_state;
-            effect_info;
+            num_inputs_no_fuel_no_state;
+            num_inputs_with_fuel_no_state;
+            num_inputs_with_fuel_with_state;
           } =
-            info
+            fwd_info
           in
 
           let inputs = filter_prefix used_info inputs in
 
-          let info =
+          let fwd_info =
             {
               has_fuel;
-              num_fwd_inputs_with_fuel_no_state =
-                num_fwd_inputs_with_fuel_no_state - num_filtered;
-              num_fwd_inputs_with_fuel_with_state =
-                num_fwd_inputs_with_fuel_with_state - num_filtered;
-              num_back_inputs_no_state;
-              num_back_inputs_with_state;
-              effect_info;
+              num_inputs_no_fuel_no_state =
+                num_inputs_no_fuel_no_state - num_filtered;
+              num_inputs_with_fuel_no_state =
+                num_inputs_with_fuel_no_state - num_filtered;
+              num_inputs_with_fuel_with_state =
+                num_inputs_with_fuel_with_state - num_filtered;
             }
           in
+
+          let fwd_info = { fwd_info; effect_info; ignore_output } in
+          assert (fun_sig_info_is_wf fwd_info);
           let signature =
-            { generics; llbc_generics; preds; inputs; output; doutputs; info }
+            {
+              generics;
+              llbc_generics;
+              preds;
+              inputs;
+              output;
+              fwd_info;
+              back_effect_info;
+            }
           in
 
           { decl with signature }
@@ -2283,6 +2413,68 @@ let filter_loop_inputs (transl : pure_fun_translation list) :
   (* Return *)
   transl
 
+(** Apply all the micro-passes to a function.
+
+    As loops are initially directly integrated into the function definition,
+    {!apply_passes_to_def} extracts those loops definitions from the body;
+    it thus returns the pair: (function def, loop defs). See {!decompose_loops}
+    for more information.
+
+    Will return [None] if the function is a backward function with no outputs.
+
+    [ctx]: used only for printing.
+ *)
+let apply_passes_to_def (ctx : trans_ctx) (def : fun_decl) :
+    fun_and_loops option =
+  (* Debug *)
+  log#ldebug
+    (lazy
+      ("PureMicroPasses.apply_passes_to_def: " ^ def.name ^ " ("
+      ^ Print.option_to_string T.RegionGroupId.to_string def.back_id
+      ^ ")"));
+
+  log#ldebug (lazy ("original decl:\n\n" ^ fun_decl_to_string ctx def ^ "\n"));
+
+  (* First, find names for the variables which are unnamed *)
+  let def = compute_pretty_names def in
+  log#ldebug
+    (lazy ("compute_pretty_name:\n\n" ^ fun_decl_to_string ctx def ^ "\n"));
+
+  (* TODO: we might want to leverage more the assignment meta-data, for
+   * aggregates for instance. *)
+
+  (* TODO: reorder the branches of the matches/switches *)
+
+  (* The meta-information is now useless: remove it.
+   * Rk.: some passes below use the fact that we removed the meta-data
+   * (otherwise we would have to "unmeta" expressions before matching) *)
+  let def = remove_meta def in
+  log#ldebug (lazy ("remove_meta:\n\n" ^ fun_decl_to_string ctx def ^ "\n"));
+
+  (* Remove the backward functions with no outputs.
+
+     Note that the *calls* to those functions should already have been removed,
+     when translating from symbolic to pure. Here, we remove the definitions
+     altogether, because they are now useless *)
+  let name = def.name ^ PrintPure.fun_suffix def.loop_id def.back_id in
+  let opt_def = filter_if_backward_with_no_outputs def in
+
+  match opt_def with
+  | None ->
+      log#ldebug (lazy ("filtered (backward with no outputs): " ^ name ^ "\n"));
+      None
+  | Some def ->
+      log#ldebug
+        (lazy ("not filtered (not backward with no outputs): " ^ name ^ "\n"));
+
+      (* Extract the loop definitions by removing the {!Loop} node *)
+      let def, loops = decompose_loops ctx def in
+
+      (* Apply the remaining passes *)
+      let f = apply_end_passes_to_def ctx def in
+      let loops = List.map (apply_end_passes_to_def ctx) loops in
+      Some { f; loops }
+
 (** Apply the micro-passes to a list of forward/backward translations.
 
     This function also extracts the loop definitions from the function body
diff --git a/compiler/PureTypeCheck.ml b/compiler/PureTypeCheck.ml
index a62a2361..a989fd3b 100644
--- a/compiler/PureTypeCheck.ml
+++ b/compiler/PureTypeCheck.ml
@@ -120,7 +120,7 @@ let rec check_texpression (ctx : tc_ctx) (e : texpression) : unit =
       assert (output_ty = e.ty);
       check_texpression ctx app;
       check_texpression ctx arg
-  | Abs (pat, body) ->
+  | Lambda (pat, body) ->
       let pat_ty, body_ty = destruct_arrow e.ty in
       assert (pat.ty = pat_ty);
       assert (body.ty = body_ty);
@@ -188,12 +188,6 @@ let rec check_texpression (ctx : tc_ctx) (e : texpression) : unit =
           List.iter check_branch branches)
   | Loop loop ->
       assert (loop.fun_end.ty = e.ty);
-      (* If we translate forward functions, the type of the loop is the same
-         as the type of the parent expression - in case of backward functions,
-         the loop doesn't necessarily give back the same values as the parent
-         function
-      *)
-      assert (Option.is_some loop.back_output_tys || loop.loop_body.ty = e.ty);
       check_texpression ctx loop.fun_end;
       check_texpression ctx loop.loop_body
   | StructUpdate supd -> (
diff --git a/compiler/PureUtils.ml b/compiler/PureUtils.ml
index 39dcd52d..80bf3c42 100644
--- a/compiler/PureUtils.ml
+++ b/compiler/PureUtils.ml
@@ -57,6 +57,23 @@ end
 module FunLoopIdMap = Collections.MakeMap (FunLoopIdOrderedType)
 module FunLoopIdSet = Collections.MakeSet (FunLoopIdOrderedType)
 
+let inputs_info_is_wf (info : inputs_info) : bool =
+  let {
+    has_fuel;
+    num_inputs_no_fuel_no_state;
+    num_inputs_with_fuel_no_state;
+    num_inputs_with_fuel_with_state;
+  } =
+    info
+  in
+  let fuel = if has_fuel then 1 else 0 in
+  num_inputs_no_fuel_no_state >= 0
+  && num_inputs_with_fuel_no_state = num_inputs_no_fuel_no_state + fuel
+  && num_inputs_with_fuel_with_state >= num_inputs_with_fuel_no_state
+
+let fun_sig_info_is_wf (info : fun_sig_info) : bool =
+  inputs_info_is_wf info.fwd_info
+
 let dest_arrow_ty (ty : ty) : ty * ty =
   match ty with
   | TArrow (arg_ty, ret_ty) -> (arg_ty, ret_ty)
@@ -187,9 +204,7 @@ 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
-  let info = sg.info in
-  { inputs; output; doutputs; info }
+  { inputs; output }
 
 (** We use this to check whether we need to add parentheses around expressions.
     We only look for outer monadic let-bindings.
@@ -200,12 +215,14 @@ let fun_sig_substitute (subst : subst) (sg : fun_sig) : inst_fun_sig =
  *)
 let rec let_group_requires_parentheses (e : texpression) : bool =
   match e.e with
-  | Var _ | CVar _ | Const _ | App _ | Abs _ | Qualif _ | StructUpdate _ ->
-      false
+  | Var _ | CVar _ | Const _ | App _ | Qualif _ | StructUpdate _ -> false
   | Let (monadic, _, _, next_e) ->
       if monadic then true else let_group_requires_parentheses next_e
   | Switch (_, _) -> false
   | Meta (_, next_e) -> let_group_requires_parentheses next_e
+  | Lambda (_, _) ->
+      (* Being conservative here *)
+      true
   | Loop _ ->
       (* Should have been eliminated *)
       raise (Failure "Unreachable")
@@ -304,14 +321,26 @@ let destruct_apps (e : texpression) : texpression * texpression list =
 
 (** Make an [App (app, arg)] expression *)
 let mk_app (app : texpression) (arg : texpression) : texpression =
+  let raise_or_return msg =
+    if !Config.fail_hard then raise (Failure msg)
+    else
+      let e = App (app, arg) in
+      (* Dummy type - TODO: introduce an error type *)
+      let ty = app.ty in
+      { e; ty }
+  in
   match app.ty with
   | TArrow (ty0, ty1) ->
       (* Sanity check *)
-      assert (ty0 = arg.ty);
-      let e = App (app, arg) in
-      let ty = ty1 in
-      { e; ty }
-  | _ -> raise (Failure "Expected an arrow type")
+      if
+        (* TODO: we need to normalize the types *)
+        !Config.type_check_pure_code && ty0 <> arg.ty
+      then raise_or_return "App: wrong input type"
+      else
+        let e = App (app, arg) in
+        let ty = ty1 in
+        { e; ty }
+  | _ -> raise_or_return "Expected an arrow type"
 
 (** The reverse of {!destruct_apps} *)
 let mk_apps (app : texpression) (args : texpression list) : texpression =
@@ -356,18 +385,6 @@ let opt_destruct_tuple (ty : ty) : ty list option =
       Some generics.types
   | _ -> None
 
-let mk_abs (x : typed_pattern) (e : texpression) : texpression =
-  let ty = TArrow (x.ty, e.ty) in
-  let e = Abs (x, e) in
-  { e; ty }
-
-let rec destruct_abs_list (e : texpression) : typed_pattern list * texpression =
-  match e.e with
-  | Abs (x, e') ->
-      let xl, e'' = destruct_abs_list e' in
-      (x :: xl, e'')
-  | _ -> ([], e)
-
 let destruct_arrow (ty : ty) : ty * ty =
   match ty with
   | TArrow (ty0, ty1) -> (ty0, ty1)
@@ -431,6 +448,7 @@ let mk_simpl_tuple_ty (tys : ty list) : ty =
 
 let mk_bool_ty : ty = TLiteral TBool
 let mk_unit_ty : ty = TAdt (TTuple, empty_generic_args)
+let ty_is_unit ty : bool = ty = mk_unit_ty
 
 let mk_unit_rvalue : texpression =
   let id = AdtCons { adt_id = TTuple; variant_id = None } in
@@ -698,3 +716,39 @@ let type_decl_from_type_id_is_tuple_struct (ctx : TypesAnalysis.type_infos)
       let info = TypeDeclId.Map.find id ctx in
       info.is_tuple_struct
   | TAssumed _ -> false
+
+let mk_lambda (x : typed_pattern) (e : texpression) : texpression =
+  let ty = TArrow (x.ty, e.ty) in
+  let e = Lambda (x, e) in
+  { e; ty }
+
+let mk_lambda_from_var (var : var) (mp : mplace option) (e : texpression) :
+    texpression =
+  let pat = PatVar (var, mp) in
+  let pat = { value = pat; ty = var.ty } in
+  mk_lambda pat e
+
+let mk_lambdas_from_vars (vars : var list) (mps : mplace option list)
+    (e : texpression) : texpression =
+  let vars = List.combine vars mps in
+  List.fold_right (fun (v, mp) e -> mk_lambda_from_var v mp e) vars e
+
+let rec destruct_lambdas (e : texpression) : typed_pattern list * texpression =
+  match e.e with
+  | Lambda (pat, e) ->
+      let pats, e = destruct_lambdas e in
+      (pat :: pats, e)
+  | _ -> ([], e)
+
+let opt_dest_tuple_texpression (e : texpression) : texpression list option =
+  let app, args = destruct_apps e in
+  match app.e with
+  | Qualif { id = AdtCons { adt_id = TTuple; variant_id = None }; generics = _ }
+    ->
+      Some args
+  | _ -> None
+
+let opt_dest_struct_pattern (pat : typed_pattern) : typed_pattern list option =
+  match pat.value with
+  | PatAdt { variant_id = None; field_values } -> Some field_values
+  | _ -> None
diff --git a/compiler/SymbolicAst.ml b/compiler/SymbolicAst.ml
index 53f99b7f..8e8cdec3 100644
--- a/compiler/SymbolicAst.ml
+++ b/compiler/SymbolicAst.ml
@@ -42,8 +42,16 @@ type call = {
           evaluated). We need it to compute the translated values for shared
           borrows (we need to perform lookups).
        *)
+  sg : fun_sig option;
+      (** The uninstantiated function signature, if this is not a unop/binop *)
+  regions_hierarchy : region_var_groups;
   abstractions : AbstractionId.id list;
+      (** The region abstractions introduced upon calling the function *)
   generics : generic_args;
+  trait_method_generics : (generic_args * trait_instance_id) option;
+      (** In case the call is to a trait method, we may need an additional type
+          parameter ([Self]) and the self trait clause to instantiate the
+          function signature. *)
   args : typed_value list;
   args_places : mplace option list;  (** Meta information *)
   dest : symbolic_value;
diff --git a/compiler/SymbolicToPure.ml b/compiler/SymbolicToPure.ml
index 84f09280..3a50e495 100644
--- a/compiler/SymbolicToPure.ml
+++ b/compiler/SymbolicToPure.ml
@@ -15,7 +15,7 @@ module PP = PrintPure
 (** The local logger *)
 let log = Logging.symbolic_to_pure_log
 
-type type_context = {
+type type_ctx = {
   llbc_type_decls : T.type_decl TypeDeclId.Map.t;
   type_decls : type_decl TypeDeclId.Map.t;
       (** We use this for type-checking (for sanity checks) when translating
@@ -43,19 +43,18 @@ type fun_sig_named_outputs = {
 }
 [@@deriving show]
 
-type fun_context = {
+type fun_ctx = {
   llbc_fun_decls : A.fun_decl A.FunDeclId.Map.t;
-  fun_sigs : fun_sig_named_outputs RegularFunIdNotLoopMap.t;  (** *)
   fun_infos : fun_info A.FunDeclId.Map.t;
   regions_hierarchies : T.region_var_groups FunIdMap.t;
 }
 [@@deriving show]
 
-type global_context = { llbc_global_decls : A.global_decl A.GlobalDeclId.Map.t }
+type global_ctx = { 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]
+type trait_decls_ctx = A.trait_decl A.TraitDeclId.Map.t [@@deriving show]
+type trait_impls_ctx = 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
@@ -68,11 +67,21 @@ type call_info = {
 
           Those inputs include the fuel and the state, if pertinent.
        *)
-  backwards : (V.abs * texpression list) T.RegionGroupId.Map.t;
-      (** A map from region group id (i.e., backward function id) to
-          pairs (abstraction, additional arguments received by the backward function)
-       
-          TODO: remove? it is also in the bs_ctx ("abstractions" field)
+  back_funs : texpression option RegionGroupId.Map.t option;
+      (** If we do not split between the forward/backward functions: the
+          variables we introduced for the backward functions.
+
+          Example:
+          {[
+            let x, back = Vec.index_mut n v in
+                   ^^^^
+                   here
+            ...
+          ]}
+
+          The expression might be [None] in case the backward function
+          has to be filtered (because it does nothing - the backward
+          functions for shared borrows for instance).
        *)
 }
 [@@deriving show]
@@ -114,33 +123,61 @@ type loop_info = {
   generics : generic_args;
   forward_inputs : texpression list option;
       (** The forward inputs are initialized at [None] *)
-  forward_output_no_state_no_result : var option;
+  forward_output_no_state_no_result : texpression option;
       (** The forward outputs are initialized at [None] *)
+  back_outputs : ty list RegionGroupId.Map.t;
+      (** The map from region group ids to the types of the values given back
+          by the corresponding loop abstractions.
+       *)
+  back_funs : texpression option RegionGroupId.Map.t option;
+      (** Same as {!call_info.back_funs}.
+          Initialized with [None], gets updated to [Some] only if we merge
+          the fwd/back functions.
+       *)
+  fwd_effect_info : fun_effect_info;
+  back_effect_infos : fun_effect_info RegionGroupId.Map.t;
 }
 [@@deriving show]
 
 (** Body synthesis context *)
 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;
+  (* TODO: there are a lot of duplications with the various decls ctx *)
+  decls_ctx : C.decls_ctx;
+  type_ctx : type_ctx;
+  fun_ctx : fun_ctx;
+  global_ctx : global_ctx;
+  trait_decls_ctx : trait_decls_ctx;
+  trait_impls_ctx : trait_impls_ctx;
+  fun_dsigs : decomposed_fun_sig FunDeclId.Map.t;
   fun_decl : A.fun_decl;
-  bid : T.RegionGroupId.id option;  (** TODO: rename *)
-  sg : fun_sig;
-      (** The function signature - useful in particular to translate [Panic] *)
-  fwd_sg : fun_sig;  (** The signature of the forward function *)
+  bid : RegionGroupId.id option;
+      (** TODO: rename
+
+        The id of the group region we are currently translating.
+        If we split the forward/backward functions, we set this id at the
+        very beginning of the translation.
+        If we don't split, we set it to `None`, then update it when we enter
+        an expression which is specific to a backward function.
+     *)
+  sg : decomposed_fun_sig;
+      (** Information about the function signature - useful in particular to
+          translate [Panic] *)
   sv_to_var : var V.SymbolicValueId.Map.t;
       (** Whenever we encounter a new symbolic value (introduced because of
           a symbolic expansion or upon ending an abstraction, for instance)
           we introduce a new variable (with a let-binding).
        *)
-  var_counter : VarId.generator;
+  var_counter : VarId.generator ref;
+      (** Using a ref to make sure all the variables identifiers are unique.
+          TODO: this is not very clean, and the code was initially written without
+          a reference (and it's shape hasn't changed). We should use DeBruijn indices.
+       *)
   state_var : VarId.id;
       (** The current state variable, in case the function is stateful *)
-  back_state_var : VarId.id;
-      (** The additional input state variable received by a stateful backward function.
+  back_state_vars : VarId.id RegionGroupId.Map.t;
+      (** The additional input state variable received by a stateful backward
+          function, **in case we are splitting the forward/backward functions**.
+
           When generating stateful functions, we generate code of the following
           form:
 
@@ -153,7 +190,9 @@ type bs_ctx = {
           When translating a backward function, we need at some point to update
           [state_var] with [back_state_var], to account for the fact that the
           state may have been updated by the caller between the call to the
-          forward function and the call to the backward function.
+          forward function and the call to the backward function. We also need
+          to make sure we use the same variable in all the branches (because
+          this variable is quantified at the definition level).
        *)
   fuel0 : VarId.id;
       (** The original fuel taken as input by the function (if we use fuel) *)
@@ -163,28 +202,50 @@ type bs_ctx = {
       (** The input parameters for the forward function corresponding to the
           translated Rust inputs (no fuel, no state).
        *)
-  backward_inputs : var list T.RegionGroupId.Map.t;
+  backward_inputs_no_state : var list RegionGroupId.Map.t;
       (** The additional input parameters for the backward functions coming
           from the borrows consumed upon ending the lifetime (as a consequence
           those don't include the backward state, if there is one).
-       *)
-  backward_outputs : var list T.RegionGroupId.Map.t;
-      (** The variables that the backward functions will output, corresponding
-          to the borrows they give back (don't include the backward state)
-       *)
-  loop_backward_outputs : var list T.RegionGroupId.Map.t option;
-      (** Same as {!backward_outputs}, but for loops (if we entered a loop).
 
-          [None] if we are not inside a loop, [Some] otherwise (and whatever
-          the kind of function we are translating: it will be [Some] even
-          though we are synthesizing a forward function).
+          If we split the forward/backward functions: we initialize this map
+          when initializing the bs_ctx, because those variables are quantified
+          at the definition level. Otherwise, we initialize it upon diving
+          into the expressions which are specific to the backward functions.
+       *)
+  backward_inputs_with_state : var list RegionGroupId.Map.t;
+      (** All the additional input parameters for the backward functions.
 
-          TODO: move to {!loop_info}
+          Same remarks as for {!backward_inputs_no_state}.
+       *)
+  backward_outputs : var list option;
+      (** The variables that the backward functions will output, corresponding
+          to the borrows they give back (don't include the backward state).
+
+          The translation is done as follows:
+          - when we detect the ended input abstraction which corresponds
+            to the backward function of the LLBC function we are translating,
+            and which consumed the values [consumed_i] (that we need to give
+            back to the caller), we introduce:
+            {[
+                let v_i = consumed_i in
+                ...
+            ]}
+            where the [v_i] are fresh, and are stored in the [backward_output].
+          - Then, upon reaching the [Return] node, we introduce:
+            {[
+                return (v_i)
+            ]}
+
+          The option is [None] before we detect the ended input abstraction,
+          and [Some] afterwards.
        *)
   calls : call_info V.FunCallId.Map.t;
       (** The function calls we encountered so far *)
   abstractions : (V.abs * texpression list) V.AbstractionId.Map.t;
-      (** The ended abstractions we encountered so far, with their additional input arguments  *)
+      (** The ended abstractions we encountered so far, with their additional
+          input arguments. We store it here and not in {!call_info} because
+          we need a map from abstraction id to abstraction (and not
+          from call id + region group id to abstraction). *)
   loop_ids_map : LoopId.id V.LoopId.Map.t;  (** Ids to use for the loops *)
   loops : loop_info LoopId.Map.t;
       (** The loops we encountered so far.
@@ -209,9 +270,9 @@ type bs_ctx = {
 
 (* TODO: move *)
 let bs_ctx_to_fmt_env (ctx : bs_ctx) : Print.fmt_env =
-  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 type_decls = ctx.type_ctx.llbc_type_decls in
+  let fun_decls = ctx.fun_ctx.llbc_fun_decls in
+  let global_decls = ctx.global_ctx.llbc_global_decls in
   let trait_decls = ctx.trait_decls_ctx in
   let trait_impls = ctx.trait_impls_ctx in
   let { regions; types; const_generics; trait_clauses } : T.generic_params =
@@ -233,9 +294,9 @@ let bs_ctx_to_fmt_env (ctx : bs_ctx) : Print.fmt_env =
   }
 
 let bs_ctx_to_pure_fmt_env (ctx : bs_ctx) : PrintPure.fmt_env =
-  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 type_decls = ctx.type_ctx.llbc_type_decls in
+  let fun_decls = ctx.fun_ctx.llbc_fun_decls in
+  let global_decls = ctx.global_ctx.llbc_global_decls in
   let trait_decls = ctx.trait_decls_ctx in
   let trait_impls = ctx.trait_impls_ctx in
   let generics = ctx.sg.generics in
@@ -300,6 +361,17 @@ let typed_pattern_to_string (ctx : bs_ctx) (p : Pure.typed_pattern) : string =
   let env = bs_ctx_to_pure_fmt_env ctx in
   PrintPure.typed_pattern_to_string env p
 
+let ctx_get_effect_info_for_bid (ctx : bs_ctx) (bid : RegionGroupId.id option) :
+    fun_effect_info =
+  match bid with
+  | None -> ctx.sg.fwd_info.effect_info
+  | Some bid ->
+      let back_sg = RegionGroupId.Map.find bid ctx.sg.back_sg in
+      back_sg.effect_info
+
+let ctx_get_effect_info (ctx : bs_ctx) : fun_effect_info =
+  ctx_get_effect_info_for_bid ctx ctx.bid
+
 (* TODO: move *)
 let abs_to_string (ctx : bs_ctx) (abs : V.abs) : string =
   let env = bs_ctx_to_fmt_env ctx in
@@ -308,33 +380,13 @@ let abs_to_string (ctx : bs_ctx) (abs : V.abs) : string =
   let indent_incr = "  " in
   Print.Values.abs_to_string env verbose indent indent_incr abs
 
-let get_instantiated_fun_sig (fun_id : A.fun_id)
-    (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 *)
-  (* 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 subst sg
-
 let bs_ctx_lookup_llbc_type_decl (id : TypeDeclId.id) (ctx : bs_ctx) :
     T.type_decl =
-  TypeDeclId.Map.find id ctx.type_context.llbc_type_decls
+  TypeDeclId.Map.find id ctx.type_ctx.llbc_type_decls
 
 let bs_ctx_lookup_llbc_fun_decl (id : A.FunDeclId.id) (ctx : bs_ctx) :
     A.fun_decl =
-  A.FunDeclId.Map.find id ctx.fun_context.llbc_fun_decls
-
-(* 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 = (E.FRegular def_id, back_id) in
-  (RegularFunIdNotLoopMap.find id ctx.fun_context.fun_sigs).sg
+  A.FunDeclId.Map.find id ctx.fun_ctx.llbc_fun_decls
 
 (* Some generic translation functions (we need to translate different "flavours"
    of types: forward types, backward types, etc.) *)
@@ -601,13 +653,13 @@ and translate_fwd_trait_instance_id (type_infos : type_infos)
 
 (** Simply calls [translate_fwd_ty] *)
 let ctx_translate_fwd_ty (ctx : bs_ctx) (ty : T.ty) : ty =
-  let type_infos = ctx.type_context.type_infos in
+  let type_infos = ctx.type_ctx.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 : T.generic_args) :
     generic_args =
-  let type_infos = ctx.type_context.type_infos in
+  let type_infos = ctx.type_ctx.type_infos in
   translate_fwd_generic_args type_infos generics
 
 (** Translate a type, when some regions may have ended.
@@ -682,17 +734,21 @@ let rec translate_back_ty (type_infos : type_infos)
       None
   | TTraitType (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 (TTraitType (trait_ref, generics, type_name))
+      assert (
+        AssociatedTypes.trait_instance_id_is_local_clause trait_ref.trait_id);
+      if inside_mut then
+        (* 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 (TTraitType (trait_ref, generics, type_name))
+      else None
   | TArrow _ -> raise (Failure "TODO")
 
 (** Simply calls [translate_back_ty] *)
 let ctx_translate_back_ty (ctx : bs_ctx) (keep_region : 'r -> bool)
     (inside_mut : bool) (ty : T.ty) : ty option =
-  let type_infos = ctx.type_context.type_infos in
+  let type_infos = ctx.type_ctx.type_infos in
   translate_back_ty type_infos keep_region inside_mut ty
 
 let mk_type_check_ctx (ctx : bs_ctx) : PureTypeCheck.tc_ctx =
@@ -705,8 +761,8 @@ let mk_type_check_ctx (ctx : bs_ctx) : PureTypeCheck.tc_ctx =
   in
   let env = VarId.Map.empty in
   {
-    PureTypeCheck.type_decls = ctx.type_context.type_decls;
-    global_decls = ctx.global_context.llbc_global_decls;
+    PureTypeCheck.type_decls = ctx.type_ctx.type_decls;
+    global_decls = ctx.global_ctx.llbc_global_decls;
     env;
     const_generics;
   }
@@ -726,31 +782,36 @@ let translate_fun_id_or_trait_method_ref (ctx : bs_ctx)
   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 type_infos = ctx.type_ctx.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 =
+    (args : texpression list)
+    (back_funs : texpression option RegionGroupId.Map.t option) (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 info = { forward; forward_inputs = args; back_funs } 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 =
+(** [inherit_args]: the list of inputs inherited from the forward function and
+    the ancestors backward functions, if pertinent.
+    [back_args]: the *additional* list of inputs received by the backward function,
+    including the state.
+
+    Returns the updated context and the expression corresponding to the function
+    that we need to call. This function may be [None] if it has to be ignored
+    (because it does nothing).
+ *)
+let bs_ctx_register_backward_call (abs : V.abs) (effect_info : fun_effect_info)
+    (call_id : V.FunCallId.id) (back_id : T.RegionGroupId.id)
+    (inherited_args : texpression list) (back_args : texpression list)
+    (generics : generic_args) (output_ty : ty) (ctx : bs_ctx) :
+    bs_ctx * texpression option =
   (* 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
@@ -758,16 +819,31 @@ let bs_ctx_register_backward_call (abs : V.abs) (call_id : V.FunCallId.id)
   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")
+  (* Compute the expression corresponding to the function *)
+  let func =
+    if !Config.return_back_funs then
+      (* Lookup the variable introduced for the backward function *)
+      RegionGroupId.Map.find back_id (Option.get info.back_funs)
+    else
+      (* 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
+      let args = List.append inherited_args back_args 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 output_ty else output_ty
+      in
+      let func_ty = mk_arrows input_tys ret_ty in
+      let func = { id = FunOrOp fun_id; generics } in
+      Some { e = Qualif func; ty = func_ty }
   in
   (* Update the context and return *)
-  ({ ctx with calls; abstractions }, fun_id)
+  ({ ctx with calls; abstractions }, func)
 
 (** List the ancestors of an abstraction *)
 let list_ancestor_abstractions_ids (ctx : bs_ctx) (abs : V.abs)
@@ -821,7 +897,7 @@ let mk_fuel_input_as_list (ctx : bs_ctx) (info : fun_effect_info) :
   if function_uses_fuel info then [ mk_fuel_texpression ctx.fuel ] else []
 
 (** Small utility. *)
-let get_fun_effect_info (fun_infos : fun_info A.FunDeclId.Map.t)
+let compute_raw_fun_effect_info (fun_infos : fun_info A.FunDeclId.Map.t)
     (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
@@ -848,33 +924,53 @@ let get_fun_effect_info (fun_infos : fun_info A.FunDeclId.Map.t)
         is_rec = false;
       }
 
-(** Translate a function signature.
+(** TODO: not very clean. *)
+let get_fun_effect_info (ctx : bs_ctx) (fun_id : A.fun_id_or_trait_method_ref)
+    (lid : V.LoopId.id option) (gid : T.RegionGroupId.id option) :
+    fun_effect_info =
+  match lid with
+  | None -> (
+      match fun_id with
+      | TraitMethod (_, _, fid) | FunId (FRegular fid) ->
+          let dsg = A.FunDeclId.Map.find fid ctx.fun_dsigs in
+          let info =
+            match gid with
+            | None -> dsg.fwd_info.effect_info
+            | Some gid -> (RegionGroupId.Map.find gid dsg.back_sg).effect_info
+          in
+          { info with is_rec = info.is_rec || Option.is_some lid }
+      | FunId (FAssumed _) ->
+          compute_raw_fun_effect_info ctx.fun_ctx.fun_infos fun_id lid gid)
+  | Some lid -> (
+      (* This is necessarily for the current function *)
+      match fun_id with
+      | FunId (FRegular fid) -> (
+          assert (fid = ctx.fun_decl.def_id);
+          (* Lookup the loop *)
+          let lid = V.LoopId.Map.find lid ctx.loop_ids_map in
+          let loop_info = LoopId.Map.find lid ctx.loops in
+          match gid with
+          | None -> loop_info.fwd_effect_info
+          | Some gid -> RegionGroupId.Map.find gid loop_info.back_effect_infos)
+      | _ -> raise (Failure "Unreachable"))
+
+(** Translate a function signature to a decomposed function signature.
 
     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
     in the extracted code.
+
+    We use [bid] ("backward function id") only if we split the forward
+    and the backward functions.
  *)
-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 translate_fun_sig_with_regions_hierarchy_to_decomposed
+    (decls_ctx : C.decls_ctx) (fun_id : A.fun_id_or_trait_method_ref)
+    (regions_hierarchy : T.region_var_groups) (sg : A.fun_sig)
+    (input_names : string option list) : decomposed_fun_sig =
   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 regions_hierarchy =
-    FunIdMap.find fun_id decls_ctx.fun_ctx.regions_hierarchies
-  in
-  let gid, parents =
-    match bid with
-    | None -> (None, T.RegionGroupId.Set.empty)
-    | Some bid ->
-        let parents = list_ancestor_region_groups regions_hierarchy bid in
-        (Some bid, parents)
-  in
-  (* Is the function stateful, and can it fail? *)
-  let lid = None 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
@@ -885,7 +981,7 @@ let translate_fun_sig (decls_ctx : C.decls_ctx) (fun_id : A.fun_id)
       List.map (fun (g : T.region_var_group) -> g.id) regions_hierarchy
     in
     let ctx =
-      InterpreterUtils.initialize_eval_context decls_ctx region_groups
+      InterpreterUtils.initialize_eval_ctx 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 *)
@@ -902,17 +998,28 @@ let translate_fun_sig (decls_ctx : C.decls_ctx) (fun_id : A.fun_id)
     { sg with A.inputs; output }
   in
 
-  (* List the inputs for:
-   * - the fuel
-   * - the forward function
-   * - the parent backward functions, in proper order
-   * - the current backward function (if it is a backward function)
-   *)
-  let fuel = mk_fuel_input_ty_as_list effect_info in
-  let fwd_inputs = List.map (translate_fwd_ty type_infos) sg.inputs in
-  (* For the backward functions: for now we don't supported nested borrows,
-   * so just check that there aren't parent regions *)
-  assert (T.RegionGroupId.Set.is_empty parents);
+  (* Is the forward function stateful, and can it fail? *)
+  let fwd_effect_info =
+    compute_raw_fun_effect_info fun_infos fun_id None None
+  in
+  (* Compute the forward inputs *)
+  let fwd_fuel = mk_fuel_input_ty_as_list fwd_effect_info in
+  let fwd_inputs_no_fuel_no_state =
+    List.map (translate_fwd_ty type_infos) sg.inputs
+  in
+  (* State input for the forward function *)
+  let fwd_state_ty =
+    (* For the forward state, we check if the *whole group* is stateful.
+       See {!effect_info}. *)
+    if fwd_effect_info.stateful_group then [ mk_state_ty ] else []
+  in
+  let fwd_inputs =
+    List.concat [ fwd_fuel; fwd_inputs_no_fuel_no_state; fwd_state_ty ]
+  in
+  (* Compute the backward output, without the effect information *)
+  let fwd_output = translate_fwd_ty type_infos sg.output in
+
+  (* Compute the type information for the backward function *)
   (* Small helper to translate types for backward functions *)
   let translate_back_ty_for_gid (gid : T.RegionGroupId.id) (ty : T.ty) :
       ty option =
@@ -939,163 +1046,336 @@ let translate_fun_sig (decls_ctx : C.decls_ctx) (fun_id : A.fun_id)
     let inside_mut = false in
     translate_back_ty type_infos keep_region inside_mut ty
   in
-  (* Compute the additinal inputs for the current function, if it is a backward
-   * function *)
-  let back_inputs =
-    match gid with
-    | None -> []
-    | Some gid ->
-        (* For now, we don't allow nested borrows, so the additional inputs to the
-           backward function can only come from borrows that were returned like
-           in (for the backward function we introduce for 'a):
-           {[
-             fn f<'a>(...) -> &'a mut u32;
-           ]}
-           Upon ending the abstraction for 'a, we need to get back the borrow
-           the function returned.
-        *)
-        List.filter_map (translate_back_ty_for_gid gid) [ sg.output ]
-  in
-  (* If the function is stateful, the inputs are:
-     - forward:  [fwd_ty0, ..., fwd_tyn, state]
-     - backward:
-       - if {!Config.backward_no_state_update}: [fwd_ty0, ..., fwd_tyn, state, back_ty, state]
-       - otherwise: [fwd_ty0, ..., fwd_tyn, state, back_ty]
-
-       The backward takes the same state as input as the forward function,
-       together with the state at the point where it gets called, if it is
-       stateful.
-
-       See the comments for {!Config.backward_no_state_update}
-  *)
-  let fwd_state_ty =
-    (* For the forward state, we check if the *whole group* is stateful.
-       See {!effect_info}. *)
-    if effect_info.stateful_group then [ mk_state_ty ] else []
+  let translate_back_inputs_for_gid (gid : T.RegionGroupId.id) : ty list =
+    (* For now we don't supported nested borrows, so we check that there
+       aren't parent regions *)
+    let parents = list_ancestor_region_groups regions_hierarchy gid in
+    assert (T.RegionGroupId.Set.is_empty parents);
+    (* For now, we don't allow nested borrows, so the additional inputs to the
+       backward function can only come from borrows that were returned like
+       in (for the backward function we introduce for 'a):
+       {[
+         fn f<'a>(...) -> &'a mut u32;
+       ]}
+       Upon ending the abstraction for 'a, we need to get back the borrow
+       the function returned.
+    *)
+    let inputs =
+      List.filter_map (translate_back_ty_for_gid gid) [ sg.output ]
+    in
+    log#ldebug
+      (lazy
+        (let ctx = Print.Contexts.decls_ctx_to_fmt_env decls_ctx in
+         let pctx = PrintPure.decls_ctx_to_fmt_env decls_ctx in
+         let output = Print.Types.ty_to_string ctx sg.output in
+         let inputs =
+           Print.list_to_string (PrintPure.ty_to_string pctx false) inputs
+         in
+         "translate_back_inputs_for_gid:" ^ "\n- gid: "
+         ^ RegionGroupId.to_string gid
+         ^ "\n- output: " ^ output ^ "\n- back inputs: " ^ inputs ^ "\n"));
+    inputs
+  in
+  let compute_back_outputs_for_gid (gid : RegionGroupId.id) :
+      string option list * ty list =
+    (* The outputs are the borrows inside the regions of the abstractions
+       and which are present in the input values. For instance, see:
+       {[
+         fn f<'a>(x : &'a mut u32) -> ...;
+       ]}
+       Upon ending the abstraction for 'a, we give back the borrow which
+       was consumed through the [x] parameter.
+    *)
+    let outputs =
+      List.map
+        (fun (name, input_ty) -> (name, translate_back_ty_for_gid gid input_ty))
+        (List.combine input_names sg.inputs)
+    in
+    (* Filter *)
+    let outputs =
+      List.filter (fun (_, opt_ty) -> Option.is_some opt_ty) outputs
+    in
+    let outputs =
+      List.map (fun (name, opt_ty) -> (name, Option.get opt_ty)) outputs
+    in
+    let names, outputs = List.split outputs in
+    log#ldebug
+      (lazy
+        (let ctx = Print.Contexts.decls_ctx_to_fmt_env decls_ctx in
+         let pctx = PrintPure.decls_ctx_to_fmt_env decls_ctx in
+         let inputs =
+           Print.list_to_string (Print.Types.ty_to_string ctx) sg.inputs
+         in
+         let outputs =
+           Print.list_to_string (PrintPure.ty_to_string pctx false) outputs
+         in
+         "compute_back_outputs_for_gid:" ^ "\n- gid: "
+         ^ RegionGroupId.to_string gid
+         ^ "\n- inputs: " ^ inputs ^ "\n- back outputs: " ^ outputs ^ "\n"));
+    (names, outputs)
+  in
+  let compute_back_info_for_group (rg : T.region_var_group) :
+      RegionGroupId.id * back_sg_info =
+    let gid = rg.id in
+    let back_effect_info =
+      compute_raw_fun_effect_info fun_infos fun_id None (Some gid)
+    in
+    let inputs_no_state = translate_back_inputs_for_gid gid in
+    let inputs_no_state =
+      List.map (fun ty -> (Some "ret", ty)) inputs_no_state
+    in
+    (* In case we merge the forward/backward functions:
+       we consider the backward function as stateful and potentially failing
+       **only if it has inputs** (for the "potentially failing": if it has
+       not inputs, we directly evaluate it in the body of the forward function).
+    *)
+    let back_effect_info =
+      if !Config.return_back_funs then
+        let b = inputs_no_state <> [] in
+        {
+          back_effect_info with
+          stateful = back_effect_info.stateful && b;
+          can_fail = back_effect_info.can_fail && b;
+        }
+      else back_effect_info
+    in
+    let state =
+      if back_effect_info.stateful then [ (None, mk_state_ty) ] else []
+    in
+    let inputs = inputs_no_state @ state in
+    let output_names, outputs = compute_back_outputs_for_gid gid in
+    let filter =
+      !Config.simplify_merged_fwd_backs
+      && !Config.return_back_funs && inputs = [] && outputs = []
+    in
+    let info =
+      {
+        inputs;
+        inputs_no_state;
+        outputs;
+        output_names;
+        effect_info = back_effect_info;
+        filter;
+      }
+    in
+    (gid, info)
   in
-  let back_state_ty =
-    (* For the backward state, we check if the function is a backward function,
-       and it is stateful *)
-    if effect_info.stateful && Option.is_some gid then [ mk_state_ty ] else []
+  let back_sg =
+    RegionGroupId.Map.of_list
+      (List.map compute_back_info_for_group regions_hierarchy)
   in
 
-  (* Concatenate the inputs, in the following order:
-   * - forward inputs
-   * - forward state input
-   * - backward inputs
-   * - backward state input
-   *)
-  let inputs =
-    List.concat [ fuel; fwd_inputs; fwd_state_ty; back_inputs; back_state_ty ]
-  in
-  (* Outputs *)
-  let output_names, doutputs =
-    match gid with
-    | None ->
-        (* This is a forward function: there is one (unnamed) output *)
-        ([ None ], [ translate_fwd_ty type_infos sg.output ])
-    | Some gid ->
-        (* This is a backward function: there might be several outputs.
-           The outputs are the borrows inside the regions of the abstractions
-           and which are present in the input values. For instance, see:
-           {[
-             fn f<'a>(x : &'a mut u32) -> ...;
-           ]}
-           Upon ending the abstraction for 'a, we give back the borrow which
-           was consumed through the [x] parameter.
-        *)
-        let outputs =
-          List.map
-            (fun (name, input_ty) ->
-              (name, translate_back_ty_for_gid gid input_ty))
-            (List.combine input_names sg.inputs)
-        in
-        (* Filter *)
-        let outputs =
-          List.filter (fun (_, opt_ty) -> Option.is_some opt_ty) outputs
-        in
-        let outputs =
-          List.map (fun (name, opt_ty) -> (name, Option.get opt_ty)) outputs
-        in
-        List.split outputs
-  in
-  (* Create the return type *)
-  let output =
-    (* Group the outputs together *)
-    let output = mk_simpl_tuple_ty doutputs in
-    (* Add the output state *)
-    let output =
-      if effect_info.stateful then mk_simpl_tuple_ty [ mk_state_ty; output ]
-      else output
+  (* The additional information about the forward function *)
+  let fwd_info =
+    (* *)
+    let has_fuel = fwd_fuel <> [] in
+    let num_inputs_no_fuel_no_state = List.length fwd_inputs_no_fuel_no_state in
+    let num_inputs_with_fuel_no_state =
+      (* We use the fact that [fuel] has length 1 if we use some fuel, 0 otherwise *)
+      List.length fwd_fuel + num_inputs_no_fuel_no_state
+    in
+    let fwd_info : inputs_info =
+      {
+        has_fuel;
+        num_inputs_no_fuel_no_state;
+        num_inputs_with_fuel_no_state;
+        num_inputs_with_fuel_with_state =
+          (* We use the fact that [fwd_state_ty] has length 1 if there is a state,
+             and 0 otherwise *)
+          num_inputs_with_fuel_no_state + List.length fwd_state_ty;
+      }
+    in
+    let ignore_output =
+      if !Config.return_back_funs && !Config.simplify_merged_fwd_backs then
+        ty_is_unit fwd_output
+        && List.exists
+             (fun (info : back_sg_info) -> not info.filter)
+             (RegionGroupId.Map.values back_sg)
+      else false
     in
-    (* Wrap in a result type *)
-    if effect_info.can_fail then mk_result_ty output else output
+    let info = { fwd_info; effect_info = fwd_effect_info; ignore_output } in
+    assert (fun_sig_info_is_wf info);
+    info
   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
-  let num_fwd_inputs_with_fuel_no_state =
-    (* We use the fact that [fuel] has length 1 if we use some fuel, 0 otherwise *)
-    List.length fuel + num_fwd_inputs_no_state
-  in
-  let num_back_inputs_no_state =
-    if bid = None then None else Some (List.length back_inputs)
+  let preds = translate_predicates sg.preds in
+  {
+    generics;
+    llbc_generics = sg.generics;
+    preds;
+    fwd_inputs;
+    fwd_output;
+    back_sg;
+    fwd_info;
+  }
+
+let translate_fun_sig_to_decomposed (decls_ctx : C.decls_ctx)
+    (fun_id : FunDeclId.id) (sg : A.fun_sig) (input_names : string option list)
+    : decomposed_fun_sig =
+  (* Retrieve the list of parent backward functions *)
+  let regions_hierarchy =
+    FunIdMap.find (FRegular fun_id) decls_ctx.fun_ctx.regions_hierarchies
   in
-  let info =
-    {
-      has_fuel;
-      num_fwd_inputs_with_fuel_no_state;
-      num_fwd_inputs_with_fuel_with_state =
-        (* We use the fact that [fwd_state_ty] has length 1 if there is a state,
-           and 0 otherwise *)
-        num_fwd_inputs_with_fuel_no_state + List.length fwd_state_ty;
-      num_back_inputs_no_state;
-      num_back_inputs_with_state =
-        (* Length of [back_state_ty]: similar trick as for [fwd_state_ty] *)
-        Option.map
-          (fun n -> n + List.length back_state_ty)
-          num_back_inputs_no_state;
-      effect_info;
-    }
+  translate_fun_sig_with_regions_hierarchy_to_decomposed decls_ctx
+    (FunId (FRegular fun_id)) regions_hierarchy sg input_names
+
+let translate_fun_sig_from_decl_to_decomposed (decls_ctx : C.decls_ctx)
+    (fdef : LlbcAst.fun_decl) : decomposed_fun_sig =
+  let input_names =
+    match fdef.body with
+    | None -> List.map (fun _ -> None) fdef.signature.inputs
+    | Some body ->
+        List.map
+          (fun (v : LlbcAst.var) -> v.name)
+          (LlbcAstUtils.fun_body_get_input_vars body)
   in
-  let preds = translate_predicates sg.preds in
   let sg =
-    {
-      generics;
-      llbc_generics = sg.generics;
-      preds;
-      inputs;
-      output;
-      doutputs;
-      info;
-    }
+    translate_fun_sig_to_decomposed decls_ctx fdef.def_id fdef.signature
+      input_names
+  in
+  log#ldebug
+    (lazy
+      ("translate_fun_sig_from_decl_to_decomposed:" ^ "\n- name: "
+     ^ T.show_name fdef.name ^ "\n- sg:\n" ^ show_decomposed_fun_sig sg ^ "\n"));
+  sg
+
+let mk_output_ty_from_effect_info (effect_info : fun_effect_info) (ty : ty) : ty
+    =
+  let output =
+    if effect_info.stateful then mk_simpl_tuple_ty [ mk_state_ty; ty ] else ty
   in
-  { sg; output_names }
+  if effect_info.can_fail then mk_result_ty output else output
 
-let bs_ctx_fresh_state_var (ctx : bs_ctx) : bs_ctx * typed_pattern =
+let mk_back_output_ty_from_effect_info (effect_info : fun_effect_info)
+    (inputs : ty list) (ty : ty) : ty =
+  let output =
+    if effect_info.stateful then mk_simpl_tuple_ty [ mk_state_ty; ty ] else ty
+  in
+  if effect_info.can_fail && inputs <> [] then mk_result_ty output else output
+
+(** Compute the arrow types for all the backward functions.
+
+    If a backward function has no inputs/outputs we filter it.
+ *)
+let compute_back_tys_with_info (dsg : Pure.decomposed_fun_sig)
+    (subst : (generic_args * trait_instance_id) option) :
+    (back_sg_info * ty) option list =
+  List.map
+    (fun (back_sg : back_sg_info) ->
+      let effect_info = back_sg.effect_info in
+      (* Compute the input/output types *)
+      let inputs = List.map snd back_sg.inputs in
+      let outputs = back_sg.outputs in
+      (* Filter if necessary *)
+      if !Config.simplify_merged_fwd_backs && inputs = [] && outputs = [] then
+        None
+      else
+        let output = mk_simpl_tuple_ty outputs in
+        let output =
+          mk_back_output_ty_from_effect_info effect_info inputs output
+        in
+        let ty = mk_arrows inputs output in
+        (* Substitute - TODO: normalize *)
+        let ty =
+          match subst with
+          | None -> ty
+          | Some (generics, tr_self) ->
+              let subst =
+                make_subst_from_generics dsg.generics generics tr_self
+              in
+              ty_substitute subst ty
+        in
+        Some (back_sg, ty))
+    (RegionGroupId.Map.values dsg.back_sg)
+
+let compute_back_tys (dsg : Pure.decomposed_fun_sig)
+    (subst : (generic_args * trait_instance_id) option) : ty option list =
+  List.map (Option.map snd) (compute_back_tys_with_info dsg subst)
+
+(** In case we merge the fwd/back functions: compute the output type of
+    a function, from a decomposed signature. *)
+let compute_output_ty_from_decomposed (dsg : Pure.decomposed_fun_sig) : ty =
+  assert !Config.return_back_funs;
+  (* Compute the arrow types for all the backward functions *)
+  let back_tys = List.filter_map (fun x -> x) (compute_back_tys dsg None) in
+  (* Group the forward output and the types of the backward functions *)
+  let effect_info = dsg.fwd_info.effect_info in
+  let output =
+    (* We might need to ignore the output of the forward function
+       (if it is unit for instance) *)
+    let tys =
+      if dsg.fwd_info.ignore_output then back_tys
+      else dsg.fwd_output :: back_tys
+    in
+    mk_simpl_tuple_ty tys
+  in
+  mk_output_ty_from_effect_info effect_info output
+
+let translate_fun_sig_from_decomposed (dsg : Pure.decomposed_fun_sig)
+    (gid : RegionGroupId.id option) : fun_sig =
+  let generics = dsg.generics in
+  let llbc_generics = dsg.llbc_generics in
+  let preds = dsg.preds in
+  (* Compute the effects info *)
+  let fwd_info = dsg.fwd_info in
+  let back_effect_info =
+    RegionGroupId.Map.of_list
+      (List.map
+         (fun ((gid, info) : RegionGroupId.id * back_sg_info) ->
+           (gid, info.effect_info))
+         (RegionGroupId.Map.bindings dsg.back_sg))
+  in
+  let mk_output_ty = mk_output_ty_from_effect_info in
+  let inputs, output =
+    (* Two cases depending on whether we split the forward/backward functions or not *)
+    if !Config.return_back_funs then (
+      assert (gid = None);
+      let output = compute_output_ty_from_decomposed dsg in
+      let inputs = dsg.fwd_inputs in
+      (inputs, output))
+    else
+      match gid with
+      | None ->
+          let effect_info = dsg.fwd_info.effect_info in
+          let output = mk_output_ty effect_info dsg.fwd_output in
+          (dsg.fwd_inputs, output)
+      | Some gid ->
+          let back_sg = RegionGroupId.Map.find gid dsg.back_sg in
+          let effect_info = back_sg.effect_info in
+          let inputs = dsg.fwd_inputs @ List.map snd back_sg.inputs in
+          let output = mk_simpl_tuple_ty back_sg.outputs in
+          let output = mk_output_ty effect_info output in
+          (inputs, output)
+  in
+  { generics; llbc_generics; preds; inputs; output; fwd_info; back_effect_info }
+
+let bs_ctx_fresh_state_var (ctx : bs_ctx) : bs_ctx * var * typed_pattern =
   (* Generate the fresh variable *)
-  let id, var_counter = VarId.fresh ctx.var_counter in
+  let id, var_counter = VarId.fresh !(ctx.var_counter) in
   let state_var =
     { id; basename = Some ConstStrings.state_basename; ty = mk_state_ty }
   in
   let state_pat = mk_typed_pattern_from_var state_var None in
   (* Update the context *)
-  let ctx = { ctx with var_counter; state_var = id } in
+  ctx.var_counter := var_counter;
+  let ctx = { ctx with state_var = id } in
   (* Return *)
-  (ctx, state_pat)
+  (ctx, state_var, state_pat)
 
 (** WARNING: do not call this function directly.
     Call [fresh_named_var_for_symbolic_value] instead. *)
 let fresh_var_llbc_ty (basename : string option) (ty : T.ty) (ctx : bs_ctx) :
     bs_ctx * var =
   (* Generate the fresh variable *)
-  let id, var_counter = VarId.fresh ctx.var_counter in
+  let id, var_counter = VarId.fresh !(ctx.var_counter) in
   let ty = ctx_translate_fwd_ty ctx ty in
   let var = { id; basename; ty } in
   (* Update the context *)
-  let ctx = { ctx with var_counter } in
+  ctx.var_counter := var_counter;
   (* Return *)
   (ctx, var)
 
@@ -1129,10 +1409,10 @@ let fresh_named_vars_for_symbolic_values
 let fresh_var (basename : string option) (ty : ty) (ctx : bs_ctx) : bs_ctx * var
     =
   (* Generate the fresh variable *)
-  let id, var_counter = VarId.fresh ctx.var_counter in
+  let id, var_counter = VarId.fresh !(ctx.var_counter) in
   let var = { id; basename; ty } in
   (* Update the context *)
-  let ctx = { ctx with var_counter } in
+  ctx.var_counter := var_counter;
   (* Return *)
   (ctx, var)
 
@@ -1140,6 +1420,58 @@ let fresh_vars (vars : (string option * ty) list) (ctx : bs_ctx) :
     bs_ctx * var list =
   List.fold_left_map (fun ctx (name, ty) -> fresh_var name ty ctx) ctx vars
 
+let fresh_opt_vars (vars : (string option * ty) option list) (ctx : bs_ctx) :
+    bs_ctx * var option list =
+  List.fold_left_map
+    (fun ctx var ->
+      match var with
+      | None -> (ctx, None)
+      | Some (name, ty) ->
+          let ctx, var = fresh_var name ty ctx in
+          (ctx, Some var))
+    ctx vars
+
+(* Introduce variables for the backward functions *)
+let fresh_back_vars_for_current_fun (ctx : bs_ctx) : bs_ctx * var option list =
+  (* We lookup the LLBC definition in an attempt to derive pretty names
+     for the backward functions. *)
+  let back_var_names =
+    let def_id = ctx.fun_decl.def_id in
+    let sg = ctx.fun_decl.signature in
+    let regions_hierarchy =
+      LlbcAstUtils.FunIdMap.find (FRegular def_id)
+        ctx.fun_ctx.regions_hierarchies
+    in
+    List.map
+      (fun (gid, _) ->
+        let rg = RegionGroupId.nth regions_hierarchy gid in
+        let region_names =
+          List.map
+            (fun rid -> (T.RegionVarId.nth sg.generics.regions rid).name)
+            rg.regions
+        in
+        let name =
+          match region_names with
+          | [] -> "back"
+          | [ Some r ] -> "back" ^ r
+          | _ ->
+              (* Concatenate all the region names *)
+              "back"
+              ^ String.concat "" (List.filter_map (fun x -> x) region_names)
+        in
+        Some name)
+      (RegionGroupId.Map.bindings ctx.sg.back_sg)
+  in
+  let back_vars = List.combine back_var_names (compute_back_tys ctx.sg None) in
+  let back_vars =
+    List.map
+      (fun (name, ty) ->
+        match ty with None -> None | Some ty -> Some (name, ty))
+      back_vars
+  in
+  fresh_opt_vars back_vars ctx
+
+(** IMPORTANT: do not use this one directly, but rather {!symbolic_value_to_texpression} *)
 let lookup_var_for_symbolic_value (sv : V.symbolic_value) (ctx : bs_ctx) : var =
   match V.SymbolicValueId.Map.find_opt sv.sv_id ctx.sv_to_var with
   | Some v -> v
@@ -1158,12 +1490,22 @@ let rec unbox_typed_value (v : V.typed_value) : V.typed_value =
       | _ -> raise (Failure "Unreachable"))
   | _ -> v
 
-(** Translate a symbolic value *)
+(** Translate a symbolic value.
+
+    Because we do not necessarily introduce variables for the symbolic values
+    of (translated) type unit, it is important that we do not lookup variables
+    in case the symbolic value has type unit.
+ *)
 let symbolic_value_to_texpression (ctx : bs_ctx) (sv : V.symbolic_value) :
     texpression =
   (* Translate the type *)
-  let var = lookup_var_for_symbolic_value sv ctx in
-  mk_texpression_from_var var
+  let ty = ctx_translate_fwd_ty ctx sv.sv_ty in
+  (* If the type is unit, directly return unit *)
+  if ty_is_unit ty then mk_unit_rvalue
+  else
+    (* Otherwise lookup the variable *)
+    let var = lookup_var_for_symbolic_value sv ctx in
+    mk_texpression_from_var var
 
 (** Translate a typed value.
 
@@ -1342,13 +1684,11 @@ and aproj_to_consumed (ctx : bs_ctx) (aproj : V.aproj) : texpression option =
   match aproj with
   | V.AEndedProjLoans (msv, []) ->
       (* The symbolic value was left unchanged *)
-      let var = lookup_var_for_symbolic_value msv ctx in
-      Some (mk_texpression_from_var var)
+      Some (symbolic_value_to_texpression ctx msv)
   | V.AEndedProjLoans (_, [ (mnv, child_aproj) ]) ->
       assert (child_aproj = AIgnoredProjBorrows);
       (* The symbolic value was updated *)
-      let var = lookup_var_for_symbolic_value mnv ctx in
-      Some (mk_texpression_from_var var)
+      Some (symbolic_value_to_texpression ctx mnv)
   | V.AEndedProjLoans (_, _) ->
       (* The symbolic value was updated, and the given back values come from sevearl
        * abstractions *)
@@ -1543,7 +1883,9 @@ let mk_emeta_symbolic_assignments (vars : var list) (values : texpression list)
 
 let rec translate_expression (e : S.expression) (ctx : bs_ctx) : texpression =
   match e with
-  | S.Return (ectx, opt_v) -> translate_return ectx opt_v ctx
+  | S.Return (ectx, opt_v) ->
+      (* Remark: we can't get there if we are inside a loop *)
+      translate_return ectx opt_v ctx
   | ReturnWithLoop (loop_id, is_continue) ->
       translate_return_with_loop loop_id is_continue ctx
   | Panic -> translate_panic ctx
@@ -1565,32 +1907,56 @@ and translate_panic (ctx : bs_ctx) : texpression =
    * but it won't be true anymore once we translate individual blocks *)
   (* If we use a state monad, we need to add a lambda for the state variable *)
   (* Note that only forward functions return a state *)
-  let output_ty =
-    if ctx.inside_loop && Option.is_some ctx.bid then
-      (* We are synthesizing the backward function of a loop body *)
-      let bid = Option.get ctx.bid in
-      let back_vars =
-        T.RegionGroupId.Map.find bid (Option.get ctx.loop_backward_outputs)
-      in
-      let tys = List.map (fun (v : var) -> v.ty) back_vars in
-      mk_simpl_tuple_ty tys
-    else
-      (* Regular function, or forward function (the forward translation for
-         a loop has the same return type as the parent function)
-      *)
-      mk_simpl_tuple_ty ctx.sg.doutputs
-  in
+  let effect_info = ctx_get_effect_info ctx in
   (* TODO: we should use a [Fail] function *)
-  if ctx.sg.info.effect_info.stateful then
-    (* Create the [Fail] value *)
-    let ret_ty = mk_simpl_tuple_ty [ mk_state_ty; output_ty ] in
-    let ret_v =
-      mk_result_fail_texpression_with_error_id error_failure_id ret_ty
-    in
-    ret_v
-  else mk_result_fail_texpression_with_error_id error_failure_id output_ty
+  let mk_output output_ty =
+    if effect_info.stateful then
+      (* Create the [Fail] value *)
+      let ret_ty = mk_simpl_tuple_ty [ mk_state_ty; output_ty ] in
+      let ret_v =
+        mk_result_fail_texpression_with_error_id error_failure_id ret_ty
+      in
+      ret_v
+    else mk_result_fail_texpression_with_error_id error_failure_id output_ty
+  in
+  if ctx.inside_loop && Option.is_some ctx.bid then
+    (* We are synthesizing the backward function of a loop body *)
+    let bid = Option.get ctx.bid in
+    let loop_id = Option.get ctx.loop_id in
+    let loop = LoopId.Map.find loop_id ctx.loops in
+    let tys = RegionGroupId.Map.find bid loop.back_outputs in
+    let output = mk_simpl_tuple_ty tys in
+    mk_output output
+  else
+    (* Regular function, or forward function (the forward translation for
+       a loop has the same return type as the parent function)
+    *)
+    match ctx.bid with
+    | None ->
+        if !Config.return_back_funs then
+          let back_tys = compute_back_tys ctx.sg None in
+          let back_tys = List.filter_map (fun x -> x) back_tys in
+          let tys =
+            if ctx.sg.fwd_info.ignore_output then back_tys
+            else ctx.sg.fwd_output :: back_tys
+          in
+          let output = mk_simpl_tuple_ty tys in
+          mk_output output
+        else mk_output ctx.sg.fwd_output
+    | Some bid ->
+        let output =
+          mk_simpl_tuple_ty (RegionGroupId.Map.find bid ctx.sg.back_sg).outputs
+        in
+        mk_output output
+
+(** [opt_v]: the value to return, in case we translate a forward body.
 
-(** [opt_v]: the value to return, in case we translate a forward body *)
+    Remark: for now, we can't get there if we are inside a loop.
+    If inside a loop, we use {!translate_return_with_loop}.
+
+    Remark: in case we merge the forward/backward functions, we introduce
+    those in [translate_forward_end].
+*)
 and translate_return (ectx : C.eval_ctx) (opt_v : V.typed_value option)
     (ctx : bs_ctx) : texpression =
   (* There are two cases:
@@ -1599,22 +1965,20 @@ and translate_return (ectx : C.eval_ctx) (opt_v : V.typed_value option)
      - or we are translating a backward function, in which case it should be [None]
   *)
   (* Compute the values that we should return *without the state and the result
-   * wrapper* *)
+     wrapper* *)
   let output =
     match ctx.bid with
     | None ->
         (* Forward function *)
         let v = Option.get opt_v in
         typed_value_to_texpression ctx ectx v
-    | Some bid ->
+    | Some _ ->
         (* Backward function *)
         (* Sanity check *)
         assert (opt_v = None);
         (* Group the variables in which we stored the values we need to give back.
-         * See the explanations for the [SynthInput] case in [translate_end_abstraction] *)
-        let backward_outputs =
-          T.RegionGroupId.Map.find bid ctx.backward_outputs
-        in
+           See the explanations for the [SynthInput] case in [translate_end_abstraction] *)
+        let backward_outputs = Option.get ctx.backward_outputs in
         let field_values = List.map mk_texpression_from_var backward_outputs in
         mk_simpl_tuple_texpression field_values
   in
@@ -1622,7 +1986,7 @@ and translate_return (ectx : C.eval_ctx) (opt_v : V.typed_value option)
    * - error-monad: Return x
    * - state-error: Return (state, x)
    * *)
-  let effect_info = ctx.sg.info.effect_info in
+  let effect_info = ctx_get_effect_info ctx in
   let output =
     if effect_info.stateful then
       let state_rvalue = mk_state_texpression ctx.state_var in
@@ -1647,24 +2011,12 @@ and translate_return_with_loop (loop_id : V.LoopId.id) (is_continue : bool)
   *)
   let output =
     match ctx.bid with
-    | None ->
-        (* Forward *)
-        mk_texpression_from_var
-          (Option.get loop_info.forward_output_no_state_no_result)
-    | Some bid ->
+    | None -> Option.get loop_info.forward_output_no_state_no_result
+    | Some _ ->
         (* Backward *)
         (* Group the variables in which we stored the values we need to give back.
          * See the explanations for the [SynthInput] case in [translate_end_abstraction] *)
-        let backward_outputs =
-          let map =
-            if ctx.inside_loop then
-              (* We are synthesizing a loop body *)
-              Option.get ctx.loop_backward_outputs
-            else (* Regular function *)
-              ctx.backward_outputs
-          in
-          T.RegionGroupId.Map.find bid map
-        in
+        let backward_outputs = Option.get ctx.backward_outputs in
         let field_values = List.map mk_texpression_from_var backward_outputs in
         mk_simpl_tuple_texpression field_values
   in
@@ -1676,7 +2028,7 @@ and translate_return_with_loop (loop_id : V.LoopId.id) (is_continue : bool)
    * effect - in particular, one manipulates a state iff the other does
    * the same.
    * *)
-  let effect_info = ctx.sg.info.effect_info in
+  let effect_info = ctx_get_effect_info ctx in
   let output =
     if effect_info.stateful then
       let state_rvalue = mk_state_texpression ctx.state_var in
@@ -1684,13 +2036,15 @@ and translate_return_with_loop (loop_id : V.LoopId.id) (is_continue : bool)
     else output
   in
   (* Wrap in a result - TODO: check effect_info.can_fail to not always wrap *)
-  mk_result_return_texpression output
+  mk_emeta (Tag "return_with_loop") (mk_result_return_texpression output)
 
 and translate_function_call (call : S.call) (e : S.expression) (ctx : bs_ctx) :
     texpression =
   log#ldebug
     (lazy
-      ("translate_function_call:\n"
+      ("translate_function_call:\n" ^ "\n- call.call_id:"
+      ^ S.show_call_id call.call_id
+      ^ "\n\n- call.generics:\n"
       ^ ctx_generic_args_to_string ctx call.generics));
   (* Translate the function call *)
   let generics = ctx_translate_fwd_generic_args ctx call.generics in
@@ -1702,10 +2056,9 @@ and translate_function_call (call : S.call) (e : S.expression) (ctx : bs_ctx) :
       (List.combine args args_mplaces)
   in
   let dest_mplace = translate_opt_mplace call.dest_place in
-  let ctx, dest = fresh_var_for_symbolic_value call.dest ctx in
   (* Retrieve the function id, and register the function call in the context
    * if necessary. *)
-  let ctx, fun_id, effect_info, args, out_state =
+  let ctx, fun_id, effect_info, args, dest_v =
     match call.call_id with
     | S.Fun (fid, call_id) ->
         (* Regular function call *)
@@ -1713,25 +2066,150 @@ and translate_function_call (call : S.call) (e : S.expression) (ctx : bs_ctx) :
         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 =
-          get_fun_effect_info ctx.fun_context.fun_infos fid None None
-        in
+        let effect_info = get_fun_effect_info ctx fid None None in
         (* Depending on the function effects:
-           * - add the fuel
-           * - add the state input argument
-           * - generate a fresh state variable for the returned state
+           - add the fuel
+           - add the state input argument
+           - generate a fresh state variable for the returned state
         *)
         let args, ctx, out_state =
           let fuel = mk_fuel_input_as_list ctx effect_info in
           if effect_info.stateful then
             let state_var = mk_state_texpression ctx.state_var in
-            let ctx, nstate_var = bs_ctx_fresh_state_var ctx in
+            let ctx, _, nstate_var = bs_ctx_fresh_state_var ctx in
             (List.concat [ fuel; args; [ state_var ] ], ctx, Some nstate_var)
           else (List.concat [ fuel; args ], ctx, None)
         in
+        (* If we do not split the forward/backward functions: generate the
+           variables for the backward functions returned by the forward
+           function. *)
+        let ctx, ignore_fwd_output, back_funs_map, back_funs =
+          if !Config.return_back_funs then (
+            (* We need to compute the signatures of the backward functions. *)
+            let sg = Option.get call.sg in
+            let decls_ctx = ctx.decls_ctx in
+            let dsg =
+              translate_fun_sig_with_regions_hierarchy_to_decomposed decls_ctx
+                fid call.regions_hierarchy sg
+                (List.map (fun _ -> None) sg.inputs)
+            in
+            log#ldebug
+              (lazy ("dsg.generics:\n" ^ show_generic_params dsg.generics));
+            let tr_self, all_generics =
+              match call.trait_method_generics with
+              | None -> (UnknownTrait __FUNCTION__, generics)
+              | Some (all_generics, tr_self) ->
+                  let all_generics =
+                    ctx_translate_fwd_generic_args ctx all_generics
+                  in
+                  let tr_self =
+                    translate_fwd_trait_instance_id ctx.type_ctx.type_infos
+                      tr_self
+                  in
+                  (tr_self, all_generics)
+            in
+            let back_tys =
+              compute_back_tys_with_info dsg (Some (all_generics, tr_self))
+            in
+            (* Introduce variables for the backward functions *)
+            (* Compute a proper basename for the variables *)
+            let back_fun_name =
+              let name =
+                match fid with
+                | FunId (FAssumed fid) -> (
+                    match fid with
+                    | BoxNew -> "box_new"
+                    | BoxFree -> "box_free"
+                    | ArrayRepeat -> "array_repeat"
+                    | ArrayIndexShared -> "index_shared"
+                    | ArrayIndexMut -> "index_mut"
+                    | ArrayToSliceShared -> "to_slice_shared"
+                    | ArrayToSliceMut -> "to_slice_mut"
+                    | SliceIndexShared -> "index_shared"
+                    | SliceIndexMut -> "index_mut")
+                | FunId (FRegular fid) | TraitMethod (_, _, fid) -> (
+                    let decl =
+                      FunDeclId.Map.find fid ctx.fun_ctx.llbc_fun_decls
+                    in
+                    match Collections.List.last decl.name with
+                    | PeIdent (s, _) -> s
+                    | PeImpl _ ->
+                        (* We shouldn't get there *)
+                        raise (Failure "Unexpected"))
+              in
+              name ^ "_back"
+            in
+            let ctx, back_vars =
+              fresh_opt_vars
+                (List.map
+                   (fun ty ->
+                     match ty with
+                     | None -> None
+                     | Some (back_sg, ty) ->
+                         (* We insert a name for the variable only if the function
+                            can fail: if it can fail, it means the call returns a backward
+                            function. Otherwise, we it directly returns the value given
+                            back by the backward function, which means we shouldn't
+                            give it a name like "back..." (it doesn't make sense) *)
+                         let name =
+                           if back_sg.effect_info.can_fail then
+                             Some back_fun_name
+                           else None
+                         in
+                         Some (name, ty))
+                   back_tys)
+                ctx
+            in
+            let back_funs =
+              List.filter_map
+                (fun v ->
+                  match v with
+                  | None -> None
+                  | Some v -> Some (mk_typed_pattern_from_var v None))
+                back_vars
+            in
+            let gids =
+              List.map
+                (fun (g : T.region_var_group) -> g.id)
+                call.regions_hierarchy
+            in
+            let back_vars =
+              List.map (Option.map mk_texpression_from_var) back_vars
+            in
+            let back_funs_map =
+              RegionGroupId.Map.of_list (List.combine gids back_vars)
+            in
+            (ctx, dsg.fwd_info.ignore_output, Some back_funs_map, back_funs))
+          else (ctx, false, None, [])
+        in
+        (* Compute the pattern for the destination *)
+        let ctx, dest = fresh_var_for_symbolic_value call.dest ctx in
+        let dest = mk_typed_pattern_from_var dest dest_mplace in
+        let dest =
+          (* Here there is something subtle: as we might ignore the output
+             of the forward function (because it translates to unit) we doNOT
+             necessarily introduce in the let-binding the variable to which we
+             map the symbolic value which was introduced for the output of the
+             function call. This would be problematic if later we need to
+             translate this symbolic value, but we implemented
+             {!symbolic_value_to_texpression} so that it doesn't perform any
+             lookups if the symbolic value has type unit.
+          *)
+          let vars =
+            if ignore_fwd_output then back_funs else dest :: back_funs
+          in
+          mk_simpl_tuple_pattern vars
+        in
+        let dest =
+          match out_state with
+          | None -> dest
+          | Some out_state -> mk_simpl_tuple_pattern [ out_state; dest ]
+        in
         (* Register the function call *)
-        let ctx = bs_ctx_register_forward_call call_id call args ctx in
-        (ctx, func, effect_info, args, out_state)
+        let ctx =
+          bs_ctx_register_forward_call call_id call args back_funs_map ctx
+        in
+        (ctx, func, effect_info, args, dest)
     | S.Unop E.Not ->
         let effect_info =
           {
@@ -1742,7 +2220,9 @@ and translate_function_call (call : S.call) (e : S.expression) (ctx : bs_ctx) :
             is_rec = false;
           }
         in
-        (ctx, Unop Not, effect_info, args, None)
+        let ctx, dest = fresh_var_for_symbolic_value call.dest ctx in
+        let dest = mk_typed_pattern_from_var dest dest_mplace in
+        (ctx, Unop Not, effect_info, args, dest)
     | S.Unop E.Neg -> (
         match args with
         | [ arg ] ->
@@ -1758,7 +2238,9 @@ and translate_function_call (call : S.call) (e : S.expression) (ctx : bs_ctx) :
                 is_rec = false;
               }
             in
-            (ctx, Unop (Neg int_ty), effect_info, args, None)
+            let ctx, dest = fresh_var_for_symbolic_value call.dest ctx in
+            let dest = mk_typed_pattern_from_var dest dest_mplace in
+            (ctx, Unop (Neg int_ty), effect_info, args, dest)
         | _ -> raise (Failure "Unreachable"))
     | S.Unop (E.Cast cast_kind) -> (
         match cast_kind with
@@ -1773,7 +2255,9 @@ and translate_function_call (call : S.call) (e : S.expression) (ctx : bs_ctx) :
                 is_rec = false;
               }
             in
-            (ctx, Unop (Cast (src_ty, tgt_ty)), effect_info, args, None)
+            let ctx, dest = fresh_var_for_symbolic_value call.dest ctx in
+            let dest = mk_typed_pattern_from_var dest dest_mplace in
+            (ctx, Unop (Cast (src_ty, tgt_ty)), effect_info, args, dest)
         | CastFnPtr _ -> raise (Failure "TODO: function casts"))
     | S.Binop binop -> (
         match args with
@@ -1793,15 +2277,11 @@ and translate_function_call (call : S.call) (e : S.expression) (ctx : bs_ctx) :
                 is_rec = false;
               }
             in
-            (ctx, Binop (binop, int_ty0), effect_info, args, None)
+            let ctx, dest = fresh_var_for_symbolic_value call.dest ctx in
+            let dest = mk_typed_pattern_from_var dest dest_mplace in
+            (ctx, Binop (binop, int_ty0), effect_info, args, dest)
         | _ -> raise (Failure "Unreachable"))
   in
-  let dest_v =
-    let dest = mk_typed_pattern_from_var dest dest_mplace in
-    match out_state with
-    | None -> dest
-    | Some out_state -> mk_simpl_tuple_pattern [ out_state; dest ]
-  in
   let func = { id = FunOrOp fun_id; generics } in
   let input_tys = (List.map (fun (x : texpression) -> x.ty)) args in
   let ret_ty =
@@ -1846,45 +2326,38 @@ and translate_end_abstraction_synth_input (ectx : C.eval_ctx) (abs : V.abs)
       ^ abs_to_string ctx abs ^ "\n"));
 
   (* When we end an input abstraction, this input abstraction gets back
-   * the borrows which it introduced in the context through the input
-   * values: by listing those values, we get the values which are given
-   * back by one of the backward functions we are synthesizing. *)
-  (* Note that we don't support nested borrows for now: if we find
-   * an ended synthesized input abstraction, it must be the one corresponding
-   * to the backward function wer are synthesizing, it can't be the one
-   * for a parent backward function.
-   *)
+     the borrows which it introduced in the context through the input
+     values: by listing those values, we get the values which are given
+     back by one of the backward functions we are synthesizing.
+
+     Note that we don't support nested borrows for now: if we find
+     an ended synthesized input abstraction, it must be the one corresponding
+     to the backward function wer are synthesizing, it can't be the one
+     for a parent backward function.
+  *)
   let bid = Option.get ctx.bid in
   assert (rg_id = bid);
 
-  (* The translation is done as follows:
-   * - for a given backward function, we choose a set of variables [v_i]
-   * - when we detect the ended input abstraction which corresponds
-   *   to the backward function, and which consumed the values [consumed_i],
-   *   we introduce:
-   *   {[
-       *   let v_i = consumed_i in
-       *   ...
-         *   ]}
-   *   Then, when we reach the [Return] node, we introduce:
-   *   {[
-       *   (v_i)
-       *   ]}
-   * *)
-  (* First, get the given back variables.
+  (* First, introduce the given back variables.
 
      We don't use the same given back variables if we translate a loop or
      the standard body of a function.
   *)
-  let given_back_variables =
-    let map =
+  let ctx, given_back_variables =
+    let vars =
       if ctx.inside_loop then
         (* We are synthesizing a loop body *)
-        Option.get ctx.loop_backward_outputs
-      else (* Regular function body *)
-        ctx.backward_outputs
+        let loop_id = Option.get ctx.loop_id in
+        let loop = LoopId.Map.find loop_id ctx.loops in
+        let tys = RegionGroupId.Map.find bid loop.back_outputs in
+        List.map (fun ty -> (None, ty)) tys
+      else
+        (* Regular function body *)
+        let back_sg = RegionGroupId.Map.find bid ctx.sg.back_sg in
+        List.combine back_sg.output_names back_sg.outputs
     in
-    T.RegionGroupId.Map.find bid map
+    let ctx, vars = fresh_vars vars ctx in
+    ({ ctx with backward_outputs = Some vars }, vars)
   in
 
   (* Get the list of values consumed by the abstraction upon ending *)
@@ -1933,9 +2406,7 @@ and translate_end_abstraction_fun_call (ectx : C.eval_ctx) (abs : V.abs)
         (* Those don't have backward functions *)
         raise (Failure "Unreachable")
   in
-  let effect_info =
-    get_fun_effect_info ctx.fun_context.fun_infos fun_id None (Some rg_id)
-  in
+  let effect_info = get_fun_effect_info ctx fun_id None (Some rg_id) 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
@@ -1959,14 +2430,16 @@ and translate_end_abstraction_fun_call (ectx : C.eval_ctx) (abs : V.abs)
   let back_state, ctx, nstate =
     if effect_info.stateful then
       let back_state = mk_state_texpression ctx.state_var in
-      let ctx, nstate = bs_ctx_fresh_state_var ctx in
+      let ctx, _, nstate = bs_ctx_fresh_state_var ctx in
       ([ back_state ], ctx, Some nstate)
     else ([], ctx, None)
   in
   (* Concatenate all the inpus *)
-  let inputs =
-    List.concat [ fwd_inputs; back_ancestors_inputs; back_inputs; back_state ]
+  let inherited_inputs =
+    if !Config.return_back_funs then []
+    else List.concat [ fwd_inputs; back_ancestors_inputs ]
   in
+  let back_inputs = List.append back_inputs back_state in
   (* Retrieve the values given back by this function: those are the output
    * values. We rely on the fact that there are no nested borrows to use the
    * meta-place information from the input values given to the forward function
@@ -1983,78 +2456,61 @@ and translate_end_abstraction_fun_call (ectx : C.eval_ctx) (abs : V.abs)
     | None -> output
     | 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 *)
-  (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 (pure_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 *)
+     if necessary.Arith_status *)
   let ctx, func =
-    bs_ctx_register_backward_call abs call_id rg_id back_inputs ctx
+    bs_ctx_register_backward_call abs effect_info call_id rg_id inherited_inputs
+      back_inputs generics output.ty ctx
   in
   (* Translate the next expression *)
   let next_e = translate_expression e ctx in
   (* Put everything together *)
+  let inputs = List.append inherited_inputs back_inputs in
   let args_mplaces = List.map (fun _ -> None) inputs in
   let args =
     List.map
       (fun (arg, mp) -> mk_opt_mplace_texpression mp arg)
       (List.combine inputs args_mplaces)
   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 output.ty else output.ty
-  in
-  let func_ty = mk_arrows input_tys ret_ty 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**:
-   * =================
-   * We do a small optimization here: if the backward function doesn't
-   * have any output, we don't introduce any function call.
-   * See the comment in {!Config.filter_useless_monadic_calls}.
-   *
-   * TODO: use an option to disallow backward functions from updating the state.
-   * TODO: a backward function which only gives back shared borrows shouldn't
-   * update the state (state updates should only be used for mutable borrows,
-   * with objects like Rc for instance).
-   *)
-  if !Config.filter_useless_monadic_calls && outputs = [] && nstate = None then (
+     =================
+     We do a small optimization here if we split the forward/backward functions.
+     If the backward function doesn't have any output, we don't introduce any function
+     call.
+     See the comment in {!Config.filter_useless_monadic_calls}.
+
+     TODO: use an option to disallow backward functions from updating the state.
+     TODO: a backward function which only gives back shared borrows shouldn't
+     update the state (state updates should only be used for mutable borrows,
+     with objects like Rc for instance).
+  *)
+  if
+    (not !Config.return_back_funs)
+    && !Config.filter_useless_monadic_calls
+    && outputs = [] && nstate = None
+  then (
     (* No outputs - we do a small sanity check: the backward function
-     * should have exactly the same number of inputs as the forward:
-     * this number can be different only if the forward function returned
-     * a value containing mutable borrows, which can't be the case... *)
+       should have exactly the same number of inputs as the forward:
+       this number can be different only if the forward function returned
+       a value containing mutable borrows, which can't be the case... *)
     assert (List.length inputs = List.length fwd_inputs);
     next_e)
-  else mk_let effect_info.can_fail output call next_e
+  else
+    (* The backward function might also have been filtered if we do not
+       split the forward/backward functions *)
+    match func with
+    | None -> next_e
+    | Some func ->
+        log#ldebug
+          (lazy
+            (let args = List.map (texpression_to_string ctx) args in
+             "func: "
+             ^ texpression_to_string ctx func
+             ^ "\nfunc type: "
+             ^ pure_ty_to_string ctx func.ty
+             ^ "\n\nargs:\n" ^ String.concat "\n" args));
+        let call = mk_apps func args in
+        mk_let effect_info.can_fail output call next_e
 
 and translate_end_abstraction_identity (ectx : C.eval_ctx) (abs : V.abs)
     (e : S.expression) (ctx : bs_ctx) : texpression =
@@ -2095,15 +2551,15 @@ and translate_end_abstraction_synth_ret (ectx : C.eval_ctx) (abs : V.abs)
      let-binding:
      {[
        let id_back x nx =
-         let s = nx in // the name [s] is not important (only collision matters)
-                                                        ...
+       let s = nx in // the name [s] is not important (only collision matters)
+       ...
      ]}
 
      This let-binding later gets inlined, during a micro-pass.
   *)
   (* First, retrieve the list of variables used for the inputs for the
    * backward function *)
-  let inputs = T.RegionGroupId.Map.find rg_id ctx.backward_inputs in
+  let inputs = T.RegionGroupId.Map.find rg_id ctx.backward_inputs_no_state in
   (* Retrieve the values consumed upon ending the loans inside this
    * abstraction: as there are no nested borrows, there should be none. *)
   let consumed = abs_to_consumed ctx ectx abs in
@@ -2150,11 +2606,12 @@ and translate_end_abstraction_loop (ectx : C.eval_ctx) (abs : V.abs)
   | V.LoopSynthInput ->
       (* Actually the same case as [SynthInput] *)
       translate_end_abstraction_synth_input ectx abs e ctx rg_id
-  | V.LoopCall ->
+  | V.LoopCall -> (
+      (* We need to introduce a call to the backward function corresponding
+         to a forward call which happened earlier *)
       let fun_id = E.FRegular ctx.fun_decl.def_id in
       let effect_info =
-        get_fun_effect_info ctx.fun_context.fun_infos (FunId fun_id)
-          (Some vloop_id) (Some rg_id)
+        get_fun_effect_info ctx (FunId fun_id) (Some vloop_id) (Some rg_id)
       in
       let loop_info = LoopId.Map.find loop_id ctx.loops in
       let generics = loop_info.generics in
@@ -2165,7 +2622,7 @@ and translate_end_abstraction_loop (ectx : C.eval_ctx) (abs : V.abs)
          values consumed upon ending the abstraction (i.e., we don't use
          [abs_to_consumed]) *)
       let back_inputs_vars =
-        T.RegionGroupId.Map.find rg_id ctx.backward_inputs
+        T.RegionGroupId.Map.find rg_id ctx.backward_inputs_no_state
       in
       let back_inputs = List.map mk_texpression_from_var back_inputs_vars in
       (* If the function is stateful:
@@ -2175,12 +2632,15 @@ and translate_end_abstraction_loop (ectx : C.eval_ctx) (abs : V.abs)
       let back_state, ctx, nstate =
         if effect_info.stateful then
           let back_state = mk_state_texpression ctx.state_var in
-          let ctx, nstate = bs_ctx_fresh_state_var ctx in
+          let ctx, _, nstate = bs_ctx_fresh_state_var ctx in
           ([ back_state ], ctx, Some nstate)
         else ([], ctx, None)
       in
       (* Concatenate all the inputs *)
-      let inputs = List.concat [ fwd_inputs; back_inputs; back_state ] in
+      let inputs =
+        if !Config.return_back_funs then List.concat [ back_inputs; back_state ]
+        else List.concat [ fwd_inputs; back_inputs; back_state ]
+      in
       (* Retrieve the values given back by this function *)
       let ctx, outputs = abs_to_given_back None abs ctx in
       (* Group the output values together: first the updated inputs *)
@@ -2204,68 +2664,88 @@ and translate_end_abstraction_loop (ectx : C.eval_ctx) (abs : V.abs)
       let ret_ty =
         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 (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
+      (* Create the expression for the function:
+         - it is either a call to a top-level function, if we split the
+           forward/backward functions
+         - or a call to the variable we introduced for the backward function,
+           if we merge the forward/backward functions *)
+      let func =
+        if !Config.return_back_funs then
+          RegionGroupId.Map.find rg_id (Option.get loop_info.back_funs)
+        else
+          let func_ty = mk_arrows input_tys ret_ty in
+          let func = Fun (FromLlbc (FunId fun_id, Some loop_id, Some rg_id)) in
+          let func = { id = FunOrOp func; generics } in
+          Some { e = Qualif func; ty = func_ty }
+      in
       (* **Optimization**:
-       * =================
-       * We do a small optimization here: if the backward function doesn't
-       * have any output, we don't introduce any function call.
-       * See the comment in {!Config.filter_useless_monadic_calls}.
-       *
-       * TODO: use an option to disallow backward functions from updating the state.
-       * TODO: a backward function which only gives back shared borrows shouldn't
-       * update the state (state updates should only be used for mutable borrows,
-       * with objects like Rc for instance).
-       *)
-      if !Config.filter_useless_monadic_calls && outputs = [] && nstate = None
+         =================
+         We do a small optimization here in case we split the forward/backward
+         functions.
+         If the backward function doesn't have any output, we don't introduce
+         any function call.
+         See the comment in {!Config.filter_useless_monadic_calls}.
+
+         TODO: use an option to disallow backward functions from updating the state.
+         TODO: a backward function which only gives back shared borrows shouldn't
+         update the state (state updates should only be used for mutable borrows,
+         with objects like Rc for instance).
+      *)
+      if
+        (not !Config.return_back_funs)
+        && !Config.filter_useless_monadic_calls
+        && outputs = [] && nstate = None
       then (
         (* No outputs - we do a small sanity check: the backward function
-         * should have exactly the same number of inputs as the forward:
-         * this number can be different only if the forward function returned
-         * a value containing mutable borrows, which can't be the case... *)
+           should have exactly the same number of inputs as the forward:
+           this number can be different only if the forward function returned
+           a value containing mutable borrows, which can't be the case... *)
         assert (List.length inputs = List.length fwd_inputs);
         next_e)
       else
-        (* Add meta-information - this is slightly hacky: we look at the
-           values consumed by the abstraction (note that those come from
-           *before* we applied the fixed-point context) and use them to
-           guide the naming of the output vars.
-
-           Also, we need to convert the backward outputs from patterns to
-           variables.
-
-           Finally, in practice, this works well only for loop bodies:
-           we do this only in this case.
-           TODO: improve the heuristics, to give weight to the hints for
-           instance.
-        *)
-        let next_e =
-          if ctx.inside_loop then
-            let consumed_values = abs_to_consumed ctx ectx abs in
-            let var_values = List.combine outputs consumed_values in
-            let var_values =
-              List.filter_map
-                (fun (var, v) ->
-                  match var.Pure.value with
-                  | PatVar (var, _) -> Some (var, v)
-                  | _ -> None)
-                var_values
+        (* In case we merge the fwd/back functions we filter the backward
+           functions elsewhere *)
+        match func with
+        | None -> next_e
+        | Some func ->
+            let call = mk_apps func args in
+            (* Add meta-information - this is slightly hacky: we look at the
+               values consumed by the abstraction (note that those come from
+               *before* we applied the fixed-point context) and use them to
+               guide the naming of the output vars.
+
+               Also, we need to convert the backward outputs from patterns to
+               variables.
+
+               Finally, in practice, this works well only for loop bodies:
+               we do this only in this case.
+               TODO: improve the heuristics, to give weight to the hints for
+               instance.
+            *)
+            let next_e =
+              if ctx.inside_loop then
+                let consumed_values = abs_to_consumed ctx ectx abs in
+                let var_values = List.combine outputs consumed_values in
+                let var_values =
+                  List.filter_map
+                    (fun (var, v) ->
+                      match var.Pure.value with
+                      | PatVar (var, _) -> Some (var, v)
+                      | _ -> None)
+                    var_values
+                in
+                let vars, values = List.split var_values in
+                mk_emeta_symbolic_assignments vars values next_e
+              else next_e
             in
-            let vars, values = List.split var_values in
-            mk_emeta_symbolic_assignments vars values next_e
-          else next_e
-        in
 
-        (* Create the let-binding *)
-        mk_let effect_info.can_fail output call next_e
+            (* Create the let-binding *)
+            mk_let effect_info.can_fail output call next_e)
 
 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 decl = A.GlobalDeclId.Map.find gid ctx.global_ctx.llbc_global_decls 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
@@ -2290,8 +2770,7 @@ and translate_assertion (ectx : C.eval_ctx) (v : V.typed_value)
 and translate_expansion (p : S.mplace option) (sv : V.symbolic_value)
     (exp : S.expansion) (ctx : bs_ctx) : texpression =
   (* Translate the scrutinee *)
-  let scrutinee_var = lookup_var_for_symbolic_value sv ctx in
-  let scrutinee = mk_texpression_from_var scrutinee_var in
+  let scrutinee = symbolic_value_to_texpression ctx sv in
   let scrutinee_mplace = translate_opt_mplace p in
   (* Translate the branches *)
   match exp with
@@ -2370,7 +2849,13 @@ and translate_expansion (p : S.mplace option) (sv : V.symbolic_value)
             If (true_e, false_e) )
       in
       let ty = true_e.ty in
-      assert (ty = false_e.ty);
+      log#ldebug
+        (lazy
+          ("true_e.ty: "
+          ^ pure_ty_to_string ctx true_e.ty
+          ^ "\n\nfalse_e.ty: "
+          ^ pure_ty_to_string ctx false_e.ty));
+      if !Config.fail_hard then assert (ty = false_e.ty);
       { e; ty }
   | ExpandInt (int_ty, branches, otherwise) ->
       let translate_branch ((v, branch_e) : V.scalar_value * S.expression) :
@@ -2441,7 +2926,7 @@ and translate_ExpandAdt_one_branch (sv : V.symbolic_value)
          - if we forbid using field projectors.
       *)
       let is_rec_def =
-        T.TypeDeclId.Set.mem adt_id ctx.type_context.recursive_decls
+        T.TypeDeclId.Set.mem adt_id ctx.type_ctx.recursive_decls
       in
       let use_let_with_cons =
         is_enum
@@ -2454,7 +2939,7 @@ and translate_ExpandAdt_one_branch (sv : V.symbolic_value)
            like Coq don't, in which case we have to deconstruct the whole ADT
            at once (`let (a, b, c) = x in`) *)
         || TypesUtils.type_decl_from_type_id_is_tuple_struct
-             ctx.type_context.type_infos type_id
+             ctx.type_ctx.type_infos type_id
            && not (Config.backend_has_tuple_projectors ())
       in
       if use_let_with_cons then
@@ -2547,7 +3032,7 @@ and translate_intro_symbolic (ectx : C.eval_ctx) (p : S.mplace option)
         { e = StructUpdate su; ty = var.ty }
     | VaCgValue cg_id -> { e = CVar cg_id; ty = var.ty }
     | VaTraitConstValue (trait_ref, generics, const_name) ->
-        let type_infos = ctx.type_context.type_infos in
+        let type_infos = ctx.type_ctx.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
@@ -2562,22 +3047,169 @@ and translate_intro_symbolic (ectx : C.eval_ctx) (p : S.mplace option)
 
 and translate_forward_end (ectx : C.eval_ctx)
     (loop_input_values : V.typed_value S.symbolic_value_id_map option)
-    (e : S.expression) (back_e : S.expression S.region_group_id_map)
+    (fwd_e : S.expression) (back_e : S.expression S.region_group_id_map)
     (ctx : bs_ctx) : texpression =
-  (* Update the current state with the additional state received by the backward
-     function, if needs be, and lookup the proper expression *)
-  let translate_end ctx =
+  let translate_one_end ctx (bid : RegionGroupId.id option) =
+    let ctx = { ctx with bid } in
     (* Update the current state with the additional state received by the backward
        function, if needs be, and lookup the proper expression *)
-    let ctx, e =
-      match ctx.bid with
-      | None -> (ctx, e)
+    let ctx, e, finish =
+      match bid with
+      | None ->
+          (* We are translating the forward function - nothing to do *)
+          (ctx, fwd_e, fun e -> e)
       | Some bid ->
-          let ctx = { ctx with state_var = ctx.back_state_var } in
+          (* There are two cases here:
+             - if we split the fwd/backward functions, we simply need to update
+               the state.
+             - if we don't split, we also need to wrap the expression in a
+               lambda, which introduces the additional inputs of the backward
+               function
+          *)
+          let ctx =
+            (* Introduce variables for the inputs and the state variable
+               and update the context. *)
+            if !Config.return_back_funs then
+              (* If the forward/backward functions are not split, we need
+                 to introduce fresh variables for the additional inputs,
+                 because they are locally introduced in a lambda *)
+              let back_sg = RegionGroupId.Map.find bid ctx.sg.back_sg in
+              let ctx, backward_inputs_no_state =
+                fresh_vars back_sg.inputs_no_state ctx
+              in
+              let ctx, backward_inputs_with_state =
+                if back_sg.effect_info.stateful then
+                  let ctx, var, _ = bs_ctx_fresh_state_var ctx in
+                  (ctx, backward_inputs_no_state @ [ var ])
+                else (ctx, backward_inputs_no_state)
+              in
+              {
+                ctx with
+                backward_inputs_no_state =
+                  RegionGroupId.Map.add bid backward_inputs_no_state
+                    ctx.backward_inputs_no_state;
+                backward_inputs_with_state =
+                  RegionGroupId.Map.add bid backward_inputs_with_state
+                    ctx.backward_inputs_with_state;
+              }
+            else
+              (* Update the state variable *)
+              let back_state_var =
+                RegionGroupId.Map.find bid ctx.back_state_vars
+              in
+              { ctx with state_var = back_state_var }
+          in
+
           let e = T.RegionGroupId.Map.find bid back_e in
-          (ctx, e)
+          let finish e =
+            (* Wrap in lambdas if necessary *)
+            if !Config.return_back_funs then
+              let inputs =
+                RegionGroupId.Map.find bid ctx.backward_inputs_with_state
+              in
+              let places = List.map (fun _ -> None) inputs in
+              mk_lambdas_from_vars inputs places e
+            else e
+          in
+          (ctx, e, finish)
     in
-    translate_expression e ctx
+    let e = translate_expression e ctx in
+    finish e
+  in
+
+  (* There are two cases, depending on whether we are splitting the forward/backward
+     functions or not.
+
+     - if we split, then we simply need to translate the proper "end" expression,
+       that is the end of the forward function, or of the backward function we
+       are currently translating.
+     - if we don't split, then we need to translate the end of the forward
+       function (this is the value we will return) and generate the bodies
+       of the backward functions (which we will also return).
+
+     Update the current state with the additional state received by the backward
+     function, if needs be, and lookup the proper expression.
+  *)
+  let translate_end ctx =
+    if !Config.return_back_funs then
+      (* Compute the output of the forward function *)
+      let fwd_effect_info = ctx.sg.fwd_info.effect_info in
+      let ctx, pure_fwd_var = fresh_var None ctx.sg.fwd_output ctx in
+      let fwd_e = translate_one_end ctx None in
+
+      (* Introduce the backward functions. *)
+      let back_el =
+        List.map
+          (fun ((gid, _) : RegionGroupId.id * back_sg_info) ->
+            translate_one_end ctx (Some gid))
+          (RegionGroupId.Map.bindings ctx.sg.back_sg)
+      in
+
+      (* Compute whether the backward expressions should be evaluated straight
+         away or not (i.e., if we should bind them with monadic let-bindings
+         or not). We evaluate them straight away if they can fail and have no
+         inputs. *)
+      let evaluate_backs =
+        List.map
+          (fun (sg : back_sg_info) ->
+            if !Config.simplify_merged_fwd_backs then
+              sg.inputs = [] && sg.effect_info.can_fail
+            else false)
+          (RegionGroupId.Map.values ctx.sg.back_sg)
+      in
+
+      (* Introduce variables for the backward functions.
+         We lookup the LLBC definition in an attempt to derive pretty names
+         for those functions. *)
+      let _, back_vars = fresh_back_vars_for_current_fun ctx in
+
+      (* Create the return expressions *)
+      let vars =
+        let back_vars = List.filter_map (fun x -> x) back_vars in
+        if ctx.sg.fwd_info.ignore_output then back_vars
+        else pure_fwd_var :: back_vars
+      in
+      let vars = List.map mk_texpression_from_var vars in
+      let ret = mk_simpl_tuple_texpression vars in
+
+      (* Introduce a fresh input state variable for the forward expression *)
+      let _ctx, state_var, state_pat =
+        if fwd_effect_info.stateful then
+          let ctx, var, pat = bs_ctx_fresh_state_var ctx in
+          (ctx, [ var ], [ pat ])
+        else (ctx, [], [])
+      in
+
+      let state_var = List.map mk_texpression_from_var state_var in
+      let ret = mk_simpl_tuple_texpression (state_var @ [ ret ]) in
+      let ret = mk_result_return_texpression ret in
+
+      (* Introduce all the let-bindings *)
+
+      (* Combine:
+         - the backward variables
+         - whether we should evaluate the expression for the backward function
+           (i.e., should we use a monadic let-binding or not - we do if the
+           backward functions don't have inputs and can fail)
+         - the expressions for the backward functions
+      *)
+      let back_vars_els =
+        List.filter_map
+          (fun (v, (eval, el)) ->
+            match v with None -> None | Some v -> Some (v, eval, el))
+          (List.combine back_vars (List.combine evaluate_backs back_el))
+      in
+      let e =
+        List.fold_right
+          (fun (var, evaluate, back_e) e ->
+            mk_let evaluate (mk_typed_pattern_from_var var None) back_e e)
+          back_vars_els ret
+      in
+      (* Bind the expression for the forward output *)
+      let fwd_var = mk_typed_pattern_from_var pure_fwd_var None in
+      let pat = mk_simpl_tuple_pattern (state_pat @ [ fwd_var ]) in
+      mk_let fwd_effect_info.can_fail pat fwd_e e
+    else translate_one_end ctx ctx.bid
   in
 
   (* If we are (re-)entering a loop, we need to introduce a call to the
@@ -2624,17 +3256,53 @@ and translate_forward_end (ectx : C.eval_ctx)
 
       (* Lookup the effect info for the loop function *)
       let fid = E.FRegular ctx.fun_decl.def_id in
-      let effect_info =
-        get_fun_effect_info ctx.fun_context.fun_infos (FunId fid) None ctx.bid
-      in
+      let effect_info = get_fun_effect_info ctx (FunId fid) None ctx.bid in
 
       (* Introduce a fresh output value for the forward function *)
-      let ctx, output_var =
-        let output_ty = mk_simpl_tuple_ty ctx.fwd_sg.doutputs in
-        fresh_var None output_ty ctx
+      let ctx, fwd_output, output_pat =
+        if ctx.sg.fwd_info.ignore_output then
+          (* Note that we still need the forward output (which is unit),
+             because even though the loop function will ignore the forward output,
+             the forward expression will still compute an output (which
+             will have type unit - otherwise we can't ignore it). *)
+          (ctx, mk_unit_rvalue, [])
+        else
+          let ctx, output_var = fresh_var None ctx.sg.fwd_output ctx in
+          ( ctx,
+            mk_texpression_from_var output_var,
+            [ mk_typed_pattern_from_var output_var None ] )
+      in
+
+      (* Introduce fresh variables for the backward functions of the loop.
+
+         For now, the backward functions of the loop are the same as the
+         backward functions of the outer function.
+      *)
+      let ctx, back_funs_map, back_funs =
+        if !Config.return_back_funs then
+          let ctx, back_vars = fresh_back_vars_for_current_fun ctx in
+          let back_funs =
+            List.filter_map
+              (fun v ->
+                match v with
+                | None -> None
+                | Some v -> Some (mk_typed_pattern_from_var v None))
+              back_vars
+          in
+          let gids = RegionGroupId.Map.keys ctx.sg.back_sg in
+          let back_funs_map =
+            RegionGroupId.Map.of_list
+              (List.combine gids
+                 (List.map (Option.map mk_texpression_from_var) back_vars))
+          in
+          (ctx, Some back_funs_map, back_funs)
+        else (ctx, None, [])
       in
+
+      (* Introduce patterns *)
       let args, ctx, out_pats =
-        let output_pat = mk_typed_pattern_from_var output_var None in
+        (* Add the returned backward functions (they might be empty) *)
+        let output_pat = mk_simpl_tuple_pattern (output_pat @ back_funs) in
 
         (* Depending on the function effects:
          * - add the fuel
@@ -2644,7 +3312,7 @@ and translate_forward_end (ectx : C.eval_ctx)
         let fuel = mk_fuel_input_as_list ctx effect_info in
         if effect_info.stateful then
           let state_var = mk_state_texpression ctx.state_var in
-          let ctx, nstate_pat = bs_ctx_fresh_state_var ctx in
+          let ctx, _, nstate_pat = bs_ctx_fresh_state_var ctx in
           ( List.concat [ fuel; args; [ state_var ] ],
             ctx,
             [ nstate_pat; output_pat ] )
@@ -2656,7 +3324,8 @@ and translate_forward_end (ectx : C.eval_ctx)
         {
           loop_info with
           forward_inputs = Some args;
-          forward_output_no_state_no_result = Some output_var;
+          forward_output_no_state_no_result = Some fwd_output;
+          back_funs = back_funs_map;
         }
       in
       let ctx =
@@ -2753,35 +3422,107 @@ and translate_loop (loop : S.loop) (ctx : bs_ctx) : texpression =
 
   (* Compute the backward outputs *)
   let ctx = ref ctx in
-  let loop_backward_outputs =
-    T.RegionGroupId.Map.map
+  let rg_to_given_back_tys =
+    RegionGroupId.Map.map
       (fun (_, tys) ->
         (* The types shouldn't contain borrows - we can translate them as forward types *)
-        let vars =
-          List.map
-            (fun ty ->
-              assert (
-                not (TypesUtils.ty_has_borrows !ctx.type_context.type_infos ty));
-              (None, ctx_translate_fwd_ty !ctx ty))
-            tys
-        in
-        (* Introduce fresh variables *)
-        let ctx', vars = fresh_vars vars !ctx in
-        ctx := ctx';
-        vars)
+        List.map
+          (fun ty ->
+            assert (not (TypesUtils.ty_has_borrows !ctx.type_ctx.type_infos ty));
+            ctx_translate_fwd_ty !ctx ty)
+          tys)
       loop.rg_to_given_back_tys
   in
   let ctx = !ctx in
 
-  let back_output_tys =
-    match ctx.bid with
-    | None -> None
-    | Some rg_id ->
-        let back_outputs =
-          T.RegionGroupId.Map.find rg_id loop_backward_outputs
-        in
-        let back_output_tys = List.map (fun (v : var) -> v.ty) back_outputs in
-        Some back_output_tys
+  (* The output type of the loop function *)
+  let fwd_effect_info = { ctx.sg.fwd_info.effect_info with is_rec = true } in
+  let back_effect_infos, output_ty =
+    if !Config.return_back_funs then
+      (* The loop backward functions consume the same additional inputs as the parent
+         function, but have custom outputs *)
+      let back_sgs = RegionGroupId.Map.bindings ctx.sg.back_sg in
+      let given_back_tys = RegionGroupId.Map.values rg_to_given_back_tys in
+      let back_info_tys =
+        List.map
+          (fun (((id, back_sg), given_back) : (_ * back_sg_info) * ty list) ->
+            (* Remark: the effect info of the backward function for the loop
+               is almost the same as for the backward function of the parent function.
+               Quite importantly, the fact that the function is stateful and/or can fail
+               mostly depends on whether it has inputs or not, and the backward functions
+               for the loops have the same inputs as the backward functions for the parent
+               function.
+            *)
+            let effect_info = back_sg.effect_info in
+            let effect_info = { effect_info with is_rec = true } in
+            (* Compute the input/output types *)
+            let inputs = List.map snd back_sg.inputs in
+            let outputs = given_back in
+            (* Filter if necessary *)
+            let ty =
+              if
+                !Config.simplify_merged_fwd_backs && inputs = [] && outputs = []
+              then None
+              else
+                let output = mk_simpl_tuple_ty outputs in
+                let output =
+                  mk_back_output_ty_from_effect_info effect_info inputs output
+                in
+                let ty = mk_arrows inputs output in
+                Some ty
+            in
+            ((id, effect_info), ty))
+          (List.combine back_sgs given_back_tys)
+      in
+      let back_info = List.map fst back_info_tys in
+      let back_info = RegionGroupId.Map.of_list back_info in
+      let back_tys = List.filter_map snd back_info_tys in
+      let output =
+        if ctx.sg.fwd_info.ignore_output then back_tys
+        else ctx.sg.fwd_output :: back_tys
+      in
+      let output = mk_simpl_tuple_ty output in
+      let effect_info = ctx.sg.fwd_info.effect_info in
+      let output =
+        if effect_info.stateful then mk_simpl_tuple_ty [ mk_state_ty; output ]
+        else output
+      in
+      let output =
+        if effect_info.can_fail && inputs <> [] then mk_result_ty output
+        else output
+      in
+      (back_info, output)
+    else
+      let back_info =
+        RegionGroupId.Map.of_list
+          (List.map
+             (fun ((id, back_sg) : _ * back_sg_info) ->
+               (id, { back_sg.effect_info with is_rec = true }))
+             (RegionGroupId.Map.bindings ctx.sg.back_sg))
+      in
+      let output =
+        match ctx.bid with
+        | None ->
+            (* Forward function: same type as the parent function *)
+            (translate_fun_sig_from_decomposed ctx.sg None).output
+        | Some rg_id ->
+            (* Backward function: custom return type *)
+            let doutputs =
+              T.RegionGroupId.Map.find rg_id rg_to_given_back_tys
+            in
+            let output = mk_simpl_tuple_ty doutputs in
+            let fwd_effect_info = ctx.sg.fwd_info.effect_info in
+            let output =
+              if fwd_effect_info.stateful then
+                mk_simpl_tuple_ty [ mk_state_ty; output ]
+              else output
+            in
+            let output =
+              if fwd_effect_info.can_fail then mk_result_ty output else output
+            in
+            output
+      in
+      (back_info, output)
   in
 
   (* Add the loop information in the context *)
@@ -2823,6 +3564,10 @@ and translate_loop (loop : S.loop) (ctx : bs_ctx) : texpression =
         generics;
         forward_inputs = None;
         forward_output_no_state_no_result = None;
+        back_outputs = rg_to_given_back_tys;
+        back_funs = None;
+        fwd_effect_info;
+        back_effect_infos;
       }
     in
     let loops = LoopId.Map.add loop_id loop_info ctx.loops in
@@ -2830,13 +3575,7 @@ and translate_loop (loop : S.loop) (ctx : bs_ctx) : texpression =
   in
 
   (* Update the context to translate the function end *)
-  let ctx_end =
-    {
-      ctx with
-      loop_id = Some loop_id;
-      loop_backward_outputs = Some loop_backward_outputs;
-    }
-  in
+  let ctx_end = { ctx with loop_id = Some loop_id } in
   let fun_end = translate_expression loop.end_expr ctx_end in
 
   (* Update the context for the loop body *)
@@ -2844,7 +3583,7 @@ and translate_loop (loop : S.loop) (ctx : bs_ctx) : texpression =
 
   (* Add the input state *)
   let input_state =
-    if ctx.sg.info.effect_info.stateful then Some ctx.state_var else None
+    if (ctx_get_effect_info ctx).stateful then Some ctx.state_var else None
   in
 
   (* Translate the loop body *)
@@ -2862,7 +3601,7 @@ and translate_loop (loop : S.loop) (ctx : bs_ctx) : texpression =
         input_state;
         inputs;
         inputs_lvs;
-        back_output_tys;
+        output_ty;
         loop_body;
       }
   in
@@ -2982,10 +3721,10 @@ let translate_fun_decl (ctx : bs_ctx) (body : S.expression option) : fun_decl =
   let def_id = def.def_id in
   let llbc_name = def.name in
   let name = name_to_string ctx llbc_name in
-  (* Retrieve the signature *)
-  let signature = ctx.sg in
+  (* Translate the signature *)
+  let signature = translate_fun_sig_from_decomposed ctx.sg ctx.bid in
   let regions_hierarchy =
-    FunIdMap.find (FRegular def_id) ctx.fun_context.regions_hierarchies
+    FunIdMap.find (FRegular def_id) ctx.fun_ctx.regions_hierarchies
   in
   (* Translate the body, if there is *)
   let body =
@@ -2993,8 +3732,7 @@ 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
-            (FunId (FRegular def_id)) None bid
+          get_fun_effect_info ctx (FunId (FRegular def_id)) None bid
         in
         let body = translate_expression body ctx in
         (* Add a match over the fuel, if necessary *)
@@ -3027,20 +3765,25 @@ let translate_fun_decl (ctx : bs_ctx) (body : S.expression option) : fun_decl =
           match bid with
           | None -> []
           | Some back_id ->
+              assert (not !Config.return_back_funs);
               let parents_ids =
                 list_ordered_ancestor_region_groups regions_hierarchy back_id
               in
               let backward_ids = List.append parents_ids [ back_id ] in
               List.concat
                 (List.map
-                   (fun id -> T.RegionGroupId.Map.find id ctx.backward_inputs)
+                   (fun id ->
+                     T.RegionGroupId.Map.find id ctx.backward_inputs_no_state)
                    backward_ids)
         in
         (* Introduce the backward input state (the state at call site of the
          * *backward* function), if necessary *)
         let back_state =
           if effect_info.stateful && Option.is_some bid then
-            [ mk_state_var ctx.back_state_var ]
+            let state_var =
+              RegionGroupId.Map.find (Option.get bid) ctx.back_state_vars
+            in
+            [ mk_state_var state_var ]
           else []
         in
         (* Group the inputs together *)
@@ -3114,63 +3857,6 @@ let translate_type_decls (ctx : Contexts.decls_ctx) : type_decl list =
   List.map (translate_type_decl ctx)
     (TypeDeclId.Map.values ctx.type_ctx.type_decls)
 
-(** Translates function signatures.
-
-    Takes as input a list of function information containing:
-    - the function id
-    - a list of optional names for the inputs
-    - the function signature
-    
-    Returns a map from forward/backward functions identifiers to:
-    - translated function signatures
-    - optional names for the outputs values (we derive them for the backward
-      functions)
- *)
-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:
-     - the forward function
-     - the backward functions
-  *)
-  let translate_one (fun_id : A.fun_id) (input_names : string option list)
-      (sg : A.fun_sig) : (regular_fun_id_not_loop * fun_sig_named_outputs) list
-      =
-    log#ldebug
-      (lazy
-        ("Translating signature of function: "
-        ^ Print.Expressions.fun_id_to_string
-            (Print.Contexts.decls_ctx_to_fmt_env decls_ctx)
-            fun_id));
-    (* Retrieve the regions hierarchy *)
-    let regions_hierarchy =
-      FunIdMap.find fun_id decls_ctx.fun_ctx.regions_hierarchies
-    in
-    (* The forward function *)
-    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 decls_ctx fun_id sg input_names (Some rg.id)
-          in
-          let id = (fun_id, Some rg.id) in
-          (id, tsg))
-        regions_hierarchy
-    in
-    (* Return *)
-    (fwd_id, fwd_sg) :: back_sgs
-  in
-  let translated =
-    List.concat
-      (List.map (fun (id, names, sg) -> translate_one id names sg) functions)
-  in
-  List.fold_left
-    (fun m (id, sg) -> RegularFunIdNotLoopMap.add id sg m)
-    RegularFunIdNotLoopMap.empty translated
-
 let translate_trait_decl (ctx : Contexts.decls_ctx) (trait_decl : A.trait_decl)
     : trait_decl =
   let {
diff --git a/compiler/SynthesizeSymbolic.ml b/compiler/SynthesizeSymbolic.ml
index efcf001a..865185a8 100644
--- a/compiler/SynthesizeSymbolic.ml
+++ b/compiler/SynthesizeSymbolic.ml
@@ -2,6 +2,7 @@ open Types
 open TypesUtils
 open Expressions
 open Values
+open LlbcAst
 open SymbolicAst
 
 let mk_mplace (p : place) (ctx : Contexts.eval_ctx) : mplace =
@@ -92,7 +93,9 @@ let synthesize_symbolic_expansion_no_branching (sv : symbolic_value)
   synthesize_symbolic_expansion sv place [ Some see ] el
 
 let synthesize_function_call (call_id : call_id) (ctx : Contexts.eval_ctx)
+    (sg : fun_sig option) (regions_hierarchy : region_var_groups)
     (abstractions : AbstractionId.id list) (generics : generic_args)
+    (trait_method_generics : (generic_args * trait_instance_id) option)
     (args : typed_value list) (args_places : mplace option list)
     (dest : symbolic_value) (dest_place : mplace option) (e : expression option)
     : expression option =
@@ -102,8 +105,11 @@ let synthesize_function_call (call_id : call_id) (ctx : Contexts.eval_ctx)
         {
           call_id;
           ctx;
+          sg;
+          regions_hierarchy;
           abstractions;
           generics;
+          trait_method_generics;
           args;
           dest;
           args_places;
@@ -118,29 +124,32 @@ let synthesize_global_eval (gid : GlobalDeclId.id) (dest : symbolic_value)
   Option.map (fun e -> EvalGlobal (gid, dest, e)) e
 
 let synthesize_regular_function_call (fun_id : fun_id_or_trait_method_ref)
-    (call_id : FunCallId.id) (ctx : Contexts.eval_ctx)
+    (call_id : FunCallId.id) (ctx : Contexts.eval_ctx) (sg : fun_sig)
+    (regions_hierarchy : region_var_groups)
     (abstractions : AbstractionId.id list) (generics : generic_args)
+    (trait_method_generics : (generic_args * trait_instance_id) option)
     (args : typed_value list) (args_places : mplace option list)
     (dest : symbolic_value) (dest_place : mplace option) (e : expression option)
     : expression option =
   synthesize_function_call
     (Fun (fun_id, call_id))
-    ctx abstractions generics args args_places dest dest_place e
+    ctx (Some sg) regions_hierarchy abstractions generics trait_method_generics
+    args args_places dest dest_place e
 
 let synthesize_unary_op (ctx : Contexts.eval_ctx) (unop : unop)
     (arg : typed_value) (arg_place : mplace option) (dest : symbolic_value)
     (dest_place : mplace option) (e : expression option) : expression option =
   let generics = empty_generic_args in
-  synthesize_function_call (Unop unop) ctx [] generics [ arg ] [ arg_place ]
-    dest dest_place e
+  synthesize_function_call (Unop unop) ctx None [] [] generics None [ arg ]
+    [ arg_place ] dest dest_place e
 
 let synthesize_binary_op (ctx : Contexts.eval_ctx) (binop : binop)
     (arg0 : typed_value) (arg0_place : mplace option) (arg1 : typed_value)
     (arg1_place : mplace option) (dest : symbolic_value)
     (dest_place : mplace option) (e : expression option) : expression option =
   let generics = empty_generic_args in
-  synthesize_function_call (Binop binop) ctx [] generics [ arg0; arg1 ]
-    [ arg0_place; arg1_place ] dest dest_place e
+  synthesize_function_call (Binop binop) ctx None [] [] generics None
+    [ arg0; arg1 ] [ arg0_place; arg1_place ] dest dest_place e
 
 let synthesize_end_abstraction (ctx : Contexts.eval_ctx) (abs : abs)
     (e : expression option) : expression option =
diff --git a/compiler/Translate.ml b/compiler/Translate.ml
index 221d4e73..55a94302 100644
--- a/compiler/Translate.ml
+++ b/compiler/Translate.ml
@@ -6,7 +6,6 @@ open LlbcAst
 open Contexts
 module SA = SymbolicAst
 module Micro = PureMicroPasses
-open PureUtils
 open TranslateCore
 
 (** The local logger *)
@@ -43,8 +42,8 @@ let translate_function_to_symbolics (trans_ctx : trans_ctx) (fdef : fun_decl) :
     TODO: maybe we should introduce a record for this.
 *)
 let translate_function_to_pure (trans_ctx : trans_ctx)
-    (fun_sigs : SymbolicToPure.fun_sig_named_outputs RegularFunIdNotLoopMap.t)
-    (pure_type_decls : Pure.type_decl Pure.TypeDeclId.Map.t) (fdef : fun_decl) :
+    (pure_type_decls : Pure.type_decl Pure.TypeDeclId.Map.t)
+    (fun_dsigs : Pure.decomposed_fun_sig FunDeclId.Map.t) (fdef : fun_decl) :
     pure_fun_translation_no_loops =
   (* Debug *)
   log#ldebug
@@ -58,13 +57,9 @@ let translate_function_to_pure (trans_ctx : trans_ctx)
   (* Convert the symbolic ASTs to pure ASTs: *)
 
   (* Initialize the context *)
-  let forward_sig =
-    RegularFunIdNotLoopMap.find (FRegular def_id, None) fun_sigs
-  in
   let sv_to_var = SymbolicValueId.Map.empty in
   let var_counter = Pure.VarId.generator_zero in
   let state_var, var_counter = Pure.VarId.fresh var_counter in
-  let back_state_var, var_counter = Pure.VarId.fresh var_counter in
   let fuel0, var_counter = Pure.VarId.fresh var_counter in
   let fuel, var_counter = Pure.VarId.fresh var_counter in
   let calls = FunCallId.Map.empty in
@@ -78,7 +73,7 @@ let translate_function_to_pure (trans_ctx : trans_ctx)
            | RecGroup _ -> Some tid)
          (TypeDeclId.Map.bindings trans_ctx.type_ctx.type_decls_groups))
   in
-  let type_context =
+  let type_ctx =
     {
       SymbolicToPure.type_infos = trans_ctx.type_ctx.type_infos;
       llbc_type_decls = trans_ctx.type_ctx.type_decls;
@@ -86,15 +81,14 @@ let translate_function_to_pure (trans_ctx : trans_ctx)
       recursive_decls = recursive_type_decls;
     }
   in
-  let fun_context =
+  let fun_ctx =
     {
       SymbolicToPure.llbc_fun_decls = trans_ctx.fun_ctx.fun_decls;
-      fun_sigs;
       fun_infos = trans_ctx.fun_ctx.fun_infos;
       regions_hierarchies = trans_ctx.fun_ctx.regions_hierarchies;
     }
   in
-  let global_context =
+  let global_ctx =
     { SymbolicToPure.llbc_global_decls = trans_ctx.global_ctx.global_decls }
   in
 
@@ -126,31 +120,51 @@ let translate_function_to_pure (trans_ctx : trans_ctx)
         !m
   in
 
+  let sg =
+    SymbolicToPure.translate_fun_sig_from_decl_to_decomposed trans_ctx fdef
+  in
+
+  let regions_hierarchy =
+    LlbcAstUtils.FunIdMap.find (FRegular def_id) fun_ctx.regions_hierarchies
+  in
+
+  let var_counter, back_state_vars =
+    if !Config.return_back_funs then (var_counter, [])
+    else
+      List.fold_left_map
+        (fun var_counter (region_vars : region_var_group) ->
+          let gid = region_vars.id in
+          let var, var_counter = Pure.VarId.fresh var_counter in
+          (var_counter, (gid, var)))
+        var_counter regions_hierarchy
+  in
+  let back_state_vars = RegionGroupId.Map.of_list back_state_vars in
+
   let ctx =
     {
+      decls_ctx = trans_ctx;
       SymbolicToPure.bid = None;
-      (* Dummy for now *)
-      sg = forward_sig.sg;
-      fwd_sg = forward_sig.sg;
+      sg;
+      fun_dsigs;
       (* Will need to be updated for the backward functions *)
       sv_to_var;
-      var_counter;
+      var_counter = ref var_counter;
       state_var;
-      back_state_var;
+      back_state_vars;
       fuel0;
       fuel;
-      type_context;
-      fun_context;
-      global_context;
+      type_ctx;
+      fun_ctx;
+      global_ctx;
       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 *)
-      backward_inputs = RegionGroupId.Map.empty;
-      (* Empty for now *)
-      backward_outputs = RegionGroupId.Map.empty;
-      loop_backward_outputs = None;
+      (* Initialized just below *)
+      backward_inputs_no_state = RegionGroupId.Map.empty;
+      (* Initialized just below *)
+      backward_inputs_with_state = RegionGroupId.Map.empty;
+      backward_outputs = None;
       (* Empty for now *)
       calls;
       abstractions;
@@ -180,6 +194,37 @@ let translate_function_to_pure (trans_ctx : trans_ctx)
     | _ -> raise (Failure "Unreachable")
   in
 
+  (* Add the backward inputs *)
+  let ctx, backward_inputs_no_state, backward_inputs_with_state =
+    if !Config.return_back_funs then (ctx, [], [])
+    else
+      let ctx, inputs_no_with_state =
+        List.fold_left_map
+          (fun ctx (region_vars : region_var_group) ->
+            let gid = region_vars.id in
+            let back_sg = RegionGroupId.Map.find gid sg.back_sg in
+            let ctx, no_state =
+              SymbolicToPure.fresh_vars back_sg.inputs_no_state ctx
+            in
+            let ctx, with_state =
+              SymbolicToPure.fresh_vars back_sg.inputs ctx
+            in
+            (ctx, ((gid, no_state), (gid, with_state))))
+          ctx regions_hierarchy
+      in
+      let inputs_no_state, inputs_with_state =
+        List.split inputs_no_with_state
+      in
+      (ctx, inputs_no_state, inputs_with_state)
+  in
+  let backward_inputs_no_state =
+    RegionGroupId.Map.of_list backward_inputs_no_state
+  in
+  let backward_inputs_with_state =
+    RegionGroupId.Map.of_list backward_inputs_with_state
+  in
+  let ctx = { ctx with backward_inputs_no_state; backward_inputs_with_state } in
+
   (* Translate the forward function *)
   let pure_forward =
     match symbolic_trans with
@@ -187,7 +232,7 @@ let translate_function_to_pure (trans_ctx : trans_ctx)
     | Some (_, ast) -> SymbolicToPure.translate_fun_decl ctx (Some ast)
   in
 
-  (* Translate the backward functions *)
+  (* Translate the backward functions, if we split the forward and backward functions *)
   let translate_backward (rg : region_var_group) : Pure.fun_decl =
     (* For the backward inputs/outputs initialization: we use the fact that
      * there are no nested borrows for now, and so that the region groups
@@ -197,77 +242,20 @@ let translate_function_to_pure (trans_ctx : trans_ctx)
 
     match symbolic_trans with
     | None ->
-        (* Initialize the context - note that the ret_ty is not really
-         * useful as we don't translate a body *)
-        let backward_sg =
-          RegularFunIdNotLoopMap.find (FRegular def_id, Some back_id) fun_sigs
-        in
-        let ctx = { ctx with bid = Some back_id; sg = backward_sg.sg } in
-
+        (* Initialize the context *)
+        let ctx = { ctx with bid = Some back_id } in
         (* Translate *)
         SymbolicToPure.translate_fun_decl ctx None
     | Some (_, symbolic) ->
-        (* Finish initializing the context by adding the additional input
-           variables required by the backward function.
-        *)
-        let backward_sg =
-          RegularFunIdNotLoopMap.find (FRegular 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 =
-          let sg = backward_sg.sg in
-          (* We need to ignore the forward state and the backward state *)
-          let num_forward_inputs =
-            sg.info.num_fwd_inputs_with_fuel_with_state
-          in
-          let num_back_inputs = Option.get sg.info.num_back_inputs_no_state in
-          Collections.List.subslice sg.inputs num_forward_inputs
-            (num_forward_inputs + num_back_inputs)
-        in
-        (* As we forbid nested borrows, the additional inputs for the backward
-         * functions come from the borrows in the return value of the rust function:
-         * we thus use the name "ret" for those inputs *)
-        let backward_inputs =
-          List.map (fun ty -> (Some "ret", ty)) backward_inputs
-        in
-        let ctx, backward_inputs =
-          SymbolicToPure.fresh_vars backward_inputs ctx
-        in
-        (* The outputs for the backward functions, however, come from borrows
-         * present in the input values of the rust function: for those we reuse
-         * the names of the input values. *)
-        let backward_outputs =
-          List.combine backward_sg.output_names backward_sg.sg.doutputs
-        in
-        let ctx, backward_outputs =
-          SymbolicToPure.fresh_vars backward_outputs ctx
-        in
-        let backward_inputs =
-          RegionGroupId.Map.singleton back_id backward_inputs
-        in
-        let backward_outputs =
-          RegionGroupId.Map.singleton back_id backward_outputs
-        in
-
-        (* Put everything in the context *)
-        let ctx =
-          {
-            ctx with
-            bid = Some back_id;
-            sg = backward_sg.sg;
-            backward_inputs;
-            backward_outputs;
-          }
-        in
-
+        (* Initialize the context *)
+        let ctx = { ctx with bid = Some back_id } in
         (* Translate *)
         SymbolicToPure.translate_fun_decl ctx (Some symbolic)
   in
-  let regions_hierarchy =
-    LlbcAstUtils.FunIdMap.find (FRegular fdef.def_id)
-      fun_context.regions_hierarchies
+  let pure_backwards =
+    if !Config.return_back_funs then []
+    else List.map translate_backward regions_hierarchy
   in
-  let pure_backwards = List.map translate_backward regions_hierarchy in
 
   (* Return *)
   (pure_forward, pure_backwards)
@@ -294,36 +282,21 @@ let translate_crate_to_pure (crate : crate) :
       (List.map (fun (def : Pure.type_decl) -> (def.def_id, def)) type_decls)
   in
 
-  (* Translate all the function *signatures* *)
-  let assumed_sigs =
-    List.map
-      (fun (info : Assumed.assumed_fun_info) ->
-        ( FAssumed info.fun_id,
-          List.map (fun _ -> None) info.fun_sig.inputs,
-          info.fun_sig ))
-      Assumed.assumed_fun_infos
-  in
-  let local_sigs =
-    List.map
-      (fun (fdef : fun_decl) ->
-        let input_names =
-          match fdef.body with
-          | None -> List.map (fun _ -> None) fdef.signature.inputs
-          | Some body ->
-              List.map
-                (fun (v : var) -> v.name)
-                (LlbcAstUtils.fun_body_get_input_vars body)
-        in
-        (FRegular fdef.def_id, input_names, fdef.signature))
-      (FunDeclId.Map.values crate.fun_decls)
+  (* Compute the decomposed fun sigs for the whole crate *)
+  let fun_dsigs =
+    FunDeclId.Map.of_list
+      (List.map
+         (fun (fdef : LlbcAst.fun_decl) ->
+           ( fdef.def_id,
+             SymbolicToPure.translate_fun_sig_from_decl_to_decomposed trans_ctx
+               fdef ))
+         (FunDeclId.Map.values crate.fun_decls))
   in
-  let sigs = List.append assumed_sigs local_sigs in
-  let fun_sigs = SymbolicToPure.translate_fun_signatures trans_ctx sigs in
 
   (* Translate all the *transparent* functions *)
   let pure_translations =
     List.map
-      (translate_function_to_pure trans_ctx fun_sigs type_decls_map)
+      (translate_function_to_pure trans_ctx type_decls_map fun_dsigs)
       (FunDeclId.Map.values crate.fun_decls)
   in
 
@@ -1030,7 +1003,7 @@ let translate_crate (filename : string) (dest_dir : string) (crate : crate) :
     List.map
       (fun { fwd; _ } ->
         let fwd_f =
-          if fwd.f.Pure.signature.info.effect_info.is_rec then
+          if fwd.f.Pure.signature.fwd_info.effect_info.is_rec then
             [ (fwd.f.def_id, None) ]
           else []
         in
@@ -1198,7 +1171,13 @@ let translate_crate (filename : string) (dest_dir : string) (crate : crate) :
     let exe_dir = Filename.dirname Sys.argv.(0) in
     let primitives_src_dest =
       match !Config.backend with
-      | FStar -> Some ("/backends/fstar/Primitives.fst", "Primitives.fst")
+      | FStar ->
+          let src =
+            if !Config.return_back_funs then
+              "/backends/fstar/merge/Primitives.fst"
+            else "/backends/fstar/split/Primitives.fst"
+          in
+          Some (src, "Primitives.fst")
       | Coq -> Some ("/backends/coq/Primitives.v", "Primitives.v")
       | Lean -> None
       | HOL4 -> None
diff --git a/flake.lock b/flake.lock
index f872fad8..2a3cf2c1 100644
--- a/flake.lock
+++ b/flake.lock
@@ -8,11 +8,11 @@
         "rust-overlay": "rust-overlay"
       },
       "locked": {
-        "lastModified": 1702482915,
-        "narHash": "sha256-7m3O/qioAomxAq5C/MyFro6WqnKB++o881EGfLJIx1w=",
+        "lastModified": 1703290921,
+        "narHash": "sha256-Jbf7JETi3XHLV19pDz8AT/Gyu8PpEfZhxO7T4W94uws=",
         "owner": "aeneasverif",
         "repo": "charon",
-        "rev": "6fc644e4ffcac98b46fc8a361f13cc7d23338ed2",
+        "rev": "f91d9d16520f0615047ccdf98b654cf47a10b0ce",
         "type": "github"
       },
       "original": {
@@ -131,11 +131,11 @@
         "nixpkgs": "nixpkgs_2"
       },
       "locked": {
-        "lastModified": 1702080800,
-        "narHash": "sha256-PbuXUutqI5iE0ZFCJPWjgfxYjonX9Pkw/qtpLMLwXuI=",
+        "lastModified": 1703180293,
+        "narHash": "sha256-zQPEPf1Q3Z4Wt86Bef9czyKfff8r8vr2LEsfR5qxoaU=",
         "owner": "fstarlang",
         "repo": "fstar",
-        "rev": "178e0f872b6a7540d6024b49c7c04ba451f7c4c7",
+        "rev": "0806a005a879f256ff5af6736fbea4d45ea6f6ca",
         "type": "github"
       },
       "original": {
@@ -164,11 +164,11 @@
         ]
       },
       "locked": {
-        "lastModified": 1701972757,
-        "narHash": "sha256-sfzmasc8uIc2COYC8xm1bchmNAV5+W8gkflUVzzBDms=",
+        "lastModified": 1703047078,
+        "narHash": "sha256-LbEoFtOMFB1LVAV4O4WvOvKNjT5QTQo44mkwbzTaA2A=",
         "owner": "hacl-star",
         "repo": "hacl-star",
-        "rev": "f280ff8fe0f285edcc25c35a811dea0c233e3482",
+        "rev": "1e571f77e1752449d48fe7361787cc7d01f93a49",
         "type": "github"
       },
       "original": {
@@ -194,11 +194,11 @@
         ]
       },
       "locked": {
-        "lastModified": 1702084487,
-        "narHash": "sha256-4P2DOWqCbx5lcMdU6gMskIs9gvOiO3ZpGBMeqNhrva0=",
+        "lastModified": 1703207646,
+        "narHash": "sha256-ZM7WeH5Inwottbxefjn0Acw3z6Q/iarkqldbTWt/2lQ=",
         "owner": "hacl-star",
         "repo": "hacl-nix",
-        "rev": "44aad8f5d2880e8b8fac54e4ba9cbdb315282751",
+        "rev": "31e836f69da3cddbc1d3324de40b4901a69de320",
         "type": "github"
       },
       "original": {
@@ -223,11 +223,11 @@
         ]
       },
       "locked": {
-        "lastModified": 1701984397,
-        "narHash": "sha256-uR77IRrczr80J7LyFIeTrfueh8+AfBecZDDo+Pfl/a4=",
+        "lastModified": 1702906344,
+        "narHash": "sha256-bfg18GolyW8/LcmUKh/bwryMjSQCR6GaGVuKmJIdBwQ=",
         "owner": "fstarlang",
         "repo": "karamel",
-        "rev": "ed6d9729569515ce55c683ebd10449543610624e",
+        "rev": "67b19d9a05f6578aec0b640fcb6e432ff18daa71",
         "type": "github"
       },
       "original": {
@@ -265,11 +265,11 @@
         "nixpkgs": "nixpkgs_4"
       },
       "locked": {
-        "lastModified": 1702475419,
-        "narHash": "sha256-2K+XqLUgXHuyibMuNkrRqPVTgrMAE3X7IiO00KPjaWE=",
+        "lastModified": 1703256773,
+        "narHash": "sha256-HuiHOhvfNVaJAOgpSMpUp24YcYxuRWMt7X77bT+sNAg=",
         "owner": "leanprover",
         "repo": "lean4",
-        "rev": "b5b664e570f8e6a112b8491bccf58b58fe2d916b",
+        "rev": "7c38649527c85116345df831254985afa2680dd0",
         "type": "github"
       },
       "original": {
@@ -318,11 +318,11 @@
         "nixpkgs": "nixpkgs_7"
       },
       "locked": {
-        "lastModified": 1702475419,
-        "narHash": "sha256-2K+XqLUgXHuyibMuNkrRqPVTgrMAE3X7IiO00KPjaWE=",
+        "lastModified": 1703256773,
+        "narHash": "sha256-HuiHOhvfNVaJAOgpSMpUp24YcYxuRWMt7X77bT+sNAg=",
         "owner": "leanprover",
         "repo": "lean4",
-        "rev": "b5b664e570f8e6a112b8491bccf58b58fe2d916b",
+        "rev": "7c38649527c85116345df831254985afa2680dd0",
         "type": "github"
       },
       "original": {
diff --git a/flake.nix b/flake.nix
index 8263174d..82179fcb 100644
--- a/flake.nix
+++ b/flake.nix
@@ -114,6 +114,18 @@
           # The tests don't generate anything - TODO: actually they do
           installPhase = "touch $out";
         };
+        # Replay the F* proofs for the cases where we split the fwd/back functions.
+        aeneas-verify-fstar-split = pkgs.stdenv.mkDerivation {
+          name = "aeneas_verify_fstar_split";
+          src = ./tests/fstar-split;
+          FSTAR_EXE = "${hacl-nix.packages.${system}.fstar}/bin/fstar.exe";
+          buildPhase= ''
+            make prepare-projects
+            make verify -j $NIX_BUILD_CORES
+          '';
+          # The tests don't generate anything - TODO: actually they do
+          installPhase = "touch $out";
+        };
         # Replay the Coq proofs.
         aeneas-verify-coq = pkgs.stdenv.mkDerivation {
           name = "aeneas_verify_coq";
@@ -170,6 +182,8 @@
           inherit aeneas;
           default = aeneas;
         };
-        checks = { inherit aeneas aeneas-tests aeneas-verify-fstar aeneas-verify-coq aeneas-verify-lean aeneas-verify-hol4; };
+        checks = {
+          inherit aeneas aeneas-tests aeneas-verify-fstar aeneas-verify-fstar-split
+                  aeneas-verify-coq aeneas-verify-lean aeneas-verify-hol4; };
       });
 }
diff --git a/tests/Makefile b/tests/Makefile
index 8d40e8da..ccdbf652 100644
--- a/tests/Makefile
+++ b/tests/Makefile
@@ -1,4 +1,4 @@
-all: test-fstar test-coq test-lean test-hol4
+all: test-fstar test-fstar-split test-coq test-lean test-hol4
 
 test-%:
 	cd $* && $(MAKE) all
diff --git a/tests/coq/array/Array.v b/tests/coq/array/Array.v
index 1f2cc0e0..3a30413a 100644
--- a/tests/coq/array/Array.v
+++ b/tests/coq/array/Array.v
@@ -12,108 +12,95 @@ Module Array.
     Source: 'src/array.rs', lines 3:0-3:11 *)
 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 ())
+(** [array::incr]:
     Source: 'src/array.rs', lines 8:0-8:24 *)
 Definition incr (x : u32) : result u32 :=
   u32_add x 1%u32.
 
-(** [array::array_to_shared_slice_]: forward function
+(** [array::array_to_shared_slice_]:
     Source: 'src/array.rs', lines 16:0-16:53 *)
 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
+(** [array::array_to_mut_slice_]:
     Source: 'src/array.rs', lines 21:0-21:58 *)
 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
-    Source: 'src/array.rs', lines 21:0-21:58 *)
-Definition array_to_mut_slice__back
-  (T : Type) (s : array T 32%usize) (ret : slice T) :
-  result (array T 32%usize)
+  (T : Type) (s : array T 32%usize) :
+  result ((slice T) * (slice T -> result (array T 32%usize)))
   :=
-  array_from_slice T 32%usize s ret
+  p <- array_to_slice_mut T 32%usize s;
+  let (s1, to_slice_mut_back) := p in
+  Return (s1, to_slice_mut_back)
 .
 
-(** [array::array_len]: forward function
+(** [array::array_len]:
     Source: 'src/array.rs', lines 25:0-25:40 *)
 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
+  s1 <- array_to_slice T 32%usize s; let i := slice_len T s1 in Return i
 .
 
-(** [array::shared_array_len]: forward function
+(** [array::shared_array_len]:
     Source: 'src/array.rs', lines 29:0-29:48 *)
 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
+  s1 <- array_to_slice T 32%usize s; let i := slice_len T s1 in Return i
 .
 
-(** [array::shared_slice_len]: forward function
+(** [array::shared_slice_len]:
     Source: 'src/array.rs', lines 33:0-33:44 *)
 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
+(** [array::index_array_shared]:
     Source: 'src/array.rs', lines 37:0-37:57 *)
 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
+(** [array::index_array_u32]:
     Source: 'src/array.rs', lines 44:0-44:53 *)
 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
+(** [array::index_array_copy]:
     Source: 'src/array.rs', lines 48:0-48:45 *)
 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
+(** [array::index_mut_array]:
     Source: 'src/array.rs', lines 52:0-52:62 *)
 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
-    Source: 'src/array.rs', lines 52:0-52:62 *)
-Definition index_mut_array_back
-  (T : Type) (s : array T 32%usize) (i : usize) (ret : T) :
-  result (array T 32%usize)
+  (T : Type) (s : array T 32%usize) (i : usize) :
+  result (T * (T -> result (array T 32%usize)))
   :=
-  array_update_usize T 32%usize s i ret
+  p <- array_index_mut_usize T 32%usize s i;
+  let (t, index_mut_back) := p in
+  Return (t, index_mut_back)
 .
 
-(** [array::index_slice]: forward function
+(** [array::index_slice]:
     Source: 'src/array.rs', lines 56:0-56:46 *)
 Definition index_slice (T : Type) (s : slice T) (i : usize) : result T :=
   slice_index_usize T s i
 .
 
-(** [array::index_mut_slice]: forward function
+(** [array::index_mut_slice]:
     Source: 'src/array.rs', lines 60:0-60:58 *)
-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
-    Source: 'src/array.rs', lines 60:0-60:58 *)
-Definition index_mut_slice_back
-  (T : Type) (s : slice T) (i : usize) (ret : T) : result (slice T) :=
-  slice_update_usize T s i ret
+Definition index_mut_slice
+  (T : Type) (s : slice T) (i : usize) :
+  result (T * (T -> result (slice T)))
+  :=
+  p <- slice_index_mut_usize T s i;
+  let (t, index_mut_back) := p in
+  Return (t, index_mut_back)
 .
 
-(** [array::slice_subslice_shared_]: forward function
+(** [array::slice_subslice_shared_]:
     Source: 'src/array.rs', lines 64:0-64:70 *)
 Definition slice_subslice_shared_
   (x : slice u32) (y : usize) (z : usize) : result (slice u32) :=
@@ -122,47 +109,39 @@ Definition slice_subslice_shared_
     {| core_ops_range_Range_start := y; core_ops_range_Range_end_ := z |}
 .
 
-(** [array::slice_subslice_mut_]: forward function
+(** [array::slice_subslice_mut_]:
     Source: 'src/array.rs', lines 68:0-68:75 *)
 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_SliceIndexRangeUsizeSliceTInst u32) x
-    {| core_ops_range_Range_start := y; core_ops_range_Range_end_ := z |}
-.
-
-(** [array::slice_subslice_mut_]: backward function 0
-    Source: 'src/array.rs', lines 68:0-68:75 *)
-Definition slice_subslice_mut__back
-  (x : slice u32) (y : usize) (z : usize) (ret : slice u32) :
-  result (slice u32)
+  (x : slice u32) (y : usize) (z : usize) :
+  result ((slice u32) * (slice u32 -> result (slice u32)))
   :=
-  core_slice_index_Slice_index_mut_back u32 (core_ops_range_Range usize)
-    (core_slice_index_SliceIndexRangeUsizeSliceTInst u32) x
-    {| core_ops_range_Range_start := y; core_ops_range_Range_end_ := z |} ret
+  p <-
+    core_slice_index_Slice_index_mut u32 (core_ops_range_Range usize)
+      (core_slice_index_SliceIndexRangeUsizeSliceTInst u32) x
+      {| core_ops_range_Range_start := y; core_ops_range_Range_end_ := z |};
+  let (s, index_mut_back) := p in
+  Return (s, index_mut_back)
 .
 
-(** [array::array_to_slice_shared_]: forward function
+(** [array::array_to_slice_shared_]:
     Source: 'src/array.rs', lines 72:0-72:54 *)
 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
+(** [array::array_to_slice_mut_]:
     Source: 'src/array.rs', lines 76:0-76:59 *)
-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
-    Source: 'src/array.rs', lines 76:0-76:59 *)
-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
+Definition array_to_slice_mut_
+  (x : array u32 32%usize) :
+  result ((slice u32) * (slice u32 -> result (array u32 32%usize)))
+  :=
+  p <- array_to_slice_mut u32 32%usize x;
+  let (s, to_slice_mut_back) := p in
+  Return (s, to_slice_mut_back)
 .
 
-(** [array::array_subslice_shared_]: forward function
+(** [array::array_subslice_shared_]:
     Source: 'src/array.rs', lines 80:0-80:74 *)
 Definition array_subslice_shared_
   (x : array u32 32%usize) (y : usize) (z : usize) : result (slice u32) :=
@@ -172,41 +151,34 @@ Definition array_subslice_shared_
     {| core_ops_range_Range_start := y; core_ops_range_Range_end_ := z |}
 .
 
-(** [array::array_subslice_mut_]: forward function
+(** [array::array_subslice_mut_]:
     Source: 'src/array.rs', lines 84:0-84:79 *)
 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_ops_index_IndexMutSliceTIInst u32 (core_ops_range_Range usize)
-    (core_slice_index_SliceIndexRangeUsizeSliceTInst u32)) x
-    {| core_ops_range_Range_start := y; core_ops_range_Range_end_ := z |}
-.
-
-(** [array::array_subslice_mut_]: backward function 0
-    Source: 'src/array.rs', lines 84:0-84:79 *)
-Definition array_subslice_mut__back
-  (x : array u32 32%usize) (y : usize) (z : usize) (ret : slice u32) :
-  result (array u32 32%usize)
+  (x : array u32 32%usize) (y : usize) (z : usize) :
+  result ((slice u32) * (slice u32 -> result (array u32 32%usize)))
   :=
-  core_array_Array_index_mut_back u32 (core_ops_range_Range usize) 32%usize
-    (core_ops_index_IndexMutSliceTIInst u32 (core_ops_range_Range usize)
-    (core_slice_index_SliceIndexRangeUsizeSliceTInst u32)) x
-    {| core_ops_range_Range_start := y; core_ops_range_Range_end_ := z |} ret
+  p <-
+    core_array_Array_index_mut u32 (core_ops_range_Range usize) 32%usize
+      (core_ops_index_IndexMutSliceTIInst u32 (core_ops_range_Range usize)
+      (core_slice_index_SliceIndexRangeUsizeSliceTInst u32)) x
+      {| core_ops_range_Range_start := y; core_ops_range_Range_end_ := z |};
+  let (s, index_mut_back) := p in
+  Return (s, index_mut_back)
 .
 
-(** [array::index_slice_0]: forward function
+(** [array::index_slice_0]:
     Source: 'src/array.rs', lines 88:0-88:38 *)
 Definition index_slice_0 (T : Type) (s : slice T) : result T :=
   slice_index_usize T s 0%usize
 .
 
-(** [array::index_array_0]: forward function
+(** [array::index_array_0]:
     Source: 'src/array.rs', lines 92:0-92:42 *)
 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
+(** [array::index_index_array]:
     Source: 'src/array.rs', lines 103:0-103:71 *)
 Definition index_index_array
   (s : array (array u32 32%usize) 32%usize) (i : usize) (j : usize) :
@@ -216,157 +188,164 @@ Definition index_index_array
   array_index_usize u32 32%usize a j
 .
 
-(** [array::update_update_array]: forward function
+(** [array::update_update_array]:
     Source: 'src/array.rs', lines 114:0-114:70 *)
 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;
+  p <- array_index_mut_usize (array u32 32%usize) 32%usize s i;
+  let (a, index_mut_back) := p in
+  p1 <- array_index_mut_usize u32 32%usize a j;
+  let (_, index_mut_back1) := p1 in
+  a1 <- index_mut_back1 0%u32;
+  _ <- index_mut_back a1;
   Return tt
 .
 
-(** [array::array_local_deep_copy]: forward function
+(** [array::array_local_deep_copy]:
     Source: 'src/array.rs', lines 118:0-118:43 *)
 Definition array_local_deep_copy (x : array u32 32%usize) : result unit :=
   Return tt
 .
 
-(** [array::take_array]: forward function
+(** [array::take_array]:
     Source: 'src/array.rs', lines 122:0-122:30 *)
 Definition take_array (a : array u32 2%usize) : result unit :=
   Return tt.
 
-(** [array::take_array_borrow]: forward function
+(** [array::take_array_borrow]:
     Source: 'src/array.rs', lines 123:0-123:38 *)
 Definition take_array_borrow (a : array u32 2%usize) : result unit :=
   Return tt
 .
 
-(** [array::take_slice]: forward function
+(** [array::take_slice]:
     Source: 'src/array.rs', lines 124:0-124:28 *)
 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 ())
+(** [array::take_mut_slice]:
     Source: 'src/array.rs', lines 125:0-125:36 *)
 Definition take_mut_slice (s : slice u32) : result (slice u32) :=
   Return s.
 
-(** [array::const_array]: forward function
+(** [array::const_array]:
     Source: 'src/array.rs', lines 127:0-127:32 *)
 Definition const_array : result (array u32 2%usize) :=
   Return (mk_array u32 2%usize [ 0%u32; 0%u32 ])
 .
 
-(** [array::const_slice]: forward function
+(** [array::const_slice]:
     Source: 'src/array.rs', lines 131:0-131:20 *)
 Definition const_slice : result unit :=
   _ <- array_to_slice u32 2%usize (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
   Return tt
 .
 
-(** [array::take_all]: forward function
+(** [array::take_all]:
     Source: 'src/array.rs', lines 141:0-141:17 *)
 Definition take_all : result unit :=
   _ <- take_array (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
+  _ <- 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;
+  p <- array_to_slice_mut u32 2%usize (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
+  let (s1, to_slice_mut_back) := p in
+  s2 <- take_mut_slice s1;
+  _ <- to_slice_mut_back s2;
   Return tt
 .
 
-(** [array::index_array]: forward function
+(** [array::index_array]:
     Source: 'src/array.rs', lines 155:0-155:38 *)
 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
+(** [array::index_array_borrow]:
     Source: 'src/array.rs', lines 158:0-158:46 *)
 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
+(** [array::index_slice_u32_0]:
     Source: 'src/array.rs', lines 162:0-162:42 *)
 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
+(** [array::index_mut_slice_u32_0]:
     Source: 'src/array.rs', lines 166:0-166:50 *)
-Definition index_mut_slice_u32_0 (x : slice u32) : result u32 :=
-  slice_index_usize u32 x 0%usize
+Definition index_mut_slice_u32_0
+  (x : slice u32) : result (u32 * (slice u32)) :=
+  i <- slice_index_usize u32 x 0%usize; Return (i, x)
 .
 
-(** [array::index_mut_slice_u32_0]: backward function 0
-    Source: 'src/array.rs', lines 166:0-166:50 *)
-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
+(** [array::index_all]:
     Source: 'src/array.rs', lines 170:0-170:25 *)
 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;
+  i1 <- index_array (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
+  i2 <- u32_add i i1;
+  i3 <- index_array_borrow (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
+  i4 <- u32_add i2 i3;
   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
+  i5 <- index_slice_u32_0 s;
+  i6 <- u32_add i4 i5;
+  p <- array_to_slice_mut u32 2%usize (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
+  let (s1, to_slice_mut_back) := p in
+  p1 <- index_mut_slice_u32_0 s1;
+  let (i7, s2) := p1 in
+  i8 <- u32_add i6 i7;
+  _ <- to_slice_mut_back s2;
+  Return i8
+.
+
+(** [array::update_array]:
     Source: 'src/array.rs', lines 184:0-184:36 *)
 Definition update_array (x : array u32 2%usize) : result unit :=
-  _ <- array_update_usize u32 2%usize x 0%usize 1%u32; Return tt
+  p <- array_index_mut_usize u32 2%usize x 0%usize;
+  let (_, index_mut_back) := p in
+  _ <- index_mut_back 1%u32;
+  Return tt
 .
 
-(** [array::update_array_mut_borrow]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ())
+(** [array::update_array_mut_borrow]:
     Source: 'src/array.rs', lines 187:0-187:48 *)
 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
+  p <- array_index_mut_usize u32 2%usize x 0%usize;
+  let (_, index_mut_back) := p in
+  index_mut_back 1%u32
 .
 
-(** [array::update_mut_slice]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ())
+(** [array::update_mut_slice]:
     Source: 'src/array.rs', lines 190:0-190:38 *)
 Definition update_mut_slice (x : slice u32) : result (slice u32) :=
-  slice_update_usize u32 x 0%usize 1%u32
+  p <- slice_index_mut_usize u32 x 0%usize;
+  let (_, index_mut_back) := p in
+  index_mut_back 1%u32
 .
 
-(** [array::update_all]: forward function
+(** [array::update_all]:
     Source: 'src/array.rs', lines 194:0-194:19 *)
 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;
+  _ <- update_array (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
+  a <- update_array_mut_borrow (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
+  p <- array_to_slice_mut u32 2%usize a;
+  let (s, to_slice_mut_back) := p in
+  s1 <- update_mut_slice s;
+  _ <- to_slice_mut_back s1;
   Return tt
 .
 
-(** [array::range_all]: forward function
+(** [array::range_all]:
     Source: 'src/array.rs', lines 205:0-205:18 *)
 Definition range_all : result unit :=
-  s <-
+  p <-
     core_array_Array_index_mut u32 (core_ops_range_Range usize) 4%usize
       (core_ops_index_IndexMutSliceTIInst u32 (core_ops_range_Range usize)
       (core_slice_index_SliceIndexRangeUsizeSliceTInst u32))
@@ -375,127 +354,119 @@ Definition range_all : result unit :=
         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_ops_index_IndexMutSliceTIInst u32 (core_ops_range_Range usize)
-      (core_slice_index_SliceIndexRangeUsizeSliceTInst 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;
+  let (s, index_mut_back) := p in
+  s1 <- update_mut_slice s;
+  _ <- index_mut_back s1;
   Return tt
 .
 
-(** [array::deref_array_borrow]: forward function
+(** [array::deref_array_borrow]:
     Source: 'src/array.rs', lines 214:0-214:46 *)
 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
-    Source: 'src/array.rs', lines 219:0-219:54 *)
-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
+(** [array::deref_array_mut_borrow]:
     Source: 'src/array.rs', lines 219:0-219:54 *)
-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
+Definition deref_array_mut_borrow
+  (x : array u32 2%usize) : result (u32 * (array u32 2%usize)) :=
+  i <- array_index_usize u32 2%usize x 0%usize; Return (i, x)
 .
 
-(** [array::take_array_t]: forward function
+(** [array::take_array_t]:
     Source: 'src/array.rs', lines 227:0-227:31 *)
 Definition take_array_t (a : array AB_t 2%usize) : result unit :=
   Return tt.
 
-(** [array::non_copyable_array]: forward function
+(** [array::non_copyable_array]:
     Source: 'src/array.rs', lines 229:0-229:27 *)
 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
+(** [array::sum]: loop 0:
     Source: 'src/array.rs', lines 242:0-250:1 *)
 Fixpoint sum_loop
-  (n : nat) (s : slice u32) (sum0 : u32) (i : usize) : result u32 :=
+  (n : nat) (s : slice u32) (sum1 : u32) (i : usize) : result u32 :=
   match n with
   | O => Fail_ OutOfFuel
-  | S n0 =>
-    let i0 := slice_len u32 s in
-    if i s< i0
+  | S n1 =>
+    let i1 := slice_len u32 s in
+    if i s< i1
     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
+      i2 <- slice_index_usize u32 s i;
+      sum3 <- u32_add sum1 i2;
+      i3 <- usize_add i 1%usize;
+      sum_loop n1 s sum3 i3)
+    else Return sum1
   end
 .
 
-(** [array::sum]: forward function
+(** [array::sum]:
     Source: 'src/array.rs', lines 242:0-242:28 *)
 Definition sum (n : nat) (s : slice u32) : result u32 :=
   sum_loop n s 0%u32 0%usize
 .
 
-(** [array::sum2]: loop 0: forward function
+(** [array::sum2]: loop 0:
     Source: 'src/array.rs', lines 252:0-261:1 *)
 Fixpoint sum2_loop
-  (n : nat) (s : slice u32) (s2 : slice u32) (sum0 : u32) (i : usize) :
+  (n : nat) (s : slice u32) (s2 : slice u32) (sum1 : u32) (i : usize) :
   result u32
   :=
   match n with
   | O => Fail_ OutOfFuel
-  | S n0 =>
-    let i0 := slice_len u32 s in
-    if i s< i0
+  | S n1 =>
+    let i1 := slice_len u32 s in
+    if i s< i1
     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
+      i2 <- slice_index_usize u32 s i;
+      i3 <- slice_index_usize u32 s2 i;
+      i4 <- u32_add i2 i3;
+      sum3 <- u32_add sum1 i4;
+      i5 <- usize_add i 1%usize;
+      sum2_loop n1 s s2 sum3 i5)
+    else Return sum1
   end
 .
 
-(** [array::sum2]: forward function
+(** [array::sum2]:
     Source: 'src/array.rs', lines 252:0-252:41 *)
 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
+  let i1 := slice_len u32 s2 in
+  if negb (i s= i1) then Fail_ Failure else sum2_loop n s s2 0%u32 0%usize
 .
 
-(** [array::f0]: forward function
+(** [array::f0]:
     Source: 'src/array.rs', lines 263:0-263:11 *)
 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;
+  p <- array_to_slice_mut u32 2%usize (mk_array u32 2%usize [ 1%u32; 2%u32 ]);
+  let (s, to_slice_mut_back) := p in
+  p1 <- slice_index_mut_usize u32 s 0%usize;
+  let (_, index_mut_back) := p1 in
+  s1 <- index_mut_back 1%u32;
+  _ <- to_slice_mut_back s1;
   Return tt
 .
 
-(** [array::f1]: forward function
+(** [array::f1]:
     Source: 'src/array.rs', lines 268:0-268:11 *)
 Definition f1 : result unit :=
-  _ <-
-    array_update_usize u32 2%usize (mk_array u32 2%usize [ 1%u32; 2%u32 ])
-      0%usize 1%u32;
+  p <-
+    array_index_mut_usize u32 2%usize (mk_array u32 2%usize [ 1%u32; 2%u32 ])
+      0%usize;
+  let (_, index_mut_back) := p in
+  _ <- index_mut_back 1%u32;
   Return tt
 .
 
-(** [array::f2]: forward function
+(** [array::f2]:
     Source: 'src/array.rs', lines 273:0-273:17 *)
 Definition f2 (i : u32) : result unit :=
   Return tt.
 
-(** [array::f4]: forward function
+(** [array::f4]:
     Source: 'src/array.rs', lines 282:0-282:54 *)
 Definition f4
   (x : array u32 32%usize) (y : usize) (z : usize) : result (slice u32) :=
@@ -505,7 +476,7 @@ Definition f4
     {| core_ops_range_Range_start := y; core_ops_range_Range_end_ := z |}
 .
 
-(** [array::f3]: forward function
+(** [array::f3]:
     Source: 'src/array.rs', lines 275:0-275:18 *)
 Definition f3 (n : nat) : result u32 :=
   i <-
@@ -514,8 +485,8 @@ Definition f3 (n : nat) : result u32 :=
   _ <- 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
+  s1 <- f4 b 16%usize 18%usize;
+  sum2 n s s1
 .
 
 (** [array::SZ]
@@ -523,21 +494,25 @@ Definition f3 (n : nat) : result u32 :=
 Definition sz_body : result usize := Return 32%usize.
 Definition sz_c : usize := sz_body%global.
 
-(** [array::f5]: forward function
+(** [array::f5]:
     Source: 'src/array.rs', lines 289:0-289:31 *)
 Definition f5 (x : array u32 32%usize) : result u32 :=
   array_index_usize u32 32%usize x 0%usize
 .
 
-(** [array::ite]: forward function
+(** [array::ite]:
     Source: 'src/array.rs', lines 294:0-294:12 *)
 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;
+  p <- array_to_slice_mut u32 2%usize (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
+  let (s, to_slice_mut_back) := p in
+  p1 <- index_mut_slice_u32_0 s;
+  let (_, s1) := p1 in
+  p2 <- array_to_slice_mut u32 2%usize (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
+  let (s2, to_slice_mut_back1) := p2 in
+  p3 <- index_mut_slice_u32_0 s2;
+  let (_, s3) := p3 in
+  _ <- to_slice_mut_back1 s3;
+  _ <- to_slice_mut_back s1;
   Return tt
 .
 
diff --git a/tests/coq/array/Primitives.v b/tests/coq/array/Primitives.v
index 84280b96..990e27e4 100644
--- a/tests/coq/array/Primitives.v
+++ b/tests/coq/array/Primitives.v
@@ -67,8 +67,7 @@ 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 .
+Definition core_mem_replace (a : Type) (x : a) (y : a) : a * a := (x, x) .
 
 Record mut_raw_ptr (T : Type) := { mut_raw_ptr_v : T }.
 Record const_raw_ptr (T : Type) := { const_raw_ptr_v : T }.
@@ -504,13 +503,15 @@ 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;
+  core_ops_index_IndexMut_index_mut :
+    Self ->
+    Idx ->
+    result (core_ops_index_IndexMut_indexInst.(core_ops_index_Index_Output) *
+            (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 {
@@ -524,13 +525,14 @@ 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;
+  core_ops_deref_DerefMut_deref_mut :
+    Self ->
+    result (core_ops_deref_DerefMut_derefInst.(core_ops_deref_Deref_target) *
+            (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;
@@ -543,8 +545,8 @@ 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.
+Definition alloc_boxed_Box_deref_mut (T : Type) (x : T) : result (T * (T -> result T)) :=
+  Return (x, fun x => Return x).
 
 (* Trait instance *)
 Definition alloc_boxed_Box_coreopsDerefInst (Self : Type) : core_ops_deref_Deref Self := {|
@@ -556,7 +558,6 @@ Definition alloc_boxed_Box_coreopsDerefInst (Self : Type) : core_ops_deref_Deref
 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;
 |}.
 
 
@@ -584,6 +585,13 @@ 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).
 
+Definition array_index_mut_usize (T : Type) (n : usize) (a : array T n) (i : usize) :
+  result (T * (T -> result (array T n))) :=
+  match array_index_usize T n a i with
+  | Fail_ e => Fail_ e
+  | Return x => Return (x, array_update_usize T n a i)
+  end.
+
 (*** Slice *)
 Definition slice T := { l: list T | Z.of_nat (length l) <= usize_max}.
 
@@ -591,11 +599,25 @@ 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).
 
+Definition slice_index_mut_usize (T : Type) (s : slice T) (i : usize) :
+  result (T * (T -> result (slice T))) :=
+  match slice_index_usize T s i with
+  | Fail_ e => Fail_ e
+  | Return x => Return (x, slice_update_usize T s i)
+  end.
+
 (*** 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).
 
+Definition array_to_slice_mut (T : Type) (n : usize) (a : array T n) :
+  result (slice T * (slice T -> result (array T n))) :=
+  match array_to_slice T n a with
+  | Fail_ e => Fail_ e
+  | Return x => Return (x, array_from_slice T n a)
+  end.
+
 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).
 
@@ -639,16 +661,9 @@ Definition alloc_vec_Vec_bind {A B} (v: alloc_vec_Vec A) (f: list A -> result (l
   | 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)
@@ -661,6 +676,14 @@ Axiom alloc_vec_Vec_index_usize : forall {T : Type} (v : alloc_vec_Vec T) (i : u
 (* Helper *)
 Axiom alloc_vec_Vec_update_usize : forall {T : Type} (v : alloc_vec_Vec T) (i : usize) (x : T), result (alloc_vec_Vec T).
 
+Definition alloc_vec_Vec_index_mut_usize {T : Type} (v: alloc_vec_Vec T) (i: usize) :
+  result (T * (T -> result (alloc_vec_Vec T))) :=
+  match alloc_vec_Vec_index_usize v i with
+  | Return x =>
+    Return (x, alloc_vec_Vec_update_usize v i)
+  | Fail_ e => Fail_ e
+  end.
+
 (* Trait declaration: [core::slice::index::private_slice_index::Sealed] *)
 Definition core_slice_index_private_slice_index_Sealed (self : Type) := unit.
 
@@ -669,25 +692,23 @@ Record core_slice_index_SliceIndex (Self T : Type) := mk_core_slice_index_SliceI
   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_mut :
+    Self -> T -> result (option core_slice_index_SliceIndex_Output * (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;
+  core_slice_index_SliceIndex_index_mut :
+    Self -> T -> result (core_slice_index_SliceIndex_Output * (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
@@ -704,11 +725,9 @@ Axiom core_slice_index_RangeUsize_get : forall (T : Type) (i : core_ops_range_Ra
 
 (* [core::slice::index::Range::get_mut]: forward function *)
 Axiom core_slice_index_RangeUsize_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_RangeUsize_get_mut_back :
-  forall (T : Type), core_ops_range_Range usize -> slice T -> option (slice T) -> result (slice T).
+  forall (T : Type),
+    core_ops_range_Range usize -> slice T ->
+    result (option (slice T) * (option (slice T) -> result (slice T))).
 
 (* [core::slice::index::Range::get_unchecked]: forward function *)
 Definition core_slice_index_RangeUsize_get_unchecked
@@ -732,21 +751,14 @@ Axiom core_slice_index_RangeUsize_index :
 
 (* [core::slice::index::Range::index_mut]: forward function *)
 Axiom core_slice_index_RangeUsize_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_RangeUsize_index_mut_back :
-  forall (T : Type), core_ops_range_Range usize -> slice T -> slice T -> result (slice T).
+  forall (T : Type), core_ops_range_Range usize -> slice T -> result (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).
+  slice T -> Idx ->
+  result (inst.(core_slice_index_SliceIndex_Output) *
+          (inst.(core_slice_index_SliceIndex_Output) -> result (slice T))).
 
 (* [core::array::[T; N]::index]: forward function *)
 Axiom core_array_Array_index :
@@ -756,12 +768,9 @@ Axiom core_array_Array_index :
 (* [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).
+  (a : array T N) (i : Idx),
+  result (inst.(core_ops_index_IndexMut_indexInst).(core_ops_index_Index_Output) *
+          (inst.(core_ops_index_IndexMut_indexInst).(core_ops_index_Index_Output) -> result (array T N))).
 
 (* Trait implementation: [core::slice::index::private_slice_index::Range] *)
 Definition core_slice_index_private_slice_index_SealedRangeUsizeInst
@@ -774,12 +783,10 @@ Definition core_slice_index_SliceIndexRangeUsizeSliceTInst (T : Type) :
   core_slice_index_SliceIndex_Output := slice T;
   core_slice_index_SliceIndex_get := core_slice_index_RangeUsize_get T;
   core_slice_index_SliceIndex_get_mut := core_slice_index_RangeUsize_get_mut T;
-  core_slice_index_SliceIndex_get_mut_back := core_slice_index_RangeUsize_get_mut_back T;
   core_slice_index_SliceIndex_get_unchecked := core_slice_index_RangeUsize_get_unchecked T;
   core_slice_index_SliceIndex_get_unchecked_mut := core_slice_index_RangeUsize_get_unchecked_mut T;
   core_slice_index_SliceIndex_index := core_slice_index_RangeUsize_index T;
   core_slice_index_SliceIndex_index_mut := core_slice_index_RangeUsize_index_mut T;
-  core_slice_index_SliceIndex_index_mut_back := core_slice_index_RangeUsize_index_mut_back T;
 |}.
 
 (* Trait implementation: [core::slice::index::[T]] *)
@@ -796,7 +803,6 @@ Definition core_ops_index_IndexMutSliceTIInst (T Idx : Type)
   core_ops_index_IndexMut (slice T) Idx := {|
   core_ops_index_IndexMut_indexInst := core_ops_index_IndexSliceTIInst 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]] *)
@@ -813,18 +819,14 @@ Definition core_ops_index_IndexMutArrayInst (T Idx : Type) (N : usize)
   core_ops_index_IndexMut (array T N) Idx := {|
   core_ops_index_IndexMut_indexInst := core_ops_index_IndexArrayInst 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).
+Axiom core_slice_index_usize_get_mut :
+  forall (T : Type), usize -> slice T -> result (option T * (option T -> result (slice T))).
 
 (* [core::slice::index::usize::get_unchecked]: forward function *)
 Axiom core_slice_index_usize_get_unchecked :
@@ -838,11 +840,8 @@ Axiom core_slice_index_usize_get_unchecked_mut :
 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).
+Axiom core_slice_index_usize_index_mut :
+  forall (T : Type), usize -> slice T -> result (T * (T -> result (slice T))).
 
 (* Trait implementation: [core::slice::index::private_slice_index::usize] *)
 Definition core_slice_index_private_slice_index_SealedUsizeInst
@@ -855,12 +854,10 @@ Definition core_slice_index_SliceIndexUsizeSliceTInst (T : Type) :
   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 *)
@@ -869,12 +866,9 @@ Axiom alloc_vec_Vec_index : forall (T Idx : Type) (inst : core_slice_index_Slice
 
 (* [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).
+  (Self : alloc_vec_Vec T) (i : Idx),
+  result (inst.(core_slice_index_SliceIndex_Output) *
+          (inst.(core_slice_index_SliceIndex_Output) -> result (alloc_vec_Vec T))).
 
 (* Trait implementation: [alloc::vec::Vec] *)
 Definition alloc_vec_Vec_coreopsindexIndexInst (T Idx : Type)
@@ -890,7 +884,6 @@ Definition alloc_vec_Vec_coreopsindexIndexMutInst (T Idx : Type)
   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 *)
@@ -901,10 +894,6 @@ Axiom alloc_vec_Vec_index_eq : forall {a : Type} (v : alloc_vec_Vec a) (i : usiz
 
 Axiom alloc_vec_Vec_index_mut_eq : forall {a : Type} (v : alloc_vec_Vec a) (i : usize) (x : a),
   alloc_vec_Vec_index_mut a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i =
-    alloc_vec_Vec_index_usize v i.
-
-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_SliceIndexUsizeSliceTInst a) v i x =
-    alloc_vec_Vec_update_usize v i x.
+    alloc_vec_Vec_index_mut_usize v i.
 
 End Primitives.
diff --git a/tests/coq/betree/BetreeMain_Funs.v b/tests/coq/betree/BetreeMain_Funs.v
index a5dd4230..cefab0f4 100644
--- a/tests/coq/betree/BetreeMain_Funs.v
+++ b/tests/coq/betree/BetreeMain_Funs.v
@@ -12,7 +12,7 @@ Require Import BetreeMain_FunsExternal.
 Include BetreeMain_FunsExternal.
 Module BetreeMain_Funs.
 
-(** [betree_main::betree::load_internal_node]: forward function
+(** [betree_main::betree::load_internal_node]:
     Source: 'src/betree.rs', lines 36:0-36:52 *)
 Definition betree_load_internal_node
   (id : u64) (st : state) :
@@ -21,70 +21,57 @@ Definition betree_load_internal_node
   betree_utils_load_internal_node id st
 .
 
-(** [betree_main::betree::store_internal_node]: forward function
+(** [betree_main::betree::store_internal_node]:
     Source: 'src/betree.rs', lines 41:0-41:60 *)
 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 id content st;
-  let (st0, _) := p in
-  Return (st0, tt)
+  let (st1, _) := p in
+  Return (st1, tt)
 .
 
-(** [betree_main::betree::load_leaf_node]: forward function
+(** [betree_main::betree::load_leaf_node]:
     Source: 'src/betree.rs', lines 46:0-46:44 *)
 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
+(** [betree_main::betree::store_leaf_node]:
     Source: 'src/betree.rs', lines 51:0-51:52 *)
 Definition betree_store_leaf_node
   (id : u64) (content : betree_List_t (u64 * u64)) (st : state) :
   result (state * unit)
   :=
   p <- betree_utils_store_leaf_node id content st;
-  let (st0, _) := p in
-  Return (st0, tt)
+  let (st1, _) := p in
+  Return (st1, tt)
 .
 
-(** [betree_main::betree::fresh_node_id]: forward function
+(** [betree_main::betree::fresh_node_id]:
     Source: 'src/betree.rs', lines 55:0-55:48 *)
-Definition betree_fresh_node_id (counter : u64) : result u64 :=
-  _ <- u64_add counter 1%u64; Return counter
+Definition betree_fresh_node_id (counter : u64) : result (u64 * u64) :=
+  counter1 <- u64_add counter 1%u64; Return (counter, counter1)
 .
 
-(** [betree_main::betree::fresh_node_id]: backward function 0
-    Source: 'src/betree.rs', lines 55:0-55:48 *)
-Definition betree_fresh_node_id_back (counter : u64) : result u64 :=
-  u64_add counter 1%u64
-.
-
-(** [betree_main::betree::{betree_main::betree::NodeIdCounter}::new]: forward function
+(** [betree_main::betree::{betree_main::betree::NodeIdCounter}::new]:
     Source: 'src/betree.rs', lines 206:4-206:20 *)
 Definition betree_NodeIdCounter_new : result betree_NodeIdCounter_t :=
   Return {| betree_NodeIdCounter_next_node_id := 0%u64 |}
 .
 
-(** [betree_main::betree::{betree_main::betree::NodeIdCounter}::fresh_id]: forward function
+(** [betree_main::betree::{betree_main::betree::NodeIdCounter}::fresh_id]:
     Source: 'src/betree.rs', lines 210:4-210:36 *)
 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::{betree_main::betree::NodeIdCounter}::fresh_id]: backward function 0
-    Source: 'src/betree.rs', lines 210:4-210:36 *)
-Definition betree_NodeIdCounter_fresh_id_back
-  (self : betree_NodeIdCounter_t) : result betree_NodeIdCounter_t :=
+  (self : betree_NodeIdCounter_t) : result (u64 * betree_NodeIdCounter_t) :=
   i <- u64_add self.(betree_NodeIdCounter_next_node_id) 1%u64;
-  Return {| betree_NodeIdCounter_next_node_id := i |}
+  Return (self.(betree_NodeIdCounter_next_node_id),
+    {| betree_NodeIdCounter_next_node_id := i |})
 .
 
-(** [betree_main::betree::upsert_update]: forward function
+(** [betree_main::betree::upsert_update]:
     Source: 'src/betree.rs', lines 234:0-234:70 *)
 Definition betree_upsert_update
   (prev : option u64) (st : betree_UpsertFunState_t) : result u64 :=
@@ -92,109 +79,95 @@ Definition betree_upsert_update
   | None =>
     match st with
     | Betree_UpsertFunState_Add v => Return v
-    | Betree_UpsertFunState_Sub i => Return 0%u64
+    | Betree_UpsertFunState_Sub _ => Return 0%u64
     end
-  | Some prev0 =>
+  | Some prev1 =>
     match st with
     | 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
+      margin <- u64_sub core_u64_max prev1;
+      if margin s>= v then u64_add prev1 v else Return core_u64_max
     | Betree_UpsertFunState_Sub v =>
-      if prev0 s>= v then u64_sub prev0 v else Return 0%u64
+      if prev1 s>= v then u64_sub prev1 v else Return 0%u64
     end
   end
 .
 
-(** [betree_main::betree::{betree_main::betree::List<T>#1}::len]: forward function
+(** [betree_main::betree::{betree_main::betree::List<T>#1}::len]:
     Source: 'src/betree.rs', lines 276:4-276:24 *)
 Fixpoint betree_List_len
   (T : Type) (n : nat) (self : betree_List_t T) : result u64 :=
   match n with
   | O => Fail_ OutOfFuel
-  | S n0 =>
+  | S n1 =>
     match self with
-    | Betree_List_Cons t tl => i <- betree_List_len T n0 tl; u64_add 1%u64 i
+    | Betree_List_Cons _ tl => i <- betree_List_len T n1 tl; u64_add 1%u64 i
     | Betree_List_Nil => Return 0%u64
     end
   end
 .
 
-(** [betree_main::betree::{betree_main::betree::List<T>#1}::split_at]: forward function
+(** [betree_main::betree::{betree_main::betree::List<T>#1}::split_at]:
     Source: 'src/betree.rs', lines 284:4-284:51 *)
 Fixpoint betree_List_split_at
-  (T : Type) (n : nat) (self : betree_List_t T) (n0 : u64) :
+  (T : Type) (n : nat) (self : betree_List_t T) (n1 : u64) :
   result ((betree_List_t T) * (betree_List_t T))
   :=
   match n with
   | O => Fail_ OutOfFuel
-  | S n1 =>
-    if n0 s= 0%u64
+  | S n2 =>
+    if n1 s= 0%u64
     then Return (Betree_List_Nil, self)
     else
       match self with
       | Betree_List_Cons hd tl =>
-        i <- u64_sub n0 1%u64;
-        p <- betree_List_split_at T n1 tl i;
+        i <- u64_sub n1 1%u64;
+        p <- betree_List_split_at T n2 tl i;
         let (ls0, ls1) := p in
-        let l := ls0 in
-        Return (Betree_List_Cons hd l, ls1)
+        Return (Betree_List_Cons hd ls0, ls1)
       | Betree_List_Nil => Fail_ Failure
       end
   end
 .
 
-(** [betree_main::betree::{betree_main::betree::List<T>#1}::push_front]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ())
+(** [betree_main::betree::{betree_main::betree::List<T>#1}::push_front]:
     Source: 'src/betree.rs', lines 299:4-299:34 *)
 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 (Betree_List_Cons x l)
+  let (tl, _) := core_mem_replace (betree_List_t T) self Betree_List_Nil in
+  Return (Betree_List_Cons x tl)
 .
 
-(** [betree_main::betree::{betree_main::betree::List<T>#1}::pop_front]: forward function
+(** [betree_main::betree::{betree_main::betree::List<T>#1}::pop_front]:
     Source: 'src/betree.rs', lines 306:4-306:32 *)
 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
+  (T : Type) (self : betree_List_t T) : result (T * (betree_List_t T)) :=
+  let (ls, _) := core_mem_replace (betree_List_t T) self Betree_List_Nil in
   match ls with
-  | Betree_List_Cons x tl => Return x
+  | Betree_List_Cons x tl => Return (x, tl)
   | Betree_List_Nil => Fail_ Failure
   end
 .
 
-(** [betree_main::betree::{betree_main::betree::List<T>#1}::pop_front]: backward function 0
-    Source: 'src/betree.rs', lines 306:4-306:32 *)
-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
-  | Betree_List_Cons x tl => Return tl
-  | Betree_List_Nil => Fail_ Failure
-  end
-.
-
-(** [betree_main::betree::{betree_main::betree::List<T>#1}::hd]: forward function
+(** [betree_main::betree::{betree_main::betree::List<T>#1}::hd]:
     Source: 'src/betree.rs', lines 318:4-318:22 *)
 Definition betree_List_hd (T : Type) (self : betree_List_t T) : result T :=
   match self with
-  | Betree_List_Cons hd l => Return hd
+  | Betree_List_Cons hd _ => Return hd
   | Betree_List_Nil => Fail_ Failure
   end
 .
 
-(** [betree_main::betree::{betree_main::betree::List<(u64, T)>#2}::head_has_key]: forward function
+(** [betree_main::betree::{betree_main::betree::List<(u64, T)>#2}::head_has_key]:
     Source: 'src/betree.rs', lines 327:4-327:44 *)
 Definition betree_ListTupleU64T_head_has_key
   (T : Type) (self : betree_List_t (u64 * T)) (key : u64) : result bool :=
   match self with
-  | Betree_List_Cons hd l => let (i, _) := hd in Return (i s= key)
+  | Betree_List_Cons hd _ => let (i, _) := hd in Return (i s= key)
   | Betree_List_Nil => Return false
   end
 .
 
-(** [betree_main::betree::{betree_main::betree::List<(u64, T)>#2}::partition_at_pivot]: forward function
+(** [betree_main::betree::{betree_main::betree::List<(u64, T)>#2}::partition_at_pivot]:
     Source: 'src/betree.rs', lines 339:4-339:73 *)
 Fixpoint betree_ListTupleU64T_partition_at_pivot
   (T : Type) (n : nat) (self : betree_List_t (u64 * T)) (pivot : u64) :
@@ -202,123 +175,85 @@ Fixpoint betree_ListTupleU64T_partition_at_pivot
   :=
   match n with
   | O => Fail_ OutOfFuel
-  | S n0 =>
+  | S n1 =>
     match self with
     | Betree_List_Cons hd tl =>
       let (i, t) := hd in
       if i s>= pivot
       then Return (Betree_List_Nil, Betree_List_Cons (i, t) tl)
       else (
-        p <- betree_ListTupleU64T_partition_at_pivot T n0 tl pivot;
+        p <- betree_ListTupleU64T_partition_at_pivot T n1 tl pivot;
         let (ls0, ls1) := p in
-        let l := ls0 in
-        Return (Betree_List_Cons (i, t) l, ls1))
+        Return (Betree_List_Cons (i, t) ls0, ls1))
     | Betree_List_Nil => Return (Betree_List_Nil, Betree_List_Nil)
     end
   end
 .
 
-(** [betree_main::betree::{betree_main::betree::Leaf#3}::split]: forward function
+(** [betree_main::betree::{betree_main::betree::Leaf#3}::split]:
     Source: 'src/betree.rs', lines 359:4-364:17 *)
 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 * betree_NodeIdCounter_t))
   :=
   p <-
     betree_List_split_at (u64 * u64) n content
       params.(betree_Params_split_size);
   let (content0, content1) := p in
-  p0 <- betree_List_hd (u64 * u64) content1;
-  let (pivot, _) := p0 in
-  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 id1 content1 st0;
-  let (st1, _) := p2 in
-  let n0 := Betree_Node_Leaf
+  p1 <- betree_List_hd (u64 * u64) content1;
+  let (pivot, _) := p1 in
+  p2 <- betree_NodeIdCounter_fresh_id node_id_cnt;
+  let (id0, nic) := p2 in
+  p3 <- betree_NodeIdCounter_fresh_id nic;
+  let (id1, nic1) := p3 in
+  p4 <- betree_store_leaf_node id0 content0 st;
+  let (st1, _) := p4 in
+  p5 <- betree_store_leaf_node id1 content1 st1;
+  let (st2, _) := p5 in
+  let n1 := Betree_Node_Leaf
     {|
       betree_Leaf_id := id0;
       betree_Leaf_size := params.(betree_Params_split_size)
     |} in
-  let n1 := Betree_Node_Leaf
+  let n2 := Betree_Node_Leaf
     {|
       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 (st2, (mkbetree_Internal_t self.(betree_Leaf_id) pivot n1 n2, nic1))
 .
 
-(** [betree_main::betree::{betree_main::betree::Leaf#3}::split]: backward function 2
-    Source: 'src/betree.rs', lines 359:4-364:17 *)
-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_NodeIdCounter_t
-  :=
-  p <-
-    betree_List_split_at (u64 * u64) n content
-      params.(betree_Params_split_size);
-  let (content0, content1) := p in
-  _ <- 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 id1 content1 st0;
-  betree_NodeIdCounter_fresh_id_back node_id_cnt0
-.
-
-(** [betree_main::betree::{betree_main::betree::Node#5}::lookup_first_message_for_key]: forward function
+(** [betree_main::betree::{betree_main::betree::Node#5}::lookup_first_message_for_key]:
     Source: 'src/betree.rs', lines 789:4-792:34 *)
 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
-    | Betree_List_Cons x next_msgs =>
-      let (i, m) := x in
-      if i s>= key
-      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::{betree_main::betree::Node#5}::lookup_first_message_for_key]: backward function 0
-    Source: 'src/betree.rs', lines 789:4-792:34 *)
-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))
+  result ((betree_List_t (u64 * betree_Message_t)) * (betree_List_t (u64 *
+    betree_Message_t) -> result (betree_List_t (u64 * betree_Message_t))))
   :=
   match n with
   | O => Fail_ OutOfFuel
-  | S n0 =>
+  | S n1 =>
     match msgs with
     | Betree_List_Cons x next_msgs =>
       let (i, m) := x in
       if i s>= key
-      then Return ret
+      then Return (Betree_List_Cons (i, m) next_msgs, Return)
       else (
-        next_msgs0 <-
-          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
+        p <- betree_Node_lookup_first_message_for_key n1 key next_msgs;
+        let (l, lookup_first_message_for_key_back) := p in
+        let back_'a :=
+          fun (ret : betree_List_t (u64 * betree_Message_t)) =>
+            next_msgs1 <- lookup_first_message_for_key_back ret;
+            Return (Betree_List_Cons (i, m) next_msgs1) in
+        Return (l, back_'a))
+    | Betree_List_Nil => Return (Betree_List_Nil, Return)
     end
   end
 .
 
-(** [betree_main::betree::{betree_main::betree::Node#5}::lookup_in_bindings]: forward function
+(** [betree_main::betree::{betree_main::betree::Node#5}::lookup_in_bindings]:
     Source: 'src/betree.rs', lines 636:4-636:80 *)
 Fixpoint betree_Node_lookup_in_bindings
   (n : nat) (key : u64) (bindings : betree_List_t (u64 * u64)) :
@@ -326,263 +261,146 @@ Fixpoint betree_Node_lookup_in_bindings
   :=
   match n with
   | O => Fail_ OutOfFuel
-  | S n0 =>
+  | S n1 =>
     match bindings with
     | Betree_List_Cons hd tl =>
-      let (i, i0) := hd in
+      let (i, i1) := hd in
       if i s= key
-      then Return (Some i0)
+      then Return (Some i1)
       else
         if i s> key
         then Return None
-        else betree_Node_lookup_in_bindings n0 key tl
+        else betree_Node_lookup_in_bindings n1 key tl
     | Betree_List_Nil => Return None
     end
   end
 .
 
-(** [betree_main::betree::{betree_main::betree::Node#5}::apply_upserts]: forward function
+(** [betree_main::betree::{betree_main::betree::Node#5}::apply_upserts]:
     Source: 'src/betree.rs', lines 819:4-819:90 *)
 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)
+  result (state * (u64 * (betree_List_t (u64 * betree_Message_t))))
   :=
   match n with
   | O => Fail_ OutOfFuel
-  | S n0 =>
+  | S n1 =>
     b <- betree_ListTupleU64T_head_has_key betree_Message_t msgs key;
     if b
     then (
-      msg <- betree_List_pop_front (u64 * betree_Message_t) msgs;
+      p <- betree_List_pop_front (u64 * betree_Message_t) msgs;
+      let (msg, l) := p in
       let (_, m) := msg in
       match m with
-      | Betree_Message_Insert i => Fail_ Failure
+      | Betree_Message_Insert _ => 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
+        betree_Node_apply_upserts n1 l (Some v) key st
       end)
     else (
       p <- core_option_Option_unwrap u64 prev st;
-      let (st0, v) := p in
-      _ <-
+      let (st1, v) := p in
+      l <-
         betree_List_push_front (u64 * betree_Message_t) msgs (key,
           Betree_Message_Insert v);
-      Return (st0, v))
-  end
-.
-
-(** [betree_main::betree::{betree_main::betree::Node#5}::apply_upserts]: backward function 0
-    Source: 'src/betree.rs', lines 819:4-819:90 *)
-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))
-  :=
-  match n with
-  | O => Fail_ OutOfFuel
-  | S n0 =>
-    b <- betree_ListTupleU64T_head_has_key betree_Message_t msgs key;
-    if b
-    then (
-      msg <- betree_List_pop_front (u64 * betree_Message_t) msgs;
-      let (_, m) := msg in
-      match m with
-      | 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 u64 prev st;
-      let (_, v) := p in
-      betree_List_push_front (u64 * betree_Message_t) msgs (key,
-        Betree_Message_Insert v))
+      Return (st1, (v, l)))
   end
 .
 
-(** [betree_main::betree::{betree_main::betree::Internal#4}::lookup_in_children]: forward function
+(** [betree_main::betree::{betree_main::betree::Internal#4}::lookup_in_children]:
     Source: 'src/betree.rs', lines 395:4-395:63 *)
 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 n0 self.(betree_Internal_left) key st
-    else betree_Node_lookup n0 self.(betree_Internal_right) key st
-  end
-
-(** [betree_main::betree::{betree_main::betree::Internal#4}::lookup_in_children]: backward function 0
-    Source: 'src/betree.rs', lines 395:4-395:63 *)
-with betree_Internal_lookup_in_children_back
-  (n : nat) (self : betree_Internal_t) (key : u64) (st : state) :
-  result betree_Internal_t
+  result (state * ((option u64) * betree_Internal_t))
   :=
   match n with
   | O => Fail_ OutOfFuel
-  | S n0 =>
+  | S n1 =>
     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)))
+      p <- betree_Node_lookup n1 self.(betree_Internal_left) key st;
+      let (st1, p1) := p in
+      let (o, n2) := p1 in
+      Return (st1, (o, mkbetree_Internal_t self.(betree_Internal_id)
+        self.(betree_Internal_pivot) n2 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))
+      p <- betree_Node_lookup n1 self.(betree_Internal_right) key st;
+      let (st1, p1) := p in
+      let (o, n2) := p1 in
+      Return (st1, (o, mkbetree_Internal_t self.(betree_Internal_id)
+        self.(betree_Internal_pivot) self.(betree_Internal_left) n2)))
   end
 
-(** [betree_main::betree::{betree_main::betree::Node#5}::lookup]: forward function
+(** [betree_main::betree::{betree_main::betree::Node#5}::lookup]:
     Source: 'src/betree.rs', lines 709:4-709:58 *)
 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
-    | 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 n0 key msgs;
-      match pending with
-      | Betree_List_Cons p0 l =>
-        let (k, msg) := p0 in
-        if k s<> key
-        then (
-          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
-              (Betree_List_Cons (k, msg) l);
-          Return (st1, o))
-        else
-          match msg with
-          | Betree_Message_Insert v =>
-            _ <-
-              betree_Node_lookup_first_message_for_key_back n0 key msgs
-                (Betree_List_Cons (k, Betree_Message_Insert v) l);
-            Return (st0, Some v)
-          | Betree_Message_Delete =>
-            _ <-
-              betree_Node_lookup_first_message_for_key_back n0 key msgs
-                (Betree_List_Cons (k, Betree_Message_Delete) l);
-            Return (st0, None)
-          | Betree_Message_Upsert ufs =>
-            p1 <- betree_Internal_lookup_in_children n0 node key st0;
-            let (st1, v) := p1 in
-            p2 <-
-              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;
-            pending0 <-
-              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
-                pending0;
-            p3 <-
-              betree_store_internal_node node0.(betree_Internal_id) msgs0 st2;
-            let (st3, _) := p3 in
-            Return (st3, Some v0)
-          end
-      | 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
-            Betree_List_Nil;
-        Return (st1, o)
-      end
-    | Betree_Node_Leaf node =>
-      p <- betree_load_leaf_node node.(betree_Leaf_id) st;
-      let (st0, bindings) := p in
-      o <- betree_Node_lookup_in_bindings n0 key bindings;
-      Return (st0, o)
-    end
-  end
-
-(** [betree_main::betree::{betree_main::betree::Node#5}::lookup]: backward function 0
-    Source: 'src/betree.rs', lines 709:4-709:58 *)
-with betree_Node_lookup_back
-  (n : nat) (self : betree_Node_t) (key : u64) (st : state) :
-  result betree_Node_t
+  result (state * ((option u64) * betree_Node_t))
   :=
   match n with
   | O => Fail_ OutOfFuel
-  | S n0 =>
+  | S n1 =>
     match self with
     | 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 n0 key msgs;
+      let (st1, msgs) := p in
+      p1 <- betree_Node_lookup_first_message_for_key n1 key msgs;
+      let (pending, lookup_first_message_for_key_back) := p1 in
       match pending with
-      | Betree_List_Cons p0 l =>
-        let (k, msg) := p0 in
+      | Betree_List_Cons p2 l =>
+        let (k, msg) := p2 in
         if k s<> key
         then (
-          _ <-
-            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))
+          p3 <- betree_Internal_lookup_in_children n1 node key st1;
+          let (st2, p4) := p3 in
+          let (o, i) := p4 in
+          _ <- lookup_first_message_for_key_back (Betree_List_Cons (k, msg) l);
+          Return (st2, (o, Betree_Node_Internal i)))
         else
           match msg with
           | Betree_Message_Insert v =>
             _ <-
-              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)
+              lookup_first_message_for_key_back (Betree_List_Cons (k,
+                Betree_Message_Insert v) l);
+            Return (st1, (Some v, Betree_Node_Internal node))
           | Betree_Message_Delete =>
             _ <-
-              betree_Node_lookup_first_message_for_key_back n0 key msgs
-                (Betree_List_Cons (k, Betree_Message_Delete) l);
-            Return (Betree_Node_Internal node)
+              lookup_first_message_for_key_back (Betree_List_Cons (k,
+                Betree_Message_Delete) l);
+            Return (st1, (None, 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 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;
-            pending0 <-
-              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
-                pending0;
-            _ <-
-              betree_store_internal_node node0.(betree_Internal_id) msgs0 st2;
-            Return (Betree_Node_Internal node0)
+            p3 <- betree_Internal_lookup_in_children n1 node key st1;
+            let (st2, p4) := p3 in
+            let (v, i) := p4 in
+            p5 <-
+              betree_Node_apply_upserts n1 (Betree_List_Cons (k,
+                Betree_Message_Upsert ufs) l) v key st2;
+            let (st3, p6) := p5 in
+            let (v1, l1) := p6 in
+            msgs1 <- lookup_first_message_for_key_back l1;
+            p7 <- betree_store_internal_node i.(betree_Internal_id) msgs1 st3;
+            let (st4, _) := p7 in
+            Return (st4, (Some v1, Betree_Node_Internal i))
           end
       | Betree_List_Nil =>
-        _ <-
-          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)
+        p2 <- betree_Internal_lookup_in_children n1 node key st1;
+        let (st2, p3) := p2 in
+        let (o, i) := p3 in
+        _ <- lookup_first_message_for_key_back Betree_List_Nil;
+        Return (st2, (o, Betree_Node_Internal i))
       end
     | Betree_Node_Leaf node =>
       p <- betree_load_leaf_node node.(betree_Leaf_id) st;
-      let (_, bindings) := p in
-      _ <- betree_Node_lookup_in_bindings n0 key bindings;
-      Return (Betree_Node_Leaf node)
+      let (st1, bindings) := p in
+      o <- betree_Node_lookup_in_bindings n1 key bindings;
+      Return (st1, (o, Betree_Node_Leaf node))
     end
   end
 .
 
-(** [betree_main::betree::{betree_main::betree::Node#5}::filter_messages_for_key]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ())
+(** [betree_main::betree::{betree_main::betree::Node#5}::filter_messages_for_key]:
     Source: 'src/betree.rs', lines 674:4-674:77 *)
 Fixpoint betree_Node_filter_messages_for_key
   (n : nat) (key : u64) (msgs : betree_List_t (u64 * betree_Message_t)) :
@@ -590,127 +408,112 @@ Fixpoint betree_Node_filter_messages_for_key
   :=
   match n with
   | O => Fail_ OutOfFuel
-  | S n0 =>
+  | S n1 =>
     match msgs with
     | 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) (Betree_List_Cons
-            (k, m) l);
-        betree_Node_filter_messages_for_key n0 key msgs0)
+        p1 <-
+          betree_List_pop_front (u64 * betree_Message_t) (Betree_List_Cons (k,
+            m) l);
+        let (_, l1) := p1 in
+        betree_Node_filter_messages_for_key n1 key l1)
       else Return (Betree_List_Cons (k, m) l)
     | Betree_List_Nil => Return Betree_List_Nil
     end
   end
 .
 
-(** [betree_main::betree::{betree_main::betree::Node#5}::lookup_first_message_after_key]: forward function
+(** [betree_main::betree::{betree_main::betree::Node#5}::lookup_first_message_after_key]:
     Source: 'src/betree.rs', lines 689:4-692:34 *)
 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
-    | Betree_List_Cons p next_msgs =>
-      let (k, m) := p in
-      if k s= key
-      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::{betree_main::betree::Node#5}::lookup_first_message_after_key]: backward function 0
-    Source: 'src/betree.rs', lines 689:4-692:34 *)
-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))
+  result ((betree_List_t (u64 * betree_Message_t)) * (betree_List_t (u64 *
+    betree_Message_t) -> result (betree_List_t (u64 * betree_Message_t))))
   :=
   match n with
   | O => Fail_ OutOfFuel
-  | S n0 =>
+  | S n1 =>
     match msgs with
     | 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 (Betree_List_Cons (k, m) next_msgs0))
-      else Return ret
-    | Betree_List_Nil => Return ret
+        p1 <- betree_Node_lookup_first_message_after_key n1 key next_msgs;
+        let (l, lookup_first_message_after_key_back) := p1 in
+        let back_'a :=
+          fun (ret : betree_List_t (u64 * betree_Message_t)) =>
+            next_msgs1 <- lookup_first_message_after_key_back ret;
+            Return (Betree_List_Cons (k, m) next_msgs1) in
+        Return (l, back_'a))
+      else Return (Betree_List_Cons (k, m) next_msgs, Return)
+    | Betree_List_Nil => Return (Betree_List_Nil, Return)
     end
   end
 .
 
-(** [betree_main::betree::{betree_main::betree::Node#5}::apply_to_internal]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ())
+(** [betree_main::betree::{betree_main::betree::Node#5}::apply_to_internal]:
     Source: 'src/betree.rs', lines 521:4-521:89 *)
 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 n key msgs;
-  b <- betree_ListTupleU64T_head_has_key betree_Message_t msgs0 key;
+  p <- betree_Node_lookup_first_message_for_key n key msgs;
+  let (msgs1, lookup_first_message_for_key_back) := p in
+  b <- betree_ListTupleU64T_head_has_key betree_Message_t msgs1 key;
   if b
   then
     match new_msg with
     | Betree_Message_Insert i =>
-      msgs1 <- betree_Node_filter_messages_for_key n key msgs0;
-      msgs2 <-
-        betree_List_push_front (u64 * betree_Message_t) msgs1 (key,
+      l <- betree_Node_filter_messages_for_key n key msgs1;
+      l1 <-
+        betree_List_push_front (u64 * betree_Message_t) l (key,
           Betree_Message_Insert i);
-      betree_Node_lookup_first_message_for_key_back n key msgs msgs2
+      lookup_first_message_for_key_back l1
     | Betree_Message_Delete =>
-      msgs1 <- betree_Node_filter_messages_for_key n key msgs0;
-      msgs2 <-
-        betree_List_push_front (u64 * betree_Message_t) msgs1 (key,
+      l <- betree_Node_filter_messages_for_key n key msgs1;
+      l1 <-
+        betree_List_push_front (u64 * betree_Message_t) l (key,
           Betree_Message_Delete);
-      betree_Node_lookup_first_message_for_key_back n key msgs msgs2
+      lookup_first_message_for_key_back l1
     | Betree_Message_Upsert s =>
-      p <- betree_List_hd (u64 * betree_Message_t) msgs0;
-      let (_, m) := p in
+      p1 <- betree_List_hd (u64 * betree_Message_t) msgs1;
+      let (_, m) := p1 in
       match m with
       | 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 (u64 * betree_Message_t) msgs1 (key,
+        p2 <- betree_List_pop_front (u64 * betree_Message_t) msgs1;
+        let (_, l) := p2 in
+        l1 <-
+          betree_List_push_front (u64 * betree_Message_t) l (key,
             Betree_Message_Insert v);
-        betree_Node_lookup_first_message_for_key_back n key msgs msgs2
+        lookup_first_message_for_key_back l1
       | Betree_Message_Delete =>
+        p2 <- betree_List_pop_front (u64 * betree_Message_t) msgs1;
+        let (_, l) := p2 in
         v <- betree_upsert_update None s;
-        msgs1 <- betree_List_pop_front_back (u64 * betree_Message_t) msgs0;
-        msgs2 <-
-          betree_List_push_front (u64 * betree_Message_t) msgs1 (key,
+        l1 <-
+          betree_List_push_front (u64 * betree_Message_t) l (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 (u64 * betree_Message_t) msgs1 (key,
+        lookup_first_message_for_key_back l1
+      | Betree_Message_Upsert _ =>
+        p2 <- betree_Node_lookup_first_message_after_key n key msgs1;
+        let (msgs2, lookup_first_message_after_key_back) := p2 in
+        l <-
+          betree_List_push_front (u64 * betree_Message_t) msgs2 (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
+        msgs3 <- lookup_first_message_after_key_back l;
+        lookup_first_message_for_key_back msgs3
       end
     end
   else (
-    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)
+    l <- betree_List_push_front (u64 * betree_Message_t) msgs1 (key, new_msg);
+    lookup_first_message_for_key_back l)
 .
 
-(** [betree_main::betree::{betree_main::betree::Node#5}::apply_messages_to_internal]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ())
+(** [betree_main::betree::{betree_main::betree::Node#5}::apply_messages_to_internal]:
     Source: 'src/betree.rs', lines 502:4-505:5 *)
 Fixpoint betree_Node_apply_messages_to_internal
   (n : nat) (msgs : betree_List_t (u64 * betree_Message_t))
@@ -719,104 +522,84 @@ Fixpoint betree_Node_apply_messages_to_internal
   :=
   match n with
   | O => Fail_ OutOfFuel
-  | S n0 =>
+  | S n1 =>
     match new_msgs with
     | Betree_List_Cons new_msg new_msgs_tl =>
       let (i, m) := new_msg in
-      msgs0 <- betree_Node_apply_to_internal n0 msgs i m;
-      betree_Node_apply_messages_to_internal n0 msgs0 new_msgs_tl
+      l <- betree_Node_apply_to_internal n1 msgs i m;
+      betree_Node_apply_messages_to_internal n1 l new_msgs_tl
     | Betree_List_Nil => Return msgs
     end
   end
 .
 
-(** [betree_main::betree::{betree_main::betree::Node#5}::lookup_mut_in_bindings]: forward function
+(** [betree_main::betree::{betree_main::betree::Node#5}::lookup_mut_in_bindings]:
     Source: 'src/betree.rs', lines 653:4-656:32 *)
 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
-    | Betree_List_Cons hd tl =>
-      let (i, i0) := hd in
-      if i s>= key
-      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::{betree_main::betree::Node#5}::lookup_mut_in_bindings]: backward function 0
-    Source: 'src/betree.rs', lines 653:4-656:32 *)
-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))
+  result ((betree_List_t (u64 * u64)) * (betree_List_t (u64 * u64) -> result
+    (betree_List_t (u64 * u64))))
   :=
   match n with
   | O => Fail_ OutOfFuel
-  | S n0 =>
+  | S n1 =>
     match bindings with
     | Betree_List_Cons hd tl =>
-      let (i, i0) := hd in
+      let (i, i1) := hd in
       if i s>= key
-      then Return ret
+      then Return (Betree_List_Cons (i, i1) tl, Return)
       else (
-        tl0 <- betree_Node_lookup_mut_in_bindings_back n0 key tl ret;
-        Return (Betree_List_Cons (i, i0) tl0))
-    | Betree_List_Nil => Return ret
+        p <- betree_Node_lookup_mut_in_bindings n1 key tl;
+        let (l, lookup_mut_in_bindings_back) := p in
+        let back_'a :=
+          fun (ret : betree_List_t (u64 * u64)) =>
+            tl1 <- lookup_mut_in_bindings_back ret;
+            Return (Betree_List_Cons (i, i1) tl1) in
+        Return (l, back_'a))
+    | Betree_List_Nil => Return (Betree_List_Nil, Return)
     end
   end
 .
 
-(** [betree_main::betree::{betree_main::betree::Node#5}::apply_to_leaf]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ())
+(** [betree_main::betree::{betree_main::betree::Node#5}::apply_to_leaf]:
     Source: 'src/betree.rs', lines 460:4-460:87 *)
 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 n key bindings;
-  b <- betree_ListTupleU64T_head_has_key u64 bindings0 key;
+  p <- betree_Node_lookup_mut_in_bindings n key bindings;
+  let (bindings1, lookup_mut_in_bindings_back) := p in
+  b <- betree_ListTupleU64T_head_has_key u64 bindings1 key;
   if b
   then (
-    hd <- betree_List_pop_front (u64 * u64) bindings0;
+    p1 <- betree_List_pop_front (u64 * u64) bindings1;
+    let (hd, l) := p1 in
     match new_msg with
     | 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
+      l1 <- betree_List_push_front (u64 * u64) l (key, v);
+      lookup_mut_in_bindings_back l1
+    | Betree_Message_Delete => lookup_mut_in_bindings_back l
     | Betree_Message_Upsert s =>
       let (_, i) := hd in
       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
+      l1 <- betree_List_push_front (u64 * u64) l (key, v);
+      lookup_mut_in_bindings_back l1
     end)
   else
     match new_msg with
     | 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
+      l <- betree_List_push_front (u64 * u64) bindings1 (key, v);
+      lookup_mut_in_bindings_back l
+    | Betree_Message_Delete => lookup_mut_in_bindings_back bindings1
     | 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
+      l <- betree_List_push_front (u64 * u64) bindings1 (key, v);
+      lookup_mut_in_bindings_back l
     end
 .
 
-(** [betree_main::betree::{betree_main::betree::Node#5}::apply_messages_to_leaf]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ())
+(** [betree_main::betree::{betree_main::betree::Node#5}::apply_messages_to_leaf]:
     Source: 'src/betree.rs', lines 444:4-447:5 *)
 Fixpoint betree_Node_apply_messages_to_leaf
   (n : nat) (bindings : betree_List_t (u64 * u64))
@@ -825,404 +608,229 @@ Fixpoint betree_Node_apply_messages_to_leaf
   :=
   match n with
   | O => Fail_ OutOfFuel
-  | S n0 =>
+  | S n1 =>
     match new_msgs with
     | Betree_List_Cons new_msg new_msgs_tl =>
       let (i, m) := new_msg in
-      bindings0 <- betree_Node_apply_to_leaf n0 bindings i m;
-      betree_Node_apply_messages_to_leaf n0 bindings0 new_msgs_tl
+      l <- betree_Node_apply_to_leaf n1 bindings i m;
+      betree_Node_apply_messages_to_leaf n1 l new_msgs_tl
     | Betree_List_Nil => Return bindings
     end
   end
 .
 
-(** [betree_main::betree::{betree_main::betree::Internal#4}::flush]: forward function
+(** [betree_main::betree::{betree_main::betree::Internal#4}::flush]:
     Source: 'src/betree.rs', lines 410:4-415:26 *)
 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_ListTupleU64T_partition_at_pivot betree_Message_t n0 content
-        self.(betree_Internal_pivot);
-    let (msgs_left, msgs_right) := p in
-    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 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
-          node_id_cnt msgs_left st;
-      let (_, node_id_cnt0) := p1 in
-      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 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)
-            params node_id_cnt0 msgs_right st0;
-        Return (st1, Betree_List_Nil))
-      else Return (st0, msgs_right))
-    else (
-      p0 <-
-        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
-          node_id_cnt msgs_right st;
-      Return (st0, msgs_left))
-  end
-
-(** [betree_main::betree::{betree_main::betree::Internal#4}::flush]: backward function 0
-    Source: 'src/betree.rs', lines 410:4-415:26 *)
-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)
+  result (state * ((betree_List_t (u64 * betree_Message_t)) *
+    (betree_Internal_t * betree_NodeIdCounter_t)))
   :=
   match n with
   | O => Fail_ OutOfFuel
-  | S n0 =>
+  | S n1 =>
     p <-
-      betree_ListTupleU64T_partition_at_pivot betree_Message_t n0 content
+      betree_ListTupleU64T_partition_at_pivot betree_Message_t n1 content
         self.(betree_Internal_pivot);
     let (msgs_left, msgs_right) := p in
-    len_left <- betree_List_len (u64 * betree_Message_t) n0 msgs_left;
+    len_left <- betree_List_len (u64 * betree_Message_t) n1 msgs_left;
     if len_left s>= params.(betree_Params_min_flush_size)
     then (
-      p0 <-
-        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 n1 self.(betree_Internal_left) params
           node_id_cnt msgs_left st;
-      let (n1, node_id_cnt0) := p1 in
-      len_right <- betree_List_len (u64 * betree_Message_t) n0 msgs_right;
+      let (st1, p2) := p1 in
+      let (n2, node_id_cnt1) := p2 in
+      len_right <- betree_List_len (u64 * betree_Message_t) n1 msgs_right;
       if len_right s>= params.(betree_Params_min_flush_size)
       then (
-        p2 <-
-          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))
+        p3 <-
+          betree_Node_apply_messages n1 self.(betree_Internal_right) params
+            node_id_cnt1 msgs_right st1;
+        let (st2, p4) := p3 in
+        let (n3, node_id_cnt2) := p4 in
+        Return (st2, (Betree_List_Nil, (mkbetree_Internal_t
+          self.(betree_Internal_id) self.(betree_Internal_pivot) n2 n3,
+          node_id_cnt2))))
       else
-        Return (mkbetree_Internal_t self.(betree_Internal_id)
-          self.(betree_Internal_pivot) n1 self.(betree_Internal_right),
-          node_id_cnt0))
+        Return (st1, (msgs_right, (mkbetree_Internal_t
+          self.(betree_Internal_id) self.(betree_Internal_pivot) n2
+          self.(betree_Internal_right), node_id_cnt1))))
     else (
-      p0 <-
-        betree_Node_apply_messages_back n0 self.(betree_Internal_right) params
+      p1 <-
+        betree_Node_apply_messages n1 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,
-        node_id_cnt0))
+      let (st1, p2) := p1 in
+      let (n2, node_id_cnt1) := p2 in
+      Return (st1, (msgs_left, (mkbetree_Internal_t self.(betree_Internal_id)
+        self.(betree_Internal_pivot) self.(betree_Internal_left) n2,
+        node_id_cnt1))))
   end
 
-(** [betree_main::betree::{betree_main::betree::Node#5}::apply_messages]: forward function
+(** [betree_main::betree::{betree_main::betree::Node#5}::apply_messages]:
     Source: 'src/betree.rs', lines 588:4-593:5 *)
 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)
+  result (state * (betree_Node_t * betree_NodeIdCounter_t))
   :=
   match n with
   | O => Fail_ OutOfFuel
-  | S n0 =>
+  | S n1 =>
     match self with
     | 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 n0 content msgs;
-      num_msgs <- betree_List_len (u64 * betree_Message_t) n0 content0;
+      let (st1, content) := p in
+      l <- betree_Node_apply_messages_to_internal n1 content msgs;
+      num_msgs <- betree_List_len (u64 * betree_Message_t) n1 l;
       if num_msgs s>= params.(betree_Params_min_flush_size)
       then (
-        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;
-        let (node0, _) := p1 in
-        p2 <-
-          betree_store_internal_node node0.(betree_Internal_id) content1 st1;
-        let (st2, _) := p2 in
-        Return (st2, tt))
+        p1 <- betree_Internal_flush n1 node params node_id_cnt l st1;
+        let (st2, p2) := p1 in
+        let (content1, p3) := p2 in
+        let (node1, node_id_cnt1) := p3 in
+        p4 <-
+          betree_store_internal_node node1.(betree_Internal_id) content1 st2;
+        let (st3, _) := p4 in
+        Return (st3, (Betree_Node_Internal node1, node_id_cnt1)))
       else (
-        p0 <-
-          betree_store_internal_node node.(betree_Internal_id) content0 st0;
-        let (st1, _) := p0 in
-        Return (st1, tt))
-    | 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 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 n0 node content0 params node_id_cnt st0;
-        let (st1, _) := p0 in
-        p1 <- betree_store_leaf_node node.(betree_Leaf_id) Betree_List_Nil st1;
+        p1 <- betree_store_internal_node node.(betree_Internal_id) l st1;
         let (st2, _) := p1 in
-        Return (st2, tt))
-      else (
-        p0 <- betree_store_leaf_node node.(betree_Leaf_id) content0 st0;
-        let (st1, _) := p0 in
-        Return (st1, tt))
-    end
-  end
-
-(** [betree_main::betree::{betree_main::betree::Node#5}::apply_messages]: backward function 0
-    Source: 'src/betree.rs', lines 588:4-593:5 *)
-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
-    | 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 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 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;
-        let (node0, node_id_cnt0) := p1 in
-        _ <-
-          betree_store_internal_node node0.(betree_Internal_id) content1 st1;
-        Return (Betree_Node_Internal node0, node_id_cnt0))
-      else (
-        _ <- betree_store_internal_node node.(betree_Internal_id) content0 st0;
-        Return (Betree_Node_Internal node, node_id_cnt))
+        Return (st2, (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 n0 content msgs;
-      len <- betree_List_len (u64 * u64) n0 content0;
+      let (st1, content) := p in
+      l <- betree_Node_apply_messages_to_leaf n1 content msgs;
+      len <- betree_List_len (u64 * u64) n1 l;
       i <- u64_mul 2%u64 params.(betree_Params_split_size);
       if len s>= i
       then (
-        p0 <- betree_Leaf_split n0 node content0 params node_id_cnt st0;
-        let (st1, new_node) := p0 in
-        _ <- 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 (Betree_Node_Internal new_node, node_id_cnt0))
+        p1 <- betree_Leaf_split n1 node l params node_id_cnt st1;
+        let (st2, p2) := p1 in
+        let (new_node, nic) := p2 in
+        p3 <- betree_store_leaf_node node.(betree_Leaf_id) Betree_List_Nil st2;
+        let (st3, _) := p3 in
+        Return (st3, (Betree_Node_Internal new_node, nic)))
       else (
-        _ <- betree_store_leaf_node node.(betree_Leaf_id) content0 st0;
-        Return (Betree_Node_Leaf
+        p1 <- betree_store_leaf_node node.(betree_Leaf_id) l st1;
+        let (st2, _) := p1 in
+        Return (st2, (Betree_Node_Leaf
           {| betree_Leaf_id := node.(betree_Leaf_id); betree_Leaf_size := len
-          |}, node_id_cnt))
+          |}, node_id_cnt)))
     end
   end
 .
 
-(** [betree_main::betree::{betree_main::betree::Node#5}::apply]: forward function
+(** [betree_main::betree::{betree_main::betree::Node#5}::apply]:
     Source: 'src/betree.rs', lines 576:4-582:5 *)
 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)
+  result (state * (betree_Node_t * betree_NodeIdCounter_t))
   :=
-  let l := Betree_List_Nil in
   p <-
     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 (Betree_List_Cons
-      (key, new_msg) l) st;
-  Return (st0, tt)
+      (key, new_msg) Betree_List_Nil) st;
+  let (st1, p1) := p in
+  let (self1, node_id_cnt1) := p1 in
+  Return (st1, (self1, node_id_cnt1))
 .
 
-(** [betree_main::betree::{betree_main::betree::Node#5}::apply]: backward function 0
-    Source: 'src/betree.rs', lines 576:4-582:5 *)
-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 := 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_main::betree::BeTree#6}::new]: forward function
+(** [betree_main::betree::{betree_main::betree::BeTree#6}::new]:
     Source: 'src/betree.rs', lines 849:4-849:60 *)
 Definition betree_BeTree_new
   (min_flush_size : u64) (split_size : u64) (st : state) :
   result (state * betree_BeTree_t)
   :=
   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_NodeIdCounter_fresh_id_back node_id_cnt;
-  Return (st0,
+  p <- betree_NodeIdCounter_fresh_id node_id_cnt;
+  let (id, nic) := p in
+  p1 <- betree_store_leaf_node id Betree_List_Nil st;
+  let (st1, _) := p1 in
+  Return (st1,
     {|
       betree_BeTree_params :=
         {|
           betree_Params_min_flush_size := min_flush_size;
           betree_Params_split_size := split_size
         |};
-      betree_BeTree_node_id_cnt := node_id_cnt0;
+      betree_BeTree_node_id_cnt := nic;
       betree_BeTree_root :=
         (Betree_Node_Leaf
           {| betree_Leaf_id := id; betree_Leaf_size := 0%u64 |})
     |})
 .
 
-(** [betree_main::betree::{betree_main::betree::BeTree#6}::apply]: forward function
+(** [betree_main::betree::{betree_main::betree::BeTree#6}::apply]:
     Source: 'src/betree.rs', lines 868:4-868:47 *)
 Definition betree_BeTree_apply
   (n : nat) (self : betree_BeTree_t) (key : u64) (msg : betree_Message_t)
   (st : state) :
-  result (state * unit)
+  result (state * betree_BeTree_t)
   :=
   p <-
     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_BeTree_root)
-      self.(betree_BeTree_params) self.(betree_BeTree_node_id_cnt) key msg st;
-  Return (st0, tt)
-.
-
-(** [betree_main::betree::{betree_main::betree::BeTree#6}::apply]: backward function 0
-    Source: 'src/betree.rs', lines 868:4-868:47 *)
-Definition betree_BeTree_apply_back
-  (n : nat) (self : betree_BeTree_t) (key : u64) (msg : betree_Message_t)
-  (st : state) :
-  result betree_BeTree_t
-  :=
-  p <-
-    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
+  let (st1, p1) := p in
+  let (n1, nic) := p1 in
+  Return (st1,
     {|
       betree_BeTree_params := self.(betree_BeTree_params);
       betree_BeTree_node_id_cnt := nic;
-      betree_BeTree_root := n0
-    |}
+      betree_BeTree_root := n1
+    |})
 .
 
-(** [betree_main::betree::{betree_main::betree::BeTree#6}::insert]: forward function
+(** [betree_main::betree::{betree_main::betree::BeTree#6}::insert]:
     Source: 'src/betree.rs', lines 874:4-874:52 *)
 Definition betree_BeTree_insert
   (n : nat) (self : betree_BeTree_t) (key : u64) (value : u64) (st : state) :
-  result (state * unit)
-  :=
-  p <- betree_BeTree_apply n self key (Betree_Message_Insert value) st;
-  let (st0, _) := p in
-  _ <- betree_BeTree_apply_back n self key (Betree_Message_Insert value) st;
-  Return (st0, tt)
-.
-
-(** [betree_main::betree::{betree_main::betree::BeTree#6}::insert]: backward function 0
-    Source: 'src/betree.rs', lines 874:4-874:52 *)
-Definition betree_BeTree_insert_back
-  (n : nat) (self : betree_BeTree_t) (key : u64) (value : u64) (st : state) :
-  result betree_BeTree_t
+  result (state * betree_BeTree_t)
   :=
-  betree_BeTree_apply_back n self key (Betree_Message_Insert value) st
+  betree_BeTree_apply n self key (Betree_Message_Insert value) st
 .
 
-(** [betree_main::betree::{betree_main::betree::BeTree#6}::delete]: forward function
+(** [betree_main::betree::{betree_main::betree::BeTree#6}::delete]:
     Source: 'src/betree.rs', lines 880:4-880:38 *)
 Definition betree_BeTree_delete
   (n : nat) (self : betree_BeTree_t) (key : u64) (st : state) :
-  result (state * unit)
-  :=
-  p <- betree_BeTree_apply n self key Betree_Message_Delete st;
-  let (st0, _) := p in
-  _ <- betree_BeTree_apply_back n self key Betree_Message_Delete st;
-  Return (st0, tt)
-.
-
-(** [betree_main::betree::{betree_main::betree::BeTree#6}::delete]: backward function 0
-    Source: 'src/betree.rs', lines 880:4-880:38 *)
-Definition betree_BeTree_delete_back
-  (n : nat) (self : betree_BeTree_t) (key : u64) (st : state) :
-  result betree_BeTree_t
+  result (state * betree_BeTree_t)
   :=
-  betree_BeTree_apply_back n self key Betree_Message_Delete st
+  betree_BeTree_apply n self key Betree_Message_Delete st
 .
 
-(** [betree_main::betree::{betree_main::betree::BeTree#6}::upsert]: forward function
+(** [betree_main::betree::{betree_main::betree::BeTree#6}::upsert]:
     Source: 'src/betree.rs', lines 886:4-886:59 *)
 Definition betree_BeTree_upsert
   (n : nat) (self : betree_BeTree_t) (key : u64)
   (upd : betree_UpsertFunState_t) (st : state) :
-  result (state * unit)
-  :=
-  p <- betree_BeTree_apply n self key (Betree_Message_Upsert upd) st;
-  let (st0, _) := p in
-  _ <- betree_BeTree_apply_back n self key (Betree_Message_Upsert upd) st;
-  Return (st0, tt)
-.
-
-(** [betree_main::betree::{betree_main::betree::BeTree#6}::upsert]: backward function 0
-    Source: 'src/betree.rs', lines 886:4-886:59 *)
-Definition betree_BeTree_upsert_back
-  (n : nat) (self : betree_BeTree_t) (key : u64)
-  (upd : betree_UpsertFunState_t) (st : state) :
-  result betree_BeTree_t
+  result (state * betree_BeTree_t)
   :=
-  betree_BeTree_apply_back n self key (Betree_Message_Upsert upd) st
+  betree_BeTree_apply n self key (Betree_Message_Upsert upd) st
 .
 
-(** [betree_main::betree::{betree_main::betree::BeTree#6}::lookup]: forward function
+(** [betree_main::betree::{betree_main::betree::BeTree#6}::lookup]:
     Source: 'src/betree.rs', lines 895:4-895:62 *)
 Definition betree_BeTree_lookup
   (n : nat) (self : betree_BeTree_t) (key : u64) (st : state) :
-  result (state * (option u64))
-  :=
-  betree_Node_lookup n self.(betree_BeTree_root) key st
-.
-
-(** [betree_main::betree::{betree_main::betree::BeTree#6}::lookup]: backward function 0
-    Source: 'src/betree.rs', lines 895:4-895:62 *)
-Definition betree_BeTree_lookup_back
-  (n : nat) (self : betree_BeTree_t) (key : u64) (st : state) :
-  result betree_BeTree_t
+  result (state * ((option u64) * betree_BeTree_t))
   :=
-  n0 <- betree_Node_lookup_back n self.(betree_BeTree_root) key st;
-  Return
+  p <- betree_Node_lookup n self.(betree_BeTree_root) key st;
+  let (st1, p1) := p in
+  let (o, n1) := p1 in
+  Return (st1, (o,
     {|
       betree_BeTree_params := self.(betree_BeTree_params);
       betree_BeTree_node_id_cnt := self.(betree_BeTree_node_id_cnt);
-      betree_BeTree_root := n0
-    |}
+      betree_BeTree_root := n1
+    |}))
 .
 
-(** [betree_main::main]: forward function
+(** [betree_main::main]:
     Source: 'src/betree_main.rs', lines 5:0-5:9 *)
 Definition main : result unit :=
   Return tt.
diff --git a/tests/coq/betree/BetreeMain_FunsExternal_Template.v b/tests/coq/betree/BetreeMain_FunsExternal_Template.v
index 36022a20..a9969448 100644
--- a/tests/coq/betree/BetreeMain_FunsExternal_Template.v
+++ b/tests/coq/betree/BetreeMain_FunsExternal_Template.v
@@ -11,13 +11,13 @@ Require Import BetreeMain_Types.
 Include BetreeMain_Types.
 Module BetreeMain_FunsExternal_Template.
 
-(** [betree_main::betree_utils::load_internal_node]: forward function
+(** [betree_main::betree_utils::load_internal_node]:
     Source: 'src/betree_utils.rs', lines 98:0-98:63 *)
 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
+(** [betree_main::betree_utils::store_internal_node]:
     Source: 'src/betree_utils.rs', lines 115:0-115:71 *)
 Axiom betree_utils_store_internal_node
   :
@@ -25,19 +25,19 @@ Axiom betree_utils_store_internal_node
     unit)
 .
 
-(** [betree_main::betree_utils::load_leaf_node]: forward function
+(** [betree_main::betree_utils::load_leaf_node]:
     Source: 'src/betree_utils.rs', lines 132:0-132:55 *)
 Axiom betree_utils_load_leaf_node
   : u64 -> state -> result (state * (betree_List_t (u64 * u64)))
 .
 
-(** [betree_main::betree_utils::store_leaf_node]: forward function
+(** [betree_main::betree_utils::store_leaf_node]:
     Source: 'src/betree_utils.rs', lines 145:0-145:63 *)
 Axiom betree_utils_store_leaf_node
   : u64 -> betree_List_t (u64 * u64) -> state -> result (state * unit)
 .
 
-(** [core::option::{core::option::Option<T>}::unwrap]: forward function
+(** [core::option::{core::option::Option<T>}::unwrap]:
     Source: '/rustc/d59363ad0b6391b7fc5bbb02c9ccf9300eef3753/library/core/src/option.rs', lines 932:4-932:34 *)
 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 22989256..acbc2085 100644
--- a/tests/coq/betree/BetreeMain_Types.v
+++ b/tests/coq/betree/BetreeMain_Types.v
@@ -61,31 +61,31 @@ with betree_Node_t :=
 .
 
 Definition betree_Internal_id (x : betree_Internal_t) :=
-  match x with | mkbetree_Internal_t x0 _ _ _ => x0 end
+  match x with | mkbetree_Internal_t x1 _ _ _ => x1 end
 .
 
-Notation "x1 .(betree_Internal_id)" := (betree_Internal_id x1) (at level 9).
+Notation "x2 .(betree_Internal_id)" := (betree_Internal_id x2) (at level 9).
 
 Definition betree_Internal_pivot (x : betree_Internal_t) :=
-  match x with | mkbetree_Internal_t _ x0 _ _ => x0 end
+  match x with | mkbetree_Internal_t _ x1 _ _ => x1 end
 .
 
-Notation "x1 .(betree_Internal_pivot)" := (betree_Internal_pivot x1)
+Notation "x2 .(betree_Internal_pivot)" := (betree_Internal_pivot x2)
   (at level 9)
 .
 
 Definition betree_Internal_left (x : betree_Internal_t) :=
-  match x with | mkbetree_Internal_t _ _ x0 _ => x0 end
+  match x with | mkbetree_Internal_t _ _ x1 _ => x1 end
 .
 
-Notation "x1 .(betree_Internal_left)" := (betree_Internal_left x1) (at level 9)
+Notation "x2 .(betree_Internal_left)" := (betree_Internal_left x2) (at level 9)
 .
 
 Definition betree_Internal_right (x : betree_Internal_t) :=
-  match x with | mkbetree_Internal_t _ _ _ x0 => x0 end
+  match x with | mkbetree_Internal_t _ _ _ x1 => x1 end
 .
 
-Notation "x1 .(betree_Internal_right)" := (betree_Internal_right x1)
+Notation "x2 .(betree_Internal_right)" := (betree_Internal_right x2)
   (at level 9)
 .
 
diff --git a/tests/coq/betree/Primitives.v b/tests/coq/betree/Primitives.v
index 84280b96..990e27e4 100644
--- a/tests/coq/betree/Primitives.v
+++ b/tests/coq/betree/Primitives.v
@@ -67,8 +67,7 @@ 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 .
+Definition core_mem_replace (a : Type) (x : a) (y : a) : a * a := (x, x) .
 
 Record mut_raw_ptr (T : Type) := { mut_raw_ptr_v : T }.
 Record const_raw_ptr (T : Type) := { const_raw_ptr_v : T }.
@@ -504,13 +503,15 @@ 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;
+  core_ops_index_IndexMut_index_mut :
+    Self ->
+    Idx ->
+    result (core_ops_index_IndexMut_indexInst.(core_ops_index_Index_Output) *
+            (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 {
@@ -524,13 +525,14 @@ 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;
+  core_ops_deref_DerefMut_deref_mut :
+    Self ->
+    result (core_ops_deref_DerefMut_derefInst.(core_ops_deref_Deref_target) *
+            (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;
@@ -543,8 +545,8 @@ 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.
+Definition alloc_boxed_Box_deref_mut (T : Type) (x : T) : result (T * (T -> result T)) :=
+  Return (x, fun x => Return x).
 
 (* Trait instance *)
 Definition alloc_boxed_Box_coreopsDerefInst (Self : Type) : core_ops_deref_Deref Self := {|
@@ -556,7 +558,6 @@ Definition alloc_boxed_Box_coreopsDerefInst (Self : Type) : core_ops_deref_Deref
 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;
 |}.
 
 
@@ -584,6 +585,13 @@ 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).
 
+Definition array_index_mut_usize (T : Type) (n : usize) (a : array T n) (i : usize) :
+  result (T * (T -> result (array T n))) :=
+  match array_index_usize T n a i with
+  | Fail_ e => Fail_ e
+  | Return x => Return (x, array_update_usize T n a i)
+  end.
+
 (*** Slice *)
 Definition slice T := { l: list T | Z.of_nat (length l) <= usize_max}.
 
@@ -591,11 +599,25 @@ 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).
 
+Definition slice_index_mut_usize (T : Type) (s : slice T) (i : usize) :
+  result (T * (T -> result (slice T))) :=
+  match slice_index_usize T s i with
+  | Fail_ e => Fail_ e
+  | Return x => Return (x, slice_update_usize T s i)
+  end.
+
 (*** 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).
 
+Definition array_to_slice_mut (T : Type) (n : usize) (a : array T n) :
+  result (slice T * (slice T -> result (array T n))) :=
+  match array_to_slice T n a with
+  | Fail_ e => Fail_ e
+  | Return x => Return (x, array_from_slice T n a)
+  end.
+
 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).
 
@@ -639,16 +661,9 @@ Definition alloc_vec_Vec_bind {A B} (v: alloc_vec_Vec A) (f: list A -> result (l
   | 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)
@@ -661,6 +676,14 @@ Axiom alloc_vec_Vec_index_usize : forall {T : Type} (v : alloc_vec_Vec T) (i : u
 (* Helper *)
 Axiom alloc_vec_Vec_update_usize : forall {T : Type} (v : alloc_vec_Vec T) (i : usize) (x : T), result (alloc_vec_Vec T).
 
+Definition alloc_vec_Vec_index_mut_usize {T : Type} (v: alloc_vec_Vec T) (i: usize) :
+  result (T * (T -> result (alloc_vec_Vec T))) :=
+  match alloc_vec_Vec_index_usize v i with
+  | Return x =>
+    Return (x, alloc_vec_Vec_update_usize v i)
+  | Fail_ e => Fail_ e
+  end.
+
 (* Trait declaration: [core::slice::index::private_slice_index::Sealed] *)
 Definition core_slice_index_private_slice_index_Sealed (self : Type) := unit.
 
@@ -669,25 +692,23 @@ Record core_slice_index_SliceIndex (Self T : Type) := mk_core_slice_index_SliceI
   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_mut :
+    Self -> T -> result (option core_slice_index_SliceIndex_Output * (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;
+  core_slice_index_SliceIndex_index_mut :
+    Self -> T -> result (core_slice_index_SliceIndex_Output * (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
@@ -704,11 +725,9 @@ Axiom core_slice_index_RangeUsize_get : forall (T : Type) (i : core_ops_range_Ra
 
 (* [core::slice::index::Range::get_mut]: forward function *)
 Axiom core_slice_index_RangeUsize_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_RangeUsize_get_mut_back :
-  forall (T : Type), core_ops_range_Range usize -> slice T -> option (slice T) -> result (slice T).
+  forall (T : Type),
+    core_ops_range_Range usize -> slice T ->
+    result (option (slice T) * (option (slice T) -> result (slice T))).
 
 (* [core::slice::index::Range::get_unchecked]: forward function *)
 Definition core_slice_index_RangeUsize_get_unchecked
@@ -732,21 +751,14 @@ Axiom core_slice_index_RangeUsize_index :
 
 (* [core::slice::index::Range::index_mut]: forward function *)
 Axiom core_slice_index_RangeUsize_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_RangeUsize_index_mut_back :
-  forall (T : Type), core_ops_range_Range usize -> slice T -> slice T -> result (slice T).
+  forall (T : Type), core_ops_range_Range usize -> slice T -> result (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).
+  slice T -> Idx ->
+  result (inst.(core_slice_index_SliceIndex_Output) *
+          (inst.(core_slice_index_SliceIndex_Output) -> result (slice T))).
 
 (* [core::array::[T; N]::index]: forward function *)
 Axiom core_array_Array_index :
@@ -756,12 +768,9 @@ Axiom core_array_Array_index :
 (* [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).
+  (a : array T N) (i : Idx),
+  result (inst.(core_ops_index_IndexMut_indexInst).(core_ops_index_Index_Output) *
+          (inst.(core_ops_index_IndexMut_indexInst).(core_ops_index_Index_Output) -> result (array T N))).
 
 (* Trait implementation: [core::slice::index::private_slice_index::Range] *)
 Definition core_slice_index_private_slice_index_SealedRangeUsizeInst
@@ -774,12 +783,10 @@ Definition core_slice_index_SliceIndexRangeUsizeSliceTInst (T : Type) :
   core_slice_index_SliceIndex_Output := slice T;
   core_slice_index_SliceIndex_get := core_slice_index_RangeUsize_get T;
   core_slice_index_SliceIndex_get_mut := core_slice_index_RangeUsize_get_mut T;
-  core_slice_index_SliceIndex_get_mut_back := core_slice_index_RangeUsize_get_mut_back T;
   core_slice_index_SliceIndex_get_unchecked := core_slice_index_RangeUsize_get_unchecked T;
   core_slice_index_SliceIndex_get_unchecked_mut := core_slice_index_RangeUsize_get_unchecked_mut T;
   core_slice_index_SliceIndex_index := core_slice_index_RangeUsize_index T;
   core_slice_index_SliceIndex_index_mut := core_slice_index_RangeUsize_index_mut T;
-  core_slice_index_SliceIndex_index_mut_back := core_slice_index_RangeUsize_index_mut_back T;
 |}.
 
 (* Trait implementation: [core::slice::index::[T]] *)
@@ -796,7 +803,6 @@ Definition core_ops_index_IndexMutSliceTIInst (T Idx : Type)
   core_ops_index_IndexMut (slice T) Idx := {|
   core_ops_index_IndexMut_indexInst := core_ops_index_IndexSliceTIInst 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]] *)
@@ -813,18 +819,14 @@ Definition core_ops_index_IndexMutArrayInst (T Idx : Type) (N : usize)
   core_ops_index_IndexMut (array T N) Idx := {|
   core_ops_index_IndexMut_indexInst := core_ops_index_IndexArrayInst 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).
+Axiom core_slice_index_usize_get_mut :
+  forall (T : Type), usize -> slice T -> result (option T * (option T -> result (slice T))).
 
 (* [core::slice::index::usize::get_unchecked]: forward function *)
 Axiom core_slice_index_usize_get_unchecked :
@@ -838,11 +840,8 @@ Axiom core_slice_index_usize_get_unchecked_mut :
 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).
+Axiom core_slice_index_usize_index_mut :
+  forall (T : Type), usize -> slice T -> result (T * (T -> result (slice T))).
 
 (* Trait implementation: [core::slice::index::private_slice_index::usize] *)
 Definition core_slice_index_private_slice_index_SealedUsizeInst
@@ -855,12 +854,10 @@ Definition core_slice_index_SliceIndexUsizeSliceTInst (T : Type) :
   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 *)
@@ -869,12 +866,9 @@ Axiom alloc_vec_Vec_index : forall (T Idx : Type) (inst : core_slice_index_Slice
 
 (* [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).
+  (Self : alloc_vec_Vec T) (i : Idx),
+  result (inst.(core_slice_index_SliceIndex_Output) *
+          (inst.(core_slice_index_SliceIndex_Output) -> result (alloc_vec_Vec T))).
 
 (* Trait implementation: [alloc::vec::Vec] *)
 Definition alloc_vec_Vec_coreopsindexIndexInst (T Idx : Type)
@@ -890,7 +884,6 @@ Definition alloc_vec_Vec_coreopsindexIndexMutInst (T Idx : Type)
   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 *)
@@ -901,10 +894,6 @@ Axiom alloc_vec_Vec_index_eq : forall {a : Type} (v : alloc_vec_Vec a) (i : usiz
 
 Axiom alloc_vec_Vec_index_mut_eq : forall {a : Type} (v : alloc_vec_Vec a) (i : usize) (x : a),
   alloc_vec_Vec_index_mut a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i =
-    alloc_vec_Vec_index_usize v i.
-
-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_SliceIndexUsizeSliceTInst a) v i x =
-    alloc_vec_Vec_update_usize v i x.
+    alloc_vec_Vec_index_mut_usize v i.
 
 End Primitives.
diff --git a/tests/coq/hashmap/Hashmap_Funs.v b/tests/coq/hashmap/Hashmap_Funs.v
index 64de44a6..0478edbe 100644
--- a/tests/coq/hashmap/Hashmap_Funs.v
+++ b/tests/coq/hashmap/Hashmap_Funs.v
@@ -10,66 +10,64 @@ Require Import Hashmap_Types.
 Include Hashmap_Types.
 Module Hashmap_Funs.
 
-(** [hashmap::hash_key]: forward function
+(** [hashmap::hash_key]:
     Source: 'src/hashmap.rs', lines 27:0-27:32 *)
 Definition hash_key (k : usize) : result usize :=
   Return k.
 
-(** [hashmap::{hashmap::HashMap<T>}::allocate_slots]: loop 0: forward function
+(** [hashmap::{hashmap::HashMap<T>}::allocate_slots]: loop 0:
     Source: 'src/hashmap.rs', lines 50:4-56:5 *)
 Fixpoint hashMap_allocate_slots_loop
-  (T : Type) (n : nat) (slots : alloc_vec_Vec (List_t T)) (n0 : usize) :
+  (T : Type) (n : nat) (slots : alloc_vec_Vec (List_t T)) (n1 : usize) :
   result (alloc_vec_Vec (List_t T))
   :=
   match n with
   | O => Fail_ OutOfFuel
-  | S n1 =>
-    if n0 s> 0%usize
+  | S n2 =>
+    if n1 s> 0%usize
     then (
-      slots0 <- alloc_vec_Vec_push (List_t T) slots List_Nil;
-      n2 <- usize_sub n0 1%usize;
-      hashMap_allocate_slots_loop T n1 slots0 n2)
+      v <- alloc_vec_Vec_push (List_t T) slots List_Nil;
+      n3 <- usize_sub n1 1%usize;
+      hashMap_allocate_slots_loop T n2 v n3)
     else Return slots
   end
 .
 
-(** [hashmap::{hashmap::HashMap<T>}::allocate_slots]: forward function
+(** [hashmap::{hashmap::HashMap<T>}::allocate_slots]:
     Source: 'src/hashmap.rs', lines 50:4-50:76 *)
 Definition hashMap_allocate_slots
-  (T : Type) (n : nat) (slots : alloc_vec_Vec (List_t T)) (n0 : usize) :
+  (T : Type) (n : nat) (slots : alloc_vec_Vec (List_t T)) (n1 : usize) :
   result (alloc_vec_Vec (List_t T))
   :=
-  hashMap_allocate_slots_loop T n slots n0
+  hashMap_allocate_slots_loop T n slots n1
 .
 
-(** [hashmap::{hashmap::HashMap<T>}::new_with_capacity]: forward function
+(** [hashmap::{hashmap::HashMap<T>}::new_with_capacity]:
     Source: 'src/hashmap.rs', lines 59:4-63:13 *)
 Definition hashMap_new_with_capacity
   (T : Type) (n : nat) (capacity : usize) (max_load_dividend : usize)
   (max_load_divisor : usize) :
   result (HashMap_t T)
   :=
-  let v := alloc_vec_Vec_new (List_t T) in
-  slots <- hashMap_allocate_slots T n v capacity;
+  slots <- hashMap_allocate_slots T n (alloc_vec_Vec_new (List_t T)) capacity;
   i <- usize_mul capacity max_load_dividend;
-  i0 <- usize_div i max_load_divisor;
+  i1 <- usize_div i max_load_divisor;
   Return
     {|
       hashMap_num_entries := 0%usize;
       hashMap_max_load_factor := (max_load_dividend, max_load_divisor);
-      hashMap_max_load := i0;
+      hashMap_max_load := i1;
       hashMap_slots := slots
     |}
 .
 
-(** [hashmap::{hashmap::HashMap<T>}::new]: forward function
+(** [hashmap::{hashmap::HashMap<T>}::new]:
     Source: 'src/hashmap.rs', lines 75:4-75:24 *)
 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::HashMap<T>}::clear]: loop 0: merged forward/backward function
-    (there is a single backward function, and the forward function returns ())
+(** [hashmap::{hashmap::HashMap<T>}::clear]: loop 0:
     Source: 'src/hashmap.rs', lines 80:4-88:5 *)
 Fixpoint hashMap_clear_loop
   (T : Type) (n : nat) (slots : alloc_vec_Vec (List_t T)) (i : usize) :
@@ -77,101 +75,73 @@ Fixpoint hashMap_clear_loop
   :=
   match n with
   | O => Fail_ OutOfFuel
-  | S n0 =>
-    let i0 := alloc_vec_Vec_len (List_t T) slots in
-    if i s< i0
+  | S n1 =>
+    let i1 := alloc_vec_Vec_len (List_t T) slots in
+    if i s< i1
     then (
-      i1 <- usize_add i 1%usize;
-      slots0 <-
-        alloc_vec_Vec_index_mut_back (List_t T) usize
-          (core_slice_index_SliceIndexUsizeSliceTInst (List_t T)) slots i
-          List_Nil;
-      hashMap_clear_loop T n0 slots0 i1)
+      p <-
+        alloc_vec_Vec_index_mut (List_t T) usize
+          (core_slice_index_SliceIndexUsizeSliceTInst (List_t T)) slots i;
+      let (_, index_mut_back) := p in
+      i2 <- usize_add i 1%usize;
+      slots1 <- index_mut_back List_Nil;
+      hashMap_clear_loop T n1 slots1 i2)
     else Return slots
   end
 .
 
-(** [hashmap::{hashmap::HashMap<T>}::clear]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ())
+(** [hashmap::{hashmap::HashMap<T>}::clear]:
     Source: 'src/hashmap.rs', lines 80:4-80:27 *)
 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;
+  back <- hashMap_clear_loop T n self.(hashMap_slots) 0%usize;
   Return
     {|
       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_slots := back
     |}
 .
 
-(** [hashmap::{hashmap::HashMap<T>}::len]: forward function
+(** [hashmap::{hashmap::HashMap<T>}::len]:
     Source: 'src/hashmap.rs', lines 90:4-90:30 *)
 Definition hashMap_len (T : Type) (self : HashMap_t T) : result usize :=
   Return self.(hashMap_num_entries)
 .
 
-(** [hashmap::{hashmap::HashMap<T>}::insert_in_list]: loop 0: forward function
+(** [hashmap::{hashmap::HashMap<T>}::insert_in_list]: loop 0:
     Source: 'src/hashmap.rs', lines 97:4-114:5 *)
 Fixpoint hashMap_insert_in_list_loop
   (T : Type) (n : nat) (key : usize) (value : T) (ls : List_t T) :
-  result bool
+  result (bool * (List_t T))
   :=
   match n with
   | O => Fail_ OutOfFuel
-  | S n0 =>
+  | S n1 =>
     match ls with
     | List_Cons ckey cvalue tl =>
       if ckey s= key
-      then Return false
-      else hashMap_insert_in_list_loop T n0 key value tl
-    | List_Nil => Return true
+      then Return (false, List_Cons ckey value tl)
+      else (
+        p <- hashMap_insert_in_list_loop T n1 key value tl;
+        let (b, back) := p in
+        Return (b, List_Cons ckey cvalue back))
+    | List_Nil => Return (true, List_Cons key value List_Nil)
     end
   end
 .
 
-(** [hashmap::{hashmap::HashMap<T>}::insert_in_list]: forward function
+(** [hashmap::{hashmap::HashMap<T>}::insert_in_list]:
     Source: 'src/hashmap.rs', lines 97:4-97:71 *)
 Definition hashMap_insert_in_list
   (T : Type) (n : nat) (key : usize) (value : T) (ls : List_t T) :
-  result bool
+  result (bool * (List_t T))
   :=
   hashMap_insert_in_list_loop T n key value ls
 .
 
-(** [hashmap::{hashmap::HashMap<T>}::insert_in_list]: loop 0: backward function 0
-    Source: 'src/hashmap.rs', lines 97:4-114:5 *)
-Fixpoint hashMap_insert_in_list_loop_back
-  (T : Type) (n : nat) (key : usize) (value : T) (ls : List_t T) :
-  result (List_t T)
-  :=
-  match n with
-  | O => Fail_ OutOfFuel
-  | S n0 =>
-    match ls with
-    | List_Cons ckey cvalue tl =>
-      if ckey s= key
-      then Return (List_Cons ckey value tl)
-      else (
-        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::HashMap<T>}::insert_in_list]: backward function 0
-    Source: 'src/hashmap.rs', lines 97:4-97:71 *)
-Definition hashMap_insert_in_list_back
-  (T : Type) (n : nat) (key : usize) (value : T) (ls : List_t T) :
-  result (List_t T)
-  :=
-  hashMap_insert_in_list_loop_back T n key value ls
-.
-
-(** [hashmap::{hashmap::HashMap<T>}::insert_no_resize]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ())
+(** [hashmap::{hashmap::HashMap<T>}::insert_no_resize]:
     Source: 'src/hashmap.rs', lines 117:4-117:54 *)
 Definition hashMap_insert_no_resize
   (T : Type) (n : nat) (self : HashMap_t T) (key : usize) (value : T) :
@@ -180,32 +150,26 @@ Definition hashMap_insert_no_resize
   hash <- hash_key key;
   let i := alloc_vec_Vec_len (List_t T) self.(hashMap_slots) in
   hash_mod <- usize_rem hash i;
-  l <-
+  p <-
     alloc_vec_Vec_index_mut (List_t T) usize
       (core_slice_index_SliceIndexUsizeSliceTInst (List_t T))
       self.(hashMap_slots) hash_mod;
-  inserted <- hashMap_insert_in_list T n key value l;
+  let (l, index_mut_back) := p in
+  p1 <- hashMap_insert_in_list T n key value l;
+  let (inserted, l1) := p1 in
   if inserted
   then (
-    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_SliceIndexUsizeSliceTInst (List_t T))
-        self.(hashMap_slots) hash_mod l0;
+    i1 <- usize_add self.(hashMap_num_entries) 1%usize;
+    v <- index_mut_back l1;
     Return
       {|
-        hashMap_num_entries := i0;
+        hashMap_num_entries := i1;
         hashMap_max_load_factor := self.(hashMap_max_load_factor);
         hashMap_max_load := self.(hashMap_max_load);
         hashMap_slots := v
       |})
   else (
-    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_SliceIndexUsizeSliceTInst (List_t T))
-        self.(hashMap_slots) hash_mod l0;
+    v <- index_mut_back l1;
     Return
       {|
         hashMap_num_entries := self.(hashMap_num_entries);
@@ -215,8 +179,7 @@ Definition hashMap_insert_no_resize
       |})
 .
 
-(** [hashmap::{hashmap::HashMap<T>}::move_elements_from_list]: loop 0: merged forward/backward function
-    (there is a single backward function, and the forward function returns ())
+(** [hashmap::{hashmap::HashMap<T>}::move_elements_from_list]: loop 0:
     Source: 'src/hashmap.rs', lines 183:4-196:5 *)
 Fixpoint hashMap_move_elements_from_list_loop
   (T : Type) (n : nat) (ntable : HashMap_t T) (ls : List_t T) :
@@ -224,18 +187,17 @@ Fixpoint hashMap_move_elements_from_list_loop
   :=
   match n with
   | O => Fail_ OutOfFuel
-  | S n0 =>
+  | S n1 =>
     match ls with
     | 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
+      hm <- hashMap_insert_no_resize T n1 ntable k v;
+      hashMap_move_elements_from_list_loop T n1 hm tl
     | List_Nil => Return ntable
     end
   end
 .
 
-(** [hashmap::{hashmap::HashMap<T>}::move_elements_from_list]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ())
+(** [hashmap::{hashmap::HashMap<T>}::move_elements_from_list]:
     Source: 'src/hashmap.rs', lines 183:4-183:72 *)
 Definition hashMap_move_elements_from_list
   (T : Type) (n : nat) (ntable : HashMap_t T) (ls : List_t T) :
@@ -244,8 +206,7 @@ Definition hashMap_move_elements_from_list
   hashMap_move_elements_from_list_loop T n ntable ls
 .
 
-(** [hashmap::{hashmap::HashMap<T>}::move_elements]: loop 0: merged forward/backward function
-    (there is a single backward function, and the forward function returns ())
+(** [hashmap::{hashmap::HashMap<T>}::move_elements]: loop 0:
     Source: 'src/hashmap.rs', lines 171:4-180:5 *)
 Fixpoint hashMap_move_elements_loop
   (T : Type) (n : nat) (ntable : HashMap_t T)
@@ -254,108 +215,105 @@ Fixpoint hashMap_move_elements_loop
   :=
   match n with
   | O => Fail_ OutOfFuel
-  | S n0 =>
-    let i0 := alloc_vec_Vec_len (List_t T) slots in
-    if i s< i0
+  | S n1 =>
+    let i1 := alloc_vec_Vec_len (List_t T) slots in
+    if i s< i1
     then (
-      l <-
+      p <-
         alloc_vec_Vec_index_mut (List_t T) usize
           (core_slice_index_SliceIndexUsizeSliceTInst (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 := 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_SliceIndexUsizeSliceTInst (List_t T)) slots i l0;
-      hashMap_move_elements_loop T n0 ntable0 slots0 i1)
+      let (l, index_mut_back) := p in
+      let (ls, l1) := core_mem_replace (List_t T) l List_Nil in
+      hm <- hashMap_move_elements_from_list T n1 ntable ls;
+      i2 <- usize_add i 1%usize;
+      slots1 <- index_mut_back l1;
+      back_'a <- hashMap_move_elements_loop T n1 hm slots1 i2;
+      let (hm1, v) := back_'a in
+      Return (hm1, v))
     else Return (ntable, slots)
   end
 .
 
-(** [hashmap::{hashmap::HashMap<T>}::move_elements]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ())
+(** [hashmap::{hashmap::HashMap<T>}::move_elements]:
     Source: 'src/hashmap.rs', lines 171:4-171:95 *)
 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)))
   :=
-  hashMap_move_elements_loop T n ntable slots i
+  back_'a <- hashMap_move_elements_loop T n ntable slots i;
+  let (hm, v) := back_'a in
+  Return (hm, v)
 .
 
-(** [hashmap::{hashmap::HashMap<T>}::try_resize]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ())
+(** [hashmap::{hashmap::HashMap<T>}::try_resize]:
     Source: 'src/hashmap.rs', lines 140:4-140:28 *)
 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.(hashMap_max_load_factor) in
-  i1 <- usize_div n1 i;
-  if capacity s<= i1
+  let (i, i1) := self.(hashMap_max_load_factor) in
+  i2 <- usize_div n1 i;
+  if capacity s<= i2
   then (
-    i2 <- usize_mul capacity 2%usize;
-    ntable <- hashMap_new_with_capacity T n i2 i i0;
+    i3 <- usize_mul capacity 2%usize;
+    ntable <- hashMap_new_with_capacity T n i3 i i1;
     p <- hashMap_move_elements T n ntable self.(hashMap_slots) 0%usize;
-    let (ntable0, _) := p in
+    let (ntable1, _) := p in
     Return
       {|
         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)
+        hashMap_max_load_factor := (i, i1);
+        hashMap_max_load := ntable1.(hashMap_max_load);
+        hashMap_slots := ntable1.(hashMap_slots)
       |})
   else
     Return
       {|
         hashMap_num_entries := self.(hashMap_num_entries);
-        hashMap_max_load_factor := (i, i0);
+        hashMap_max_load_factor := (i, i1);
         hashMap_max_load := self.(hashMap_max_load);
         hashMap_slots := self.(hashMap_slots)
       |}
 .
 
-(** [hashmap::{hashmap::HashMap<T>}::insert]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ())
+(** [hashmap::{hashmap::HashMap<T>}::insert]:
     Source: 'src/hashmap.rs', lines 129:4-129:48 *)
 Definition hashMap_insert
   (T : Type) (n : nat) (self : HashMap_t T) (key : usize) (value : T) :
   result (HashMap_t T)
   :=
-  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
+  hm <- hashMap_insert_no_resize T n self key value;
+  i <- hashMap_len T hm;
+  if i s> hm.(hashMap_max_load) then hashMap_try_resize T n hm else Return hm
 .
 
-(** [hashmap::{hashmap::HashMap<T>}::contains_key_in_list]: loop 0: forward function
+(** [hashmap::{hashmap::HashMap<T>}::contains_key_in_list]: loop 0:
     Source: 'src/hashmap.rs', lines 206:4-219:5 *)
 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 =>
+  | S n1 =>
     match ls with
-    | List_Cons ckey t tl =>
+    | List_Cons ckey _ tl =>
       if ckey s= key
       then Return true
-      else hashMap_contains_key_in_list_loop T n0 key tl
+      else hashMap_contains_key_in_list_loop T n1 key tl
     | List_Nil => Return false
     end
   end
 .
 
-(** [hashmap::{hashmap::HashMap<T>}::contains_key_in_list]: forward function
+(** [hashmap::{hashmap::HashMap<T>}::contains_key_in_list]:
     Source: 'src/hashmap.rs', lines 206:4-206:68 *)
 Definition hashMap_contains_key_in_list
   (T : Type) (n : nat) (key : usize) (ls : List_t T) : result bool :=
   hashMap_contains_key_in_list_loop T n key ls
 .
 
-(** [hashmap::{hashmap::HashMap<T>}::contains_key]: forward function
+(** [hashmap::{hashmap::HashMap<T>}::contains_key]:
     Source: 'src/hashmap.rs', lines 199:4-199:49 *)
 Definition hashMap_contains_key
   (T : Type) (n : nat) (self : HashMap_t T) (key : usize) : result bool :=
@@ -369,31 +327,31 @@ Definition hashMap_contains_key
   hashMap_contains_key_in_list T n key l
 .
 
-(** [hashmap::{hashmap::HashMap<T>}::get_in_list]: loop 0: forward function
+(** [hashmap::{hashmap::HashMap<T>}::get_in_list]: loop 0:
     Source: 'src/hashmap.rs', lines 224:4-237:5 *)
 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 =>
+  | S n1 =>
     match ls with
     | List_Cons ckey cvalue tl =>
       if ckey s= key
       then Return cvalue
-      else hashMap_get_in_list_loop T n0 key tl
+      else hashMap_get_in_list_loop T n1 key tl
     | List_Nil => Fail_ Failure
     end
   end
 .
 
-(** [hashmap::{hashmap::HashMap<T>}::get_in_list]: forward function
+(** [hashmap::{hashmap::HashMap<T>}::get_in_list]:
     Source: 'src/hashmap.rs', lines 224:4-224:70 *)
 Definition hashMap_get_in_list
   (T : Type) (n : nat) (key : usize) (ls : List_t T) : result T :=
   hashMap_get_in_list_loop T n key ls
 .
 
-(** [hashmap::{hashmap::HashMap<T>}::get]: forward function
+(** [hashmap::{hashmap::HashMap<T>}::get]:
     Source: 'src/hashmap.rs', lines 239:4-239:55 *)
 Definition hashMap_get
   (T : Type) (n : nat) (self : HashMap_t T) (key : usize) : result T :=
@@ -407,264 +365,187 @@ Definition hashMap_get
   hashMap_get_in_list T n key l
 .
 
-(** [hashmap::{hashmap::HashMap<T>}::get_mut_in_list]: loop 0: forward function
+(** [hashmap::{hashmap::HashMap<T>}::get_mut_in_list]: loop 0:
     Source: 'src/hashmap.rs', lines 245:4-254:5 *)
 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
-    | List_Cons ckey cvalue tl =>
-      if ckey s= key
-      then Return cvalue
-      else hashMap_get_mut_in_list_loop T n0 tl key
-    | List_Nil => Fail_ Failure
-    end
-  end
-.
-
-(** [hashmap::{hashmap::HashMap<T>}::get_mut_in_list]: forward function
-    Source: 'src/hashmap.rs', lines 245:4-245:86 *)
-Definition hashMap_get_mut_in_list
-  (T : Type) (n : nat) (ls : List_t T) (key : usize) : result T :=
-  hashMap_get_mut_in_list_loop T n ls key
-.
-
-(** [hashmap::{hashmap::HashMap<T>}::get_mut_in_list]: loop 0: backward function 0
-    Source: 'src/hashmap.rs', lines 245:4-254:5 *)
-Fixpoint hashMap_get_mut_in_list_loop_back
-  (T : Type) (n : nat) (ls : List_t T) (key : usize) (ret : T) :
-  result (List_t T)
+  (T : Type) (n : nat) (ls : List_t T) (key : usize) :
+  result (T * (T -> result (List_t T)))
   :=
   match n with
   | O => Fail_ OutOfFuel
-  | S n0 =>
+  | S n1 =>
     match ls with
     | List_Cons ckey cvalue tl =>
       if ckey s= key
-      then Return (List_Cons ckey ret tl)
+      then
+        let back_'a := fun (ret : T) => Return (List_Cons ckey ret tl) in
+        Return (cvalue, back_'a)
       else (
-        tl0 <- hashMap_get_mut_in_list_loop_back T n0 tl key ret;
-        Return (List_Cons ckey cvalue tl0))
+        p <- hashMap_get_mut_in_list_loop T n1 tl key;
+        let (t, back_'a) := p in
+        let back_'a1 :=
+          fun (ret : T) =>
+            tl1 <- back_'a ret; Return (List_Cons ckey cvalue tl1) in
+        Return (t, back_'a1))
     | List_Nil => Fail_ Failure
     end
   end
 .
 
-(** [hashmap::{hashmap::HashMap<T>}::get_mut_in_list]: backward function 0
+(** [hashmap::{hashmap::HashMap<T>}::get_mut_in_list]:
     Source: 'src/hashmap.rs', lines 245:4-245:86 *)
-Definition hashMap_get_mut_in_list_back
-  (T : Type) (n : nat) (ls : List_t T) (key : usize) (ret : T) :
-  result (List_t T)
+Definition hashMap_get_mut_in_list
+  (T : Type) (n : nat) (ls : List_t T) (key : usize) :
+  result (T * (T -> result (List_t T)))
   :=
-  hashMap_get_mut_in_list_loop_back T n ls key ret
+  p <- hashMap_get_mut_in_list_loop T n ls key;
+  let (t, back_'a) := p in
+  Return (t, back_'a)
 .
 
-(** [hashmap::{hashmap::HashMap<T>}::get_mut]: forward function
+(** [hashmap::{hashmap::HashMap<T>}::get_mut]:
     Source: 'src/hashmap.rs', lines 257:4-257:67 *)
 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 <-
-    alloc_vec_Vec_index_mut (List_t T) usize
-      (core_slice_index_SliceIndexUsizeSliceTInst (List_t T))
-      self.(hashMap_slots) hash_mod;
-  hashMap_get_mut_in_list T n l key
-.
-
-(** [hashmap::{hashmap::HashMap<T>}::get_mut]: backward function 0
-    Source: 'src/hashmap.rs', lines 257:4-257:67 *)
-Definition hashMap_get_mut_back
-  (T : Type) (n : nat) (self : HashMap_t T) (key : usize) (ret : T) :
-  result (HashMap_t T)
+  (T : Type) (n : nat) (self : HashMap_t T) (key : usize) :
+  result (T * (T -> result (HashMap_t 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 <-
+  p <-
     alloc_vec_Vec_index_mut (List_t T) usize
       (core_slice_index_SliceIndexUsizeSliceTInst (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_SliceIndexUsizeSliceTInst (List_t T))
-      self.(hashMap_slots) hash_mod l0;
-  Return
-    {|
-      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::HashMap<T>}::remove_from_list]: loop 0: forward function
+  let (l, index_mut_back) := p in
+  p1 <- hashMap_get_mut_in_list T n l key;
+  let (t, get_mut_in_list_back) := p1 in
+  let back_'a :=
+    fun (ret : T) =>
+      l1 <- get_mut_in_list_back ret;
+      v <- index_mut_back l1;
+      Return
+        {|
+          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
+        |} in
+  Return (t, back_'a)
+.
+
+(** [hashmap::{hashmap::HashMap<T>}::remove_from_list]: loop 0:
     Source: 'src/hashmap.rs', lines 265:4-291:5 *)
 Fixpoint hashMap_remove_from_list_loop
-  (T : Type) (n : nat) (key : usize) (ls : List_t T) : result (option T) :=
+  (T : Type) (n : nat) (key : usize) (ls : List_t T) :
+  result ((option T) * (List_t T))
+  :=
   match n with
   | O => Fail_ OutOfFuel
-  | S n0 =>
+  | S n1 =>
     match ls with
     | List_Cons ckey t tl =>
       if ckey s= key
       then
-        let mv_ls := core_mem_replace (List_t T) (List_Cons ckey t tl) List_Nil
-          in
+        let (mv_ls, _) :=
+          core_mem_replace (List_t T) (List_Cons ckey t tl) List_Nil in
         match mv_ls with
-        | List_Cons i cvalue tl0 => Return (Some cvalue)
+        | List_Cons _ cvalue tl1 => Return (Some cvalue, tl1)
         | List_Nil => Fail_ Failure
         end
-      else hashMap_remove_from_list_loop T n0 key tl
-    | List_Nil => Return None
+      else (
+        p <- hashMap_remove_from_list_loop T n1 key tl;
+        let (o, back) := p in
+        Return (o, List_Cons ckey t back))
+    | List_Nil => Return (None, List_Nil)
     end
   end
 .
 
-(** [hashmap::{hashmap::HashMap<T>}::remove_from_list]: forward function
+(** [hashmap::{hashmap::HashMap<T>}::remove_from_list]:
     Source: 'src/hashmap.rs', lines 265:4-265:69 *)
 Definition hashMap_remove_from_list
-  (T : Type) (n : nat) (key : usize) (ls : List_t T) : result (option T) :=
+  (T : Type) (n : nat) (key : usize) (ls : List_t T) :
+  result ((option T) * (List_t T))
+  :=
   hashMap_remove_from_list_loop T n key ls
 .
 
-(** [hashmap::{hashmap::HashMap<T>}::remove_from_list]: loop 0: backward function 1
-    Source: 'src/hashmap.rs', lines 265:4-291:5 *)
-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
-    | List_Cons ckey t tl =>
-      if ckey s= key
-      then
-        let mv_ls := core_mem_replace (List_t T) (List_Cons ckey t tl) List_Nil
-          in
-        match mv_ls with
-        | List_Cons i cvalue tl0 => Return tl0
-        | List_Nil => Fail_ Failure
-        end
-      else (
-        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::HashMap<T>}::remove_from_list]: backward function 1
-    Source: 'src/hashmap.rs', lines 265:4-265:69 *)
-Definition hashMap_remove_from_list_back
-  (T : Type) (n : nat) (key : usize) (ls : List_t T) : result (List_t T) :=
-  hashMap_remove_from_list_loop_back T n key ls
-.
-
-(** [hashmap::{hashmap::HashMap<T>}::remove]: forward function
+(** [hashmap::{hashmap::HashMap<T>}::remove]:
     Source: 'src/hashmap.rs', lines 294:4-294:52 *)
 Definition hashMap_remove
   (T : Type) (n : nat) (self : HashMap_t T) (key : usize) :
-  result (option 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 <-
-    alloc_vec_Vec_index_mut (List_t T) usize
-      (core_slice_index_SliceIndexUsizeSliceTInst (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.(hashMap_num_entries) 1%usize; Return (Some x0)
-  end
-.
-
-(** [hashmap::{hashmap::HashMap<T>}::remove]: backward function 0
-    Source: 'src/hashmap.rs', lines 294:4-294:52 *)
-Definition hashMap_remove_back
-  (T : Type) (n : nat) (self : HashMap_t T) (key : usize) :
-  result (HashMap_t T)
+  result ((option T) * (HashMap_t 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 <-
+  p <-
     alloc_vec_Vec_index_mut (List_t T) usize
       (core_slice_index_SliceIndexUsizeSliceTInst (List_t T))
       self.(hashMap_slots) hash_mod;
-  x <- hashMap_remove_from_list T n key l;
+  let (l, index_mut_back) := p in
+  p1 <- hashMap_remove_from_list T n key l;
+  let (x, l1) := p1 in
   match x with
   | None =>
-    l0 <- hashMap_remove_from_list_back T n key l;
-    v <-
-      alloc_vec_Vec_index_mut_back (List_t T) usize
-        (core_slice_index_SliceIndexUsizeSliceTInst (List_t T))
-        self.(hashMap_slots) hash_mod l0;
-    Return
+    v <- index_mut_back l1;
+    Return (None,
       {|
         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.(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_SliceIndexUsizeSliceTInst (List_t T))
-        self.(hashMap_slots) hash_mod l0;
-    Return
+      |})
+  | Some x1 =>
+    i1 <- usize_sub self.(hashMap_num_entries) 1%usize;
+    v <- index_mut_back l1;
+    Return (Some x1,
       {|
-        hashMap_num_entries := i0;
+        hashMap_num_entries := i1;
         hashMap_max_load_factor := self.(hashMap_max_load_factor);
         hashMap_max_load := self.(hashMap_max_load);
         hashMap_slots := v
-      |}
+      |})
   end
 .
 
-(** [hashmap::test1]: forward function
+(** [hashmap::test1]:
     Source: 'src/hashmap.rs', lines 315:0-315:10 *)
 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;
+  hm1 <- hashMap_insert u64 n hm 0%usize 42%u64;
+  hm2 <- hashMap_insert u64 n hm1 128%usize 18%u64;
+  hm3 <- hashMap_insert u64 n hm2 1024%usize 138%u64;
+  hm4 <- hashMap_insert u64 n hm3 1056%usize 256%u64;
+  i <- hashMap_get u64 n hm4 128%usize;
   if negb (i s= 18%u64)
   then Fail_ Failure
   else (
-    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)
+    p <- hashMap_get_mut u64 n hm4 1024%usize;
+    let (_, get_mut_back) := p in
+    hm5 <- get_mut_back 56%u64;
+    i1 <- hashMap_get u64 n hm5 1024%usize;
+    if negb (i1 s= 56%u64)
     then Fail_ Failure
     else (
-      x <- hashMap_remove u64 n hm4 1024%usize;
+      p1 <- hashMap_remove u64 n hm5 1024%usize;
+      let (x, hm6) := p1 in
       match x with
       | None => Fail_ Failure
-      | Some x0 =>
-        if negb (x0 s= 56%u64)
+      | Some x1 =>
+        if negb (x1 s= 56%u64)
         then Fail_ Failure
         else (
-          hm5 <- hashMap_remove_back u64 n hm4 1024%usize;
-          i1 <- hashMap_get u64 n hm5 0%usize;
-          if negb (i1 s= 42%u64)
+          i2 <- hashMap_get u64 n hm6 0%usize;
+          if negb (i2 s= 42%u64)
           then Fail_ Failure
           else (
-            i2 <- hashMap_get u64 n hm5 128%usize;
-            if negb (i2 s= 18%u64)
+            i3 <- hashMap_get u64 n hm6 128%usize;
+            if negb (i3 s= 18%u64)
             then Fail_ Failure
             else (
-              i3 <- hashMap_get u64 n hm5 1056%usize;
-              if negb (i3 s= 256%u64) then Fail_ Failure else Return tt)))
+              i4 <- hashMap_get u64 n hm6 1056%usize;
+              if negb (i4 s= 256%u64) then Fail_ Failure else Return tt)))
       end))
 .
 
diff --git a/tests/coq/hashmap/Primitives.v b/tests/coq/hashmap/Primitives.v
index 84280b96..990e27e4 100644
--- a/tests/coq/hashmap/Primitives.v
+++ b/tests/coq/hashmap/Primitives.v
@@ -67,8 +67,7 @@ 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 .
+Definition core_mem_replace (a : Type) (x : a) (y : a) : a * a := (x, x) .
 
 Record mut_raw_ptr (T : Type) := { mut_raw_ptr_v : T }.
 Record const_raw_ptr (T : Type) := { const_raw_ptr_v : T }.
@@ -504,13 +503,15 @@ 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;
+  core_ops_index_IndexMut_index_mut :
+    Self ->
+    Idx ->
+    result (core_ops_index_IndexMut_indexInst.(core_ops_index_Index_Output) *
+            (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 {
@@ -524,13 +525,14 @@ 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;
+  core_ops_deref_DerefMut_deref_mut :
+    Self ->
+    result (core_ops_deref_DerefMut_derefInst.(core_ops_deref_Deref_target) *
+            (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;
@@ -543,8 +545,8 @@ 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.
+Definition alloc_boxed_Box_deref_mut (T : Type) (x : T) : result (T * (T -> result T)) :=
+  Return (x, fun x => Return x).
 
 (* Trait instance *)
 Definition alloc_boxed_Box_coreopsDerefInst (Self : Type) : core_ops_deref_Deref Self := {|
@@ -556,7 +558,6 @@ Definition alloc_boxed_Box_coreopsDerefInst (Self : Type) : core_ops_deref_Deref
 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;
 |}.
 
 
@@ -584,6 +585,13 @@ 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).
 
+Definition array_index_mut_usize (T : Type) (n : usize) (a : array T n) (i : usize) :
+  result (T * (T -> result (array T n))) :=
+  match array_index_usize T n a i with
+  | Fail_ e => Fail_ e
+  | Return x => Return (x, array_update_usize T n a i)
+  end.
+
 (*** Slice *)
 Definition slice T := { l: list T | Z.of_nat (length l) <= usize_max}.
 
@@ -591,11 +599,25 @@ 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).
 
+Definition slice_index_mut_usize (T : Type) (s : slice T) (i : usize) :
+  result (T * (T -> result (slice T))) :=
+  match slice_index_usize T s i with
+  | Fail_ e => Fail_ e
+  | Return x => Return (x, slice_update_usize T s i)
+  end.
+
 (*** 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).
 
+Definition array_to_slice_mut (T : Type) (n : usize) (a : array T n) :
+  result (slice T * (slice T -> result (array T n))) :=
+  match array_to_slice T n a with
+  | Fail_ e => Fail_ e
+  | Return x => Return (x, array_from_slice T n a)
+  end.
+
 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).
 
@@ -639,16 +661,9 @@ Definition alloc_vec_Vec_bind {A B} (v: alloc_vec_Vec A) (f: list A -> result (l
   | 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)
@@ -661,6 +676,14 @@ Axiom alloc_vec_Vec_index_usize : forall {T : Type} (v : alloc_vec_Vec T) (i : u
 (* Helper *)
 Axiom alloc_vec_Vec_update_usize : forall {T : Type} (v : alloc_vec_Vec T) (i : usize) (x : T), result (alloc_vec_Vec T).
 
+Definition alloc_vec_Vec_index_mut_usize {T : Type} (v: alloc_vec_Vec T) (i: usize) :
+  result (T * (T -> result (alloc_vec_Vec T))) :=
+  match alloc_vec_Vec_index_usize v i with
+  | Return x =>
+    Return (x, alloc_vec_Vec_update_usize v i)
+  | Fail_ e => Fail_ e
+  end.
+
 (* Trait declaration: [core::slice::index::private_slice_index::Sealed] *)
 Definition core_slice_index_private_slice_index_Sealed (self : Type) := unit.
 
@@ -669,25 +692,23 @@ Record core_slice_index_SliceIndex (Self T : Type) := mk_core_slice_index_SliceI
   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_mut :
+    Self -> T -> result (option core_slice_index_SliceIndex_Output * (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;
+  core_slice_index_SliceIndex_index_mut :
+    Self -> T -> result (core_slice_index_SliceIndex_Output * (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
@@ -704,11 +725,9 @@ Axiom core_slice_index_RangeUsize_get : forall (T : Type) (i : core_ops_range_Ra
 
 (* [core::slice::index::Range::get_mut]: forward function *)
 Axiom core_slice_index_RangeUsize_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_RangeUsize_get_mut_back :
-  forall (T : Type), core_ops_range_Range usize -> slice T -> option (slice T) -> result (slice T).
+  forall (T : Type),
+    core_ops_range_Range usize -> slice T ->
+    result (option (slice T) * (option (slice T) -> result (slice T))).
 
 (* [core::slice::index::Range::get_unchecked]: forward function *)
 Definition core_slice_index_RangeUsize_get_unchecked
@@ -732,21 +751,14 @@ Axiom core_slice_index_RangeUsize_index :
 
 (* [core::slice::index::Range::index_mut]: forward function *)
 Axiom core_slice_index_RangeUsize_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_RangeUsize_index_mut_back :
-  forall (T : Type), core_ops_range_Range usize -> slice T -> slice T -> result (slice T).
+  forall (T : Type), core_ops_range_Range usize -> slice T -> result (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).
+  slice T -> Idx ->
+  result (inst.(core_slice_index_SliceIndex_Output) *
+          (inst.(core_slice_index_SliceIndex_Output) -> result (slice T))).
 
 (* [core::array::[T; N]::index]: forward function *)
 Axiom core_array_Array_index :
@@ -756,12 +768,9 @@ Axiom core_array_Array_index :
 (* [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).
+  (a : array T N) (i : Idx),
+  result (inst.(core_ops_index_IndexMut_indexInst).(core_ops_index_Index_Output) *
+          (inst.(core_ops_index_IndexMut_indexInst).(core_ops_index_Index_Output) -> result (array T N))).
 
 (* Trait implementation: [core::slice::index::private_slice_index::Range] *)
 Definition core_slice_index_private_slice_index_SealedRangeUsizeInst
@@ -774,12 +783,10 @@ Definition core_slice_index_SliceIndexRangeUsizeSliceTInst (T : Type) :
   core_slice_index_SliceIndex_Output := slice T;
   core_slice_index_SliceIndex_get := core_slice_index_RangeUsize_get T;
   core_slice_index_SliceIndex_get_mut := core_slice_index_RangeUsize_get_mut T;
-  core_slice_index_SliceIndex_get_mut_back := core_slice_index_RangeUsize_get_mut_back T;
   core_slice_index_SliceIndex_get_unchecked := core_slice_index_RangeUsize_get_unchecked T;
   core_slice_index_SliceIndex_get_unchecked_mut := core_slice_index_RangeUsize_get_unchecked_mut T;
   core_slice_index_SliceIndex_index := core_slice_index_RangeUsize_index T;
   core_slice_index_SliceIndex_index_mut := core_slice_index_RangeUsize_index_mut T;
-  core_slice_index_SliceIndex_index_mut_back := core_slice_index_RangeUsize_index_mut_back T;
 |}.
 
 (* Trait implementation: [core::slice::index::[T]] *)
@@ -796,7 +803,6 @@ Definition core_ops_index_IndexMutSliceTIInst (T Idx : Type)
   core_ops_index_IndexMut (slice T) Idx := {|
   core_ops_index_IndexMut_indexInst := core_ops_index_IndexSliceTIInst 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]] *)
@@ -813,18 +819,14 @@ Definition core_ops_index_IndexMutArrayInst (T Idx : Type) (N : usize)
   core_ops_index_IndexMut (array T N) Idx := {|
   core_ops_index_IndexMut_indexInst := core_ops_index_IndexArrayInst 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).
+Axiom core_slice_index_usize_get_mut :
+  forall (T : Type), usize -> slice T -> result (option T * (option T -> result (slice T))).
 
 (* [core::slice::index::usize::get_unchecked]: forward function *)
 Axiom core_slice_index_usize_get_unchecked :
@@ -838,11 +840,8 @@ Axiom core_slice_index_usize_get_unchecked_mut :
 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).
+Axiom core_slice_index_usize_index_mut :
+  forall (T : Type), usize -> slice T -> result (T * (T -> result (slice T))).
 
 (* Trait implementation: [core::slice::index::private_slice_index::usize] *)
 Definition core_slice_index_private_slice_index_SealedUsizeInst
@@ -855,12 +854,10 @@ Definition core_slice_index_SliceIndexUsizeSliceTInst (T : Type) :
   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 *)
@@ -869,12 +866,9 @@ Axiom alloc_vec_Vec_index : forall (T Idx : Type) (inst : core_slice_index_Slice
 
 (* [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).
+  (Self : alloc_vec_Vec T) (i : Idx),
+  result (inst.(core_slice_index_SliceIndex_Output) *
+          (inst.(core_slice_index_SliceIndex_Output) -> result (alloc_vec_Vec T))).
 
 (* Trait implementation: [alloc::vec::Vec] *)
 Definition alloc_vec_Vec_coreopsindexIndexInst (T Idx : Type)
@@ -890,7 +884,6 @@ Definition alloc_vec_Vec_coreopsindexIndexMutInst (T Idx : Type)
   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 *)
@@ -901,10 +894,6 @@ Axiom alloc_vec_Vec_index_eq : forall {a : Type} (v : alloc_vec_Vec a) (i : usiz
 
 Axiom alloc_vec_Vec_index_mut_eq : forall {a : Type} (v : alloc_vec_Vec a) (i : usize) (x : a),
   alloc_vec_Vec_index_mut a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i =
-    alloc_vec_Vec_index_usize v i.
-
-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_SliceIndexUsizeSliceTInst a) v i x =
-    alloc_vec_Vec_update_usize v i x.
+    alloc_vec_Vec_index_mut_usize v i.
 
 End Primitives.
diff --git a/tests/coq/hashmap_on_disk/HashmapMain_Funs.v b/tests/coq/hashmap_on_disk/HashmapMain_Funs.v
index faba0afe..6a7eeb2d 100644
--- a/tests/coq/hashmap_on_disk/HashmapMain_Funs.v
+++ b/tests/coq/hashmap_on_disk/HashmapMain_Funs.v
@@ -12,69 +12,69 @@ Require Import HashmapMain_FunsExternal.
 Include HashmapMain_FunsExternal.
 Module HashmapMain_Funs.
 
-(** [hashmap_main::hashmap::hash_key]: forward function
+(** [hashmap_main::hashmap::hash_key]:
     Source: 'src/hashmap.rs', lines 27:0-27:32 *)
 Definition hashmap_hash_key (k : usize) : result usize :=
   Return k.
 
-(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::allocate_slots]: loop 0: forward function
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::allocate_slots]: loop 0:
     Source: 'src/hashmap.rs', lines 50:4-56:5 *)
 Fixpoint hashmap_HashMap_allocate_slots_loop
-  (T : Type) (n : nat) (slots : alloc_vec_Vec (hashmap_List_t T)) (n0 : usize)
+  (T : Type) (n : nat) (slots : alloc_vec_Vec (hashmap_List_t T)) (n1 : usize)
   :
   result (alloc_vec_Vec (hashmap_List_t T))
   :=
   match n with
   | O => Fail_ OutOfFuel
-  | S n1 =>
-    if n0 s> 0%usize
+  | S n2 =>
+    if n1 s> 0%usize
     then (
-      slots0 <- alloc_vec_Vec_push (hashmap_List_t T) slots Hashmap_List_Nil;
-      n2 <- usize_sub n0 1%usize;
-      hashmap_HashMap_allocate_slots_loop T n1 slots0 n2)
+      v <- alloc_vec_Vec_push (hashmap_List_t T) slots Hashmap_List_Nil;
+      n3 <- usize_sub n1 1%usize;
+      hashmap_HashMap_allocate_slots_loop T n2 v n3)
     else Return slots
   end
 .
 
-(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::allocate_slots]: forward function
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::allocate_slots]:
     Source: 'src/hashmap.rs', lines 50:4-50:76 *)
 Definition hashmap_HashMap_allocate_slots
-  (T : Type) (n : nat) (slots : alloc_vec_Vec (hashmap_List_t T)) (n0 : usize)
+  (T : Type) (n : nat) (slots : alloc_vec_Vec (hashmap_List_t T)) (n1 : usize)
   :
   result (alloc_vec_Vec (hashmap_List_t T))
   :=
-  hashmap_HashMap_allocate_slots_loop T n slots n0
+  hashmap_HashMap_allocate_slots_loop T n slots n1
 .
 
-(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::new_with_capacity]: forward function
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::new_with_capacity]:
     Source: 'src/hashmap.rs', lines 59:4-63:13 *)
 Definition hashmap_HashMap_new_with_capacity
   (T : Type) (n : nat) (capacity : usize) (max_load_dividend : usize)
   (max_load_divisor : usize) :
   result (hashmap_HashMap_t T)
   :=
-  let v := alloc_vec_Vec_new (hashmap_List_t T) in
-  slots <- hashmap_HashMap_allocate_slots T n v capacity;
+  slots <-
+    hashmap_HashMap_allocate_slots T n (alloc_vec_Vec_new (hashmap_List_t T))
+      capacity;
   i <- usize_mul capacity max_load_dividend;
-  i0 <- usize_div i max_load_divisor;
+  i1 <- usize_div i max_load_divisor;
   Return
     {|
       hashmap_HashMap_num_entries := 0%usize;
       hashmap_HashMap_max_load_factor := (max_load_dividend, max_load_divisor);
-      hashmap_HashMap_max_load := i0;
+      hashmap_HashMap_max_load := i1;
       hashmap_HashMap_slots := slots
     |}
 .
 
-(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::new]: forward function
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::new]:
     Source: 'src/hashmap.rs', lines 75:4-75:24 *)
 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_main::hashmap::HashMap<T>}::clear]: loop 0: merged forward/backward function
-    (there is a single backward function, and the forward function returns ())
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::clear]: loop 0:
     Source: 'src/hashmap.rs', lines 80:4-88:5 *)
 Fixpoint hashmap_HashMap_clear_loop
   (T : Type) (n : nat) (slots : alloc_vec_Vec (hashmap_List_t T)) (i : usize) :
@@ -82,105 +82,78 @@ Fixpoint hashmap_HashMap_clear_loop
   :=
   match n with
   | O => Fail_ OutOfFuel
-  | S n0 =>
-    let i0 := alloc_vec_Vec_len (hashmap_List_t T) slots in
-    if i s< i0
+  | S n1 =>
+    let i1 := alloc_vec_Vec_len (hashmap_List_t T) slots in
+    if i s< i1
     then (
-      i1 <- usize_add i 1%usize;
-      slots0 <-
-        alloc_vec_Vec_index_mut_back (hashmap_List_t T) usize
+      p <-
+        alloc_vec_Vec_index_mut (hashmap_List_t T) usize
           (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t T)) slots
-          i Hashmap_List_Nil;
-      hashmap_HashMap_clear_loop T n0 slots0 i1)
+          i;
+      let (_, index_mut_back) := p in
+      i2 <- usize_add i 1%usize;
+      slots1 <- index_mut_back Hashmap_List_Nil;
+      hashmap_HashMap_clear_loop T n1 slots1 i2)
     else Return slots
   end
 .
 
-(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::clear]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ())
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::clear]:
     Source: 'src/hashmap.rs', lines 80:4-80:27 *)
 Definition hashmap_HashMap_clear
   (T : Type) (n : nat) (self : hashmap_HashMap_t T) :
   result (hashmap_HashMap_t T)
   :=
-  v <- hashmap_HashMap_clear_loop T n self.(hashmap_HashMap_slots) 0%usize;
+  back <- hashmap_HashMap_clear_loop T n self.(hashmap_HashMap_slots) 0%usize;
   Return
     {|
       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_HashMap_slots := back
     |}
 .
 
-(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::len]: forward function
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::len]:
     Source: 'src/hashmap.rs', lines 90:4-90:30 *)
 Definition hashmap_HashMap_len
   (T : Type) (self : hashmap_HashMap_t T) : result usize :=
   Return self.(hashmap_HashMap_num_entries)
 .
 
-(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::insert_in_list]: loop 0: forward function
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::insert_in_list]: loop 0:
     Source: 'src/hashmap.rs', lines 97:4-114:5 *)
 Fixpoint hashmap_HashMap_insert_in_list_loop
   (T : Type) (n : nat) (key : usize) (value : T) (ls : hashmap_List_t T) :
-  result bool
+  result (bool * (hashmap_List_t T))
   :=
   match n with
   | O => Fail_ OutOfFuel
-  | S n0 =>
-    match ls with
-    | Hashmap_List_Cons ckey cvalue tl =>
-      if ckey s= key
-      then Return false
-      else hashmap_HashMap_insert_in_list_loop T n0 key value tl
-    | Hashmap_List_Nil => Return true
-    end
-  end
-.
-
-(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::insert_in_list]: forward function
-    Source: 'src/hashmap.rs', lines 97:4-97:71 *)
-Definition hashmap_HashMap_insert_in_list
-  (T : Type) (n : nat) (key : usize) (value : T) (ls : hashmap_List_t T) :
-  result bool
-  :=
-  hashmap_HashMap_insert_in_list_loop T n key value ls
-.
-
-(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::insert_in_list]: loop 0: backward function 0
-    Source: 'src/hashmap.rs', lines 97:4-114:5 *)
-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 =>
+  | S n1 =>
     match ls with
     | Hashmap_List_Cons ckey cvalue tl =>
       if ckey s= key
-      then Return (Hashmap_List_Cons ckey value tl)
+      then Return (false, Hashmap_List_Cons ckey value tl)
       else (
-        tl0 <- hashmap_HashMap_insert_in_list_loop_back T n0 key value tl;
-        Return (Hashmap_List_Cons ckey cvalue tl0))
+        p <- hashmap_HashMap_insert_in_list_loop T n1 key value tl;
+        let (b, back) := p in
+        Return (b, Hashmap_List_Cons ckey cvalue back))
     | Hashmap_List_Nil =>
-      let l := Hashmap_List_Nil in Return (Hashmap_List_Cons key value l)
+      Return (true, Hashmap_List_Cons key value Hashmap_List_Nil)
     end
   end
 .
 
-(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::insert_in_list]: backward function 0
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::insert_in_list]:
     Source: 'src/hashmap.rs', lines 97:4-97:71 *)
-Definition hashmap_HashMap_insert_in_list_back
+Definition hashmap_HashMap_insert_in_list
   (T : Type) (n : nat) (key : usize) (value : T) (ls : hashmap_List_t T) :
-  result (hashmap_List_t T)
+  result (bool * (hashmap_List_t T))
   :=
-  hashmap_HashMap_insert_in_list_loop_back T n key value ls
+  hashmap_HashMap_insert_in_list_loop T n key value ls
 .
 
-(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::insert_no_resize]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ())
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::insert_no_resize]:
     Source: 'src/hashmap.rs', lines 117:4-117:54 *)
 Definition hashmap_HashMap_insert_no_resize
   (T : Type) (n : nat) (self : hashmap_HashMap_t T) (key : usize) (value : T) :
@@ -189,33 +162,27 @@ Definition hashmap_HashMap_insert_no_resize
   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 <-
+  p <-
     alloc_vec_Vec_index_mut (hashmap_List_t T) usize
       (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t T))
       self.(hashmap_HashMap_slots) hash_mod;
-  inserted <- hashmap_HashMap_insert_in_list T n key value l;
+  let (l, index_mut_back) := p in
+  p1 <- hashmap_HashMap_insert_in_list T n key value l;
+  let (inserted, l1) := p1 in
   if inserted
   then (
-    i0 <- usize_add self.(hashmap_HashMap_num_entries) 1%usize;
-    l0 <- hashmap_HashMap_insert_in_list_back T n key value l;
-    v <-
-      alloc_vec_Vec_index_mut_back (hashmap_List_t T) usize
-        (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t T))
-        self.(hashmap_HashMap_slots) hash_mod l0;
+    i1 <- usize_add self.(hashmap_HashMap_num_entries) 1%usize;
+    v <- index_mut_back l1;
     Return
       {|
-        hashmap_HashMap_num_entries := i0;
+        hashmap_HashMap_num_entries := i1;
         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_HashMap_insert_in_list_back T n key value l;
-    v <-
-      alloc_vec_Vec_index_mut_back (hashmap_List_t T) usize
-        (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t T))
-        self.(hashmap_HashMap_slots) hash_mod l0;
+    v <- index_mut_back l1;
     Return
       {|
         hashmap_HashMap_num_entries := self.(hashmap_HashMap_num_entries);
@@ -226,8 +193,7 @@ Definition hashmap_HashMap_insert_no_resize
       |})
 .
 
-(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::move_elements_from_list]: loop 0: merged forward/backward function
-    (there is a single backward function, and the forward function returns ())
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::move_elements_from_list]: loop 0:
     Source: 'src/hashmap.rs', lines 183:4-196:5 *)
 Fixpoint hashmap_HashMap_move_elements_from_list_loop
   (T : Type) (n : nat) (ntable : hashmap_HashMap_t T) (ls : hashmap_List_t T) :
@@ -235,18 +201,17 @@ Fixpoint hashmap_HashMap_move_elements_from_list_loop
   :=
   match n with
   | O => Fail_ OutOfFuel
-  | S n0 =>
+  | S n1 =>
     match ls with
     | 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
+      hm <- hashmap_HashMap_insert_no_resize T n1 ntable k v;
+      hashmap_HashMap_move_elements_from_list_loop T n1 hm tl
     | Hashmap_List_Nil => Return ntable
     end
   end
 .
 
-(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::move_elements_from_list]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ())
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::move_elements_from_list]:
     Source: 'src/hashmap.rs', lines 183:4-183:72 *)
 Definition hashmap_HashMap_move_elements_from_list
   (T : Type) (n : nat) (ntable : hashmap_HashMap_t T) (ls : hashmap_List_t T) :
@@ -255,8 +220,7 @@ Definition hashmap_HashMap_move_elements_from_list
   hashmap_HashMap_move_elements_from_list_loop T n ntable ls
 .
 
-(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::move_elements]: loop 0: merged forward/backward function
-    (there is a single backward function, and the forward function returns ())
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::move_elements]: loop 0:
     Source: 'src/hashmap.rs', lines 171:4-180:5 *)
 Fixpoint hashmap_HashMap_move_elements_loop
   (T : Type) (n : nat) (ntable : hashmap_HashMap_t T)
@@ -265,40 +229,39 @@ Fixpoint hashmap_HashMap_move_elements_loop
   :=
   match n with
   | O => Fail_ OutOfFuel
-  | S n0 =>
-    let i0 := alloc_vec_Vec_len (hashmap_List_t T) slots in
-    if i s< i0
+  | S n1 =>
+    let i1 := alloc_vec_Vec_len (hashmap_List_t T) slots in
+    if i s< i1
     then (
-      l <-
+      p <-
         alloc_vec_Vec_index_mut (hashmap_List_t T) usize
           (core_slice_index_SliceIndexUsizeSliceTInst (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 := 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_SliceIndexUsizeSliceTInst (hashmap_List_t T)) slots
-          i l0;
-      hashmap_HashMap_move_elements_loop T n0 ntable0 slots0 i1)
+      let (l, index_mut_back) := p in
+      let (ls, l1) := core_mem_replace (hashmap_List_t T) l Hashmap_List_Nil in
+      hm <- hashmap_HashMap_move_elements_from_list T n1 ntable ls;
+      i2 <- usize_add i 1%usize;
+      slots1 <- index_mut_back l1;
+      back_'a <- hashmap_HashMap_move_elements_loop T n1 hm slots1 i2;
+      let (hm1, v) := back_'a in
+      Return (hm1, v))
     else Return (ntable, slots)
   end
 .
 
-(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::move_elements]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ())
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::move_elements]:
     Source: 'src/hashmap.rs', lines 171:4-171:95 *)
 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_HashMap_move_elements_loop T n ntable slots i
+  back_'a <- hashmap_HashMap_move_elements_loop T n ntable slots i;
+  let (hm, v) := back_'a in
+  Return (hm, v)
 .
 
-(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::try_resize]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ())
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::try_resize]:
     Source: 'src/hashmap.rs', lines 140:4-140:28 *)
 Definition hashmap_HashMap_try_resize
   (T : Type) (n : nat) (self : hashmap_HashMap_t T) :
@@ -308,72 +271,71 @@ Definition hashmap_HashMap_try_resize
   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_HashMap_max_load_factor) in
-  i1 <- usize_div n1 i;
-  if capacity s<= i1
+  let (i, i1) := self.(hashmap_HashMap_max_load_factor) in
+  i2 <- usize_div n1 i;
+  if capacity s<= i2
   then (
-    i2 <- usize_mul capacity 2%usize;
-    ntable <- hashmap_HashMap_new_with_capacity T n i2 i i0;
+    i3 <- usize_mul capacity 2%usize;
+    ntable <- hashmap_HashMap_new_with_capacity T n i3 i i1;
     p <-
       hashmap_HashMap_move_elements T n ntable self.(hashmap_HashMap_slots)
         0%usize;
-    let (ntable0, _) := p in
+    let (ntable1, _) := p in
     Return
       {|
         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)
+        hashmap_HashMap_max_load_factor := (i, i1);
+        hashmap_HashMap_max_load := ntable1.(hashmap_HashMap_max_load);
+        hashmap_HashMap_slots := ntable1.(hashmap_HashMap_slots)
       |})
   else
     Return
       {|
         hashmap_HashMap_num_entries := self.(hashmap_HashMap_num_entries);
-        hashmap_HashMap_max_load_factor := (i, i0);
+        hashmap_HashMap_max_load_factor := (i, i1);
         hashmap_HashMap_max_load := self.(hashmap_HashMap_max_load);
         hashmap_HashMap_slots := self.(hashmap_HashMap_slots)
       |}
 .
 
-(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::insert]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ())
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::insert]:
     Source: 'src/hashmap.rs', lines 129:4-129:48 *)
 Definition hashmap_HashMap_insert
   (T : Type) (n : nat) (self : hashmap_HashMap_t T) (key : usize) (value : T) :
   result (hashmap_HashMap_t T)
   :=
-  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
+  hm <- hashmap_HashMap_insert_no_resize T n self key value;
+  i <- hashmap_HashMap_len T hm;
+  if i s> hm.(hashmap_HashMap_max_load)
+  then hashmap_HashMap_try_resize T n hm
+  else Return hm
 .
 
-(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::contains_key_in_list]: loop 0: forward function
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::contains_key_in_list]: loop 0:
     Source: 'src/hashmap.rs', lines 206:4-219:5 *)
 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 =>
+  | S n1 =>
     match ls with
-    | Hashmap_List_Cons ckey t tl =>
+    | Hashmap_List_Cons ckey _ tl =>
       if ckey s= key
       then Return true
-      else hashmap_HashMap_contains_key_in_list_loop T n0 key tl
+      else hashmap_HashMap_contains_key_in_list_loop T n1 key tl
     | Hashmap_List_Nil => Return false
     end
   end
 .
 
-(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::contains_key_in_list]: forward function
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::contains_key_in_list]:
     Source: 'src/hashmap.rs', lines 206:4-206:68 *)
 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_main::hashmap::HashMap<T>}::contains_key]: forward function
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::contains_key]:
     Source: 'src/hashmap.rs', lines 199:4-199:49 *)
 Definition hashmap_HashMap_contains_key
   (T : Type) (n : nat) (self : hashmap_HashMap_t T) (key : usize) :
@@ -389,31 +351,31 @@ Definition hashmap_HashMap_contains_key
   hashmap_HashMap_contains_key_in_list T n key l
 .
 
-(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_in_list]: loop 0: forward function
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_in_list]: loop 0:
     Source: 'src/hashmap.rs', lines 224:4-237:5 *)
 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 =>
+  | S n1 =>
     match ls with
     | Hashmap_List_Cons ckey cvalue tl =>
       if ckey s= key
       then Return cvalue
-      else hashmap_HashMap_get_in_list_loop T n0 key tl
+      else hashmap_HashMap_get_in_list_loop T n1 key tl
     | Hashmap_List_Nil => Fail_ Failure
     end
   end
 .
 
-(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_in_list]: forward function
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_in_list]:
     Source: 'src/hashmap.rs', lines 224:4-224:70 *)
 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_main::hashmap::HashMap<T>}::get]: forward function
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get]:
     Source: 'src/hashmap.rs', lines 239:4-239:55 *)
 Definition hashmap_HashMap_get
   (T : Type) (n : nat) (self : hashmap_HashMap_t T) (key : usize) : result T :=
@@ -427,292 +389,208 @@ Definition hashmap_HashMap_get
   hashmap_HashMap_get_in_list T n key l
 .
 
-(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_mut_in_list]: loop 0: forward function
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_mut_in_list]: loop 0:
     Source: 'src/hashmap.rs', lines 245:4-254:5 *)
 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
-    | Hashmap_List_Cons ckey cvalue tl =>
-      if ckey s= key
-      then Return cvalue
-      else hashmap_HashMap_get_mut_in_list_loop T n0 tl key
-    | Hashmap_List_Nil => Fail_ Failure
-    end
-  end
-.
-
-(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_mut_in_list]: forward function
-    Source: 'src/hashmap.rs', lines 245:4-245:86 *)
-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_main::hashmap::HashMap<T>}::get_mut_in_list]: loop 0: backward function 0
-    Source: 'src/hashmap.rs', lines 245:4-254:5 *)
-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)
+  (T : Type) (n : nat) (ls : hashmap_List_t T) (key : usize) :
+  result (T * (T -> result (hashmap_List_t T)))
   :=
   match n with
   | O => Fail_ OutOfFuel
-  | S n0 =>
+  | S n1 =>
     match ls with
     | Hashmap_List_Cons ckey cvalue tl =>
       if ckey s= key
-      then Return (Hashmap_List_Cons ckey ret tl)
+      then
+        let back_'a := fun (ret : T) => Return (Hashmap_List_Cons ckey ret tl)
+          in
+        Return (cvalue, back_'a)
       else (
-        tl0 <- hashmap_HashMap_get_mut_in_list_loop_back T n0 tl key ret;
-        Return (Hashmap_List_Cons ckey cvalue tl0))
+        p <- hashmap_HashMap_get_mut_in_list_loop T n1 tl key;
+        let (t, back_'a) := p in
+        let back_'a1 :=
+          fun (ret : T) =>
+            tl1 <- back_'a ret; Return (Hashmap_List_Cons ckey cvalue tl1) in
+        Return (t, back_'a1))
     | Hashmap_List_Nil => Fail_ Failure
     end
   end
 .
 
-(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_mut_in_list]: backward function 0
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_mut_in_list]:
     Source: 'src/hashmap.rs', lines 245:4-245:86 *)
-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)
+Definition hashmap_HashMap_get_mut_in_list
+  (T : Type) (n : nat) (ls : hashmap_List_t T) (key : usize) :
+  result (T * (T -> result (hashmap_List_t T)))
   :=
-  hashmap_HashMap_get_mut_in_list_loop_back T n ls key ret
+  p <- hashmap_HashMap_get_mut_in_list_loop T n ls key;
+  let (t, back_'a) := p in
+  Return (t, back_'a)
 .
 
-(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_mut]: forward function
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_mut]:
     Source: 'src/hashmap.rs', lines 257:4-257:67 *)
 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 <-
-    alloc_vec_Vec_index_mut (hashmap_List_t T) usize
-      (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t T))
-      self.(hashmap_HashMap_slots) hash_mod;
-  hashmap_HashMap_get_mut_in_list T n l key
-.
-
-(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_mut]: backward function 0
-    Source: 'src/hashmap.rs', lines 257:4-257:67 *)
-Definition hashmap_HashMap_get_mut_back
-  (T : Type) (n : nat) (self : hashmap_HashMap_t T) (key : usize) (ret : T) :
-  result (hashmap_HashMap_t T)
+  (T : Type) (n : nat) (self : hashmap_HashMap_t T) (key : usize) :
+  result (T * (T -> result (hashmap_HashMap_t 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 <-
+  p <-
     alloc_vec_Vec_index_mut (hashmap_List_t T) usize
       (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t T))
       self.(hashmap_HashMap_slots) hash_mod;
-  l0 <- hashmap_HashMap_get_mut_in_list_back T n l key ret;
-  v <-
-    alloc_vec_Vec_index_mut_back (hashmap_List_t T) usize
-      (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t T))
-      self.(hashmap_HashMap_slots) hash_mod l0;
-  Return
-    {|
-      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_main::hashmap::HashMap<T>}::remove_from_list]: loop 0: forward function
+  let (l, index_mut_back) := p in
+  p1 <- hashmap_HashMap_get_mut_in_list T n l key;
+  let (t, get_mut_in_list_back) := p1 in
+  let back_'a :=
+    fun (ret : T) =>
+      l1 <- get_mut_in_list_back ret;
+      v <- index_mut_back l1;
+      Return
+        {|
+          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
+        |} in
+  Return (t, back_'a)
+.
+
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::remove_from_list]: loop 0:
     Source: 'src/hashmap.rs', lines 265:4-291:5 *)
 Fixpoint hashmap_HashMap_remove_from_list_loop
   (T : Type) (n : nat) (key : usize) (ls : hashmap_List_t T) :
-  result (option T)
+  result ((option T) * (hashmap_List_t T))
   :=
   match n with
   | O => Fail_ OutOfFuel
-  | S n0 =>
+  | S n1 =>
     match ls with
     | Hashmap_List_Cons ckey t tl =>
       if ckey s= key
       then
-        let mv_ls :=
+        let (mv_ls, _) :=
           core_mem_replace (hashmap_List_t T) (Hashmap_List_Cons ckey t tl)
             Hashmap_List_Nil in
         match mv_ls with
-        | Hashmap_List_Cons i cvalue tl0 => Return (Some cvalue)
+        | Hashmap_List_Cons _ cvalue tl1 => Return (Some cvalue, tl1)
         | Hashmap_List_Nil => Fail_ Failure
         end
-      else hashmap_HashMap_remove_from_list_loop T n0 key tl
-    | Hashmap_List_Nil => Return None
+      else (
+        p <- hashmap_HashMap_remove_from_list_loop T n1 key tl;
+        let (o, back) := p in
+        Return (o, Hashmap_List_Cons ckey t back))
+    | Hashmap_List_Nil => Return (None, Hashmap_List_Nil)
     end
   end
 .
 
-(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::remove_from_list]: forward function
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::remove_from_list]:
     Source: 'src/hashmap.rs', lines 265:4-265:69 *)
 Definition hashmap_HashMap_remove_from_list
   (T : Type) (n : nat) (key : usize) (ls : hashmap_List_t T) :
-  result (option T)
+  result ((option T) * (hashmap_List_t T))
   :=
   hashmap_HashMap_remove_from_list_loop T n key ls
 .
 
-(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::remove_from_list]: loop 0: backward function 1
-    Source: 'src/hashmap.rs', lines 265:4-291:5 *)
-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
-    | Hashmap_List_Cons ckey t tl =>
-      if ckey s= key
-      then
-        let mv_ls :=
-          core_mem_replace (hashmap_List_t T) (Hashmap_List_Cons ckey t tl)
-            Hashmap_List_Nil in
-        match mv_ls with
-        | Hashmap_List_Cons i cvalue tl0 => Return tl0
-        | Hashmap_List_Nil => Fail_ Failure
-        end
-      else (
-        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_main::hashmap::HashMap<T>}::remove_from_list]: backward function 1
-    Source: 'src/hashmap.rs', lines 265:4-265:69 *)
-Definition hashmap_HashMap_remove_from_list_back
-  (T : Type) (n : nat) (key : usize) (ls : hashmap_List_t T) :
-  result (hashmap_List_t T)
-  :=
-  hashmap_HashMap_remove_from_list_loop_back T n key ls
-.
-
-(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::remove]: forward function
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::remove]:
     Source: 'src/hashmap.rs', lines 294:4-294:52 *)
 Definition hashmap_HashMap_remove
   (T : Type) (n : nat) (self : hashmap_HashMap_t T) (key : usize) :
-  result (option T)
+  result ((option T) * (hashmap_HashMap_t 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 <-
+  p <-
     alloc_vec_Vec_index_mut (hashmap_List_t T) usize
       (core_slice_index_SliceIndexUsizeSliceTInst (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_HashMap_num_entries) 1%usize; Return (Some x0)
-  end
-.
-
-(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::remove]: backward function 0
-    Source: 'src/hashmap.rs', lines 294:4-294:52 *)
-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 key;
-  let i := alloc_vec_Vec_len (hashmap_List_t T) self.(hashmap_HashMap_slots) in
-  hash_mod <- usize_rem hash i;
-  l <-
-    alloc_vec_Vec_index_mut (hashmap_List_t T) usize
-      (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t T))
-      self.(hashmap_HashMap_slots) hash_mod;
-  x <- hashmap_HashMap_remove_from_list T n key l;
+  let (l, index_mut_back) := p in
+  p1 <- hashmap_HashMap_remove_from_list T n key l;
+  let (x, l1) := p1 in
   match x with
   | None =>
-    l0 <- hashmap_HashMap_remove_from_list_back T n key l;
-    v <-
-      alloc_vec_Vec_index_mut_back (hashmap_List_t T) usize
-        (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t T))
-        self.(hashmap_HashMap_slots) hash_mod l0;
-    Return
+    v <- index_mut_back l1;
+    Return (None,
       {|
         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_HashMap_num_entries) 1%usize;
-    l0 <- hashmap_HashMap_remove_from_list_back T n key l;
-    v <-
-      alloc_vec_Vec_index_mut_back (hashmap_List_t T) usize
-        (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t T))
-        self.(hashmap_HashMap_slots) hash_mod l0;
-    Return
+      |})
+  | Some x1 =>
+    i1 <- usize_sub self.(hashmap_HashMap_num_entries) 1%usize;
+    v <- index_mut_back l1;
+    Return (Some x1,
       {|
-        hashmap_HashMap_num_entries := i0;
+        hashmap_HashMap_num_entries := i1;
         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
+(** [hashmap_main::hashmap::test1]:
     Source: 'src/hashmap.rs', lines 315:0-315:10 *)
 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;
+  hm1 <- hashmap_HashMap_insert u64 n hm 0%usize 42%u64;
+  hm2 <- hashmap_HashMap_insert u64 n hm1 128%usize 18%u64;
+  hm3 <- hashmap_HashMap_insert u64 n hm2 1024%usize 138%u64;
+  hm4 <- hashmap_HashMap_insert u64 n hm3 1056%usize 256%u64;
+  i <- hashmap_HashMap_get u64 n hm4 128%usize;
   if negb (i s= 18%u64)
   then Fail_ Failure
   else (
-    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)
+    p <- hashmap_HashMap_get_mut u64 n hm4 1024%usize;
+    let (_, get_mut_back) := p in
+    hm5 <- get_mut_back 56%u64;
+    i1 <- hashmap_HashMap_get u64 n hm5 1024%usize;
+    if negb (i1 s= 56%u64)
     then Fail_ Failure
     else (
-      x <- hashmap_HashMap_remove u64 n hm4 1024%usize;
+      p1 <- hashmap_HashMap_remove u64 n hm5 1024%usize;
+      let (x, hm6) := p1 in
       match x with
       | None => Fail_ Failure
-      | Some x0 =>
-        if negb (x0 s= 56%u64)
+      | Some x1 =>
+        if negb (x1 s= 56%u64)
         then Fail_ Failure
         else (
-          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)
+          i2 <- hashmap_HashMap_get u64 n hm6 0%usize;
+          if negb (i2 s= 42%u64)
           then Fail_ Failure
           else (
-            i2 <- hashmap_HashMap_get u64 n hm5 128%usize;
-            if negb (i2 s= 18%u64)
+            i3 <- hashmap_HashMap_get u64 n hm6 128%usize;
+            if negb (i3 s= 18%u64)
             then Fail_ Failure
             else (
-              i3 <- hashmap_HashMap_get u64 n hm5 1056%usize;
-              if negb (i3 s= 256%u64) then Fail_ Failure else Return tt)))
+              i4 <- hashmap_HashMap_get u64 n hm6 1056%usize;
+              if negb (i4 s= 256%u64) then Fail_ Failure else Return tt)))
       end))
 .
 
-(** [hashmap_main::insert_on_disk]: forward function
+(** [hashmap_main::insert_on_disk]:
     Source: 'src/hashmap_main.rs', lines 7:0-7:43 *)
 Definition insert_on_disk
   (n : nat) (key : usize) (value : u64) (st : state) : result (state * unit) :=
   p <- hashmap_utils_deserialize st;
-  let (st0, hm) := p in
-  hm0 <- hashmap_HashMap_insert u64 n hm key value;
-  p0 <- hashmap_utils_serialize hm0 st0;
-  let (st1, _) := p0 in
-  Return (st1, tt)
+  let (st1, hm) := p in
+  hm1 <- hashmap_HashMap_insert u64 n hm key value;
+  p1 <- hashmap_utils_serialize hm1 st1;
+  let (st2, _) := p1 in
+  Return (st2, tt)
 .
 
-(** [hashmap_main::main]: forward function
+(** [hashmap_main::main]:
     Source: 'src/hashmap_main.rs', lines 16:0-16:13 *)
 Definition main : result unit :=
   Return tt.
diff --git a/tests/coq/hashmap_on_disk/HashmapMain_FunsExternal_Template.v b/tests/coq/hashmap_on_disk/HashmapMain_FunsExternal_Template.v
index e10d02f6..fb2e052a 100644
--- a/tests/coq/hashmap_on_disk/HashmapMain_FunsExternal_Template.v
+++ b/tests/coq/hashmap_on_disk/HashmapMain_FunsExternal_Template.v
@@ -11,13 +11,13 @@ Require Import HashmapMain_Types.
 Include HashmapMain_Types.
 Module HashmapMain_FunsExternal_Template.
 
-(** [hashmap_main::hashmap_utils::deserialize]: forward function
+(** [hashmap_main::hashmap_utils::deserialize]:
     Source: 'src/hashmap_utils.rs', lines 10:0-10:43 *)
 Axiom hashmap_utils_deserialize
   : state -> result (state * (hashmap_HashMap_t u64))
 .
 
-(** [hashmap_main::hashmap_utils::serialize]: forward function
+(** [hashmap_main::hashmap_utils::serialize]:
     Source: 'src/hashmap_utils.rs', lines 5:0-5:42 *)
 Axiom hashmap_utils_serialize
   : hashmap_HashMap_t u64 -> state -> result (state * unit)
diff --git a/tests/coq/hashmap_on_disk/Primitives.v b/tests/coq/hashmap_on_disk/Primitives.v
index 84280b96..990e27e4 100644
--- a/tests/coq/hashmap_on_disk/Primitives.v
+++ b/tests/coq/hashmap_on_disk/Primitives.v
@@ -67,8 +67,7 @@ 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 .
+Definition core_mem_replace (a : Type) (x : a) (y : a) : a * a := (x, x) .
 
 Record mut_raw_ptr (T : Type) := { mut_raw_ptr_v : T }.
 Record const_raw_ptr (T : Type) := { const_raw_ptr_v : T }.
@@ -504,13 +503,15 @@ 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;
+  core_ops_index_IndexMut_index_mut :
+    Self ->
+    Idx ->
+    result (core_ops_index_IndexMut_indexInst.(core_ops_index_Index_Output) *
+            (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 {
@@ -524,13 +525,14 @@ 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;
+  core_ops_deref_DerefMut_deref_mut :
+    Self ->
+    result (core_ops_deref_DerefMut_derefInst.(core_ops_deref_Deref_target) *
+            (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;
@@ -543,8 +545,8 @@ 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.
+Definition alloc_boxed_Box_deref_mut (T : Type) (x : T) : result (T * (T -> result T)) :=
+  Return (x, fun x => Return x).
 
 (* Trait instance *)
 Definition alloc_boxed_Box_coreopsDerefInst (Self : Type) : core_ops_deref_Deref Self := {|
@@ -556,7 +558,6 @@ Definition alloc_boxed_Box_coreopsDerefInst (Self : Type) : core_ops_deref_Deref
 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;
 |}.
 
 
@@ -584,6 +585,13 @@ 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).
 
+Definition array_index_mut_usize (T : Type) (n : usize) (a : array T n) (i : usize) :
+  result (T * (T -> result (array T n))) :=
+  match array_index_usize T n a i with
+  | Fail_ e => Fail_ e
+  | Return x => Return (x, array_update_usize T n a i)
+  end.
+
 (*** Slice *)
 Definition slice T := { l: list T | Z.of_nat (length l) <= usize_max}.
 
@@ -591,11 +599,25 @@ 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).
 
+Definition slice_index_mut_usize (T : Type) (s : slice T) (i : usize) :
+  result (T * (T -> result (slice T))) :=
+  match slice_index_usize T s i with
+  | Fail_ e => Fail_ e
+  | Return x => Return (x, slice_update_usize T s i)
+  end.
+
 (*** 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).
 
+Definition array_to_slice_mut (T : Type) (n : usize) (a : array T n) :
+  result (slice T * (slice T -> result (array T n))) :=
+  match array_to_slice T n a with
+  | Fail_ e => Fail_ e
+  | Return x => Return (x, array_from_slice T n a)
+  end.
+
 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).
 
@@ -639,16 +661,9 @@ Definition alloc_vec_Vec_bind {A B} (v: alloc_vec_Vec A) (f: list A -> result (l
   | 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)
@@ -661,6 +676,14 @@ Axiom alloc_vec_Vec_index_usize : forall {T : Type} (v : alloc_vec_Vec T) (i : u
 (* Helper *)
 Axiom alloc_vec_Vec_update_usize : forall {T : Type} (v : alloc_vec_Vec T) (i : usize) (x : T), result (alloc_vec_Vec T).
 
+Definition alloc_vec_Vec_index_mut_usize {T : Type} (v: alloc_vec_Vec T) (i: usize) :
+  result (T * (T -> result (alloc_vec_Vec T))) :=
+  match alloc_vec_Vec_index_usize v i with
+  | Return x =>
+    Return (x, alloc_vec_Vec_update_usize v i)
+  | Fail_ e => Fail_ e
+  end.
+
 (* Trait declaration: [core::slice::index::private_slice_index::Sealed] *)
 Definition core_slice_index_private_slice_index_Sealed (self : Type) := unit.
 
@@ -669,25 +692,23 @@ Record core_slice_index_SliceIndex (Self T : Type) := mk_core_slice_index_SliceI
   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_mut :
+    Self -> T -> result (option core_slice_index_SliceIndex_Output * (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;
+  core_slice_index_SliceIndex_index_mut :
+    Self -> T -> result (core_slice_index_SliceIndex_Output * (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
@@ -704,11 +725,9 @@ Axiom core_slice_index_RangeUsize_get : forall (T : Type) (i : core_ops_range_Ra
 
 (* [core::slice::index::Range::get_mut]: forward function *)
 Axiom core_slice_index_RangeUsize_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_RangeUsize_get_mut_back :
-  forall (T : Type), core_ops_range_Range usize -> slice T -> option (slice T) -> result (slice T).
+  forall (T : Type),
+    core_ops_range_Range usize -> slice T ->
+    result (option (slice T) * (option (slice T) -> result (slice T))).
 
 (* [core::slice::index::Range::get_unchecked]: forward function *)
 Definition core_slice_index_RangeUsize_get_unchecked
@@ -732,21 +751,14 @@ Axiom core_slice_index_RangeUsize_index :
 
 (* [core::slice::index::Range::index_mut]: forward function *)
 Axiom core_slice_index_RangeUsize_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_RangeUsize_index_mut_back :
-  forall (T : Type), core_ops_range_Range usize -> slice T -> slice T -> result (slice T).
+  forall (T : Type), core_ops_range_Range usize -> slice T -> result (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).
+  slice T -> Idx ->
+  result (inst.(core_slice_index_SliceIndex_Output) *
+          (inst.(core_slice_index_SliceIndex_Output) -> result (slice T))).
 
 (* [core::array::[T; N]::index]: forward function *)
 Axiom core_array_Array_index :
@@ -756,12 +768,9 @@ Axiom core_array_Array_index :
 (* [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).
+  (a : array T N) (i : Idx),
+  result (inst.(core_ops_index_IndexMut_indexInst).(core_ops_index_Index_Output) *
+          (inst.(core_ops_index_IndexMut_indexInst).(core_ops_index_Index_Output) -> result (array T N))).
 
 (* Trait implementation: [core::slice::index::private_slice_index::Range] *)
 Definition core_slice_index_private_slice_index_SealedRangeUsizeInst
@@ -774,12 +783,10 @@ Definition core_slice_index_SliceIndexRangeUsizeSliceTInst (T : Type) :
   core_slice_index_SliceIndex_Output := slice T;
   core_slice_index_SliceIndex_get := core_slice_index_RangeUsize_get T;
   core_slice_index_SliceIndex_get_mut := core_slice_index_RangeUsize_get_mut T;
-  core_slice_index_SliceIndex_get_mut_back := core_slice_index_RangeUsize_get_mut_back T;
   core_slice_index_SliceIndex_get_unchecked := core_slice_index_RangeUsize_get_unchecked T;
   core_slice_index_SliceIndex_get_unchecked_mut := core_slice_index_RangeUsize_get_unchecked_mut T;
   core_slice_index_SliceIndex_index := core_slice_index_RangeUsize_index T;
   core_slice_index_SliceIndex_index_mut := core_slice_index_RangeUsize_index_mut T;
-  core_slice_index_SliceIndex_index_mut_back := core_slice_index_RangeUsize_index_mut_back T;
 |}.
 
 (* Trait implementation: [core::slice::index::[T]] *)
@@ -796,7 +803,6 @@ Definition core_ops_index_IndexMutSliceTIInst (T Idx : Type)
   core_ops_index_IndexMut (slice T) Idx := {|
   core_ops_index_IndexMut_indexInst := core_ops_index_IndexSliceTIInst 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]] *)
@@ -813,18 +819,14 @@ Definition core_ops_index_IndexMutArrayInst (T Idx : Type) (N : usize)
   core_ops_index_IndexMut (array T N) Idx := {|
   core_ops_index_IndexMut_indexInst := core_ops_index_IndexArrayInst 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).
+Axiom core_slice_index_usize_get_mut :
+  forall (T : Type), usize -> slice T -> result (option T * (option T -> result (slice T))).
 
 (* [core::slice::index::usize::get_unchecked]: forward function *)
 Axiom core_slice_index_usize_get_unchecked :
@@ -838,11 +840,8 @@ Axiom core_slice_index_usize_get_unchecked_mut :
 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).
+Axiom core_slice_index_usize_index_mut :
+  forall (T : Type), usize -> slice T -> result (T * (T -> result (slice T))).
 
 (* Trait implementation: [core::slice::index::private_slice_index::usize] *)
 Definition core_slice_index_private_slice_index_SealedUsizeInst
@@ -855,12 +854,10 @@ Definition core_slice_index_SliceIndexUsizeSliceTInst (T : Type) :
   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 *)
@@ -869,12 +866,9 @@ Axiom alloc_vec_Vec_index : forall (T Idx : Type) (inst : core_slice_index_Slice
 
 (* [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).
+  (Self : alloc_vec_Vec T) (i : Idx),
+  result (inst.(core_slice_index_SliceIndex_Output) *
+          (inst.(core_slice_index_SliceIndex_Output) -> result (alloc_vec_Vec T))).
 
 (* Trait implementation: [alloc::vec::Vec] *)
 Definition alloc_vec_Vec_coreopsindexIndexInst (T Idx : Type)
@@ -890,7 +884,6 @@ Definition alloc_vec_Vec_coreopsindexIndexMutInst (T Idx : Type)
   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 *)
@@ -901,10 +894,6 @@ Axiom alloc_vec_Vec_index_eq : forall {a : Type} (v : alloc_vec_Vec a) (i : usiz
 
 Axiom alloc_vec_Vec_index_mut_eq : forall {a : Type} (v : alloc_vec_Vec a) (i : usize) (x : a),
   alloc_vec_Vec_index_mut a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i =
-    alloc_vec_Vec_index_usize v i.
-
-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_SliceIndexUsizeSliceTInst a) v i x =
-    alloc_vec_Vec_update_usize v i x.
+    alloc_vec_Vec_index_mut_usize v i.
 
 End Primitives.
diff --git a/tests/coq/misc/Bitwise.v b/tests/coq/misc/Bitwise.v
index 94771b37..b04c95f2 100644
--- a/tests/coq/misc/Bitwise.v
+++ b/tests/coq/misc/Bitwise.v
@@ -8,29 +8,29 @@ Import ListNotations.
 Local Open Scope Primitives_scope.
 Module Bitwise.
 
-(** [bitwise::shift_u32]: forward function
+(** [bitwise::shift_u32]:
     Source: 'src/bitwise.rs', lines 3:0-3:31 *)
 Definition shift_u32 (a : u32) : result u32 :=
   t <- u32_shr a 16%usize; u32_shl t 16%usize
 .
 
-(** [bitwise::shift_i32]: forward function
+(** [bitwise::shift_i32]:
     Source: 'src/bitwise.rs', lines 10:0-10:31 *)
 Definition shift_i32 (a : i32) : result i32 :=
   t <- i32_shr a 16%isize; i32_shl t 16%isize
 .
 
-(** [bitwise::xor_u32]: forward function
+(** [bitwise::xor_u32]:
     Source: 'src/bitwise.rs', lines 17:0-17:37 *)
 Definition xor_u32 (a : u32) (b : u32) : result u32 :=
   Return (u32_xor a b).
 
-(** [bitwise::or_u32]: forward function
+(** [bitwise::or_u32]:
     Source: 'src/bitwise.rs', lines 21:0-21:36 *)
 Definition or_u32 (a : u32) (b : u32) : result u32 :=
   Return (u32_or a b).
 
-(** [bitwise::and_u32]: forward function
+(** [bitwise::and_u32]:
     Source: 'src/bitwise.rs', lines 25:0-25:37 *)
 Definition and_u32 (a : u32) (b : u32) : result u32 :=
   Return (u32_and a b).
diff --git a/tests/coq/misc/Constants.v b/tests/coq/misc/Constants.v
index ad899f25..0f33cbd6 100644
--- a/tests/coq/misc/Constants.v
+++ b/tests/coq/misc/Constants.v
@@ -23,7 +23,7 @@ Definition x1_c : u32 := x1_body%global.
 Definition x2_body : result u32 := Return 3%u32.
 Definition x2_c : u32 := x2_body%global.
 
-(** [constants::incr]: forward function
+(** [constants::incr]:
     Source: 'src/constants.rs', lines 17:0-17:32 *)
 Definition incr (n : u32) : result u32 :=
   u32_add n 1%u32.
@@ -33,7 +33,7 @@ Definition incr (n : u32) : result u32 :=
 Definition x3_body : result u32 := incr 32%u32.
 Definition x3_c : u32 := x3_body%global.
 
-(** [constants::mk_pair0]: forward function
+(** [constants::mk_pair0]:
     Source: 'src/constants.rs', lines 23:0-23:51 *)
 Definition mk_pair0 (x : u32) (y : u32) : result (u32 * u32) :=
   Return (x, y).
@@ -46,7 +46,7 @@ Arguments mkPair_t { _ _ }.
 Arguments pair_x { _ _ }.
 Arguments pair_y { _ _ }.
 
-(** [constants::mk_pair1]: forward function
+(** [constants::mk_pair1]:
     Source: 'src/constants.rs', lines 27:0-27:55 *)
 Definition mk_pair1 (x : u32) (y : u32) : result (Pair_t u32 u32) :=
   Return {| pair_x := x; pair_y := y |}
@@ -81,7 +81,7 @@ Record Wrap_t (T : Type) := mkWrap_t { wrap_value : T; }.
 Arguments mkWrap_t { _ }.
 Arguments wrap_value { _ }.
 
-(** [constants::{constants::Wrap<T>}::new]: forward function
+(** [constants::{constants::Wrap<T>}::new]:
     Source: 'src/constants.rs', lines 54:4-54:41 *)
 Definition wrap_new (T : Type) (value : T) : result (Wrap_t T) :=
   Return {| wrap_value := value |}
@@ -92,7 +92,7 @@ Definition wrap_new (T : Type) (value : T) : result (Wrap_t T) :=
 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
+(** [constants::unwrap_y]:
     Source: 'src/constants.rs', lines 43:0-43:30 *)
 Definition unwrap_y : result i32 :=
   Return y_c.(wrap_value).
@@ -107,12 +107,12 @@ Definition yval_c : i32 := yval_body%global.
 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
+(** [constants::get_z1]:
     Source: 'src/constants.rs', lines 61:0-61:28 *)
 Definition get_z1 : result i32 :=
   Return get_z1_z1_c.
 
-(** [constants::add]: forward function
+(** [constants::add]:
     Source: 'src/constants.rs', lines 66:0-66:39 *)
 Definition add (a : i32) (b : i32) : result i32 :=
   i32_add a b.
@@ -132,10 +132,10 @@ Definition q2_c : i32 := q2_body%global.
 Definition q3_body : result i32 := add q2_c 3%i32.
 Definition q3_c : i32 := q3_body%global.
 
-(** [constants::get_z2]: forward function
+(** [constants::get_z2]:
     Source: 'src/constants.rs', lines 70:0-70:28 *)
 Definition get_z2 : result i32 :=
-  i <- get_z1; i0 <- add i q3_c; add q1_c i0.
+  i <- get_z1; i1 <- add i q3_c; add q1_c i1.
 
 (** [constants::S1]
     Source: 'src/constants.rs', lines 80:0-80:18 *)
diff --git a/tests/coq/misc/External_Funs.v b/tests/coq/misc/External_Funs.v
index e9d39f66..91ea88c9 100644
--- a/tests/coq/misc/External_Funs.v
+++ b/tests/coq/misc/External_Funs.v
@@ -12,107 +12,64 @@ Require Import External_FunsExternal.
 Include External_FunsExternal.
 Module External_Funs.
 
-(** [external::swap]: forward function
+(** [external::swap]:
     Source: 'src/external.rs', lines 6:0-6:46 *)
 Definition swap
-  (T : Type) (x : T) (y : T) (st : state) : result (state * unit) :=
-  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
-  p1 <- core_mem_swap_back1 T x y st st1;
-  let (st2, _) := p1 in
-  Return (st2, tt)
+  (T : Type) (x : T) (y : T) (st : state) : result (state * (T * T)) :=
+  core_mem_swap T x y st
 .
 
-(** [external::swap]: backward function 0
-    Source: 'src/external.rs', lines 6:0-6:46 *)
-Definition swap_back
-  (T : Type) (x : T) (y : T) (st : state) (st0 : state) :
-  result (state * (T * T))
-  :=
-  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
-  p1 <- core_mem_swap_back1 T x y st st2;
-  let (_, y0) := p1 in
-  Return (st0, (x0, y0))
-.
-
-(** [external::test_new_non_zero_u32]: forward function
+(** [external::test_new_non_zero_u32]:
     Source: 'src/external.rs', lines 11:0-11:60 *)
 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
+  let (st1, o) := p in
+  core_option_Option_unwrap core_num_nonzero_NonZeroU32_t o st1
 .
 
-(** [external::test_vec]: forward function
+(** [external::test_vec]:
     Source: 'src/external.rs', lines 17:0-17:17 *)
 Definition test_vec : result unit :=
-  let v := alloc_vec_Vec_new u32 in
-  _ <- alloc_vec_Vec_push u32 v 0%u32;
-  Return tt
+  _ <- alloc_vec_Vec_push u32 (alloc_vec_Vec_new u32) 0%u32; Return tt
 .
 
 (** Unit test for [external::test_vec] *)
 Check (test_vec )%return.
 
-(** [external::custom_swap]: forward function
+(** [external::custom_swap]:
     Source: 'src/external.rs', lines 24:0-24:66 *)
 Definition custom_swap
-  (T : Type) (x : T) (y : T) (st : state) : result (state * T) :=
-  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
-  p1 <- core_mem_swap_back1 T x y st st1;
-  let (st2, _) := p1 in
-  Return (st2, x0)
-.
-
-(** [external::custom_swap]: backward function 0
-    Source: 'src/external.rs', lines 24:0-24:66 *)
-Definition custom_swap_back
-  (T : Type) (x : T) (y : T) (st : state) (ret : T) (st0 : state) :
-  result (state * (T * T))
+  (T : Type) (x : T) (y : T) (st : state) :
+  result (state * (T * (T -> state -> result (state * (T * T)))))
   :=
   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
-  p1 <- core_mem_swap_back1 T x y st st2;
-  let (_, y0) := p1 in
-  Return (st0, (ret, y0))
+  let (st1, p1) := p in
+  let (t, t1) := p1 in
+  let back_'a := fun (ret : T) (st2 : state) => Return (st2, (ret, t1)) in
+  Return (st1, (t, back_'a))
 .
 
-(** [external::test_custom_swap]: forward function
+(** [external::test_custom_swap]:
     Source: 'src/external.rs', lines 29:0-29:59 *)
 Definition test_custom_swap
-  (x : u32) (y : u32) (st : state) : result (state * unit) :=
-  p <- custom_swap u32 x y st; let (st0, _) := p in Return (st0, tt)
-.
-
-(** [external::test_custom_swap]: backward function 0
-    Source: 'src/external.rs', lines 29:0-29:59 *)
-Definition test_custom_swap_back
-  (x : u32) (y : u32) (st : state) (st0 : state) :
-  result (state * (u32 * u32))
-  :=
-  custom_swap_back u32 x y st 1%u32 st0
+  (x : u32) (y : u32) (st : state) : result (state * (u32 * u32)) :=
+  p <- custom_swap u32 x y st;
+  let (st1, p1) := p in
+  let (_, custom_swap_back) := p1 in
+  p2 <- custom_swap_back 1%u32 st1;
+  let (_, p3) := p2 in
+  let (x1, y1) := p3 in
+  Return (st1, (x1, y1))
 .
 
-(** [external::test_swap_non_zero]: forward function
+(** [external::test_swap_non_zero]:
     Source: 'src/external.rs', lines 35:0-35:44 *)
 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
-  let (x0, _) := p1 in
-  if x0 s= 0%u32 then Fail_ Failure else Return (st1, x0)
+  let (st1, p1) := p in
+  let (x1, _) := p1 in
+  if x1 s= 0%u32 then Fail_ Failure else Return (st1, x1)
 .
 
 End External_Funs.
diff --git a/tests/coq/misc/External_FunsExternal.v b/tests/coq/misc/External_FunsExternal.v
index a8c5756a..e9655f57 100644
--- a/tests/coq/misc/External_FunsExternal.v
+++ b/tests/coq/misc/External_FunsExternal.v
@@ -10,22 +10,10 @@ Require Export External_Types.
 Include External_Types.
 Module External_FunsExternal.
 
-(** [core::mem::swap]: forward function
+(** [core::mem::swap]:
     Source: '/rustc/d59363ad0b6391b7fc5bbb02c9ccf9300eef3753/library/core/src/mem/mod.rs', lines 726:0-726:42 *)
-Axiom core_mem_swap :
-  forall(T : Type), T -> T -> state -> result (state * unit)
-.
-
-(** [core::mem::swap]: backward function 0
-    Source: '/rustc/d59363ad0b6391b7fc5bbb02c9ccf9300eef3753/library/core/src/mem/mod.rs', lines 726:0-726:42 *)
-Axiom core_mem_swap_back0 :
-  forall(T : Type), T -> T -> state -> state -> result (state * T)
-.
-
-(** [core::mem::swap]: backward function 1
-    Source: '/rustc/d59363ad0b6391b7fc5bbb02c9ccf9300eef3753/library/core/src/mem/mod.rs', lines 726:0-726:42 *)
-Axiom core_mem_swap_back1 :
-  forall(T : Type), T -> T -> state -> state -> result (state * T)
+Definition core_mem_swap (T : Type) (x : T) (y : T) (s : state) :=
+  Return (s, (y, x))
 .
 
 (** [core::num::nonzero::{core::num::nonzero::NonZeroU32#14}::new]: forward function
diff --git a/tests/coq/misc/External_FunsExternal_Template.v b/tests/coq/misc/External_FunsExternal_Template.v
index 31e69c39..6773ac18 100644
--- a/tests/coq/misc/External_FunsExternal_Template.v
+++ b/tests/coq/misc/External_FunsExternal_Template.v
@@ -11,31 +11,19 @@ Require Import External_Types.
 Include External_Types.
 Module External_FunsExternal_Template.
 
-(** [core::mem::swap]: forward function
+(** [core::mem::swap]:
     Source: '/rustc/d59363ad0b6391b7fc5bbb02c9ccf9300eef3753/library/core/src/mem/mod.rs', lines 726:0-726:42 *)
 Axiom core_mem_swap :
-  forall(T : Type), T -> T -> state -> result (state * unit)
+  forall(T : Type), T -> T -> state -> result (state * (T * T))
 .
 
-(** [core::mem::swap]: backward function 0
-    Source: '/rustc/d59363ad0b6391b7fc5bbb02c9ccf9300eef3753/library/core/src/mem/mod.rs', lines 726:0-726:42 *)
-Axiom core_mem_swap_back0 :
-  forall(T : Type), T -> T -> state -> state -> result (state * T)
-.
-
-(** [core::mem::swap]: backward function 1
-    Source: '/rustc/d59363ad0b6391b7fc5bbb02c9ccf9300eef3753/library/core/src/mem/mod.rs', lines 726:0-726:42 *)
-Axiom core_mem_swap_back1 :
-  forall(T : Type), T -> T -> state -> state -> result (state * T)
-.
-
-(** [core::num::nonzero::{core::num::nonzero::NonZeroU32#14}::new]: forward function
+(** [core::num::nonzero::{core::num::nonzero::NonZeroU32#14}::new]:
     Source: '/rustc/d59363ad0b6391b7fc5bbb02c9ccf9300eef3753/library/core/src/num/nonzero.rs', lines 79:16-79:57 *)
 Axiom core_num_nonzero_NonZeroU32_new
   : u32 -> state -> result (state * (option core_num_nonzero_NonZeroU32_t))
 .
 
-(** [core::option::{core::option::Option<T>}::unwrap]: forward function
+(** [core::option::{core::option::Option<T>}::unwrap]:
     Source: '/rustc/d59363ad0b6391b7fc5bbb02c9ccf9300eef3753/library/core/src/option.rs', lines 932:4-932:34 *)
 Axiom core_option_Option_unwrap :
   forall(T : Type), option T -> state -> result (state * T)
diff --git a/tests/coq/misc/Loops.v b/tests/coq/misc/Loops.v
index 83c249c1..af920d41 100644
--- a/tests/coq/misc/Loops.v
+++ b/tests/coq/misc/Loops.v
@@ -8,90 +8,90 @@ Import ListNotations.
 Local Open Scope Primitives_scope.
 Module Loops.
 
-(** [loops::sum]: loop 0: forward function
+(** [loops::sum]: loop 0:
     Source: 'src/loops.rs', lines 4:0-14:1 *)
 Fixpoint sum_loop (n : nat) (max : u32) (i : u32) (s : u32) : result u32 :=
   match n with
   | O => Fail_ OutOfFuel
-  | S n0 =>
+  | S n1 =>
     if i s< max
-    then (s0 <- u32_add s i; i0 <- u32_add i 1%u32; sum_loop n0 max i0 s0)
+    then (s1 <- u32_add s i; i1 <- u32_add i 1%u32; sum_loop n1 max i1 s1)
     else u32_mul s 2%u32
   end
 .
 
-(** [loops::sum]: forward function
+(** [loops::sum]:
     Source: 'src/loops.rs', lines 4:0-4:27 *)
 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
+(** [loops::sum_with_mut_borrows]: loop 0:
     Source: 'src/loops.rs', lines 19:0-31:1 *)
 Fixpoint sum_with_mut_borrows_loop
   (n : nat) (max : u32) (mi : u32) (ms : u32) : result u32 :=
   match n with
   | O => Fail_ OutOfFuel
-  | S n0 =>
+  | S n1 =>
     if mi s< max
     then (
-      ms0 <- u32_add ms mi;
-      mi0 <- u32_add mi 1%u32;
-      sum_with_mut_borrows_loop n0 max mi0 ms0)
+      ms1 <- u32_add ms mi;
+      mi1 <- u32_add mi 1%u32;
+      sum_with_mut_borrows_loop n1 max mi1 ms1)
     else u32_mul ms 2%u32
   end
 .
 
-(** [loops::sum_with_mut_borrows]: forward function
+(** [loops::sum_with_mut_borrows]:
     Source: 'src/loops.rs', lines 19:0-19:44 *)
 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
+(** [loops::sum_with_shared_borrows]: loop 0:
     Source: 'src/loops.rs', lines 34:0-48:1 *)
 Fixpoint sum_with_shared_borrows_loop
   (n : nat) (max : u32) (i : u32) (s : u32) : result u32 :=
   match n with
   | O => Fail_ OutOfFuel
-  | S n0 =>
+  | S n1 =>
     if i s< max
     then (
-      i0 <- u32_add i 1%u32;
-      s0 <- u32_add s i0;
-      sum_with_shared_borrows_loop n0 max i0 s0)
+      i1 <- u32_add i 1%u32;
+      s1 <- u32_add s i1;
+      sum_with_shared_borrows_loop n1 max i1 s1)
     else u32_mul s 2%u32
   end
 .
 
-(** [loops::sum_with_shared_borrows]: forward function
+(** [loops::sum_with_shared_borrows]:
     Source: 'src/loops.rs', lines 34:0-34:47 *)
 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 ())
+(** [loops::clear]: loop 0:
     Source: 'src/loops.rs', lines 52:0-58:1 *)
 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 := alloc_vec_Vec_len u32 v in
-    if i s< i0
+  | S n1 =>
+    let i1 := alloc_vec_Vec_len u32 v in
+    if i s< i1
     then (
-      i1 <- usize_add i 1%usize;
-      v0 <-
-        alloc_vec_Vec_index_mut_back u32 usize
-          (core_slice_index_SliceIndexUsizeSliceTInst u32) v i 0%u32;
-      clear_loop n0 v0 i1)
+      p <-
+        alloc_vec_Vec_index_mut u32 usize
+          (core_slice_index_SliceIndexUsizeSliceTInst u32) v i;
+      let (_, index_mut_back) := p in
+      i2 <- usize_add i 1%usize;
+      v1 <- index_mut_back 0%u32;
+      clear_loop n1 v1 i2)
     else Return v
   end
 .
 
-(** [loops::clear]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ())
+(** [loops::clear]:
     Source: 'src/loops.rs', lines 52:0-52:30 *)
 Definition clear
   (n : nat) (v : alloc_vec_Vec u32) : result (alloc_vec_Vec u32) :=
@@ -108,181 +108,143 @@ Inductive List_t (T : Type) :=
 Arguments List_Cons { _ }.
 Arguments List_Nil { _ }.
 
-(** [loops::list_mem]: loop 0: forward function
+(** [loops::list_mem]: loop 0:
     Source: 'src/loops.rs', lines 66:0-75:1 *)
 Fixpoint list_mem_loop (n : nat) (x : u32) (ls : List_t u32) : result bool :=
   match n with
   | O => Fail_ OutOfFuel
-  | S n0 =>
+  | S n1 =>
     match ls with
-    | List_Cons y tl => if y s= x then Return true else list_mem_loop n0 x tl
+    | List_Cons y tl => if y s= x then Return true else list_mem_loop n1 x tl
     | List_Nil => Return false
     end
   end
 .
 
-(** [loops::list_mem]: forward function
+(** [loops::list_mem]:
     Source: 'src/loops.rs', lines 66:0-66:52 *)
 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
+(** [loops::list_nth_mut_loop]: loop 0:
     Source: 'src/loops.rs', lines 78:0-88:1 *)
 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
-    | List_Cons x tl =>
-      if i s= 0%u32
-      then Return x
-      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
-    Source: 'src/loops.rs', lines 78:0-78:71 *)
-Definition list_nth_mut_loop
-  (T : Type) (n : nat) (ls : List_t T) (i : u32) : result T :=
-  list_nth_mut_loop_loop T n ls i
-.
-
-(** [loops::list_nth_mut_loop]: loop 0: backward function 0
-    Source: 'src/loops.rs', lines 78:0-88:1 *)
-Fixpoint list_nth_mut_loop_loop_back
-  (T : Type) (n : nat) (ls : List_t T) (i : u32) (ret : T) :
-  result (List_t T)
+  (T : Type) (n : nat) (ls : List_t T) (i : u32) :
+  result (T * (T -> result (List_t T)))
   :=
   match n with
   | O => Fail_ OutOfFuel
-  | S n0 =>
+  | S n1 =>
     match ls with
     | List_Cons x tl =>
       if i s= 0%u32
-      then Return (List_Cons ret tl)
+      then
+        let back := fun (ret : T) => Return (List_Cons ret tl) in
+        Return (x, back)
       else (
-        i0 <- u32_sub i 1%u32;
-        tl0 <- list_nth_mut_loop_loop_back T n0 tl i0 ret;
-        Return (List_Cons x tl0))
+        i1 <- u32_sub i 1%u32;
+        p <- list_nth_mut_loop_loop T n1 tl i1;
+        let (t, back) := p in
+        let back1 := fun (ret : T) => tl1 <- back ret; Return (List_Cons x tl1)
+          in
+        Return (t, back1))
     | List_Nil => Fail_ Failure
     end
   end
 .
 
-(** [loops::list_nth_mut_loop]: backward function 0
+(** [loops::list_nth_mut_loop]:
     Source: 'src/loops.rs', lines 78:0-78:71 *)
-Definition list_nth_mut_loop_back
-  (T : Type) (n : nat) (ls : List_t T) (i : u32) (ret : T) :
-  result (List_t T)
+Definition list_nth_mut_loop
+  (T : Type) (n : nat) (ls : List_t T) (i : u32) :
+  result (T * (T -> result (List_t T)))
   :=
-  list_nth_mut_loop_loop_back T n ls i ret
+  p <- list_nth_mut_loop_loop T n ls i; let (t, back) := p in Return (t, back)
 .
 
-(** [loops::list_nth_shared_loop]: loop 0: forward function
+(** [loops::list_nth_shared_loop]: loop 0:
     Source: 'src/loops.rs', lines 91:0-101:1 *)
 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 =>
+  | S n1 =>
     match ls with
     | List_Cons x tl =>
       if i s= 0%u32
       then Return x
-      else (i0 <- u32_sub i 1%u32; list_nth_shared_loop_loop T n0 tl i0)
+      else (i1 <- u32_sub i 1%u32; list_nth_shared_loop_loop T n1 tl i1)
     | List_Nil => Fail_ Failure
     end
   end
 .
 
-(** [loops::list_nth_shared_loop]: forward function
+(** [loops::list_nth_shared_loop]:
     Source: 'src/loops.rs', lines 91:0-91:66 *)
 Definition list_nth_shared_loop
   (T : Type) (n : nat) (ls : List_t T) (i : u32) : result T :=
   list_nth_shared_loop_loop T n ls i
 .
 
-(** [loops::get_elem_mut]: loop 0: forward function
+(** [loops::get_elem_mut]: loop 0:
     Source: 'src/loops.rs', lines 103:0-117:1 *)
 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
-    | 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
-    Source: 'src/loops.rs', lines 103:0-103:73 *)
-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_SliceIndexUsizeSliceTInst (List_t usize)) slots 0%usize;
-  get_elem_mut_loop n x l
-.
-
-(** [loops::get_elem_mut]: loop 0: backward function 0
-    Source: 'src/loops.rs', lines 103:0-117:1 *)
-Fixpoint get_elem_mut_loop_back
-  (n : nat) (x : usize) (ls : List_t usize) (ret : usize) :
-  result (List_t usize)
+  (n : nat) (x : usize) (ls : List_t usize) :
+  result (usize * (usize -> result (List_t usize)))
   :=
   match n with
   | O => Fail_ OutOfFuel
-  | S n0 =>
+  | S n1 =>
     match ls with
     | List_Cons y tl =>
       if y s= x
-      then Return (List_Cons ret tl)
+      then
+        let back := fun (ret : usize) => Return (List_Cons ret tl) in
+        Return (y, back)
       else (
-        tl0 <- get_elem_mut_loop_back n0 x tl ret; Return (List_Cons y tl0))
+        p <- get_elem_mut_loop n1 x tl;
+        let (i, back) := p in
+        let back1 :=
+          fun (ret : usize) => tl1 <- back ret; Return (List_Cons y tl1) in
+        Return (i, back1))
     | List_Nil => Fail_ Failure
     end
   end
 .
 
-(** [loops::get_elem_mut]: backward function 0
+(** [loops::get_elem_mut]:
     Source: 'src/loops.rs', lines 103:0-103:73 *)
-Definition get_elem_mut_back
-  (n : nat) (slots : alloc_vec_Vec (List_t usize)) (x : usize) (ret : usize) :
-  result (alloc_vec_Vec (List_t usize))
+Definition get_elem_mut
+  (n : nat) (slots : alloc_vec_Vec (List_t usize)) (x : usize) :
+  result (usize * (usize -> result (alloc_vec_Vec (List_t usize))))
   :=
-  l <-
+  p <-
     alloc_vec_Vec_index_mut (List_t usize) usize
       (core_slice_index_SliceIndexUsizeSliceTInst (List_t usize)) slots 0%usize;
-  l0 <- get_elem_mut_loop_back n x l ret;
-  alloc_vec_Vec_index_mut_back (List_t usize) usize
-    (core_slice_index_SliceIndexUsizeSliceTInst (List_t usize)) slots 0%usize
-    l0
+  let (l, index_mut_back) := p in
+  p1 <- get_elem_mut_loop n x l;
+  let (i, back) := p1 in
+  let back1 := fun (ret : usize) => l1 <- back ret; index_mut_back l1 in
+  Return (i, back1)
 .
 
-(** [loops::get_elem_shared]: loop 0: forward function
+(** [loops::get_elem_shared]: loop 0:
     Source: 'src/loops.rs', lines 119:0-133:1 *)
 Fixpoint get_elem_shared_loop
   (n : nat) (x : usize) (ls : List_t usize) : result usize :=
   match n with
   | O => Fail_ OutOfFuel
-  | S n0 =>
+  | S n1 =>
     match ls with
     | List_Cons y tl =>
-      if y s= x then Return y else get_elem_shared_loop n0 x tl
+      if y s= x then Return y else get_elem_shared_loop n1 x tl
     | List_Nil => Fail_ Failure
     end
   end
 .
 
-(** [loops::get_elem_shared]: forward function
+(** [loops::get_elem_shared]:
     Source: 'src/loops.rs', lines 119:0-119:68 *)
 Definition get_elem_shared
   (n : nat) (slots : alloc_vec_Vec (List_t usize)) (x : usize) :
@@ -294,123 +256,114 @@ Definition get_elem_shared
   get_elem_shared_loop n x l
 .
 
-(** [loops::id_mut]: forward function
-    Source: 'src/loops.rs', lines 135:0-135:50 *)
-Definition id_mut (T : Type) (ls : List_t T) : result (List_t T) :=
-  Return ls.
-
-(** [loops::id_mut]: backward function 0
+(** [loops::id_mut]:
     Source: 'src/loops.rs', lines 135:0-135:50 *)
-Definition id_mut_back
-  (T : Type) (ls : List_t T) (ret : List_t T) : result (List_t T) :=
-  Return ret
+Definition id_mut
+  (T : Type) (ls : List_t T) :
+  result ((List_t T) * (List_t T -> result (List_t T)))
+  :=
+  Return (ls, Return)
 .
 
-(** [loops::id_shared]: forward function
+(** [loops::id_shared]:
     Source: 'src/loops.rs', lines 139:0-139:45 *)
 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
+(** [loops::list_nth_mut_loop_with_id]: loop 0:
     Source: 'src/loops.rs', lines 144:0-155:1 *)
 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
-    | 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 T n0 i0 tl)
-    | List_Nil => Fail_ Failure
-    end
-  end
-.
-
-(** [loops::list_nth_mut_loop_with_id]: forward function
-    Source: 'src/loops.rs', lines 144:0-144:75 *)
-Definition list_nth_mut_loop_with_id
-  (T : Type) (n : nat) (ls : List_t T) (i : u32) : result T :=
-  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
-    Source: 'src/loops.rs', lines 144:0-155:1 *)
-Fixpoint list_nth_mut_loop_with_id_loop_back
-  (T : Type) (n : nat) (i : u32) (ls : List_t T) (ret : T) :
-  result (List_t T)
+  (T : Type) (n : nat) (i : u32) (ls : List_t T) :
+  result (T * (T -> result (List_t T)))
   :=
   match n with
   | O => Fail_ OutOfFuel
-  | S n0 =>
+  | S n1 =>
     match ls with
     | List_Cons x tl =>
       if i s= 0%u32
-      then Return (List_Cons ret tl)
+      then
+        let back := fun (ret : T) => Return (List_Cons ret tl) in
+        Return (x, back)
       else (
-        i0 <- u32_sub i 1%u32;
-        tl0 <- list_nth_mut_loop_with_id_loop_back T n0 i0 tl ret;
-        Return (List_Cons x tl0))
+        i1 <- u32_sub i 1%u32;
+        p <- list_nth_mut_loop_with_id_loop T n1 i1 tl;
+        let (t, back) := p in
+        let back1 := fun (ret : T) => tl1 <- back ret; Return (List_Cons x tl1)
+          in
+        Return (t, back1))
     | List_Nil => Fail_ Failure
     end
   end
 .
 
-(** [loops::list_nth_mut_loop_with_id]: backward function 0
+(** [loops::list_nth_mut_loop_with_id]:
     Source: 'src/loops.rs', lines 144:0-144:75 *)
-Definition list_nth_mut_loop_with_id_back
-  (T : Type) (n : nat) (ls : List_t T) (i : u32) (ret : T) :
-  result (List_t T)
+Definition list_nth_mut_loop_with_id
+  (T : Type) (n : nat) (ls : List_t T) (i : u32) :
+  result (T * (T -> result (List_t T)))
   :=
-  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
+  p <- id_mut T ls;
+  let (ls1, id_mut_back) := p in
+  p1 <- list_nth_mut_loop_with_id_loop T n i ls1;
+  let (t, back) := p1 in
+  let back1 := fun (ret : T) => l <- back ret; id_mut_back l in
+  Return (t, back1)
 .
 
-(** [loops::list_nth_shared_loop_with_id]: loop 0: forward function
+(** [loops::list_nth_shared_loop_with_id]: loop 0:
     Source: 'src/loops.rs', lines 158:0-169:1 *)
 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 =>
+  | S n1 =>
     match ls with
     | 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 T n0 i0 tl)
+        i1 <- u32_sub i 1%u32; list_nth_shared_loop_with_id_loop T n1 i1 tl)
     | List_Nil => Fail_ Failure
     end
   end
 .
 
-(** [loops::list_nth_shared_loop_with_id]: forward function
+(** [loops::list_nth_shared_loop_with_id]:
     Source: 'src/loops.rs', lines 158:0-158:70 *)
 Definition list_nth_shared_loop_with_id
   (T : Type) (n : nat) (ls : List_t T) (i : u32) : result T :=
-  ls0 <- id_shared T ls; list_nth_shared_loop_with_id_loop T n i ls0
+  ls1 <- id_shared T ls; list_nth_shared_loop_with_id_loop T n i ls1
 .
 
-(** [loops::list_nth_mut_loop_pair]: loop 0: forward function
+(** [loops::list_nth_mut_loop_pair]: loop 0:
     Source: 'src/loops.rs', lines 174:0-195:1 *)
 Fixpoint list_nth_mut_loop_pair_loop
   (T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) :
-  result (T * T)
+  result ((T * T) * (T -> result (List_t T)) * (T -> result (List_t T)))
   :=
   match n with
   | O => Fail_ OutOfFuel
-  | S n0 =>
+  | S n1 =>
     match ls0 with
     | List_Cons x0 tl0 =>
       match ls1 with
       | List_Cons x1 tl1 =>
         if i s= 0%u32
-        then Return (x0, x1)
+        then
+          let back_'a := fun (ret : T) => Return (List_Cons ret tl0) in
+          let back_'b := fun (ret : T) => Return (List_Cons ret tl1) in
+          Return ((x0, x1), back_'a, back_'b)
         else (
-          i0 <- u32_sub i 1%u32; list_nth_mut_loop_pair_loop T n0 tl0 tl1 i0)
+          i1 <- u32_sub i 1%u32;
+          t <- list_nth_mut_loop_pair_loop T n1 tl0 tl1 i1;
+          let '(p, back_'a, back_'b) := t in
+          let back_'a1 :=
+            fun (ret : T) => tl01 <- back_'a ret; Return (List_Cons x0 tl01) in
+          let back_'b1 :=
+            fun (ret : T) => tl11 <- back_'b ret; Return (List_Cons x1 tl11) in
+          Return (p, back_'a1, back_'b1))
       | List_Nil => Fail_ Failure
       end
     | List_Nil => Fail_ Failure
@@ -418,86 +371,18 @@ Fixpoint list_nth_mut_loop_pair_loop
   end
 .
 
-(** [loops::list_nth_mut_loop_pair]: forward function
+(** [loops::list_nth_mut_loop_pair]:
     Source: 'src/loops.rs', lines 174:0-178:27 *)
 Definition list_nth_mut_loop_pair
   (T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) :
-  result (T * T)
+  result ((T * T) * (T -> result (List_t T)) * (T -> result (List_t T)))
   :=
-  list_nth_mut_loop_pair_loop T n ls0 ls1 i
+  t <- list_nth_mut_loop_pair_loop T n ls0 ls1 i;
+  let '(p, back_'a, back_'b) := t in
+  Return (p, back_'a, back_'b)
 .
 
-(** [loops::list_nth_mut_loop_pair]: loop 0: backward function 0
-    Source: 'src/loops.rs', lines 174:0-195:1 *)
-Fixpoint list_nth_mut_loop_pair_loop_back'a
-  (T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) (ret : T) :
-  result (List_t T)
-  :=
-  match n with
-  | O => Fail_ OutOfFuel
-  | S n0 =>
-    match ls0 with
-    | List_Cons x0 tl0 =>
-      match ls1 with
-      | List_Cons x1 tl1 =>
-        if i s= 0%u32
-        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 (List_Cons x0 tl00))
-      | List_Nil => Fail_ Failure
-      end
-    | List_Nil => Fail_ Failure
-    end
-  end
-.
-
-(** [loops::list_nth_mut_loop_pair]: backward function 0
-    Source: 'src/loops.rs', lines 174:0-178:27 *)
-Definition list_nth_mut_loop_pair_back'a
-  (T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) (ret : T) :
-  result (List_t T)
-  :=
-  list_nth_mut_loop_pair_loop_back'a T n ls0 ls1 i ret
-.
-
-(** [loops::list_nth_mut_loop_pair]: loop 0: backward function 1
-    Source: 'src/loops.rs', lines 174:0-195:1 *)
-Fixpoint list_nth_mut_loop_pair_loop_back'b
-  (T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) (ret : T) :
-  result (List_t T)
-  :=
-  match n with
-  | O => Fail_ OutOfFuel
-  | S n0 =>
-    match ls0 with
-    | List_Cons x0 tl0 =>
-      match ls1 with
-      | List_Cons x1 tl1 =>
-        if i s= 0%u32
-        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 (List_Cons x1 tl10))
-      | List_Nil => Fail_ Failure
-      end
-    | List_Nil => Fail_ Failure
-    end
-  end
-.
-
-(** [loops::list_nth_mut_loop_pair]: backward function 1
-    Source: 'src/loops.rs', lines 174:0-178:27 *)
-Definition list_nth_mut_loop_pair_back'b
-  (T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) (ret : T) :
-  result (List_t T)
-  :=
-  list_nth_mut_loop_pair_loop_back'b T n ls0 ls1 i ret
-.
-
-(** [loops::list_nth_shared_loop_pair]: loop 0: forward function
+(** [loops::list_nth_shared_loop_pair]: loop 0:
     Source: 'src/loops.rs', lines 198:0-219:1 *)
 Fixpoint list_nth_shared_loop_pair_loop
   (T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) :
@@ -505,7 +390,7 @@ Fixpoint list_nth_shared_loop_pair_loop
   :=
   match n with
   | O => Fail_ OutOfFuel
-  | S n0 =>
+  | S n1 =>
     match ls0 with
     | List_Cons x0 tl0 =>
       match ls1 with
@@ -513,7 +398,7 @@ Fixpoint list_nth_shared_loop_pair_loop
         if i s= 0%u32
         then Return (x0, x1)
         else (
-          i0 <- u32_sub i 1%u32; list_nth_shared_loop_pair_loop T n0 tl0 tl1 i0)
+          i1 <- u32_sub i 1%u32; list_nth_shared_loop_pair_loop T n1 tl0 tl1 i1)
       | List_Nil => Fail_ Failure
       end
     | List_Nil => Fail_ Failure
@@ -521,7 +406,7 @@ Fixpoint list_nth_shared_loop_pair_loop
   end
 .
 
-(** [loops::list_nth_shared_loop_pair]: forward function
+(** [loops::list_nth_shared_loop_pair]:
     Source: 'src/loops.rs', lines 198:0-202:19 *)
 Definition list_nth_shared_loop_pair
   (T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) :
@@ -530,24 +415,36 @@ Definition list_nth_shared_loop_pair
   list_nth_shared_loop_pair_loop T n ls0 ls1 i
 .
 
-(** [loops::list_nth_mut_loop_pair_merge]: loop 0: forward function
+(** [loops::list_nth_mut_loop_pair_merge]: loop 0:
     Source: 'src/loops.rs', lines 223:0-238:1 *)
 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)
+  result ((T * T) * ((T * T) -> result ((List_t T) * (List_t T))))
   :=
   match n with
   | O => Fail_ OutOfFuel
-  | S n0 =>
+  | S n1 =>
     match ls0 with
     | List_Cons x0 tl0 =>
       match ls1 with
       | List_Cons x1 tl1 =>
         if i s= 0%u32
-        then Return (x0, x1)
+        then
+          let back_'a :=
+            fun (ret : (T * T)) =>
+              let (t, t1) := ret in Return (List_Cons t tl0, List_Cons t1 tl1)
+            in
+          Return ((x0, x1), back_'a)
         else (
-          i0 <- u32_sub i 1%u32;
-          list_nth_mut_loop_pair_merge_loop T n0 tl0 tl1 i0)
+          i1 <- u32_sub i 1%u32;
+          p <- list_nth_mut_loop_pair_merge_loop T n1 tl0 tl1 i1;
+          let (p1, back_'a) := p in
+          let back_'a1 :=
+            fun (ret : (T * T)) =>
+              p2 <- back_'a ret;
+              let (tl01, tl11) := p2 in
+              Return (List_Cons x0 tl01, List_Cons x1 tl11) in
+          Return (p1, back_'a1))
       | List_Nil => Fail_ Failure
       end
     | List_Nil => Fail_ Failure
@@ -555,54 +452,18 @@ Fixpoint list_nth_mut_loop_pair_merge_loop
   end
 .
 
-(** [loops::list_nth_mut_loop_pair_merge]: forward function
+(** [loops::list_nth_mut_loop_pair_merge]:
     Source: 'src/loops.rs', lines 223:0-227:27 *)
 Definition list_nth_mut_loop_pair_merge
   (T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) :
-  result (T * T)
+  result ((T * T) * ((T * T) -> result ((List_t T) * (List_t T))))
   :=
-  list_nth_mut_loop_pair_merge_loop T n ls0 ls1 i
+  p <- list_nth_mut_loop_pair_merge_loop T n ls0 ls1 i;
+  let (p1, back_'a) := p in
+  Return (p1, back_'a)
 .
 
-(** [loops::list_nth_mut_loop_pair_merge]: loop 0: backward function 0
-    Source: 'src/loops.rs', lines 223:0-238:1 *)
-Fixpoint list_nth_mut_loop_pair_merge_loop_back
-  (T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32)
-  (ret : (T * T)) :
-  result ((List_t T) * (List_t T))
-  :=
-  match n with
-  | O => Fail_ OutOfFuel
-  | S n0 =>
-    match ls0 with
-    | List_Cons x0 tl0 =>
-      match ls1 with
-      | List_Cons x1 tl1 =>
-        if i s= 0%u32
-        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 (List_Cons x0 tl00, List_Cons x1 tl10))
-      | List_Nil => Fail_ Failure
-      end
-    | List_Nil => Fail_ Failure
-    end
-  end
-.
-
-(** [loops::list_nth_mut_loop_pair_merge]: backward function 0
-    Source: 'src/loops.rs', lines 223:0-227:27 *)
-Definition list_nth_mut_loop_pair_merge_back
-  (T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32)
-  (ret : (T * T)) :
-  result ((List_t T) * (List_t T))
-  :=
-  list_nth_mut_loop_pair_merge_loop_back T n ls0 ls1 i ret
-.
-
-(** [loops::list_nth_shared_loop_pair_merge]: loop 0: forward function
+(** [loops::list_nth_shared_loop_pair_merge]: loop 0:
     Source: 'src/loops.rs', lines 241:0-256:1 *)
 Fixpoint list_nth_shared_loop_pair_merge_loop
   (T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) :
@@ -610,7 +471,7 @@ Fixpoint list_nth_shared_loop_pair_merge_loop
   :=
   match n with
   | O => Fail_ OutOfFuel
-  | S n0 =>
+  | S n1 =>
     match ls0 with
     | List_Cons x0 tl0 =>
       match ls1 with
@@ -618,8 +479,8 @@ Fixpoint list_nth_shared_loop_pair_merge_loop
         if i s= 0%u32
         then Return (x0, x1)
         else (
-          i0 <- u32_sub i 1%u32;
-          list_nth_shared_loop_pair_merge_loop T n0 tl0 tl1 i0)
+          i1 <- u32_sub i 1%u32;
+          list_nth_shared_loop_pair_merge_loop T n1 tl0 tl1 i1)
       | List_Nil => Fail_ Failure
       end
     | List_Nil => Fail_ Failure
@@ -627,7 +488,7 @@ Fixpoint list_nth_shared_loop_pair_merge_loop
   end
 .
 
-(** [loops::list_nth_shared_loop_pair_merge]: forward function
+(** [loops::list_nth_shared_loop_pair_merge]:
     Source: 'src/loops.rs', lines 241:0-245:19 *)
 Definition list_nth_shared_loop_pair_merge
   (T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) :
@@ -636,24 +497,30 @@ Definition list_nth_shared_loop_pair_merge
   list_nth_shared_loop_pair_merge_loop T n ls0 ls1 i
 .
 
-(** [loops::list_nth_mut_shared_loop_pair]: loop 0: forward function
+(** [loops::list_nth_mut_shared_loop_pair]: loop 0:
     Source: 'src/loops.rs', lines 259:0-274:1 *)
 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)
+  result ((T * T) * (T -> result (List_t T)))
   :=
   match n with
   | O => Fail_ OutOfFuel
-  | S n0 =>
+  | S n1 =>
     match ls0 with
     | List_Cons x0 tl0 =>
       match ls1 with
       | List_Cons x1 tl1 =>
         if i s= 0%u32
-        then Return (x0, x1)
+        then
+          let back_'a := fun (ret : T) => Return (List_Cons ret tl0) in
+          Return ((x0, x1), back_'a)
         else (
-          i0 <- u32_sub i 1%u32;
-          list_nth_mut_shared_loop_pair_loop T n0 tl0 tl1 i0)
+          i1 <- u32_sub i 1%u32;
+          p <- list_nth_mut_shared_loop_pair_loop T n1 tl0 tl1 i1;
+          let (p1, back_'a) := p in
+          let back_'a1 :=
+            fun (ret : T) => tl01 <- back_'a ret; Return (List_Cons x0 tl01) in
+          Return (p1, back_'a1))
       | List_Nil => Fail_ Failure
       end
     | List_Nil => Fail_ Failure
@@ -661,68 +528,41 @@ Fixpoint list_nth_mut_shared_loop_pair_loop
   end
 .
 
-(** [loops::list_nth_mut_shared_loop_pair]: forward function
+(** [loops::list_nth_mut_shared_loop_pair]:
     Source: 'src/loops.rs', lines 259:0-263:23 *)
 Definition list_nth_mut_shared_loop_pair
   (T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) :
-  result (T * T)
+  result ((T * T) * (T -> result (List_t T)))
   :=
-  list_nth_mut_shared_loop_pair_loop T n ls0 ls1 i
+  p <- list_nth_mut_shared_loop_pair_loop T n ls0 ls1 i;
+  let (p1, back_'a) := p in
+  Return (p1, back_'a)
 .
 
-(** [loops::list_nth_mut_shared_loop_pair]: loop 0: backward function 0
-    Source: 'src/loops.rs', lines 259:0-274:1 *)
-Fixpoint list_nth_mut_shared_loop_pair_loop_back
-  (T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) (ret : T) :
-  result (List_t T)
-  :=
-  match n with
-  | O => Fail_ OutOfFuel
-  | S n0 =>
-    match ls0 with
-    | List_Cons x0 tl0 =>
-      match ls1 with
-      | List_Cons x1 tl1 =>
-        if i s= 0%u32
-        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 (List_Cons x0 tl00))
-      | List_Nil => Fail_ Failure
-      end
-    | List_Nil => Fail_ Failure
-    end
-  end
-.
-
-(** [loops::list_nth_mut_shared_loop_pair]: backward function 0
-    Source: 'src/loops.rs', lines 259:0-263:23 *)
-Definition list_nth_mut_shared_loop_pair_back
-  (T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) (ret : T) :
-  result (List_t T)
-  :=
-  list_nth_mut_shared_loop_pair_loop_back T n ls0 ls1 i ret
-.
-
-(** [loops::list_nth_mut_shared_loop_pair_merge]: loop 0: forward function
+(** [loops::list_nth_mut_shared_loop_pair_merge]: loop 0:
     Source: 'src/loops.rs', lines 278:0-293:1 *)
 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)
+  result ((T * T) * (T -> result (List_t T)))
   :=
   match n with
   | O => Fail_ OutOfFuel
-  | S n0 =>
+  | S n1 =>
     match ls0 with
     | List_Cons x0 tl0 =>
       match ls1 with
       | List_Cons x1 tl1 =>
         if i s= 0%u32
-        then Return (x0, x1)
+        then
+          let back_'a := fun (ret : T) => Return (List_Cons ret tl0) in
+          Return ((x0, x1), back_'a)
         else (
-          i0 <- u32_sub i 1%u32;
-          list_nth_mut_shared_loop_pair_merge_loop T n0 tl0 tl1 i0)
+          i1 <- u32_sub i 1%u32;
+          p <- list_nth_mut_shared_loop_pair_merge_loop T n1 tl0 tl1 i1;
+          let (p1, back_'a) := p in
+          let back_'a1 :=
+            fun (ret : T) => tl01 <- back_'a ret; Return (List_Cons x0 tl01) in
+          Return (p1, back_'a1))
       | List_Nil => Fail_ Failure
       end
     | List_Nil => Fail_ Failure
@@ -730,69 +570,41 @@ Fixpoint list_nth_mut_shared_loop_pair_merge_loop
   end
 .
 
-(** [loops::list_nth_mut_shared_loop_pair_merge]: forward function
+(** [loops::list_nth_mut_shared_loop_pair_merge]:
     Source: 'src/loops.rs', lines 278:0-282:23 *)
 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 T n ls0 ls1 i
-.
-
-(** [loops::list_nth_mut_shared_loop_pair_merge]: loop 0: backward function 0
-    Source: 'src/loops.rs', lines 278:0-293:1 *)
-Fixpoint list_nth_mut_shared_loop_pair_merge_loop_back
-  (T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) (ret : T) :
-  result (List_t T)
-  :=
-  match n with
-  | O => Fail_ OutOfFuel
-  | S n0 =>
-    match ls0 with
-    | List_Cons x0 tl0 =>
-      match ls1 with
-      | List_Cons x1 tl1 =>
-        if i s= 0%u32
-        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 (List_Cons x0 tl00))
-      | List_Nil => Fail_ Failure
-      end
-    | List_Nil => Fail_ Failure
-    end
-  end
-.
-
-(** [loops::list_nth_mut_shared_loop_pair_merge]: backward function 0
-    Source: 'src/loops.rs', lines 278:0-282:23 *)
-Definition list_nth_mut_shared_loop_pair_merge_back
-  (T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) (ret : T) :
-  result (List_t T)
+  result ((T * T) * (T -> result (List_t T)))
   :=
-  list_nth_mut_shared_loop_pair_merge_loop_back T n ls0 ls1 i ret
+  p <- list_nth_mut_shared_loop_pair_merge_loop T n ls0 ls1 i;
+  let (p1, back_'a) := p in
+  Return (p1, back_'a)
 .
 
-(** [loops::list_nth_shared_mut_loop_pair]: loop 0: forward function
+(** [loops::list_nth_shared_mut_loop_pair]: loop 0:
     Source: 'src/loops.rs', lines 297:0-312:1 *)
 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)
+  result ((T * T) * (T -> result (List_t T)))
   :=
   match n with
   | O => Fail_ OutOfFuel
-  | S n0 =>
+  | S n1 =>
     match ls0 with
     | List_Cons x0 tl0 =>
       match ls1 with
       | List_Cons x1 tl1 =>
         if i s= 0%u32
-        then Return (x0, x1)
+        then
+          let back_'b := fun (ret : T) => Return (List_Cons ret tl1) in
+          Return ((x0, x1), back_'b)
         else (
-          i0 <- u32_sub i 1%u32;
-          list_nth_shared_mut_loop_pair_loop T n0 tl0 tl1 i0)
+          i1 <- u32_sub i 1%u32;
+          p <- list_nth_shared_mut_loop_pair_loop T n1 tl0 tl1 i1;
+          let (p1, back_'b) := p in
+          let back_'b1 :=
+            fun (ret : T) => tl11 <- back_'b ret; Return (List_Cons x1 tl11) in
+          Return (p1, back_'b1))
       | List_Nil => Fail_ Failure
       end
     | List_Nil => Fail_ Failure
@@ -800,68 +612,41 @@ Fixpoint list_nth_shared_mut_loop_pair_loop
   end
 .
 
-(** [loops::list_nth_shared_mut_loop_pair]: forward function
+(** [loops::list_nth_shared_mut_loop_pair]:
     Source: 'src/loops.rs', lines 297:0-301:23 *)
 Definition list_nth_shared_mut_loop_pair
   (T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) :
-  result (T * T)
+  result ((T * T) * (T -> result (List_t T)))
   :=
-  list_nth_shared_mut_loop_pair_loop T n ls0 ls1 i
-.
-
-(** [loops::list_nth_shared_mut_loop_pair]: loop 0: backward function 1
-    Source: 'src/loops.rs', lines 297:0-312:1 *)
-Fixpoint list_nth_shared_mut_loop_pair_loop_back
-  (T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) (ret : T) :
-  result (List_t T)
-  :=
-  match n with
-  | O => Fail_ OutOfFuel
-  | S n0 =>
-    match ls0 with
-    | List_Cons x0 tl0 =>
-      match ls1 with
-      | List_Cons x1 tl1 =>
-        if i s= 0%u32
-        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 (List_Cons x1 tl10))
-      | List_Nil => Fail_ Failure
-      end
-    | List_Nil => Fail_ Failure
-    end
-  end
+  p <- list_nth_shared_mut_loop_pair_loop T n ls0 ls1 i;
+  let (p1, back_'b) := p in
+  Return (p1, back_'b)
 .
 
-(** [loops::list_nth_shared_mut_loop_pair]: backward function 1
-    Source: 'src/loops.rs', lines 297:0-301:23 *)
-Definition list_nth_shared_mut_loop_pair_back
-  (T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) (ret : T) :
-  result (List_t T)
-  :=
-  list_nth_shared_mut_loop_pair_loop_back T n ls0 ls1 i ret
-.
-
-(** [loops::list_nth_shared_mut_loop_pair_merge]: loop 0: forward function
+(** [loops::list_nth_shared_mut_loop_pair_merge]: loop 0:
     Source: 'src/loops.rs', lines 316:0-331:1 *)
 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)
+  result ((T * T) * (T -> result (List_t T)))
   :=
   match n with
   | O => Fail_ OutOfFuel
-  | S n0 =>
+  | S n1 =>
     match ls0 with
     | List_Cons x0 tl0 =>
       match ls1 with
       | List_Cons x1 tl1 =>
         if i s= 0%u32
-        then Return (x0, x1)
+        then
+          let back_'a := fun (ret : T) => Return (List_Cons ret tl1) in
+          Return ((x0, x1), back_'a)
         else (
-          i0 <- u32_sub i 1%u32;
-          list_nth_shared_mut_loop_pair_merge_loop T n0 tl0 tl1 i0)
+          i1 <- u32_sub i 1%u32;
+          p <- list_nth_shared_mut_loop_pair_merge_loop T n1 tl0 tl1 i1;
+          let (p1, back_'a) := p in
+          let back_'a1 :=
+            fun (ret : T) => tl11 <- back_'a ret; Return (List_Cons x1 tl11) in
+          Return (p1, back_'a1))
       | List_Nil => Fail_ Failure
       end
     | List_Nil => Fail_ Failure
@@ -869,49 +654,15 @@ Fixpoint list_nth_shared_mut_loop_pair_merge_loop
   end
 .
 
-(** [loops::list_nth_shared_mut_loop_pair_merge]: forward function
+(** [loops::list_nth_shared_mut_loop_pair_merge]:
     Source: 'src/loops.rs', lines 316:0-320:23 *)
 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 T n ls0 ls1 i
-.
-
-(** [loops::list_nth_shared_mut_loop_pair_merge]: loop 0: backward function 0
-    Source: 'src/loops.rs', lines 316:0-331:1 *)
-Fixpoint list_nth_shared_mut_loop_pair_merge_loop_back
-  (T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) (ret : T) :
-  result (List_t T)
-  :=
-  match n with
-  | O => Fail_ OutOfFuel
-  | S n0 =>
-    match ls0 with
-    | List_Cons x0 tl0 =>
-      match ls1 with
-      | List_Cons x1 tl1 =>
-        if i s= 0%u32
-        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 (List_Cons x1 tl10))
-      | List_Nil => Fail_ Failure
-      end
-    | List_Nil => Fail_ Failure
-    end
-  end
-.
-
-(** [loops::list_nth_shared_mut_loop_pair_merge]: backward function 0
-    Source: 'src/loops.rs', lines 316:0-320:23 *)
-Definition list_nth_shared_mut_loop_pair_merge_back
-  (T : Type) (n : nat) (ls0 : List_t T) (ls1 : List_t T) (i : u32) (ret : T) :
-  result (List_t T)
+  result ((T * T) * (T -> result (List_t T)))
   :=
-  list_nth_shared_mut_loop_pair_merge_loop_back T n ls0 ls1 i ret
+  p <- list_nth_shared_mut_loop_pair_merge_loop T n ls0 ls1 i;
+  let (p1, back_'a) := p in
+  Return (p1, back_'a)
 .
 
 End Loops.
diff --git a/tests/coq/misc/NoNestedBorrows.v b/tests/coq/misc/NoNestedBorrows.v
index 65164ac5..8857d4b6 100644
--- a/tests/coq/misc/NoNestedBorrows.v
+++ b/tests/coq/misc/NoNestedBorrows.v
@@ -54,97 +54,97 @@ Inductive Sum_t (T1 T2 : Type) :=
 Arguments Sum_Left { _ _ }.
 Arguments Sum_Right { _ _ }.
 
-(** [no_nested_borrows::neg_test]: forward function
+(** [no_nested_borrows::neg_test]:
     Source: 'src/no_nested_borrows.rs', lines 48:0-48:30 *)
 Definition neg_test (x : i32) : result i32 :=
   i32_neg x.
 
-(** [no_nested_borrows::add_u32]: forward function
+(** [no_nested_borrows::add_u32]:
     Source: 'src/no_nested_borrows.rs', lines 54:0-54:37 *)
 Definition add_u32 (x : u32) (y : u32) : result u32 :=
   u32_add x y.
 
-(** [no_nested_borrows::subs_u32]: forward function
+(** [no_nested_borrows::subs_u32]:
     Source: 'src/no_nested_borrows.rs', lines 60:0-60:38 *)
 Definition subs_u32 (x : u32) (y : u32) : result u32 :=
   u32_sub x y.
 
-(** [no_nested_borrows::div_u32]: forward function
+(** [no_nested_borrows::div_u32]:
     Source: 'src/no_nested_borrows.rs', lines 66:0-66:37 *)
 Definition div_u32 (x : u32) (y : u32) : result u32 :=
   u32_div x y.
 
-(** [no_nested_borrows::div_u32_const]: forward function
+(** [no_nested_borrows::div_u32_const]:
     Source: 'src/no_nested_borrows.rs', lines 73:0-73:35 *)
 Definition div_u32_const (x : u32) : result u32 :=
   u32_div x 2%u32.
 
-(** [no_nested_borrows::rem_u32]: forward function
+(** [no_nested_borrows::rem_u32]:
     Source: 'src/no_nested_borrows.rs', lines 78:0-78:37 *)
 Definition rem_u32 (x : u32) (y : u32) : result u32 :=
   u32_rem x y.
 
-(** [no_nested_borrows::mul_u32]: forward function
+(** [no_nested_borrows::mul_u32]:
     Source: 'src/no_nested_borrows.rs', lines 82:0-82:37 *)
 Definition mul_u32 (x : u32) (y : u32) : result u32 :=
   u32_mul x y.
 
-(** [no_nested_borrows::add_i32]: forward function
+(** [no_nested_borrows::add_i32]:
     Source: 'src/no_nested_borrows.rs', lines 88:0-88:37 *)
 Definition add_i32 (x : i32) (y : i32) : result i32 :=
   i32_add x y.
 
-(** [no_nested_borrows::subs_i32]: forward function
+(** [no_nested_borrows::subs_i32]:
     Source: 'src/no_nested_borrows.rs', lines 92:0-92:38 *)
 Definition subs_i32 (x : i32) (y : i32) : result i32 :=
   i32_sub x y.
 
-(** [no_nested_borrows::div_i32]: forward function
+(** [no_nested_borrows::div_i32]:
     Source: 'src/no_nested_borrows.rs', lines 96:0-96:37 *)
 Definition div_i32 (x : i32) (y : i32) : result i32 :=
   i32_div x y.
 
-(** [no_nested_borrows::div_i32_const]: forward function
+(** [no_nested_borrows::div_i32_const]:
     Source: 'src/no_nested_borrows.rs', lines 100:0-100:35 *)
 Definition div_i32_const (x : i32) : result i32 :=
   i32_div x 2%i32.
 
-(** [no_nested_borrows::rem_i32]: forward function
+(** [no_nested_borrows::rem_i32]:
     Source: 'src/no_nested_borrows.rs', lines 104:0-104:37 *)
 Definition rem_i32 (x : i32) (y : i32) : result i32 :=
   i32_rem x y.
 
-(** [no_nested_borrows::mul_i32]: forward function
+(** [no_nested_borrows::mul_i32]:
     Source: 'src/no_nested_borrows.rs', lines 108:0-108:37 *)
 Definition mul_i32 (x : i32) (y : i32) : result i32 :=
   i32_mul x y.
 
-(** [no_nested_borrows::mix_arith_u32]: forward function
+(** [no_nested_borrows::mix_arith_u32]:
     Source: 'src/no_nested_borrows.rs', lines 112:0-112:51 *)
 Definition mix_arith_u32 (x : u32) (y : u32) (z : u32) : result u32 :=
   i <- u32_add x y;
-  i0 <- u32_div x y;
-  i1 <- u32_mul i i0;
-  i2 <- u32_rem z y;
-  i3 <- u32_sub x i2;
-  i4 <- u32_add i1 i3;
-  i5 <- u32_add x y;
-  i6 <- u32_add i5 z;
-  u32_rem i4 i6
+  i1 <- u32_div x y;
+  i2 <- u32_mul i i1;
+  i3 <- u32_rem z y;
+  i4 <- u32_sub x i3;
+  i5 <- u32_add i2 i4;
+  i6 <- u32_add x y;
+  i7 <- u32_add i6 z;
+  u32_rem i5 i7
 .
 
-(** [no_nested_borrows::mix_arith_i32]: forward function
+(** [no_nested_borrows::mix_arith_i32]:
     Source: 'src/no_nested_borrows.rs', lines 116:0-116:51 *)
 Definition mix_arith_i32 (x : i32) (y : i32) (z : i32) : result i32 :=
   i <- i32_add x y;
-  i0 <- i32_div x y;
-  i1 <- i32_mul i i0;
-  i2 <- i32_rem z y;
-  i3 <- i32_sub x i2;
-  i4 <- i32_add i1 i3;
-  i5 <- i32_add x y;
-  i6 <- i32_add i5 z;
-  i32_rem i4 i6
+  i1 <- i32_div x y;
+  i2 <- i32_mul i i1;
+  i3 <- i32_rem z y;
+  i4 <- i32_sub x i3;
+  i5 <- i32_add i2 i4;
+  i6 <- i32_add x y;
+  i7 <- i32_add i6 z;
+  i32_rem i5 i7
 .
 
 (** [no_nested_borrows::CONST0]
@@ -157,22 +157,22 @@ Definition const0_c : usize := const0_body%global.
 Definition const1_body : result usize := usize_mul 2%usize 2%usize.
 Definition const1_c : usize := const1_body%global.
 
-(** [no_nested_borrows::cast_u32_to_i32]: forward function
+(** [no_nested_borrows::cast_u32_to_i32]:
     Source: 'src/no_nested_borrows.rs', lines 128:0-128:37 *)
 Definition cast_u32_to_i32 (x : u32) : result i32 :=
   scalar_cast U32 I32 x.
 
-(** [no_nested_borrows::cast_bool_to_i32]: forward function
+(** [no_nested_borrows::cast_bool_to_i32]:
     Source: 'src/no_nested_borrows.rs', lines 132:0-132:39 *)
 Definition cast_bool_to_i32 (x : bool) : result i32 :=
   scalar_cast_bool I32 x.
 
-(** [no_nested_borrows::cast_bool_to_bool]: forward function
+(** [no_nested_borrows::cast_bool_to_bool]:
     Source: 'src/no_nested_borrows.rs', lines 137:0-137:41 *)
 Definition cast_bool_to_bool (x : bool) : result bool :=
   Return x.
 
-(** [no_nested_borrows::test2]: forward function
+(** [no_nested_borrows::test2]:
     Source: 'src/no_nested_borrows.rs', lines 142:0-142:14 *)
 Definition test2 : result unit :=
   _ <- u32_add 23%u32 44%u32; Return tt.
@@ -180,13 +180,13 @@ Definition test2 : result unit :=
 (** Unit test for [no_nested_borrows::test2] *)
 Check (test2 )%return.
 
-(** [no_nested_borrows::get_max]: forward function
+(** [no_nested_borrows::get_max]:
     Source: 'src/no_nested_borrows.rs', lines 154:0-154:37 *)
 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
+(** [no_nested_borrows::test3]:
     Source: 'src/no_nested_borrows.rs', lines 162:0-162:14 *)
 Definition test3 : result unit :=
   x <- get_max 4%u32 3%u32;
@@ -198,7 +198,7 @@ Definition test3 : result unit :=
 (** Unit test for [no_nested_borrows::test3] *)
 Check (test3 )%return.
 
-(** [no_nested_borrows::test_neg1]: forward function
+(** [no_nested_borrows::test_neg1]:
     Source: 'src/no_nested_borrows.rs', lines 169:0-169:18 *)
 Definition test_neg1 : result unit :=
   y <- i32_neg 3%i32; if negb (y s= (-3)%i32) then Fail_ Failure else Return tt
@@ -207,7 +207,7 @@ Definition test_neg1 : result unit :=
 (** Unit test for [no_nested_borrows::test_neg1] *)
 Check (test_neg1 )%return.
 
-(** [no_nested_borrows::refs_test1]: forward function
+(** [no_nested_borrows::refs_test1]:
     Source: 'src/no_nested_borrows.rs', lines 176:0-176:19 *)
 Definition refs_test1 : result unit :=
   if negb (1%i32 s= 1%i32) then Fail_ Failure else Return tt
@@ -216,7 +216,7 @@ Definition refs_test1 : result unit :=
 (** Unit test for [no_nested_borrows::refs_test1] *)
 Check (refs_test1 )%return.
 
-(** [no_nested_borrows::refs_test2]: forward function
+(** [no_nested_borrows::refs_test2]:
     Source: 'src/no_nested_borrows.rs', lines 187:0-187:19 *)
 Definition refs_test2 : result unit :=
   if negb (2%i32 s= 2%i32)
@@ -233,7 +233,7 @@ Definition refs_test2 : result unit :=
 (** Unit test for [no_nested_borrows::refs_test2] *)
 Check (refs_test2 )%return.
 
-(** [no_nested_borrows::test_list1]: forward function
+(** [no_nested_borrows::test_list1]:
     Source: 'src/no_nested_borrows.rs', lines 203:0-203:19 *)
 Definition test_list1 : result unit :=
   Return tt.
@@ -241,36 +241,37 @@ Definition test_list1 : result unit :=
 (** Unit test for [no_nested_borrows::test_list1] *)
 Check (test_list1 )%return.
 
-(** [no_nested_borrows::test_box1]: forward function
+(** [no_nested_borrows::test_box1]:
     Source: 'src/no_nested_borrows.rs', lines 208:0-208:18 *)
 Definition test_box1 : result unit :=
-  let b := 0%i32 in
-  b0 <- alloc_boxed_Box_deref_mut_back i32 b 1%i32;
-  x <- alloc_boxed_Box_deref i32 b0;
+  p <- alloc_boxed_Box_deref_mut i32 0%i32;
+  let (_, deref_mut_back) := p in
+  b <- deref_mut_back 1%i32;
+  x <- alloc_boxed_Box_deref i32 b;
   if negb (x s= 1%i32) then Fail_ Failure else Return tt
 .
 
 (** Unit test for [no_nested_borrows::test_box1] *)
 Check (test_box1 )%return.
 
-(** [no_nested_borrows::copy_int]: forward function
+(** [no_nested_borrows::copy_int]:
     Source: 'src/no_nested_borrows.rs', lines 218:0-218:30 *)
 Definition copy_int (x : i32) : result i32 :=
   Return x.
 
-(** [no_nested_borrows::test_unreachable]: forward function
+(** [no_nested_borrows::test_unreachable]:
     Source: 'src/no_nested_borrows.rs', lines 224:0-224:32 *)
 Definition test_unreachable (b : bool) : result unit :=
   if b then Fail_ Failure else Return tt
 .
 
-(** [no_nested_borrows::test_panic]: forward function
+(** [no_nested_borrows::test_panic]:
     Source: 'src/no_nested_borrows.rs', lines 232:0-232:26 *)
 Definition test_panic (b : bool) : result unit :=
   if b then Fail_ Failure else Return tt
 .
 
-(** [no_nested_borrows::test_copy_int]: forward function
+(** [no_nested_borrows::test_copy_int]:
     Source: 'src/no_nested_borrows.rs', lines 239:0-239:22 *)
 Definition test_copy_int : result unit :=
   y <- copy_int 0%i32; if negb (0%i32 s= y) then Fail_ Failure else Return tt
@@ -279,24 +280,23 @@ Definition test_copy_int : result unit :=
 (** Unit test for [no_nested_borrows::test_copy_int] *)
 Check (test_copy_int )%return.
 
-(** [no_nested_borrows::is_cons]: forward function
+(** [no_nested_borrows::is_cons]:
     Source: 'src/no_nested_borrows.rs', lines 246:0-246:38 *)
 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
+  match l with | List_Cons _ _ => Return true | List_Nil => Return false end
 .
 
-(** [no_nested_borrows::test_is_cons]: forward function
+(** [no_nested_borrows::test_is_cons]:
     Source: 'src/no_nested_borrows.rs', lines 253:0-253:21 *)
 Definition test_is_cons : result unit :=
-  let l := List_Nil in
-  b <- is_cons i32 (List_Cons 0%i32 l);
+  b <- is_cons i32 (List_Cons 0%i32 List_Nil);
   if negb b then Fail_ Failure else Return tt
 .
 
 (** Unit test for [no_nested_borrows::test_is_cons] *)
 Check (test_is_cons )%return.
 
-(** [no_nested_borrows::split_list]: forward function
+(** [no_nested_borrows::split_list]:
     Source: 'src/no_nested_borrows.rs', lines 259:0-259:48 *)
 Definition split_list (T : Type) (l : List_t T) : result (T * (List_t T)) :=
   match l with
@@ -305,11 +305,10 @@ Definition split_list (T : Type) (l : List_t T) : result (T * (List_t T)) :=
   end
 .
 
-(** [no_nested_borrows::test_split_list]: forward function
+(** [no_nested_borrows::test_split_list]:
     Source: 'src/no_nested_borrows.rs', lines 267:0-267:24 *)
 Definition test_split_list : result unit :=
-  let l := List_Nil in
-  p <- split_list i32 (List_Cons 0%i32 l);
+  p <- split_list i32 (List_Cons 0%i32 List_Nil);
   let (hd, _) := p in
   if negb (hd s= 0%i32) then Fail_ Failure else Return tt
 .
@@ -317,29 +316,26 @@ Definition test_split_list : result unit :=
 (** Unit test for [no_nested_borrows::test_split_list] *)
 Check (test_split_list )%return.
 
-(** [no_nested_borrows::choose]: forward function
+(** [no_nested_borrows::choose]:
     Source: 'src/no_nested_borrows.rs', lines 274:0-274:70 *)
-Definition choose (T : Type) (b : bool) (x : T) (y : T) : result T :=
-  if b then Return x else Return y
+Definition choose
+  (T : Type) (b : bool) (x : T) (y : T) : result (T * (T -> result (T * T))) :=
+  if b
+  then let back_'a := fun (ret : T) => Return (ret, y) in Return (x, back_'a)
+  else let back_'a := fun (ret : T) => Return (x, ret) in Return (y, back_'a)
 .
 
-(** [no_nested_borrows::choose]: backward function 0
-    Source: 'src/no_nested_borrows.rs', lines 274:0-274:70 *)
-Definition choose_back
-  (T : Type) (b : bool) (x : T) (y : T) (ret : T) : result (T * T) :=
-  if b then Return (ret, y) else Return (x, ret)
-.
-
-(** [no_nested_borrows::choose_test]: forward function
+(** [no_nested_borrows::choose_test]:
     Source: 'src/no_nested_borrows.rs', lines 282:0-282:20 *)
 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)
+  p <- choose i32 true 0%i32 0%i32;
+  let (z, choose_back) := p in
+  z1 <- i32_add z 1%i32;
+  if negb (z1 s= 1%i32)
   then Fail_ Failure
   else (
-    p <- choose_back i32 true 0%i32 0%i32 z0;
-    let (x, y) := p in
+    p1 <- choose_back z1;
+    let (x, y) := p1 in
     if negb (x s= 1%i32)
     then Fail_ Failure
     else if negb (y s= 0%i32) then Fail_ Failure else Return tt)
@@ -348,7 +344,7 @@ Definition choose_test : result unit :=
 (** Unit test for [no_nested_borrows::choose_test] *)
 Check (choose_test )%return.
 
-(** [no_nested_borrows::test_char]: forward function
+(** [no_nested_borrows::test_char]:
     Source: 'src/no_nested_borrows.rs', lines 294:0-294:26 *)
 Definition test_char : result char :=
   Return (char_of_byte Coq.Init.Byte.x61).
@@ -372,56 +368,52 @@ Arguments Tree_Node { _ }.
 Arguments NodeElem_Cons { _ }.
 Arguments NodeElem_Nil { _ }.
 
-(** [no_nested_borrows::list_length]: forward function
+(** [no_nested_borrows::list_length]:
     Source: 'src/no_nested_borrows.rs', lines 339:0-339:48 *)
 Fixpoint list_length (T : Type) (l : List_t T) : result u32 :=
   match l with
-  | List_Cons t l1 => i <- list_length T l1; u32_add 1%u32 i
+  | List_Cons _ 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
+(** [no_nested_borrows::list_nth_shared]:
     Source: 'src/no_nested_borrows.rs', lines 347:0-347:62 *)
 Fixpoint list_nth_shared (T : Type) (l : List_t T) (i : u32) : result T :=
   match l with
   | List_Cons x tl =>
     if i s= 0%u32
     then Return x
-    else (i0 <- u32_sub i 1%u32; list_nth_shared T tl i0)
+    else (i1 <- u32_sub i 1%u32; list_nth_shared T tl i1)
   | List_Nil => Fail_ Failure
   end
 .
 
-(** [no_nested_borrows::list_nth_mut]: forward function
+(** [no_nested_borrows::list_nth_mut]:
     Source: 'src/no_nested_borrows.rs', lines 363:0-363:67 *)
-Fixpoint list_nth_mut (T : Type) (l : List_t T) (i : u32) : result T :=
+Fixpoint list_nth_mut
+  (T : Type) (l : List_t T) (i : u32) :
+  result (T * (T -> result (List_t T)))
+  :=
   match l with
   | List_Cons x tl =>
     if i s= 0%u32
-    then Return x
-    else (i0 <- u32_sub i 1%u32; list_nth_mut T tl i0)
-  | List_Nil => Fail_ Failure
-  end
-.
-
-(** [no_nested_borrows::list_nth_mut]: backward function 0
-    Source: 'src/no_nested_borrows.rs', lines 363:0-363:67 *)
-Fixpoint list_nth_mut_back
-  (T : Type) (l : List_t T) (i : u32) (ret : T) : result (List_t T) :=
-  match l with
-  | List_Cons x tl =>
-    if i s= 0%u32
-    then Return (List_Cons ret tl)
+    then
+      let back_'a := fun (ret : T) => Return (List_Cons ret tl) in
+      Return (x, back_'a)
     else (
-      i0 <- u32_sub i 1%u32;
-      tl0 <- list_nth_mut_back T tl i0 ret;
-      Return (List_Cons x tl0))
+      i1 <- u32_sub i 1%u32;
+      p <- list_nth_mut T tl i1;
+      let (t, list_nth_mut_back) := p in
+      let back_'a :=
+        fun (ret : T) => tl1 <- list_nth_mut_back ret; Return (List_Cons x tl1)
+        in
+      Return (t, back_'a))
   | List_Nil => Fail_ Failure
   end
 .
 
-(** [no_nested_borrows::list_rev_aux]: forward function
+(** [no_nested_borrows::list_rev_aux]:
     Source: 'src/no_nested_borrows.rs', lines 379:0-379:63 *)
 Fixpoint list_rev_aux
   (T : Type) (li : List_t T) (lo : List_t T) : result (List_t T) :=
@@ -431,116 +423,91 @@ Fixpoint list_rev_aux
   end
 .
 
-(** [no_nested_borrows::list_rev]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ())
+(** [no_nested_borrows::list_rev]:
     Source: 'src/no_nested_borrows.rs', lines 393:0-393:42 *)
 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
+  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
+(** [no_nested_borrows::test_list_functions]:
     Source: 'src/no_nested_borrows.rs', lines 398:0-398:28 *)
 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
+  let l := List_Cons 2%i32 List_Nil in
+  let l1 := List_Cons 1%i32 l in
   i <- list_length i32 (List_Cons 0%i32 l1);
   if negb (i s= 3%u32)
   then Fail_ Failure
   else (
-    i0 <- list_nth_shared i32 (List_Cons 0%i32 l1) 0%u32;
-    if negb (i0 s= 0%i32)
+    i1 <- list_nth_shared i32 (List_Cons 0%i32 l1) 0%u32;
+    if negb (i1 s= 0%i32)
     then Fail_ Failure
     else (
-      i1 <- list_nth_shared i32 (List_Cons 0%i32 l1) 1%u32;
-      if negb (i1 s= 1%i32)
+      i2 <- list_nth_shared i32 (List_Cons 0%i32 l1) 1%u32;
+      if negb (i2 s= 1%i32)
       then Fail_ Failure
       else (
-        i2 <- list_nth_shared i32 (List_Cons 0%i32 l1) 2%u32;
-        if negb (i2 s= 2%i32)
+        i3 <- list_nth_shared i32 (List_Cons 0%i32 l1) 2%u32;
+        if negb (i3 s= 2%i32)
         then Fail_ Failure
         else (
-          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)
+          p <- list_nth_mut i32 (List_Cons 0%i32 l1) 1%u32;
+          let (_, list_nth_mut_back) := p in
+          ls <- list_nth_mut_back 3%i32;
+          i4 <- list_nth_shared i32 ls 0%u32;
+          if negb (i4 s= 0%i32)
           then Fail_ Failure
           else (
-            i4 <- list_nth_shared i32 ls 1%u32;
-            if negb (i4 s= 3%i32)
+            i5 <- list_nth_shared i32 ls 1%u32;
+            if negb (i5 s= 3%i32)
             then Fail_ Failure
             else (
-              i5 <- list_nth_shared i32 ls 2%u32;
-              if negb (i5 s= 2%i32) then Fail_ Failure else Return tt))))))
+              i6 <- list_nth_shared i32 ls 2%u32;
+              if negb (i6 s= 2%i32) then Fail_ Failure else Return tt))))))
 .
 
 (** Unit test for [no_nested_borrows::test_list_functions] *)
 Check (test_list_functions )%return.
 
-(** [no_nested_borrows::id_mut_pair1]: forward function
+(** [no_nested_borrows::id_mut_pair1]:
     Source: 'src/no_nested_borrows.rs', lines 414:0-414:89 *)
-Definition id_mut_pair1 (T1 T2 : Type) (x : T1) (y : T2) : result (T1 * T2) :=
-  Return (x, y)
-.
-
-(** [no_nested_borrows::id_mut_pair1]: backward function 0
-    Source: 'src/no_nested_borrows.rs', lines 414:0-414:89 *)
-Definition id_mut_pair1_back
-  (T1 T2 : Type) (x : T1) (y : T2) (ret : (T1 * T2)) : result (T1 * T2) :=
-  let (t, t0) := ret in Return (t, t0)
-.
-
-(** [no_nested_borrows::id_mut_pair2]: forward function
-    Source: 'src/no_nested_borrows.rs', lines 418:0-418:88 *)
-Definition id_mut_pair2 (T1 T2 : Type) (p : (T1 * T2)) : result (T1 * T2) :=
-  let (t, t0) := p in Return (t, t0)
+Definition id_mut_pair1
+  (T1 T2 : Type) (x : T1) (y : T2) :
+  result ((T1 * T2) * ((T1 * T2) -> result (T1 * T2)))
+  :=
+  let back_'a := fun (ret : (T1 * T2)) => let (t, t1) := ret in Return (t, t1)
+    in
+  Return ((x, y), back_'a)
 .
 
-(** [no_nested_borrows::id_mut_pair2]: backward function 0
+(** [no_nested_borrows::id_mut_pair2]:
     Source: 'src/no_nested_borrows.rs', lines 418:0-418:88 *)
-Definition id_mut_pair2_back
-  (T1 T2 : Type) (p : (T1 * T2)) (ret : (T1 * T2)) : result (T1 * T2) :=
-  let (t, t0) := ret in Return (t, t0)
+Definition id_mut_pair2
+  (T1 T2 : Type) (p : (T1 * T2)) :
+  result ((T1 * T2) * ((T1 * T2) -> result (T1 * T2)))
+  :=
+  let (t, t1) := p in
+  let back_'a :=
+    fun (ret : (T1 * T2)) => let (t2, t3) := ret in Return (t2, t3) in
+  Return ((t, t1), back_'a)
 .
 
-(** [no_nested_borrows::id_mut_pair3]: forward function
+(** [no_nested_borrows::id_mut_pair3]:
     Source: 'src/no_nested_borrows.rs', lines 422:0-422:93 *)
-Definition id_mut_pair3 (T1 T2 : Type) (x : T1) (y : T2) : result (T1 * T2) :=
-  Return (x, y)
-.
-
-(** [no_nested_borrows::id_mut_pair3]: backward function 0
-    Source: 'src/no_nested_borrows.rs', lines 422:0-422:93 *)
-Definition id_mut_pair3_back'a
-  (T1 T2 : Type) (x : T1) (y : T2) (ret : T1) : result T1 :=
-  Return ret
-.
-
-(** [no_nested_borrows::id_mut_pair3]: backward function 1
-    Source: 'src/no_nested_borrows.rs', lines 422:0-422:93 *)
-Definition id_mut_pair3_back'b
-  (T1 T2 : Type) (x : T1) (y : T2) (ret : T2) : result T2 :=
-  Return ret
-.
-
-(** [no_nested_borrows::id_mut_pair4]: forward function
-    Source: 'src/no_nested_borrows.rs', lines 426:0-426:92 *)
-Definition id_mut_pair4 (T1 T2 : Type) (p : (T1 * T2)) : result (T1 * T2) :=
-  let (t, t0) := p in Return (t, t0)
+Definition id_mut_pair3
+  (T1 T2 : Type) (x : T1) (y : T2) :
+  result ((T1 * T2) * (T1 -> result T1) * (T2 -> result T2))
+  :=
+  Return ((x, y), Return, Return)
 .
 
-(** [no_nested_borrows::id_mut_pair4]: backward function 0
+(** [no_nested_borrows::id_mut_pair4]:
     Source: 'src/no_nested_borrows.rs', lines 426:0-426:92 *)
-Definition id_mut_pair4_back'a
-  (T1 T2 : Type) (p : (T1 * T2)) (ret : T1) : result T1 :=
-  Return ret
-.
-
-(** [no_nested_borrows::id_mut_pair4]: backward function 1
-    Source: 'src/no_nested_borrows.rs', lines 426:0-426:92 *)
-Definition id_mut_pair4_back'b
-  (T1 T2 : Type) (p : (T1 * T2)) (ret : T2) : result T2 :=
-  Return ret
+Definition id_mut_pair4
+  (T1 T2 : Type) (p : (T1 * T2)) :
+  result ((T1 * T2) * (T1 -> result T1) * (T2 -> result T2))
+  :=
+  let (t, t1) := p in Return ((t, t1), Return, Return)
 .
 
 (** [no_nested_borrows::StructWithTuple]
@@ -554,19 +521,19 @@ mkStructWithTuple_t {
 Arguments mkStructWithTuple_t { _ _ }.
 Arguments structWithTuple_p { _ _ }.
 
-(** [no_nested_borrows::new_tuple1]: forward function
+(** [no_nested_borrows::new_tuple1]:
     Source: 'src/no_nested_borrows.rs', lines 437:0-437:48 *)
 Definition new_tuple1 : result (StructWithTuple_t u32 u32) :=
   Return {| structWithTuple_p := (1%u32, 2%u32) |}
 .
 
-(** [no_nested_borrows::new_tuple2]: forward function
+(** [no_nested_borrows::new_tuple2]:
     Source: 'src/no_nested_borrows.rs', lines 441:0-441:48 *)
 Definition new_tuple2 : result (StructWithTuple_t i16 i16) :=
   Return {| structWithTuple_p := (1%i16, 2%i16) |}
 .
 
-(** [no_nested_borrows::new_tuple3]: forward function
+(** [no_nested_borrows::new_tuple3]:
     Source: 'src/no_nested_borrows.rs', lines 445:0-445:48 *)
 Definition new_tuple3 : result (StructWithTuple_t u64 i64) :=
   Return {| structWithTuple_p := (1%u64, 2%i64) |}
@@ -583,13 +550,13 @@ mkStructWithPair_t {
 Arguments mkStructWithPair_t { _ _ }.
 Arguments structWithPair_p { _ _ }.
 
-(** [no_nested_borrows::new_pair1]: forward function
+(** [no_nested_borrows::new_pair1]:
     Source: 'src/no_nested_borrows.rs', lines 454:0-454:46 *)
 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
+(** [no_nested_borrows::test_constants]:
     Source: 'src/no_nested_borrows.rs', lines 462:0-462:23 *)
 Definition test_constants : result unit :=
   swt <- new_tuple1;
@@ -597,14 +564,14 @@ Definition test_constants : result unit :=
   if negb (i s= 1%u32)
   then Fail_ Failure
   else (
-    swt0 <- new_tuple2;
-    let (i0, _) := swt0.(structWithTuple_p) in
-    if negb (i0 s= 1%i16)
+    swt1 <- new_tuple2;
+    let (i1, _) := swt1.(structWithTuple_p) in
+    if negb (i1 s= 1%i16)
     then Fail_ Failure
     else (
-      swt1 <- new_tuple3;
-      let (i1, _) := swt1.(structWithTuple_p) in
-      if negb (i1 s= 1%u64)
+      swt2 <- new_tuple3;
+      let (i2, _) := swt2.(structWithTuple_p) in
+      if negb (i2 s= 1%u64)
       then Fail_ Failure
       else (
         swp <- new_pair1;
@@ -616,7 +583,7 @@ Definition test_constants : result unit :=
 (** Unit test for [no_nested_borrows::test_constants] *)
 Check (test_constants )%return.
 
-(** [no_nested_borrows::test_weird_borrows1]: forward function
+(** [no_nested_borrows::test_weird_borrows1]:
     Source: 'src/no_nested_borrows.rs', lines 471:0-471:28 *)
 Definition test_weird_borrows1 : result unit :=
   Return tt.
@@ -624,65 +591,79 @@ Definition test_weird_borrows1 : result unit :=
 (** Unit test for [no_nested_borrows::test_weird_borrows1] *)
 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 ())
+(** [no_nested_borrows::test_mem_replace]:
     Source: 'src/no_nested_borrows.rs', lines 481:0-481:37 *)
 Definition test_mem_replace (px : u32) : result u32 :=
-  let y := core_mem_replace u32 px 1%u32 in
+  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
+(** [no_nested_borrows::test_shared_borrow_bool1]:
     Source: 'src/no_nested_borrows.rs', lines 488:0-488:47 *)
 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
+(** [no_nested_borrows::test_shared_borrow_bool2]:
     Source: 'src/no_nested_borrows.rs', lines 501:0-501:40 *)
 Definition test_shared_borrow_bool2 : result u32 :=
   Return 0%u32.
 
-(** [no_nested_borrows::test_shared_borrow_enum1]: forward function
+(** [no_nested_borrows::test_shared_borrow_enum1]:
     Source: 'src/no_nested_borrows.rs', lines 516:0-516:52 *)
 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
+  match l with | List_Cons _ _ => Return 1%u32 | List_Nil => Return 0%u32 end
 .
 
-(** [no_nested_borrows::test_shared_borrow_enum2]: forward function
+(** [no_nested_borrows::test_shared_borrow_enum2]:
     Source: 'src/no_nested_borrows.rs', lines 528:0-528:40 *)
 Definition test_shared_borrow_enum2 : result u32 :=
   Return 0%u32.
 
-(** [no_nested_borrows::Tuple]
+(** [no_nested_borrows::incr]:
     Source: 'src/no_nested_borrows.rs', lines 539:0-539:24 *)
+Definition incr (x : u32) : result u32 :=
+  u32_add x 1%u32.
+
+(** [no_nested_borrows::call_incr]:
+    Source: 'src/no_nested_borrows.rs', lines 543:0-543:35 *)
+Definition call_incr (x : u32) : result u32 :=
+  incr x.
+
+(** [no_nested_borrows::read_then_incr]:
+    Source: 'src/no_nested_borrows.rs', lines 548:0-548:41 *)
+Definition read_then_incr (x : u32) : result (u32 * u32) :=
+  x1 <- u32_add x 1%u32; Return (x, x1)
+.
+
+(** [no_nested_borrows::Tuple]
+    Source: 'src/no_nested_borrows.rs', lines 554:0-554:24 *)
 Definition Tuple_t (T1 T2 : Type) : Type := T1 * T2.
 
-(** [no_nested_borrows::use_tuple_struct]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ())
-    Source: 'src/no_nested_borrows.rs', lines 541:0-541:48 *)
+(** [no_nested_borrows::use_tuple_struct]:
+    Source: 'src/no_nested_borrows.rs', lines 556:0-556:48 *)
 Definition use_tuple_struct (x : Tuple_t u32 u32) : result (Tuple_t u32 u32) :=
   let (_, i) := x in Return (1%u32, i)
 .
 
-(** [no_nested_borrows::create_tuple_struct]: forward function
-    Source: 'src/no_nested_borrows.rs', lines 545:0-545:61 *)
+(** [no_nested_borrows::create_tuple_struct]:
+    Source: 'src/no_nested_borrows.rs', lines 560:0-560:61 *)
 Definition create_tuple_struct
   (x : u32) (y : u64) : result (Tuple_t u32 u64) :=
   Return (x, y)
 .
 
 (** [no_nested_borrows::IdType]
-    Source: 'src/no_nested_borrows.rs', lines 550:0-550:20 *)
+    Source: 'src/no_nested_borrows.rs', lines 565:0-565:20 *)
 Definition IdType_t (T : Type) : Type := T.
 
-(** [no_nested_borrows::use_id_type]: forward function
-    Source: 'src/no_nested_borrows.rs', lines 552:0-552:40 *)
+(** [no_nested_borrows::use_id_type]:
+    Source: 'src/no_nested_borrows.rs', lines 567:0-567:40 *)
 Definition use_id_type (T : Type) (x : IdType_t T) : result T :=
   Return x.
 
-(** [no_nested_borrows::create_id_type]: forward function
-    Source: 'src/no_nested_borrows.rs', lines 556:0-556:43 *)
+(** [no_nested_borrows::create_id_type]:
+    Source: 'src/no_nested_borrows.rs', lines 571:0-571:43 *)
 Definition create_id_type (T : Type) (x : T) : result (IdType_t T) :=
   Return x.
 
diff --git a/tests/coq/misc/Paper.v b/tests/coq/misc/Paper.v
index 6b110193..769cf34c 100644
--- a/tests/coq/misc/Paper.v
+++ b/tests/coq/misc/Paper.v
@@ -8,44 +8,40 @@ Import ListNotations.
 Local Open Scope Primitives_scope.
 Module Paper.
 
-(** [paper::ref_incr]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ())
+(** [paper::ref_incr]:
     Source: 'src/paper.rs', lines 4:0-4:28 *)
 Definition ref_incr (x : i32) : result i32 :=
   i32_add x 1%i32.
 
-(** [paper::test_incr]: forward function
+(** [paper::test_incr]:
     Source: 'src/paper.rs', lines 8:0-8:18 *)
 Definition test_incr : result unit :=
-  x <- ref_incr 0%i32; if negb (x s= 1%i32) then Fail_ Failure else Return tt
+  i <- ref_incr 0%i32; if negb (i s= 1%i32) then Fail_ Failure else Return tt
 .
 
 (** Unit test for [paper::test_incr] *)
 Check (test_incr )%return.
 
-(** [paper::choose]: forward function
+(** [paper::choose]:
     Source: 'src/paper.rs', lines 15:0-15:70 *)
-Definition choose (T : Type) (b : bool) (x : T) (y : T) : result T :=
-  if b then Return x else Return y
+Definition choose
+  (T : Type) (b : bool) (x : T) (y : T) : result (T * (T -> result (T * T))) :=
+  if b
+  then let back_'a := fun (ret : T) => Return (ret, y) in Return (x, back_'a)
+  else let back_'a := fun (ret : T) => Return (x, ret) in Return (y, back_'a)
 .
 
-(** [paper::choose]: backward function 0
-    Source: 'src/paper.rs', lines 15:0-15:70 *)
-Definition choose_back
-  (T : Type) (b : bool) (x : T) (y : T) (ret : T) : result (T * T) :=
-  if b then Return (ret, y) else Return (x, ret)
-.
-
-(** [paper::test_choose]: forward function
+(** [paper::test_choose]:
     Source: 'src/paper.rs', lines 23:0-23:20 *)
 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)
+  p <- choose i32 true 0%i32 0%i32;
+  let (z, choose_back) := p in
+  z1 <- i32_add z 1%i32;
+  if negb (z1 s= 1%i32)
   then Fail_ Failure
   else (
-    p <- choose_back i32 true 0%i32 0%i32 z0;
-    let (x, y) := p in
+    p1 <- choose_back z1;
+    let (x, y) := p1 in
     if negb (x s= 1%i32)
     then Fail_ Failure
     else if negb (y s= 0%i32) then Fail_ Failure else Return tt)
@@ -64,35 +60,31 @@ Inductive List_t (T : Type) :=
 Arguments List_Cons { _ }.
 Arguments List_Nil { _ }.
 
-(** [paper::list_nth_mut]: forward function
-    Source: 'src/paper.rs', lines 42:0-42:67 *)
-Fixpoint list_nth_mut (T : Type) (l : List_t T) (i : u32) : result T :=
-  match l with
-  | List_Cons x tl =>
-    if i s= 0%u32
-    then Return x
-    else (i0 <- u32_sub i 1%u32; list_nth_mut T tl i0)
-  | List_Nil => Fail_ Failure
-  end
-.
-
-(** [paper::list_nth_mut]: backward function 0
+(** [paper::list_nth_mut]:
     Source: 'src/paper.rs', lines 42:0-42:67 *)
-Fixpoint list_nth_mut_back
-  (T : Type) (l : List_t T) (i : u32) (ret : T) : result (List_t T) :=
+Fixpoint list_nth_mut
+  (T : Type) (l : List_t T) (i : u32) :
+  result (T * (T -> result (List_t T)))
+  :=
   match l with
   | List_Cons x tl =>
     if i s= 0%u32
-    then Return (List_Cons ret tl)
+    then
+      let back_'a := fun (ret : T) => Return (List_Cons ret tl) in
+      Return (x, back_'a)
     else (
-      i0 <- u32_sub i 1%u32;
-      tl0 <- list_nth_mut_back T tl i0 ret;
-      Return (List_Cons x tl0))
+      i1 <- u32_sub i 1%u32;
+      p <- list_nth_mut T tl i1;
+      let (t, list_nth_mut_back) := p in
+      let back_'a :=
+        fun (ret : T) => tl1 <- list_nth_mut_back ret; Return (List_Cons x tl1)
+        in
+      Return (t, back_'a))
   | List_Nil => Fail_ Failure
   end
 .
 
-(** [paper::sum]: forward function
+(** [paper::sum]:
     Source: 'src/paper.rs', lines 57:0-57:32 *)
 Fixpoint sum (l : List_t i32) : result i32 :=
   match l with
@@ -101,15 +93,15 @@ Fixpoint sum (l : List_t i32) : result i32 :=
   end
 .
 
-(** [paper::test_nth]: forward function
+(** [paper::test_nth]:
     Source: 'src/paper.rs', lines 68:0-68:17 *)
 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 (List_Cons 1%i32 l1) 2%u32 x0;
+  let l := List_Cons 3%i32 List_Nil in
+  let l1 := List_Cons 2%i32 l in
+  p <- list_nth_mut i32 (List_Cons 1%i32 l1) 2%u32;
+  let (x, list_nth_mut_back) := p in
+  x1 <- i32_add x 1%i32;
+  l2 <- list_nth_mut_back x1;
   i <- sum l2;
   if negb (i s= 7%i32) then Fail_ Failure else Return tt
 .
@@ -117,15 +109,16 @@ Definition test_nth : result unit :=
 (** Unit test for [paper::test_nth] *)
 Check (test_nth )%return.
 
-(** [paper::call_choose]: forward function
+(** [paper::call_choose]:
     Source: 'src/paper.rs', lines 76:0-76:44 *)
 Definition call_choose (p : (u32 * u32)) : result u32 :=
   let (px, py) := p in
-  pz <- choose u32 true px py;
-  pz0 <- u32_add pz 1%u32;
-  p0 <- choose_back u32 true px py pz0;
-  let (px0, _) := p0 in
-  Return px0
+  p1 <- choose u32 true px py;
+  let (pz, choose_back) := p1 in
+  pz1 <- u32_add pz 1%u32;
+  p2 <- choose_back pz1;
+  let (px1, _) := p2 in
+  Return px1
 .
 
 End Paper.
diff --git a/tests/coq/misc/PoloniusList.v b/tests/coq/misc/PoloniusList.v
index 2371b1cc..8f403a8e 100644
--- a/tests/coq/misc/PoloniusList.v
+++ b/tests/coq/misc/PoloniusList.v
@@ -18,26 +18,24 @@ Inductive List_t (T : Type) :=
 Arguments List_Cons { _ }.
 Arguments List_Nil { _ }.
 
-(** [polonius_list::get_list_at_x]: forward function
+(** [polonius_list::get_list_at_x]:
     Source: 'src/polonius_list.rs', lines 13:0-13:76 *)
-Fixpoint get_list_at_x (ls : List_t u32) (x : u32) : result (List_t u32) :=
-  match ls with
-  | 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
-.
-
-(** [polonius_list::get_list_at_x]: backward function 0
-    Source: 'src/polonius_list.rs', lines 13:0-13:76 *)
-Fixpoint get_list_at_x_back
-  (ls : List_t u32) (x : u32) (ret : List_t u32) : result (List_t u32) :=
+Fixpoint get_list_at_x
+  (ls : List_t u32) (x : u32) :
+  result ((List_t u32) * (List_t u32 -> result (List_t u32)))
+  :=
   match ls with
   | List_Cons hd tl =>
     if hd s= x
-    then Return ret
-    else (tl0 <- get_list_at_x_back tl x ret; Return (List_Cons hd tl0))
-  | List_Nil => Return ret
+    then Return (List_Cons hd tl, Return)
+    else (
+      p <- get_list_at_x tl x;
+      let (l, get_list_at_x_back) := p in
+      let back_'a :=
+        fun (ret : List_t u32) =>
+          tl1 <- get_list_at_x_back ret; Return (List_Cons hd tl1) in
+      Return (l, back_'a))
+  | List_Nil => Return (List_Nil, Return)
   end
 .
 
diff --git a/tests/coq/misc/Primitives.v b/tests/coq/misc/Primitives.v
index 84280b96..990e27e4 100644
--- a/tests/coq/misc/Primitives.v
+++ b/tests/coq/misc/Primitives.v
@@ -67,8 +67,7 @@ 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 .
+Definition core_mem_replace (a : Type) (x : a) (y : a) : a * a := (x, x) .
 
 Record mut_raw_ptr (T : Type) := { mut_raw_ptr_v : T }.
 Record const_raw_ptr (T : Type) := { const_raw_ptr_v : T }.
@@ -504,13 +503,15 @@ 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;
+  core_ops_index_IndexMut_index_mut :
+    Self ->
+    Idx ->
+    result (core_ops_index_IndexMut_indexInst.(core_ops_index_Index_Output) *
+            (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 {
@@ -524,13 +525,14 @@ 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;
+  core_ops_deref_DerefMut_deref_mut :
+    Self ->
+    result (core_ops_deref_DerefMut_derefInst.(core_ops_deref_Deref_target) *
+            (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;
@@ -543,8 +545,8 @@ 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.
+Definition alloc_boxed_Box_deref_mut (T : Type) (x : T) : result (T * (T -> result T)) :=
+  Return (x, fun x => Return x).
 
 (* Trait instance *)
 Definition alloc_boxed_Box_coreopsDerefInst (Self : Type) : core_ops_deref_Deref Self := {|
@@ -556,7 +558,6 @@ Definition alloc_boxed_Box_coreopsDerefInst (Self : Type) : core_ops_deref_Deref
 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;
 |}.
 
 
@@ -584,6 +585,13 @@ 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).
 
+Definition array_index_mut_usize (T : Type) (n : usize) (a : array T n) (i : usize) :
+  result (T * (T -> result (array T n))) :=
+  match array_index_usize T n a i with
+  | Fail_ e => Fail_ e
+  | Return x => Return (x, array_update_usize T n a i)
+  end.
+
 (*** Slice *)
 Definition slice T := { l: list T | Z.of_nat (length l) <= usize_max}.
 
@@ -591,11 +599,25 @@ 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).
 
+Definition slice_index_mut_usize (T : Type) (s : slice T) (i : usize) :
+  result (T * (T -> result (slice T))) :=
+  match slice_index_usize T s i with
+  | Fail_ e => Fail_ e
+  | Return x => Return (x, slice_update_usize T s i)
+  end.
+
 (*** 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).
 
+Definition array_to_slice_mut (T : Type) (n : usize) (a : array T n) :
+  result (slice T * (slice T -> result (array T n))) :=
+  match array_to_slice T n a with
+  | Fail_ e => Fail_ e
+  | Return x => Return (x, array_from_slice T n a)
+  end.
+
 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).
 
@@ -639,16 +661,9 @@ Definition alloc_vec_Vec_bind {A B} (v: alloc_vec_Vec A) (f: list A -> result (l
   | 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)
@@ -661,6 +676,14 @@ Axiom alloc_vec_Vec_index_usize : forall {T : Type} (v : alloc_vec_Vec T) (i : u
 (* Helper *)
 Axiom alloc_vec_Vec_update_usize : forall {T : Type} (v : alloc_vec_Vec T) (i : usize) (x : T), result (alloc_vec_Vec T).
 
+Definition alloc_vec_Vec_index_mut_usize {T : Type} (v: alloc_vec_Vec T) (i: usize) :
+  result (T * (T -> result (alloc_vec_Vec T))) :=
+  match alloc_vec_Vec_index_usize v i with
+  | Return x =>
+    Return (x, alloc_vec_Vec_update_usize v i)
+  | Fail_ e => Fail_ e
+  end.
+
 (* Trait declaration: [core::slice::index::private_slice_index::Sealed] *)
 Definition core_slice_index_private_slice_index_Sealed (self : Type) := unit.
 
@@ -669,25 +692,23 @@ Record core_slice_index_SliceIndex (Self T : Type) := mk_core_slice_index_SliceI
   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_mut :
+    Self -> T -> result (option core_slice_index_SliceIndex_Output * (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;
+  core_slice_index_SliceIndex_index_mut :
+    Self -> T -> result (core_slice_index_SliceIndex_Output * (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
@@ -704,11 +725,9 @@ Axiom core_slice_index_RangeUsize_get : forall (T : Type) (i : core_ops_range_Ra
 
 (* [core::slice::index::Range::get_mut]: forward function *)
 Axiom core_slice_index_RangeUsize_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_RangeUsize_get_mut_back :
-  forall (T : Type), core_ops_range_Range usize -> slice T -> option (slice T) -> result (slice T).
+  forall (T : Type),
+    core_ops_range_Range usize -> slice T ->
+    result (option (slice T) * (option (slice T) -> result (slice T))).
 
 (* [core::slice::index::Range::get_unchecked]: forward function *)
 Definition core_slice_index_RangeUsize_get_unchecked
@@ -732,21 +751,14 @@ Axiom core_slice_index_RangeUsize_index :
 
 (* [core::slice::index::Range::index_mut]: forward function *)
 Axiom core_slice_index_RangeUsize_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_RangeUsize_index_mut_back :
-  forall (T : Type), core_ops_range_Range usize -> slice T -> slice T -> result (slice T).
+  forall (T : Type), core_ops_range_Range usize -> slice T -> result (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).
+  slice T -> Idx ->
+  result (inst.(core_slice_index_SliceIndex_Output) *
+          (inst.(core_slice_index_SliceIndex_Output) -> result (slice T))).
 
 (* [core::array::[T; N]::index]: forward function *)
 Axiom core_array_Array_index :
@@ -756,12 +768,9 @@ Axiom core_array_Array_index :
 (* [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).
+  (a : array T N) (i : Idx),
+  result (inst.(core_ops_index_IndexMut_indexInst).(core_ops_index_Index_Output) *
+          (inst.(core_ops_index_IndexMut_indexInst).(core_ops_index_Index_Output) -> result (array T N))).
 
 (* Trait implementation: [core::slice::index::private_slice_index::Range] *)
 Definition core_slice_index_private_slice_index_SealedRangeUsizeInst
@@ -774,12 +783,10 @@ Definition core_slice_index_SliceIndexRangeUsizeSliceTInst (T : Type) :
   core_slice_index_SliceIndex_Output := slice T;
   core_slice_index_SliceIndex_get := core_slice_index_RangeUsize_get T;
   core_slice_index_SliceIndex_get_mut := core_slice_index_RangeUsize_get_mut T;
-  core_slice_index_SliceIndex_get_mut_back := core_slice_index_RangeUsize_get_mut_back T;
   core_slice_index_SliceIndex_get_unchecked := core_slice_index_RangeUsize_get_unchecked T;
   core_slice_index_SliceIndex_get_unchecked_mut := core_slice_index_RangeUsize_get_unchecked_mut T;
   core_slice_index_SliceIndex_index := core_slice_index_RangeUsize_index T;
   core_slice_index_SliceIndex_index_mut := core_slice_index_RangeUsize_index_mut T;
-  core_slice_index_SliceIndex_index_mut_back := core_slice_index_RangeUsize_index_mut_back T;
 |}.
 
 (* Trait implementation: [core::slice::index::[T]] *)
@@ -796,7 +803,6 @@ Definition core_ops_index_IndexMutSliceTIInst (T Idx : Type)
   core_ops_index_IndexMut (slice T) Idx := {|
   core_ops_index_IndexMut_indexInst := core_ops_index_IndexSliceTIInst 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]] *)
@@ -813,18 +819,14 @@ Definition core_ops_index_IndexMutArrayInst (T Idx : Type) (N : usize)
   core_ops_index_IndexMut (array T N) Idx := {|
   core_ops_index_IndexMut_indexInst := core_ops_index_IndexArrayInst 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).
+Axiom core_slice_index_usize_get_mut :
+  forall (T : Type), usize -> slice T -> result (option T * (option T -> result (slice T))).
 
 (* [core::slice::index::usize::get_unchecked]: forward function *)
 Axiom core_slice_index_usize_get_unchecked :
@@ -838,11 +840,8 @@ Axiom core_slice_index_usize_get_unchecked_mut :
 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).
+Axiom core_slice_index_usize_index_mut :
+  forall (T : Type), usize -> slice T -> result (T * (T -> result (slice T))).
 
 (* Trait implementation: [core::slice::index::private_slice_index::usize] *)
 Definition core_slice_index_private_slice_index_SealedUsizeInst
@@ -855,12 +854,10 @@ Definition core_slice_index_SliceIndexUsizeSliceTInst (T : Type) :
   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 *)
@@ -869,12 +866,9 @@ Axiom alloc_vec_Vec_index : forall (T Idx : Type) (inst : core_slice_index_Slice
 
 (* [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).
+  (Self : alloc_vec_Vec T) (i : Idx),
+  result (inst.(core_slice_index_SliceIndex_Output) *
+          (inst.(core_slice_index_SliceIndex_Output) -> result (alloc_vec_Vec T))).
 
 (* Trait implementation: [alloc::vec::Vec] *)
 Definition alloc_vec_Vec_coreopsindexIndexInst (T Idx : Type)
@@ -890,7 +884,6 @@ Definition alloc_vec_Vec_coreopsindexIndexMutInst (T Idx : Type)
   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 *)
@@ -901,10 +894,6 @@ Axiom alloc_vec_Vec_index_eq : forall {a : Type} (v : alloc_vec_Vec a) (i : usiz
 
 Axiom alloc_vec_Vec_index_mut_eq : forall {a : Type} (v : alloc_vec_Vec a) (i : usize) (x : a),
   alloc_vec_Vec_index_mut a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i =
-    alloc_vec_Vec_index_usize v i.
-
-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_SliceIndexUsizeSliceTInst a) v i x =
-    alloc_vec_Vec_update_usize v i x.
+    alloc_vec_Vec_index_mut_usize v i.
 
 End Primitives.
diff --git a/tests/coq/misc/_CoqProject b/tests/coq/misc/_CoqProject
index 869cdb4d..64cddedd 100644
--- a/tests/coq/misc/_CoqProject
+++ b/tests/coq/misc/_CoqProject
@@ -8,9 +8,9 @@ External_Types.v
 Primitives.v
 External_Funs.v
 External_TypesExternal.v
+Paper.v
 Constants.v
 PoloniusList.v
-Paper.v
 NoNestedBorrows.v
 External_FunsExternal.v
 Bitwise.v
diff --git a/tests/coq/traits/Primitives.v b/tests/coq/traits/Primitives.v
index 84280b96..990e27e4 100644
--- a/tests/coq/traits/Primitives.v
+++ b/tests/coq/traits/Primitives.v
@@ -67,8 +67,7 @@ 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 .
+Definition core_mem_replace (a : Type) (x : a) (y : a) : a * a := (x, x) .
 
 Record mut_raw_ptr (T : Type) := { mut_raw_ptr_v : T }.
 Record const_raw_ptr (T : Type) := { const_raw_ptr_v : T }.
@@ -504,13 +503,15 @@ 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;
+  core_ops_index_IndexMut_index_mut :
+    Self ->
+    Idx ->
+    result (core_ops_index_IndexMut_indexInst.(core_ops_index_Index_Output) *
+            (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 {
@@ -524,13 +525,14 @@ 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;
+  core_ops_deref_DerefMut_deref_mut :
+    Self ->
+    result (core_ops_deref_DerefMut_derefInst.(core_ops_deref_Deref_target) *
+            (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;
@@ -543,8 +545,8 @@ 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.
+Definition alloc_boxed_Box_deref_mut (T : Type) (x : T) : result (T * (T -> result T)) :=
+  Return (x, fun x => Return x).
 
 (* Trait instance *)
 Definition alloc_boxed_Box_coreopsDerefInst (Self : Type) : core_ops_deref_Deref Self := {|
@@ -556,7 +558,6 @@ Definition alloc_boxed_Box_coreopsDerefInst (Self : Type) : core_ops_deref_Deref
 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;
 |}.
 
 
@@ -584,6 +585,13 @@ 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).
 
+Definition array_index_mut_usize (T : Type) (n : usize) (a : array T n) (i : usize) :
+  result (T * (T -> result (array T n))) :=
+  match array_index_usize T n a i with
+  | Fail_ e => Fail_ e
+  | Return x => Return (x, array_update_usize T n a i)
+  end.
+
 (*** Slice *)
 Definition slice T := { l: list T | Z.of_nat (length l) <= usize_max}.
 
@@ -591,11 +599,25 @@ 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).
 
+Definition slice_index_mut_usize (T : Type) (s : slice T) (i : usize) :
+  result (T * (T -> result (slice T))) :=
+  match slice_index_usize T s i with
+  | Fail_ e => Fail_ e
+  | Return x => Return (x, slice_update_usize T s i)
+  end.
+
 (*** 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).
 
+Definition array_to_slice_mut (T : Type) (n : usize) (a : array T n) :
+  result (slice T * (slice T -> result (array T n))) :=
+  match array_to_slice T n a with
+  | Fail_ e => Fail_ e
+  | Return x => Return (x, array_from_slice T n a)
+  end.
+
 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).
 
@@ -639,16 +661,9 @@ Definition alloc_vec_Vec_bind {A B} (v: alloc_vec_Vec A) (f: list A -> result (l
   | 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)
@@ -661,6 +676,14 @@ Axiom alloc_vec_Vec_index_usize : forall {T : Type} (v : alloc_vec_Vec T) (i : u
 (* Helper *)
 Axiom alloc_vec_Vec_update_usize : forall {T : Type} (v : alloc_vec_Vec T) (i : usize) (x : T), result (alloc_vec_Vec T).
 
+Definition alloc_vec_Vec_index_mut_usize {T : Type} (v: alloc_vec_Vec T) (i: usize) :
+  result (T * (T -> result (alloc_vec_Vec T))) :=
+  match alloc_vec_Vec_index_usize v i with
+  | Return x =>
+    Return (x, alloc_vec_Vec_update_usize v i)
+  | Fail_ e => Fail_ e
+  end.
+
 (* Trait declaration: [core::slice::index::private_slice_index::Sealed] *)
 Definition core_slice_index_private_slice_index_Sealed (self : Type) := unit.
 
@@ -669,25 +692,23 @@ Record core_slice_index_SliceIndex (Self T : Type) := mk_core_slice_index_SliceI
   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_mut :
+    Self -> T -> result (option core_slice_index_SliceIndex_Output * (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;
+  core_slice_index_SliceIndex_index_mut :
+    Self -> T -> result (core_slice_index_SliceIndex_Output * (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
@@ -704,11 +725,9 @@ Axiom core_slice_index_RangeUsize_get : forall (T : Type) (i : core_ops_range_Ra
 
 (* [core::slice::index::Range::get_mut]: forward function *)
 Axiom core_slice_index_RangeUsize_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_RangeUsize_get_mut_back :
-  forall (T : Type), core_ops_range_Range usize -> slice T -> option (slice T) -> result (slice T).
+  forall (T : Type),
+    core_ops_range_Range usize -> slice T ->
+    result (option (slice T) * (option (slice T) -> result (slice T))).
 
 (* [core::slice::index::Range::get_unchecked]: forward function *)
 Definition core_slice_index_RangeUsize_get_unchecked
@@ -732,21 +751,14 @@ Axiom core_slice_index_RangeUsize_index :
 
 (* [core::slice::index::Range::index_mut]: forward function *)
 Axiom core_slice_index_RangeUsize_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_RangeUsize_index_mut_back :
-  forall (T : Type), core_ops_range_Range usize -> slice T -> slice T -> result (slice T).
+  forall (T : Type), core_ops_range_Range usize -> slice T -> result (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).
+  slice T -> Idx ->
+  result (inst.(core_slice_index_SliceIndex_Output) *
+          (inst.(core_slice_index_SliceIndex_Output) -> result (slice T))).
 
 (* [core::array::[T; N]::index]: forward function *)
 Axiom core_array_Array_index :
@@ -756,12 +768,9 @@ Axiom core_array_Array_index :
 (* [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).
+  (a : array T N) (i : Idx),
+  result (inst.(core_ops_index_IndexMut_indexInst).(core_ops_index_Index_Output) *
+          (inst.(core_ops_index_IndexMut_indexInst).(core_ops_index_Index_Output) -> result (array T N))).
 
 (* Trait implementation: [core::slice::index::private_slice_index::Range] *)
 Definition core_slice_index_private_slice_index_SealedRangeUsizeInst
@@ -774,12 +783,10 @@ Definition core_slice_index_SliceIndexRangeUsizeSliceTInst (T : Type) :
   core_slice_index_SliceIndex_Output := slice T;
   core_slice_index_SliceIndex_get := core_slice_index_RangeUsize_get T;
   core_slice_index_SliceIndex_get_mut := core_slice_index_RangeUsize_get_mut T;
-  core_slice_index_SliceIndex_get_mut_back := core_slice_index_RangeUsize_get_mut_back T;
   core_slice_index_SliceIndex_get_unchecked := core_slice_index_RangeUsize_get_unchecked T;
   core_slice_index_SliceIndex_get_unchecked_mut := core_slice_index_RangeUsize_get_unchecked_mut T;
   core_slice_index_SliceIndex_index := core_slice_index_RangeUsize_index T;
   core_slice_index_SliceIndex_index_mut := core_slice_index_RangeUsize_index_mut T;
-  core_slice_index_SliceIndex_index_mut_back := core_slice_index_RangeUsize_index_mut_back T;
 |}.
 
 (* Trait implementation: [core::slice::index::[T]] *)
@@ -796,7 +803,6 @@ Definition core_ops_index_IndexMutSliceTIInst (T Idx : Type)
   core_ops_index_IndexMut (slice T) Idx := {|
   core_ops_index_IndexMut_indexInst := core_ops_index_IndexSliceTIInst 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]] *)
@@ -813,18 +819,14 @@ Definition core_ops_index_IndexMutArrayInst (T Idx : Type) (N : usize)
   core_ops_index_IndexMut (array T N) Idx := {|
   core_ops_index_IndexMut_indexInst := core_ops_index_IndexArrayInst 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).
+Axiom core_slice_index_usize_get_mut :
+  forall (T : Type), usize -> slice T -> result (option T * (option T -> result (slice T))).
 
 (* [core::slice::index::usize::get_unchecked]: forward function *)
 Axiom core_slice_index_usize_get_unchecked :
@@ -838,11 +840,8 @@ Axiom core_slice_index_usize_get_unchecked_mut :
 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).
+Axiom core_slice_index_usize_index_mut :
+  forall (T : Type), usize -> slice T -> result (T * (T -> result (slice T))).
 
 (* Trait implementation: [core::slice::index::private_slice_index::usize] *)
 Definition core_slice_index_private_slice_index_SealedUsizeInst
@@ -855,12 +854,10 @@ Definition core_slice_index_SliceIndexUsizeSliceTInst (T : Type) :
   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 *)
@@ -869,12 +866,9 @@ Axiom alloc_vec_Vec_index : forall (T Idx : Type) (inst : core_slice_index_Slice
 
 (* [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).
+  (Self : alloc_vec_Vec T) (i : Idx),
+  result (inst.(core_slice_index_SliceIndex_Output) *
+          (inst.(core_slice_index_SliceIndex_Output) -> result (alloc_vec_Vec T))).
 
 (* Trait implementation: [alloc::vec::Vec] *)
 Definition alloc_vec_Vec_coreopsindexIndexInst (T Idx : Type)
@@ -890,7 +884,6 @@ Definition alloc_vec_Vec_coreopsindexIndexMutInst (T Idx : Type)
   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 *)
@@ -901,10 +894,6 @@ Axiom alloc_vec_Vec_index_eq : forall {a : Type} (v : alloc_vec_Vec a) (i : usiz
 
 Axiom alloc_vec_Vec_index_mut_eq : forall {a : Type} (v : alloc_vec_Vec a) (i : usize) (x : a),
   alloc_vec_Vec_index_mut a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i =
-    alloc_vec_Vec_index_usize v i.
-
-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_SliceIndexUsizeSliceTInst a) v i x =
-    alloc_vec_Vec_update_usize v i x.
+    alloc_vec_Vec_index_mut_usize v i.
 
 End Primitives.
diff --git a/tests/coq/traits/Traits.v b/tests/coq/traits/Traits.v
index 2448e8f3..7abf2021 100644
--- a/tests/coq/traits/Traits.v
+++ b/tests/coq/traits/Traits.v
@@ -17,7 +17,7 @@ Record BoolTrait_t (Self : Type) := mkBoolTrait_t {
 Arguments mkBoolTrait_t { _ }.
 Arguments BoolTrait_t_get_bool { _ }.
 
-(** [traits::{bool}::get_bool]: forward function
+(** [traits::{bool}::get_bool]:
     Source: 'src/traits.rs', lines 12:4-12:30 *)
 Definition bool_get_bool (self : bool) : result bool :=
   Return self.
@@ -28,24 +28,24 @@ Definition traits_BoolTraitBoolInst : BoolTrait_t bool := {|
   BoolTrait_t_get_bool := bool_get_bool;
 |}.
 
-(** [traits::BoolTrait::ret_true]: forward function
+(** [traits::BoolTrait::ret_true]:
     Source: 'src/traits.rs', lines 6:4-6:30 *)
 Definition boolTrait_ret_true
   {Self : Type} (self_clause : BoolTrait_t Self) (self : Self) : result bool :=
   Return true
 .
 
-(** [traits::test_bool_trait_bool]: forward function
+(** [traits::test_bool_trait_bool]:
     Source: 'src/traits.rs', lines 17:0-17:44 *)
 Definition test_bool_trait_bool (x : bool) : result bool :=
   b <- bool_get_bool x;
   if b then boolTrait_ret_true traits_BoolTraitBoolInst x else Return false
 .
 
-(** [traits::{core::option::Option<T>#1}::get_bool]: forward function
+(** [traits::{core::option::Option<T>#1}::get_bool]:
     Source: 'src/traits.rs', lines 23:4-23:30 *)
 Definition option_get_bool (T : Type) (self : option T) : result bool :=
-  match self with | None => Return false | Some t => Return true end
+  match self with | None => Return false | Some _ => Return true end
 .
 
 (** Trait implementation: [traits::{core::option::Option<T>#1}]
@@ -55,7 +55,7 @@ Definition traits_BoolTraitcoreoptionOptionTInst (T : Type) : BoolTrait_t
   BoolTrait_t_get_bool := option_get_bool T;
 |}.
 
-(** [traits::test_bool_trait_option]: forward function
+(** [traits::test_bool_trait_option]:
     Source: 'src/traits.rs', lines 31:0-31:54 *)
 Definition test_bool_trait_option (T : Type) (x : option T) : result bool :=
   b <- option_get_bool T x;
@@ -64,7 +64,7 @@ Definition test_bool_trait_option (T : Type) (x : option T) : result bool :=
   else Return false
 .
 
-(** [traits::test_bool_trait]: forward function
+(** [traits::test_bool_trait]:
     Source: 'src/traits.rs', lines 35:0-35:50 *)
 Definition test_bool_trait
   (T : Type) (boolTraitTInst : BoolTrait_t T) (x : T) : result bool :=
@@ -80,7 +80,7 @@ Record ToU64_t (Self : Type) := mkToU64_t {
 Arguments mkToU64_t { _ }.
 Arguments ToU64_t_to_u64 { _ }.
 
-(** [traits::{u64#2}::to_u64]: forward function
+(** [traits::{u64#2}::to_u64]:
     Source: 'src/traits.rs', lines 44:4-44:26 *)
 Definition u64_to_u64 (self : u64) : result u64 :=
   Return self.
@@ -91,14 +91,14 @@ Definition traits_ToU64U64Inst : ToU64_t u64 := {|
   ToU64_t_to_u64 := u64_to_u64;
 |}.
 
-(** [traits::{(A, A)#3}::to_u64]: forward function
+(** [traits::{(A, A)#3}::to_u64]:
     Source: 'src/traits.rs', lines 50:4-50:26 *)
 Definition pair_to_u64
   (A : Type) (toU64AInst : ToU64_t A) (self : (A * A)) : result u64 :=
-  let (t, t0) := self in
+  let (t, t1) := self in
   i <- toU64AInst.(ToU64_t_to_u64) t;
-  i0 <- toU64AInst.(ToU64_t_to_u64) t0;
-  u64_add i i0
+  i1 <- toU64AInst.(ToU64_t_to_u64) t1;
+  u64_add i i1
 .
 
 (** Trait implementation: [traits::{(A, A)#3}]
@@ -108,20 +108,20 @@ Definition traits_ToU64TupleAAInst (A : Type) (toU64AInst : ToU64_t A) :
   ToU64_t_to_u64 := pair_to_u64 A toU64AInst;
 |}.
 
-(** [traits::f]: forward function
+(** [traits::f]:
     Source: 'src/traits.rs', lines 55:0-55:36 *)
 Definition f (T : Type) (toU64TInst : ToU64_t T) (x : (T * T)) : result u64 :=
   pair_to_u64 T toU64TInst x
 .
 
-(** [traits::g]: forward function
+(** [traits::g]:
     Source: 'src/traits.rs', lines 59:0-61:18 *)
 Definition g
   (T : Type) (toU64TupleTTInst : ToU64_t (T * T)) (x : (T * T)) : result u64 :=
   toU64TupleTTInst.(ToU64_t_to_u64) x
 .
 
-(** [traits::h0]: forward function
+(** [traits::h0]:
     Source: 'src/traits.rs', lines 66:0-66:24 *)
 Definition h0 (x : u64) : result u64 :=
   u64_to_u64 x.
@@ -133,7 +133,7 @@ Record Wrapper_t (T : Type) := mkWrapper_t { wrapper_x : T; }.
 Arguments mkWrapper_t { _ }.
 Arguments wrapper_x { _ }.
 
-(** [traits::{traits::Wrapper<T>#4}::to_u64]: forward function
+(** [traits::{traits::Wrapper<T>#4}::to_u64]:
     Source: 'src/traits.rs', lines 75:4-75:26 *)
 Definition wrapper_to_u64
   (T : Type) (toU64TInst : ToU64_t T) (self : Wrapper_t T) : result u64 :=
@@ -147,13 +147,13 @@ Definition traits_ToU64traitsWrapperTInst (T : Type) (toU64TInst : ToU64_t T) :
   ToU64_t_to_u64 := wrapper_to_u64 T toU64TInst;
 |}.
 
-(** [traits::h1]: forward function
+(** [traits::h1]:
     Source: 'src/traits.rs', lines 80:0-80:33 *)
 Definition h1 (x : Wrapper_t u64) : result u64 :=
   wrapper_to_u64 u64 traits_ToU64U64Inst x
 .
 
-(** [traits::h2]: forward function
+(** [traits::h2]:
     Source: 'src/traits.rs', lines 84:0-84:41 *)
 Definition h2
   (T : Type) (toU64TInst : ToU64_t T) (x : Wrapper_t T) : result u64 :=
@@ -169,7 +169,7 @@ Record ToType_t (Self T : Type) := mkToType_t {
 Arguments mkToType_t { _ _ }.
 Arguments ToType_t_to_type { _ _ }.
 
-(** [traits::{u64#5}::to_type]: forward function
+(** [traits::{u64#5}::to_type]:
     Source: 'src/traits.rs', lines 93:4-93:28 *)
 Definition u64_to_type (self : u64) : result bool :=
   Return (self s> 0%u64).
@@ -190,7 +190,7 @@ Record OfType_t (Self : Type) := mkOfType_t {
 Arguments mkOfType_t { _ }.
 Arguments OfType_t_of_type { _ }.
 
-(** [traits::h3]: forward function
+(** [traits::h3]:
     Source: 'src/traits.rs', lines 104:0-104:50 *)
 Definition h3
   (T1 T2 : Type) (ofTypeT1Inst : OfType_t T1) (toTypeT2T1Inst : ToType_t T2 T1)
@@ -211,7 +211,7 @@ Arguments mkOfTypeBis_t { _ _ }.
 Arguments OfTypeBis_tOfTypeBis_t_ToTypeTSelfInst { _ _ }.
 Arguments OfTypeBis_t_of_type { _ _ }.
 
-(** [traits::h4]: forward function
+(** [traits::h4]:
     Source: 'src/traits.rs', lines 118:0-118:57 *)
 Definition h4
   (T1 T2 : Type) (ofTypeBisT1T2Inst : OfTypeBis_t T1 T2) (toTypeT2T1Inst :
@@ -238,7 +238,7 @@ Record TestType_test_TestTrait_t (Self : Type) := mkTestType_test_TestTrait_t {
 Arguments mkTestType_test_TestTrait_t { _ }.
 Arguments TestType_test_TestTrait_t_test { _ }.
 
-(** [traits::{traits::TestType<T>#6}::test::{traits::{traits::TestType<T>#6}::test::TestType1}::test]: forward function
+(** [traits::{traits::TestType<T>#6}::test::{traits::{traits::TestType<T>#6}::test::TestType1}::test]:
     Source: 'src/traits.rs', lines 139:12-139:34 *)
 Definition testType_test_TestType1_test
   (self : TestType_test_TestType1_t) : result bool :=
@@ -252,21 +252,21 @@ Definition traits_TestType_test_TestTraittraitstraitsTestTypeTtestTestType1Inst
   TestType_test_TestTrait_t_test := testType_test_TestType1_test;
 |}.
 
-(** [traits::{traits::TestType<T>#6}::test]: forward function
+(** [traits::{traits::TestType<T>#6}::test]:
     Source: 'src/traits.rs', lines 126:4-126:36 *)
 Definition testType_test
   (T : Type) (toU64TInst : ToU64_t T) (self : TestType_t T) (x : T) :
   result bool
   :=
-  x0 <- toU64TInst.(ToU64_t_to_u64) x;
-  if x0 s> 0%u64 then testType_test_TestType1_test 0%u64 else Return false
+  x1 <- toU64TInst.(ToU64_t_to_u64) x;
+  if x1 s> 0%u64 then testType_test_TestType1_test 0%u64 else Return false
 .
 
 (** [traits::BoolWrapper]
     Source: 'src/traits.rs', lines 150:0-150:22 *)
 Definition BoolWrapper_t : Type := bool.
 
-(** [traits::{traits::BoolWrapper#7}::to_type]: forward function
+(** [traits::{traits::BoolWrapper#7}::to_type]:
     Source: 'src/traits.rs', lines 156:4-156:25 *)
 Definition boolWrapper_to_type
   (T : Type) (toTypeBoolTInst : ToType_t bool T) (self : BoolWrapper_t) :
@@ -312,8 +312,7 @@ Arguments WithConstTy_t_f { _ _ }.
 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 ())
+(** [traits::{bool#8}::f]:
     Source: 'src/traits.rs', lines 180:4-180:39 *)
 Definition bool_f (i : u64) (a : array u8 32%usize) : result u64 :=
   Return i.
@@ -329,16 +328,16 @@ Definition traits_WithConstTyBool32Inst : WithConstTy_t bool 32%usize := {|
   WithConstTy_t_f := bool_f;
 |}.
 
-(** [traits::use_with_const_ty1]: forward function
+(** [traits::use_with_const_ty1]:
     Source: 'src/traits.rs', lines 183:0-183:75 *)
 Definition use_with_const_ty1
   (H : Type) (LEN : usize) (withConstTyHLENInst : WithConstTy_t H LEN) :
   result usize
   :=
-  let i := withConstTyHLENInst.(WithConstTy_tWithConstTy_t_LEN1) in Return i
+  Return withConstTyHLENInst.(WithConstTy_tWithConstTy_t_LEN1)
 .
 
-(** [traits::use_with_const_ty2]: forward function
+(** [traits::use_with_const_ty2]:
     Source: 'src/traits.rs', lines 187:0-187:73 *)
 Definition use_with_const_ty2
   (H : Type) (LEN : usize) (withConstTyHLENInst : WithConstTy_t H LEN)
@@ -348,7 +347,7 @@ Definition use_with_const_ty2
   Return tt
 .
 
-(** [traits::use_with_const_ty3]: forward function
+(** [traits::use_with_const_ty3]:
     Source: 'src/traits.rs', lines 189:0-189:80 *)
 Definition use_with_const_ty3
   (H : Type) (LEN : usize) (withConstTyHLENInst : WithConstTy_t H LEN)
@@ -359,12 +358,12 @@ Definition use_with_const_ty3
     x
 .
 
-(** [traits::test_where1]: forward function
+(** [traits::test_where1]:
     Source: 'src/traits.rs', lines 193:0-193:40 *)
 Definition test_where1 (T : Type) (_x : T) : result unit :=
   Return tt.
 
-(** [traits::test_where2]: forward function
+(** [traits::test_where2]:
     Source: 'src/traits.rs', lines 194:0-194:57 *)
 Definition test_where2
   (T : Type) (withConstTyT32Inst : WithConstTy_t T 32%usize) (_x : u32) :
@@ -403,16 +402,25 @@ Arguments mkChildTrait_t { _ }.
 Arguments ChildTrait_tChildTrait_t_ParentTrait0SelfInst { _ }.
 Arguments ChildTrait_tChildTrait_t_ParentTrait1SelfInst { _ }.
 
-(** [traits::test_child_trait1]: forward function
-    Source: 'src/traits.rs', lines 209:0-209:56 *)
+(** [traits::test_parent_trait0]:
+    Source: 'src/traits.rs', lines 208:0-208:57 *)
+Definition test_parent_trait0
+  (T : Type) (parentTrait0TInst : ParentTrait0_t T) (x : T) :
+  result parentTrait0TInst.(ParentTrait0_tParentTrait0_t_W)
+  :=
+  parentTrait0TInst.(ParentTrait0_t_get_w) x
+.
+
+(** [traits::test_child_trait1]:
+    Source: 'src/traits.rs', lines 213:0-213:56 *)
 Definition test_child_trait1
   (T : Type) (childTraitTInst : ChildTrait_t T) (x : T) : result string :=
   childTraitTInst.(ChildTrait_tChildTrait_t_ParentTrait0SelfInst).(ParentTrait0_t_get_name)
     x
 .
 
-(** [traits::test_child_trait2]: forward function
-    Source: 'src/traits.rs', lines 213:0-213:54 *)
+(** [traits::test_child_trait2]:
+    Source: 'src/traits.rs', lines 217:0-217:54 *)
 Definition test_child_trait2
   (T : Type) (childTraitTInst : ChildTrait_t T) (x : T) :
   result
@@ -422,8 +430,8 @@ Definition test_child_trait2
     x
 .
 
-(** [traits::order1]: forward function
-    Source: 'src/traits.rs', lines 219:0-219:59 *)
+(** [traits::order1]:
+    Source: 'src/traits.rs', lines 223:0-223:59 *)
 Definition order1
   (T U : Type) (parentTrait0TInst : ParentTrait0_t T) (parentTrait0UInst :
   ParentTrait0_t U) :
@@ -433,7 +441,7 @@ Definition order1
 .
 
 (** Trait declaration: [traits::ChildTrait1]
-    Source: 'src/traits.rs', lines 222:0-222:35 *)
+    Source: 'src/traits.rs', lines 226:0-226:35 *)
 Record ChildTrait1_t (Self : Type) := mkChildTrait1_t {
   ChildTrait1_tChildTrait1_t_ParentTrait1SelfInst : ParentTrait1_t Self;
 }.
@@ -442,19 +450,19 @@ Arguments mkChildTrait1_t { _ }.
 Arguments ChildTrait1_tChildTrait1_t_ParentTrait1SelfInst { _ }.
 
 (** Trait implementation: [traits::{usize#9}]
-    Source: 'src/traits.rs', lines 224:0-224:27 *)
+    Source: 'src/traits.rs', lines 228:0-228:27 *)
 Definition traits_ParentTrait1UsizeInst : ParentTrait1_t usize
   := mkParentTrait1_t.
 
 (** Trait implementation: [traits::{usize#10}]
-    Source: 'src/traits.rs', lines 225:0-225:26 *)
+    Source: 'src/traits.rs', lines 229:0-229:26 *)
 Definition traits_ChildTrait1UsizeInst : ChildTrait1_t usize := {|
   ChildTrait1_tChildTrait1_t_ParentTrait1SelfInst :=
     traits_ParentTrait1UsizeInst;
 |}.
 
 (** Trait declaration: [traits::Iterator]
-    Source: 'src/traits.rs', lines 229:0-229:18 *)
+    Source: 'src/traits.rs', lines 233:0-233:18 *)
 Record Iterator_t (Self : Type) := mkIterator_t {
   Iterator_tIterator_t_Item : Type;
 }.
@@ -463,7 +471,7 @@ Arguments mkIterator_t { _ }.
 Arguments Iterator_tIterator_t_Item { _ }.
 
 (** Trait declaration: [traits::IntoIterator]
-    Source: 'src/traits.rs', lines 233:0-233:22 *)
+    Source: 'src/traits.rs', lines 237:0-237:22 *)
 Record IntoIterator_t (Self : Type) := mkIntoIterator_t {
   IntoIterator_tIntoIterator_t_Item : Type;
   IntoIterator_tIntoIterator_t_IntoIter : Type;
@@ -480,13 +488,13 @@ Arguments IntoIterator_tIntoIterator_t_IntoIter_clause_0 { _ }.
 Arguments IntoIterator_t_into_iter { _ }.
 
 (** Trait declaration: [traits::FromResidual]
-    Source: 'src/traits.rs', lines 250:0-250:21 *)
+    Source: 'src/traits.rs', lines 254:0-254:21 *)
 Record FromResidual_t (Self T : Type) := mkFromResidual_t{}.
 
 Arguments mkFromResidual_t { _ _ }.
 
 (** Trait declaration: [traits::Try]
-    Source: 'src/traits.rs', lines 246:0-246:48 *)
+    Source: 'src/traits.rs', lines 250:0-250:48 *)
 Record Try_t (Self : Type) := mkTry_t {
   Try_tTry_t_Residual : Type;
   Try_tTry_t_FromResidualSelftraitsTrySelfResidualInst : FromResidual_t Self
@@ -498,7 +506,7 @@ Arguments Try_tTry_t_Residual { _ }.
 Arguments Try_tTry_t_FromResidualSelftraitsTrySelfResidualInst { _ }.
 
 (** Trait declaration: [traits::WithTarget]
-    Source: 'src/traits.rs', lines 252:0-252:20 *)
+    Source: 'src/traits.rs', lines 256:0-256:20 *)
 Record WithTarget_t (Self : Type) := mkWithTarget_t {
   WithTarget_tWithTarget_t_Target : Type;
 }.
@@ -507,7 +515,7 @@ Arguments mkWithTarget_t { _ }.
 Arguments WithTarget_tWithTarget_t_Target { _ }.
 
 (** Trait declaration: [traits::ParentTrait2]
-    Source: 'src/traits.rs', lines 256:0-256:22 *)
+    Source: 'src/traits.rs', lines 260:0-260:22 *)
 Record ParentTrait2_t (Self : Type) := mkParentTrait2_t {
   ParentTrait2_tParentTrait2_t_U : Type;
   ParentTrait2_tParentTrait2_t_U_clause_0 : WithTarget_t
@@ -519,7 +527,7 @@ Arguments ParentTrait2_tParentTrait2_t_U { _ }.
 Arguments ParentTrait2_tParentTrait2_t_U_clause_0 { _ }.
 
 (** Trait declaration: [traits::ChildTrait2]
-    Source: 'src/traits.rs', lines 260:0-260:35 *)
+    Source: 'src/traits.rs', lines 264:0-264:35 *)
 Record ChildTrait2_t (Self : Type) := mkChildTrait2_t {
   ChildTrait2_tChildTrait2_t_ParentTrait2SelfInst : ParentTrait2_t Self;
   ChildTrait2_t_convert :
@@ -533,25 +541,25 @@ Arguments ChildTrait2_tChildTrait2_t_ParentTrait2SelfInst { _ }.
 Arguments ChildTrait2_t_convert { _ }.
 
 (** Trait implementation: [traits::{u32#11}]
-    Source: 'src/traits.rs', lines 264:0-264:23 *)
+    Source: 'src/traits.rs', lines 268:0-268:23 *)
 Definition traits_WithTargetU32Inst : WithTarget_t u32 := {|
   WithTarget_tWithTarget_t_Target := u32;
 |}.
 
 (** Trait implementation: [traits::{u32#12}]
-    Source: 'src/traits.rs', lines 268:0-268:25 *)
+    Source: 'src/traits.rs', lines 272:0-272:25 *)
 Definition traits_ParentTrait2U32Inst : ParentTrait2_t u32 := {|
   ParentTrait2_tParentTrait2_t_U := u32;
   ParentTrait2_tParentTrait2_t_U_clause_0 := traits_WithTargetU32Inst;
 |}.
 
-(** [traits::{u32#13}::convert]: forward function
-    Source: 'src/traits.rs', lines 273:4-273:29 *)
+(** [traits::{u32#13}::convert]:
+    Source: 'src/traits.rs', lines 277:4-277:29 *)
 Definition u32_convert (x : u32) : result u32 :=
   Return x.
 
 (** Trait implementation: [traits::{u32#13}]
-    Source: 'src/traits.rs', lines 272:0-272:24 *)
+    Source: 'src/traits.rs', lines 276:0-276:24 *)
 Definition traits_ChildTrait2U32Inst : ChildTrait2_t u32 := {|
   ChildTrait2_tChildTrait2_t_ParentTrait2SelfInst :=
     traits_ParentTrait2U32Inst;
@@ -559,7 +567,7 @@ Definition traits_ChildTrait2U32Inst : ChildTrait2_t u32 := {|
 |}.
 
 (** Trait declaration: [traits::CFnOnce]
-    Source: 'src/traits.rs', lines 286:0-286:23 *)
+    Source: 'src/traits.rs', lines 290:0-290:23 *)
 Record CFnOnce_t (Self Args : Type) := mkCFnOnce_t {
   CFnOnce_tCFnOnce_t_Output : Type;
   CFnOnce_t_call_once : Self -> Args -> result CFnOnce_tCFnOnce_t_Output;
@@ -570,31 +578,48 @@ Arguments CFnOnce_tCFnOnce_t_Output { _ _ }.
 Arguments CFnOnce_t_call_once { _ _ }.
 
 (** Trait declaration: [traits::CFnMut]
-    Source: 'src/traits.rs', lines 292:0-292:37 *)
+    Source: 'src/traits.rs', lines 296:0-296:37 *)
 Record CFnMut_t (Self Args : Type) := mkCFnMut_t {
   CFnMut_tCFnMut_t_CFnOnceSelfArgsInst : CFnOnce_t Self Args;
   CFnMut_t_call_mut : Self -> Args -> result
-    (CFnMut_tCFnMut_t_CFnOnceSelfArgsInst).(CFnOnce_tCFnOnce_t_Output);
-  CFnMut_t_call_mut_back : Self -> Args ->
-    (CFnMut_tCFnMut_t_CFnOnceSelfArgsInst).(CFnOnce_tCFnOnce_t_Output) ->
-    result Self;
+    ((CFnMut_tCFnMut_t_CFnOnceSelfArgsInst).(CFnOnce_tCFnOnce_t_Output) *
+    Self);
 }.
 
 Arguments mkCFnMut_t { _ _ }.
 Arguments CFnMut_tCFnMut_t_CFnOnceSelfArgsInst { _ _ }.
 Arguments CFnMut_t_call_mut { _ _ }.
-Arguments CFnMut_t_call_mut_back { _ _ }.
 
 (** Trait declaration: [traits::CFn]
-    Source: 'src/traits.rs', lines 296:0-296:33 *)
+    Source: 'src/traits.rs', lines 300:0-300:33 *)
 Record CFn_t (Self Args : Type) := mkCFn_t {
   CFn_tCFn_t_CFnMutSelfArgsInst : CFnMut_t Self Args;
-  CFn_t_call_mut : Self -> Args -> result
+  CFn_t_call : Self -> Args -> result
     (CFn_tCFn_t_CFnMutSelfArgsInst).(CFnMut_tCFnMut_t_CFnOnceSelfArgsInst).(CFnOnce_tCFnOnce_t_Output);
 }.
 
 Arguments mkCFn_t { _ _ }.
 Arguments CFn_tCFn_t_CFnMutSelfArgsInst { _ _ }.
-Arguments CFn_t_call_mut { _ _ }.
+Arguments CFn_t_call { _ _ }.
+
+(** Trait declaration: [traits::GetTrait]
+    Source: 'src/traits.rs', lines 304:0-304:18 *)
+Record GetTrait_t (Self : Type) := mkGetTrait_t {
+  GetTrait_tGetTrait_t_W : Type;
+  GetTrait_t_get_w : Self -> result GetTrait_tGetTrait_t_W;
+}.
+
+Arguments mkGetTrait_t { _ }.
+Arguments GetTrait_tGetTrait_t_W { _ }.
+Arguments GetTrait_t_get_w { _ }.
+
+(** [traits::test_get_trait]:
+    Source: 'src/traits.rs', lines 309:0-309:49 *)
+Definition test_get_trait
+  (T : Type) (getTraitTInst : GetTrait_t T) (x : T) :
+  result getTraitTInst.(GetTrait_tGetTrait_t_W)
+  :=
+  getTraitTInst.(GetTrait_t_get_w) x
+.
 
 End Traits.
diff --git a/tests/fstar-split/.gitignore b/tests/fstar-split/.gitignore
new file mode 100644
index 00000000..28a11147
--- /dev/null
+++ b/tests/fstar-split/.gitignore
@@ -0,0 +1 @@
+*/obj
\ No newline at end of file
diff --git a/tests/fstar-split/Makefile b/tests/fstar-split/Makefile
new file mode 100644
index 00000000..6cf03386
--- /dev/null
+++ b/tests/fstar-split/Makefile
@@ -0,0 +1,33 @@
+ALL_DIRS ?= $(filter-out Makefile%, $(wildcard *))
+
+VERIFY_DIRS = $(addprefix verif-,$(ALL_DIRS))
+
+CLEAN_DIRS = $(addprefix clean-,$(ALL_DIRS))
+
+COPY_MAKEFILES = $(addprefix copy-makefile-,$(ALL_DIRS))
+
+.PHONY: all
+all: prepare-projects verify
+
+.PHONY: prepare-projects
+prepare-projects: $(COPY_MAKEFILES)
+
+.PHONY: verify
+verify: $(VERIFY_DIRS)
+
+.PHONY: verif-%
+verif-%:
+	cd $* && make all
+
+.PHONY: copy-makefile-%
+copy-makefile-%:
+	rm -f $*/Makefile
+	echo "# This file was automatically generated - modify ../Makefile.template instead" >> $*/Makefile
+	cat Makefile.template >> $*/Makefile
+
+.PHONY: clean
+clean: $(CLEAN_DIRS)
+
+.PHONY: clean-%
+clean-%:
+	cd $* && make clean
diff --git a/tests/fstar-split/Makefile.template b/tests/fstar-split/Makefile.template
new file mode 100644
index 00000000..14790d6d
--- /dev/null
+++ b/tests/fstar-split/Makefile.template
@@ -0,0 +1,48 @@
+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-split/array/Array.Clauses.Template.fst b/tests/fstar-split/array/Array.Clauses.Template.fst
new file mode 100644
index 00000000..b2f2649c
--- /dev/null
+++ b/tests/fstar-split/array/Array.Clauses.Template.fst
@@ -0,0 +1,21 @@
+(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
+(** [array]: templates for the decreases clauses *)
+module Array.Clauses.Template
+open Primitives
+open Array.Types
+
+#set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
+
+(** [array::sum]: decreases clause
+    Source: 'src/array.rs', lines 242:0-250:1 *)
+unfold
+let sum_loop_decreases (s : slice u32) (sum1 : u32) (i : usize) : nat =
+  admit ()
+
+(** [array::sum2]: decreases clause
+    Source: 'src/array.rs', lines 252:0-261:1 *)
+unfold
+let sum2_loop_decreases (s : slice u32) (s2 : slice u32) (sum1 : u32)
+  (i : usize) : nat =
+  admit ()
+
diff --git a/tests/fstar-split/array/Array.Clauses.fst b/tests/fstar-split/array/Array.Clauses.fst
new file mode 100644
index 00000000..68cbf216
--- /dev/null
+++ b/tests/fstar-split/array/Array.Clauses.fst
@@ -0,0 +1,19 @@
+(** [array]: decreases clauses *)
+module Array.Clauses
+open Primitives
+open Array.Types
+open FStar.List.Tot
+
+#set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
+
+(** [array::sum]: decreases clause *)
+unfold
+let sum_loop_decreases (s : slice u32) (sum : u32) (i : usize) : nat =
+  if i < length s then length s - i else 0
+
+(** [array::sum2]: decreases clause *)
+unfold
+let sum2_loop_decreases (s : slice u32) (s2 : slice u32) (sum : u32)
+  (i : usize) : nat =
+  if i < length s then length s - i else 0
+
diff --git a/tests/fstar-split/array/Array.Funs.fst b/tests/fstar-split/array/Array.Funs.fst
new file mode 100644
index 00000000..30b19702
--- /dev/null
+++ b/tests/fstar-split/array/Array.Funs.fst
@@ -0,0 +1,445 @@
+(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
+(** [array]: function definitions *)
+module Array.Funs
+open Primitives
+include Array.Types
+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 ())
+    Source: 'src/array.rs', lines 8:0-8:24 *)
+let incr (x : u32) : result u32 =
+  u32_add x 1
+
+(** [array::array_to_shared_slice_]: forward function
+    Source: 'src/array.rs', lines 16:0-16:53 *)
+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
+    Source: 'src/array.rs', lines 21:0-21:58 *)
+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
+    Source: 'src/array.rs', lines 21:0-21:58 *)
+let array_to_mut_slice__back
+  (t : Type0) (s : array t 32) (ret : slice t) : result (array t 32) =
+  array_from_slice t 32 s ret
+
+(** [array::array_len]: forward function
+    Source: 'src/array.rs', lines 25:0-25:40 *)
+let array_len (t : Type0) (s : array t 32) : result usize =
+  let* s1 = array_to_slice t 32 s in let i = slice_len t s1 in Return i
+
+(** [array::shared_array_len]: forward function
+    Source: 'src/array.rs', lines 29:0-29:48 *)
+let shared_array_len (t : Type0) (s : array t 32) : result usize =
+  let* s1 = array_to_slice t 32 s in let i = slice_len t s1 in Return i
+
+(** [array::shared_slice_len]: forward function
+    Source: 'src/array.rs', lines 33:0-33:44 *)
+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
+    Source: 'src/array.rs', lines 37:0-37:57 *)
+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
+    Source: 'src/array.rs', lines 44:0-44:53 *)
+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
+    Source: 'src/array.rs', lines 48:0-48:45 *)
+let index_array_copy (x : array u32 32) : result u32 =
+  array_index_usize u32 32 x 0
+
+(** [array::index_mut_array]: forward function
+    Source: 'src/array.rs', lines 52:0-52:62 *)
+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
+    Source: 'src/array.rs', lines 52:0-52:62 *)
+let index_mut_array_back
+  (t : Type0) (s : array t 32) (i : usize) (ret : t) : result (array t 32) =
+  array_update_usize t 32 s i ret
+
+(** [array::index_slice]: forward function
+    Source: 'src/array.rs', lines 56:0-56:46 *)
+let index_slice (t : Type0) (s : slice t) (i : usize) : result t =
+  slice_index_usize t s i
+
+(** [array::index_mut_slice]: forward function
+    Source: 'src/array.rs', lines 60:0-60:58 *)
+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
+    Source: 'src/array.rs', lines 60:0-60:58 *)
+let index_mut_slice_back
+  (t : Type0) (s : slice t) (i : usize) (ret : t) : result (slice t) =
+  slice_update_usize t s i ret
+
+(** [array::slice_subslice_shared_]: forward function
+    Source: 'src/array.rs', lines 64:0-64:70 *)
+let 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_SliceIndexRangeUsizeSliceTInst u32) x
+    { start = y; end_ = z }
+
+(** [array::slice_subslice_mut_]: forward function
+    Source: 'src/array.rs', lines 68:0-68:75 *)
+let 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_SliceIndexRangeUsizeSliceTInst u32) x
+    { start = y; end_ = z }
+
+(** [array::slice_subslice_mut_]: backward function 0
+    Source: 'src/array.rs', lines 68:0-68:75 *)
+let 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_SliceIndexRangeUsizeSliceTInst u32) x
+    { start = y; end_ = z } ret
+
+(** [array::array_to_slice_shared_]: forward function
+    Source: 'src/array.rs', lines 72:0-72:54 *)
+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
+    Source: 'src/array.rs', lines 76:0-76:59 *)
+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
+    Source: 'src/array.rs', lines 76:0-76:59 *)
+let array_to_slice_mut__back
+  (x : array u32 32) (ret : slice u32) : result (array u32 32) =
+  array_from_slice u32 32 x ret
+
+(** [array::array_subslice_shared_]: forward function
+    Source: 'src/array.rs', lines 80:0-80:74 *)
+let array_subslice_shared_
+  (x : array u32 32) (y : usize) (z : usize) : result (slice u32) =
+  core_array_Array_index u32 (core_ops_range_Range usize) 32
+    (core_ops_index_IndexSliceTIInst u32 (core_ops_range_Range usize)
+    (core_slice_index_SliceIndexRangeUsizeSliceTInst u32)) x
+    { start = y; end_ = z }
+
+(** [array::array_subslice_mut_]: forward function
+    Source: 'src/array.rs', lines 84:0-84:79 *)
+let array_subslice_mut_
+  (x : array u32 32) (y : usize) (z : usize) : result (slice u32) =
+  core_array_Array_index_mut u32 (core_ops_range_Range usize) 32
+    (core_ops_index_IndexMutSliceTIInst u32 (core_ops_range_Range usize)
+    (core_slice_index_SliceIndexRangeUsizeSliceTInst u32)) x
+    { start = y; end_ = z }
+
+(** [array::array_subslice_mut_]: backward function 0
+    Source: 'src/array.rs', lines 84:0-84:79 *)
+let array_subslice_mut__back
+  (x : array u32 32) (y : usize) (z : usize) (ret : slice u32) :
+  result (array u32 32)
+  =
+  core_array_Array_index_mut_back u32 (core_ops_range_Range usize) 32
+    (core_ops_index_IndexMutSliceTIInst u32 (core_ops_range_Range usize)
+    (core_slice_index_SliceIndexRangeUsizeSliceTInst u32)) x
+    { start = y; end_ = z } ret
+
+(** [array::index_slice_0]: forward function
+    Source: 'src/array.rs', lines 88:0-88:38 *)
+let index_slice_0 (t : Type0) (s : slice t) : result t =
+  slice_index_usize t s 0
+
+(** [array::index_array_0]: forward function
+    Source: 'src/array.rs', lines 92:0-92:42 *)
+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
+    Source: 'src/array.rs', lines 103:0-103:71 *)
+let index_index_array
+  (s : array (array u32 32) 32) (i : usize) (j : usize) : result u32 =
+  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
+    Source: 'src/array.rs', lines 114:0-114:70 *)
+let update_update_array
+  (s : array (array u32 32) 32) (i : usize) (j : usize) : result unit =
+  let* a = array_index_usize (array u32 32) 32 s i in
+  let* a1 = array_update_usize u32 32 a j 0 in
+  let* _ = array_update_usize (array u32 32) 32 s i a1 in
+  Return ()
+
+(** [array::array_local_deep_copy]: forward function
+    Source: 'src/array.rs', lines 118:0-118:43 *)
+let array_local_deep_copy (x : array u32 32) : result unit =
+  Return ()
+
+(** [array::take_array]: forward function
+    Source: 'src/array.rs', lines 122:0-122:30 *)
+let take_array (a : array u32 2) : result unit =
+  Return ()
+
+(** [array::take_array_borrow]: forward function
+    Source: 'src/array.rs', lines 123:0-123:38 *)
+let take_array_borrow (a : array u32 2) : result unit =
+  Return ()
+
+(** [array::take_slice]: forward function
+    Source: 'src/array.rs', lines 124:0-124:28 *)
+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 ())
+    Source: 'src/array.rs', lines 125:0-125:36 *)
+let take_mut_slice (s : slice u32) : result (slice u32) =
+  Return s
+
+(** [array::const_array]: forward function
+    Source: 'src/array.rs', lines 127:0-127:32 *)
+let const_array : result (array u32 2) =
+  Return (mk_array u32 2 [ 0; 0 ])
+
+(** [array::const_slice]: forward function
+    Source: 'src/array.rs', lines 131:0-131:20 *)
+let const_slice : result unit =
+  let* _ = array_to_slice u32 2 (mk_array u32 2 [ 0; 0 ]) in Return ()
+
+(** [array::take_all]: forward function
+    Source: 'src/array.rs', lines 141:0-141:17 *)
+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* s1 = array_to_slice u32 2 (mk_array u32 2 [ 0; 0 ]) in
+  let* s2 = take_mut_slice s1 in
+  let* _ = array_from_slice u32 2 (mk_array u32 2 [ 0; 0 ]) s2 in
+  Return ()
+
+(** [array::index_array]: forward function
+    Source: 'src/array.rs', lines 155:0-155:38 *)
+let index_array (x : array u32 2) : result u32 =
+  array_index_usize u32 2 x 0
+
+(** [array::index_array_borrow]: forward function
+    Source: 'src/array.rs', lines 158:0-158:46 *)
+let index_array_borrow (x : array u32 2) : result u32 =
+  array_index_usize u32 2 x 0
+
+(** [array::index_slice_u32_0]: forward function
+    Source: 'src/array.rs', lines 162:0-162:42 *)
+let index_slice_u32_0 (x : slice u32) : result u32 =
+  slice_index_usize u32 x 0
+
+(** [array::index_mut_slice_u32_0]: forward function
+    Source: 'src/array.rs', lines 166:0-166:50 *)
+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
+    Source: 'src/array.rs', lines 166:0-166:50 *)
+let index_mut_slice_u32_0_back (x : slice u32) : result (slice u32) =
+  let* _ = slice_index_usize u32 x 0 in Return x
+
+(** [array::index_all]: forward function
+    Source: 'src/array.rs', lines 170:0-170:25 *)
+let index_all : result u32 =
+  let* i = index_array (mk_array u32 2 [ 0; 0 ]) in
+  let* i1 = index_array (mk_array u32 2 [ 0; 0 ]) in
+  let* i2 = u32_add i i1 in
+  let* i3 = index_array_borrow (mk_array u32 2 [ 0; 0 ]) in
+  let* i4 = u32_add i2 i3 in
+  let* s = array_to_slice u32 2 (mk_array u32 2 [ 0; 0 ]) in
+  let* i5 = index_slice_u32_0 s in
+  let* i6 = u32_add i4 i5 in
+  let* s1 = array_to_slice u32 2 (mk_array u32 2 [ 0; 0 ]) in
+  let* i7 = index_mut_slice_u32_0 s1 in
+  let* i8 = u32_add i6 i7 in
+  let* s2 = index_mut_slice_u32_0_back s1 in
+  let* _ = array_from_slice u32 2 (mk_array u32 2 [ 0; 0 ]) s2 in
+  Return i8
+
+(** [array::update_array]: forward function
+    Source: 'src/array.rs', lines 184:0-184:36 *)
+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 ())
+    Source: 'src/array.rs', lines 187:0-187:48 *)
+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 ())
+    Source: 'src/array.rs', lines 190:0-190:38 *)
+let update_mut_slice (x : slice u32) : result (slice u32) =
+  slice_update_usize u32 x 0 1
+
+(** [array::update_all]: forward function
+    Source: 'src/array.rs', lines 194:0-194:19 *)
+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* s1 = update_mut_slice s in
+  let* _ = array_from_slice u32 2 x s1 in
+  Return ()
+
+(** [array::range_all]: forward function
+    Source: 'src/array.rs', lines 205:0-205:18 *)
+let range_all : result unit =
+  let* s =
+    core_array_Array_index_mut u32 (core_ops_range_Range usize) 4
+      (core_ops_index_IndexMutSliceTIInst u32 (core_ops_range_Range usize)
+      (core_slice_index_SliceIndexRangeUsizeSliceTInst u32))
+      (mk_array u32 4 [ 0; 0; 0; 0 ]) { start = 1; end_ = 3 } in
+  let* s1 = update_mut_slice s in
+  let* _ =
+    core_array_Array_index_mut_back u32 (core_ops_range_Range usize) 4
+      (core_ops_index_IndexMutSliceTIInst u32 (core_ops_range_Range usize)
+      (core_slice_index_SliceIndexRangeUsizeSliceTInst u32))
+      (mk_array u32 4 [ 0; 0; 0; 0 ]) { start = 1; end_ = 3 } s1 in
+  Return ()
+
+(** [array::deref_array_borrow]: forward function
+    Source: 'src/array.rs', lines 214:0-214:46 *)
+let deref_array_borrow (x : array u32 2) : result u32 =
+  array_index_usize u32 2 x 0
+
+(** [array::deref_array_mut_borrow]: forward function
+    Source: 'src/array.rs', lines 219:0-219:54 *)
+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
+    Source: 'src/array.rs', lines 219:0-219:54 *)
+let deref_array_mut_borrow_back (x : array u32 2) : result (array u32 2) =
+  let* _ = array_index_usize u32 2 x 0 in Return x
+
+(** [array::take_array_t]: forward function
+    Source: 'src/array.rs', lines 227:0-227:31 *)
+let take_array_t (a : array aB_t 2) : result unit =
+  Return ()
+
+(** [array::non_copyable_array]: forward function
+    Source: 'src/array.rs', lines 229:0-229:27 *)
+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
+    Source: 'src/array.rs', lines 242:0-250:1 *)
+let rec sum_loop
+  (s : slice u32) (sum1 : u32) (i : usize) :
+  Tot (result u32) (decreases (sum_loop_decreases s sum1 i))
+  =
+  let i1 = slice_len u32 s in
+  if i < i1
+  then
+    let* i2 = slice_index_usize u32 s i in
+    let* sum3 = u32_add sum1 i2 in
+    let* i3 = usize_add i 1 in
+    sum_loop s sum3 i3
+  else Return sum1
+
+(** [array::sum]: forward function
+    Source: 'src/array.rs', lines 242:0-242:28 *)
+let sum (s : slice u32) : result u32 =
+  sum_loop s 0 0
+
+(** [array::sum2]: loop 0: forward function
+    Source: 'src/array.rs', lines 252:0-261:1 *)
+let rec sum2_loop
+  (s : slice u32) (s2 : slice u32) (sum1 : u32) (i : usize) :
+  Tot (result u32) (decreases (sum2_loop_decreases s s2 sum1 i))
+  =
+  let i1 = slice_len u32 s in
+  if i < i1
+  then
+    let* i2 = slice_index_usize u32 s i in
+    let* i3 = slice_index_usize u32 s2 i in
+    let* i4 = u32_add i2 i3 in
+    let* sum3 = u32_add sum1 i4 in
+    let* i5 = usize_add i 1 in
+    sum2_loop s s2 sum3 i5
+  else Return sum1
+
+(** [array::sum2]: forward function
+    Source: 'src/array.rs', lines 252:0-252:41 *)
+let sum2 (s : slice u32) (s2 : slice u32) : result u32 =
+  let i = slice_len u32 s in
+  let i1 = slice_len u32 s2 in
+  if not (i = i1) then Fail Failure else sum2_loop s s2 0 0
+
+(** [array::f0]: forward function
+    Source: 'src/array.rs', lines 263:0-263:11 *)
+let f0 : result unit =
+  let* s = array_to_slice u32 2 (mk_array u32 2 [ 1; 2 ]) in
+  let* s1 = slice_update_usize u32 s 0 1 in
+  let* _ = array_from_slice u32 2 (mk_array u32 2 [ 1; 2 ]) s1 in
+  Return ()
+
+(** [array::f1]: forward function
+    Source: 'src/array.rs', lines 268:0-268:11 *)
+let f1 : result unit =
+  let* _ = array_update_usize u32 2 (mk_array u32 2 [ 1; 2 ]) 0 1 in Return ()
+
+(** [array::f2]: forward function
+    Source: 'src/array.rs', lines 273:0-273:17 *)
+let f2 (i : u32) : result unit =
+  Return ()
+
+(** [array::f4]: forward function
+    Source: 'src/array.rs', lines 282:0-282:54 *)
+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_ops_index_IndexSliceTIInst u32 (core_ops_range_Range usize)
+    (core_slice_index_SliceIndexRangeUsizeSliceTInst u32)) x
+    { start = y; end_ = z }
+
+(** [array::f3]: forward function
+    Source: 'src/array.rs', lines 275:0-275:18 *)
+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* s1 = f4 b 16 18 in
+  sum2 s s1
+
+(** [array::SZ]
+    Source: 'src/array.rs', lines 286:0-286:19 *)
+let sz_body : result usize = Return 32
+let sz_c : usize = eval_global sz_body
+
+(** [array::f5]: forward function
+    Source: 'src/array.rs', lines 289:0-289:31 *)
+let f5 (x : array u32 32) : result u32 =
+  array_index_usize u32 32 x 0
+
+(** [array::ite]: forward function
+    Source: 'src/array.rs', lines 294:0-294:12 *)
+let ite : result unit =
+  let* s = array_to_slice u32 2 (mk_array u32 2 [ 0; 0 ]) in
+  let* s1 = array_to_slice u32 2 (mk_array u32 2 [ 0; 0 ]) in
+  let* s2 = index_mut_slice_u32_0_back s1 in
+  let* _ = array_from_slice u32 2 (mk_array u32 2 [ 0; 0 ]) s2 in
+  let* s3 = index_mut_slice_u32_0_back s in
+  let* _ = array_from_slice u32 2 (mk_array u32 2 [ 0; 0 ]) s3 in
+  Return ()
+
diff --git a/tests/fstar-split/array/Array.Types.fst b/tests/fstar-split/array/Array.Types.fst
new file mode 100644
index 00000000..312f6018
--- /dev/null
+++ b/tests/fstar-split/array/Array.Types.fst
@@ -0,0 +1,11 @@
+(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
+(** [array]: type definitions *)
+module Array.Types
+open Primitives
+
+#set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
+
+(** [array::AB]
+    Source: 'src/array.rs', lines 3:0-3:11 *)
+type aB_t = | AB_A : aB_t | AB_B : aB_t
+
diff --git a/tests/fstar-split/array/Makefile b/tests/fstar-split/array/Makefile
new file mode 100644
index 00000000..fa7d1f36
--- /dev/null
+++ b/tests/fstar-split/array/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-split/array/Primitives.fst b/tests/fstar-split/array/Primitives.fst
new file mode 100644
index 00000000..a3ffbde4
--- /dev/null
+++ b/tests/fstar-split/array/Primitives.fst
@@ -0,0 +1,884 @@
+/// 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
+
+assume val size_numbits : pos
+
+// TODO: we could use FStar.Int.int_t and FStar.UInt.int_t
+
+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_xor (#ty : scalar_ty)
+    (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
+  | Usize -> admit() // TODO
+  | I8 ->
+    // Encoding issues...
+    normalize_spec (FStar.Int.int_t 8);
+    normalize_spec (scalar I8);
+    FStar.Int.logxor #8 x y
+  | I16 ->
+    // Encoding issues...
+    normalize_spec (FStar.Int.int_t 16);
+    normalize_spec (scalar I16);
+    FStar.Int.logxor #16 x y
+  | I32 -> FStar.Int.logxor #32 x y
+  | I64 -> FStar.Int.logxor #64 x y
+  | I128 ->
+    // Encoding issues...
+    normalize_spec (FStar.Int.int_t 128);
+    normalize_spec (scalar I128);
+    FStar.Int.logxor #128 x y
+  | Isize -> admit() // TODO
+
+let scalar_or (#ty : scalar_ty)
+    (x : scalar ty) (y : scalar ty) : scalar ty =
+  match ty with
+  | U8 -> FStar.UInt.logor #8 x y
+  | U16 -> FStar.UInt.logor #16 x y
+  | U32 -> FStar.UInt.logor #32 x y
+  | U64 -> FStar.UInt.logor #64 x y
+  | U128 -> FStar.UInt.logor #128 x y
+  | Usize -> admit() // TODO
+  | I8 ->
+    // Encoding issues...
+    normalize_spec (FStar.Int.int_t 8);
+    normalize_spec (scalar I8);
+    FStar.Int.logor #8 x y
+  | I16 ->
+    // Encoding issues...
+    normalize_spec (FStar.Int.int_t 16);
+    normalize_spec (scalar I16);
+    FStar.Int.logor #16 x y
+  | I32 -> FStar.Int.logor #32 x y
+  | I64 -> FStar.Int.logor #64 x y
+  | I128 ->
+    // Encoding issues...
+    normalize_spec (FStar.Int.int_t 128);
+    normalize_spec (scalar I128);
+    FStar.Int.logor #128 x y
+  | Isize -> admit() // TODO
+
+let scalar_and (#ty : scalar_ty)
+    (x : scalar ty) (y : scalar ty) : scalar ty =
+  match ty with
+  | U8 -> FStar.UInt.logand #8 x y
+  | U16 -> FStar.UInt.logand #16 x y
+  | U32 -> FStar.UInt.logand #32 x y
+  | U64 -> FStar.UInt.logand #64 x y
+  | U128 -> FStar.UInt.logand #128 x y
+  | Usize -> admit() // TODO
+  | I8 ->
+    // Encoding issues...
+    normalize_spec (FStar.Int.int_t 8);
+    normalize_spec (scalar I8);
+    FStar.Int.logand #8 x y
+  | I16 ->
+    // Encoding issues...
+    normalize_spec (FStar.Int.int_t 16);
+    normalize_spec (scalar I16);
+    FStar.Int.logand #16 x y
+  | I32 -> FStar.Int.logand #32 x y
+  | I64 -> FStar.Int.logand #64 x y
+  | I128 ->
+    // Encoding issues...
+    normalize_spec (FStar.Int.int_t 128);
+    normalize_spec (scalar I128);
+    FStar.Int.logand #128 x y
+  | Isize -> admit() // TODO
+
+// Shift left
+let scalar_shl (#ty0 #ty1 : scalar_ty)
+    (x : scalar ty0) (y : scalar ty1) : result (scalar ty0) =
+  admit()
+
+// Shift right
+let scalar_shr (#ty0 #ty1 : scalar_ty)
+    (x : scalar ty0) (y : scalar ty1) : result (scalar ty0) =
+  admit()
+
+(** 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
+
+// This can't fail, but for now we make all casts faillible (easier for the translation)
+let scalar_cast_bool (tgt_ty : scalar_ty) (x : bool) : result (scalar tgt_ty) =
+  mk_scalar tgt_ty (if x then 1 else 0)
+
+/// 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
+
+/// Xor
+let u8_xor = scalar_xor #U8
+let u16_xor = scalar_xor #U16
+let u32_xor = scalar_xor #U32
+let u64_xor = scalar_xor #U64
+let u128_xor = scalar_xor #U128
+let usize_xor = scalar_xor #Usize
+let i8_xor = scalar_xor #I8
+let i16_xor = scalar_xor #I16
+let i32_xor = scalar_xor #I32
+let i64_xor = scalar_xor #I64
+let i128_xor = scalar_xor #I128
+let isize_xor = scalar_xor #Isize
+
+/// Or
+let u8_or = scalar_or #U8
+let u16_or = scalar_or #U16
+let u32_or = scalar_or #U32
+let u64_or = scalar_or #U64
+let u128_or = scalar_or #U128
+let usize_or = scalar_or #Usize
+let i8_or = scalar_or #I8
+let i16_or = scalar_or #I16
+let i32_or = scalar_or #I32
+let i64_or = scalar_or #I64
+let i128_or = scalar_or #I128
+let isize_or = scalar_or #Isize
+
+/// And
+let u8_and = scalar_and #U8
+let u16_and = scalar_and #U16
+let u32_and = scalar_and #U32
+let u64_and = scalar_and #U64
+let u128_and = scalar_and #U128
+let usize_and = scalar_and #Usize
+let i8_and = scalar_and #I8
+let i16_and = scalar_and #I16
+let i32_and = scalar_and #I32
+let i64_and = scalar_and #I64
+let i128_and = scalar_and #I128
+let isize_and = scalar_and #Isize
+
+/// Shift left
+let u8_shl #ty = scalar_shl #U8 #ty
+let u16_shl #ty = scalar_shl #U16 #ty
+let u32_shl #ty = scalar_shl #U32 #ty
+let u64_shl #ty = scalar_shl #U64 #ty
+let u128_shl #ty = scalar_shl #U128 #ty
+let usize_shl #ty = scalar_shl #Usize #ty
+let i8_shl #ty = scalar_shl #I8 #ty
+let i16_shl #ty = scalar_shl #I16 #ty
+let i32_shl #ty = scalar_shl #I32 #ty
+let i64_shl #ty = scalar_shl #I64 #ty
+let i128_shl #ty = scalar_shl #I128 #ty
+let isize_shl #ty = scalar_shl #Isize #ty
+
+/// Shift right
+let u8_shr #ty = scalar_shr #U8 #ty
+let u16_shr #ty = scalar_shr #U16 #ty
+let u32_shr #ty = scalar_shr #U32 #ty
+let u64_shr #ty = scalar_shr #U64 #ty
+let u128_shr #ty = scalar_shr #U128 #ty
+let usize_shr #ty = scalar_shr #Usize #ty
+let i8_shr #ty = scalar_shr #I8 #ty
+let i16_shr #ty = scalar_shr #I16 #ty
+let i32_shr #ty = scalar_shr #I32 #ty
+let i64_shr #ty = scalar_shr #I64 #ty
+let i128_shr #ty = scalar_shr #I128 #ty
+let isize_shr #ty = scalar_shr #Isize #ty
+
+(*** 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_RangeUsize_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_RangeUsize_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_RangeUsize_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_RangeUsize_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_RangeUsize_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_RangeUsize_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_RangeUsize_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_RangeUsize_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::private_slice_index::Range]
+let core_slice_index_private_slice_index_SealedRangeUsizeInst
+  : core_slice_index_private_slice_index_Sealed (core_ops_range_Range usize) = ()
+
+// Trait implementation: [core::slice::index::Range]
+let core_slice_index_SliceIndexRangeUsizeSliceTInst (t : Type0) :
+  core_slice_index_SliceIndex (core_ops_range_Range usize) (slice t) = {
+  sealedInst = core_slice_index_private_slice_index_SealedRangeUsizeInst;
+  output = slice t;
+  get = core_slice_index_RangeUsize_get t;
+  get_mut = core_slice_index_RangeUsize_get_mut t;
+  get_mut_back = core_slice_index_RangeUsize_get_mut_back t;
+  get_unchecked = core_slice_index_RangeUsize_get_unchecked t;
+  get_unchecked_mut = core_slice_index_RangeUsize_get_unchecked_mut t;
+  index = core_slice_index_RangeUsize_index t;
+  index_mut = core_slice_index_RangeUsize_index_mut t;
+  index_mut_back = core_slice_index_RangeUsize_index_mut_back t;
+}
+
+// Trait implementation: [core::slice::index::[T]]
+let core_ops_index_IndexSliceTIInst (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::[T]]
+let core_ops_index_IndexMutSliceTIInst (t idx : Type0)
+  (inst : core_slice_index_SliceIndex idx (slice t)) :
+  core_ops_index_IndexMut (slice t) idx = {
+  indexInst = core_ops_index_IndexSliceTIInst 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_ops_index_IndexArrayInst (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_ops_index_IndexMutArrayIInst (t idx : Type0) (n : usize)
+  (inst : core_ops_index_IndexMut (slice t) idx) :
+  core_ops_index_IndexMut (array t n) idx = {
+  indexInst = core_ops_index_IndexArrayInst 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_SealedUsizeInst
+  : core_slice_index_private_slice_index_Sealed usize = ()
+
+// Trait implementation: [core::slice::index::usize]
+let core_slice_index_SliceIndexUsizeSliceTInst (t : Type0) :
+  core_slice_index_SliceIndex usize (slice t) = {
+  sealedInst = core_slice_index_private_slice_index_SealedUsizeInst;
+  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_SliceIndexUsizeSliceTInst a) v i ==
+      alloc_vec_Vec_index_usize v i)
+  [SMTPat (alloc_vec_Vec_index a usize (core_slice_index_SliceIndexUsizeSliceTInst 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_SliceIndexUsizeSliceTInst a) v i ==
+      alloc_vec_Vec_index_usize v i)
+  [SMTPat (alloc_vec_Vec_index_mut a usize (core_slice_index_SliceIndexUsizeSliceTInst 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_SliceIndexUsizeSliceTInst a) v i x ==
+      alloc_vec_Vec_update_usize v i x)
+  [SMTPat (alloc_vec_Vec_index_mut_back a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i x)]
+  =
+  admit()
diff --git a/tests/fstar-split/betree/BetreeMain.Clauses.Template.fst b/tests/fstar-split/betree/BetreeMain.Clauses.Template.fst
new file mode 100644
index 00000000..537705c5
--- /dev/null
+++ b/tests/fstar-split/betree/BetreeMain.Clauses.Template.fst
@@ -0,0 +1,117 @@
+(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
+(** [betree_main]: templates for the decreases clauses *)
+module BetreeMain.Clauses.Template
+open Primitives
+open BetreeMain.Types
+
+#set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
+
+(** [betree_main::betree::{betree_main::betree::List<T>#1}::len]: decreases clause
+    Source: 'src/betree.rs', lines 276:4-276:24 *)
+unfold
+let betree_List_len_decreases (t : Type0) (self : betree_List_t t) : nat =
+  admit ()
+
+(** [betree_main::betree::{betree_main::betree::List<T>#1}::split_at]: decreases clause
+    Source: 'src/betree.rs', lines 284:4-284:51 *)
+unfold
+let betree_List_split_at_decreases (t : Type0) (self : betree_List_t t)
+  (n : u64) : nat =
+  admit ()
+
+(** [betree_main::betree::{betree_main::betree::List<(u64, T)>#2}::partition_at_pivot]: decreases clause
+    Source: 'src/betree.rs', lines 339:4-339:73 *)
+unfold
+let betree_ListTupleU64T_partition_at_pivot_decreases (t : Type0)
+  (self : betree_List_t (u64 & t)) (pivot : u64) : nat =
+  admit ()
+
+(** [betree_main::betree::{betree_main::betree::Node#5}::lookup_first_message_for_key]: decreases clause
+    Source: 'src/betree.rs', lines 789:4-792:34 *)
+unfold
+let betree_Node_lookup_first_message_for_key_decreases (key : u64)
+  (msgs : betree_List_t (u64 & betree_Message_t)) : nat =
+  admit ()
+
+(** [betree_main::betree::{betree_main::betree::Node#5}::lookup_in_bindings]: decreases clause
+    Source: 'src/betree.rs', lines 636:4-636:80 *)
+unfold
+let betree_Node_lookup_in_bindings_decreases (key : u64)
+  (bindings : betree_List_t (u64 & u64)) : nat =
+  admit ()
+
+(** [betree_main::betree::{betree_main::betree::Node#5}::apply_upserts]: decreases clause
+    Source: 'src/betree.rs', lines 819:4-819:90 *)
+unfold
+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::{betree_main::betree::Internal#4}::lookup_in_children]: decreases clause
+    Source: 'src/betree.rs', lines 395:4-395:63 *)
+unfold
+let betree_Internal_lookup_in_children_decreases (self : betree_Internal_t)
+  (key : u64) (st : state) : nat =
+  admit ()
+
+(** [betree_main::betree::{betree_main::betree::Node#5}::lookup]: decreases clause
+    Source: 'src/betree.rs', lines 709:4-709:58 *)
+unfold
+let betree_Node_lookup_decreases (self : betree_Node_t) (key : u64)
+  (st : state) : nat =
+  admit ()
+
+(** [betree_main::betree::{betree_main::betree::Node#5}::filter_messages_for_key]: decreases clause
+    Source: 'src/betree.rs', lines 674:4-674:77 *)
+unfold
+let betree_Node_filter_messages_for_key_decreases (key : u64)
+  (msgs : betree_List_t (u64 & betree_Message_t)) : nat =
+  admit ()
+
+(** [betree_main::betree::{betree_main::betree::Node#5}::lookup_first_message_after_key]: decreases clause
+    Source: 'src/betree.rs', lines 689:4-692:34 *)
+unfold
+let betree_Node_lookup_first_message_after_key_decreases (key : u64)
+  (msgs : betree_List_t (u64 & betree_Message_t)) : nat =
+  admit ()
+
+(** [betree_main::betree::{betree_main::betree::Node#5}::apply_messages_to_internal]: decreases clause
+    Source: 'src/betree.rs', lines 502:4-505:5 *)
+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 =
+  admit ()
+
+(** [betree_main::betree::{betree_main::betree::Node#5}::lookup_mut_in_bindings]: decreases clause
+    Source: 'src/betree.rs', lines 653:4-656:32 *)
+unfold
+let betree_Node_lookup_mut_in_bindings_decreases (key : u64)
+  (bindings : betree_List_t (u64 & u64)) : nat =
+  admit ()
+
+(** [betree_main::betree::{betree_main::betree::Node#5}::apply_messages_to_leaf]: decreases clause
+    Source: 'src/betree.rs', lines 444:4-447:5 *)
+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 =
+  admit ()
+
+(** [betree_main::betree::{betree_main::betree::Internal#4}::flush]: decreases clause
+    Source: 'src/betree.rs', lines 410:4-415:26 *)
+unfold
+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::{betree_main::betree::Node#5}::apply_messages]: decreases clause
+    Source: 'src/betree.rs', lines 588:4-593:5 *)
+unfold
+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-split/betree/BetreeMain.Clauses.fst b/tests/fstar-split/betree/BetreeMain.Clauses.fst
new file mode 100644
index 00000000..21f953d1
--- /dev/null
+++ b/tests/fstar-split/betree/BetreeMain.Clauses.fst
@@ -0,0 +1,210 @@
+(** [betree_main]: templates for the decreases clauses *)
+module BetreeMain.Clauses
+open Primitives
+open BetreeMain.Types
+
+#set-options "--z3rlimit 50 --fuel 0 --ifuel 1"
+
+(*** Well-founded relations *)
+
+(* We had a few issues when proving termination of the mutually recursive functions:
+ * - betree_Internal_flush
+ * - betree_Node_apply_messages
+ *
+ * The quantity which effectively decreases is:
+ *   (betree_size, messages_length)
+ *   where messages_length is 0 when there are no messages
+ *   (and where we use the lexicographic ordering, of course)
+ *
+ * However, the `%[...]` and `{:well-founded ...} notations are not available outside
+ * of `decrease` clauses.
+ * 
+ * We thus resorted to writing and proving correct a well-founded relation over
+ * pairs of natural numbers. The trick is that `<<` can be used outside of decrease
+ * clauses, and can be used to trigger SMT patterns.
+ *
+ * What follows is adapted from:
+ * https://www.fstar-lang.org/tutorial/book/part2/part2_well_founded.html
+ *
+ * Also, the following PR might make things easier:
+ * https://github.com/FStarLang/FStar/pull/2561
+ *)
+
+module P = FStar.Preorder
+module W = FStar.WellFounded
+module L = FStar.LexicographicOrdering
+
+let lt_nat (x y:nat) : Type = x < y == true
+let rec wf_lt_nat (x:nat)
+  : W.acc lt_nat x
+  = W.AccIntro (fun y _ -> wf_lt_nat y)
+
+// A type abbreviation for a pair of nats
+let nat_pair = (x:nat & nat)
+
+// Making a lexicographic ordering from a pair of nat ordering
+let lex_order_nat_pair  : P.relation nat_pair =
+  L.lex_t lt_nat (fun _ -> lt_nat)
+
+// The lex order on nat pairs is well-founded, using our general proof
+// of lexicographic composition of well-founded orders
+let lex_order_nat_pair_wf : W.well_founded lex_order_nat_pair =
+  L.lex_t_wf wf_lt_nat (fun _ -> wf_lt_nat)
+
+// A utility to introduce lt_nat
+let mk_lt_nat (x:nat) (y:nat { x < y }) : lt_nat x y =
+  let _ : equals (x < y) true = Refl in
+  ()
+    
+// A utility to make a lex ordering of nat pairs
+let mk_lex_order_nat_pair (xy0:nat_pair) 
+                          (xy1:nat_pair {
+                            let (|x0, y0|) = xy0 in
+                            let (|x1, y1|) = xy1 in
+                            x0 < x1 \/ (x0 == x1 /\ y0 < y1)
+                          }) : lex_order_nat_pair xy0 xy1 =
+  let (|x0, y0|) = xy0 in
+  let (|x1, y1|) = xy1 in
+  if x0 < x1 then L.Left_lex x0 x1 y0 y1 (mk_lt_nat x0 x1)
+  else L.Right_lex x0 y0 y1 (mk_lt_nat y0 y1)
+
+let rec coerce #a #r #x (p:W.acc #a r x) : Tot (W.acc r x) (decreases p) =
+  W.AccIntro (fun y r -> coerce (p.access_smaller y r))
+
+let coerce_wf #a #r (p: (x:a -> W.acc r x)) : x:a -> W.acc r x =
+  fun x -> coerce (p x)
+
+(* We need this axiom, which comes from the following discussion:
+ * https://github.com/FStarLang/FStar/issues/1916
+ * An issue here is that the `{well-founded ... }` notation
+ *)
+assume
+val axiom_well_founded (a : Type) (rel : a -> a -> Type0)
+  (rwf : W.well_founded #a rel) (x y : a) :
+  Lemma (requires (rel x y)) (ensures (x << y))
+
+(* This lemma has a pattern (which makes it work) *)
+let wf_nat_pair_lem (p0 p1 : nat_pair) :
+  Lemma
+  (requires (
+    let (|x0, y0|) = p0 in
+    let (|x1, y1|) = p1 in
+    x0 < x1 || (x0 = x1 && y0 < y1)))
+  (ensures (p0 << p1))
+  [SMTPat (p0 << p1)] =
+  let rel = lex_order_nat_pair in
+  let rel_wf = lex_order_nat_pair_wf in
+  let _ = mk_lex_order_nat_pair p0 p1 in
+  assert(rel p0 p1);
+  axiom_well_founded nat_pair rel rel_wf p0 p1
+
+(*** Decrease clauses *)
+/// "Standard" decrease clauses
+
+(** [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 =
+  self
+
+(** [betree_main::betree::List::{1}::split_at]: decreases clause *)
+unfold
+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_ListTupleU64T_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) =
+  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) =
+  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) =
+  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 =
+  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 =
+  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) =
+  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) =
+  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) =
+  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) =
+  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) =
+  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 =
+  match bt with
+  | 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.left + betree_size node.right
+
+let rec betree_List_len (#a : Type0) (ls : betree_List_t a) : nat =
+  match ls with
+  | 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_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_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-split/betree/BetreeMain.Funs.fst b/tests/fstar-split/betree/BetreeMain.Funs.fst
new file mode 100644
index 00000000..33133236
--- /dev/null
+++ b/tests/fstar-split/betree/BetreeMain.Funs.fst
@@ -0,0 +1,1006 @@
+(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
+(** [betree_main]: function definitions *)
+module BetreeMain.Funs
+open Primitives
+include BetreeMain.Types
+include BetreeMain.FunsExternal
+include BetreeMain.Clauses
+
+#set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
+
+(** [betree_main::betree::load_internal_node]: forward function
+    Source: 'src/betree.rs', lines 36:0-36:52 *)
+let betree_load_internal_node
+  (id : u64) (st : state) :
+  result (state & (betree_List_t (u64 & betree_Message_t)))
+  =
+  betree_utils_load_internal_node id st
+
+(** [betree_main::betree::store_internal_node]: forward function
+    Source: 'src/betree.rs', lines 41:0-41:60 *)
+let betree_store_internal_node
+  (id : u64) (content : betree_List_t (u64 & betree_Message_t)) (st : state) :
+  result (state & unit)
+  =
+  let* (st1, _) = betree_utils_store_internal_node id content st in
+  Return (st1, ())
+
+(** [betree_main::betree::load_leaf_node]: forward function
+    Source: 'src/betree.rs', lines 46:0-46:44 *)
+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
+    Source: 'src/betree.rs', lines 51:0-51:52 *)
+let betree_store_leaf_node
+  (id : u64) (content : betree_List_t (u64 & u64)) (st : state) :
+  result (state & unit)
+  =
+  let* (st1, _) = betree_utils_store_leaf_node id content st in
+  Return (st1, ())
+
+(** [betree_main::betree::fresh_node_id]: forward function
+    Source: 'src/betree.rs', lines 55:0-55:48 *)
+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
+    Source: 'src/betree.rs', lines 55:0-55:48 *)
+let betree_fresh_node_id_back (counter : u64) : result u64 =
+  u64_add counter 1
+
+(** [betree_main::betree::{betree_main::betree::NodeIdCounter}::new]: forward function
+    Source: 'src/betree.rs', lines 206:4-206:20 *)
+let betree_NodeIdCounter_new : result betree_NodeIdCounter_t =
+  Return { next_node_id = 0 }
+
+(** [betree_main::betree::{betree_main::betree::NodeIdCounter}::fresh_id]: forward function
+    Source: 'src/betree.rs', lines 210:4-210:36 *)
+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::{betree_main::betree::NodeIdCounter}::fresh_id]: backward function 0
+    Source: 'src/betree.rs', lines 210:4-210:36 *)
+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
+    Source: 'src/betree.rs', lines 234:0-234:70 *)
+let betree_upsert_update
+  (prev : option u64) (st : betree_UpsertFunState_t) : result u64 =
+  begin match prev with
+  | None ->
+    begin match st with
+    | Betree_UpsertFunState_Add v -> Return v
+    | Betree_UpsertFunState_Sub _ -> Return 0
+    end
+  | Some prev1 ->
+    begin match st with
+    | Betree_UpsertFunState_Add v ->
+      let* margin = u64_sub core_u64_max prev1 in
+      if margin >= v then u64_add prev1 v else Return core_u64_max
+    | Betree_UpsertFunState_Sub v ->
+      if prev1 >= v then u64_sub prev1 v else Return 0
+    end
+  end
+
+(** [betree_main::betree::{betree_main::betree::List<T>#1}::len]: forward function
+    Source: 'src/betree.rs', lines 276:4-276:24 *)
+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
+  | Betree_List_Cons _ tl -> let* i = betree_List_len t tl in u64_add 1 i
+  | Betree_List_Nil -> Return 0
+  end
+
+(** [betree_main::betree::{betree_main::betree::List<T>#1}::split_at]: forward function
+    Source: 'src/betree.rs', lines 284:4-284:51 *)
+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 (Betree_List_Nil, self)
+  else
+    begin match self with
+    | Betree_List_Cons hd tl ->
+      let* i = u64_sub n 1 in
+      let* p = betree_List_split_at t tl i in
+      let (ls0, ls1) = p in
+      Return (Betree_List_Cons hd ls0, ls1)
+    | Betree_List_Nil -> Fail Failure
+    end
+
+(** [betree_main::betree::{betree_main::betree::List<T>#1}::push_front]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ())
+    Source: 'src/betree.rs', lines 299:4-299:34 *)
+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
+  Return (Betree_List_Cons x tl)
+
+(** [betree_main::betree::{betree_main::betree::List<T>#1}::pop_front]: forward function
+    Source: 'src/betree.rs', lines 306:4-306:32 *)
+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
+  | Betree_List_Cons x _ -> Return x
+  | Betree_List_Nil -> Fail Failure
+  end
+
+(** [betree_main::betree::{betree_main::betree::List<T>#1}::pop_front]: backward function 0
+    Source: 'src/betree.rs', lines 306:4-306:32 *)
+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
+  | Betree_List_Cons _ tl -> Return tl
+  | Betree_List_Nil -> Fail Failure
+  end
+
+(** [betree_main::betree::{betree_main::betree::List<T>#1}::hd]: forward function
+    Source: 'src/betree.rs', lines 318:4-318:22 *)
+let betree_List_hd (t : Type0) (self : betree_List_t t) : result t =
+  begin match self with
+  | Betree_List_Cons hd _ -> Return hd
+  | Betree_List_Nil -> Fail Failure
+  end
+
+(** [betree_main::betree::{betree_main::betree::List<(u64, T)>#2}::head_has_key]: forward function
+    Source: 'src/betree.rs', lines 327:4-327:44 *)
+let betree_ListTupleU64T_head_has_key
+  (t : Type0) (self : betree_List_t (u64 & t)) (key : u64) : result bool =
+  begin match self with
+  | Betree_List_Cons hd _ -> let (i, _) = hd in Return (i = key)
+  | Betree_List_Nil -> Return false
+  end
+
+(** [betree_main::betree::{betree_main::betree::List<(u64, T)>#2}::partition_at_pivot]: forward function
+    Source: 'src/betree.rs', lines 339:4-339:73 *)
+let rec betree_ListTupleU64T_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_ListTupleU64T_partition_at_pivot_decreases t self pivot))
+  =
+  begin match self with
+  | Betree_List_Cons hd tl ->
+    let (i, x) = hd in
+    if i >= pivot
+    then Return (Betree_List_Nil, Betree_List_Cons (i, x) tl)
+    else
+      let* p = betree_ListTupleU64T_partition_at_pivot t tl pivot in
+      let (ls0, ls1) = p in
+      Return (Betree_List_Cons (i, x) ls0, ls1)
+  | Betree_List_Nil -> Return (Betree_List_Nil, Betree_List_Nil)
+  end
+
+(** [betree_main::betree::{betree_main::betree::Leaf#3}::split]: forward function
+    Source: 'src/betree.rs', lines 359:4-364:17 *)
+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)
+  =
+  let* p = betree_List_split_at (u64 & u64) content params.split_size in
+  let (content0, content1) = p in
+  let* p1 = betree_List_hd (u64 & u64) content1 in
+  let (pivot, _) = p1 in
+  let* id0 = betree_NodeIdCounter_fresh_id node_id_cnt in
+  let* node_id_cnt1 = betree_NodeIdCounter_fresh_id_back node_id_cnt in
+  let* id1 = betree_NodeIdCounter_fresh_id node_id_cnt1 in
+  let* (st1, _) = betree_store_leaf_node id0 content0 st in
+  let* (st2, _) = betree_store_leaf_node id1 content1 st1 in
+  let n = Betree_Node_Leaf { id = id0; size = params.split_size } in
+  let n1 = Betree_Node_Leaf { id = id1; size = params.split_size } in
+  Return (st2, { id = self.id; pivot = pivot; left = n; right = n1 })
+
+(** [betree_main::betree::{betree_main::betree::Leaf#3}::split]: backward function 2
+    Source: 'src/betree.rs', lines 359:4-364:17 *)
+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_NodeIdCounter_t
+  =
+  let* p = betree_List_split_at (u64 & u64) content params.split_size in
+  let (content0, content1) = p in
+  let* _ = betree_List_hd (u64 & u64) content1 in
+  let* id0 = betree_NodeIdCounter_fresh_id node_id_cnt in
+  let* node_id_cnt1 = betree_NodeIdCounter_fresh_id_back node_id_cnt in
+  let* id1 = betree_NodeIdCounter_fresh_id node_id_cnt1 in
+  let* (st1, _) = betree_store_leaf_node id0 content0 st in
+  let* _ = betree_store_leaf_node id1 content1 st1 in
+  betree_NodeIdCounter_fresh_id_back node_id_cnt1
+
+(** [betree_main::betree::{betree_main::betree::Node#5}::lookup_first_message_for_key]: forward function
+    Source: 'src/betree.rs', lines 789:4-792:34 *)
+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
+  | Betree_List_Cons x next_msgs ->
+    let (i, m) = x in
+    if i >= key
+    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::{betree_main::betree::Node#5}::lookup_first_message_for_key]: backward function 0
+    Source: 'src/betree.rs', lines 789:4-792:34 *)
+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
+  | Betree_List_Cons x next_msgs ->
+    let (i, m) = x in
+    if i >= key
+    then Return ret
+    else
+      let* next_msgs1 =
+        betree_Node_lookup_first_message_for_key_back key next_msgs ret in
+      Return (Betree_List_Cons (i, m) next_msgs1)
+  | Betree_List_Nil -> Return ret
+  end
+
+(** [betree_main::betree::{betree_main::betree::Node#5}::lookup_in_bindings]: forward function
+    Source: 'src/betree.rs', lines 636:4-636:80 *)
+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))
+  =
+  begin match bindings with
+  | Betree_List_Cons hd tl ->
+    let (i, i1) = hd in
+    if i = key
+    then Return (Some i1)
+    else if i > key then Return None else betree_Node_lookup_in_bindings key tl
+  | Betree_List_Nil -> Return None
+  end
+
+(** [betree_main::betree::{betree_main::betree::Node#5}::apply_upserts]: forward function
+    Source: 'src/betree.rs', lines 819:4-819:90 *)
+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))
+  =
+  let* b = betree_ListTupleU64T_head_has_key betree_Message_t msgs key in
+  if b
+  then
+    let* msg = betree_List_pop_front (u64 & betree_Message_t) msgs in
+    let (_, m) = msg in
+    begin match m with
+    | Betree_Message_Insert _ -> Fail Failure
+    | Betree_Message_Delete -> Fail Failure
+    | Betree_Message_Upsert s ->
+      let* v = betree_upsert_update prev s in
+      let* msgs1 = betree_List_pop_front_back (u64 & betree_Message_t) msgs in
+      betree_Node_apply_upserts msgs1 (Some v) key st
+    end
+  else
+    let* (st1, v) = core_option_Option_unwrap u64 prev st in
+    let* _ =
+      betree_List_push_front (u64 & betree_Message_t) msgs (key,
+        Betree_Message_Insert v) in
+    Return (st1, v)
+
+(** [betree_main::betree::{betree_main::betree::Node#5}::apply_upserts]: backward function 0
+    Source: 'src/betree.rs', lines 819:4-819:90 *)
+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))
+  =
+  let* b = betree_ListTupleU64T_head_has_key betree_Message_t msgs key in
+  if b
+  then
+    let* msg = betree_List_pop_front (u64 & betree_Message_t) msgs in
+    let (_, m) = msg in
+    begin match m with
+    | Betree_Message_Insert _ -> Fail Failure
+    | Betree_Message_Delete -> Fail Failure
+    | Betree_Message_Upsert s ->
+      let* v = betree_upsert_update prev s in
+      let* msgs1 = betree_List_pop_front_back (u64 & betree_Message_t) msgs in
+      betree_Node_apply_upserts_back msgs1 (Some v) key st
+    end
+  else
+    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::{betree_main::betree::Internal#4}::lookup_in_children]: forward function
+    Source: 'src/betree.rs', lines 395:4-395:63 *)
+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))
+  =
+  if key < self.pivot
+  then betree_Node_lookup self.left key st
+  else betree_Node_lookup self.right key st
+
+(** [betree_main::betree::{betree_main::betree::Internal#4}::lookup_in_children]: backward function 0
+    Source: 'src/betree.rs', lines 395:4-395:63 *)
+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.pivot
+  then
+    let* n = betree_Node_lookup_back self.left key st in
+    Return { self with left = n }
+  else
+    let* n = betree_Node_lookup_back self.right key st in
+    Return { self with right = n }
+
+(** [betree_main::betree::{betree_main::betree::Node#5}::lookup]: forward function
+    Source: 'src/betree.rs', lines 709:4-709:58 *)
+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))
+  =
+  begin match self with
+  | 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
+    | Betree_List_Cons p l ->
+      let (k, msg) = p in
+      if k <> key
+      then
+        let* (st2, o) = betree_Internal_lookup_in_children node key st1 in
+        let* _ =
+          betree_Node_lookup_first_message_for_key_back key msgs
+            (Betree_List_Cons (k, msg) l) in
+        Return (st2, o)
+      else
+        begin match msg with
+        | Betree_Message_Insert v ->
+          let* _ =
+            betree_Node_lookup_first_message_for_key_back key msgs
+              (Betree_List_Cons (k, Betree_Message_Insert v) l) in
+          Return (st1, Some v)
+        | Betree_Message_Delete ->
+          let* _ =
+            betree_Node_lookup_first_message_for_key_back key msgs
+              (Betree_List_Cons (k, Betree_Message_Delete) l) in
+          Return (st1, None)
+        | Betree_Message_Upsert ufs ->
+          let* (st2, v) = betree_Internal_lookup_in_children node key st1 in
+          let* (st3, v1) =
+            betree_Node_apply_upserts (Betree_List_Cons (k,
+              Betree_Message_Upsert ufs) l) v key st2 in
+          let* node1 = betree_Internal_lookup_in_children_back node key st1 in
+          let* pending1 =
+            betree_Node_apply_upserts_back (Betree_List_Cons (k,
+              Betree_Message_Upsert ufs) l) v key st2 in
+          let* msgs1 =
+            betree_Node_lookup_first_message_for_key_back key msgs pending1 in
+          let* (st4, _) = betree_store_internal_node node1.id msgs1 st3 in
+          Return (st4, Some v1)
+        end
+    | Betree_List_Nil ->
+      let* (st2, o) = betree_Internal_lookup_in_children node key st1 in
+      let* _ =
+        betree_Node_lookup_first_message_for_key_back key msgs Betree_List_Nil
+        in
+      Return (st2, o)
+    end
+  | Betree_Node_Leaf node ->
+    let* (st1, bindings) = betree_load_leaf_node node.id st in
+    let* o = betree_Node_lookup_in_bindings key bindings in
+    Return (st1, o)
+  end
+
+(** [betree_main::betree::{betree_main::betree::Node#5}::lookup]: backward function 0
+    Source: 'src/betree.rs', lines 709:4-709:58 *)
+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
+  | 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
+    | 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
+            (Betree_List_Cons (k, msg) l) in
+        let* node1 = betree_Internal_lookup_in_children_back node key st1 in
+        Return (Betree_Node_Internal node1)
+      else
+        begin match msg with
+        | Betree_Message_Insert v ->
+          let* _ =
+            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
+              (Betree_List_Cons (k, Betree_Message_Delete) l) in
+          Return (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 (Betree_List_Cons (k,
+              Betree_Message_Upsert ufs) l) v key st2 in
+          let* node1 = betree_Internal_lookup_in_children_back node key st1 in
+          let* pending1 =
+            betree_Node_apply_upserts_back (Betree_List_Cons (k,
+              Betree_Message_Upsert ufs) l) v key st2 in
+          let* msgs1 =
+            betree_Node_lookup_first_message_for_key_back key msgs pending1 in
+          let* _ = betree_store_internal_node node1.id msgs1 st3 in
+          Return (Betree_Node_Internal node1)
+        end
+    | Betree_List_Nil ->
+      let* _ =
+        betree_Node_lookup_first_message_for_key_back key msgs Betree_List_Nil
+        in
+      let* node1 = betree_Internal_lookup_in_children_back node key st1 in
+      Return (Betree_Node_Internal node1)
+    end
+  | 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::{betree_main::betree::Node#5}::filter_messages_for_key]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ())
+    Source: 'src/betree.rs', lines 674:4-674:77 *)
+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
+  | Betree_List_Cons p l ->
+    let (k, m) = p in
+    if k = key
+    then
+      let* msgs1 =
+        betree_List_pop_front_back (u64 & betree_Message_t) (Betree_List_Cons
+          (k, m) l) in
+      betree_Node_filter_messages_for_key key msgs1
+    else Return (Betree_List_Cons (k, m) l)
+  | Betree_List_Nil -> Return Betree_List_Nil
+  end
+
+(** [betree_main::betree::{betree_main::betree::Node#5}::lookup_first_message_after_key]: forward function
+    Source: 'src/betree.rs', lines 689:4-692:34 *)
+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
+  | Betree_List_Cons p next_msgs ->
+    let (k, m) = p in
+    if k = key
+    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::{betree_main::betree::Node#5}::lookup_first_message_after_key]: backward function 0
+    Source: 'src/betree.rs', lines 689:4-692:34 *)
+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
+  | Betree_List_Cons p next_msgs ->
+    let (k, m) = p in
+    if k = key
+    then
+      let* next_msgs1 =
+        betree_Node_lookup_first_message_after_key_back key next_msgs ret in
+      Return (Betree_List_Cons (k, m) next_msgs1)
+    else Return ret
+  | Betree_List_Nil -> Return ret
+  end
+
+(** [betree_main::betree::{betree_main::betree::Node#5}::apply_to_internal]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ())
+    Source: 'src/betree.rs', lines 521:4-521:89 *)
+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* msgs1 = betree_Node_lookup_first_message_for_key key msgs in
+  let* b = betree_ListTupleU64T_head_has_key betree_Message_t msgs1 key in
+  if b
+  then
+    begin match new_msg with
+    | Betree_Message_Insert i ->
+      let* msgs2 = betree_Node_filter_messages_for_key key msgs1 in
+      let* msgs3 =
+        betree_List_push_front (u64 & betree_Message_t) msgs2 (key,
+          Betree_Message_Insert i) in
+      betree_Node_lookup_first_message_for_key_back key msgs msgs3
+    | Betree_Message_Delete ->
+      let* msgs2 = betree_Node_filter_messages_for_key key msgs1 in
+      let* msgs3 =
+        betree_List_push_front (u64 & betree_Message_t) msgs2 (key,
+          Betree_Message_Delete) in
+      betree_Node_lookup_first_message_for_key_back key msgs msgs3
+    | Betree_Message_Upsert s ->
+      let* p = betree_List_hd (u64 & betree_Message_t) msgs1 in
+      let (_, m) = p in
+      begin match m with
+      | Betree_Message_Insert prev ->
+        let* v = betree_upsert_update (Some prev) s in
+        let* msgs2 = betree_List_pop_front_back (u64 & betree_Message_t) msgs1
+          in
+        let* msgs3 =
+          betree_List_push_front (u64 & betree_Message_t) msgs2 (key,
+            Betree_Message_Insert v) in
+        betree_Node_lookup_first_message_for_key_back key msgs msgs3
+      | Betree_Message_Delete ->
+        let* v = betree_upsert_update None s in
+        let* msgs2 = betree_List_pop_front_back (u64 & betree_Message_t) msgs1
+          in
+        let* msgs3 =
+          betree_List_push_front (u64 & betree_Message_t) msgs2 (key,
+            Betree_Message_Insert v) in
+        betree_Node_lookup_first_message_for_key_back key msgs msgs3
+      | Betree_Message_Upsert _ ->
+        let* msgs2 = betree_Node_lookup_first_message_after_key key msgs1 in
+        let* msgs3 =
+          betree_List_push_front (u64 & betree_Message_t) msgs2 (key,
+            Betree_Message_Upsert s) in
+        let* msgs4 =
+          betree_Node_lookup_first_message_after_key_back key msgs1 msgs3 in
+        betree_Node_lookup_first_message_for_key_back key msgs msgs4
+      end
+    end
+  else
+    let* msgs2 =
+      betree_List_push_front (u64 & betree_Message_t) msgs1 (key, new_msg) in
+    betree_Node_lookup_first_message_for_key_back key msgs msgs2
+
+(** [betree_main::betree::{betree_main::betree::Node#5}::apply_messages_to_internal]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ())
+    Source: 'src/betree.rs', lines 502:4-505:5 *)
+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
+  | Betree_List_Cons new_msg new_msgs_tl ->
+    let (i, m) = new_msg in
+    let* msgs1 = betree_Node_apply_to_internal msgs i m in
+    betree_Node_apply_messages_to_internal msgs1 new_msgs_tl
+  | Betree_List_Nil -> Return msgs
+  end
+
+(** [betree_main::betree::{betree_main::betree::Node#5}::lookup_mut_in_bindings]: forward function
+    Source: 'src/betree.rs', lines 653:4-656:32 *)
+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
+  | Betree_List_Cons hd tl ->
+    let (i, i1) = hd in
+    if i >= key
+    then Return (Betree_List_Cons (i, i1) tl)
+    else betree_Node_lookup_mut_in_bindings key tl
+  | Betree_List_Nil -> Return Betree_List_Nil
+  end
+
+(** [betree_main::betree::{betree_main::betree::Node#5}::lookup_mut_in_bindings]: backward function 0
+    Source: 'src/betree.rs', lines 653:4-656:32 *)
+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
+  | Betree_List_Cons hd tl ->
+    let (i, i1) = hd in
+    if i >= key
+    then Return ret
+    else
+      let* tl1 = betree_Node_lookup_mut_in_bindings_back key tl ret in
+      Return (Betree_List_Cons (i, i1) tl1)
+  | Betree_List_Nil -> Return ret
+  end
+
+(** [betree_main::betree::{betree_main::betree::Node#5}::apply_to_leaf]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ())
+    Source: 'src/betree.rs', lines 460:4-460:87 *)
+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* bindings1 = betree_Node_lookup_mut_in_bindings key bindings in
+  let* b = betree_ListTupleU64T_head_has_key u64 bindings1 key in
+  if b
+  then
+    let* hd = betree_List_pop_front (u64 & u64) bindings1 in
+    begin match new_msg with
+    | Betree_Message_Insert v ->
+      let* bindings2 = betree_List_pop_front_back (u64 & u64) bindings1 in
+      let* bindings3 = betree_List_push_front (u64 & u64) bindings2 (key, v) in
+      betree_Node_lookup_mut_in_bindings_back key bindings bindings3
+    | Betree_Message_Delete ->
+      let* bindings2 = betree_List_pop_front_back (u64 & u64) bindings1 in
+      betree_Node_lookup_mut_in_bindings_back key bindings bindings2
+    | Betree_Message_Upsert s ->
+      let (_, i) = hd in
+      let* v = betree_upsert_update (Some i) s in
+      let* bindings2 = betree_List_pop_front_back (u64 & u64) bindings1 in
+      let* bindings3 = betree_List_push_front (u64 & u64) bindings2 (key, v) in
+      betree_Node_lookup_mut_in_bindings_back key bindings bindings3
+    end
+  else
+    begin match new_msg with
+    | Betree_Message_Insert v ->
+      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 ->
+      betree_Node_lookup_mut_in_bindings_back key bindings bindings1
+    | Betree_Message_Upsert s ->
+      let* v = betree_upsert_update None s in
+      let* bindings2 = betree_List_push_front (u64 & u64) bindings1 (key, v) in
+      betree_Node_lookup_mut_in_bindings_back key bindings bindings2
+    end
+
+(** [betree_main::betree::{betree_main::betree::Node#5}::apply_messages_to_leaf]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ())
+    Source: 'src/betree.rs', lines 444:4-447:5 *)
+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
+  | Betree_List_Cons new_msg new_msgs_tl ->
+    let (i, m) = new_msg in
+    let* bindings1 = betree_Node_apply_to_leaf bindings i m in
+    betree_Node_apply_messages_to_leaf bindings1 new_msgs_tl
+  | Betree_List_Nil -> Return bindings
+  end
+
+(** [betree_main::betree::{betree_main::betree::Internal#4}::flush]: forward function
+    Source: 'src/betree.rs', lines 410:4-415:26 *)
+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))
+  =
+  let* p =
+    betree_ListTupleU64T_partition_at_pivot betree_Message_t content self.pivot
+    in
+  let (msgs_left, msgs_right) = p in
+  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 self.left params node_id_cnt msgs_left st in
+    let* (_, node_id_cnt1) =
+      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* (st2, _) =
+        betree_Node_apply_messages self.right params node_id_cnt1 msgs_right
+          st1 in
+      let* _ =
+        betree_Node_apply_messages_back self.right params node_id_cnt1
+          msgs_right st1 in
+      Return (st2, Betree_List_Nil)
+    else Return (st1, msgs_right)
+  else
+    let* (st1, _) =
+      betree_Node_apply_messages self.right params node_id_cnt msgs_right st in
+    let* _ =
+      betree_Node_apply_messages_back self.right params node_id_cnt msgs_right
+        st in
+    Return (st1, msgs_left)
+
+(** [betree_main::betree::{betree_main::betree::Internal#4}::flush]: backward function 0
+    Source: 'src/betree.rs', lines 410:4-415:26 *)
+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))
+  =
+  let* p =
+    betree_ListTupleU64T_partition_at_pivot betree_Message_t content self.pivot
+    in
+  let (msgs_left, msgs_right) = p in
+  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 self.left params node_id_cnt msgs_left st in
+    let* (n, node_id_cnt1) =
+      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* (n1, node_id_cnt2) =
+        betree_Node_apply_messages_back self.right params node_id_cnt1
+          msgs_right st1 in
+      Return ({ self with left = n; right = n1 }, node_id_cnt2)
+    else Return ({ self with left = n }, node_id_cnt1)
+  else
+    let* (n, node_id_cnt1) =
+      betree_Node_apply_messages_back self.right params node_id_cnt msgs_right
+        st in
+    Return ({ self with right = n }, node_id_cnt1)
+
+(** [betree_main::betree::{betree_main::betree::Node#5}::apply_messages]: forward function
+    Source: 'src/betree.rs', lines 588:4-593:5 *)
+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))
+  =
+  begin match self with
+  | Betree_Node_Internal node ->
+    let* (st1, content) = betree_load_internal_node node.id st in
+    let* content1 = betree_Node_apply_messages_to_internal content msgs in
+    let* num_msgs = betree_List_len (u64 & betree_Message_t) content1 in
+    if num_msgs >= params.min_flush_size
+    then
+      let* (st2, content2) =
+        betree_Internal_flush node params node_id_cnt content1 st1 in
+      let* (node1, _) =
+        betree_Internal_flush_back node params node_id_cnt content1 st1 in
+      let* (st3, _) = betree_store_internal_node node1.id content2 st2 in
+      Return (st3, ())
+    else
+      let* (st2, _) = betree_store_internal_node node.id content1 st1 in
+      Return (st2, ())
+  | Betree_Node_Leaf node ->
+    let* (st1, content) = betree_load_leaf_node node.id st in
+    let* content1 = betree_Node_apply_messages_to_leaf content msgs in
+    let* len = betree_List_len (u64 & u64) content1 in
+    let* i = u64_mul 2 params.split_size in
+    if len >= i
+    then
+      let* (st2, _) = betree_Leaf_split node content1 params node_id_cnt st1 in
+      let* (st3, _) = betree_store_leaf_node node.id Betree_List_Nil st2 in
+      Return (st3, ())
+    else
+      let* (st2, _) = betree_store_leaf_node node.id content1 st1 in
+      Return (st2, ())
+  end
+
+(** [betree_main::betree::{betree_main::betree::Node#5}::apply_messages]: backward function 0
+    Source: 'src/betree.rs', lines 588:4-593:5 *)
+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))
+  =
+  begin match self with
+  | Betree_Node_Internal node ->
+    let* (st1, content) = betree_load_internal_node node.id st in
+    let* content1 = betree_Node_apply_messages_to_internal content msgs in
+    let* num_msgs = betree_List_len (u64 & betree_Message_t) content1 in
+    if num_msgs >= params.min_flush_size
+    then
+      let* (st2, content2) =
+        betree_Internal_flush node params node_id_cnt content1 st1 in
+      let* (node1, node_id_cnt1) =
+        betree_Internal_flush_back node params node_id_cnt content1 st1 in
+      let* _ = betree_store_internal_node node1.id content2 st2 in
+      Return (Betree_Node_Internal node1, node_id_cnt1)
+    else
+      let* _ = betree_store_internal_node node.id content1 st1 in
+      Return (Betree_Node_Internal node, node_id_cnt)
+  | Betree_Node_Leaf node ->
+    let* (st1, content) = betree_load_leaf_node node.id st in
+    let* content1 = betree_Node_apply_messages_to_leaf content msgs in
+    let* len = betree_List_len (u64 & u64) content1 in
+    let* i = u64_mul 2 params.split_size in
+    if len >= i
+    then
+      let* (st2, new_node) =
+        betree_Leaf_split node content1 params node_id_cnt st1 in
+      let* _ = betree_store_leaf_node node.id Betree_List_Nil st2 in
+      let* node_id_cnt1 =
+        betree_Leaf_split_back node content1 params node_id_cnt st1 in
+      Return (Betree_Node_Internal new_node, node_id_cnt1)
+    else
+      let* _ = betree_store_leaf_node node.id content1 st1 in
+      Return (Betree_Node_Leaf { node with size = len }, node_id_cnt)
+  end
+
+(** [betree_main::betree::{betree_main::betree::Node#5}::apply]: forward function
+    Source: 'src/betree.rs', lines 576:4-582:5 *)
+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* (st1, _) =
+    betree_Node_apply_messages self params node_id_cnt (Betree_List_Cons (key,
+      new_msg) Betree_List_Nil) st in
+  let* _ =
+    betree_Node_apply_messages_back self params node_id_cnt (Betree_List_Cons
+      (key, new_msg) Betree_List_Nil) st in
+  Return (st1, ())
+
+(** [betree_main::betree::{betree_main::betree::Node#5}::apply]: backward function 0
+    Source: 'src/betree.rs', lines 576:4-582:5 *)
+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)
+  =
+  betree_Node_apply_messages_back self params node_id_cnt (Betree_List_Cons
+    (key, new_msg) Betree_List_Nil) st
+
+(** [betree_main::betree::{betree_main::betree::BeTree#6}::new]: forward function
+    Source: 'src/betree.rs', lines 849:4-849:60 *)
+let betree_BeTree_new
+  (min_flush_size : u64) (split_size : u64) (st : state) :
+  result (state & betree_BeTree_t)
+  =
+  let* node_id_cnt = betree_NodeIdCounter_new in
+  let* id = betree_NodeIdCounter_fresh_id node_id_cnt in
+  let* (st1, _) = betree_store_leaf_node id Betree_List_Nil st in
+  let* node_id_cnt1 = betree_NodeIdCounter_fresh_id_back node_id_cnt in
+  Return (st1,
+    {
+      params = { min_flush_size = min_flush_size; split_size = split_size };
+      node_id_cnt = node_id_cnt1;
+      root = (Betree_Node_Leaf { id = id; size = 0 })
+    })
+
+(** [betree_main::betree::{betree_main::betree::BeTree#6}::apply]: forward function
+    Source: 'src/betree.rs', lines 868:4-868:47 *)
+let betree_BeTree_apply
+  (self : betree_BeTree_t) (key : u64) (msg : betree_Message_t) (st : state) :
+  result (state & unit)
+  =
+  let* (st1, _) =
+    betree_Node_apply self.root self.params self.node_id_cnt key msg st in
+  let* _ =
+    betree_Node_apply_back self.root self.params self.node_id_cnt key msg st in
+  Return (st1, ())
+
+(** [betree_main::betree::{betree_main::betree::BeTree#6}::apply]: backward function 0
+    Source: 'src/betree.rs', lines 868:4-868:47 *)
+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.root self.params self.node_id_cnt key msg st in
+  Return { self with node_id_cnt = nic; root = n }
+
+(** [betree_main::betree::{betree_main::betree::BeTree#6}::insert]: forward function
+    Source: 'src/betree.rs', lines 874:4-874:52 *)
+let betree_BeTree_insert
+  (self : betree_BeTree_t) (key : u64) (value : u64) (st : state) :
+  result (state & unit)
+  =
+  let* (st1, _) = 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 (st1, ())
+
+(** [betree_main::betree::{betree_main::betree::BeTree#6}::insert]: backward function 0
+    Source: 'src/betree.rs', lines 874:4-874:52 *)
+let betree_BeTree_insert_back
+  (self : betree_BeTree_t) (key : u64) (value : u64) (st : state) :
+  result betree_BeTree_t
+  =
+  betree_BeTree_apply_back self key (Betree_Message_Insert value) st
+
+(** [betree_main::betree::{betree_main::betree::BeTree#6}::delete]: forward function
+    Source: 'src/betree.rs', lines 880:4-880:38 *)
+let betree_BeTree_delete
+  (self : betree_BeTree_t) (key : u64) (st : state) : result (state & unit) =
+  let* (st1, _) = betree_BeTree_apply self key Betree_Message_Delete st in
+  let* _ = betree_BeTree_apply_back self key Betree_Message_Delete st in
+  Return (st1, ())
+
+(** [betree_main::betree::{betree_main::betree::BeTree#6}::delete]: backward function 0
+    Source: 'src/betree.rs', lines 880:4-880:38 *)
+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_main::betree::BeTree#6}::upsert]: forward function
+    Source: 'src/betree.rs', lines 886:4-886:59 *)
+let betree_BeTree_upsert
+  (self : betree_BeTree_t) (key : u64) (upd : betree_UpsertFunState_t)
+  (st : state) :
+  result (state & unit)
+  =
+  let* (st1, _) = 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 (st1, ())
+
+(** [betree_main::betree::{betree_main::betree::BeTree#6}::upsert]: backward function 0
+    Source: 'src/betree.rs', lines 886:4-886:59 *)
+let betree_BeTree_upsert_back
+  (self : betree_BeTree_t) (key : u64) (upd : betree_UpsertFunState_t)
+  (st : state) :
+  result betree_BeTree_t
+  =
+  betree_BeTree_apply_back self key (Betree_Message_Upsert upd) st
+
+(** [betree_main::betree::{betree_main::betree::BeTree#6}::lookup]: forward function
+    Source: 'src/betree.rs', lines 895:4-895:62 *)
+let betree_BeTree_lookup
+  (self : betree_BeTree_t) (key : u64) (st : state) :
+  result (state & (option u64))
+  =
+  betree_Node_lookup self.root key st
+
+(** [betree_main::betree::{betree_main::betree::BeTree#6}::lookup]: backward function 0
+    Source: 'src/betree.rs', lines 895:4-895:62 *)
+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
+    Source: 'src/betree_main.rs', lines 5:0-5:9 *)
+let main : result unit =
+  Return ()
+
+(** Unit test for [betree_main::main] *)
+let _ = assert_norm (main = Return ())
+
diff --git a/tests/fstar-split/betree/BetreeMain.FunsExternal.fsti b/tests/fstar-split/betree/BetreeMain.FunsExternal.fsti
new file mode 100644
index 00000000..cd2f956f
--- /dev/null
+++ b/tests/fstar-split/betree/BetreeMain.FunsExternal.fsti
@@ -0,0 +1,35 @@
+(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
+(** [betree_main]: external function declarations *)
+module BetreeMain.FunsExternal
+open Primitives
+include BetreeMain.Types
+
+#set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
+
+(** [betree_main::betree_utils::load_internal_node]: forward function
+    Source: 'src/betree_utils.rs', lines 98:0-98:63 *)
+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
+    Source: 'src/betree_utils.rs', lines 115:0-115:71 *)
+val betree_utils_store_internal_node
+  :
+  u64 -> betree_List_t (u64 & betree_Message_t) -> state -> result (state &
+    unit)
+
+(** [betree_main::betree_utils::load_leaf_node]: forward function
+    Source: 'src/betree_utils.rs', lines 132:0-132:55 *)
+val betree_utils_load_leaf_node
+  : u64 -> state -> result (state & (betree_List_t (u64 & u64)))
+
+(** [betree_main::betree_utils::store_leaf_node]: forward function
+    Source: 'src/betree_utils.rs', lines 145:0-145:63 *)
+val betree_utils_store_leaf_node
+  : u64 -> betree_List_t (u64 & u64) -> state -> result (state & unit)
+
+(** [core::option::{core::option::Option<T>}::unwrap]: forward function
+    Source: '/rustc/d59363ad0b6391b7fc5bbb02c9ccf9300eef3753/library/core/src/option.rs', lines 932:4-932:34 *)
+val core_option_Option_unwrap
+  (t : Type0) : option t -> state -> result (state & t)
+
diff --git a/tests/fstar-split/betree/BetreeMain.Types.fst b/tests/fstar-split/betree/BetreeMain.Types.fst
new file mode 100644
index 00000000..b87219b2
--- /dev/null
+++ b/tests/fstar-split/betree/BetreeMain.Types.fst
@@ -0,0 +1,61 @@
+(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
+(** [betree_main]: type definitions *)
+module BetreeMain.Types
+open Primitives
+include BetreeMain.TypesExternal
+
+#set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
+
+(** [betree_main::betree::List]
+    Source: 'src/betree.rs', lines 17:0-17:23 *)
+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]
+    Source: 'src/betree.rs', lines 63:0-63:23 *)
+type betree_UpsertFunState_t =
+| Betree_UpsertFunState_Add : u64 -> betree_UpsertFunState_t
+| Betree_UpsertFunState_Sub : u64 -> betree_UpsertFunState_t
+
+(** [betree_main::betree::Message]
+    Source: 'src/betree.rs', lines 69:0-69:23 *)
+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]
+    Source: 'src/betree.rs', lines 167:0-167:11 *)
+type betree_Leaf_t = { id : u64; size : u64; }
+
+(** [betree_main::betree::Internal]
+    Source: 'src/betree.rs', lines 156:0-156:15 *)
+type betree_Internal_t =
+{
+  id : u64; pivot : u64; left : betree_Node_t; right : betree_Node_t;
+}
+
+(** [betree_main::betree::Node]
+    Source: 'src/betree.rs', lines 179:0-179:9 *)
+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]
+    Source: 'src/betree.rs', lines 187:0-187:13 *)
+type betree_Params_t = { min_flush_size : u64; split_size : u64; }
+
+(** [betree_main::betree::NodeIdCounter]
+    Source: 'src/betree.rs', lines 201:0-201:20 *)
+type betree_NodeIdCounter_t = { next_node_id : u64; }
+
+(** [betree_main::betree::BeTree]
+    Source: 'src/betree.rs', lines 218:0-218:17 *)
+type betree_BeTree_t =
+{
+  params : betree_Params_t;
+  node_id_cnt : betree_NodeIdCounter_t;
+  root : betree_Node_t;
+}
+
diff --git a/tests/fstar-split/betree/BetreeMain.TypesExternal.fsti b/tests/fstar-split/betree/BetreeMain.TypesExternal.fsti
new file mode 100644
index 00000000..1b2c53a6
--- /dev/null
+++ b/tests/fstar-split/betree/BetreeMain.TypesExternal.fsti
@@ -0,0 +1,10 @@
+(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
+(** [betree_main]: external type declarations *)
+module BetreeMain.TypesExternal
+open Primitives
+
+#set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
+
+(** The state type used in the state-error monad *)
+val state : Type0
+
diff --git a/tests/fstar-split/betree/Makefile b/tests/fstar-split/betree/Makefile
new file mode 100644
index 00000000..fa7d1f36
--- /dev/null
+++ b/tests/fstar-split/betree/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-split/betree/Primitives.fst b/tests/fstar-split/betree/Primitives.fst
new file mode 100644
index 00000000..a3ffbde4
--- /dev/null
+++ b/tests/fstar-split/betree/Primitives.fst
@@ -0,0 +1,884 @@
+/// 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
+
+assume val size_numbits : pos
+
+// TODO: we could use FStar.Int.int_t and FStar.UInt.int_t
+
+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_xor (#ty : scalar_ty)
+    (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
+  | Usize -> admit() // TODO
+  | I8 ->
+    // Encoding issues...
+    normalize_spec (FStar.Int.int_t 8);
+    normalize_spec (scalar I8);
+    FStar.Int.logxor #8 x y
+  | I16 ->
+    // Encoding issues...
+    normalize_spec (FStar.Int.int_t 16);
+    normalize_spec (scalar I16);
+    FStar.Int.logxor #16 x y
+  | I32 -> FStar.Int.logxor #32 x y
+  | I64 -> FStar.Int.logxor #64 x y
+  | I128 ->
+    // Encoding issues...
+    normalize_spec (FStar.Int.int_t 128);
+    normalize_spec (scalar I128);
+    FStar.Int.logxor #128 x y
+  | Isize -> admit() // TODO
+
+let scalar_or (#ty : scalar_ty)
+    (x : scalar ty) (y : scalar ty) : scalar ty =
+  match ty with
+  | U8 -> FStar.UInt.logor #8 x y
+  | U16 -> FStar.UInt.logor #16 x y
+  | U32 -> FStar.UInt.logor #32 x y
+  | U64 -> FStar.UInt.logor #64 x y
+  | U128 -> FStar.UInt.logor #128 x y
+  | Usize -> admit() // TODO
+  | I8 ->
+    // Encoding issues...
+    normalize_spec (FStar.Int.int_t 8);
+    normalize_spec (scalar I8);
+    FStar.Int.logor #8 x y
+  | I16 ->
+    // Encoding issues...
+    normalize_spec (FStar.Int.int_t 16);
+    normalize_spec (scalar I16);
+    FStar.Int.logor #16 x y
+  | I32 -> FStar.Int.logor #32 x y
+  | I64 -> FStar.Int.logor #64 x y
+  | I128 ->
+    // Encoding issues...
+    normalize_spec (FStar.Int.int_t 128);
+    normalize_spec (scalar I128);
+    FStar.Int.logor #128 x y
+  | Isize -> admit() // TODO
+
+let scalar_and (#ty : scalar_ty)
+    (x : scalar ty) (y : scalar ty) : scalar ty =
+  match ty with
+  | U8 -> FStar.UInt.logand #8 x y
+  | U16 -> FStar.UInt.logand #16 x y
+  | U32 -> FStar.UInt.logand #32 x y
+  | U64 -> FStar.UInt.logand #64 x y
+  | U128 -> FStar.UInt.logand #128 x y
+  | Usize -> admit() // TODO
+  | I8 ->
+    // Encoding issues...
+    normalize_spec (FStar.Int.int_t 8);
+    normalize_spec (scalar I8);
+    FStar.Int.logand #8 x y
+  | I16 ->
+    // Encoding issues...
+    normalize_spec (FStar.Int.int_t 16);
+    normalize_spec (scalar I16);
+    FStar.Int.logand #16 x y
+  | I32 -> FStar.Int.logand #32 x y
+  | I64 -> FStar.Int.logand #64 x y
+  | I128 ->
+    // Encoding issues...
+    normalize_spec (FStar.Int.int_t 128);
+    normalize_spec (scalar I128);
+    FStar.Int.logand #128 x y
+  | Isize -> admit() // TODO
+
+// Shift left
+let scalar_shl (#ty0 #ty1 : scalar_ty)
+    (x : scalar ty0) (y : scalar ty1) : result (scalar ty0) =
+  admit()
+
+// Shift right
+let scalar_shr (#ty0 #ty1 : scalar_ty)
+    (x : scalar ty0) (y : scalar ty1) : result (scalar ty0) =
+  admit()
+
+(** 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
+
+// This can't fail, but for now we make all casts faillible (easier for the translation)
+let scalar_cast_bool (tgt_ty : scalar_ty) (x : bool) : result (scalar tgt_ty) =
+  mk_scalar tgt_ty (if x then 1 else 0)
+
+/// 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
+
+/// Xor
+let u8_xor = scalar_xor #U8
+let u16_xor = scalar_xor #U16
+let u32_xor = scalar_xor #U32
+let u64_xor = scalar_xor #U64
+let u128_xor = scalar_xor #U128
+let usize_xor = scalar_xor #Usize
+let i8_xor = scalar_xor #I8
+let i16_xor = scalar_xor #I16
+let i32_xor = scalar_xor #I32
+let i64_xor = scalar_xor #I64
+let i128_xor = scalar_xor #I128
+let isize_xor = scalar_xor #Isize
+
+/// Or
+let u8_or = scalar_or #U8
+let u16_or = scalar_or #U16
+let u32_or = scalar_or #U32
+let u64_or = scalar_or #U64
+let u128_or = scalar_or #U128
+let usize_or = scalar_or #Usize
+let i8_or = scalar_or #I8
+let i16_or = scalar_or #I16
+let i32_or = scalar_or #I32
+let i64_or = scalar_or #I64
+let i128_or = scalar_or #I128
+let isize_or = scalar_or #Isize
+
+/// And
+let u8_and = scalar_and #U8
+let u16_and = scalar_and #U16
+let u32_and = scalar_and #U32
+let u64_and = scalar_and #U64
+let u128_and = scalar_and #U128
+let usize_and = scalar_and #Usize
+let i8_and = scalar_and #I8
+let i16_and = scalar_and #I16
+let i32_and = scalar_and #I32
+let i64_and = scalar_and #I64
+let i128_and = scalar_and #I128
+let isize_and = scalar_and #Isize
+
+/// Shift left
+let u8_shl #ty = scalar_shl #U8 #ty
+let u16_shl #ty = scalar_shl #U16 #ty
+let u32_shl #ty = scalar_shl #U32 #ty
+let u64_shl #ty = scalar_shl #U64 #ty
+let u128_shl #ty = scalar_shl #U128 #ty
+let usize_shl #ty = scalar_shl #Usize #ty
+let i8_shl #ty = scalar_shl #I8 #ty
+let i16_shl #ty = scalar_shl #I16 #ty
+let i32_shl #ty = scalar_shl #I32 #ty
+let i64_shl #ty = scalar_shl #I64 #ty
+let i128_shl #ty = scalar_shl #I128 #ty
+let isize_shl #ty = scalar_shl #Isize #ty
+
+/// Shift right
+let u8_shr #ty = scalar_shr #U8 #ty
+let u16_shr #ty = scalar_shr #U16 #ty
+let u32_shr #ty = scalar_shr #U32 #ty
+let u64_shr #ty = scalar_shr #U64 #ty
+let u128_shr #ty = scalar_shr #U128 #ty
+let usize_shr #ty = scalar_shr #Usize #ty
+let i8_shr #ty = scalar_shr #I8 #ty
+let i16_shr #ty = scalar_shr #I16 #ty
+let i32_shr #ty = scalar_shr #I32 #ty
+let i64_shr #ty = scalar_shr #I64 #ty
+let i128_shr #ty = scalar_shr #I128 #ty
+let isize_shr #ty = scalar_shr #Isize #ty
+
+(*** 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_RangeUsize_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_RangeUsize_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_RangeUsize_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_RangeUsize_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_RangeUsize_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_RangeUsize_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_RangeUsize_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_RangeUsize_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::private_slice_index::Range]
+let core_slice_index_private_slice_index_SealedRangeUsizeInst
+  : core_slice_index_private_slice_index_Sealed (core_ops_range_Range usize) = ()
+
+// Trait implementation: [core::slice::index::Range]
+let core_slice_index_SliceIndexRangeUsizeSliceTInst (t : Type0) :
+  core_slice_index_SliceIndex (core_ops_range_Range usize) (slice t) = {
+  sealedInst = core_slice_index_private_slice_index_SealedRangeUsizeInst;
+  output = slice t;
+  get = core_slice_index_RangeUsize_get t;
+  get_mut = core_slice_index_RangeUsize_get_mut t;
+  get_mut_back = core_slice_index_RangeUsize_get_mut_back t;
+  get_unchecked = core_slice_index_RangeUsize_get_unchecked t;
+  get_unchecked_mut = core_slice_index_RangeUsize_get_unchecked_mut t;
+  index = core_slice_index_RangeUsize_index t;
+  index_mut = core_slice_index_RangeUsize_index_mut t;
+  index_mut_back = core_slice_index_RangeUsize_index_mut_back t;
+}
+
+// Trait implementation: [core::slice::index::[T]]
+let core_ops_index_IndexSliceTIInst (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::[T]]
+let core_ops_index_IndexMutSliceTIInst (t idx : Type0)
+  (inst : core_slice_index_SliceIndex idx (slice t)) :
+  core_ops_index_IndexMut (slice t) idx = {
+  indexInst = core_ops_index_IndexSliceTIInst 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_ops_index_IndexArrayInst (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_ops_index_IndexMutArrayIInst (t idx : Type0) (n : usize)
+  (inst : core_ops_index_IndexMut (slice t) idx) :
+  core_ops_index_IndexMut (array t n) idx = {
+  indexInst = core_ops_index_IndexArrayInst 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_SealedUsizeInst
+  : core_slice_index_private_slice_index_Sealed usize = ()
+
+// Trait implementation: [core::slice::index::usize]
+let core_slice_index_SliceIndexUsizeSliceTInst (t : Type0) :
+  core_slice_index_SliceIndex usize (slice t) = {
+  sealedInst = core_slice_index_private_slice_index_SealedUsizeInst;
+  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_SliceIndexUsizeSliceTInst a) v i ==
+      alloc_vec_Vec_index_usize v i)
+  [SMTPat (alloc_vec_Vec_index a usize (core_slice_index_SliceIndexUsizeSliceTInst 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_SliceIndexUsizeSliceTInst a) v i ==
+      alloc_vec_Vec_index_usize v i)
+  [SMTPat (alloc_vec_Vec_index_mut a usize (core_slice_index_SliceIndexUsizeSliceTInst 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_SliceIndexUsizeSliceTInst a) v i x ==
+      alloc_vec_Vec_update_usize v i x)
+  [SMTPat (alloc_vec_Vec_index_mut_back a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i x)]
+  =
+  admit()
diff --git a/tests/fstar-split/hashmap/Hashmap.Clauses.Template.fst b/tests/fstar-split/hashmap/Hashmap.Clauses.Template.fst
new file mode 100644
index 00000000..2733b371
--- /dev/null
+++ b/tests/fstar-split/hashmap/Hashmap.Clauses.Template.fst
@@ -0,0 +1,71 @@
+(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
+(** [hashmap]: templates for the decreases clauses *)
+module Hashmap.Clauses.Template
+open Primitives
+open Hashmap.Types
+
+#set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
+
+(** [hashmap::{hashmap::HashMap<T>}::allocate_slots]: decreases clause
+    Source: 'src/hashmap.rs', lines 50:4-56:5 *)
+unfold
+let hashMap_allocate_slots_loop_decreases (t : Type0)
+  (slots : alloc_vec_Vec (list_t t)) (n : usize) : nat =
+  admit ()
+
+(** [hashmap::{hashmap::HashMap<T>}::clear]: decreases clause
+    Source: 'src/hashmap.rs', lines 80:4-88:5 *)
+unfold
+let hashMap_clear_loop_decreases (t : Type0) (slots : alloc_vec_Vec (list_t t))
+  (i : usize) : nat =
+  admit ()
+
+(** [hashmap::{hashmap::HashMap<T>}::insert_in_list]: decreases clause
+    Source: 'src/hashmap.rs', lines 97:4-114:5 *)
+unfold
+let hashMap_insert_in_list_loop_decreases (t : Type0) (key : usize) (value : t)
+  (ls : list_t t) : nat =
+  admit ()
+
+(** [hashmap::{hashmap::HashMap<T>}::move_elements_from_list]: decreases clause
+    Source: 'src/hashmap.rs', lines 183:4-196:5 *)
+unfold
+let hashMap_move_elements_from_list_loop_decreases (t : Type0)
+  (ntable : hashMap_t t) (ls : list_t t) : nat =
+  admit ()
+
+(** [hashmap::{hashmap::HashMap<T>}::move_elements]: decreases clause
+    Source: 'src/hashmap.rs', lines 171:4-180:5 *)
+unfold
+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::HashMap<T>}::contains_key_in_list]: decreases clause
+    Source: 'src/hashmap.rs', lines 206:4-219:5 *)
+unfold
+let hashMap_contains_key_in_list_loop_decreases (t : Type0) (key : usize)
+  (ls : list_t t) : nat =
+  admit ()
+
+(** [hashmap::{hashmap::HashMap<T>}::get_in_list]: decreases clause
+    Source: 'src/hashmap.rs', lines 224:4-237:5 *)
+unfold
+let hashMap_get_in_list_loop_decreases (t : Type0) (key : usize)
+  (ls : list_t t) : nat =
+  admit ()
+
+(** [hashmap::{hashmap::HashMap<T>}::get_mut_in_list]: decreases clause
+    Source: 'src/hashmap.rs', lines 245:4-254:5 *)
+unfold
+let hashMap_get_mut_in_list_loop_decreases (t : Type0) (ls : list_t t)
+  (key : usize) : nat =
+  admit ()
+
+(** [hashmap::{hashmap::HashMap<T>}::remove_from_list]: decreases clause
+    Source: 'src/hashmap.rs', lines 265:4-291:5 *)
+unfold
+let hashMap_remove_from_list_loop_decreases (t : Type0) (key : usize)
+  (ls : list_t t) : nat =
+  admit ()
+
diff --git a/tests/fstar-split/hashmap/Hashmap.Clauses.fst b/tests/fstar-split/hashmap/Hashmap.Clauses.fst
new file mode 100644
index 00000000..6c699d05
--- /dev/null
+++ b/tests/fstar-split/hashmap/Hashmap.Clauses.fst
@@ -0,0 +1,61 @@
+(** [hashmap]: the decreases clauses *)
+module Hashmap.Clauses
+open Primitives
+open FStar.List.Tot
+open Hashmap.Types
+
+#set-options "--z3rlimit 50 --fuel 0 --ifuel 1"
+
+(** [hashmap::HashMap::allocate_slots]: decreases clause *)
+unfold
+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 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 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 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 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 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 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 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 hashMap_remove_from_list_loop_decreases (t : Type0) (key : usize)
+  (ls : list_t t) : list_t t =
+  ls
+
diff --git a/tests/fstar-split/hashmap/Hashmap.Funs.fst b/tests/fstar-split/hashmap/Hashmap.Funs.fst
new file mode 100644
index 00000000..290d49ee
--- /dev/null
+++ b/tests/fstar-split/hashmap/Hashmap.Funs.fst
@@ -0,0 +1,529 @@
+(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
+(** [hashmap]: function definitions *)
+module Hashmap.Funs
+open Primitives
+include Hashmap.Types
+include Hashmap.Clauses
+
+#set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
+
+(** [hashmap::hash_key]: forward function
+    Source: 'src/hashmap.rs', lines 27:0-27:32 *)
+let hash_key (k : usize) : result usize =
+  Return k
+
+(** [hashmap::{hashmap::HashMap<T>}::allocate_slots]: loop 0: forward function
+    Source: 'src/hashmap.rs', lines 50:4-56:5 *)
+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* slots1 = alloc_vec_Vec_push (list_t t) slots List_Nil in
+    let* n1 = usize_sub n 1 in
+    hashMap_allocate_slots_loop t slots1 n1
+  else Return slots
+
+(** [hashmap::{hashmap::HashMap<T>}::allocate_slots]: forward function
+    Source: 'src/hashmap.rs', lines 50:4-50:76 *)
+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::HashMap<T>}::new_with_capacity]: forward function
+    Source: 'src/hashmap.rs', lines 59:4-63:13 *)
+let hashMap_new_with_capacity
+  (t : Type0) (capacity : usize) (max_load_dividend : usize)
+  (max_load_divisor : usize) :
+  result (hashMap_t t)
+  =
+  let* slots = hashMap_allocate_slots t (alloc_vec_Vec_new (list_t t)) capacity
+    in
+  let* i = usize_mul capacity max_load_dividend in
+  let* i1 = usize_div i max_load_divisor in
+  Return
+    {
+      num_entries = 0;
+      max_load_factor = (max_load_dividend, max_load_divisor);
+      max_load = i1;
+      slots = slots
+    }
+
+(** [hashmap::{hashmap::HashMap<T>}::new]: forward function
+    Source: 'src/hashmap.rs', lines 75:4-75:24 *)
+let hashMap_new (t : Type0) : result (hashMap_t t) =
+  hashMap_new_with_capacity t 32 4 5
+
+(** [hashmap::{hashmap::HashMap<T>}::clear]: loop 0: merged forward/backward function
+    (there is a single backward function, and the forward function returns ())
+    Source: 'src/hashmap.rs', lines 80:4-88:5 *)
+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 i1 = alloc_vec_Vec_len (list_t t) slots in
+  if i < i1
+  then
+    let* i2 = usize_add i 1 in
+    let* slots1 =
+      alloc_vec_Vec_index_mut_back (list_t t) usize
+        (core_slice_index_SliceIndexUsizeSliceTInst (list_t t)) slots i
+        List_Nil in
+    hashMap_clear_loop t slots1 i2
+  else Return slots
+
+(** [hashmap::{hashmap::HashMap<T>}::clear]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ())
+    Source: 'src/hashmap.rs', lines 80:4-80:27 *)
+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::HashMap<T>}::len]: forward function
+    Source: 'src/hashmap.rs', lines 90:4-90:30 *)
+let hashMap_len (t : Type0) (self : hashMap_t t) : result usize =
+  Return self.num_entries
+
+(** [hashmap::{hashmap::HashMap<T>}::insert_in_list]: loop 0: forward function
+    Source: 'src/hashmap.rs', lines 97:4-114:5 *)
+let rec hashMap_insert_in_list_loop
+  (t : Type0) (key : usize) (value : t) (ls : list_t t) :
+  Tot (result bool)
+  (decreases (hashMap_insert_in_list_loop_decreases t key value ls))
+  =
+  begin match ls with
+  | List_Cons ckey _ tl ->
+    if ckey = key
+    then Return false
+    else hashMap_insert_in_list_loop t key value tl
+  | List_Nil -> Return true
+  end
+
+(** [hashmap::{hashmap::HashMap<T>}::insert_in_list]: forward function
+    Source: 'src/hashmap.rs', lines 97:4-97:71 *)
+let hashMap_insert_in_list
+  (t : Type0) (key : usize) (value : t) (ls : list_t t) : result bool =
+  hashMap_insert_in_list_loop t key value ls
+
+(** [hashmap::{hashmap::HashMap<T>}::insert_in_list]: loop 0: backward function 0
+    Source: 'src/hashmap.rs', lines 97:4-114:5 *)
+let rec hashMap_insert_in_list_loop_back
+  (t : Type0) (key : usize) (value : t) (ls : list_t t) :
+  Tot (result (list_t t))
+  (decreases (hashMap_insert_in_list_loop_decreases t key value ls))
+  =
+  begin match ls with
+  | List_Cons ckey cvalue tl ->
+    if ckey = key
+    then Return (List_Cons ckey value tl)
+    else
+      let* tl1 = hashMap_insert_in_list_loop_back t key value tl in
+      Return (List_Cons ckey cvalue tl1)
+  | List_Nil -> Return (List_Cons key value List_Nil)
+  end
+
+(** [hashmap::{hashmap::HashMap<T>}::insert_in_list]: backward function 0
+    Source: 'src/hashmap.rs', lines 97:4-97:71 *)
+let hashMap_insert_in_list_back
+  (t : Type0) (key : usize) (value : t) (ls : list_t t) : result (list_t t) =
+  hashMap_insert_in_list_loop_back t key value ls
+
+(** [hashmap::{hashmap::HashMap<T>}::insert_no_resize]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ())
+    Source: 'src/hashmap.rs', lines 117:4-117:54 *)
+let hashMap_insert_no_resize
+  (t : Type0) (self : hashMap_t t) (key : usize) (value : t) :
+  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 =
+    alloc_vec_Vec_index_mut (list_t t) usize
+      (core_slice_index_SliceIndexUsizeSliceTInst (list_t t)) self.slots
+      hash_mod in
+  let* inserted = hashMap_insert_in_list t key value l in
+  if inserted
+  then
+    let* i1 = usize_add self.num_entries 1 in
+    let* l1 = 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_SliceIndexUsizeSliceTInst (list_t t)) self.slots
+        hash_mod l1 in
+    Return { self with num_entries = i1; slots = v }
+  else
+    let* l1 = 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_SliceIndexUsizeSliceTInst (list_t t)) self.slots
+        hash_mod l1 in
+    Return { self with slots = v }
+
+(** [hashmap::{hashmap::HashMap<T>}::move_elements_from_list]: loop 0: merged forward/backward function
+    (there is a single backward function, and the forward function returns ())
+    Source: 'src/hashmap.rs', lines 183:4-196:5 *)
+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
+  | List_Cons k v tl ->
+    let* ntable1 = hashMap_insert_no_resize t ntable k v in
+    hashMap_move_elements_from_list_loop t ntable1 tl
+  | List_Nil -> Return ntable
+  end
+
+(** [hashmap::{hashmap::HashMap<T>}::move_elements_from_list]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ())
+    Source: 'src/hashmap.rs', lines 183:4-183:72 *)
+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::HashMap<T>}::move_elements]: loop 0: merged forward/backward function
+    (there is a single backward function, and the forward function returns ())
+    Source: 'src/hashmap.rs', lines 171:4-180:5 *)
+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 i1 = alloc_vec_Vec_len (list_t t) slots in
+  if i < i1
+  then
+    let* l =
+      alloc_vec_Vec_index_mut (list_t t) usize
+        (core_slice_index_SliceIndexUsizeSliceTInst (list_t t)) slots i in
+    let ls = core_mem_replace (list_t t) l List_Nil in
+    let* ntable1 = hashMap_move_elements_from_list t ntable ls in
+    let* i2 = usize_add i 1 in
+    let l1 = core_mem_replace_back (list_t t) l List_Nil in
+    let* slots1 =
+      alloc_vec_Vec_index_mut_back (list_t t) usize
+        (core_slice_index_SliceIndexUsizeSliceTInst (list_t t)) slots i l1 in
+    hashMap_move_elements_loop t ntable1 slots1 i2
+  else Return (ntable, slots)
+
+(** [hashmap::{hashmap::HashMap<T>}::move_elements]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ())
+    Source: 'src/hashmap.rs', lines 171:4-171:95 *)
+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)))
+  =
+  hashMap_move_elements_loop t ntable slots i
+
+(** [hashmap::{hashmap::HashMap<T>}::try_resize]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ())
+    Source: 'src/hashmap.rs', lines 140:4-140:28 *)
+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, i1) = self.max_load_factor in
+  let* i2 = usize_div n1 i in
+  if capacity <= i2
+  then
+    let* i3 = usize_mul capacity 2 in
+    let* ntable = hashMap_new_with_capacity t i3 i i1 in
+    let* (ntable1, _) = hashMap_move_elements t ntable self.slots 0 in
+    Return
+      { ntable1 with num_entries = self.num_entries; max_load_factor = (i, i1)
+      }
+  else Return { self with max_load_factor = (i, i1) }
+
+(** [hashmap::{hashmap::HashMap<T>}::insert]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ())
+    Source: 'src/hashmap.rs', lines 129:4-129:48 *)
+let hashMap_insert
+  (t : Type0) (self : hashMap_t t) (key : usize) (value : t) :
+  result (hashMap_t t)
+  =
+  let* self1 = hashMap_insert_no_resize t self key value in
+  let* i = hashMap_len t self1 in
+  if i > self1.max_load then hashMap_try_resize t self1 else Return self1
+
+(** [hashmap::{hashmap::HashMap<T>}::contains_key_in_list]: loop 0: forward function
+    Source: 'src/hashmap.rs', lines 206:4-219:5 *)
+let rec hashMap_contains_key_in_list_loop
+  (t : Type0) (key : usize) (ls : list_t t) :
+  Tot (result bool)
+  (decreases (hashMap_contains_key_in_list_loop_decreases t key ls))
+  =
+  begin match ls with
+  | List_Cons ckey _ tl ->
+    if ckey = key
+    then Return true
+    else hashMap_contains_key_in_list_loop t key tl
+  | List_Nil -> Return false
+  end
+
+(** [hashmap::{hashmap::HashMap<T>}::contains_key_in_list]: forward function
+    Source: 'src/hashmap.rs', lines 206:4-206:68 *)
+let hashMap_contains_key_in_list
+  (t : Type0) (key : usize) (ls : list_t t) : result bool =
+  hashMap_contains_key_in_list_loop t key ls
+
+(** [hashmap::{hashmap::HashMap<T>}::contains_key]: forward function
+    Source: 'src/hashmap.rs', lines 199:4-199:49 *)
+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 =
+    alloc_vec_Vec_index (list_t t) usize
+      (core_slice_index_SliceIndexUsizeSliceTInst (list_t t)) self.slots
+      hash_mod in
+  hashMap_contains_key_in_list t key l
+
+(** [hashmap::{hashmap::HashMap<T>}::get_in_list]: loop 0: forward function
+    Source: 'src/hashmap.rs', lines 224:4-237:5 *)
+let rec hashMap_get_in_list_loop
+  (t : Type0) (key : usize) (ls : list_t t) :
+  Tot (result t) (decreases (hashMap_get_in_list_loop_decreases t key ls))
+  =
+  begin match ls with
+  | 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::HashMap<T>}::get_in_list]: forward function
+    Source: 'src/hashmap.rs', lines 224:4-224:70 *)
+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::HashMap<T>}::get]: forward function
+    Source: 'src/hashmap.rs', lines 239:4-239:55 *)
+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 =
+    alloc_vec_Vec_index (list_t t) usize
+      (core_slice_index_SliceIndexUsizeSliceTInst (list_t t)) self.slots
+      hash_mod in
+  hashMap_get_in_list t key l
+
+(** [hashmap::{hashmap::HashMap<T>}::get_mut_in_list]: loop 0: forward function
+    Source: 'src/hashmap.rs', lines 245:4-254:5 *)
+let rec hashMap_get_mut_in_list_loop
+  (t : Type0) (ls : list_t t) (key : usize) :
+  Tot (result t) (decreases (hashMap_get_mut_in_list_loop_decreases t ls key))
+  =
+  begin match ls with
+  | 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::HashMap<T>}::get_mut_in_list]: forward function
+    Source: 'src/hashmap.rs', lines 245:4-245:86 *)
+let hashMap_get_mut_in_list
+  (t : Type0) (ls : list_t t) (key : usize) : result t =
+  hashMap_get_mut_in_list_loop t ls key
+
+(** [hashmap::{hashmap::HashMap<T>}::get_mut_in_list]: loop 0: backward function 0
+    Source: 'src/hashmap.rs', lines 245:4-254:5 *)
+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 (hashMap_get_mut_in_list_loop_decreases t ls key))
+  =
+  begin match ls with
+  | List_Cons ckey cvalue tl ->
+    if ckey = key
+    then Return (List_Cons ckey ret tl)
+    else
+      let* tl1 = hashMap_get_mut_in_list_loop_back t tl key ret in
+      Return (List_Cons ckey cvalue tl1)
+  | List_Nil -> Fail Failure
+  end
+
+(** [hashmap::{hashmap::HashMap<T>}::get_mut_in_list]: backward function 0
+    Source: 'src/hashmap.rs', lines 245:4-245:86 *)
+let hashMap_get_mut_in_list_back
+  (t : Type0) (ls : list_t t) (key : usize) (ret : t) : result (list_t t) =
+  hashMap_get_mut_in_list_loop_back t ls key ret
+
+(** [hashmap::{hashmap::HashMap<T>}::get_mut]: forward function
+    Source: 'src/hashmap.rs', lines 257:4-257:67 *)
+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 =
+    alloc_vec_Vec_index_mut (list_t t) usize
+      (core_slice_index_SliceIndexUsizeSliceTInst (list_t t)) self.slots
+      hash_mod in
+  hashMap_get_mut_in_list t l key
+
+(** [hashmap::{hashmap::HashMap<T>}::get_mut]: backward function 0
+    Source: 'src/hashmap.rs', lines 257:4-257:67 *)
+let hashMap_get_mut_back
+  (t : Type0) (self : hashMap_t t) (key : usize) (ret : t) :
+  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 =
+    alloc_vec_Vec_index_mut (list_t t) usize
+      (core_slice_index_SliceIndexUsizeSliceTInst (list_t t)) self.slots
+      hash_mod in
+  let* l1 = 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_SliceIndexUsizeSliceTInst (list_t t)) self.slots
+      hash_mod l1 in
+  Return { self with slots = v }
+
+(** [hashmap::{hashmap::HashMap<T>}::remove_from_list]: loop 0: forward function
+    Source: 'src/hashmap.rs', lines 265:4-291:5 *)
+let rec hashMap_remove_from_list_loop
+  (t : Type0) (key : usize) (ls : list_t t) :
+  Tot (result (option t))
+  (decreases (hashMap_remove_from_list_loop_decreases t key ls))
+  =
+  begin match ls with
+  | List_Cons ckey x tl ->
+    if ckey = key
+    then
+      let mv_ls = core_mem_replace (list_t t) (List_Cons ckey x tl) List_Nil in
+      begin match mv_ls with
+      | List_Cons _ cvalue _ -> Return (Some cvalue)
+      | List_Nil -> Fail Failure
+      end
+    else hashMap_remove_from_list_loop t key tl
+  | List_Nil -> Return None
+  end
+
+(** [hashmap::{hashmap::HashMap<T>}::remove_from_list]: forward function
+    Source: 'src/hashmap.rs', lines 265:4-265:69 *)
+let hashMap_remove_from_list
+  (t : Type0) (key : usize) (ls : list_t t) : result (option t) =
+  hashMap_remove_from_list_loop t key ls
+
+(** [hashmap::{hashmap::HashMap<T>}::remove_from_list]: loop 0: backward function 1
+    Source: 'src/hashmap.rs', lines 265:4-291:5 *)
+let rec hashMap_remove_from_list_loop_back
+  (t : Type0) (key : usize) (ls : list_t t) :
+  Tot (result (list_t t))
+  (decreases (hashMap_remove_from_list_loop_decreases t key ls))
+  =
+  begin match ls with
+  | List_Cons ckey x tl ->
+    if ckey = key
+    then
+      let mv_ls = core_mem_replace (list_t t) (List_Cons ckey x tl) List_Nil in
+      begin match mv_ls with
+      | List_Cons _ _ tl1 -> Return tl1
+      | List_Nil -> Fail Failure
+      end
+    else
+      let* tl1 = hashMap_remove_from_list_loop_back t key tl in
+      Return (List_Cons ckey x tl1)
+  | List_Nil -> Return List_Nil
+  end
+
+(** [hashmap::{hashmap::HashMap<T>}::remove_from_list]: backward function 1
+    Source: 'src/hashmap.rs', lines 265:4-265:69 *)
+let hashMap_remove_from_list_back
+  (t : Type0) (key : usize) (ls : list_t t) : result (list_t t) =
+  hashMap_remove_from_list_loop_back t key ls
+
+(** [hashmap::{hashmap::HashMap<T>}::remove]: forward function
+    Source: 'src/hashmap.rs', lines 294:4-294:52 *)
+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 =
+    alloc_vec_Vec_index_mut (list_t t) usize
+      (core_slice_index_SliceIndexUsizeSliceTInst (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 x1 -> let* _ = usize_sub self.num_entries 1 in Return (Some x1)
+  end
+
+(** [hashmap::{hashmap::HashMap<T>}::remove]: backward function 0
+    Source: 'src/hashmap.rs', lines 294:4-294:52 *)
+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 =
+    alloc_vec_Vec_index_mut (list_t t) usize
+      (core_slice_index_SliceIndexUsizeSliceTInst (list_t t)) self.slots
+      hash_mod in
+  let* x = hashMap_remove_from_list t key l in
+  begin match x with
+  | None ->
+    let* l1 = hashMap_remove_from_list_back t key l in
+    let* v =
+      alloc_vec_Vec_index_mut_back (list_t t) usize
+        (core_slice_index_SliceIndexUsizeSliceTInst (list_t t)) self.slots
+        hash_mod l1 in
+    Return { self with slots = v }
+  | Some _ ->
+    let* i1 = usize_sub self.num_entries 1 in
+    let* l1 = hashMap_remove_from_list_back t key l in
+    let* v =
+      alloc_vec_Vec_index_mut_back (list_t t) usize
+        (core_slice_index_SliceIndexUsizeSliceTInst (list_t t)) self.slots
+        hash_mod l1 in
+    Return { self with num_entries = i1; slots = v }
+  end
+
+(** [hashmap::test1]: forward function
+    Source: 'src/hashmap.rs', lines 315:0-315:10 *)
+let test1 : result unit =
+  let* hm = hashMap_new u64 in
+  let* hm1 = hashMap_insert u64 hm 0 42 in
+  let* hm2 = hashMap_insert u64 hm1 128 18 in
+  let* hm3 = hashMap_insert u64 hm2 1024 138 in
+  let* hm4 = hashMap_insert u64 hm3 1056 256 in
+  let* i = hashMap_get u64 hm4 128 in
+  if not (i = 18)
+  then Fail Failure
+  else
+    let* hm5 = hashMap_get_mut_back u64 hm4 1024 56 in
+    let* i1 = hashMap_get u64 hm5 1024 in
+    if not (i1 = 56)
+    then Fail Failure
+    else
+      let* x = hashMap_remove u64 hm5 1024 in
+      begin match x with
+      | None -> Fail Failure
+      | Some x1 ->
+        if not (x1 = 56)
+        then Fail Failure
+        else
+          let* hm6 = hashMap_remove_back u64 hm5 1024 in
+          let* i2 = hashMap_get u64 hm6 0 in
+          if not (i2 = 42)
+          then Fail Failure
+          else
+            let* i3 = hashMap_get u64 hm6 128 in
+            if not (i3 = 18)
+            then Fail Failure
+            else
+              let* i4 = hashMap_get u64 hm6 1056 in
+              if not (i4 = 256) then Fail Failure else Return ()
+      end
+
diff --git a/tests/fstar/hashmap/Hashmap.Properties.fst b/tests/fstar-split/hashmap/Hashmap.Properties.fst
index def520f0..def520f0 100644
--- a/tests/fstar/hashmap/Hashmap.Properties.fst
+++ b/tests/fstar-split/hashmap/Hashmap.Properties.fst
diff --git a/tests/fstar/hashmap/Hashmap.Properties.fsti b/tests/fstar-split/hashmap/Hashmap.Properties.fsti
index 26c0ec06..26c0ec06 100644
--- a/tests/fstar/hashmap/Hashmap.Properties.fsti
+++ b/tests/fstar-split/hashmap/Hashmap.Properties.fsti
diff --git a/tests/fstar-split/hashmap/Hashmap.Types.fst b/tests/fstar-split/hashmap/Hashmap.Types.fst
new file mode 100644
index 00000000..ef96b1e9
--- /dev/null
+++ b/tests/fstar-split/hashmap/Hashmap.Types.fst
@@ -0,0 +1,23 @@
+(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
+(** [hashmap]: type definitions *)
+module Hashmap.Types
+open Primitives
+
+#set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
+
+(** [hashmap::List]
+    Source: 'src/hashmap.rs', lines 19:0-19:16 *)
+type list_t (t : Type0) =
+| List_Cons : usize -> t -> list_t t -> list_t t
+| List_Nil : list_t t
+
+(** [hashmap::HashMap]
+    Source: 'src/hashmap.rs', lines 35:0-35:21 *)
+type hashMap_t (t : Type0) =
+{
+  num_entries : usize;
+  max_load_factor : (usize & usize);
+  max_load : usize;
+  slots : alloc_vec_Vec (list_t t);
+}
+
diff --git a/tests/fstar-split/hashmap/Makefile b/tests/fstar-split/hashmap/Makefile
new file mode 100644
index 00000000..fa7d1f36
--- /dev/null
+++ b/tests/fstar-split/hashmap/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-split/hashmap/Primitives.fst b/tests/fstar-split/hashmap/Primitives.fst
new file mode 100644
index 00000000..a3ffbde4
--- /dev/null
+++ b/tests/fstar-split/hashmap/Primitives.fst
@@ -0,0 +1,884 @@
+/// 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
+
+assume val size_numbits : pos
+
+// TODO: we could use FStar.Int.int_t and FStar.UInt.int_t
+
+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_xor (#ty : scalar_ty)
+    (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
+  | Usize -> admit() // TODO
+  | I8 ->
+    // Encoding issues...
+    normalize_spec (FStar.Int.int_t 8);
+    normalize_spec (scalar I8);
+    FStar.Int.logxor #8 x y
+  | I16 ->
+    // Encoding issues...
+    normalize_spec (FStar.Int.int_t 16);
+    normalize_spec (scalar I16);
+    FStar.Int.logxor #16 x y
+  | I32 -> FStar.Int.logxor #32 x y
+  | I64 -> FStar.Int.logxor #64 x y
+  | I128 ->
+    // Encoding issues...
+    normalize_spec (FStar.Int.int_t 128);
+    normalize_spec (scalar I128);
+    FStar.Int.logxor #128 x y
+  | Isize -> admit() // TODO
+
+let scalar_or (#ty : scalar_ty)
+    (x : scalar ty) (y : scalar ty) : scalar ty =
+  match ty with
+  | U8 -> FStar.UInt.logor #8 x y
+  | U16 -> FStar.UInt.logor #16 x y
+  | U32 -> FStar.UInt.logor #32 x y
+  | U64 -> FStar.UInt.logor #64 x y
+  | U128 -> FStar.UInt.logor #128 x y
+  | Usize -> admit() // TODO
+  | I8 ->
+    // Encoding issues...
+    normalize_spec (FStar.Int.int_t 8);
+    normalize_spec (scalar I8);
+    FStar.Int.logor #8 x y
+  | I16 ->
+    // Encoding issues...
+    normalize_spec (FStar.Int.int_t 16);
+    normalize_spec (scalar I16);
+    FStar.Int.logor #16 x y
+  | I32 -> FStar.Int.logor #32 x y
+  | I64 -> FStar.Int.logor #64 x y
+  | I128 ->
+    // Encoding issues...
+    normalize_spec (FStar.Int.int_t 128);
+    normalize_spec (scalar I128);
+    FStar.Int.logor #128 x y
+  | Isize -> admit() // TODO
+
+let scalar_and (#ty : scalar_ty)
+    (x : scalar ty) (y : scalar ty) : scalar ty =
+  match ty with
+  | U8 -> FStar.UInt.logand #8 x y
+  | U16 -> FStar.UInt.logand #16 x y
+  | U32 -> FStar.UInt.logand #32 x y
+  | U64 -> FStar.UInt.logand #64 x y
+  | U128 -> FStar.UInt.logand #128 x y
+  | Usize -> admit() // TODO
+  | I8 ->
+    // Encoding issues...
+    normalize_spec (FStar.Int.int_t 8);
+    normalize_spec (scalar I8);
+    FStar.Int.logand #8 x y
+  | I16 ->
+    // Encoding issues...
+    normalize_spec (FStar.Int.int_t 16);
+    normalize_spec (scalar I16);
+    FStar.Int.logand #16 x y
+  | I32 -> FStar.Int.logand #32 x y
+  | I64 -> FStar.Int.logand #64 x y
+  | I128 ->
+    // Encoding issues...
+    normalize_spec (FStar.Int.int_t 128);
+    normalize_spec (scalar I128);
+    FStar.Int.logand #128 x y
+  | Isize -> admit() // TODO
+
+// Shift left
+let scalar_shl (#ty0 #ty1 : scalar_ty)
+    (x : scalar ty0) (y : scalar ty1) : result (scalar ty0) =
+  admit()
+
+// Shift right
+let scalar_shr (#ty0 #ty1 : scalar_ty)
+    (x : scalar ty0) (y : scalar ty1) : result (scalar ty0) =
+  admit()
+
+(** 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
+
+// This can't fail, but for now we make all casts faillible (easier for the translation)
+let scalar_cast_bool (tgt_ty : scalar_ty) (x : bool) : result (scalar tgt_ty) =
+  mk_scalar tgt_ty (if x then 1 else 0)
+
+/// 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
+
+/// Xor
+let u8_xor = scalar_xor #U8
+let u16_xor = scalar_xor #U16
+let u32_xor = scalar_xor #U32
+let u64_xor = scalar_xor #U64
+let u128_xor = scalar_xor #U128
+let usize_xor = scalar_xor #Usize
+let i8_xor = scalar_xor #I8
+let i16_xor = scalar_xor #I16
+let i32_xor = scalar_xor #I32
+let i64_xor = scalar_xor #I64
+let i128_xor = scalar_xor #I128
+let isize_xor = scalar_xor #Isize
+
+/// Or
+let u8_or = scalar_or #U8
+let u16_or = scalar_or #U16
+let u32_or = scalar_or #U32
+let u64_or = scalar_or #U64
+let u128_or = scalar_or #U128
+let usize_or = scalar_or #Usize
+let i8_or = scalar_or #I8
+let i16_or = scalar_or #I16
+let i32_or = scalar_or #I32
+let i64_or = scalar_or #I64
+let i128_or = scalar_or #I128
+let isize_or = scalar_or #Isize
+
+/// And
+let u8_and = scalar_and #U8
+let u16_and = scalar_and #U16
+let u32_and = scalar_and #U32
+let u64_and = scalar_and #U64
+let u128_and = scalar_and #U128
+let usize_and = scalar_and #Usize
+let i8_and = scalar_and #I8
+let i16_and = scalar_and #I16
+let i32_and = scalar_and #I32
+let i64_and = scalar_and #I64
+let i128_and = scalar_and #I128
+let isize_and = scalar_and #Isize
+
+/// Shift left
+let u8_shl #ty = scalar_shl #U8 #ty
+let u16_shl #ty = scalar_shl #U16 #ty
+let u32_shl #ty = scalar_shl #U32 #ty
+let u64_shl #ty = scalar_shl #U64 #ty
+let u128_shl #ty = scalar_shl #U128 #ty
+let usize_shl #ty = scalar_shl #Usize #ty
+let i8_shl #ty = scalar_shl #I8 #ty
+let i16_shl #ty = scalar_shl #I16 #ty
+let i32_shl #ty = scalar_shl #I32 #ty
+let i64_shl #ty = scalar_shl #I64 #ty
+let i128_shl #ty = scalar_shl #I128 #ty
+let isize_shl #ty = scalar_shl #Isize #ty
+
+/// Shift right
+let u8_shr #ty = scalar_shr #U8 #ty
+let u16_shr #ty = scalar_shr #U16 #ty
+let u32_shr #ty = scalar_shr #U32 #ty
+let u64_shr #ty = scalar_shr #U64 #ty
+let u128_shr #ty = scalar_shr #U128 #ty
+let usize_shr #ty = scalar_shr #Usize #ty
+let i8_shr #ty = scalar_shr #I8 #ty
+let i16_shr #ty = scalar_shr #I16 #ty
+let i32_shr #ty = scalar_shr #I32 #ty
+let i64_shr #ty = scalar_shr #I64 #ty
+let i128_shr #ty = scalar_shr #I128 #ty
+let isize_shr #ty = scalar_shr #Isize #ty
+
+(*** 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_RangeUsize_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_RangeUsize_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_RangeUsize_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_RangeUsize_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_RangeUsize_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_RangeUsize_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_RangeUsize_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_RangeUsize_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::private_slice_index::Range]
+let core_slice_index_private_slice_index_SealedRangeUsizeInst
+  : core_slice_index_private_slice_index_Sealed (core_ops_range_Range usize) = ()
+
+// Trait implementation: [core::slice::index::Range]
+let core_slice_index_SliceIndexRangeUsizeSliceTInst (t : Type0) :
+  core_slice_index_SliceIndex (core_ops_range_Range usize) (slice t) = {
+  sealedInst = core_slice_index_private_slice_index_SealedRangeUsizeInst;
+  output = slice t;
+  get = core_slice_index_RangeUsize_get t;
+  get_mut = core_slice_index_RangeUsize_get_mut t;
+  get_mut_back = core_slice_index_RangeUsize_get_mut_back t;
+  get_unchecked = core_slice_index_RangeUsize_get_unchecked t;
+  get_unchecked_mut = core_slice_index_RangeUsize_get_unchecked_mut t;
+  index = core_slice_index_RangeUsize_index t;
+  index_mut = core_slice_index_RangeUsize_index_mut t;
+  index_mut_back = core_slice_index_RangeUsize_index_mut_back t;
+}
+
+// Trait implementation: [core::slice::index::[T]]
+let core_ops_index_IndexSliceTIInst (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::[T]]
+let core_ops_index_IndexMutSliceTIInst (t idx : Type0)
+  (inst : core_slice_index_SliceIndex idx (slice t)) :
+  core_ops_index_IndexMut (slice t) idx = {
+  indexInst = core_ops_index_IndexSliceTIInst 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_ops_index_IndexArrayInst (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_ops_index_IndexMutArrayIInst (t idx : Type0) (n : usize)
+  (inst : core_ops_index_IndexMut (slice t) idx) :
+  core_ops_index_IndexMut (array t n) idx = {
+  indexInst = core_ops_index_IndexArrayInst 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_SealedUsizeInst
+  : core_slice_index_private_slice_index_Sealed usize = ()
+
+// Trait implementation: [core::slice::index::usize]
+let core_slice_index_SliceIndexUsizeSliceTInst (t : Type0) :
+  core_slice_index_SliceIndex usize (slice t) = {
+  sealedInst = core_slice_index_private_slice_index_SealedUsizeInst;
+  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_SliceIndexUsizeSliceTInst a) v i ==
+      alloc_vec_Vec_index_usize v i)
+  [SMTPat (alloc_vec_Vec_index a usize (core_slice_index_SliceIndexUsizeSliceTInst 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_SliceIndexUsizeSliceTInst a) v i ==
+      alloc_vec_Vec_index_usize v i)
+  [SMTPat (alloc_vec_Vec_index_mut a usize (core_slice_index_SliceIndexUsizeSliceTInst 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_SliceIndexUsizeSliceTInst a) v i x ==
+      alloc_vec_Vec_update_usize v i x)
+  [SMTPat (alloc_vec_Vec_index_mut_back a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i x)]
+  =
+  admit()
diff --git a/tests/fstar-split/hashmap_on_disk/HashmapMain.Clauses.Template.fst b/tests/fstar-split/hashmap_on_disk/HashmapMain.Clauses.Template.fst
new file mode 100644
index 00000000..7b274f59
--- /dev/null
+++ b/tests/fstar-split/hashmap_on_disk/HashmapMain.Clauses.Template.fst
@@ -0,0 +1,72 @@
+(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
+(** [hashmap_main]: templates for the decreases clauses *)
+module HashmapMain.Clauses.Template
+open Primitives
+open HashmapMain.Types
+
+#set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
+
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::allocate_slots]: decreases clause
+    Source: 'src/hashmap.rs', lines 50:4-56:5 *)
+unfold
+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_main::hashmap::HashMap<T>}::clear]: decreases clause
+    Source: 'src/hashmap.rs', lines 80:4-88:5 *)
+unfold
+let hashmap_HashMap_clear_loop_decreases (t : Type0)
+  (slots : alloc_vec_Vec (hashmap_List_t t)) (i : usize) : nat =
+  admit ()
+
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::insert_in_list]: decreases clause
+    Source: 'src/hashmap.rs', lines 97:4-114:5 *)
+unfold
+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_main::hashmap::HashMap<T>}::move_elements_from_list]: decreases clause
+    Source: 'src/hashmap.rs', lines 183:4-196:5 *)
+unfold
+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_main::hashmap::HashMap<T>}::move_elements]: decreases clause
+    Source: 'src/hashmap.rs', lines 171:4-180:5 *)
+unfold
+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_main::hashmap::HashMap<T>}::contains_key_in_list]: decreases clause
+    Source: 'src/hashmap.rs', lines 206:4-219:5 *)
+unfold
+let hashmap_HashMap_contains_key_in_list_loop_decreases (t : Type0)
+  (key : usize) (ls : hashmap_List_t t) : nat =
+  admit ()
+
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_in_list]: decreases clause
+    Source: 'src/hashmap.rs', lines 224:4-237:5 *)
+unfold
+let hashmap_HashMap_get_in_list_loop_decreases (t : Type0) (key : usize)
+  (ls : hashmap_List_t t) : nat =
+  admit ()
+
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_mut_in_list]: decreases clause
+    Source: 'src/hashmap.rs', lines 245:4-254:5 *)
+unfold
+let hashmap_HashMap_get_mut_in_list_loop_decreases (t : Type0)
+  (ls : hashmap_List_t t) (key : usize) : nat =
+  admit ()
+
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::remove_from_list]: decreases clause
+    Source: 'src/hashmap.rs', lines 265:4-291:5 *)
+unfold
+let hashmap_HashMap_remove_from_list_loop_decreases (t : Type0) (key : usize)
+  (ls : hashmap_List_t t) : nat =
+  admit ()
+
diff --git a/tests/fstar-split/hashmap_on_disk/HashmapMain.Clauses.fst b/tests/fstar-split/hashmap_on_disk/HashmapMain.Clauses.fst
new file mode 100644
index 00000000..be5a4ab1
--- /dev/null
+++ b/tests/fstar-split/hashmap_on_disk/HashmapMain.Clauses.fst
@@ -0,0 +1,61 @@
+(** [hashmap]: the decreases clauses *)
+module HashmapMain.Clauses
+open Primitives
+open FStar.List.Tot
+open HashmapMain.Types
+
+#set-options "--z3rlimit 50 --fuel 0 --ifuel 1"
+
+(** [hashmap::HashMap::allocate_slots]: decreases clause *)
+unfold
+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_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_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_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_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_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_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_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_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-split/hashmap_on_disk/HashmapMain.Funs.fst b/tests/fstar-split/hashmap_on_disk/HashmapMain.Funs.fst
new file mode 100644
index 00000000..2e2d54b8
--- /dev/null
+++ b/tests/fstar-split/hashmap_on_disk/HashmapMain.Funs.fst
@@ -0,0 +1,576 @@
+(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
+(** [hashmap_main]: function definitions *)
+module HashmapMain.Funs
+open Primitives
+include HashmapMain.Types
+include HashmapMain.FunsExternal
+include HashmapMain.Clauses
+
+#set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
+
+(** [hashmap_main::hashmap::hash_key]: forward function
+    Source: 'src/hashmap.rs', lines 27:0-27:32 *)
+let hashmap_hash_key (k : usize) : result usize =
+  Return k
+
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::allocate_slots]: loop 0: forward function
+    Source: 'src/hashmap.rs', lines 50:4-56:5 *)
+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* slots1 = alloc_vec_Vec_push (hashmap_List_t t) slots Hashmap_List_Nil
+      in
+    let* n1 = usize_sub n 1 in
+    hashmap_HashMap_allocate_slots_loop t slots1 n1
+  else Return slots
+
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::allocate_slots]: forward function
+    Source: 'src/hashmap.rs', lines 50:4-50:76 *)
+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_HashMap_allocate_slots_loop t slots n
+
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::new_with_capacity]: forward function
+    Source: 'src/hashmap.rs', lines 59:4-63:13 *)
+let hashmap_HashMap_new_with_capacity
+  (t : Type0) (capacity : usize) (max_load_dividend : usize)
+  (max_load_divisor : usize) :
+  result (hashmap_HashMap_t t)
+  =
+  let* slots =
+    hashmap_HashMap_allocate_slots t (alloc_vec_Vec_new (hashmap_List_t t))
+      capacity in
+  let* i = usize_mul capacity max_load_dividend in
+  let* i1 = usize_div i max_load_divisor in
+  Return
+    {
+      num_entries = 0;
+      max_load_factor = (max_load_dividend, max_load_divisor);
+      max_load = i1;
+      slots = slots
+    }
+
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::new]: forward function
+    Source: 'src/hashmap.rs', lines 75:4-75:24 *)
+let hashmap_HashMap_new (t : Type0) : result (hashmap_HashMap_t t) =
+  hashmap_HashMap_new_with_capacity t 32 4 5
+
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::clear]: loop 0: merged forward/backward function
+    (there is a single backward function, and the forward function returns ())
+    Source: 'src/hashmap.rs', lines 80:4-88:5 *)
+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 i1 = alloc_vec_Vec_len (hashmap_List_t t) slots in
+  if i < i1
+  then
+    let* i2 = usize_add i 1 in
+    let* slots1 =
+      alloc_vec_Vec_index_mut_back (hashmap_List_t t) usize
+        (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t t)) slots i
+        Hashmap_List_Nil in
+    hashmap_HashMap_clear_loop t slots1 i2
+  else Return slots
+
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::clear]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ())
+    Source: 'src/hashmap.rs', lines 80:4-80:27 *)
+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_main::hashmap::HashMap<T>}::len]: forward function
+    Source: 'src/hashmap.rs', lines 90:4-90:30 *)
+let hashmap_HashMap_len
+  (t : Type0) (self : hashmap_HashMap_t t) : result usize =
+  Return self.num_entries
+
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::insert_in_list]: loop 0: forward function
+    Source: 'src/hashmap.rs', lines 97:4-114:5 *)
+let rec hashmap_HashMap_insert_in_list_loop
+  (t : Type0) (key : usize) (value : t) (ls : hashmap_List_t t) :
+  Tot (result bool)
+  (decreases (hashmap_HashMap_insert_in_list_loop_decreases t key value ls))
+  =
+  begin match ls with
+  | Hashmap_List_Cons ckey _ tl ->
+    if ckey = key
+    then Return false
+    else hashmap_HashMap_insert_in_list_loop t key value tl
+  | Hashmap_List_Nil -> Return true
+  end
+
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::insert_in_list]: forward function
+    Source: 'src/hashmap.rs', lines 97:4-97:71 *)
+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_main::hashmap::HashMap<T>}::insert_in_list]: loop 0: backward function 0
+    Source: 'src/hashmap.rs', lines 97:4-114:5 *)
+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
+  | Hashmap_List_Cons ckey cvalue tl ->
+    if ckey = key
+    then Return (Hashmap_List_Cons ckey value tl)
+    else
+      let* tl1 = hashmap_HashMap_insert_in_list_loop_back t key value tl in
+      Return (Hashmap_List_Cons ckey cvalue tl1)
+  | Hashmap_List_Nil -> Return (Hashmap_List_Cons key value Hashmap_List_Nil)
+  end
+
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::insert_in_list]: backward function 0
+    Source: 'src/hashmap.rs', lines 97:4-97:71 *)
+let hashmap_HashMap_insert_in_list_back
+  (t : Type0) (key : usize) (value : t) (ls : hashmap_List_t t) :
+  result (hashmap_List_t t)
+  =
+  hashmap_HashMap_insert_in_list_loop_back t key value ls
+
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::insert_no_resize]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ())
+    Source: 'src/hashmap.rs', lines 117:4-117:54 *)
+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 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 =
+    alloc_vec_Vec_index_mut (hashmap_List_t t) usize
+      (core_slice_index_SliceIndexUsizeSliceTInst (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* i1 = usize_add self.num_entries 1 in
+    let* l1 = hashmap_HashMap_insert_in_list_back t key value l in
+    let* v =
+      alloc_vec_Vec_index_mut_back (hashmap_List_t t) usize
+        (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t t))
+        self.slots hash_mod l1 in
+    Return { self with num_entries = i1; slots = v }
+  else
+    let* l1 = hashmap_HashMap_insert_in_list_back t key value l in
+    let* v =
+      alloc_vec_Vec_index_mut_back (hashmap_List_t t) usize
+        (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t t))
+        self.slots hash_mod l1 in
+    Return { self with slots = v }
+
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::move_elements_from_list]: loop 0: merged forward/backward function
+    (there is a single backward function, and the forward function returns ())
+    Source: 'src/hashmap.rs', lines 183:4-196:5 *)
+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_HashMap_move_elements_from_list_loop_decreases t ntable ls))
+  =
+  begin match ls with
+  | Hashmap_List_Cons k v tl ->
+    let* ntable1 = hashmap_HashMap_insert_no_resize t ntable k v in
+    hashmap_HashMap_move_elements_from_list_loop t ntable1 tl
+  | Hashmap_List_Nil -> Return ntable
+  end
+
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::move_elements_from_list]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ())
+    Source: 'src/hashmap.rs', lines 183:4-183:72 *)
+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_HashMap_move_elements_from_list_loop t ntable ls
+
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::move_elements]: loop 0: merged forward/backward function
+    (there is a single backward function, and the forward function returns ())
+    Source: 'src/hashmap.rs', lines 171:4-180:5 *)
+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 i1 = alloc_vec_Vec_len (hashmap_List_t t) slots in
+  if i < i1
+  then
+    let* l =
+      alloc_vec_Vec_index_mut (hashmap_List_t t) usize
+        (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t t)) slots i
+      in
+    let ls = core_mem_replace (hashmap_List_t t) l Hashmap_List_Nil in
+    let* ntable1 = hashmap_HashMap_move_elements_from_list t ntable ls in
+    let* i2 = usize_add i 1 in
+    let l1 = core_mem_replace_back (hashmap_List_t t) l Hashmap_List_Nil in
+    let* slots1 =
+      alloc_vec_Vec_index_mut_back (hashmap_List_t t) usize
+        (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t t)) slots i
+        l1 in
+    hashmap_HashMap_move_elements_loop t ntable1 slots1 i2
+  else Return (ntable, slots)
+
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::move_elements]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ())
+    Source: 'src/hashmap.rs', lines 171:4-171:95 *)
+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_HashMap_move_elements_loop t ntable slots i
+
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::try_resize]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ())
+    Source: 'src/hashmap.rs', lines 140:4-140:28 *)
+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, i1) = self.max_load_factor in
+  let* i2 = usize_div n1 i in
+  if capacity <= i2
+  then
+    let* i3 = usize_mul capacity 2 in
+    let* ntable = hashmap_HashMap_new_with_capacity t i3 i i1 in
+    let* (ntable1, _) = hashmap_HashMap_move_elements t ntable self.slots 0 in
+    Return
+      { ntable1 with num_entries = self.num_entries; max_load_factor = (i, i1)
+      }
+  else Return { self with max_load_factor = (i, i1) }
+
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::insert]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ())
+    Source: 'src/hashmap.rs', lines 129:4-129:48 *)
+let hashmap_HashMap_insert
+  (t : Type0) (self : hashmap_HashMap_t t) (key : usize) (value : t) :
+  result (hashmap_HashMap_t t)
+  =
+  let* self1 = hashmap_HashMap_insert_no_resize t self key value in
+  let* i = hashmap_HashMap_len t self1 in
+  if i > self1.max_load
+  then hashmap_HashMap_try_resize t self1
+  else Return self1
+
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::contains_key_in_list]: loop 0: forward function
+    Source: 'src/hashmap.rs', lines 206:4-219:5 *)
+let rec hashmap_HashMap_contains_key_in_list_loop
+  (t : Type0) (key : usize) (ls : hashmap_List_t t) :
+  Tot (result bool)
+  (decreases (hashmap_HashMap_contains_key_in_list_loop_decreases t key ls))
+  =
+  begin match ls with
+  | Hashmap_List_Cons ckey _ tl ->
+    if ckey = key
+    then Return true
+    else hashmap_HashMap_contains_key_in_list_loop t key tl
+  | Hashmap_List_Nil -> Return false
+  end
+
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::contains_key_in_list]: forward function
+    Source: 'src/hashmap.rs', lines 206:4-206:68 *)
+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_main::hashmap::HashMap<T>}::contains_key]: forward function
+    Source: 'src/hashmap.rs', lines 199:4-199:49 *)
+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 =
+    alloc_vec_Vec_index (hashmap_List_t t) usize
+      (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t t))
+      self.slots hash_mod in
+  hashmap_HashMap_contains_key_in_list t key l
+
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_in_list]: loop 0: forward function
+    Source: 'src/hashmap.rs', lines 224:4-237:5 *)
+let rec hashmap_HashMap_get_in_list_loop
+  (t : Type0) (key : usize) (ls : hashmap_List_t t) :
+  Tot (result t)
+  (decreases (hashmap_HashMap_get_in_list_loop_decreases t key ls))
+  =
+  begin match ls with
+  | Hashmap_List_Cons ckey cvalue tl ->
+    if ckey = key
+    then Return cvalue
+    else hashmap_HashMap_get_in_list_loop t key tl
+  | Hashmap_List_Nil -> Fail Failure
+  end
+
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_in_list]: forward function
+    Source: 'src/hashmap.rs', lines 224:4-224:70 *)
+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_main::hashmap::HashMap<T>}::get]: forward function
+    Source: 'src/hashmap.rs', lines 239:4-239:55 *)
+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 =
+    alloc_vec_Vec_index (hashmap_List_t t) usize
+      (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t t))
+      self.slots hash_mod in
+  hashmap_HashMap_get_in_list t key l
+
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_mut_in_list]: loop 0: forward function
+    Source: 'src/hashmap.rs', lines 245:4-254:5 *)
+let rec hashmap_HashMap_get_mut_in_list_loop
+  (t : Type0) (ls : hashmap_List_t t) (key : usize) :
+  Tot (result t)
+  (decreases (hashmap_HashMap_get_mut_in_list_loop_decreases t ls key))
+  =
+  begin match ls with
+  | Hashmap_List_Cons ckey cvalue tl ->
+    if ckey = key
+    then Return cvalue
+    else hashmap_HashMap_get_mut_in_list_loop t tl key
+  | Hashmap_List_Nil -> Fail Failure
+  end
+
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_mut_in_list]: forward function
+    Source: 'src/hashmap.rs', lines 245:4-245:86 *)
+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_main::hashmap::HashMap<T>}::get_mut_in_list]: loop 0: backward function 0
+    Source: 'src/hashmap.rs', lines 245:4-254:5 *)
+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
+  | Hashmap_List_Cons ckey cvalue tl ->
+    if ckey = key
+    then Return (Hashmap_List_Cons ckey ret tl)
+    else
+      let* tl1 = hashmap_HashMap_get_mut_in_list_loop_back t tl key ret in
+      Return (Hashmap_List_Cons ckey cvalue tl1)
+  | Hashmap_List_Nil -> Fail Failure
+  end
+
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_mut_in_list]: backward function 0
+    Source: 'src/hashmap.rs', lines 245:4-245:86 *)
+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_HashMap_get_mut_in_list_loop_back t ls key ret
+
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_mut]: forward function
+    Source: 'src/hashmap.rs', lines 257:4-257:67 *)
+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 =
+    alloc_vec_Vec_index_mut (hashmap_List_t t) usize
+      (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t t))
+      self.slots hash_mod in
+  hashmap_HashMap_get_mut_in_list t l key
+
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_mut]: backward function 0
+    Source: 'src/hashmap.rs', lines 257:4-257:67 *)
+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 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 =
+    alloc_vec_Vec_index_mut (hashmap_List_t t) usize
+      (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t t))
+      self.slots hash_mod in
+  let* l1 = hashmap_HashMap_get_mut_in_list_back t l key ret in
+  let* v =
+    alloc_vec_Vec_index_mut_back (hashmap_List_t t) usize
+      (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t t))
+      self.slots hash_mod l1 in
+  Return { self with slots = v }
+
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::remove_from_list]: loop 0: forward function
+    Source: 'src/hashmap.rs', lines 265:4-291:5 *)
+let rec hashmap_HashMap_remove_from_list_loop
+  (t : Type0) (key : usize) (ls : hashmap_List_t t) :
+  Tot (result (option t))
+  (decreases (hashmap_HashMap_remove_from_list_loop_decreases t key ls))
+  =
+  begin match ls with
+  | Hashmap_List_Cons ckey x tl ->
+    if ckey = key
+    then
+      let mv_ls =
+        core_mem_replace (hashmap_List_t t) (Hashmap_List_Cons ckey x tl)
+          Hashmap_List_Nil in
+      begin match mv_ls with
+      | Hashmap_List_Cons _ cvalue _ -> Return (Some cvalue)
+      | Hashmap_List_Nil -> Fail Failure
+      end
+    else hashmap_HashMap_remove_from_list_loop t key tl
+  | Hashmap_List_Nil -> Return None
+  end
+
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::remove_from_list]: forward function
+    Source: 'src/hashmap.rs', lines 265:4-265:69 *)
+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_main::hashmap::HashMap<T>}::remove_from_list]: loop 0: backward function 1
+    Source: 'src/hashmap.rs', lines 265:4-291:5 *)
+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
+  | Hashmap_List_Cons ckey x tl ->
+    if ckey = key
+    then
+      let mv_ls =
+        core_mem_replace (hashmap_List_t t) (Hashmap_List_Cons ckey x tl)
+          Hashmap_List_Nil in
+      begin match mv_ls with
+      | Hashmap_List_Cons _ _ tl1 -> Return tl1
+      | Hashmap_List_Nil -> Fail Failure
+      end
+    else
+      let* tl1 = hashmap_HashMap_remove_from_list_loop_back t key tl in
+      Return (Hashmap_List_Cons ckey x tl1)
+  | Hashmap_List_Nil -> Return Hashmap_List_Nil
+  end
+
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::remove_from_list]: backward function 1
+    Source: 'src/hashmap.rs', lines 265:4-265:69 *)
+let hashmap_HashMap_remove_from_list_back
+  (t : Type0) (key : usize) (ls : hashmap_List_t t) :
+  result (hashmap_List_t t)
+  =
+  hashmap_HashMap_remove_from_list_loop_back t key ls
+
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::remove]: forward function
+    Source: 'src/hashmap.rs', lines 294:4-294:52 *)
+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 =
+    alloc_vec_Vec_index_mut (hashmap_List_t t) usize
+      (core_slice_index_SliceIndexUsizeSliceTInst (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 x1 -> let* _ = usize_sub self.num_entries 1 in Return (Some x1)
+  end
+
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::remove]: backward function 0
+    Source: 'src/hashmap.rs', lines 294:4-294:52 *)
+let hashmap_HashMap_remove_back
+  (t : Type0) (self : hashmap_HashMap_t t) (key : usize) :
+  result (hashmap_HashMap_t 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 =
+    alloc_vec_Vec_index_mut (hashmap_List_t t) usize
+      (core_slice_index_SliceIndexUsizeSliceTInst (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* l1 = hashmap_HashMap_remove_from_list_back t key l in
+    let* v =
+      alloc_vec_Vec_index_mut_back (hashmap_List_t t) usize
+        (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t t))
+        self.slots hash_mod l1 in
+    Return { self with slots = v }
+  | Some _ ->
+    let* i1 = usize_sub self.num_entries 1 in
+    let* l1 = hashmap_HashMap_remove_from_list_back t key l in
+    let* v =
+      alloc_vec_Vec_index_mut_back (hashmap_List_t t) usize
+        (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t t))
+        self.slots hash_mod l1 in
+    Return { self with num_entries = i1; slots = v }
+  end
+
+(** [hashmap_main::hashmap::test1]: forward function
+    Source: 'src/hashmap.rs', lines 315:0-315:10 *)
+let hashmap_test1 : result unit =
+  let* hm = hashmap_HashMap_new u64 in
+  let* hm1 = hashmap_HashMap_insert u64 hm 0 42 in
+  let* hm2 = hashmap_HashMap_insert u64 hm1 128 18 in
+  let* hm3 = hashmap_HashMap_insert u64 hm2 1024 138 in
+  let* hm4 = hashmap_HashMap_insert u64 hm3 1056 256 in
+  let* i = hashmap_HashMap_get u64 hm4 128 in
+  if not (i = 18)
+  then Fail Failure
+  else
+    let* hm5 = hashmap_HashMap_get_mut_back u64 hm4 1024 56 in
+    let* i1 = hashmap_HashMap_get u64 hm5 1024 in
+    if not (i1 = 56)
+    then Fail Failure
+    else
+      let* x = hashmap_HashMap_remove u64 hm5 1024 in
+      begin match x with
+      | None -> Fail Failure
+      | Some x1 ->
+        if not (x1 = 56)
+        then Fail Failure
+        else
+          let* hm6 = hashmap_HashMap_remove_back u64 hm5 1024 in
+          let* i2 = hashmap_HashMap_get u64 hm6 0 in
+          if not (i2 = 42)
+          then Fail Failure
+          else
+            let* i3 = hashmap_HashMap_get u64 hm6 128 in
+            if not (i3 = 18)
+            then Fail Failure
+            else
+              let* i4 = hashmap_HashMap_get u64 hm6 1056 in
+              if not (i4 = 256) then Fail Failure else Return ()
+      end
+
+(** [hashmap_main::insert_on_disk]: forward function
+    Source: 'src/hashmap_main.rs', lines 7:0-7:43 *)
+let insert_on_disk
+  (key : usize) (value : u64) (st : state) : result (state & unit) =
+  let* (st1, hm) = hashmap_utils_deserialize st in
+  let* hm1 = hashmap_HashMap_insert u64 hm key value in
+  let* (st2, _) = hashmap_utils_serialize hm1 st1 in
+  Return (st2, ())
+
+(** [hashmap_main::main]: forward function
+    Source: 'src/hashmap_main.rs', lines 16:0-16:13 *)
+let main : result unit =
+  Return ()
+
diff --git a/tests/fstar-split/hashmap_on_disk/HashmapMain.FunsExternal.fsti b/tests/fstar-split/hashmap_on_disk/HashmapMain.FunsExternal.fsti
new file mode 100644
index 00000000..b00bbcde
--- /dev/null
+++ b/tests/fstar-split/hashmap_on_disk/HashmapMain.FunsExternal.fsti
@@ -0,0 +1,18 @@
+(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
+(** [hashmap_main]: external function declarations *)
+module HashmapMain.FunsExternal
+open Primitives
+include HashmapMain.Types
+
+#set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
+
+(** [hashmap_main::hashmap_utils::deserialize]: forward function
+    Source: 'src/hashmap_utils.rs', lines 10:0-10:43 *)
+val hashmap_utils_deserialize
+  : state -> result (state & (hashmap_HashMap_t u64))
+
+(** [hashmap_main::hashmap_utils::serialize]: forward function
+    Source: 'src/hashmap_utils.rs', lines 5:0-5:42 *)
+val hashmap_utils_serialize
+  : hashmap_HashMap_t u64 -> state -> result (state & unit)
+
diff --git a/tests/fstar-split/hashmap_on_disk/HashmapMain.Properties.fst b/tests/fstar-split/hashmap_on_disk/HashmapMain.Properties.fst
new file mode 100644
index 00000000..358df29e
--- /dev/null
+++ b/tests/fstar-split/hashmap_on_disk/HashmapMain.Properties.fst
@@ -0,0 +1,48 @@
+(** Properties about the hashmap written on disk *)
+module HashmapMain.Properties
+open Primitives
+open HashmapMain.Funs
+
+#set-options "--z3rlimit 50 --fuel 0 --ifuel 1"
+
+/// Below, we focus on the functions to read from disk/write to disk to showcase
+/// how such reasoning which mixes opaque functions together with a state-error
+/// monad can be performed.
+
+(*** Hypotheses *)
+
+/// [state_v] gives us the hash map currently stored on disk
+assume
+val state_v : state -> hashmap_HashMap_t u64
+
+/// [serialize] updates the hash map stored on disk
+assume
+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 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 st with
+  | Fail _ -> True
+  | Return (st', hm) -> hm == state_v st /\ st' == 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_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_HashMap_insert u64 hm key value with
+    | Fail _ -> False
+    | Return hm' -> hm' == state_v st')
+
+let insert_on_disk_lem key value st = ()
diff --git a/tests/fstar-split/hashmap_on_disk/HashmapMain.Types.fst b/tests/fstar-split/hashmap_on_disk/HashmapMain.Types.fst
new file mode 100644
index 00000000..afebcde3
--- /dev/null
+++ b/tests/fstar-split/hashmap_on_disk/HashmapMain.Types.fst
@@ -0,0 +1,24 @@
+(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
+(** [hashmap_main]: type definitions *)
+module HashmapMain.Types
+open Primitives
+include HashmapMain.TypesExternal
+
+#set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
+
+(** [hashmap_main::hashmap::List]
+    Source: 'src/hashmap.rs', lines 19:0-19:16 *)
+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]
+    Source: 'src/hashmap.rs', lines 35:0-35:21 *)
+type hashmap_HashMap_t (t : Type0) =
+{
+  num_entries : usize;
+  max_load_factor : (usize & usize);
+  max_load : usize;
+  slots : alloc_vec_Vec (hashmap_List_t t);
+}
+
diff --git a/tests/fstar-split/hashmap_on_disk/HashmapMain.TypesExternal.fsti b/tests/fstar-split/hashmap_on_disk/HashmapMain.TypesExternal.fsti
new file mode 100644
index 00000000..75747408
--- /dev/null
+++ b/tests/fstar-split/hashmap_on_disk/HashmapMain.TypesExternal.fsti
@@ -0,0 +1,10 @@
+(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
+(** [hashmap_main]: external type declarations *)
+module HashmapMain.TypesExternal
+open Primitives
+
+#set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
+
+(** The state type used in the state-error monad *)
+val state : Type0
+
diff --git a/tests/fstar-split/hashmap_on_disk/Makefile b/tests/fstar-split/hashmap_on_disk/Makefile
new file mode 100644
index 00000000..fa7d1f36
--- /dev/null
+++ b/tests/fstar-split/hashmap_on_disk/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-split/hashmap_on_disk/Primitives.fst b/tests/fstar-split/hashmap_on_disk/Primitives.fst
new file mode 100644
index 00000000..a3ffbde4
--- /dev/null
+++ b/tests/fstar-split/hashmap_on_disk/Primitives.fst
@@ -0,0 +1,884 @@
+/// 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
+
+assume val size_numbits : pos
+
+// TODO: we could use FStar.Int.int_t and FStar.UInt.int_t
+
+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_xor (#ty : scalar_ty)
+    (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
+  | Usize -> admit() // TODO
+  | I8 ->
+    // Encoding issues...
+    normalize_spec (FStar.Int.int_t 8);
+    normalize_spec (scalar I8);
+    FStar.Int.logxor #8 x y
+  | I16 ->
+    // Encoding issues...
+    normalize_spec (FStar.Int.int_t 16);
+    normalize_spec (scalar I16);
+    FStar.Int.logxor #16 x y
+  | I32 -> FStar.Int.logxor #32 x y
+  | I64 -> FStar.Int.logxor #64 x y
+  | I128 ->
+    // Encoding issues...
+    normalize_spec (FStar.Int.int_t 128);
+    normalize_spec (scalar I128);
+    FStar.Int.logxor #128 x y
+  | Isize -> admit() // TODO
+
+let scalar_or (#ty : scalar_ty)
+    (x : scalar ty) (y : scalar ty) : scalar ty =
+  match ty with
+  | U8 -> FStar.UInt.logor #8 x y
+  | U16 -> FStar.UInt.logor #16 x y
+  | U32 -> FStar.UInt.logor #32 x y
+  | U64 -> FStar.UInt.logor #64 x y
+  | U128 -> FStar.UInt.logor #128 x y
+  | Usize -> admit() // TODO
+  | I8 ->
+    // Encoding issues...
+    normalize_spec (FStar.Int.int_t 8);
+    normalize_spec (scalar I8);
+    FStar.Int.logor #8 x y
+  | I16 ->
+    // Encoding issues...
+    normalize_spec (FStar.Int.int_t 16);
+    normalize_spec (scalar I16);
+    FStar.Int.logor #16 x y
+  | I32 -> FStar.Int.logor #32 x y
+  | I64 -> FStar.Int.logor #64 x y
+  | I128 ->
+    // Encoding issues...
+    normalize_spec (FStar.Int.int_t 128);
+    normalize_spec (scalar I128);
+    FStar.Int.logor #128 x y
+  | Isize -> admit() // TODO
+
+let scalar_and (#ty : scalar_ty)
+    (x : scalar ty) (y : scalar ty) : scalar ty =
+  match ty with
+  | U8 -> FStar.UInt.logand #8 x y
+  | U16 -> FStar.UInt.logand #16 x y
+  | U32 -> FStar.UInt.logand #32 x y
+  | U64 -> FStar.UInt.logand #64 x y
+  | U128 -> FStar.UInt.logand #128 x y
+  | Usize -> admit() // TODO
+  | I8 ->
+    // Encoding issues...
+    normalize_spec (FStar.Int.int_t 8);
+    normalize_spec (scalar I8);
+    FStar.Int.logand #8 x y
+  | I16 ->
+    // Encoding issues...
+    normalize_spec (FStar.Int.int_t 16);
+    normalize_spec (scalar I16);
+    FStar.Int.logand #16 x y
+  | I32 -> FStar.Int.logand #32 x y
+  | I64 -> FStar.Int.logand #64 x y
+  | I128 ->
+    // Encoding issues...
+    normalize_spec (FStar.Int.int_t 128);
+    normalize_spec (scalar I128);
+    FStar.Int.logand #128 x y
+  | Isize -> admit() // TODO
+
+// Shift left
+let scalar_shl (#ty0 #ty1 : scalar_ty)
+    (x : scalar ty0) (y : scalar ty1) : result (scalar ty0) =
+  admit()
+
+// Shift right
+let scalar_shr (#ty0 #ty1 : scalar_ty)
+    (x : scalar ty0) (y : scalar ty1) : result (scalar ty0) =
+  admit()
+
+(** 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
+
+// This can't fail, but for now we make all casts faillible (easier for the translation)
+let scalar_cast_bool (tgt_ty : scalar_ty) (x : bool) : result (scalar tgt_ty) =
+  mk_scalar tgt_ty (if x then 1 else 0)
+
+/// 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
+
+/// Xor
+let u8_xor = scalar_xor #U8
+let u16_xor = scalar_xor #U16
+let u32_xor = scalar_xor #U32
+let u64_xor = scalar_xor #U64
+let u128_xor = scalar_xor #U128
+let usize_xor = scalar_xor #Usize
+let i8_xor = scalar_xor #I8
+let i16_xor = scalar_xor #I16
+let i32_xor = scalar_xor #I32
+let i64_xor = scalar_xor #I64
+let i128_xor = scalar_xor #I128
+let isize_xor = scalar_xor #Isize
+
+/// Or
+let u8_or = scalar_or #U8
+let u16_or = scalar_or #U16
+let u32_or = scalar_or #U32
+let u64_or = scalar_or #U64
+let u128_or = scalar_or #U128
+let usize_or = scalar_or #Usize
+let i8_or = scalar_or #I8
+let i16_or = scalar_or #I16
+let i32_or = scalar_or #I32
+let i64_or = scalar_or #I64
+let i128_or = scalar_or #I128
+let isize_or = scalar_or #Isize
+
+/// And
+let u8_and = scalar_and #U8
+let u16_and = scalar_and #U16
+let u32_and = scalar_and #U32
+let u64_and = scalar_and #U64
+let u128_and = scalar_and #U128
+let usize_and = scalar_and #Usize
+let i8_and = scalar_and #I8
+let i16_and = scalar_and #I16
+let i32_and = scalar_and #I32
+let i64_and = scalar_and #I64
+let i128_and = scalar_and #I128
+let isize_and = scalar_and #Isize
+
+/// Shift left
+let u8_shl #ty = scalar_shl #U8 #ty
+let u16_shl #ty = scalar_shl #U16 #ty
+let u32_shl #ty = scalar_shl #U32 #ty
+let u64_shl #ty = scalar_shl #U64 #ty
+let u128_shl #ty = scalar_shl #U128 #ty
+let usize_shl #ty = scalar_shl #Usize #ty
+let i8_shl #ty = scalar_shl #I8 #ty
+let i16_shl #ty = scalar_shl #I16 #ty
+let i32_shl #ty = scalar_shl #I32 #ty
+let i64_shl #ty = scalar_shl #I64 #ty
+let i128_shl #ty = scalar_shl #I128 #ty
+let isize_shl #ty = scalar_shl #Isize #ty
+
+/// Shift right
+let u8_shr #ty = scalar_shr #U8 #ty
+let u16_shr #ty = scalar_shr #U16 #ty
+let u32_shr #ty = scalar_shr #U32 #ty
+let u64_shr #ty = scalar_shr #U64 #ty
+let u128_shr #ty = scalar_shr #U128 #ty
+let usize_shr #ty = scalar_shr #Usize #ty
+let i8_shr #ty = scalar_shr #I8 #ty
+let i16_shr #ty = scalar_shr #I16 #ty
+let i32_shr #ty = scalar_shr #I32 #ty
+let i64_shr #ty = scalar_shr #I64 #ty
+let i128_shr #ty = scalar_shr #I128 #ty
+let isize_shr #ty = scalar_shr #Isize #ty
+
+(*** 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_RangeUsize_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_RangeUsize_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_RangeUsize_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_RangeUsize_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_RangeUsize_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_RangeUsize_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_RangeUsize_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_RangeUsize_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::private_slice_index::Range]
+let core_slice_index_private_slice_index_SealedRangeUsizeInst
+  : core_slice_index_private_slice_index_Sealed (core_ops_range_Range usize) = ()
+
+// Trait implementation: [core::slice::index::Range]
+let core_slice_index_SliceIndexRangeUsizeSliceTInst (t : Type0) :
+  core_slice_index_SliceIndex (core_ops_range_Range usize) (slice t) = {
+  sealedInst = core_slice_index_private_slice_index_SealedRangeUsizeInst;
+  output = slice t;
+  get = core_slice_index_RangeUsize_get t;
+  get_mut = core_slice_index_RangeUsize_get_mut t;
+  get_mut_back = core_slice_index_RangeUsize_get_mut_back t;
+  get_unchecked = core_slice_index_RangeUsize_get_unchecked t;
+  get_unchecked_mut = core_slice_index_RangeUsize_get_unchecked_mut t;
+  index = core_slice_index_RangeUsize_index t;
+  index_mut = core_slice_index_RangeUsize_index_mut t;
+  index_mut_back = core_slice_index_RangeUsize_index_mut_back t;
+}
+
+// Trait implementation: [core::slice::index::[T]]
+let core_ops_index_IndexSliceTIInst (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::[T]]
+let core_ops_index_IndexMutSliceTIInst (t idx : Type0)
+  (inst : core_slice_index_SliceIndex idx (slice t)) :
+  core_ops_index_IndexMut (slice t) idx = {
+  indexInst = core_ops_index_IndexSliceTIInst 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_ops_index_IndexArrayInst (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_ops_index_IndexMutArrayIInst (t idx : Type0) (n : usize)
+  (inst : core_ops_index_IndexMut (slice t) idx) :
+  core_ops_index_IndexMut (array t n) idx = {
+  indexInst = core_ops_index_IndexArrayInst 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_SealedUsizeInst
+  : core_slice_index_private_slice_index_Sealed usize = ()
+
+// Trait implementation: [core::slice::index::usize]
+let core_slice_index_SliceIndexUsizeSliceTInst (t : Type0) :
+  core_slice_index_SliceIndex usize (slice t) = {
+  sealedInst = core_slice_index_private_slice_index_SealedUsizeInst;
+  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_SliceIndexUsizeSliceTInst a) v i ==
+      alloc_vec_Vec_index_usize v i)
+  [SMTPat (alloc_vec_Vec_index a usize (core_slice_index_SliceIndexUsizeSliceTInst 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_SliceIndexUsizeSliceTInst a) v i ==
+      alloc_vec_Vec_index_usize v i)
+  [SMTPat (alloc_vec_Vec_index_mut a usize (core_slice_index_SliceIndexUsizeSliceTInst 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_SliceIndexUsizeSliceTInst a) v i x ==
+      alloc_vec_Vec_update_usize v i x)
+  [SMTPat (alloc_vec_Vec_index_mut_back a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i x)]
+  =
+  admit()
diff --git a/tests/fstar-split/misc/Bitwise.fst b/tests/fstar-split/misc/Bitwise.fst
new file mode 100644
index 00000000..d7ba2c57
--- /dev/null
+++ b/tests/fstar-split/misc/Bitwise.fst
@@ -0,0 +1,32 @@
+(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
+(** [bitwise] *)
+module Bitwise
+open Primitives
+
+#set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
+
+(** [bitwise::shift_u32]: forward function
+    Source: 'src/bitwise.rs', lines 3:0-3:31 *)
+let shift_u32 (a : u32) : result u32 =
+  let* t = u32_shr #Usize a 16 in u32_shl #Usize t 16
+
+(** [bitwise::shift_i32]: forward function
+    Source: 'src/bitwise.rs', lines 10:0-10:31 *)
+let shift_i32 (a : i32) : result i32 =
+  let* t = i32_shr #Isize a 16 in i32_shl #Isize t 16
+
+(** [bitwise::xor_u32]: forward function
+    Source: 'src/bitwise.rs', lines 17:0-17:37 *)
+let xor_u32 (a : u32) (b : u32) : result u32 =
+  Return (u32_xor a b)
+
+(** [bitwise::or_u32]: forward function
+    Source: 'src/bitwise.rs', lines 21:0-21:36 *)
+let or_u32 (a : u32) (b : u32) : result u32 =
+  Return (u32_or a b)
+
+(** [bitwise::and_u32]: forward function
+    Source: 'src/bitwise.rs', lines 25:0-25:37 *)
+let and_u32 (a : u32) (b : u32) : result u32 =
+  Return (u32_and a b)
+
diff --git a/tests/fstar-split/misc/Constants.fst b/tests/fstar-split/misc/Constants.fst
new file mode 100644
index 00000000..7e56cc20
--- /dev/null
+++ b/tests/fstar-split/misc/Constants.fst
@@ -0,0 +1,145 @@
+(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
+(** [constants] *)
+module Constants
+open Primitives
+
+#set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
+
+(** [constants::X0]
+    Source: 'src/constants.rs', lines 5:0-5:17 *)
+let x0_body : result u32 = Return 0
+let x0_c : u32 = eval_global x0_body
+
+(** [constants::X1]
+    Source: 'src/constants.rs', lines 7:0-7:17 *)
+let x1_body : result u32 = Return core_u32_max
+let x1_c : u32 = eval_global x1_body
+
+(** [constants::X2]
+    Source: 'src/constants.rs', lines 10:0-10:17 *)
+let x2_body : result u32 = Return 3
+let x2_c : u32 = eval_global x2_body
+
+(** [constants::incr]: forward function
+    Source: 'src/constants.rs', lines 17:0-17:32 *)
+let incr (n : u32) : result u32 =
+  u32_add n 1
+
+(** [constants::X3]
+    Source: 'src/constants.rs', lines 15:0-15:17 *)
+let x3_body : result u32 = incr 32
+let x3_c : u32 = eval_global x3_body
+
+(** [constants::mk_pair0]: forward function
+    Source: 'src/constants.rs', lines 23:0-23:51 *)
+let mk_pair0 (x : u32) (y : u32) : result (u32 & u32) =
+  Return (x, y)
+
+(** [constants::Pair]
+    Source: 'src/constants.rs', lines 36:0-36:23 *)
+type pair_t (t1 t2 : Type0) = { x : t1; y : t2; }
+
+(** [constants::mk_pair1]: forward function
+    Source: 'src/constants.rs', lines 27:0-27:55 *)
+let mk_pair1 (x : u32) (y : u32) : result (pair_t u32 u32) =
+  Return { x = x; y = y }
+
+(** [constants::P0]
+    Source: 'src/constants.rs', lines 31:0-31:24 *)
+let p0_body : result (u32 & u32) = mk_pair0 0 1
+let p0_c : (u32 & u32) = eval_global p0_body
+
+(** [constants::P1]
+    Source: 'src/constants.rs', lines 32:0-32:28 *)
+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]
+    Source: 'src/constants.rs', lines 33:0-33:24 *)
+let p2_body : result (u32 & u32) = Return (0, 1)
+let p2_c : (u32 & u32) = eval_global p2_body
+
+(** [constants::P3]
+    Source: 'src/constants.rs', lines 34:0-34:28 *)
+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]
+    Source: 'src/constants.rs', lines 49:0-49:18 *)
+type wrap_t (t : Type0) = { value : t; }
+
+(** [constants::{constants::Wrap<T>}::new]: forward function
+    Source: 'src/constants.rs', lines 54:4-54:41 *)
+let wrap_new (t : Type0) (value : t) : result (wrap_t t) =
+  Return { value = value }
+
+(** [constants::Y]
+    Source: 'src/constants.rs', lines 41:0-41:22 *)
+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
+    Source: 'src/constants.rs', lines 43:0-43:30 *)
+let unwrap_y : result i32 =
+  Return y_c.value
+
+(** [constants::YVAL]
+    Source: 'src/constants.rs', lines 47:0-47:19 *)
+let yval_body : result i32 = unwrap_y
+let yval_c : i32 = eval_global yval_body
+
+(** [constants::get_z1::Z1]
+    Source: 'src/constants.rs', lines 62:4-62:17 *)
+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
+    Source: 'src/constants.rs', lines 61:0-61:28 *)
+let get_z1 : result i32 =
+  Return get_z1_z1_c
+
+(** [constants::add]: forward function
+    Source: 'src/constants.rs', lines 66:0-66:39 *)
+let add (a : i32) (b : i32) : result i32 =
+  i32_add a b
+
+(** [constants::Q1]
+    Source: 'src/constants.rs', lines 74:0-74:17 *)
+let q1_body : result i32 = Return 5
+let q1_c : i32 = eval_global q1_body
+
+(** [constants::Q2]
+    Source: 'src/constants.rs', lines 75:0-75:17 *)
+let q2_body : result i32 = Return q1_c
+let q2_c : i32 = eval_global q2_body
+
+(** [constants::Q3]
+    Source: 'src/constants.rs', lines 76:0-76:17 *)
+let q3_body : result i32 = add q2_c 3
+let q3_c : i32 = eval_global q3_body
+
+(** [constants::get_z2]: forward function
+    Source: 'src/constants.rs', lines 70:0-70:28 *)
+let get_z2 : result i32 =
+  let* i = get_z1 in let* i1 = add i q3_c in add q1_c i1
+
+(** [constants::S1]
+    Source: 'src/constants.rs', lines 80:0-80:18 *)
+let s1_body : result u32 = Return 6
+let s1_c : u32 = eval_global s1_body
+
+(** [constants::S2]
+    Source: 'src/constants.rs', lines 81:0-81:18 *)
+let s2_body : result u32 = incr s1_c
+let s2_c : u32 = eval_global s2_body
+
+(** [constants::S3]
+    Source: 'src/constants.rs', lines 82:0-82:29 *)
+let s3_body : result (pair_t u32 u32) = Return p3_c
+let s3_c : pair_t u32 u32 = eval_global s3_body
+
+(** [constants::S4]
+    Source: 'src/constants.rs', lines 83:0-83:29 *)
+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-split/misc/External.Funs.fst b/tests/fstar-split/misc/External.Funs.fst
new file mode 100644
index 00000000..65382549
--- /dev/null
+++ b/tests/fstar-split/misc/External.Funs.fst
@@ -0,0 +1,82 @@
+(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
+(** [external]: function definitions *)
+module External.Funs
+open Primitives
+include External.Types
+include External.FunsExternal
+
+#set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
+
+(** [external::swap]: forward function
+    Source: 'src/external.rs', lines 6:0-6:46 *)
+let swap (t : Type0) (x : t) (y : t) (st : state) : result (state & unit) =
+  let* (st1, _) = core_mem_swap t x y st in
+  let* (st2, _) = core_mem_swap_back0 t x y st st1 in
+  let* (st3, _) = core_mem_swap_back1 t x y st st2 in
+  Return (st3, ())
+
+(** [external::swap]: backward function 0
+    Source: 'src/external.rs', lines 6:0-6:46 *)
+let swap_back
+  (t : Type0) (x : t) (y : t) (st : state) (st1 : state) :
+  result (state & (t & t))
+  =
+  let* (st2, _) = core_mem_swap t x y st in
+  let* (st3, x1) = core_mem_swap_back0 t x y st st2 in
+  let* (_, y1) = core_mem_swap_back1 t x y st st3 in
+  Return (st1, (x1, y1))
+
+(** [external::test_new_non_zero_u32]: forward function
+    Source: 'src/external.rs', lines 11:0-11:60 *)
+let test_new_non_zero_u32
+  (x : u32) (st : state) : result (state & core_num_nonzero_NonZeroU32_t) =
+  let* (st1, o) = core_num_nonzero_NonZeroU32_new x st in
+  core_option_Option_unwrap core_num_nonzero_NonZeroU32_t o st1
+
+(** [external::test_vec]: forward function
+    Source: 'src/external.rs', lines 17:0-17:17 *)
+let test_vec : result unit =
+  let* _ = alloc_vec_Vec_push u32 (alloc_vec_Vec_new u32) 0 in Return ()
+
+(** Unit test for [external::test_vec] *)
+let _ = assert_norm (test_vec = Return ())
+
+(** [external::custom_swap]: forward function
+    Source: 'src/external.rs', lines 24:0-24:66 *)
+let custom_swap (t : Type0) (x : t) (y : t) (st : state) : result (state & t) =
+  let* (st1, _) = core_mem_swap t x y st in
+  let* (st2, x1) = core_mem_swap_back0 t x y st st1 in
+  let* (st3, _) = core_mem_swap_back1 t x y st st2 in
+  Return (st3, x1)
+
+(** [external::custom_swap]: backward function 0
+    Source: 'src/external.rs', lines 24:0-24:66 *)
+let custom_swap_back
+  (t : Type0) (x : t) (y : t) (st : state) (ret : t) (st1 : state) :
+  result (state & (t & t))
+  =
+  let* (st2, _) = core_mem_swap t x y st in
+  let* (st3, _) = core_mem_swap_back0 t x y st st2 in
+  let* (_, y1) = core_mem_swap_back1 t x y st st3 in
+  Return (st1, (ret, y1))
+
+(** [external::test_custom_swap]: forward function
+    Source: 'src/external.rs', lines 29:0-29:59 *)
+let test_custom_swap (x : u32) (y : u32) (st : state) : result (state & unit) =
+  let* (st1, _) = custom_swap u32 x y st in Return (st1, ())
+
+(** [external::test_custom_swap]: backward function 0
+    Source: 'src/external.rs', lines 29:0-29:59 *)
+let test_custom_swap_back
+  (x : u32) (y : u32) (st : state) (st1 : state) :
+  result (state & (u32 & u32))
+  =
+  custom_swap_back u32 x y st 1 st1
+
+(** [external::test_swap_non_zero]: forward function
+    Source: 'src/external.rs', lines 35:0-35:44 *)
+let test_swap_non_zero (x : u32) (st : state) : result (state & u32) =
+  let* (st1, _) = swap u32 x 0 st in
+  let* (st2, (x1, _)) = swap_back u32 x 0 st st1 in
+  if x1 = 0 then Fail Failure else Return (st2, x1)
+
diff --git a/tests/fstar-split/misc/External.FunsExternal.fsti b/tests/fstar-split/misc/External.FunsExternal.fsti
new file mode 100644
index 00000000..923a1101
--- /dev/null
+++ b/tests/fstar-split/misc/External.FunsExternal.fsti
@@ -0,0 +1,32 @@
+(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
+(** [external]: external function declarations *)
+module External.FunsExternal
+open Primitives
+include External.Types
+
+#set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
+
+(** [core::mem::swap]: forward function
+    Source: '/rustc/d59363ad0b6391b7fc5bbb02c9ccf9300eef3753/library/core/src/mem/mod.rs', lines 726:0-726:42 *)
+val core_mem_swap (t : Type0) : t -> t -> state -> result (state & unit)
+
+(** [core::mem::swap]: backward function 0
+    Source: '/rustc/d59363ad0b6391b7fc5bbb02c9ccf9300eef3753/library/core/src/mem/mod.rs', lines 726:0-726:42 *)
+val core_mem_swap_back0
+  (t : Type0) : t -> t -> state -> state -> result (state & t)
+
+(** [core::mem::swap]: backward function 1
+    Source: '/rustc/d59363ad0b6391b7fc5bbb02c9ccf9300eef3753/library/core/src/mem/mod.rs', lines 726:0-726:42 *)
+val core_mem_swap_back1
+  (t : Type0) : t -> t -> state -> state -> result (state & t)
+
+(** [core::num::nonzero::{core::num::nonzero::NonZeroU32#14}::new]: forward function
+    Source: '/rustc/d59363ad0b6391b7fc5bbb02c9ccf9300eef3753/library/core/src/num/nonzero.rs', lines 79:16-79:57 *)
+val core_num_nonzero_NonZeroU32_new
+  : u32 -> state -> result (state & (option core_num_nonzero_NonZeroU32_t))
+
+(** [core::option::{core::option::Option<T>}::unwrap]: forward function
+    Source: '/rustc/d59363ad0b6391b7fc5bbb02c9ccf9300eef3753/library/core/src/option.rs', lines 932:4-932:34 *)
+val core_option_Option_unwrap
+  (t : Type0) : option t -> state -> result (state & t)
+
diff --git a/tests/fstar-split/misc/External.Types.fst b/tests/fstar-split/misc/External.Types.fst
new file mode 100644
index 00000000..4fbcec47
--- /dev/null
+++ b/tests/fstar-split/misc/External.Types.fst
@@ -0,0 +1,8 @@
+(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
+(** [external]: type definitions *)
+module External.Types
+open Primitives
+include External.TypesExternal
+
+#set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
+
diff --git a/tests/fstar-split/misc/External.TypesExternal.fsti b/tests/fstar-split/misc/External.TypesExternal.fsti
new file mode 100644
index 00000000..4bfbe0c5
--- /dev/null
+++ b/tests/fstar-split/misc/External.TypesExternal.fsti
@@ -0,0 +1,14 @@
+(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
+(** [external]: external type declarations *)
+module External.TypesExternal
+open Primitives
+
+#set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
+
+(** [core::num::nonzero::NonZeroU32]
+    Source: '/rustc/d59363ad0b6391b7fc5bbb02c9ccf9300eef3753/library/core/src/num/nonzero.rs', lines 50:12-50:33 *)
+val core_num_nonzero_NonZeroU32_t : Type0
+
+(** The state type used in the state-error monad *)
+val state : Type0
+
diff --git a/tests/fstar-split/misc/Loops.Clauses.Template.fst b/tests/fstar-split/misc/Loops.Clauses.Template.fst
new file mode 100644
index 00000000..6be351c6
--- /dev/null
+++ b/tests/fstar-split/misc/Loops.Clauses.Template.fst
@@ -0,0 +1,131 @@
+(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
+(** [loops]: templates for the decreases clauses *)
+module Loops.Clauses.Template
+open Primitives
+open Loops.Types
+
+#set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
+
+(** [loops::sum]: decreases clause
+    Source: 'src/loops.rs', lines 4:0-14:1 *)
+unfold let sum_loop_decreases (max : u32) (i : u32) (s : u32) : nat = admit ()
+
+(** [loops::sum_with_mut_borrows]: decreases clause
+    Source: 'src/loops.rs', lines 19:0-31:1 *)
+unfold
+let sum_with_mut_borrows_loop_decreases (max : u32) (mi : u32) (ms : u32) : nat
+  =
+  admit ()
+
+(** [loops::sum_with_shared_borrows]: decreases clause
+    Source: 'src/loops.rs', lines 34:0-48:1 *)
+unfold
+let sum_with_shared_borrows_loop_decreases (max : u32) (i : u32) (s : u32) :
+  nat =
+  admit ()
+
+(** [loops::clear]: decreases clause
+    Source: 'src/loops.rs', lines 52:0-58:1 *)
+unfold
+let clear_loop_decreases (v : alloc_vec_Vec u32) (i : usize) : nat = admit ()
+
+(** [loops::list_mem]: decreases clause
+    Source: 'src/loops.rs', lines 66:0-75:1 *)
+unfold let list_mem_loop_decreases (x : u32) (ls : list_t u32) : nat = admit ()
+
+(** [loops::list_nth_mut_loop]: decreases clause
+    Source: 'src/loops.rs', lines 78:0-88:1 *)
+unfold
+let list_nth_mut_loop_loop_decreases (t : Type0) (ls : list_t t) (i : u32) :
+  nat =
+  admit ()
+
+(** [loops::list_nth_shared_loop]: decreases clause
+    Source: 'src/loops.rs', lines 91:0-101:1 *)
+unfold
+let list_nth_shared_loop_loop_decreases (t : Type0) (ls : list_t t) (i : u32) :
+  nat =
+  admit ()
+
+(** [loops::get_elem_mut]: decreases clause
+    Source: 'src/loops.rs', lines 103:0-117:1 *)
+unfold
+let get_elem_mut_loop_decreases (x : usize) (ls : list_t usize) : nat =
+  admit ()
+
+(** [loops::get_elem_shared]: decreases clause
+    Source: 'src/loops.rs', lines 119:0-133:1 *)
+unfold
+let get_elem_shared_loop_decreases (x : usize) (ls : list_t usize) : nat =
+  admit ()
+
+(** [loops::list_nth_mut_loop_with_id]: decreases clause
+    Source: 'src/loops.rs', lines 144:0-155:1 *)
+unfold
+let list_nth_mut_loop_with_id_loop_decreases (t : Type0) (i : u32)
+  (ls : list_t t) : nat =
+  admit ()
+
+(** [loops::list_nth_shared_loop_with_id]: decreases clause
+    Source: 'src/loops.rs', lines 158:0-169:1 *)
+unfold
+let list_nth_shared_loop_with_id_loop_decreases (t : Type0) (i : u32)
+  (ls : list_t t) : nat =
+  admit ()
+
+(** [loops::list_nth_mut_loop_pair]: decreases clause
+    Source: 'src/loops.rs', lines 174:0-195:1 *)
+unfold
+let list_nth_mut_loop_pair_loop_decreases (t : Type0) (ls0 : list_t t)
+  (ls1 : list_t t) (i : u32) : nat =
+  admit ()
+
+(** [loops::list_nth_shared_loop_pair]: decreases clause
+    Source: 'src/loops.rs', lines 198:0-219:1 *)
+unfold
+let list_nth_shared_loop_pair_loop_decreases (t : Type0) (ls0 : list_t t)
+  (ls1 : list_t t) (i : u32) : nat =
+  admit ()
+
+(** [loops::list_nth_mut_loop_pair_merge]: decreases clause
+    Source: 'src/loops.rs', lines 223:0-238:1 *)
+unfold
+let list_nth_mut_loop_pair_merge_loop_decreases (t : Type0) (ls0 : list_t t)
+  (ls1 : list_t t) (i : u32) : nat =
+  admit ()
+
+(** [loops::list_nth_shared_loop_pair_merge]: decreases clause
+    Source: 'src/loops.rs', lines 241:0-256:1 *)
+unfold
+let list_nth_shared_loop_pair_merge_loop_decreases (t : Type0) (ls0 : list_t t)
+  (ls1 : list_t t) (i : u32) : nat =
+  admit ()
+
+(** [loops::list_nth_mut_shared_loop_pair]: decreases clause
+    Source: 'src/loops.rs', lines 259:0-274:1 *)
+unfold
+let list_nth_mut_shared_loop_pair_loop_decreases (t : Type0) (ls0 : list_t t)
+  (ls1 : list_t t) (i : u32) : nat =
+  admit ()
+
+(** [loops::list_nth_mut_shared_loop_pair_merge]: decreases clause
+    Source: 'src/loops.rs', lines 278:0-293:1 *)
+unfold
+let list_nth_mut_shared_loop_pair_merge_loop_decreases (t : Type0)
+  (ls0 : list_t t) (ls1 : list_t t) (i : u32) : nat =
+  admit ()
+
+(** [loops::list_nth_shared_mut_loop_pair]: decreases clause
+    Source: 'src/loops.rs', lines 297:0-312:1 *)
+unfold
+let list_nth_shared_mut_loop_pair_loop_decreases (t : Type0) (ls0 : list_t t)
+  (ls1 : list_t t) (i : u32) : nat =
+  admit ()
+
+(** [loops::list_nth_shared_mut_loop_pair_merge]: decreases clause
+    Source: 'src/loops.rs', lines 316:0-331:1 *)
+unfold
+let list_nth_shared_mut_loop_pair_merge_loop_decreases (t : Type0)
+  (ls0 : list_t t) (ls1 : list_t t) (i : u32) : nat =
+  admit ()
+
diff --git a/tests/fstar-split/misc/Loops.Clauses.fst b/tests/fstar-split/misc/Loops.Clauses.fst
new file mode 100644
index 00000000..75194437
--- /dev/null
+++ b/tests/fstar-split/misc/Loops.Clauses.fst
@@ -0,0 +1,107 @@
+(** [loops]: templates for the decreases clauses *)
+module Loops.Clauses
+open Primitives
+open Loops.Types
+
+#set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
+
+(** [loops::sum]: decreases clause *)
+unfold let sum_loop_decreases (max : u32) (i : u32) (s : u32) : nat =
+  if i <= max then max - i else 0
+
+(** [loops::sum_with_mut_borrows]: decreases clause *)
+unfold
+let sum_with_mut_borrows_loop_decreases (max : u32) (mi : u32) (ms : u32) : nat =
+  if max >= mi then max - mi else 0
+
+(** [loops::sum_with_shared_borrows]: decreases clause *)
+unfold
+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 : 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 *)
+unfold let list_mem_loop_decreases (i : u32) (ls : list_t u32) : list_t u32 =
+  ls
+
+(** [loops::list_nth_mut_loop]: decreases clause *)
+unfold
+let list_nth_mut_loop_loop_decreases (t : Type0) (ls : list_t t) (i : u32) : nat =
+  i
+
+(** [loops::list_nth_shared_loop]: decreases clause *)
+unfold
+let list_nth_shared_loop_loop_decreases (t : Type0) (ls : list_t t) (i : u32) : list_t t =
+  ls
+
+(** [loops::get_elem_mut]: decreases clause *)
+unfold
+let get_elem_mut_loop_decreases (x : usize) (ls : list_t usize) : list_t usize = ls
+
+(** [loops::get_elem_shared]: decreases clause *)
+unfold
+let get_elem_shared_loop_decreases (x : usize) (ls : list_t usize) : list_t usize =
+  ls
+
+(** [loops::list_nth_mut_loop_with_id]: decreases clause *)
+unfold
+let list_nth_mut_loop_with_id_loop_decreases (t : Type0) (i : u32) (ls : list_t t) :
+  list_t t =
+  ls
+
+(** [loops::list_nth_shared_loop_with_id]: decreases clause *)
+unfold
+let list_nth_shared_loop_with_id_loop_decreases (t : Type0) (i : u32)
+  (ls : list_t t) : list_t t =
+  ls
+
+(** [loops::list_nth_mut_loop_pair]: decreases clause *)
+unfold
+let list_nth_mut_loop_pair_loop_decreases (t : Type0) (l : list_t t) (l0 : list_t t)
+  (i : u32) : nat =
+  i
+
+(** [loops::list_nth_shared_loop_pair]: decreases clause *)
+unfold
+let list_nth_shared_loop_pair_loop_decreases (t : Type0) (l : list_t t)
+  (l0 : list_t t) (i : u32) : list_t t =
+  l
+
+(** [loops::list_nth_mut_loop_pair_merge]: decreases clause *)
+unfold
+let list_nth_mut_loop_pair_merge_loop_decreases (t : Type0) (l : list_t t)
+  (l0 : list_t t) (i : u32) : nat =
+  i
+
+(** [loops::list_nth_shared_loop_pair_merge]: decreases clause *)
+unfold
+let list_nth_shared_loop_pair_merge_loop_decreases (t : Type0) (l : list_t t)
+  (l0 : list_t t) (i : u32) : list_t t =
+  l
+
+(** [loops::list_nth_mut_shared_loop_pair]: decreases clause *)
+unfold
+let list_nth_mut_shared_loop_pair_loop_decreases (t : Type0) (l : list_t t)
+  (l0 : list_t t) (i : u32) : list_t t =
+  l
+
+(** [loops::list_nth_mut_shared_loop_pair_merge]: decreases clause *)
+unfold
+let list_nth_mut_shared_loop_pair_merge_loop_decreases (t : Type0) (l : list_t t)
+  (l0 : list_t t) (i : u32) : list_t t =
+  l
+
+(** [loops::list_nth_shared_mut_loop_pair]: decreases clause *)
+unfold
+let list_nth_shared_mut_loop_pair_loop_decreases (t : Type0) (l : list_t t)
+  (l0 : list_t t) (i : u32) : list_t t =
+  l
+
+(** [loops::list_nth_shared_mut_loop_pair_merge]: decreases clause *)
+unfold
+let list_nth_shared_mut_loop_pair_merge_loop_decreases (t : Type0) (l : list_t t)
+  (l0 : list_t t) (i : u32) : list_t t =
+  l
diff --git a/tests/fstar-split/misc/Loops.Funs.fst b/tests/fstar-split/misc/Loops.Funs.fst
new file mode 100644
index 00000000..3168fddb
--- /dev/null
+++ b/tests/fstar-split/misc/Loops.Funs.fst
@@ -0,0 +1,734 @@
+(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
+(** [loops]: function definitions *)
+module Loops.Funs
+open Primitives
+include Loops.Types
+include Loops.Clauses
+
+#set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
+
+(** [loops::sum]: loop 0: forward function
+    Source: 'src/loops.rs', lines 4:0-14:1 *)
+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* s1 = u32_add s i in let* i1 = u32_add i 1 in sum_loop max i1 s1
+  else u32_mul s 2
+
+(** [loops::sum]: forward function
+    Source: 'src/loops.rs', lines 4:0-4:27 *)
+let sum (max : u32) : result u32 =
+  sum_loop max 0 0
+
+(** [loops::sum_with_mut_borrows]: loop 0: forward function
+    Source: 'src/loops.rs', lines 19:0-31:1 *)
+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))
+  =
+  if mi < max
+  then
+    let* ms1 = u32_add ms mi in
+    let* mi1 = u32_add mi 1 in
+    sum_with_mut_borrows_loop max mi1 ms1
+  else u32_mul ms 2
+
+(** [loops::sum_with_mut_borrows]: forward function
+    Source: 'src/loops.rs', lines 19:0-19:44 *)
+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
+    Source: 'src/loops.rs', lines 34:0-48:1 *)
+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))
+  =
+  if i < max
+  then
+    let* i1 = u32_add i 1 in
+    let* s1 = u32_add s i1 in
+    sum_with_shared_borrows_loop max i1 s1
+  else u32_mul s 2
+
+(** [loops::sum_with_shared_borrows]: forward function
+    Source: 'src/loops.rs', lines 34:0-34:47 *)
+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 ())
+    Source: 'src/loops.rs', lines 52:0-58:1 *)
+let rec clear_loop
+  (v : alloc_vec_Vec u32) (i : usize) :
+  Tot (result (alloc_vec_Vec u32)) (decreases (clear_loop_decreases v i))
+  =
+  let i1 = alloc_vec_Vec_len u32 v in
+  if i < i1
+  then
+    let* i2 = usize_add i 1 in
+    let* v1 =
+      alloc_vec_Vec_index_mut_back u32 usize
+        (core_slice_index_SliceIndexUsizeSliceTInst u32) v i 0 in
+    clear_loop v1 i2
+  else Return v
+
+(** [loops::clear]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ())
+    Source: 'src/loops.rs', lines 52:0-52:30 *)
+let clear (v : alloc_vec_Vec u32) : result (alloc_vec_Vec u32) =
+  clear_loop v 0
+
+(** [loops::list_mem]: loop 0: forward function
+    Source: 'src/loops.rs', lines 66:0-75:1 *)
+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
+  | 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
+    Source: 'src/loops.rs', lines 66:0-66:52 *)
+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
+    Source: 'src/loops.rs', lines 78:0-88:1 *)
+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
+  | List_Cons x tl ->
+    if i = 0
+    then Return x
+    else let* i1 = u32_sub i 1 in list_nth_mut_loop_loop t tl i1
+  | List_Nil -> Fail Failure
+  end
+
+(** [loops::list_nth_mut_loop]: forward function
+    Source: 'src/loops.rs', lines 78:0-78:71 *)
+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
+    Source: 'src/loops.rs', lines 78:0-88:1 *)
+let rec list_nth_mut_loop_loop_back
+  (t : Type0) (ls : list_t t) (i : u32) (ret : t) :
+  Tot (result (list_t t)) (decreases (list_nth_mut_loop_loop_decreases t ls i))
+  =
+  begin match ls with
+  | List_Cons x tl ->
+    if i = 0
+    then Return (List_Cons ret tl)
+    else
+      let* i1 = u32_sub i 1 in
+      let* tl1 = list_nth_mut_loop_loop_back t tl i1 ret in
+      Return (List_Cons x tl1)
+  | List_Nil -> Fail Failure
+  end
+
+(** [loops::list_nth_mut_loop]: backward function 0
+    Source: 'src/loops.rs', lines 78:0-78:71 *)
+let list_nth_mut_loop_back
+  (t : Type0) (ls : list_t t) (i : u32) (ret : t) : result (list_t t) =
+  list_nth_mut_loop_loop_back t ls i ret
+
+(** [loops::list_nth_shared_loop]: loop 0: forward function
+    Source: 'src/loops.rs', lines 91:0-101:1 *)
+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
+  | List_Cons x tl ->
+    if i = 0
+    then Return x
+    else let* i1 = u32_sub i 1 in list_nth_shared_loop_loop t tl i1
+  | List_Nil -> Fail Failure
+  end
+
+(** [loops::list_nth_shared_loop]: forward function
+    Source: 'src/loops.rs', lines 91:0-91:66 *)
+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
+    Source: 'src/loops.rs', lines 103:0-117:1 *)
+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
+  | 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
+    Source: 'src/loops.rs', lines 103:0-103:73 *)
+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_SliceIndexUsizeSliceTInst (list_t usize)) slots 0 in
+  get_elem_mut_loop x l
+
+(** [loops::get_elem_mut]: loop 0: backward function 0
+    Source: 'src/loops.rs', lines 103:0-117:1 *)
+let rec get_elem_mut_loop_back
+  (x : usize) (ls : list_t usize) (ret : usize) :
+  Tot (result (list_t usize)) (decreases (get_elem_mut_loop_decreases x ls))
+  =
+  begin match ls with
+  | List_Cons y tl ->
+    if y = x
+    then Return (List_Cons ret tl)
+    else let* tl1 = get_elem_mut_loop_back x tl ret in Return (List_Cons y tl1)
+  | List_Nil -> Fail Failure
+  end
+
+(** [loops::get_elem_mut]: backward function 0
+    Source: 'src/loops.rs', lines 103:0-103:73 *)
+let get_elem_mut_back
+  (slots : alloc_vec_Vec (list_t usize)) (x : usize) (ret : usize) :
+  result (alloc_vec_Vec (list_t usize))
+  =
+  let* l =
+    alloc_vec_Vec_index_mut (list_t usize) usize
+      (core_slice_index_SliceIndexUsizeSliceTInst (list_t usize)) slots 0 in
+  let* l1 = get_elem_mut_loop_back x l ret in
+  alloc_vec_Vec_index_mut_back (list_t usize) usize
+    (core_slice_index_SliceIndexUsizeSliceTInst (list_t usize)) slots 0 l1
+
+(** [loops::get_elem_shared]: loop 0: forward function
+    Source: 'src/loops.rs', lines 119:0-133:1 *)
+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
+  | 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
+    Source: 'src/loops.rs', lines 119:0-119:68 *)
+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_SliceIndexUsizeSliceTInst (list_t usize)) slots 0 in
+  get_elem_shared_loop x l
+
+(** [loops::id_mut]: forward function
+    Source: 'src/loops.rs', lines 135:0-135:50 *)
+let id_mut (t : Type0) (ls : list_t t) : result (list_t t) =
+  Return ls
+
+(** [loops::id_mut]: backward function 0
+    Source: 'src/loops.rs', lines 135:0-135:50 *)
+let id_mut_back
+  (t : Type0) (ls : list_t t) (ret : list_t t) : result (list_t t) =
+  Return ret
+
+(** [loops::id_shared]: forward function
+    Source: 'src/loops.rs', lines 139:0-139:45 *)
+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
+    Source: 'src/loops.rs', lines 144:0-155:1 *)
+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
+  | List_Cons x tl ->
+    if i = 0
+    then Return x
+    else let* i1 = u32_sub i 1 in list_nth_mut_loop_with_id_loop t i1 tl
+  | List_Nil -> Fail Failure
+  end
+
+(** [loops::list_nth_mut_loop_with_id]: forward function
+    Source: 'src/loops.rs', lines 144:0-144:75 *)
+let list_nth_mut_loop_with_id
+  (t : Type0) (ls : list_t t) (i : u32) : result t =
+  let* ls1 = id_mut t ls in list_nth_mut_loop_with_id_loop t i ls1
+
+(** [loops::list_nth_mut_loop_with_id]: loop 0: backward function 0
+    Source: 'src/loops.rs', lines 144:0-155:1 *)
+let rec list_nth_mut_loop_with_id_loop_back
+  (t : Type0) (i : u32) (ls : list_t t) (ret : t) :
+  Tot (result (list_t t))
+  (decreases (list_nth_mut_loop_with_id_loop_decreases t i ls))
+  =
+  begin match ls with
+  | List_Cons x tl ->
+    if i = 0
+    then Return (List_Cons ret tl)
+    else
+      let* i1 = u32_sub i 1 in
+      let* tl1 = list_nth_mut_loop_with_id_loop_back t i1 tl ret in
+      Return (List_Cons x tl1)
+  | List_Nil -> Fail Failure
+  end
+
+(** [loops::list_nth_mut_loop_with_id]: backward function 0
+    Source: 'src/loops.rs', lines 144:0-144:75 *)
+let list_nth_mut_loop_with_id_back
+  (t : Type0) (ls : list_t t) (i : u32) (ret : t) : result (list_t t) =
+  let* ls1 = id_mut t ls in
+  let* l = list_nth_mut_loop_with_id_loop_back t i ls1 ret in
+  id_mut_back t ls l
+
+(** [loops::list_nth_shared_loop_with_id]: loop 0: forward function
+    Source: 'src/loops.rs', lines 158:0-169:1 *)
+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
+  | List_Cons x tl ->
+    if i = 0
+    then Return x
+    else let* i1 = u32_sub i 1 in list_nth_shared_loop_with_id_loop t i1 tl
+  | List_Nil -> Fail Failure
+  end
+
+(** [loops::list_nth_shared_loop_with_id]: forward function
+    Source: 'src/loops.rs', lines 158:0-158:70 *)
+let list_nth_shared_loop_with_id
+  (t : Type0) (ls : list_t t) (i : u32) : result t =
+  let* ls1 = id_shared t ls in list_nth_shared_loop_with_id_loop t i ls1
+
+(** [loops::list_nth_mut_loop_pair]: loop 0: forward function
+    Source: 'src/loops.rs', lines 174:0-195:1 *)
+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
+  | List_Cons x0 tl0 ->
+    begin match ls1 with
+    | List_Cons x1 tl1 ->
+      if i = 0
+      then Return (x0, x1)
+      else let* i1 = u32_sub i 1 in list_nth_mut_loop_pair_loop t tl0 tl1 i1
+    | List_Nil -> Fail Failure
+    end
+  | List_Nil -> Fail Failure
+  end
+
+(** [loops::list_nth_mut_loop_pair]: forward function
+    Source: 'src/loops.rs', lines 174:0-178:27 *)
+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 t ls0 ls1 i
+
+(** [loops::list_nth_mut_loop_pair]: loop 0: backward function 0
+    Source: 'src/loops.rs', lines 174:0-195:1 *)
+let rec list_nth_mut_loop_pair_loop_back'a
+  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : t) :
+  Tot (result (list_t t))
+  (decreases (list_nth_mut_loop_pair_loop_decreases t ls0 ls1 i))
+  =
+  begin match ls0 with
+  | List_Cons x0 tl0 ->
+    begin match ls1 with
+    | List_Cons _ tl1 ->
+      if i = 0
+      then Return (List_Cons ret tl0)
+      else
+        let* i1 = u32_sub i 1 in
+        let* tl01 = list_nth_mut_loop_pair_loop_back'a t tl0 tl1 i1 ret in
+        Return (List_Cons x0 tl01)
+    | List_Nil -> Fail Failure
+    end
+  | List_Nil -> Fail Failure
+  end
+
+(** [loops::list_nth_mut_loop_pair]: backward function 0
+    Source: 'src/loops.rs', lines 174:0-178:27 *)
+let list_nth_mut_loop_pair_back'a
+  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : t) :
+  result (list_t t)
+  =
+  list_nth_mut_loop_pair_loop_back'a t ls0 ls1 i ret
+
+(** [loops::list_nth_mut_loop_pair]: loop 0: backward function 1
+    Source: 'src/loops.rs', lines 174:0-195:1 *)
+let rec list_nth_mut_loop_pair_loop_back'b
+  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : t) :
+  Tot (result (list_t t))
+  (decreases (list_nth_mut_loop_pair_loop_decreases t ls0 ls1 i))
+  =
+  begin match ls0 with
+  | List_Cons _ tl0 ->
+    begin match ls1 with
+    | List_Cons x1 tl1 ->
+      if i = 0
+      then Return (List_Cons ret tl1)
+      else
+        let* i1 = u32_sub i 1 in
+        let* tl11 = list_nth_mut_loop_pair_loop_back'b t tl0 tl1 i1 ret in
+        Return (List_Cons x1 tl11)
+    | List_Nil -> Fail Failure
+    end
+  | List_Nil -> Fail Failure
+  end
+
+(** [loops::list_nth_mut_loop_pair]: backward function 1
+    Source: 'src/loops.rs', lines 174:0-178:27 *)
+let list_nth_mut_loop_pair_back'b
+  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : t) :
+  result (list_t t)
+  =
+  list_nth_mut_loop_pair_loop_back'b t ls0 ls1 i ret
+
+(** [loops::list_nth_shared_loop_pair]: loop 0: forward function
+    Source: 'src/loops.rs', lines 198:0-219:1 *)
+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
+  | List_Cons x0 tl0 ->
+    begin match ls1 with
+    | List_Cons x1 tl1 ->
+      if i = 0
+      then Return (x0, x1)
+      else let* i1 = u32_sub i 1 in list_nth_shared_loop_pair_loop t tl0 tl1 i1
+    | List_Nil -> Fail Failure
+    end
+  | List_Nil -> Fail Failure
+  end
+
+(** [loops::list_nth_shared_loop_pair]: forward function
+    Source: 'src/loops.rs', lines 198:0-202:19 *)
+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 t ls0 ls1 i
+
+(** [loops::list_nth_mut_loop_pair_merge]: loop 0: forward function
+    Source: 'src/loops.rs', lines 223:0-238:1 *)
+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
+  | List_Cons x0 tl0 ->
+    begin match ls1 with
+    | List_Cons x1 tl1 ->
+      if i = 0
+      then Return (x0, x1)
+      else
+        let* i1 = u32_sub i 1 in list_nth_mut_loop_pair_merge_loop t tl0 tl1 i1
+    | List_Nil -> Fail Failure
+    end
+  | List_Nil -> Fail Failure
+  end
+
+(** [loops::list_nth_mut_loop_pair_merge]: forward function
+    Source: 'src/loops.rs', lines 223:0-227:27 *)
+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 t ls0 ls1 i
+
+(** [loops::list_nth_mut_loop_pair_merge]: loop 0: backward function 0
+    Source: 'src/loops.rs', lines 223:0-238:1 *)
+let rec list_nth_mut_loop_pair_merge_loop_back
+  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : (t & t)) :
+  Tot (result ((list_t t) & (list_t t)))
+  (decreases (list_nth_mut_loop_pair_merge_loop_decreases t ls0 ls1 i))
+  =
+  begin match ls0 with
+  | List_Cons x0 tl0 ->
+    begin match ls1 with
+    | List_Cons x1 tl1 ->
+      if i = 0
+      then let (x, x2) = ret in Return (List_Cons x tl0, List_Cons x2 tl1)
+      else
+        let* i1 = u32_sub i 1 in
+        let* (tl01, tl11) =
+          list_nth_mut_loop_pair_merge_loop_back t tl0 tl1 i1 ret in
+        Return (List_Cons x0 tl01, List_Cons x1 tl11)
+    | List_Nil -> Fail Failure
+    end
+  | List_Nil -> Fail Failure
+  end
+
+(** [loops::list_nth_mut_loop_pair_merge]: backward function 0
+    Source: 'src/loops.rs', lines 223:0-227:27 *)
+let list_nth_mut_loop_pair_merge_back
+  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : (t & t)) :
+  result ((list_t t) & (list_t t))
+  =
+  list_nth_mut_loop_pair_merge_loop_back t ls0 ls1 i ret
+
+(** [loops::list_nth_shared_loop_pair_merge]: loop 0: forward function
+    Source: 'src/loops.rs', lines 241:0-256:1 *)
+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
+  | List_Cons x0 tl0 ->
+    begin match ls1 with
+    | List_Cons x1 tl1 ->
+      if i = 0
+      then Return (x0, x1)
+      else
+        let* i1 = u32_sub i 1 in
+        list_nth_shared_loop_pair_merge_loop t tl0 tl1 i1
+    | List_Nil -> Fail Failure
+    end
+  | List_Nil -> Fail Failure
+  end
+
+(** [loops::list_nth_shared_loop_pair_merge]: forward function
+    Source: 'src/loops.rs', lines 241:0-245:19 *)
+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 t ls0 ls1 i
+
+(** [loops::list_nth_mut_shared_loop_pair]: loop 0: forward function
+    Source: 'src/loops.rs', lines 259:0-274:1 *)
+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
+  | List_Cons x0 tl0 ->
+    begin match ls1 with
+    | List_Cons x1 tl1 ->
+      if i = 0
+      then Return (x0, x1)
+      else
+        let* i1 = u32_sub i 1 in
+        list_nth_mut_shared_loop_pair_loop t tl0 tl1 i1
+    | List_Nil -> Fail Failure
+    end
+  | List_Nil -> Fail Failure
+  end
+
+(** [loops::list_nth_mut_shared_loop_pair]: forward function
+    Source: 'src/loops.rs', lines 259:0-263:23 *)
+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 t ls0 ls1 i
+
+(** [loops::list_nth_mut_shared_loop_pair]: loop 0: backward function 0
+    Source: 'src/loops.rs', lines 259:0-274:1 *)
+let rec list_nth_mut_shared_loop_pair_loop_back
+  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : t) :
+  Tot (result (list_t t))
+  (decreases (list_nth_mut_shared_loop_pair_loop_decreases t ls0 ls1 i))
+  =
+  begin match ls0 with
+  | List_Cons x0 tl0 ->
+    begin match ls1 with
+    | List_Cons _ tl1 ->
+      if i = 0
+      then Return (List_Cons ret tl0)
+      else
+        let* i1 = u32_sub i 1 in
+        let* tl01 = list_nth_mut_shared_loop_pair_loop_back t tl0 tl1 i1 ret in
+        Return (List_Cons x0 tl01)
+    | List_Nil -> Fail Failure
+    end
+  | List_Nil -> Fail Failure
+  end
+
+(** [loops::list_nth_mut_shared_loop_pair]: backward function 0
+    Source: 'src/loops.rs', lines 259:0-263:23 *)
+let list_nth_mut_shared_loop_pair_back
+  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : t) :
+  result (list_t t)
+  =
+  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
+    Source: 'src/loops.rs', lines 278:0-293:1 *)
+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
+  | List_Cons x0 tl0 ->
+    begin match ls1 with
+    | List_Cons x1 tl1 ->
+      if i = 0
+      then Return (x0, x1)
+      else
+        let* i1 = u32_sub i 1 in
+        list_nth_mut_shared_loop_pair_merge_loop t tl0 tl1 i1
+    | List_Nil -> Fail Failure
+    end
+  | List_Nil -> Fail Failure
+  end
+
+(** [loops::list_nth_mut_shared_loop_pair_merge]: forward function
+    Source: 'src/loops.rs', lines 278:0-282:23 *)
+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 t ls0 ls1 i
+
+(** [loops::list_nth_mut_shared_loop_pair_merge]: loop 0: backward function 0
+    Source: 'src/loops.rs', lines 278:0-293:1 *)
+let rec list_nth_mut_shared_loop_pair_merge_loop_back
+  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : t) :
+  Tot (result (list_t t))
+  (decreases (list_nth_mut_shared_loop_pair_merge_loop_decreases t ls0 ls1 i))
+  =
+  begin match ls0 with
+  | List_Cons x0 tl0 ->
+    begin match ls1 with
+    | List_Cons _ tl1 ->
+      if i = 0
+      then Return (List_Cons ret tl0)
+      else
+        let* i1 = u32_sub i 1 in
+        let* tl01 =
+          list_nth_mut_shared_loop_pair_merge_loop_back t tl0 tl1 i1 ret in
+        Return (List_Cons x0 tl01)
+    | List_Nil -> Fail Failure
+    end
+  | List_Nil -> Fail Failure
+  end
+
+(** [loops::list_nth_mut_shared_loop_pair_merge]: backward function 0
+    Source: 'src/loops.rs', lines 278:0-282:23 *)
+let list_nth_mut_shared_loop_pair_merge_back
+  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : t) :
+  result (list_t t)
+  =
+  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
+    Source: 'src/loops.rs', lines 297:0-312:1 *)
+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
+  | List_Cons x0 tl0 ->
+    begin match ls1 with
+    | List_Cons x1 tl1 ->
+      if i = 0
+      then Return (x0, x1)
+      else
+        let* i1 = u32_sub i 1 in
+        list_nth_shared_mut_loop_pair_loop t tl0 tl1 i1
+    | List_Nil -> Fail Failure
+    end
+  | List_Nil -> Fail Failure
+  end
+
+(** [loops::list_nth_shared_mut_loop_pair]: forward function
+    Source: 'src/loops.rs', lines 297:0-301:23 *)
+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 t ls0 ls1 i
+
+(** [loops::list_nth_shared_mut_loop_pair]: loop 0: backward function 1
+    Source: 'src/loops.rs', lines 297:0-312:1 *)
+let rec list_nth_shared_mut_loop_pair_loop_back
+  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : t) :
+  Tot (result (list_t t))
+  (decreases (list_nth_shared_mut_loop_pair_loop_decreases t ls0 ls1 i))
+  =
+  begin match ls0 with
+  | List_Cons _ tl0 ->
+    begin match ls1 with
+    | List_Cons x1 tl1 ->
+      if i = 0
+      then Return (List_Cons ret tl1)
+      else
+        let* i1 = u32_sub i 1 in
+        let* tl11 = list_nth_shared_mut_loop_pair_loop_back t tl0 tl1 i1 ret in
+        Return (List_Cons x1 tl11)
+    | List_Nil -> Fail Failure
+    end
+  | List_Nil -> Fail Failure
+  end
+
+(** [loops::list_nth_shared_mut_loop_pair]: backward function 1
+    Source: 'src/loops.rs', lines 297:0-301:23 *)
+let list_nth_shared_mut_loop_pair_back
+  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : t) :
+  result (list_t t)
+  =
+  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
+    Source: 'src/loops.rs', lines 316:0-331:1 *)
+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
+  | List_Cons x0 tl0 ->
+    begin match ls1 with
+    | List_Cons x1 tl1 ->
+      if i = 0
+      then Return (x0, x1)
+      else
+        let* i1 = u32_sub i 1 in
+        list_nth_shared_mut_loop_pair_merge_loop t tl0 tl1 i1
+    | List_Nil -> Fail Failure
+    end
+  | List_Nil -> Fail Failure
+  end
+
+(** [loops::list_nth_shared_mut_loop_pair_merge]: forward function
+    Source: 'src/loops.rs', lines 316:0-320:23 *)
+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 t ls0 ls1 i
+
+(** [loops::list_nth_shared_mut_loop_pair_merge]: loop 0: backward function 0
+    Source: 'src/loops.rs', lines 316:0-331:1 *)
+let rec list_nth_shared_mut_loop_pair_merge_loop_back
+  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : t) :
+  Tot (result (list_t t))
+  (decreases (list_nth_shared_mut_loop_pair_merge_loop_decreases t ls0 ls1 i))
+  =
+  begin match ls0 with
+  | List_Cons _ tl0 ->
+    begin match ls1 with
+    | List_Cons x1 tl1 ->
+      if i = 0
+      then Return (List_Cons ret tl1)
+      else
+        let* i1 = u32_sub i 1 in
+        let* tl11 =
+          list_nth_shared_mut_loop_pair_merge_loop_back t tl0 tl1 i1 ret in
+        Return (List_Cons x1 tl11)
+    | List_Nil -> Fail Failure
+    end
+  | List_Nil -> Fail Failure
+  end
+
+(** [loops::list_nth_shared_mut_loop_pair_merge]: backward function 0
+    Source: 'src/loops.rs', lines 316:0-320:23 *)
+let list_nth_shared_mut_loop_pair_merge_back
+  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : t) :
+  result (list_t t)
+  =
+  list_nth_shared_mut_loop_pair_merge_loop_back t ls0 ls1 i ret
+
diff --git a/tests/fstar-split/misc/Loops.Types.fst b/tests/fstar-split/misc/Loops.Types.fst
new file mode 100644
index 00000000..8aa38290
--- /dev/null
+++ b/tests/fstar-split/misc/Loops.Types.fst
@@ -0,0 +1,13 @@
+(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
+(** [loops]: type definitions *)
+module Loops.Types
+open Primitives
+
+#set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
+
+(** [loops::List]
+    Source: 'src/loops.rs', lines 60:0-60:16 *)
+type list_t (t : Type0) =
+| List_Cons : t -> list_t t -> list_t t
+| List_Nil : list_t t
+
diff --git a/tests/fstar-split/misc/Makefile b/tests/fstar-split/misc/Makefile
new file mode 100644
index 00000000..fa7d1f36
--- /dev/null
+++ b/tests/fstar-split/misc/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-split/misc/NoNestedBorrows.fst b/tests/fstar-split/misc/NoNestedBorrows.fst
new file mode 100644
index 00000000..53e1d300
--- /dev/null
+++ b/tests/fstar-split/misc/NoNestedBorrows.fst
@@ -0,0 +1,618 @@
+(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
+(** [no_nested_borrows] *)
+module NoNestedBorrows
+open Primitives
+
+#set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
+
+(** [no_nested_borrows::Pair]
+    Source: 'src/no_nested_borrows.rs', lines 4:0-4:23 *)
+type pair_t (t1 t2 : Type0) = { x : t1; y : t2; }
+
+(** [no_nested_borrows::List]
+    Source: 'src/no_nested_borrows.rs', lines 9:0-9:16 *)
+type list_t (t : Type0) =
+| List_Cons : t -> list_t t -> list_t t
+| List_Nil : list_t t
+
+(** [no_nested_borrows::One]
+    Source: 'src/no_nested_borrows.rs', lines 20:0-20:16 *)
+type one_t (t1 : Type0) = | One_One : t1 -> one_t t1
+
+(** [no_nested_borrows::EmptyEnum]
+    Source: 'src/no_nested_borrows.rs', lines 26:0-26:18 *)
+type emptyEnum_t = | EmptyEnum_Empty : emptyEnum_t
+
+(** [no_nested_borrows::Enum]
+    Source: 'src/no_nested_borrows.rs', lines 32:0-32:13 *)
+type enum_t = | Enum_Variant1 : enum_t | Enum_Variant2 : enum_t
+
+(** [no_nested_borrows::EmptyStruct]
+    Source: 'src/no_nested_borrows.rs', lines 39:0-39:22 *)
+type emptyStruct_t = unit
+
+(** [no_nested_borrows::Sum]
+    Source: 'src/no_nested_borrows.rs', lines 41:0-41:20 *)
+type sum_t (t1 t2 : Type0) =
+| Sum_Left : t1 -> sum_t t1 t2
+| Sum_Right : t2 -> sum_t t1 t2
+
+(** [no_nested_borrows::neg_test]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 48:0-48:30 *)
+let neg_test (x : i32) : result i32 =
+  i32_neg x
+
+(** [no_nested_borrows::add_u32]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 54:0-54:37 *)
+let add_u32 (x : u32) (y : u32) : result u32 =
+  u32_add x y
+
+(** [no_nested_borrows::subs_u32]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 60:0-60:38 *)
+let subs_u32 (x : u32) (y : u32) : result u32 =
+  u32_sub x y
+
+(** [no_nested_borrows::div_u32]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 66:0-66:37 *)
+let div_u32 (x : u32) (y : u32) : result u32 =
+  u32_div x y
+
+(** [no_nested_borrows::div_u32_const]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 73:0-73:35 *)
+let div_u32_const (x : u32) : result u32 =
+  u32_div x 2
+
+(** [no_nested_borrows::rem_u32]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 78:0-78:37 *)
+let rem_u32 (x : u32) (y : u32) : result u32 =
+  u32_rem x y
+
+(** [no_nested_borrows::mul_u32]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 82:0-82:37 *)
+let mul_u32 (x : u32) (y : u32) : result u32 =
+  u32_mul x y
+
+(** [no_nested_borrows::add_i32]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 88:0-88:37 *)
+let add_i32 (x : i32) (y : i32) : result i32 =
+  i32_add x y
+
+(** [no_nested_borrows::subs_i32]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 92:0-92:38 *)
+let subs_i32 (x : i32) (y : i32) : result i32 =
+  i32_sub x y
+
+(** [no_nested_borrows::div_i32]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 96:0-96:37 *)
+let div_i32 (x : i32) (y : i32) : result i32 =
+  i32_div x y
+
+(** [no_nested_borrows::div_i32_const]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 100:0-100:35 *)
+let div_i32_const (x : i32) : result i32 =
+  i32_div x 2
+
+(** [no_nested_borrows::rem_i32]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 104:0-104:37 *)
+let rem_i32 (x : i32) (y : i32) : result i32 =
+  i32_rem x y
+
+(** [no_nested_borrows::mul_i32]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 108:0-108:37 *)
+let mul_i32 (x : i32) (y : i32) : result i32 =
+  i32_mul x y
+
+(** [no_nested_borrows::mix_arith_u32]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 112:0-112:51 *)
+let mix_arith_u32 (x : u32) (y : u32) (z : u32) : result u32 =
+  let* i = u32_add x y in
+  let* i1 = u32_div x y in
+  let* i2 = u32_mul i i1 in
+  let* i3 = u32_rem z y in
+  let* i4 = u32_sub x i3 in
+  let* i5 = u32_add i2 i4 in
+  let* i6 = u32_add x y in
+  let* i7 = u32_add i6 z in
+  u32_rem i5 i7
+
+(** [no_nested_borrows::mix_arith_i32]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 116:0-116:51 *)
+let mix_arith_i32 (x : i32) (y : i32) (z : i32) : result i32 =
+  let* i = i32_add x y in
+  let* i1 = i32_div x y in
+  let* i2 = i32_mul i i1 in
+  let* i3 = i32_rem z y in
+  let* i4 = i32_sub x i3 in
+  let* i5 = i32_add i2 i4 in
+  let* i6 = i32_add x y in
+  let* i7 = i32_add i6 z in
+  i32_rem i5 i7
+
+(** [no_nested_borrows::CONST0]
+    Source: 'src/no_nested_borrows.rs', lines 125:0-125:23 *)
+let const0_body : result usize = usize_add 1 1
+let const0_c : usize = eval_global const0_body
+
+(** [no_nested_borrows::CONST1]
+    Source: 'src/no_nested_borrows.rs', lines 126:0-126:23 *)
+let const1_body : result usize = usize_mul 2 2
+let const1_c : usize = eval_global const1_body
+
+(** [no_nested_borrows::cast_u32_to_i32]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 128:0-128:37 *)
+let cast_u32_to_i32 (x : u32) : result i32 =
+  scalar_cast U32 I32 x
+
+(** [no_nested_borrows::cast_bool_to_i32]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 132:0-132:39 *)
+let cast_bool_to_i32 (x : bool) : result i32 =
+  scalar_cast_bool I32 x
+
+(** [no_nested_borrows::cast_bool_to_bool]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 137:0-137:41 *)
+let cast_bool_to_bool (x : bool) : result bool =
+  Return x
+
+(** [no_nested_borrows::test2]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 142:0-142:14 *)
+let test2 : result unit =
+  let* _ = u32_add 23 44 in Return ()
+
+(** Unit test for [no_nested_borrows::test2] *)
+let _ = assert_norm (test2 = Return ())
+
+(** [no_nested_borrows::get_max]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 154:0-154:37 *)
+let get_max (x : u32) (y : u32) : result u32 =
+  if x >= y then Return x else Return y
+
+(** [no_nested_borrows::test3]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 162:0-162:14 *)
+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 = Return ())
+
+(** [no_nested_borrows::test_neg1]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 169:0-169:18 *)
+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 = Return ())
+
+(** [no_nested_borrows::refs_test1]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 176:0-176:19 *)
+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 = Return ())
+
+(** [no_nested_borrows::refs_test2]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 187:0-187:19 *)
+let refs_test2 : result unit =
+  if not (2 = 2)
+  then Fail Failure
+  else
+    if not (0 = 0)
+    then Fail Failure
+    else
+      if not (2 = 2)
+      then Fail Failure
+      else if not (2 = 2) then Fail Failure else Return ()
+
+(** Unit test for [no_nested_borrows::refs_test2] *)
+let _ = assert_norm (refs_test2 = Return ())
+
+(** [no_nested_borrows::test_list1]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 203:0-203:19 *)
+let test_list1 : result unit =
+  Return ()
+
+(** Unit test for [no_nested_borrows::test_list1] *)
+let _ = assert_norm (test_list1 = Return ())
+
+(** [no_nested_borrows::test_box1]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 208:0-208:18 *)
+let test_box1 : result unit =
+  let* b = alloc_boxed_Box_deref_mut_back i32 0 1 in
+  let* x = alloc_boxed_Box_deref i32 b in
+  if not (x = 1) then Fail Failure else Return ()
+
+(** Unit test for [no_nested_borrows::test_box1] *)
+let _ = assert_norm (test_box1 = Return ())
+
+(** [no_nested_borrows::copy_int]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 218:0-218:30 *)
+let copy_int (x : i32) : result i32 =
+  Return x
+
+(** [no_nested_borrows::test_unreachable]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 224:0-224:32 *)
+let test_unreachable (b : bool) : result unit =
+  if b then Fail Failure else Return ()
+
+(** [no_nested_borrows::test_panic]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 232:0-232:26 *)
+let test_panic (b : bool) : result unit =
+  if b then Fail Failure else Return ()
+
+(** [no_nested_borrows::test_copy_int]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 239:0-239:22 *)
+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 = Return ())
+
+(** [no_nested_borrows::is_cons]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 246:0-246:38 *)
+let is_cons (t : Type0) (l : list_t t) : result bool =
+  begin match l with
+  | List_Cons _ _ -> Return true
+  | List_Nil -> Return false
+  end
+
+(** [no_nested_borrows::test_is_cons]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 253:0-253:21 *)
+let test_is_cons : result unit =
+  let* b = is_cons i32 (List_Cons 0 List_Nil) in
+  if not b then Fail Failure else Return ()
+
+(** Unit test for [no_nested_borrows::test_is_cons] *)
+let _ = assert_norm (test_is_cons = Return ())
+
+(** [no_nested_borrows::split_list]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 259:0-259:48 *)
+let split_list (t : Type0) (l : list_t t) : result (t & (list_t t)) =
+  begin match l with
+  | List_Cons hd tl -> Return (hd, tl)
+  | List_Nil -> Fail Failure
+  end
+
+(** [no_nested_borrows::test_split_list]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 267:0-267:24 *)
+let test_split_list : result unit =
+  let* p = split_list i32 (List_Cons 0 List_Nil) 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 = Return ())
+
+(** [no_nested_borrows::choose]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 274:0-274:70 *)
+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
+    Source: 'src/no_nested_borrows.rs', lines 274:0-274:70 *)
+let choose_back
+  (t : Type0) (b : bool) (x : t) (y : t) (ret : t) : result (t & t) =
+  if b then Return (ret, y) else Return (x, ret)
+
+(** [no_nested_borrows::choose_test]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 282:0-282:20 *)
+let choose_test : result unit =
+  let* z = choose i32 true 0 0 in
+  let* z1 = i32_add z 1 in
+  if not (z1 = 1)
+  then Fail Failure
+  else
+    let* (x, y) = choose_back i32 true 0 0 z1 in
+    if not (x = 1)
+    then Fail Failure
+    else if not (y = 0) then Fail Failure else Return ()
+
+(** Unit test for [no_nested_borrows::choose_test] *)
+let _ = assert_norm (choose_test = Return ())
+
+(** [no_nested_borrows::test_char]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 294:0-294:26 *)
+let test_char : result char =
+  Return 'a'
+
+(** [no_nested_borrows::Tree]
+    Source: 'src/no_nested_borrows.rs', lines 299:0-299:16 *)
+type tree_t (t : Type0) =
+| Tree_Leaf : t -> tree_t t
+| Tree_Node : t -> nodeElem_t t -> tree_t t -> tree_t t
+
+(** [no_nested_borrows::NodeElem]
+    Source: 'src/no_nested_borrows.rs', lines 304:0-304:20 *)
+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
+    Source: 'src/no_nested_borrows.rs', lines 339:0-339:48 *)
+let rec list_length (t : Type0) (l : list_t t) : result u32 =
+  begin match l with
+  | List_Cons _ 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
+    Source: 'src/no_nested_borrows.rs', lines 347:0-347:62 *)
+let rec list_nth_shared (t : Type0) (l : list_t t) (i : u32) : result t =
+  begin match l with
+  | List_Cons x tl ->
+    if i = 0
+    then Return x
+    else let* i1 = u32_sub i 1 in list_nth_shared t tl i1
+  | List_Nil -> Fail Failure
+  end
+
+(** [no_nested_borrows::list_nth_mut]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 363:0-363:67 *)
+let rec list_nth_mut (t : Type0) (l : list_t t) (i : u32) : result t =
+  begin match l with
+  | List_Cons x tl ->
+    if i = 0 then Return x else let* i1 = u32_sub i 1 in list_nth_mut t tl i1
+  | List_Nil -> Fail Failure
+  end
+
+(** [no_nested_borrows::list_nth_mut]: backward function 0
+    Source: 'src/no_nested_borrows.rs', lines 363:0-363:67 *)
+let rec list_nth_mut_back
+  (t : Type0) (l : list_t t) (i : u32) (ret : t) : result (list_t t) =
+  begin match l with
+  | List_Cons x tl ->
+    if i = 0
+    then Return (List_Cons ret tl)
+    else
+      let* i1 = u32_sub i 1 in
+      let* tl1 = list_nth_mut_back t tl i1 ret in
+      Return (List_Cons x tl1)
+  | List_Nil -> Fail Failure
+  end
+
+(** [no_nested_borrows::list_rev_aux]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 379:0-379:63 *)
+let rec list_rev_aux
+  (t : Type0) (li : list_t t) (lo : list_t t) : result (list_t t) =
+  begin match li with
+  | 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 ())
+    Source: 'src/no_nested_borrows.rs', lines 393:0-393:42 *)
+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
+    Source: 'src/no_nested_borrows.rs', lines 398:0-398:28 *)
+let test_list_functions : result unit =
+  let l = List_Cons 2 List_Nil in
+  let l1 = List_Cons 1 l in
+  let* i = list_length i32 (List_Cons 0 l1) in
+  if not (i = 3)
+  then Fail Failure
+  else
+    let* i1 = list_nth_shared i32 (List_Cons 0 l1) 0 in
+    if not (i1 = 0)
+    then Fail Failure
+    else
+      let* i2 = list_nth_shared i32 (List_Cons 0 l1) 1 in
+      if not (i2 = 1)
+      then Fail Failure
+      else
+        let* i3 = list_nth_shared i32 (List_Cons 0 l1) 2 in
+        if not (i3 = 2)
+        then Fail Failure
+        else
+          let* ls = list_nth_mut_back i32 (List_Cons 0 l1) 1 3 in
+          let* i4 = list_nth_shared i32 ls 0 in
+          if not (i4 = 0)
+          then Fail Failure
+          else
+            let* i5 = list_nth_shared i32 ls 1 in
+            if not (i5 = 3)
+            then Fail Failure
+            else
+              let* i6 = list_nth_shared i32 ls 2 in
+              if not (i6 = 2) then Fail Failure else Return ()
+
+(** Unit test for [no_nested_borrows::test_list_functions] *)
+let _ = assert_norm (test_list_functions = Return ())
+
+(** [no_nested_borrows::id_mut_pair1]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 414:0-414:89 *)
+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
+    Source: 'src/no_nested_borrows.rs', lines 414:0-414:89 *)
+let id_mut_pair1_back
+  (t1 t2 : Type0) (x : t1) (y : t2) (ret : (t1 & t2)) : result (t1 & t2) =
+  let (x1, x2) = ret in Return (x1, x2)
+
+(** [no_nested_borrows::id_mut_pair2]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 418:0-418:88 *)
+let id_mut_pair2 (t1 t2 : Type0) (p : (t1 & t2)) : result (t1 & t2) =
+  let (x, x1) = p in Return (x, x1)
+
+(** [no_nested_borrows::id_mut_pair2]: backward function 0
+    Source: 'src/no_nested_borrows.rs', lines 418:0-418:88 *)
+let id_mut_pair2_back
+  (t1 t2 : Type0) (p : (t1 & t2)) (ret : (t1 & t2)) : result (t1 & t2) =
+  let (x, x1) = ret in Return (x, x1)
+
+(** [no_nested_borrows::id_mut_pair3]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 422:0-422:93 *)
+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
+    Source: 'src/no_nested_borrows.rs', lines 422:0-422:93 *)
+let id_mut_pair3_back'a
+  (t1 t2 : Type0) (x : t1) (y : t2) (ret : t1) : result t1 =
+  Return ret
+
+(** [no_nested_borrows::id_mut_pair3]: backward function 1
+    Source: 'src/no_nested_borrows.rs', lines 422:0-422:93 *)
+let id_mut_pair3_back'b
+  (t1 t2 : Type0) (x : t1) (y : t2) (ret : t2) : result t2 =
+  Return ret
+
+(** [no_nested_borrows::id_mut_pair4]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 426:0-426:92 *)
+let id_mut_pair4 (t1 t2 : Type0) (p : (t1 & t2)) : result (t1 & t2) =
+  let (x, x1) = p in Return (x, x1)
+
+(** [no_nested_borrows::id_mut_pair4]: backward function 0
+    Source: 'src/no_nested_borrows.rs', lines 426:0-426:92 *)
+let id_mut_pair4_back'a
+  (t1 t2 : Type0) (p : (t1 & t2)) (ret : t1) : result t1 =
+  Return ret
+
+(** [no_nested_borrows::id_mut_pair4]: backward function 1
+    Source: 'src/no_nested_borrows.rs', lines 426:0-426:92 *)
+let id_mut_pair4_back'b
+  (t1 t2 : Type0) (p : (t1 & t2)) (ret : t2) : result t2 =
+  Return ret
+
+(** [no_nested_borrows::StructWithTuple]
+    Source: 'src/no_nested_borrows.rs', lines 433:0-433:34 *)
+type structWithTuple_t (t1 t2 : Type0) = { p : (t1 & t2); }
+
+(** [no_nested_borrows::new_tuple1]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 437:0-437:48 *)
+let new_tuple1 : result (structWithTuple_t u32 u32) =
+  Return { p = (1, 2) }
+
+(** [no_nested_borrows::new_tuple2]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 441:0-441:48 *)
+let new_tuple2 : result (structWithTuple_t i16 i16) =
+  Return { p = (1, 2) }
+
+(** [no_nested_borrows::new_tuple3]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 445:0-445:48 *)
+let new_tuple3 : result (structWithTuple_t u64 i64) =
+  Return { p = (1, 2) }
+
+(** [no_nested_borrows::StructWithPair]
+    Source: 'src/no_nested_borrows.rs', lines 450:0-450:33 *)
+type structWithPair_t (t1 t2 : Type0) = { p : pair_t t1 t2; }
+
+(** [no_nested_borrows::new_pair1]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 454:0-454:46 *)
+let new_pair1 : result (structWithPair_t u32 u32) =
+  Return { p = { x = 1; y = 2 } }
+
+(** [no_nested_borrows::test_constants]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 462:0-462:23 *)
+let test_constants : result unit =
+  let* swt = new_tuple1 in
+  let (i, _) = swt.p in
+  if not (i = 1)
+  then Fail Failure
+  else
+    let* swt1 = new_tuple2 in
+    let (i1, _) = swt1.p in
+    if not (i1 = 1)
+    then Fail Failure
+    else
+      let* swt2 = new_tuple3 in
+      let (i2, _) = swt2.p in
+      if not (i2 = 1)
+      then Fail Failure
+      else
+        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 = Return ())
+
+(** [no_nested_borrows::test_weird_borrows1]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 471:0-471:28 *)
+let test_weird_borrows1 : result unit =
+  Return ()
+
+(** Unit test for [no_nested_borrows::test_weird_borrows1] *)
+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 ())
+    Source: 'src/no_nested_borrows.rs', lines 481:0-481:37 *)
+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
+    Source: 'src/no_nested_borrows.rs', lines 488:0-488:47 *)
+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
+    Source: 'src/no_nested_borrows.rs', lines 501:0-501:40 *)
+let test_shared_borrow_bool2 : result u32 =
+  Return 0
+
+(** [no_nested_borrows::test_shared_borrow_enum1]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 516:0-516:52 *)
+let test_shared_borrow_enum1 (l : list_t u32) : result u32 =
+  begin match l with | List_Cons _ _ -> Return 1 | List_Nil -> Return 0 end
+
+(** [no_nested_borrows::test_shared_borrow_enum2]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 528:0-528:40 *)
+let test_shared_borrow_enum2 : result u32 =
+  Return 0
+
+(** [no_nested_borrows::incr]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ())
+    Source: 'src/no_nested_borrows.rs', lines 539:0-539:24 *)
+let incr (x : u32) : result u32 =
+  u32_add x 1
+
+(** [no_nested_borrows::call_incr]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 543:0-543:35 *)
+let call_incr (x : u32) : result u32 =
+  incr x
+
+(** [no_nested_borrows::read_then_incr]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 548:0-548:41 *)
+let read_then_incr (x : u32) : result u32 =
+  let* _ = u32_add x 1 in Return x
+
+(** [no_nested_borrows::read_then_incr]: backward function 0
+    Source: 'src/no_nested_borrows.rs', lines 548:0-548:41 *)
+let read_then_incr_back (x : u32) : result u32 =
+  u32_add x 1
+
+(** [no_nested_borrows::Tuple]
+    Source: 'src/no_nested_borrows.rs', lines 554:0-554:24 *)
+type tuple_t (t1 t2 : Type0) = t1 * t2
+
+(** [no_nested_borrows::use_tuple_struct]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ())
+    Source: 'src/no_nested_borrows.rs', lines 556:0-556:48 *)
+let use_tuple_struct (x : tuple_t u32 u32) : result (tuple_t u32 u32) =
+  let (_, i) = x in Return (1, i)
+
+(** [no_nested_borrows::create_tuple_struct]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 560:0-560:61 *)
+let create_tuple_struct (x : u32) (y : u64) : result (tuple_t u32 u64) =
+  Return (x, y)
+
+(** [no_nested_borrows::IdType]
+    Source: 'src/no_nested_borrows.rs', lines 565:0-565:20 *)
+type idType_t (t : Type0) = t
+
+(** [no_nested_borrows::use_id_type]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 567:0-567:40 *)
+let use_id_type (t : Type0) (x : idType_t t) : result t =
+  Return x
+
+(** [no_nested_borrows::create_id_type]: forward function
+    Source: 'src/no_nested_borrows.rs', lines 571:0-571:43 *)
+let create_id_type (t : Type0) (x : t) : result (idType_t t) =
+  Return x
+
diff --git a/tests/fstar-split/misc/Paper.fst b/tests/fstar-split/misc/Paper.fst
new file mode 100644
index 00000000..0c44d78b
--- /dev/null
+++ b/tests/fstar-split/misc/Paper.fst
@@ -0,0 +1,109 @@
+(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
+(** [paper] *)
+module Paper
+open Primitives
+
+#set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
+
+(** [paper::ref_incr]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ())
+    Source: 'src/paper.rs', lines 4:0-4:28 *)
+let ref_incr (x : i32) : result i32 =
+  i32_add x 1
+
+(** [paper::test_incr]: forward function
+    Source: 'src/paper.rs', lines 8:0-8:18 *)
+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 = Return ())
+
+(** [paper::choose]: forward function
+    Source: 'src/paper.rs', lines 15:0-15:70 *)
+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
+    Source: 'src/paper.rs', lines 15:0-15:70 *)
+let choose_back
+  (t : Type0) (b : bool) (x : t) (y : t) (ret : t) : result (t & t) =
+  if b then Return (ret, y) else Return (x, ret)
+
+(** [paper::test_choose]: forward function
+    Source: 'src/paper.rs', lines 23:0-23:20 *)
+let test_choose : result unit =
+  let* z = choose i32 true 0 0 in
+  let* z1 = i32_add z 1 in
+  if not (z1 = 1)
+  then Fail Failure
+  else
+    let* (x, y) = choose_back i32 true 0 0 z1 in
+    if not (x = 1)
+    then Fail Failure
+    else if not (y = 0) then Fail Failure else Return ()
+
+(** Unit test for [paper::test_choose] *)
+let _ = assert_norm (test_choose = Return ())
+
+(** [paper::List]
+    Source: 'src/paper.rs', lines 35:0-35:16 *)
+type list_t (t : Type0) =
+| List_Cons : t -> list_t t -> list_t t
+| List_Nil : list_t t
+
+(** [paper::list_nth_mut]: forward function
+    Source: 'src/paper.rs', lines 42:0-42:67 *)
+let rec list_nth_mut (t : Type0) (l : list_t t) (i : u32) : result t =
+  begin match l with
+  | List_Cons x tl ->
+    if i = 0 then Return x else let* i1 = u32_sub i 1 in list_nth_mut t tl i1
+  | List_Nil -> Fail Failure
+  end
+
+(** [paper::list_nth_mut]: backward function 0
+    Source: 'src/paper.rs', lines 42:0-42:67 *)
+let rec list_nth_mut_back
+  (t : Type0) (l : list_t t) (i : u32) (ret : t) : result (list_t t) =
+  begin match l with
+  | List_Cons x tl ->
+    if i = 0
+    then Return (List_Cons ret tl)
+    else
+      let* i1 = u32_sub i 1 in
+      let* tl1 = list_nth_mut_back t tl i1 ret in
+      Return (List_Cons x tl1)
+  | List_Nil -> Fail Failure
+  end
+
+(** [paper::sum]: forward function
+    Source: 'src/paper.rs', lines 57:0-57:32 *)
+let rec sum (l : list_t i32) : result i32 =
+  begin match l with
+  | List_Cons x tl -> let* i = sum tl in i32_add x i
+  | List_Nil -> Return 0
+  end
+
+(** [paper::test_nth]: forward function
+    Source: 'src/paper.rs', lines 68:0-68:17 *)
+let test_nth : result unit =
+  let l = List_Cons 3 List_Nil in
+  let l1 = List_Cons 2 l in
+  let* x = list_nth_mut i32 (List_Cons 1 l1) 2 in
+  let* x1 = i32_add x 1 in
+  let* l2 = list_nth_mut_back i32 (List_Cons 1 l1) 2 x1 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 = Return ())
+
+(** [paper::call_choose]: forward function
+    Source: 'src/paper.rs', lines 76:0-76:44 *)
+let call_choose (p : (u32 & u32)) : result u32 =
+  let (px, py) = p in
+  let* pz = choose u32 true px py in
+  let* pz1 = u32_add pz 1 in
+  let* (px1, _) = choose_back u32 true px py pz1 in
+  Return px1
+
diff --git a/tests/fstar-split/misc/PoloniusList.fst b/tests/fstar-split/misc/PoloniusList.fst
new file mode 100644
index 00000000..8a8b7ae3
--- /dev/null
+++ b/tests/fstar-split/misc/PoloniusList.fst
@@ -0,0 +1,34 @@
+(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
+(** [polonius_list] *)
+module PoloniusList
+open Primitives
+
+#set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
+
+(** [polonius_list::List]
+    Source: 'src/polonius_list.rs', lines 3:0-3:16 *)
+type list_t (t : Type0) =
+| List_Cons : t -> list_t t -> list_t t
+| List_Nil : list_t t
+
+(** [polonius_list::get_list_at_x]: forward function
+    Source: 'src/polonius_list.rs', lines 13:0-13:76 *)
+let rec get_list_at_x (ls : list_t u32) (x : u32) : result (list_t u32) =
+  begin match ls with
+  | 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
+    Source: 'src/polonius_list.rs', lines 13:0-13:76 *)
+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
+  | List_Cons hd tl ->
+    if hd = x
+    then Return ret
+    else let* tl1 = get_list_at_x_back tl x ret in Return (List_Cons hd tl1)
+  | List_Nil -> Return ret
+  end
+
diff --git a/tests/fstar-split/misc/Primitives.fst b/tests/fstar-split/misc/Primitives.fst
new file mode 100644
index 00000000..a3ffbde4
--- /dev/null
+++ b/tests/fstar-split/misc/Primitives.fst
@@ -0,0 +1,884 @@
+/// 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
+
+assume val size_numbits : pos
+
+// TODO: we could use FStar.Int.int_t and FStar.UInt.int_t
+
+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_xor (#ty : scalar_ty)
+    (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
+  | Usize -> admit() // TODO
+  | I8 ->
+    // Encoding issues...
+    normalize_spec (FStar.Int.int_t 8);
+    normalize_spec (scalar I8);
+    FStar.Int.logxor #8 x y
+  | I16 ->
+    // Encoding issues...
+    normalize_spec (FStar.Int.int_t 16);
+    normalize_spec (scalar I16);
+    FStar.Int.logxor #16 x y
+  | I32 -> FStar.Int.logxor #32 x y
+  | I64 -> FStar.Int.logxor #64 x y
+  | I128 ->
+    // Encoding issues...
+    normalize_spec (FStar.Int.int_t 128);
+    normalize_spec (scalar I128);
+    FStar.Int.logxor #128 x y
+  | Isize -> admit() // TODO
+
+let scalar_or (#ty : scalar_ty)
+    (x : scalar ty) (y : scalar ty) : scalar ty =
+  match ty with
+  | U8 -> FStar.UInt.logor #8 x y
+  | U16 -> FStar.UInt.logor #16 x y
+  | U32 -> FStar.UInt.logor #32 x y
+  | U64 -> FStar.UInt.logor #64 x y
+  | U128 -> FStar.UInt.logor #128 x y
+  | Usize -> admit() // TODO
+  | I8 ->
+    // Encoding issues...
+    normalize_spec (FStar.Int.int_t 8);
+    normalize_spec (scalar I8);
+    FStar.Int.logor #8 x y
+  | I16 ->
+    // Encoding issues...
+    normalize_spec (FStar.Int.int_t 16);
+    normalize_spec (scalar I16);
+    FStar.Int.logor #16 x y
+  | I32 -> FStar.Int.logor #32 x y
+  | I64 -> FStar.Int.logor #64 x y
+  | I128 ->
+    // Encoding issues...
+    normalize_spec (FStar.Int.int_t 128);
+    normalize_spec (scalar I128);
+    FStar.Int.logor #128 x y
+  | Isize -> admit() // TODO
+
+let scalar_and (#ty : scalar_ty)
+    (x : scalar ty) (y : scalar ty) : scalar ty =
+  match ty with
+  | U8 -> FStar.UInt.logand #8 x y
+  | U16 -> FStar.UInt.logand #16 x y
+  | U32 -> FStar.UInt.logand #32 x y
+  | U64 -> FStar.UInt.logand #64 x y
+  | U128 -> FStar.UInt.logand #128 x y
+  | Usize -> admit() // TODO
+  | I8 ->
+    // Encoding issues...
+    normalize_spec (FStar.Int.int_t 8);
+    normalize_spec (scalar I8);
+    FStar.Int.logand #8 x y
+  | I16 ->
+    // Encoding issues...
+    normalize_spec (FStar.Int.int_t 16);
+    normalize_spec (scalar I16);
+    FStar.Int.logand #16 x y
+  | I32 -> FStar.Int.logand #32 x y
+  | I64 -> FStar.Int.logand #64 x y
+  | I128 ->
+    // Encoding issues...
+    normalize_spec (FStar.Int.int_t 128);
+    normalize_spec (scalar I128);
+    FStar.Int.logand #128 x y
+  | Isize -> admit() // TODO
+
+// Shift left
+let scalar_shl (#ty0 #ty1 : scalar_ty)
+    (x : scalar ty0) (y : scalar ty1) : result (scalar ty0) =
+  admit()
+
+// Shift right
+let scalar_shr (#ty0 #ty1 : scalar_ty)
+    (x : scalar ty0) (y : scalar ty1) : result (scalar ty0) =
+  admit()
+
+(** 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
+
+// This can't fail, but for now we make all casts faillible (easier for the translation)
+let scalar_cast_bool (tgt_ty : scalar_ty) (x : bool) : result (scalar tgt_ty) =
+  mk_scalar tgt_ty (if x then 1 else 0)
+
+/// 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
+
+/// Xor
+let u8_xor = scalar_xor #U8
+let u16_xor = scalar_xor #U16
+let u32_xor = scalar_xor #U32
+let u64_xor = scalar_xor #U64
+let u128_xor = scalar_xor #U128
+let usize_xor = scalar_xor #Usize
+let i8_xor = scalar_xor #I8
+let i16_xor = scalar_xor #I16
+let i32_xor = scalar_xor #I32
+let i64_xor = scalar_xor #I64
+let i128_xor = scalar_xor #I128
+let isize_xor = scalar_xor #Isize
+
+/// Or
+let u8_or = scalar_or #U8
+let u16_or = scalar_or #U16
+let u32_or = scalar_or #U32
+let u64_or = scalar_or #U64
+let u128_or = scalar_or #U128
+let usize_or = scalar_or #Usize
+let i8_or = scalar_or #I8
+let i16_or = scalar_or #I16
+let i32_or = scalar_or #I32
+let i64_or = scalar_or #I64
+let i128_or = scalar_or #I128
+let isize_or = scalar_or #Isize
+
+/// And
+let u8_and = scalar_and #U8
+let u16_and = scalar_and #U16
+let u32_and = scalar_and #U32
+let u64_and = scalar_and #U64
+let u128_and = scalar_and #U128
+let usize_and = scalar_and #Usize
+let i8_and = scalar_and #I8
+let i16_and = scalar_and #I16
+let i32_and = scalar_and #I32
+let i64_and = scalar_and #I64
+let i128_and = scalar_and #I128
+let isize_and = scalar_and #Isize
+
+/// Shift left
+let u8_shl #ty = scalar_shl #U8 #ty
+let u16_shl #ty = scalar_shl #U16 #ty
+let u32_shl #ty = scalar_shl #U32 #ty
+let u64_shl #ty = scalar_shl #U64 #ty
+let u128_shl #ty = scalar_shl #U128 #ty
+let usize_shl #ty = scalar_shl #Usize #ty
+let i8_shl #ty = scalar_shl #I8 #ty
+let i16_shl #ty = scalar_shl #I16 #ty
+let i32_shl #ty = scalar_shl #I32 #ty
+let i64_shl #ty = scalar_shl #I64 #ty
+let i128_shl #ty = scalar_shl #I128 #ty
+let isize_shl #ty = scalar_shl #Isize #ty
+
+/// Shift right
+let u8_shr #ty = scalar_shr #U8 #ty
+let u16_shr #ty = scalar_shr #U16 #ty
+let u32_shr #ty = scalar_shr #U32 #ty
+let u64_shr #ty = scalar_shr #U64 #ty
+let u128_shr #ty = scalar_shr #U128 #ty
+let usize_shr #ty = scalar_shr #Usize #ty
+let i8_shr #ty = scalar_shr #I8 #ty
+let i16_shr #ty = scalar_shr #I16 #ty
+let i32_shr #ty = scalar_shr #I32 #ty
+let i64_shr #ty = scalar_shr #I64 #ty
+let i128_shr #ty = scalar_shr #I128 #ty
+let isize_shr #ty = scalar_shr #Isize #ty
+
+(*** 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_RangeUsize_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_RangeUsize_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_RangeUsize_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_RangeUsize_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_RangeUsize_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_RangeUsize_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_RangeUsize_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_RangeUsize_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::private_slice_index::Range]
+let core_slice_index_private_slice_index_SealedRangeUsizeInst
+  : core_slice_index_private_slice_index_Sealed (core_ops_range_Range usize) = ()
+
+// Trait implementation: [core::slice::index::Range]
+let core_slice_index_SliceIndexRangeUsizeSliceTInst (t : Type0) :
+  core_slice_index_SliceIndex (core_ops_range_Range usize) (slice t) = {
+  sealedInst = core_slice_index_private_slice_index_SealedRangeUsizeInst;
+  output = slice t;
+  get = core_slice_index_RangeUsize_get t;
+  get_mut = core_slice_index_RangeUsize_get_mut t;
+  get_mut_back = core_slice_index_RangeUsize_get_mut_back t;
+  get_unchecked = core_slice_index_RangeUsize_get_unchecked t;
+  get_unchecked_mut = core_slice_index_RangeUsize_get_unchecked_mut t;
+  index = core_slice_index_RangeUsize_index t;
+  index_mut = core_slice_index_RangeUsize_index_mut t;
+  index_mut_back = core_slice_index_RangeUsize_index_mut_back t;
+}
+
+// Trait implementation: [core::slice::index::[T]]
+let core_ops_index_IndexSliceTIInst (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::[T]]
+let core_ops_index_IndexMutSliceTIInst (t idx : Type0)
+  (inst : core_slice_index_SliceIndex idx (slice t)) :
+  core_ops_index_IndexMut (slice t) idx = {
+  indexInst = core_ops_index_IndexSliceTIInst 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_ops_index_IndexArrayInst (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_ops_index_IndexMutArrayIInst (t idx : Type0) (n : usize)
+  (inst : core_ops_index_IndexMut (slice t) idx) :
+  core_ops_index_IndexMut (array t n) idx = {
+  indexInst = core_ops_index_IndexArrayInst 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_SealedUsizeInst
+  : core_slice_index_private_slice_index_Sealed usize = ()
+
+// Trait implementation: [core::slice::index::usize]
+let core_slice_index_SliceIndexUsizeSliceTInst (t : Type0) :
+  core_slice_index_SliceIndex usize (slice t) = {
+  sealedInst = core_slice_index_private_slice_index_SealedUsizeInst;
+  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_SliceIndexUsizeSliceTInst a) v i ==
+      alloc_vec_Vec_index_usize v i)
+  [SMTPat (alloc_vec_Vec_index a usize (core_slice_index_SliceIndexUsizeSliceTInst 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_SliceIndexUsizeSliceTInst a) v i ==
+      alloc_vec_Vec_index_usize v i)
+  [SMTPat (alloc_vec_Vec_index_mut a usize (core_slice_index_SliceIndexUsizeSliceTInst 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_SliceIndexUsizeSliceTInst a) v i x ==
+      alloc_vec_Vec_update_usize v i x)
+  [SMTPat (alloc_vec_Vec_index_mut_back a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i x)]
+  =
+  admit()
diff --git a/tests/fstar-split/traits/Makefile b/tests/fstar-split/traits/Makefile
new file mode 100644
index 00000000..fa7d1f36
--- /dev/null
+++ b/tests/fstar-split/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-split/traits/Primitives.fst b/tests/fstar-split/traits/Primitives.fst
new file mode 100644
index 00000000..a3ffbde4
--- /dev/null
+++ b/tests/fstar-split/traits/Primitives.fst
@@ -0,0 +1,884 @@
+/// 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
+
+assume val size_numbits : pos
+
+// TODO: we could use FStar.Int.int_t and FStar.UInt.int_t
+
+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_xor (#ty : scalar_ty)
+    (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
+  | Usize -> admit() // TODO
+  | I8 ->
+    // Encoding issues...
+    normalize_spec (FStar.Int.int_t 8);
+    normalize_spec (scalar I8);
+    FStar.Int.logxor #8 x y
+  | I16 ->
+    // Encoding issues...
+    normalize_spec (FStar.Int.int_t 16);
+    normalize_spec (scalar I16);
+    FStar.Int.logxor #16 x y
+  | I32 -> FStar.Int.logxor #32 x y
+  | I64 -> FStar.Int.logxor #64 x y
+  | I128 ->
+    // Encoding issues...
+    normalize_spec (FStar.Int.int_t 128);
+    normalize_spec (scalar I128);
+    FStar.Int.logxor #128 x y
+  | Isize -> admit() // TODO
+
+let scalar_or (#ty : scalar_ty)
+    (x : scalar ty) (y : scalar ty) : scalar ty =
+  match ty with
+  | U8 -> FStar.UInt.logor #8 x y
+  | U16 -> FStar.UInt.logor #16 x y
+  | U32 -> FStar.UInt.logor #32 x y
+  | U64 -> FStar.UInt.logor #64 x y
+  | U128 -> FStar.UInt.logor #128 x y
+  | Usize -> admit() // TODO
+  | I8 ->
+    // Encoding issues...
+    normalize_spec (FStar.Int.int_t 8);
+    normalize_spec (scalar I8);
+    FStar.Int.logor #8 x y
+  | I16 ->
+    // Encoding issues...
+    normalize_spec (FStar.Int.int_t 16);
+    normalize_spec (scalar I16);
+    FStar.Int.logor #16 x y
+  | I32 -> FStar.Int.logor #32 x y
+  | I64 -> FStar.Int.logor #64 x y
+  | I128 ->
+    // Encoding issues...
+    normalize_spec (FStar.Int.int_t 128);
+    normalize_spec (scalar I128);
+    FStar.Int.logor #128 x y
+  | Isize -> admit() // TODO
+
+let scalar_and (#ty : scalar_ty)
+    (x : scalar ty) (y : scalar ty) : scalar ty =
+  match ty with
+  | U8 -> FStar.UInt.logand #8 x y
+  | U16 -> FStar.UInt.logand #16 x y
+  | U32 -> FStar.UInt.logand #32 x y
+  | U64 -> FStar.UInt.logand #64 x y
+  | U128 -> FStar.UInt.logand #128 x y
+  | Usize -> admit() // TODO
+  | I8 ->
+    // Encoding issues...
+    normalize_spec (FStar.Int.int_t 8);
+    normalize_spec (scalar I8);
+    FStar.Int.logand #8 x y
+  | I16 ->
+    // Encoding issues...
+    normalize_spec (FStar.Int.int_t 16);
+    normalize_spec (scalar I16);
+    FStar.Int.logand #16 x y
+  | I32 -> FStar.Int.logand #32 x y
+  | I64 -> FStar.Int.logand #64 x y
+  | I128 ->
+    // Encoding issues...
+    normalize_spec (FStar.Int.int_t 128);
+    normalize_spec (scalar I128);
+    FStar.Int.logand #128 x y
+  | Isize -> admit() // TODO
+
+// Shift left
+let scalar_shl (#ty0 #ty1 : scalar_ty)
+    (x : scalar ty0) (y : scalar ty1) : result (scalar ty0) =
+  admit()
+
+// Shift right
+let scalar_shr (#ty0 #ty1 : scalar_ty)
+    (x : scalar ty0) (y : scalar ty1) : result (scalar ty0) =
+  admit()
+
+(** 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
+
+// This can't fail, but for now we make all casts faillible (easier for the translation)
+let scalar_cast_bool (tgt_ty : scalar_ty) (x : bool) : result (scalar tgt_ty) =
+  mk_scalar tgt_ty (if x then 1 else 0)
+
+/// 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
+
+/// Xor
+let u8_xor = scalar_xor #U8
+let u16_xor = scalar_xor #U16
+let u32_xor = scalar_xor #U32
+let u64_xor = scalar_xor #U64
+let u128_xor = scalar_xor #U128
+let usize_xor = scalar_xor #Usize
+let i8_xor = scalar_xor #I8
+let i16_xor = scalar_xor #I16
+let i32_xor = scalar_xor #I32
+let i64_xor = scalar_xor #I64
+let i128_xor = scalar_xor #I128
+let isize_xor = scalar_xor #Isize
+
+/// Or
+let u8_or = scalar_or #U8
+let u16_or = scalar_or #U16
+let u32_or = scalar_or #U32
+let u64_or = scalar_or #U64
+let u128_or = scalar_or #U128
+let usize_or = scalar_or #Usize
+let i8_or = scalar_or #I8
+let i16_or = scalar_or #I16
+let i32_or = scalar_or #I32
+let i64_or = scalar_or #I64
+let i128_or = scalar_or #I128
+let isize_or = scalar_or #Isize
+
+/// And
+let u8_and = scalar_and #U8
+let u16_and = scalar_and #U16
+let u32_and = scalar_and #U32
+let u64_and = scalar_and #U64
+let u128_and = scalar_and #U128
+let usize_and = scalar_and #Usize
+let i8_and = scalar_and #I8
+let i16_and = scalar_and #I16
+let i32_and = scalar_and #I32
+let i64_and = scalar_and #I64
+let i128_and = scalar_and #I128
+let isize_and = scalar_and #Isize
+
+/// Shift left
+let u8_shl #ty = scalar_shl #U8 #ty
+let u16_shl #ty = scalar_shl #U16 #ty
+let u32_shl #ty = scalar_shl #U32 #ty
+let u64_shl #ty = scalar_shl #U64 #ty
+let u128_shl #ty = scalar_shl #U128 #ty
+let usize_shl #ty = scalar_shl #Usize #ty
+let i8_shl #ty = scalar_shl #I8 #ty
+let i16_shl #ty = scalar_shl #I16 #ty
+let i32_shl #ty = scalar_shl #I32 #ty
+let i64_shl #ty = scalar_shl #I64 #ty
+let i128_shl #ty = scalar_shl #I128 #ty
+let isize_shl #ty = scalar_shl #Isize #ty
+
+/// Shift right
+let u8_shr #ty = scalar_shr #U8 #ty
+let u16_shr #ty = scalar_shr #U16 #ty
+let u32_shr #ty = scalar_shr #U32 #ty
+let u64_shr #ty = scalar_shr #U64 #ty
+let u128_shr #ty = scalar_shr #U128 #ty
+let usize_shr #ty = scalar_shr #Usize #ty
+let i8_shr #ty = scalar_shr #I8 #ty
+let i16_shr #ty = scalar_shr #I16 #ty
+let i32_shr #ty = scalar_shr #I32 #ty
+let i64_shr #ty = scalar_shr #I64 #ty
+let i128_shr #ty = scalar_shr #I128 #ty
+let isize_shr #ty = scalar_shr #Isize #ty
+
+(*** 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_RangeUsize_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_RangeUsize_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_RangeUsize_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_RangeUsize_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_RangeUsize_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_RangeUsize_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_RangeUsize_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_RangeUsize_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::private_slice_index::Range]
+let core_slice_index_private_slice_index_SealedRangeUsizeInst
+  : core_slice_index_private_slice_index_Sealed (core_ops_range_Range usize) = ()
+
+// Trait implementation: [core::slice::index::Range]
+let core_slice_index_SliceIndexRangeUsizeSliceTInst (t : Type0) :
+  core_slice_index_SliceIndex (core_ops_range_Range usize) (slice t) = {
+  sealedInst = core_slice_index_private_slice_index_SealedRangeUsizeInst;
+  output = slice t;
+  get = core_slice_index_RangeUsize_get t;
+  get_mut = core_slice_index_RangeUsize_get_mut t;
+  get_mut_back = core_slice_index_RangeUsize_get_mut_back t;
+  get_unchecked = core_slice_index_RangeUsize_get_unchecked t;
+  get_unchecked_mut = core_slice_index_RangeUsize_get_unchecked_mut t;
+  index = core_slice_index_RangeUsize_index t;
+  index_mut = core_slice_index_RangeUsize_index_mut t;
+  index_mut_back = core_slice_index_RangeUsize_index_mut_back t;
+}
+
+// Trait implementation: [core::slice::index::[T]]
+let core_ops_index_IndexSliceTIInst (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::[T]]
+let core_ops_index_IndexMutSliceTIInst (t idx : Type0)
+  (inst : core_slice_index_SliceIndex idx (slice t)) :
+  core_ops_index_IndexMut (slice t) idx = {
+  indexInst = core_ops_index_IndexSliceTIInst 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_ops_index_IndexArrayInst (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_ops_index_IndexMutArrayIInst (t idx : Type0) (n : usize)
+  (inst : core_ops_index_IndexMut (slice t) idx) :
+  core_ops_index_IndexMut (array t n) idx = {
+  indexInst = core_ops_index_IndexArrayInst 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_SealedUsizeInst
+  : core_slice_index_private_slice_index_Sealed usize = ()
+
+// Trait implementation: [core::slice::index::usize]
+let core_slice_index_SliceIndexUsizeSliceTInst (t : Type0) :
+  core_slice_index_SliceIndex usize (slice t) = {
+  sealedInst = core_slice_index_private_slice_index_SealedUsizeInst;
+  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_SliceIndexUsizeSliceTInst a) v i ==
+      alloc_vec_Vec_index_usize v i)
+  [SMTPat (alloc_vec_Vec_index a usize (core_slice_index_SliceIndexUsizeSliceTInst 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_SliceIndexUsizeSliceTInst a) v i ==
+      alloc_vec_Vec_index_usize v i)
+  [SMTPat (alloc_vec_Vec_index_mut a usize (core_slice_index_SliceIndexUsizeSliceTInst 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_SliceIndexUsizeSliceTInst a) v i x ==
+      alloc_vec_Vec_update_usize v i x)
+  [SMTPat (alloc_vec_Vec_index_mut_back a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i x)]
+  =
+  admit()
diff --git a/tests/fstar-split/traits/Traits.fst b/tests/fstar-split/traits/Traits.fst
new file mode 100644
index 00000000..d3847590
--- /dev/null
+++ b/tests/fstar-split/traits/Traits.fst
@@ -0,0 +1,476 @@
+(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
+(** [traits] *)
+module Traits
+open Primitives
+
+#set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
+
+(** Trait declaration: [traits::BoolTrait]
+    Source: 'src/traits.rs', lines 1:0-1:19 *)
+noeq type boolTrait_t (self : Type0) = { get_bool : self -> result bool; }
+
+(** [traits::{bool}::get_bool]: forward function
+    Source: 'src/traits.rs', lines 12:4-12:30 *)
+let bool_get_bool (self : bool) : result bool =
+  Return self
+
+(** Trait implementation: [traits::{bool}]
+    Source: 'src/traits.rs', lines 11:0-11:23 *)
+let traits_BoolTraitBoolInst : boolTrait_t bool = { get_bool = bool_get_bool; }
+
+(** [traits::BoolTrait::ret_true]: forward function
+    Source: 'src/traits.rs', lines 6:4-6:30 *)
+let boolTrait_ret_true
+  (#self : Type0) (self_clause : boolTrait_t self) (self1 : self) :
+  result bool
+  =
+  Return true
+
+(** [traits::test_bool_trait_bool]: forward function
+    Source: 'src/traits.rs', lines 17:0-17:44 *)
+let test_bool_trait_bool (x : bool) : result bool =
+  let* b = bool_get_bool x in
+  if b then boolTrait_ret_true traits_BoolTraitBoolInst x else Return false
+
+(** [traits::{core::option::Option<T>#1}::get_bool]: forward function
+    Source: 'src/traits.rs', lines 23:4-23:30 *)
+let option_get_bool (t : Type0) (self : option t) : result bool =
+  begin match self with | None -> Return false | Some _ -> Return true end
+
+(** Trait implementation: [traits::{core::option::Option<T>#1}]
+    Source: 'src/traits.rs', lines 22:0-22:31 *)
+let traits_BoolTraitcoreoptionOptionTInst (t : Type0) : boolTrait_t (option t)
+  = {
+  get_bool = option_get_bool t;
+}
+
+(** [traits::test_bool_trait_option]: forward function
+    Source: 'src/traits.rs', lines 31:0-31:54 *)
+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 (traits_BoolTraitcoreoptionOptionTInst t) x
+  else Return false
+
+(** [traits::test_bool_trait]: forward function
+    Source: 'src/traits.rs', lines 35:0-35:50 *)
+let test_bool_trait
+  (t : Type0) (boolTraitTInst : boolTrait_t t) (x : t) : result bool =
+  boolTraitTInst.get_bool x
+
+(** Trait declaration: [traits::ToU64]
+    Source: 'src/traits.rs', lines 39:0-39:15 *)
+noeq type toU64_t (self : Type0) = { to_u64 : self -> result u64; }
+
+(** [traits::{u64#2}::to_u64]: forward function
+    Source: 'src/traits.rs', lines 44:4-44:26 *)
+let u64_to_u64 (self : u64) : result u64 =
+  Return self
+
+(** Trait implementation: [traits::{u64#2}]
+    Source: 'src/traits.rs', lines 43:0-43:18 *)
+let traits_ToU64U64Inst : toU64_t u64 = { to_u64 = u64_to_u64; }
+
+(** [traits::{(A, A)#3}::to_u64]: forward function
+    Source: 'src/traits.rs', lines 50:4-50:26 *)
+let pair_to_u64
+  (a : Type0) (toU64AInst : toU64_t a) (self : (a & a)) : result u64 =
+  let (x, x1) = self in
+  let* i = toU64AInst.to_u64 x in
+  let* i1 = toU64AInst.to_u64 x1 in
+  u64_add i i1
+
+(** Trait implementation: [traits::{(A, A)#3}]
+    Source: 'src/traits.rs', lines 49:0-49:31 *)
+let traits_ToU64TupleAAInst (a : Type0) (toU64AInst : toU64_t a) : toU64_t (a &
+  a) = {
+  to_u64 = pair_to_u64 a toU64AInst;
+}
+
+(** [traits::f]: forward function
+    Source: 'src/traits.rs', lines 55:0-55:36 *)
+let f (t : Type0) (toU64TInst : toU64_t t) (x : (t & t)) : result u64 =
+  pair_to_u64 t toU64TInst x
+
+(** [traits::g]: forward function
+    Source: 'src/traits.rs', lines 59:0-61:18 *)
+let g
+  (t : Type0) (toU64TupleTTInst : toU64_t (t & t)) (x : (t & t)) : result u64 =
+  toU64TupleTTInst.to_u64 x
+
+(** [traits::h0]: forward function
+    Source: 'src/traits.rs', lines 66:0-66:24 *)
+let h0 (x : u64) : result u64 =
+  u64_to_u64 x
+
+(** [traits::Wrapper]
+    Source: 'src/traits.rs', lines 70:0-70:21 *)
+type wrapper_t (t : Type0) = { x : t; }
+
+(** [traits::{traits::Wrapper<T>#4}::to_u64]: forward function
+    Source: 'src/traits.rs', lines 75:4-75:26 *)
+let wrapper_to_u64
+  (t : Type0) (toU64TInst : toU64_t t) (self : wrapper_t t) : result u64 =
+  toU64TInst.to_u64 self.x
+
+(** Trait implementation: [traits::{traits::Wrapper<T>#4}]
+    Source: 'src/traits.rs', lines 74:0-74:35 *)
+let traits_ToU64traitsWrapperTInst (t : Type0) (toU64TInst : toU64_t t) :
+  toU64_t (wrapper_t t) = {
+  to_u64 = wrapper_to_u64 t toU64TInst;
+}
+
+(** [traits::h1]: forward function
+    Source: 'src/traits.rs', lines 80:0-80:33 *)
+let h1 (x : wrapper_t u64) : result u64 =
+  wrapper_to_u64 u64 traits_ToU64U64Inst x
+
+(** [traits::h2]: forward function
+    Source: 'src/traits.rs', lines 84:0-84:41 *)
+let h2 (t : Type0) (toU64TInst : toU64_t t) (x : wrapper_t t) : result u64 =
+  wrapper_to_u64 t toU64TInst x
+
+(** Trait declaration: [traits::ToType]
+    Source: 'src/traits.rs', lines 88:0-88:19 *)
+noeq type toType_t (self t : Type0) = { to_type : self -> result t; }
+
+(** [traits::{u64#5}::to_type]: forward function
+    Source: 'src/traits.rs', lines 93:4-93:28 *)
+let u64_to_type (self : u64) : result bool =
+  Return (self > 0)
+
+(** Trait implementation: [traits::{u64#5}]
+    Source: 'src/traits.rs', lines 92:0-92:25 *)
+let traits_ToTypeU64BoolInst : toType_t u64 bool = { to_type = u64_to_type; }
+
+(** Trait declaration: [traits::OfType]
+    Source: 'src/traits.rs', lines 98:0-98:16 *)
+noeq type ofType_t (self : Type0) = {
+  of_type : (t : Type0) -> (toTypeTSelfInst : toType_t t self) -> t -> result
+    self;
+}
+
+(** [traits::h3]: forward function
+    Source: 'src/traits.rs', lines 104:0-104:50 *)
+let h3
+  (t1 t2 : Type0) (ofTypeT1Inst : ofType_t t1) (toTypeT2T1Inst : toType_t t2
+  t1) (y : t2) :
+  result t1
+  =
+  ofTypeT1Inst.of_type t2 toTypeT2T1Inst y
+
+(** Trait declaration: [traits::OfTypeBis]
+    Source: 'src/traits.rs', lines 109:0-109:36 *)
+noeq type ofTypeBis_t (self t : Type0) = {
+  toTypeTSelfInst : toType_t t self;
+  of_type : t -> result self;
+}
+
+(** [traits::h4]: forward function
+    Source: 'src/traits.rs', lines 118:0-118:57 *)
+let h4
+  (t1 t2 : Type0) (ofTypeBisT1T2Inst : ofTypeBis_t t1 t2) (toTypeT2T1Inst :
+  toType_t t2 t1) (y : t2) :
+  result t1
+  =
+  ofTypeBisT1T2Inst.of_type y
+
+(** [traits::TestType]
+    Source: 'src/traits.rs', lines 122:0-122:22 *)
+type testType_t (t : Type0) = t
+
+(** [traits::{traits::TestType<T>#6}::test::TestType1]
+    Source: 'src/traits.rs', lines 127:8-127:24 *)
+type testType_test_TestType1_t = u64
+
+(** Trait declaration: [traits::{traits::TestType<T>#6}::test::TestTrait]
+    Source: 'src/traits.rs', lines 128:8-128:23 *)
+noeq type testType_test_TestTrait_t (self : Type0) = {
+  test : self -> result bool;
+}
+
+(** [traits::{traits::TestType<T>#6}::test::{traits::{traits::TestType<T>#6}::test::TestType1}::test]: forward function
+    Source: 'src/traits.rs', lines 139:12-139:34 *)
+let testType_test_TestType1_test
+  (self : testType_test_TestType1_t) : result bool =
+  Return (self > 1)
+
+(** Trait implementation: [traits::{traits::TestType<T>#6}::test::{traits::{traits::TestType<T>#6}::test::TestType1}]
+    Source: 'src/traits.rs', lines 138:8-138:36 *)
+let traits_TestType_test_TestTraittraitstraitsTestTypeTtestTestType1Inst :
+  testType_test_TestTrait_t testType_test_TestType1_t = {
+  test = testType_test_TestType1_test;
+}
+
+(** [traits::{traits::TestType<T>#6}::test]: forward function
+    Source: 'src/traits.rs', lines 126:4-126:36 *)
+let testType_test
+  (t : Type0) (toU64TInst : toU64_t t) (self : testType_t t) (x : t) :
+  result bool
+  =
+  let* x1 = toU64TInst.to_u64 x in
+  if x1 > 0 then testType_test_TestType1_test 0 else Return false
+
+(** [traits::BoolWrapper]
+    Source: 'src/traits.rs', lines 150:0-150:22 *)
+type boolWrapper_t = bool
+
+(** [traits::{traits::BoolWrapper#7}::to_type]: forward function
+    Source: 'src/traits.rs', lines 156:4-156:25 *)
+let boolWrapper_to_type
+  (t : Type0) (toTypeBoolTInst : toType_t bool t) (self : boolWrapper_t) :
+  result t
+  =
+  toTypeBoolTInst.to_type self
+
+(** Trait implementation: [traits::{traits::BoolWrapper#7}]
+    Source: 'src/traits.rs', lines 152:0-152:33 *)
+let traits_ToTypetraitsBoolWrapperTInst (t : Type0) (toTypeBoolTInst : toType_t
+  bool t) : toType_t boolWrapper_t t = {
+  to_type = boolWrapper_to_type t toTypeBoolTInst;
+}
+
+(** [traits::WithConstTy::LEN2]
+    Source: 'src/traits.rs', lines 164:4-164:21 *)
+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]
+    Source: 'src/traits.rs', lines 161:0-161:39 *)
+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]
+    Source: 'src/traits.rs', lines 175:4-175:21 *)
+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 ())
+    Source: 'src/traits.rs', lines 180:4-180:39 *)
+let bool_f (i : u64) (a : array u8 32) : result u64 =
+  Return i
+
+(** Trait implementation: [traits::{bool#8}]
+    Source: 'src/traits.rs', lines 174:0-174:29 *)
+let traits_WithConstTyBool32Inst : withConstTy_t bool 32 = {
+  cLEN1 = bool_len1_c;
+  cLEN2 = with_const_ty_len2_c;
+  tV = u8;
+  tW = u64;
+  tW_clause_0 = traits_ToU64U64Inst;
+  f = bool_f;
+}
+
+(** [traits::use_with_const_ty1]: forward function
+    Source: 'src/traits.rs', lines 183:0-183:75 *)
+let use_with_const_ty1
+  (h : Type0) (len : usize) (withConstTyHLENInst : withConstTy_t h len) :
+  result usize
+  =
+  Return withConstTyHLENInst.cLEN1
+
+(** [traits::use_with_const_ty2]: forward function
+    Source: 'src/traits.rs', lines 187:0-187:73 *)
+let use_with_const_ty2
+  (h : Type0) (len : usize) (withConstTyHLENInst : withConstTy_t h len)
+  (w : withConstTyHLENInst.tW) :
+  result unit
+  =
+  Return ()
+
+(** [traits::use_with_const_ty3]: forward function
+    Source: 'src/traits.rs', lines 189:0-189:80 *)
+let use_with_const_ty3
+  (h : Type0) (len : usize) (withConstTyHLENInst : withConstTy_t h len)
+  (x : withConstTyHLENInst.tW) :
+  result u64
+  =
+  withConstTyHLENInst.tW_clause_0.to_u64 x
+
+(** [traits::test_where1]: forward function
+    Source: 'src/traits.rs', lines 193:0-193:40 *)
+let test_where1 (t : Type0) (_x : t) : result unit =
+  Return ()
+
+(** [traits::test_where2]: forward function
+    Source: 'src/traits.rs', lines 194:0-194:57 *)
+let test_where2
+  (t : Type0) (withConstTyT32Inst : withConstTy_t t 32) (_x : u32) :
+  result unit
+  =
+  Return ()
+
+(** Trait declaration: [traits::ParentTrait0]
+    Source: 'src/traits.rs', lines 200:0-200:22 *)
+noeq type parentTrait0_t (self : Type0) = {
+  tW : Type0;
+  get_name : self -> result string;
+  get_w : self -> result tW;
+}
+
+(** Trait declaration: [traits::ParentTrait1]
+    Source: 'src/traits.rs', lines 205:0-205:22 *)
+type parentTrait1_t (self : Type0) = unit
+
+(** Trait declaration: [traits::ChildTrait]
+    Source: 'src/traits.rs', lines 206:0-206:49 *)
+noeq type childTrait_t (self : Type0) = {
+  parentTrait0SelfInst : parentTrait0_t self;
+  parentTrait1SelfInst : parentTrait1_t self;
+}
+
+(** [traits::test_parent_trait0]: forward function
+    Source: 'src/traits.rs', lines 208:0-208:57 *)
+let test_parent_trait0
+  (t : Type0) (parentTrait0TInst : parentTrait0_t t) (x : t) :
+  result parentTrait0TInst.tW
+  =
+  parentTrait0TInst.get_w x
+
+(** [traits::test_child_trait1]: forward function
+    Source: 'src/traits.rs', lines 213:0-213:56 *)
+let test_child_trait1
+  (t : Type0) (childTraitTInst : childTrait_t t) (x : t) : result string =
+  childTraitTInst.parentTrait0SelfInst.get_name x
+
+(** [traits::test_child_trait2]: forward function
+    Source: 'src/traits.rs', lines 217:0-217:54 *)
+let test_child_trait2
+  (t : Type0) (childTraitTInst : childTrait_t t) (x : t) :
+  result childTraitTInst.parentTrait0SelfInst.tW
+  =
+  childTraitTInst.parentTrait0SelfInst.get_w x
+
+(** [traits::order1]: forward function
+    Source: 'src/traits.rs', lines 223:0-223:59 *)
+let order1
+  (t u : Type0) (parentTrait0TInst : parentTrait0_t t) (parentTrait0UInst :
+  parentTrait0_t u) :
+  result unit
+  =
+  Return ()
+
+(** Trait declaration: [traits::ChildTrait1]
+    Source: 'src/traits.rs', lines 226:0-226:35 *)
+noeq type childTrait1_t (self : Type0) = {
+  parentTrait1SelfInst : parentTrait1_t self;
+}
+
+(** Trait implementation: [traits::{usize#9}]
+    Source: 'src/traits.rs', lines 228:0-228:27 *)
+let traits_ParentTrait1UsizeInst : parentTrait1_t usize = ()
+
+(** Trait implementation: [traits::{usize#10}]
+    Source: 'src/traits.rs', lines 229:0-229:26 *)
+let traits_ChildTrait1UsizeInst : childTrait1_t usize = {
+  parentTrait1SelfInst = traits_ParentTrait1UsizeInst;
+}
+
+(** Trait declaration: [traits::Iterator]
+    Source: 'src/traits.rs', lines 233:0-233:18 *)
+noeq type iterator_t (self : Type0) = { tItem : Type0; }
+
+(** Trait declaration: [traits::IntoIterator]
+    Source: 'src/traits.rs', lines 237:0-237:22 *)
+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]
+    Source: 'src/traits.rs', lines 254:0-254:21 *)
+type fromResidual_t (self t : Type0) = unit
+
+(** Trait declaration: [traits::Try]
+    Source: 'src/traits.rs', lines 250:0-250:48 *)
+noeq type try_t (self : Type0) = {
+  tResidual : Type0;
+  fromResidualSelftraitsTrySelfResidualInst : fromResidual_t self tResidual;
+}
+
+(** Trait declaration: [traits::WithTarget]
+    Source: 'src/traits.rs', lines 256:0-256:20 *)
+noeq type withTarget_t (self : Type0) = { tTarget : Type0; }
+
+(** Trait declaration: [traits::ParentTrait2]
+    Source: 'src/traits.rs', lines 260:0-260:22 *)
+noeq type parentTrait2_t (self : Type0) = {
+  tU : Type0;
+  tU_clause_0 : withTarget_t tU;
+}
+
+(** Trait declaration: [traits::ChildTrait2]
+    Source: 'src/traits.rs', lines 264:0-264:35 *)
+noeq type childTrait2_t (self : Type0) = {
+  parentTrait2SelfInst : parentTrait2_t self;
+  convert : parentTrait2SelfInst.tU -> result
+    parentTrait2SelfInst.tU_clause_0.tTarget;
+}
+
+(** Trait implementation: [traits::{u32#11}]
+    Source: 'src/traits.rs', lines 268:0-268:23 *)
+let traits_WithTargetU32Inst : withTarget_t u32 = { tTarget = u32; }
+
+(** Trait implementation: [traits::{u32#12}]
+    Source: 'src/traits.rs', lines 272:0-272:25 *)
+let traits_ParentTrait2U32Inst : parentTrait2_t u32 = {
+  tU = u32;
+  tU_clause_0 = traits_WithTargetU32Inst;
+}
+
+(** [traits::{u32#13}::convert]: forward function
+    Source: 'src/traits.rs', lines 277:4-277:29 *)
+let u32_convert (x : u32) : result u32 =
+  Return x
+
+(** Trait implementation: [traits::{u32#13}]
+    Source: 'src/traits.rs', lines 276:0-276:24 *)
+let traits_ChildTrait2U32Inst : childTrait2_t u32 = {
+  parentTrait2SelfInst = traits_ParentTrait2U32Inst;
+  convert = u32_convert;
+}
+
+(** Trait declaration: [traits::CFnOnce]
+    Source: 'src/traits.rs', lines 290:0-290:23 *)
+noeq type cFnOnce_t (self args : Type0) = {
+  tOutput : Type0;
+  call_once : self -> args -> result tOutput;
+}
+
+(** Trait declaration: [traits::CFnMut]
+    Source: 'src/traits.rs', lines 296:0-296:37 *)
+noeq type cFnMut_t (self args : Type0) = {
+  cFnOnceSelfArgsInst : cFnOnce_t self args;
+  call_mut : self -> args -> result cFnOnceSelfArgsInst.tOutput;
+  call_mut_back : self -> args -> result self;
+}
+
+(** Trait declaration: [traits::CFn]
+    Source: 'src/traits.rs', lines 300:0-300:33 *)
+noeq type cFn_t (self args : Type0) = {
+  cFnMutSelfArgsInst : cFnMut_t self args;
+  call : self -> args -> result cFnMutSelfArgsInst.cFnOnceSelfArgsInst.tOutput;
+}
+
+(** Trait declaration: [traits::GetTrait]
+    Source: 'src/traits.rs', lines 304:0-304:18 *)
+noeq type getTrait_t (self : Type0) = { tW : Type0; get_w : self -> result tW;
+}
+
+(** [traits::test_get_trait]: forward function
+    Source: 'src/traits.rs', lines 309:0-309:49 *)
+let test_get_trait
+  (t : Type0) (getTraitTInst : getTrait_t t) (x : t) :
+  result getTraitTInst.tW
+  =
+  getTraitTInst.get_w x
+
diff --git a/tests/fstar/array/Array.Clauses.Template.fst b/tests/fstar/array/Array.Clauses.Template.fst
index 84347ab9..b2f2649c 100644
--- a/tests/fstar/array/Array.Clauses.Template.fst
+++ b/tests/fstar/array/Array.Clauses.Template.fst
@@ -9,13 +9,13 @@ open Array.Types
 (** [array::sum]: decreases clause
     Source: 'src/array.rs', lines 242:0-250:1 *)
 unfold
-let sum_loop_decreases (s : slice u32) (sum0 : u32) (i : usize) : nat =
+let sum_loop_decreases (s : slice u32) (sum1 : u32) (i : usize) : nat =
   admit ()
 
 (** [array::sum2]: decreases clause
     Source: 'src/array.rs', lines 252:0-261:1 *)
 unfold
-let sum2_loop_decreases (s : slice u32) (s2 : slice u32) (sum0 : u32)
+let sum2_loop_decreases (s : slice u32) (s2 : slice u32) (sum1 : u32)
   (i : usize) : nat =
   admit ()
 
diff --git a/tests/fstar/array/Array.Funs.fst b/tests/fstar/array/Array.Funs.fst
index 935bd9c9..4193ba7d 100644
--- a/tests/fstar/array/Array.Funs.fst
+++ b/tests/fstar/array/Array.Funs.fst
@@ -7,86 +7,79 @@ 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 ())
+(** [array::incr]:
     Source: 'src/array.rs', lines 8:0-8:24 *)
 let incr (x : u32) : result u32 =
   u32_add x 1
 
-(** [array::array_to_shared_slice_]: forward function
+(** [array::array_to_shared_slice_]:
     Source: 'src/array.rs', lines 16:0-16:53 *)
 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
+(** [array::array_to_mut_slice_]:
     Source: 'src/array.rs', lines 21:0-21:58 *)
-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
-    Source: 'src/array.rs', lines 21:0-21:58 *)
-let array_to_mut_slice__back
-  (t : Type0) (s : array t 32) (ret : slice t) : result (array t 32) =
-  array_from_slice t 32 s ret
+let array_to_mut_slice_
+  (t : Type0) (s : array t 32) :
+  result ((slice t) & (slice t -> result (array t 32)))
+  =
+  let* (s1, to_slice_mut_back) = array_to_slice_mut t 32 s in
+  Return (s1, to_slice_mut_back)
 
-(** [array::array_len]: forward function
+(** [array::array_len]:
     Source: 'src/array.rs', lines 25:0-25:40 *)
 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
+  let* s1 = array_to_slice t 32 s in let i = slice_len t s1 in Return i
 
-(** [array::shared_array_len]: forward function
+(** [array::shared_array_len]:
     Source: 'src/array.rs', lines 29:0-29:48 *)
 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
+  let* s1 = array_to_slice t 32 s in let i = slice_len t s1 in Return i
 
-(** [array::shared_slice_len]: forward function
+(** [array::shared_slice_len]:
     Source: 'src/array.rs', lines 33:0-33:44 *)
 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
+(** [array::index_array_shared]:
     Source: 'src/array.rs', lines 37:0-37:57 *)
 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
+(** [array::index_array_u32]:
     Source: 'src/array.rs', lines 44:0-44:53 *)
 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
+(** [array::index_array_copy]:
     Source: 'src/array.rs', lines 48:0-48:45 *)
 let index_array_copy (x : array u32 32) : result u32 =
   array_index_usize u32 32 x 0
 
-(** [array::index_mut_array]: forward function
+(** [array::index_mut_array]:
     Source: 'src/array.rs', lines 52:0-52:62 *)
-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
-    Source: 'src/array.rs', lines 52:0-52:62 *)
-let index_mut_array_back
-  (t : Type0) (s : array t 32) (i : usize) (ret : t) : result (array t 32) =
-  array_update_usize t 32 s i ret
+let index_mut_array
+  (t : Type0) (s : array t 32) (i : usize) :
+  result (t & (t -> result (array t 32)))
+  =
+  let* (x, index_mut_back) = array_index_mut_usize t 32 s i in
+  Return (x, index_mut_back)
 
-(** [array::index_slice]: forward function
+(** [array::index_slice]:
     Source: 'src/array.rs', lines 56:0-56:46 *)
 let index_slice (t : Type0) (s : slice t) (i : usize) : result t =
   slice_index_usize t s i
 
-(** [array::index_mut_slice]: forward function
-    Source: 'src/array.rs', lines 60:0-60:58 *)
-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
+(** [array::index_mut_slice]:
     Source: 'src/array.rs', lines 60:0-60:58 *)
-let index_mut_slice_back
-  (t : Type0) (s : slice t) (i : usize) (ret : t) : result (slice t) =
-  slice_update_usize t s i ret
+let index_mut_slice
+  (t : Type0) (s : slice t) (i : usize) :
+  result (t & (t -> result (slice t)))
+  =
+  let* (x, index_mut_back) = slice_index_mut_usize t s i in
+  Return (x, index_mut_back)
 
-(** [array::slice_subslice_shared_]: forward function
+(** [array::slice_subslice_shared_]:
     Source: 'src/array.rs', lines 64:0-64:70 *)
 let slice_subslice_shared_
   (x : slice u32) (y : usize) (z : usize) : result (slice u32) =
@@ -94,41 +87,33 @@ let slice_subslice_shared_
     (core_slice_index_SliceIndexRangeUsizeSliceTInst u32) x
     { start = y; end_ = z }
 
-(** [array::slice_subslice_mut_]: forward function
+(** [array::slice_subslice_mut_]:
     Source: 'src/array.rs', lines 68:0-68:75 *)
 let 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_SliceIndexRangeUsizeSliceTInst u32) x
-    { start = y; end_ = z }
-
-(** [array::slice_subslice_mut_]: backward function 0
-    Source: 'src/array.rs', lines 68:0-68:75 *)
-let slice_subslice_mut__back
-  (x : slice u32) (y : usize) (z : usize) (ret : slice u32) :
-  result (slice u32)
+  (x : slice u32) (y : usize) (z : usize) :
+  result ((slice u32) & (slice u32 -> result (slice u32)))
   =
-  core_slice_index_Slice_index_mut_back u32 (core_ops_range_Range usize)
-    (core_slice_index_SliceIndexRangeUsizeSliceTInst u32) x
-    { start = y; end_ = z } ret
+  let* (s, index_mut_back) =
+    core_slice_index_Slice_index_mut u32 (core_ops_range_Range usize)
+      (core_slice_index_SliceIndexRangeUsizeSliceTInst u32) x
+      { start = y; end_ = z } in
+  Return (s, index_mut_back)
 
-(** [array::array_to_slice_shared_]: forward function
+(** [array::array_to_slice_shared_]:
     Source: 'src/array.rs', lines 72:0-72:54 *)
 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
+(** [array::array_to_slice_mut_]:
     Source: 'src/array.rs', lines 76:0-76:59 *)
-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
-    Source: 'src/array.rs', lines 76:0-76:59 *)
-let array_to_slice_mut__back
-  (x : array u32 32) (ret : slice u32) : result (array u32 32) =
-  array_from_slice u32 32 x ret
+let array_to_slice_mut_
+  (x : array u32 32) :
+  result ((slice u32) & (slice u32 -> result (array u32 32)))
+  =
+  let* (s, to_slice_mut_back) = array_to_slice_mut u32 32 x in
+  Return (s, to_slice_mut_back)
 
-(** [array::array_subslice_shared_]: forward function
+(** [array::array_subslice_shared_]:
     Source: 'src/array.rs', lines 80:0-80:74 *)
 let array_subslice_shared_
   (x : array u32 32) (y : usize) (z : usize) : result (slice u32) =
@@ -137,274 +122,262 @@ let array_subslice_shared_
     (core_slice_index_SliceIndexRangeUsizeSliceTInst u32)) x
     { start = y; end_ = z }
 
-(** [array::array_subslice_mut_]: forward function
+(** [array::array_subslice_mut_]:
     Source: 'src/array.rs', lines 84:0-84:79 *)
 let array_subslice_mut_
-  (x : array u32 32) (y : usize) (z : usize) : result (slice u32) =
-  core_array_Array_index_mut u32 (core_ops_range_Range usize) 32
-    (core_ops_index_IndexMutSliceTIInst u32 (core_ops_range_Range usize)
-    (core_slice_index_SliceIndexRangeUsizeSliceTInst u32)) x
-    { start = y; end_ = z }
-
-(** [array::array_subslice_mut_]: backward function 0
-    Source: 'src/array.rs', lines 84:0-84:79 *)
-let array_subslice_mut__back
-  (x : array u32 32) (y : usize) (z : usize) (ret : slice u32) :
-  result (array u32 32)
+  (x : array u32 32) (y : usize) (z : usize) :
+  result ((slice u32) & (slice u32 -> result (array u32 32)))
   =
-  core_array_Array_index_mut_back u32 (core_ops_range_Range usize) 32
-    (core_ops_index_IndexMutSliceTIInst u32 (core_ops_range_Range usize)
-    (core_slice_index_SliceIndexRangeUsizeSliceTInst u32)) x
-    { start = y; end_ = z } ret
+  let* (s, index_mut_back) =
+    core_array_Array_index_mut u32 (core_ops_range_Range usize) 32
+      (core_ops_index_IndexMutSliceTIInst u32 (core_ops_range_Range usize)
+      (core_slice_index_SliceIndexRangeUsizeSliceTInst u32)) x
+      { start = y; end_ = z } in
+  Return (s, index_mut_back)
 
-(** [array::index_slice_0]: forward function
+(** [array::index_slice_0]:
     Source: 'src/array.rs', lines 88:0-88:38 *)
 let index_slice_0 (t : Type0) (s : slice t) : result t =
   slice_index_usize t s 0
 
-(** [array::index_array_0]: forward function
+(** [array::index_array_0]:
     Source: 'src/array.rs', lines 92:0-92:42 *)
 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
+(** [array::index_index_array]:
     Source: 'src/array.rs', lines 103:0-103:71 *)
 let index_index_array
   (s : array (array u32 32) 32) (i : usize) (j : usize) : result u32 =
   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
+(** [array::update_update_array]:
     Source: 'src/array.rs', lines 114:0-114:70 *)
 let update_update_array
   (s : array (array u32 32) 32) (i : usize) (j : usize) : result unit =
-  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
+  let* (a, index_mut_back) = array_index_mut_usize (array u32 32) 32 s i in
+  let* (_, index_mut_back1) = array_index_mut_usize u32 32 a j in
+  let* a1 = index_mut_back1 0 in
+  let* _ = index_mut_back a1 in
   Return ()
 
-(** [array::array_local_deep_copy]: forward function
+(** [array::array_local_deep_copy]:
     Source: 'src/array.rs', lines 118:0-118:43 *)
 let array_local_deep_copy (x : array u32 32) : result unit =
   Return ()
 
-(** [array::take_array]: forward function
+(** [array::take_array]:
     Source: 'src/array.rs', lines 122:0-122:30 *)
 let take_array (a : array u32 2) : result unit =
   Return ()
 
-(** [array::take_array_borrow]: forward function
+(** [array::take_array_borrow]:
     Source: 'src/array.rs', lines 123:0-123:38 *)
 let take_array_borrow (a : array u32 2) : result unit =
   Return ()
 
-(** [array::take_slice]: forward function
+(** [array::take_slice]:
     Source: 'src/array.rs', lines 124:0-124:28 *)
 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 ())
+(** [array::take_mut_slice]:
     Source: 'src/array.rs', lines 125:0-125:36 *)
 let take_mut_slice (s : slice u32) : result (slice u32) =
   Return s
 
-(** [array::const_array]: forward function
+(** [array::const_array]:
     Source: 'src/array.rs', lines 127:0-127:32 *)
 let const_array : result (array u32 2) =
   Return (mk_array u32 2 [ 0; 0 ])
 
-(** [array::const_slice]: forward function
+(** [array::const_slice]:
     Source: 'src/array.rs', lines 131:0-131:20 *)
 let const_slice : result unit =
   let* _ = array_to_slice u32 2 (mk_array u32 2 [ 0; 0 ]) in Return ()
 
-(** [array::take_all]: forward function
+(** [array::take_all]:
     Source: 'src/array.rs', lines 141:0-141:17 *)
 let take_all : result unit =
   let* _ = take_array (mk_array u32 2 [ 0; 0 ]) in
+  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
+  let* (s1, to_slice_mut_back) =
+    array_to_slice_mut u32 2 (mk_array u32 2 [ 0; 0 ]) in
+  let* s2 = take_mut_slice s1 in
+  let* _ = to_slice_mut_back s2 in
   Return ()
 
-(** [array::index_array]: forward function
+(** [array::index_array]:
     Source: 'src/array.rs', lines 155:0-155:38 *)
 let index_array (x : array u32 2) : result u32 =
   array_index_usize u32 2 x 0
 
-(** [array::index_array_borrow]: forward function
+(** [array::index_array_borrow]:
     Source: 'src/array.rs', lines 158:0-158:46 *)
 let index_array_borrow (x : array u32 2) : result u32 =
   array_index_usize u32 2 x 0
 
-(** [array::index_slice_u32_0]: forward function
+(** [array::index_slice_u32_0]:
     Source: 'src/array.rs', lines 162:0-162:42 *)
 let index_slice_u32_0 (x : slice u32) : result u32 =
   slice_index_usize u32 x 0
 
-(** [array::index_mut_slice_u32_0]: forward function
-    Source: 'src/array.rs', lines 166:0-166:50 *)
-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
+(** [array::index_mut_slice_u32_0]:
     Source: 'src/array.rs', lines 166:0-166:50 *)
-let index_mut_slice_u32_0_back (x : slice u32) : result (slice u32) =
-  let* _ = slice_index_usize u32 x 0 in Return x
+let index_mut_slice_u32_0 (x : slice u32) : result (u32 & (slice u32)) =
+  let* i = slice_index_usize u32 x 0 in Return (i, x)
 
-(** [array::index_all]: forward function
+(** [array::index_all]:
     Source: 'src/array.rs', lines 170:0-170:25 *)
 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 (mk_array u32 2 [ 0; 0 ]) in
-  let* i3 = u32_add i1 i2 in
+  let* i1 = index_array (mk_array u32 2 [ 0; 0 ]) in
+  let* i2 = u32_add i i1 in
+  let* i3 = index_array_borrow (mk_array u32 2 [ 0; 0 ]) in
+  let* i4 = u32_add i2 i3 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 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_from_slice u32 2 (mk_array u32 2 [ 0; 0 ]) s1 in
-  Return i7
-
-(** [array::update_array]: forward function
+  let* i5 = index_slice_u32_0 s in
+  let* i6 = u32_add i4 i5 in
+  let* (s1, to_slice_mut_back) =
+    array_to_slice_mut u32 2 (mk_array u32 2 [ 0; 0 ]) in
+  let* (i7, s2) = index_mut_slice_u32_0 s1 in
+  let* i8 = u32_add i6 i7 in
+  let* _ = to_slice_mut_back s2 in
+  Return i8
+
+(** [array::update_array]:
     Source: 'src/array.rs', lines 184:0-184:36 *)
 let update_array (x : array u32 2) : result unit =
-  let* _ = array_update_usize u32 2 x 0 1 in Return ()
+  let* (_, index_mut_back) = array_index_mut_usize u32 2 x 0 in
+  let* _ = index_mut_back 1 in
+  Return ()
 
-(** [array::update_array_mut_borrow]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ())
+(** [array::update_array_mut_borrow]:
     Source: 'src/array.rs', lines 187:0-187:48 *)
 let update_array_mut_borrow (x : array u32 2) : result (array u32 2) =
-  array_update_usize u32 2 x 0 1
+  let* (_, index_mut_back) = array_index_mut_usize u32 2 x 0 in
+  index_mut_back 1
 
-(** [array::update_mut_slice]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ())
+(** [array::update_mut_slice]:
     Source: 'src/array.rs', lines 190:0-190:38 *)
 let update_mut_slice (x : slice u32) : result (slice u32) =
-  slice_update_usize u32 x 0 1
+  let* (_, index_mut_back) = slice_index_mut_usize u32 x 0 in index_mut_back 1
 
-(** [array::update_all]: forward function
+(** [array::update_all]:
     Source: 'src/array.rs', lines 194:0-194:19 *)
 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
+  let* _ = update_array (mk_array u32 2 [ 0; 0 ]) in
+  let* a = update_array_mut_borrow (mk_array u32 2 [ 0; 0 ]) in
+  let* (s, to_slice_mut_back) = array_to_slice_mut u32 2 a in
+  let* s1 = update_mut_slice s in
+  let* _ = to_slice_mut_back s1 in
   Return ()
 
-(** [array::range_all]: forward function
+(** [array::range_all]:
     Source: 'src/array.rs', lines 205:0-205:18 *)
 let range_all : result unit =
-  let* s =
+  let* (s, index_mut_back) =
     core_array_Array_index_mut u32 (core_ops_range_Range usize) 4
       (core_ops_index_IndexMutSliceTIInst u32 (core_ops_range_Range usize)
       (core_slice_index_SliceIndexRangeUsizeSliceTInst u32))
       (mk_array u32 4 [ 0; 0; 0; 0 ]) { start = 1; end_ = 3 } in
-  let* s0 = update_mut_slice s in
-  let* _ =
-    core_array_Array_index_mut_back u32 (core_ops_range_Range usize) 4
-      (core_ops_index_IndexMutSliceTIInst u32 (core_ops_range_Range usize)
-      (core_slice_index_SliceIndexRangeUsizeSliceTInst u32))
-      (mk_array u32 4 [ 0; 0; 0; 0 ]) { start = 1; end_ = 3 } s0 in
+  let* s1 = update_mut_slice s in
+  let* _ = index_mut_back s1 in
   Return ()
 
-(** [array::deref_array_borrow]: forward function
+(** [array::deref_array_borrow]:
     Source: 'src/array.rs', lines 214:0-214:46 *)
 let deref_array_borrow (x : array u32 2) : result u32 =
   array_index_usize u32 2 x 0
 
-(** [array::deref_array_mut_borrow]: forward function
+(** [array::deref_array_mut_borrow]:
     Source: 'src/array.rs', lines 219:0-219:54 *)
-let deref_array_mut_borrow (x : array u32 2) : result u32 =
-  array_index_usize u32 2 x 0
+let deref_array_mut_borrow (x : array u32 2) : result (u32 & (array u32 2)) =
+  let* i = array_index_usize u32 2 x 0 in Return (i, x)
 
-(** [array::deref_array_mut_borrow]: backward function 0
-    Source: 'src/array.rs', lines 219:0-219:54 *)
-let deref_array_mut_borrow_back (x : array u32 2) : result (array u32 2) =
-  let* _ = array_index_usize u32 2 x 0 in Return x
-
-(** [array::take_array_t]: forward function
+(** [array::take_array_t]:
     Source: 'src/array.rs', lines 227:0-227:31 *)
 let take_array_t (a : array aB_t 2) : result unit =
   Return ()
 
-(** [array::non_copyable_array]: forward function
+(** [array::non_copyable_array]:
     Source: 'src/array.rs', lines 229:0-229:27 *)
 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
+(** [array::sum]: loop 0:
     Source: 'src/array.rs', lines 242:0-250:1 *)
 let rec sum_loop
-  (s : slice u32) (sum0 : u32) (i : usize) :
-  Tot (result u32) (decreases (sum_loop_decreases s sum0 i))
+  (s : slice u32) (sum1 : u32) (i : usize) :
+  Tot (result u32) (decreases (sum_loop_decreases s sum1 i))
   =
-  let i0 = slice_len u32 s in
-  if i < i0
+  let i1 = slice_len u32 s in
+  if i < i1
   then
-    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 s sum1 i2
-  else Return sum0
+    let* i2 = slice_index_usize u32 s i in
+    let* sum3 = u32_add sum1 i2 in
+    let* i3 = usize_add i 1 in
+    sum_loop s sum3 i3
+  else Return sum1
 
-(** [array::sum]: forward function
+(** [array::sum]:
     Source: 'src/array.rs', lines 242:0-242:28 *)
 let sum (s : slice u32) : result u32 =
   sum_loop s 0 0
 
-(** [array::sum2]: loop 0: forward function
+(** [array::sum2]: loop 0:
     Source: 'src/array.rs', lines 252:0-261:1 *)
 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))
+  (s : slice u32) (s2 : slice u32) (sum1 : u32) (i : usize) :
+  Tot (result u32) (decreases (sum2_loop_decreases s s2 sum1 i))
   =
-  let i0 = slice_len u32 s in
-  if i < i0
+  let i1 = slice_len u32 s in
+  if i < i1
   then
-    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* sum1 = u32_add sum0 i3 in
-    let* i4 = usize_add i 1 in
-    sum2_loop s s2 sum1 i4
-  else Return sum0
-
-(** [array::sum2]: forward function
+    let* i2 = slice_index_usize u32 s i in
+    let* i3 = slice_index_usize u32 s2 i in
+    let* i4 = u32_add i2 i3 in
+    let* sum3 = u32_add sum1 i4 in
+    let* i5 = usize_add i 1 in
+    sum2_loop s s2 sum3 i5
+  else Return sum1
+
+(** [array::sum2]:
     Source: 'src/array.rs', lines 252:0-252:41 *)
 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 s s2 0 0
+  let i1 = slice_len u32 s2 in
+  if not (i = i1) then Fail Failure else sum2_loop s s2 0 0
 
-(** [array::f0]: forward function
+(** [array::f0]:
     Source: 'src/array.rs', lines 263:0-263:11 *)
 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
+  let* (s, to_slice_mut_back) =
+    array_to_slice_mut u32 2 (mk_array u32 2 [ 1; 2 ]) in
+  let* (_, index_mut_back) = slice_index_mut_usize u32 s 0 in
+  let* s1 = index_mut_back 1 in
+  let* _ = to_slice_mut_back s1 in
   Return ()
 
-(** [array::f1]: forward function
+(** [array::f1]:
     Source: 'src/array.rs', lines 268:0-268:11 *)
 let f1 : result unit =
-  let* _ = array_update_usize u32 2 (mk_array u32 2 [ 1; 2 ]) 0 1 in Return ()
+  let* (_, index_mut_back) =
+    array_index_mut_usize u32 2 (mk_array u32 2 [ 1; 2 ]) 0 in
+  let* _ = index_mut_back 1 in
+  Return ()
 
-(** [array::f2]: forward function
+(** [array::f2]:
     Source: 'src/array.rs', lines 273:0-273:17 *)
 let f2 (i : u32) : result unit =
   Return ()
 
-(** [array::f4]: forward function
+(** [array::f4]:
     Source: 'src/array.rs', lines 282:0-282:54 *)
 let f4 (x : array u32 32) (y : usize) (z : usize) : result (slice u32) =
   core_array_Array_index u32 (core_ops_range_Range usize) 32
@@ -412,34 +385,36 @@ let f4 (x : array u32 32) (y : usize) (z : usize) : result (slice u32) =
     (core_slice_index_SliceIndexRangeUsizeSliceTInst u32)) x
     { start = y; end_ = z }
 
-(** [array::f3]: forward function
+(** [array::f3]:
     Source: 'src/array.rs', lines 275:0-275:18 *)
 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
+  let* s1 = f4 b 16 18 in
+  sum2 s s1
 
 (** [array::SZ]
     Source: 'src/array.rs', lines 286:0-286:19 *)
 let sz_body : result usize = Return 32
 let sz_c : usize = eval_global sz_body
 
-(** [array::f5]: forward function
+(** [array::f5]:
     Source: 'src/array.rs', lines 289:0-289:31 *)
 let f5 (x : array u32 32) : result u32 =
   array_index_usize u32 32 x 0
 
-(** [array::ite]: forward function
+(** [array::ite]:
     Source: 'src/array.rs', lines 294:0-294:12 *)
 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_from_slice u32 2 (mk_array u32 2 [ 0; 0 ]) s1 in
-  let* s2 = index_mut_slice_u32_0_back s in
-  let* _ = array_from_slice u32 2 (mk_array u32 2 [ 0; 0 ]) s2 in
+  let* (s, to_slice_mut_back) =
+    array_to_slice_mut u32 2 (mk_array u32 2 [ 0; 0 ]) in
+  let* (_, s1) = index_mut_slice_u32_0 s in
+  let* (s2, to_slice_mut_back1) =
+    array_to_slice_mut u32 2 (mk_array u32 2 [ 0; 0 ]) in
+  let* (_, s3) = index_mut_slice_u32_0 s2 in
+  let* _ = to_slice_mut_back1 s3 in
+  let* _ = to_slice_mut_back s1 in
   Return ()
 
diff --git a/tests/fstar/array/Primitives.fst b/tests/fstar/array/Primitives.fst
index a3ffbde4..fca80829 100644
--- a/tests/fstar/array/Primitives.fst
+++ b/tests/fstar/array/Primitives.fst
@@ -55,8 +55,7 @@ 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
+let core_mem_replace (a : Type0) (x : a) (y : a) : a & a = (x, x)
 
 // We don't really use raw pointers for now
 type mut_raw_ptr (t : Type0) = { v : t }
@@ -477,8 +476,7 @@ noeq type core_ops_index_Index (self idx : Type0) = {
 // 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;
+  index_mut : self → idx → result (indexInst.output & (indexInst.output → result self));
 }
 
 // Trait declaration [core::ops::deref::Deref]
@@ -490,8 +488,7 @@ noeq type core_ops_deref_Deref (self : Type0) = {
 // 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;
+  deref_mut : self → result (derefInst.target & (derefInst.target → result self));
 }
 
 type core_ops_range_Range (a : Type0) = {
@@ -502,8 +499,8 @@ type core_ops_range_Range (a : Type0) = {
 (*** [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
+let alloc_boxed_Box_deref_mut (t : Type0) (x : t) : result (t & (t -> result t)) =
+  Return (x, (fun x -> Return x))
 
 // Trait instance
 let alloc_boxed_Box_coreopsDerefInst (self : Type0) : core_ops_deref_Deref self = {
@@ -515,7 +512,6 @@ let alloc_boxed_Box_coreopsDerefInst (self : Type0) : core_ops_deref_Deref self
 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 *)
@@ -535,10 +531,18 @@ let array_index_usize (a : Type0) (n : usize) (x : array a n) (i : usize) : resu
   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) =
+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
 
+let array_index_mut_usize (a : Type0) (n : usize) (x : array a n) (i : usize) :
+  result (a & (a -> result (array a n))) =
+  match array_index_usize a n x i with
+  | Fail e -> Fail e
+  | Return v ->
+    Return (v, array_update_usize a n x i)
+
 (*** Slice *)
 type slice (a : Type0) = s:list a{length s <= usize_max}
 
@@ -552,6 +556,13 @@ let slice_update_usize (a : Type0) (x : slice a) (i : usize) (nx : a) : result (
   if i < length x then Return (list_update x i nx)
   else Fail Failure
 
+let slice_index_mut_usize (a : Type0) (s : slice a) (i : usize) :
+  result (a & (a -> result (slice a))) =
+  match slice_index_usize a s i with
+  | Fail e -> Fail e
+  | Return x ->
+    Return (x, slice_update_usize a s i)
+
 (*** Subslices *)
 
 let array_to_slice (a : Type0) (n : usize) (x : array a n) : result (slice a) = Return x
@@ -559,6 +570,10 @@ let array_from_slice (a : Type0) (n : usize) (x : array a n) (s : slice a) : res
   if length s = n then Return s
   else Fail Failure
 
+let array_to_slice_mut (a : Type0) (n : usize) (x : array a n) :
+  result (slice a & (slice a -> result (array a n))) =
+  Return (x, array_from_slice a n x)
+
 // 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()
@@ -588,8 +603,13 @@ let alloc_vec_Vec_index_usize (#a : Type0) (v : alloc_vec_Vec a) (i : usize) : r
 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_index_mut_usize (#a : Type0) (v: alloc_vec_Vec a) (i: usize) :
+  result (a & (a → result (alloc_vec_Vec a))) =
+  match alloc_vec_Vec_index_usize v i with
+  | Return x ->
+    Return (x, alloc_vec_Vec_update_usize v i)
+  | Fail e -> Fail e
+
 let alloc_vec_Vec_push (a  : Type0) (v : alloc_vec_Vec a) (x : a) :
   Pure (result (alloc_vec_Vec a))
   (requires True)
@@ -605,9 +625,6 @@ let alloc_vec_Vec_push (a  : Type0) (v : alloc_vec_Vec a) (x : a) :
     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
 
@@ -619,13 +636,11 @@ 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_mut : self → t → result (option output & (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;
+  index_mut : self → t → result (output & (output -> result t));
 }
 
 // [core::slice::index::[T]::index]: forward function
@@ -643,14 +658,8 @@ let core_slice_index_RangeUsize_get (t : Type0) (i : core_ops_range_Range usize)
   admit () // TODO
 
 // [core::slice::index::Range::get_mut]: forward function
-let core_slice_index_RangeUsize_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_RangeUsize_get_mut_back
-  (t : Type0) :
-  core_ops_range_Range usize → slice t → option (slice t) → result (slice t) =
+let core_slice_index_RangeUsize_get_mut (t : Type0) :
+  core_ops_range_Range usize → slice t → result (option (slice t) & (option (slice t) -> result (slice t))) =
   admit () // TODO
 
 // [core::slice::index::Range::get_unchecked]: forward function
@@ -675,27 +684,16 @@ let core_slice_index_RangeUsize_index
   admit () // TODO
 
 // [core::slice::index::Range::index_mut]: forward function
-let core_slice_index_RangeUsize_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_RangeUsize_index_mut_back
-  (t : Type0) : core_ops_range_Range usize → slice t → slice t → result (slice t) =
+let core_slice_index_RangeUsize_index_mut (t : Type0) :
+  core_ops_range_Range usize → slice t → result (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 =
+  slice t → idx → result (inst.output & (inst.output -> result (slice t))) =
   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)
@@ -705,13 +703,8 @@ let core_array_Array_index
 // [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) =
+  (a : array t n) (i : idx) :
+  result (inst.indexInst.output & (inst.indexInst.output -> result (array t n))) =
   admit () // TODO
 
 // Trait implementation: [core::slice::index::private_slice_index::Range]
@@ -725,12 +718,10 @@ let core_slice_index_SliceIndexRangeUsizeSliceTInst (t : Type0) :
   output = slice t;
   get = core_slice_index_RangeUsize_get t;
   get_mut = core_slice_index_RangeUsize_get_mut t;
-  get_mut_back = core_slice_index_RangeUsize_get_mut_back t;
   get_unchecked = core_slice_index_RangeUsize_get_unchecked t;
   get_unchecked_mut = core_slice_index_RangeUsize_get_unchecked_mut t;
   index = core_slice_index_RangeUsize_index t;
   index_mut = core_slice_index_RangeUsize_index_mut t;
-  index_mut_back = core_slice_index_RangeUsize_index_mut_back t;
 }
 
 // Trait implementation: [core::slice::index::[T]]
@@ -747,7 +738,6 @@ let core_ops_index_IndexMutSliceTIInst (t idx : Type0)
   core_ops_index_IndexMut (slice t) idx = {
   indexInst = core_ops_index_IndexSliceTIInst 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]]
@@ -764,7 +754,6 @@ let core_ops_index_IndexMutArrayIInst (t idx : Type0) (n : usize)
   core_ops_index_IndexMut (array t n) idx = {
   indexInst = core_ops_index_IndexArrayInst 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
@@ -773,13 +762,8 @@ let core_slice_index_usize_get
   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) =
+let core_slice_index_usize_get_mut (t : Type0) :
+  usize → slice t → result (option t & (option t -> result (slice t))) =
   admit () // TODO
 
 // [core::slice::index::usize::get_unchecked]: forward function
@@ -797,12 +781,8 @@ 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) =
+let core_slice_index_usize_index_mut (t : Type0) :
+  usize → slice t → result (t & (t -> result (slice t))) =
   admit () // TODO
 
 // Trait implementation: [core::slice::index::private_slice_index::usize]
@@ -816,12 +796,10 @@ let core_slice_index_SliceIndexUsizeSliceTInst (t : Type0) :
   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
@@ -831,13 +809,8 @@ let alloc_vec_Vec_index (t idx : Type0) (inst : core_slice_index_SliceIndex idx
 
 // [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) =
+  (self : alloc_vec_Vec t) (i : idx) :
+  result (inst.output & (inst.output -> result (alloc_vec_Vec t))) =
   admit () // TODO
 
 // Trait implementation: [alloc::vec::Vec]
@@ -854,7 +827,6 @@ let alloc_vec_Vec_coreopsindexIndexMutInst (t idx : Type0)
   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 *)
@@ -870,15 +842,7 @@ let alloc_vec_Vec_index_eq (#a : Type0) (v : alloc_vec_Vec a) (i : usize) :
 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_SliceIndexUsizeSliceTInst a) v i ==
-      alloc_vec_Vec_index_usize v i)
+      alloc_vec_Vec_index_mut_usize v i)
   [SMTPat (alloc_vec_Vec_index_mut a usize (core_slice_index_SliceIndexUsizeSliceTInst 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_SliceIndexUsizeSliceTInst a) v i x ==
-      alloc_vec_Vec_update_usize v i x)
-  [SMTPat (alloc_vec_Vec_index_mut_back a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i x)]
-  =
-  admit()
diff --git a/tests/fstar/betree/BetreeMain.Funs.fst b/tests/fstar/betree/BetreeMain.Funs.fst
index f844b0ec..196f120c 100644
--- a/tests/fstar/betree/BetreeMain.Funs.fst
+++ b/tests/fstar/betree/BetreeMain.Funs.fst
@@ -8,7 +8,7 @@ include BetreeMain.Clauses
 
 #set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
 
-(** [betree_main::betree::load_internal_node]: forward function
+(** [betree_main::betree::load_internal_node]:
     Source: 'src/betree.rs', lines 36:0-36:52 *)
 let betree_load_internal_node
   (id : u64) (st : state) :
@@ -16,58 +16,48 @@ let betree_load_internal_node
   =
   betree_utils_load_internal_node id st
 
-(** [betree_main::betree::store_internal_node]: forward function
+(** [betree_main::betree::store_internal_node]:
     Source: 'src/betree.rs', lines 41:0-41:60 *)
 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 id content st in
-  Return (st0, ())
+  let* (st1, _) = betree_utils_store_internal_node id content st in
+  Return (st1, ())
 
-(** [betree_main::betree::load_leaf_node]: forward function
+(** [betree_main::betree::load_leaf_node]:
     Source: 'src/betree.rs', lines 46:0-46:44 *)
 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
+(** [betree_main::betree::store_leaf_node]:
     Source: 'src/betree.rs', lines 51:0-51:52 *)
 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 id content st in
-  Return (st0, ())
+  let* (st1, _) = betree_utils_store_leaf_node id content st in
+  Return (st1, ())
 
-(** [betree_main::betree::fresh_node_id]: forward function
+(** [betree_main::betree::fresh_node_id]:
     Source: 'src/betree.rs', lines 55:0-55:48 *)
-let betree_fresh_node_id (counter : u64) : result u64 =
-  let* _ = u64_add counter 1 in Return counter
+let betree_fresh_node_id (counter : u64) : result (u64 & u64) =
+  let* counter1 = u64_add counter 1 in Return (counter, counter1)
 
-(** [betree_main::betree::fresh_node_id]: backward function 0
-    Source: 'src/betree.rs', lines 55:0-55:48 *)
-let betree_fresh_node_id_back (counter : u64) : result u64 =
-  u64_add counter 1
-
-(** [betree_main::betree::{betree_main::betree::NodeIdCounter}::new]: forward function
+(** [betree_main::betree::{betree_main::betree::NodeIdCounter}::new]:
     Source: 'src/betree.rs', lines 206:4-206:20 *)
 let betree_NodeIdCounter_new : result betree_NodeIdCounter_t =
   Return { next_node_id = 0 }
 
-(** [betree_main::betree::{betree_main::betree::NodeIdCounter}::fresh_id]: forward function
+(** [betree_main::betree::{betree_main::betree::NodeIdCounter}::fresh_id]:
     Source: 'src/betree.rs', lines 210:4-210:36 *)
 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::{betree_main::betree::NodeIdCounter}::fresh_id]: backward function 0
-    Source: 'src/betree.rs', lines 210:4-210:36 *)
-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 }
+  (self : betree_NodeIdCounter_t) : result (u64 & betree_NodeIdCounter_t) =
+  let* i = u64_add self.next_node_id 1 in
+  Return (self.next_node_id, { next_node_id = i })
 
-(** [betree_main::betree::upsert_update]: forward function
+(** [betree_main::betree::upsert_update]:
     Source: 'src/betree.rs', lines 234:0-234:70 *)
 let betree_upsert_update
   (prev : option u64) (st : betree_UpsertFunState_t) : result u64 =
@@ -75,30 +65,30 @@ let betree_upsert_update
   | None ->
     begin match st with
     | Betree_UpsertFunState_Add v -> Return v
-    | Betree_UpsertFunState_Sub i -> Return 0
+    | Betree_UpsertFunState_Sub _ -> Return 0
     end
-  | Some prev0 ->
+  | Some prev1 ->
     begin match st with
     | 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
+      let* margin = u64_sub core_u64_max prev1 in
+      if margin >= v then u64_add prev1 v else Return core_u64_max
     | Betree_UpsertFunState_Sub v ->
-      if prev0 >= v then u64_sub prev0 v else Return 0
+      if prev1 >= v then u64_sub prev1 v else Return 0
     end
   end
 
-(** [betree_main::betree::{betree_main::betree::List<T>#1}::len]: forward function
+(** [betree_main::betree::{betree_main::betree::List<T>#1}::len]:
     Source: 'src/betree.rs', lines 276:4-276:24 *)
 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
-  | Betree_List_Cons x tl -> let* i = betree_List_len t tl in u64_add 1 i
+  | Betree_List_Cons _ tl -> let* i = betree_List_len t tl in u64_add 1 i
   | Betree_List_Nil -> Return 0
   end
 
-(** [betree_main::betree::{betree_main::betree::List<T>#1}::split_at]: forward function
+(** [betree_main::betree::{betree_main::betree::List<T>#1}::split_at]:
     Source: 'src/betree.rs', lines 284:4-284:51 *)
 let rec betree_List_split_at
   (t : Type0) (self : betree_List_t t) (n : u64) :
@@ -113,57 +103,45 @@ let rec betree_List_split_at
       let* i = u64_sub n 1 in
       let* p = betree_List_split_at t tl i in
       let (ls0, ls1) = p in
-      let l = ls0 in
-      Return (Betree_List_Cons hd l, ls1)
+      Return (Betree_List_Cons hd ls0, ls1)
     | Betree_List_Nil -> Fail Failure
     end
 
-(** [betree_main::betree::{betree_main::betree::List<T>#1}::push_front]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ())
+(** [betree_main::betree::{betree_main::betree::List<T>#1}::push_front]:
     Source: 'src/betree.rs', lines 299:4-299:34 *)
 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 (Betree_List_Cons x l)
-
-(** [betree_main::betree::{betree_main::betree::List<T>#1}::pop_front]: forward function
-    Source: 'src/betree.rs', lines 306:4-306:32 *)
-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
-  | Betree_List_Cons x tl -> Return x
-  | Betree_List_Nil -> Fail Failure
-  end
+  let (tl, _) = core_mem_replace (betree_List_t t) self Betree_List_Nil in
+  Return (Betree_List_Cons x tl)
 
-(** [betree_main::betree::{betree_main::betree::List<T>#1}::pop_front]: backward function 0
+(** [betree_main::betree::{betree_main::betree::List<T>#1}::pop_front]:
     Source: 'src/betree.rs', lines 306:4-306:32 *)
-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
+let betree_List_pop_front
+  (t : Type0) (self : betree_List_t t) : result (t & (betree_List_t t)) =
+  let (ls, _) = core_mem_replace (betree_List_t t) self Betree_List_Nil in
   begin match ls with
-  | Betree_List_Cons x tl -> Return tl
+  | Betree_List_Cons x tl -> Return (x, tl)
   | Betree_List_Nil -> Fail Failure
   end
 
-(** [betree_main::betree::{betree_main::betree::List<T>#1}::hd]: forward function
+(** [betree_main::betree::{betree_main::betree::List<T>#1}::hd]:
     Source: 'src/betree.rs', lines 318:4-318:22 *)
 let betree_List_hd (t : Type0) (self : betree_List_t t) : result t =
   begin match self with
-  | Betree_List_Cons hd l -> Return hd
+  | Betree_List_Cons hd _ -> Return hd
   | Betree_List_Nil -> Fail Failure
   end
 
-(** [betree_main::betree::{betree_main::betree::List<(u64, T)>#2}::head_has_key]: forward function
+(** [betree_main::betree::{betree_main::betree::List<(u64, T)>#2}::head_has_key]:
     Source: 'src/betree.rs', lines 327:4-327:44 *)
 let betree_ListTupleU64T_head_has_key
   (t : Type0) (self : betree_List_t (u64 & t)) (key : u64) : result bool =
   begin match self with
-  | Betree_List_Cons hd l -> let (i, _) = hd in Return (i = key)
+  | Betree_List_Cons hd _ -> let (i, _) = hd in Return (i = key)
   | Betree_List_Nil -> Return false
   end
 
-(** [betree_main::betree::{betree_main::betree::List<(u64, T)>#2}::partition_at_pivot]: forward function
+(** [betree_main::betree::{betree_main::betree::List<(u64, T)>#2}::partition_at_pivot]:
     Source: 'src/betree.rs', lines 339:4-339:73 *)
 let rec betree_ListTupleU64T_partition_at_pivot
   (t : Type0) (self : betree_List_t (u64 & t)) (pivot : u64) :
@@ -178,87 +156,55 @@ let rec betree_ListTupleU64T_partition_at_pivot
     else
       let* p = betree_ListTupleU64T_partition_at_pivot t tl pivot in
       let (ls0, ls1) = p in
-      let l = ls0 in
-      Return (Betree_List_Cons (i, x) l, ls1)
+      Return (Betree_List_Cons (i, x) ls0, ls1)
   | Betree_List_Nil -> Return (Betree_List_Nil, Betree_List_Nil)
   end
 
-(** [betree_main::betree::{betree_main::betree::Leaf#3}::split]: forward function
+(** [betree_main::betree::{betree_main::betree::Leaf#3}::split]:
     Source: 'src/betree.rs', lines 359:4-364:17 *)
 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 & betree_NodeIdCounter_t))
   =
   let* p = betree_List_split_at (u64 & u64) content params.split_size in
   let (content0, content1) = p in
-  let* p0 = betree_List_hd (u64 & u64) content1 in
-  let (pivot, _) = p0 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* (st1, _) = betree_store_leaf_node id1 content1 st0 in
+  let* p1 = betree_List_hd (u64 & u64) content1 in
+  let (pivot, _) = p1 in
+  let* (id0, nic) = betree_NodeIdCounter_fresh_id node_id_cnt in
+  let* (id1, nic1) = betree_NodeIdCounter_fresh_id nic in
+  let* (st1, _) = betree_store_leaf_node id0 content0 st in
+  let* (st2, _) = betree_store_leaf_node id1 content1 st1 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 })
+  let n1 = Betree_Node_Leaf { id = id1; size = params.split_size } in
+  Return (st2, ({ id = self.id; pivot = pivot; left = n; right = n1 }, nic1))
 
-(** [betree_main::betree::{betree_main::betree::Leaf#3}::split]: backward function 2
-    Source: 'src/betree.rs', lines 359:4-364:17 *)
-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_NodeIdCounter_t
-  =
-  let* p = betree_List_split_at (u64 & u64) content params.split_size in
-  let (content0, content1) = p 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* (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::{betree_main::betree::Node#5}::lookup_first_message_for_key]: forward function
+(** [betree_main::betree::{betree_main::betree::Node#5}::lookup_first_message_for_key]:
     Source: 'src/betree.rs', lines 789:4-792:34 *)
 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)))
+  Tot (result ((betree_List_t (u64 & betree_Message_t)) & (betree_List_t (u64 &
+    betree_Message_t) -> result (betree_List_t (u64 & betree_Message_t)))))
   (decreases (betree_Node_lookup_first_message_for_key_decreases key msgs))
   =
   begin match msgs with
   | Betree_List_Cons x next_msgs ->
     let (i, m) = x in
     if i >= key
-    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::{betree_main::betree::Node#5}::lookup_first_message_for_key]: backward function 0
-    Source: 'src/betree.rs', lines 789:4-792:34 *)
-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
-  | Betree_List_Cons x next_msgs ->
-    let (i, m) = x in
-    if i >= key
-    then Return ret
+    then Return (Betree_List_Cons (i, m) next_msgs, Return)
     else
-      let* next_msgs0 =
-        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
+      let* (l, lookup_first_message_for_key_back) =
+        betree_Node_lookup_first_message_for_key key next_msgs in
+      let back_'a =
+        fun ret ->
+          let* next_msgs1 = lookup_first_message_for_key_back ret in
+          Return (Betree_List_Cons (i, m) next_msgs1) in
+      Return (l, back_'a)
+  | Betree_List_Nil -> Return (Betree_List_Nil, Return)
   end
 
-(** [betree_main::betree::{betree_main::betree::Node#5}::lookup_in_bindings]: forward function
+(** [betree_main::betree::{betree_main::betree::Node#5}::lookup_in_bindings]:
     Source: 'src/betree.rs', lines 636:4-636:80 *)
 let rec betree_Node_lookup_in_bindings
   (key : u64) (bindings : betree_List_t (u64 & u64)) :
@@ -267,215 +213,110 @@ let rec betree_Node_lookup_in_bindings
   =
   begin match bindings with
   | Betree_List_Cons hd tl ->
-    let (i, i0) = hd in
+    let (i, i1) = hd in
     if i = key
-    then Return (Some i0)
+    then Return (Some i1)
     else if i > key then Return None else betree_Node_lookup_in_bindings key tl
   | Betree_List_Nil -> Return None
   end
 
-(** [betree_main::betree::{betree_main::betree::Node#5}::apply_upserts]: forward function
+(** [betree_main::betree::{betree_main::betree::Node#5}::apply_upserts]:
     Source: 'src/betree.rs', lines 819:4-819:90 *)
 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))
+  Tot (result (state & (u64 & (betree_List_t (u64 & betree_Message_t)))))
   (decreases (betree_Node_apply_upserts_decreases msgs prev key st))
   =
   let* b = betree_ListTupleU64T_head_has_key betree_Message_t msgs key in
   if b
   then
-    let* msg = betree_List_pop_front (u64 & betree_Message_t) msgs in
+    let* (msg, l) = betree_List_pop_front (u64 & betree_Message_t) msgs in
     let (_, m) = msg in
     begin match m with
-    | Betree_Message_Insert i -> Fail Failure
+    | Betree_Message_Insert _ -> 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
+      betree_Node_apply_upserts l (Some v) key st
     end
   else
-    let* (st0, v) = core_option_Option_unwrap u64 prev st in
-    let* _ =
+    let* (st1, v) = core_option_Option_unwrap u64 prev st in
+    let* l =
       betree_List_push_front (u64 & betree_Message_t) msgs (key,
         Betree_Message_Insert v) in
-    Return (st0, v)
-
-(** [betree_main::betree::{betree_main::betree::Node#5}::apply_upserts]: backward function 0
-    Source: 'src/betree.rs', lines 819:4-819:90 *)
-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))
-  =
-  let* b = betree_ListTupleU64T_head_has_key betree_Message_t msgs key in
-  if b
-  then
-    let* msg = betree_List_pop_front (u64 & betree_Message_t) msgs in
-    let (_, m) = msg in
-    begin match m with
-    | 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 u64 prev st in
-    betree_List_push_front (u64 & betree_Message_t) msgs (key,
-      Betree_Message_Insert v)
+    Return (st1, (v, l))
 
-(** [betree_main::betree::{betree_main::betree::Internal#4}::lookup_in_children]: forward function
+(** [betree_main::betree::{betree_main::betree::Internal#4}::lookup_in_children]:
     Source: 'src/betree.rs', lines 395:4-395:63 *)
 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))
-  =
-  if key < self.pivot
-  then betree_Node_lookup self.left key st
-  else betree_Node_lookup self.right key st
-
-(** [betree_main::betree::{betree_main::betree::Internal#4}::lookup_in_children]: backward function 0
-    Source: 'src/betree.rs', lines 395:4-395:63 *)
-and betree_Internal_lookup_in_children_back
-  (self : betree_Internal_t) (key : u64) (st : state) :
-  Tot (result betree_Internal_t)
+  Tot (result (state & ((option u64) & betree_Internal_t)))
   (decreases (betree_Internal_lookup_in_children_decreases self key st))
   =
   if key < self.pivot
   then
-    let* n = betree_Node_lookup_back self.left key st in
-    Return { self with left = n }
+    let* (st1, (o, n)) = betree_Node_lookup self.left key st in
+    Return (st1, (o, { self with left = n }))
   else
-    let* n = betree_Node_lookup_back self.right key st in
-    Return { self with right = n }
+    let* (st1, (o, n)) = betree_Node_lookup self.right key st in
+    Return (st1, (o, { self with right = n }))
 
-(** [betree_main::betree::{betree_main::betree::Node#5}::lookup]: forward function
+(** [betree_main::betree::{betree_main::betree::Node#5}::lookup]:
     Source: 'src/betree.rs', lines 709:4-709:58 *)
 and betree_Node_lookup
   (self : betree_Node_t) (key : u64) (st : state) :
-  Tot (result (state & (option u64)))
+  Tot (result (state & ((option u64) & betree_Node_t)))
   (decreases (betree_Node_lookup_decreases self key st))
   =
   begin match self with
   | 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
+    let* (st1, msgs) = betree_load_internal_node node.id st in
+    let* (pending, lookup_first_message_for_key_back) =
+      betree_Node_lookup_first_message_for_key key msgs in
     begin match pending with
     | Betree_List_Cons p l ->
       let (k, msg) = p in
       if k <> key
       then
-        let* (st1, o) = betree_Internal_lookup_in_children node key st0 in
+        let* (st2, (o, i)) = betree_Internal_lookup_in_children node key st1 in
         let* _ =
-          betree_Node_lookup_first_message_for_key_back key msgs
-            (Betree_List_Cons (k, msg) l) in
-        Return (st1, o)
+          lookup_first_message_for_key_back (Betree_List_Cons (k, msg) l) in
+        Return (st2, (o, Betree_Node_Internal i))
       else
         begin match msg with
         | Betree_Message_Insert v ->
           let* _ =
-            betree_Node_lookup_first_message_for_key_back key msgs
-              (Betree_List_Cons (k, Betree_Message_Insert v) l) in
-          Return (st0, Some v)
+            lookup_first_message_for_key_back (Betree_List_Cons (k,
+              Betree_Message_Insert v) l) in
+          Return (st1, (Some v, Betree_Node_Internal node))
         | Betree_Message_Delete ->
           let* _ =
-            betree_Node_lookup_first_message_for_key_back key msgs
-              (Betree_List_Cons (k, Betree_Message_Delete) l) in
-          Return (st0, None)
+            lookup_first_message_for_key_back (Betree_List_Cons (k,
+              Betree_Message_Delete) l) in
+          Return (st1, (None, Betree_Node_Internal node))
         | Betree_Message_Upsert ufs ->
-          let* (st1, v) = betree_Internal_lookup_in_children node key st0 in
-          let* (st2, v0) =
+          let* (st2, (v, i)) = betree_Internal_lookup_in_children node key st1
+            in
+          let* (st3, (v1, l1)) =
             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 (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 node0.id msgs0 st2 in
-          Return (st3, Some v0)
+              Betree_Message_Upsert ufs) l) v key st2 in
+          let* msgs1 = lookup_first_message_for_key_back l1 in
+          let* (st4, _) = betree_store_internal_node i.id msgs1 st3 in
+          Return (st4, (Some v1, Betree_Node_Internal i))
         end
     | 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 Betree_List_Nil
-        in
-      Return (st1, o)
+      let* (st2, (o, i)) = betree_Internal_lookup_in_children node key st1 in
+      let* _ = lookup_first_message_for_key_back Betree_List_Nil in
+      Return (st2, (o, Betree_Node_Internal i))
     end
   | Betree_Node_Leaf node ->
-    let* (st0, bindings) = betree_load_leaf_node node.id st in
+    let* (st1, 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::{betree_main::betree::Node#5}::lookup]: backward function 0
-    Source: 'src/betree.rs', lines 709:4-709:58 *)
-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
-  | 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
-    | 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
-            (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
-        | Betree_Message_Insert v ->
-          let* _ =
-            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
-              (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 (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 (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 node0.id msgs0 st2 in
-          Return (Betree_Node_Internal node0)
-        end
-    | Betree_List_Nil ->
-      let* _ =
-        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
-  | 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)
+    Return (st1, (o, Betree_Node_Leaf node))
   end
 
-(** [betree_main::betree::{betree_main::betree::Node#5}::filter_messages_for_key]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ())
+(** [betree_main::betree::{betree_main::betree::Node#5}::filter_messages_for_key]:
     Source: 'src/betree.rs', lines 674:4-674:77 *)
 let rec betree_Node_filter_messages_for_key
   (key : u64) (msgs : betree_List_t (u64 & betree_Message_t)) :
@@ -487,36 +328,20 @@ let rec betree_Node_filter_messages_for_key
     let (k, m) = p in
     if k = key
     then
-      let* msgs0 =
-        betree_List_pop_front_back (u64 & betree_Message_t) (Betree_List_Cons
-          (k, m) l) in
-      betree_Node_filter_messages_for_key key msgs0
+      let* (_, l1) =
+        betree_List_pop_front (u64 & betree_Message_t) (Betree_List_Cons (k, m)
+          l) in
+      betree_Node_filter_messages_for_key key l1
     else Return (Betree_List_Cons (k, m) l)
   | Betree_List_Nil -> Return Betree_List_Nil
   end
 
-(** [betree_main::betree::{betree_main::betree::Node#5}::lookup_first_message_after_key]: forward function
+(** [betree_main::betree::{betree_main::betree::Node#5}::lookup_first_message_after_key]:
     Source: 'src/betree.rs', lines 689:4-692:34 *)
 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
-  | Betree_List_Cons p next_msgs ->
-    let (k, m) = p in
-    if k = key
-    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::{betree_main::betree::Node#5}::lookup_first_message_after_key]: backward function 0
-    Source: 'src/betree.rs', lines 689:4-692:34 *)
-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)))
+  Tot (result ((betree_List_t (u64 & betree_Message_t)) & (betree_List_t (u64 &
+    betree_Message_t) -> result (betree_List_t (u64 & betree_Message_t)))))
   (decreases (betree_Node_lookup_first_message_after_key_decreases key msgs))
   =
   begin match msgs with
@@ -524,75 +349,76 @@ let rec betree_Node_lookup_first_message_after_key_back
     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 (Betree_List_Cons (k, m) next_msgs0)
-    else Return ret
-  | Betree_List_Nil -> Return ret
+      let* (l, lookup_first_message_after_key_back) =
+        betree_Node_lookup_first_message_after_key key next_msgs in
+      let back_'a =
+        fun ret ->
+          let* next_msgs1 = lookup_first_message_after_key_back ret in
+          Return (Betree_List_Cons (k, m) next_msgs1) in
+      Return (l, back_'a)
+    else Return (Betree_List_Cons (k, m) next_msgs, Return)
+  | Betree_List_Nil -> Return (Betree_List_Nil, Return)
   end
 
-(** [betree_main::betree::{betree_main::betree::Node#5}::apply_to_internal]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ())
+(** [betree_main::betree::{betree_main::betree::Node#5}::apply_to_internal]:
     Source: 'src/betree.rs', lines 521:4-521:89 *)
 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 key msgs in
-  let* b = betree_ListTupleU64T_head_has_key betree_Message_t msgs0 key in
+  let* (msgs1, lookup_first_message_for_key_back) =
+    betree_Node_lookup_first_message_for_key key msgs in
+  let* b = betree_ListTupleU64T_head_has_key betree_Message_t msgs1 key in
   if b
   then
     begin match new_msg with
     | Betree_Message_Insert i ->
-      let* msgs1 = betree_Node_filter_messages_for_key key msgs0 in
-      let* msgs2 =
-        betree_List_push_front (u64 & betree_Message_t) msgs1 (key,
+      let* l = betree_Node_filter_messages_for_key key msgs1 in
+      let* l1 =
+        betree_List_push_front (u64 & betree_Message_t) l (key,
           Betree_Message_Insert i) in
-      betree_Node_lookup_first_message_for_key_back key msgs msgs2
+      lookup_first_message_for_key_back l1
     | Betree_Message_Delete ->
-      let* msgs1 = betree_Node_filter_messages_for_key key msgs0 in
-      let* msgs2 =
-        betree_List_push_front (u64 & betree_Message_t) msgs1 (key,
+      let* l = betree_Node_filter_messages_for_key key msgs1 in
+      let* l1 =
+        betree_List_push_front (u64 & betree_Message_t) l (key,
           Betree_Message_Delete) in
-      betree_Node_lookup_first_message_for_key_back key msgs msgs2
+      lookup_first_message_for_key_back l1
     | Betree_Message_Upsert s ->
-      let* p = betree_List_hd (u64 & betree_Message_t) msgs0 in
+      let* p = betree_List_hd (u64 & betree_Message_t) msgs1 in
       let (_, m) = p in
       begin match m with
       | 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 (u64 & betree_Message_t) msgs1 (key,
+        let* (_, l) = betree_List_pop_front (u64 & betree_Message_t) msgs1 in
+        let* l1 =
+          betree_List_push_front (u64 & betree_Message_t) l (key,
             Betree_Message_Insert v) in
-        betree_Node_lookup_first_message_for_key_back key msgs msgs2
+        lookup_first_message_for_key_back l1
       | Betree_Message_Delete ->
+        let* (_, l) = betree_List_pop_front (u64 & betree_Message_t) msgs1 in
         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 (u64 & betree_Message_t) msgs1 (key,
+        let* l1 =
+          betree_List_push_front (u64 & betree_Message_t) l (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 (u64 & betree_Message_t) msgs1 (key,
+        lookup_first_message_for_key_back l1
+      | Betree_Message_Upsert _ ->
+        let* (msgs2, lookup_first_message_after_key_back) =
+          betree_Node_lookup_first_message_after_key key msgs1 in
+        let* l =
+          betree_List_push_front (u64 & betree_Message_t) msgs2 (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
+        let* msgs3 = lookup_first_message_after_key_back l in
+        lookup_first_message_for_key_back msgs3
       end
     end
   else
-    let* 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
+    let* l =
+      betree_List_push_front (u64 & betree_Message_t) msgs1 (key, new_msg) in
+    lookup_first_message_for_key_back l
 
-(** [betree_main::betree::{betree_main::betree::Node#5}::apply_messages_to_internal]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ())
+(** [betree_main::betree::{betree_main::betree::Node#5}::apply_messages_to_internal]:
     Source: 'src/betree.rs', lines 502:4-505:5 *)
 let rec betree_Node_apply_messages_to_internal
   (msgs : betree_List_t (u64 & betree_Message_t))
@@ -603,89 +429,72 @@ let rec betree_Node_apply_messages_to_internal
   begin match new_msgs with
   | Betree_List_Cons new_msg new_msgs_tl ->
     let (i, m) = new_msg in
-    let* msgs0 = betree_Node_apply_to_internal msgs i m in
-    betree_Node_apply_messages_to_internal msgs0 new_msgs_tl
+    let* l = betree_Node_apply_to_internal msgs i m in
+    betree_Node_apply_messages_to_internal l new_msgs_tl
   | Betree_List_Nil -> Return msgs
   end
 
-(** [betree_main::betree::{betree_main::betree::Node#5}::lookup_mut_in_bindings]: forward function
+(** [betree_main::betree::{betree_main::betree::Node#5}::lookup_mut_in_bindings]:
     Source: 'src/betree.rs', lines 653:4-656:32 *)
 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
-  | Betree_List_Cons hd tl ->
-    let (i, i0) = hd in
-    if i >= key
-    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::{betree_main::betree::Node#5}::lookup_mut_in_bindings]: backward function 0
-    Source: 'src/betree.rs', lines 653:4-656:32 *)
-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)))
+  Tot (result ((betree_List_t (u64 & u64)) & (betree_List_t (u64 & u64) ->
+    result (betree_List_t (u64 & u64)))))
   (decreases (betree_Node_lookup_mut_in_bindings_decreases key bindings))
   =
   begin match bindings with
   | Betree_List_Cons hd tl ->
-    let (i, i0) = hd in
+    let (i, i1) = hd in
     if i >= key
-    then Return ret
+    then Return (Betree_List_Cons (i, i1) tl, Return)
     else
-      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
+      let* (l, lookup_mut_in_bindings_back) =
+        betree_Node_lookup_mut_in_bindings key tl in
+      let back_'a =
+        fun ret ->
+          let* tl1 = lookup_mut_in_bindings_back ret in
+          Return (Betree_List_Cons (i, i1) tl1) in
+      Return (l, back_'a)
+  | Betree_List_Nil -> Return (Betree_List_Nil, Return)
   end
 
-(** [betree_main::betree::{betree_main::betree::Node#5}::apply_to_leaf]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ())
+(** [betree_main::betree::{betree_main::betree::Node#5}::apply_to_leaf]:
     Source: 'src/betree.rs', lines 460:4-460:87 *)
 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 key bindings in
-  let* b = betree_ListTupleU64T_head_has_key u64 bindings0 key in
+  let* (bindings1, lookup_mut_in_bindings_back) =
+    betree_Node_lookup_mut_in_bindings key bindings in
+  let* b = betree_ListTupleU64T_head_has_key u64 bindings1 key in
   if b
   then
-    let* hd = betree_List_pop_front (u64 & u64) bindings0 in
+    let* (hd, l) = betree_List_pop_front (u64 & u64) bindings1 in
     begin match new_msg with
     | 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
+      let* l1 = betree_List_push_front (u64 & u64) l (key, v) in
+      lookup_mut_in_bindings_back l1
+    | Betree_Message_Delete -> lookup_mut_in_bindings_back l
     | Betree_Message_Upsert s ->
       let (_, i) = hd in
       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
+      let* l1 = betree_List_push_front (u64 & u64) l (key, v) in
+      lookup_mut_in_bindings_back l1
     end
   else
     begin match new_msg with
     | 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
+      let* l = betree_List_push_front (u64 & u64) bindings1 (key, v) in
+      lookup_mut_in_bindings_back l
+    | Betree_Message_Delete -> lookup_mut_in_bindings_back bindings1
     | 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
+      let* l = betree_List_push_front (u64 & u64) bindings1 (key, v) in
+      lookup_mut_in_bindings_back l
     end
 
-(** [betree_main::betree::{betree_main::betree::Node#5}::apply_messages_to_leaf]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ())
+(** [betree_main::betree::{betree_main::betree::Node#5}::apply_messages_to_leaf]:
     Source: 'src/betree.rs', lines 444:4-447:5 *)
 let rec betree_Node_apply_messages_to_leaf
   (bindings : betree_List_t (u64 & u64))
@@ -696,18 +505,19 @@ let rec betree_Node_apply_messages_to_leaf
   begin match new_msgs with
   | Betree_List_Cons new_msg new_msgs_tl ->
     let (i, m) = new_msg in
-    let* bindings0 = betree_Node_apply_to_leaf bindings i m in
-    betree_Node_apply_messages_to_leaf bindings0 new_msgs_tl
+    let* l = betree_Node_apply_to_leaf bindings i m in
+    betree_Node_apply_messages_to_leaf l new_msgs_tl
   | Betree_List_Nil -> Return bindings
   end
 
-(** [betree_main::betree::{betree_main::betree::Internal#4}::flush]: forward function
+(** [betree_main::betree::{betree_main::betree::Internal#4}::flush]:
     Source: 'src/betree.rs', lines 410:4-415:26 *)
 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))))
+  Tot (result (state & ((betree_List_t (u64 & betree_Message_t)) &
+    (betree_Internal_t & betree_NodeIdCounter_t))))
   (decreases (
     betree_Internal_flush_decreases self params node_id_cnt content st))
   =
@@ -718,290 +528,142 @@ let rec betree_Internal_flush
   let* len_left = betree_List_len (u64 & betree_Message_t) msgs_left in
   if len_left >= params.min_flush_size
   then
-    let* (st0, _) =
+    let* (st1, p1) =
       betree_Node_apply_messages self.left params node_id_cnt msgs_left st in
-    let* (_, node_id_cnt0) =
-      betree_Node_apply_messages_back self.left params node_id_cnt msgs_left st
-      in
+    let (n, node_id_cnt1) = p1 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 self.right params node_id_cnt0 msgs_right
-          st0 in
-      let* _ =
-        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)
+      let* (st2, p2) =
+        betree_Node_apply_messages self.right params node_id_cnt1 msgs_right
+          st1 in
+      let (n1, node_id_cnt2) = p2 in
+      Return (st2, (Betree_List_Nil, ({ self with left = n; right = n1 },
+        node_id_cnt2)))
+    else Return (st1, (msgs_right, ({ self with left = n }, node_id_cnt1)))
   else
-    let* (st0, _) =
+    let* (st1, p1) =
       betree_Node_apply_messages self.right params node_id_cnt msgs_right st in
-    let* _ =
-      betree_Node_apply_messages_back self.right params node_id_cnt msgs_right
-        st in
-    Return (st0, msgs_left)
-
-(** [betree_main::betree::{betree_main::betree::Internal#4}::flush]: backward function 0
-    Source: 'src/betree.rs', lines 410:4-415:26 *)
-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))
-  =
-  let* p =
-    betree_ListTupleU64T_partition_at_pivot betree_Message_t content self.pivot
-    in
-  let (msgs_left, msgs_right) = p in
-  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 self.left params node_id_cnt msgs_left st in
-    let* (n, node_id_cnt0) =
-      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.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.right params node_id_cnt msgs_right
-        st in
-    Return ({ self with right = n }, node_id_cnt0)
+    let (n, node_id_cnt1) = p1 in
+    Return (st1, (msgs_left, ({ self with right = n }, node_id_cnt1)))
 
-(** [betree_main::betree::{betree_main::betree::Node#5}::apply_messages]: forward function
+(** [betree_main::betree::{betree_main::betree::Node#5}::apply_messages]:
     Source: 'src/betree.rs', lines 588:4-593:5 *)
 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))
-  =
-  begin match self with
-  | 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 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 node0.id content1 st1 in
-      Return (st2, ())
-    else
-      let* (st1, _) = betree_store_internal_node node.id content0 st0 in
-      Return (st1, ())
-  | 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 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 node.id content0 st0 in
-      Return (st1, ())
-  end
-
-(** [betree_main::betree::{betree_main::betree::Node#5}::apply_messages]: backward function 0
-    Source: 'src/betree.rs', lines 588:4-593:5 *)
-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))
+  Tot (result (state & (betree_Node_t & betree_NodeIdCounter_t)))
   (decreases (
     betree_Node_apply_messages_decreases self params node_id_cnt msgs st))
   =
   begin match self with
   | 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
+    let* (st1, content) = betree_load_internal_node node.id st in
+    let* l = betree_Node_apply_messages_to_internal content msgs in
+    let* num_msgs = betree_List_len (u64 & betree_Message_t) l in
     if num_msgs >= params.min_flush_size
     then
-      let* (st1, content1) =
-        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 node0.id content1 st1 in
-      Return (Betree_Node_Internal node0, node_id_cnt0)
+      let* (st2, (content1, p)) =
+        betree_Internal_flush node params node_id_cnt l st1 in
+      let (node1, node_id_cnt1) = p in
+      let* (st3, _) = betree_store_internal_node node1.id content1 st2 in
+      Return (st3, (Betree_Node_Internal node1, node_id_cnt1))
     else
-      let* _ = betree_store_internal_node node.id content0 st0 in
-      Return (Betree_Node_Internal node, node_id_cnt)
+      let* (st2, _) = betree_store_internal_node node.id l st1 in
+      Return (st2, (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* (st1, content) = betree_load_leaf_node node.id st in
+    let* l = betree_Node_apply_messages_to_leaf content msgs in
+    let* len = betree_List_len (u64 & u64) l in
     let* i = u64_mul 2 params.split_size in
     if len >= i
     then
-      let* (st1, new_node) =
-        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 (Betree_Node_Internal new_node, node_id_cnt0)
+      let* (st2, (new_node, nic)) =
+        betree_Leaf_split node l params node_id_cnt st1 in
+      let* (st3, _) = betree_store_leaf_node node.id Betree_List_Nil st2 in
+      Return (st3, (Betree_Node_Internal new_node, nic))
     else
-      let* _ = betree_store_leaf_node node.id content0 st0 in
-      Return (Betree_Node_Leaf { node with size = len }, node_id_cnt)
+      let* (st2, _) = betree_store_leaf_node node.id l st1 in
+      Return (st2, (Betree_Node_Leaf { node with size = len }, node_id_cnt))
   end
 
-(** [betree_main::betree::{betree_main::betree::Node#5}::apply]: forward function
+(** [betree_main::betree::{betree_main::betree::Node#5}::apply]:
     Source: 'src/betree.rs', lines 576:4-582:5 *)
 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)
+  result (state & (betree_Node_t & betree_NodeIdCounter_t))
   =
-  let l = Betree_List_Nil in
-  let* (st0, _) =
+  let* (st1, p) =
     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 (Betree_List_Cons
-      (key, new_msg) l) st in
-  Return (st0, ())
-
-(** [betree_main::betree::{betree_main::betree::Node#5}::apply]: backward function 0
-    Source: 'src/betree.rs', lines 576:4-582:5 *)
-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 = Betree_List_Nil in
-  betree_Node_apply_messages_back self params node_id_cnt (Betree_List_Cons
-    (key, new_msg) l) st
+      new_msg) Betree_List_Nil) st in
+  let (self1, node_id_cnt1) = p in
+  Return (st1, (self1, node_id_cnt1))
 
-(** [betree_main::betree::{betree_main::betree::BeTree#6}::new]: forward function
+(** [betree_main::betree::{betree_main::betree::BeTree#6}::new]:
     Source: 'src/betree.rs', lines 849:4-849:60 *)
 let betree_BeTree_new
   (min_flush_size : u64) (split_size : u64) (st : state) :
   result (state & betree_BeTree_t)
   =
   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,
+  let* (id, nic) = betree_NodeIdCounter_fresh_id node_id_cnt in
+  let* (st1, _) = betree_store_leaf_node id Betree_List_Nil st in
+  Return (st1,
     {
       params = { min_flush_size = min_flush_size; split_size = split_size };
-      node_id_cnt = node_id_cnt0;
+      node_id_cnt = nic;
       root = (Betree_Node_Leaf { id = id; size = 0 })
     })
 
-(** [betree_main::betree::{betree_main::betree::BeTree#6}::apply]: forward function
+(** [betree_main::betree::{betree_main::betree::BeTree#6}::apply]:
     Source: 'src/betree.rs', lines 868:4-868:47 *)
 let betree_BeTree_apply
   (self : betree_BeTree_t) (key : u64) (msg : betree_Message_t) (st : state) :
-  result (state & unit)
+  result (state & betree_BeTree_t)
   =
-  let* (st0, _) =
+  let* (st1, p) =
     betree_Node_apply self.root self.params self.node_id_cnt key msg st in
-  let* _ =
-    betree_Node_apply_back self.root self.params self.node_id_cnt key msg st in
-  Return (st0, ())
+  let (n, nic) = p in
+  Return (st1, { self with node_id_cnt = nic; root = n })
 
-(** [betree_main::betree::{betree_main::betree::BeTree#6}::apply]: backward function 0
-    Source: 'src/betree.rs', lines 868:4-868:47 *)
-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.root self.params self.node_id_cnt key msg st in
-  Return { self with node_id_cnt = nic; root = n }
-
-(** [betree_main::betree::{betree_main::betree::BeTree#6}::insert]: forward function
+(** [betree_main::betree::{betree_main::betree::BeTree#6}::insert]:
     Source: 'src/betree.rs', lines 874:4-874:52 *)
 let betree_BeTree_insert
   (self : betree_BeTree_t) (key : u64) (value : u64) (st : state) :
-  result (state & unit)
-  =
-  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_main::betree::BeTree#6}::insert]: backward function 0
-    Source: 'src/betree.rs', lines 874:4-874:52 *)
-let betree_BeTree_insert_back
-  (self : betree_BeTree_t) (key : u64) (value : u64) (st : state) :
-  result betree_BeTree_t
+  result (state & betree_BeTree_t)
   =
-  betree_BeTree_apply_back self key (Betree_Message_Insert value) st
+  betree_BeTree_apply self key (Betree_Message_Insert value) st
 
-(** [betree_main::betree::{betree_main::betree::BeTree#6}::delete]: forward function
+(** [betree_main::betree::{betree_main::betree::BeTree#6}::delete]:
     Source: 'src/betree.rs', lines 880:4-880:38 *)
 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_main::betree::BeTree#6}::delete]: backward function 0
-    Source: 'src/betree.rs', lines 880:4-880:38 *)
-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_main::betree::BeTree#6}::upsert]: forward function
-    Source: 'src/betree.rs', lines 886:4-886:59 *)
-let betree_BeTree_upsert
-  (self : betree_BeTree_t) (key : u64) (upd : betree_UpsertFunState_t)
-  (st : state) :
-  result (state & unit)
+  (self : betree_BeTree_t) (key : u64) (st : state) :
+  result (state & betree_BeTree_t)
   =
-  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_BeTree_apply self key Betree_Message_Delete st
 
-(** [betree_main::betree::{betree_main::betree::BeTree#6}::upsert]: backward function 0
+(** [betree_main::betree::{betree_main::betree::BeTree#6}::upsert]:
     Source: 'src/betree.rs', lines 886:4-886:59 *)
-let betree_BeTree_upsert_back
+let betree_BeTree_upsert
   (self : betree_BeTree_t) (key : u64) (upd : betree_UpsertFunState_t)
   (st : state) :
-  result betree_BeTree_t
+  result (state & betree_BeTree_t)
   =
-  betree_BeTree_apply_back self key (Betree_Message_Upsert upd) st
+  betree_BeTree_apply self key (Betree_Message_Upsert upd) st
 
-(** [betree_main::betree::{betree_main::betree::BeTree#6}::lookup]: forward function
+(** [betree_main::betree::{betree_main::betree::BeTree#6}::lookup]:
     Source: 'src/betree.rs', lines 895:4-895:62 *)
 let betree_BeTree_lookup
   (self : betree_BeTree_t) (key : u64) (st : state) :
-  result (state & (option u64))
+  result (state & ((option u64) & betree_BeTree_t))
   =
-  betree_Node_lookup self.root key st
-
-(** [betree_main::betree::{betree_main::betree::BeTree#6}::lookup]: backward function 0
-    Source: 'src/betree.rs', lines 895:4-895:62 *)
-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 }
+  let* (st1, (o, n)) = betree_Node_lookup self.root key st in
+  Return (st1, (o, { self with root = n }))
 
-(** [betree_main::main]: forward function
+(** [betree_main::main]:
     Source: 'src/betree_main.rs', lines 5:0-5:9 *)
 let main : result unit =
   Return ()
diff --git a/tests/fstar/betree/BetreeMain.FunsExternal.fsti b/tests/fstar/betree/BetreeMain.FunsExternal.fsti
index cd2f956f..de9b96fd 100644
--- a/tests/fstar/betree/BetreeMain.FunsExternal.fsti
+++ b/tests/fstar/betree/BetreeMain.FunsExternal.fsti
@@ -6,29 +6,29 @@ include BetreeMain.Types
 
 #set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
 
-(** [betree_main::betree_utils::load_internal_node]: forward function
+(** [betree_main::betree_utils::load_internal_node]:
     Source: 'src/betree_utils.rs', lines 98:0-98:63 *)
 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
+(** [betree_main::betree_utils::store_internal_node]:
     Source: 'src/betree_utils.rs', lines 115:0-115:71 *)
 val betree_utils_store_internal_node
   :
   u64 -> betree_List_t (u64 & betree_Message_t) -> state -> result (state &
     unit)
 
-(** [betree_main::betree_utils::load_leaf_node]: forward function
+(** [betree_main::betree_utils::load_leaf_node]:
     Source: 'src/betree_utils.rs', lines 132:0-132:55 *)
 val betree_utils_load_leaf_node
   : u64 -> state -> result (state & (betree_List_t (u64 & u64)))
 
-(** [betree_main::betree_utils::store_leaf_node]: forward function
+(** [betree_main::betree_utils::store_leaf_node]:
     Source: 'src/betree_utils.rs', lines 145:0-145:63 *)
 val betree_utils_store_leaf_node
   : u64 -> betree_List_t (u64 & u64) -> state -> result (state & unit)
 
-(** [core::option::{core::option::Option<T>}::unwrap]: forward function
+(** [core::option::{core::option::Option<T>}::unwrap]:
     Source: '/rustc/d59363ad0b6391b7fc5bbb02c9ccf9300eef3753/library/core/src/option.rs', lines 932:4-932:34 *)
 val core_option_Option_unwrap
   (t : Type0) : option t -> state -> result (state & t)
diff --git a/tests/fstar/betree/Primitives.fst b/tests/fstar/betree/Primitives.fst
index a3ffbde4..fca80829 100644
--- a/tests/fstar/betree/Primitives.fst
+++ b/tests/fstar/betree/Primitives.fst
@@ -55,8 +55,7 @@ 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
+let core_mem_replace (a : Type0) (x : a) (y : a) : a & a = (x, x)
 
 // We don't really use raw pointers for now
 type mut_raw_ptr (t : Type0) = { v : t }
@@ -477,8 +476,7 @@ noeq type core_ops_index_Index (self idx : Type0) = {
 // 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;
+  index_mut : self → idx → result (indexInst.output & (indexInst.output → result self));
 }
 
 // Trait declaration [core::ops::deref::Deref]
@@ -490,8 +488,7 @@ noeq type core_ops_deref_Deref (self : Type0) = {
 // 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;
+  deref_mut : self → result (derefInst.target & (derefInst.target → result self));
 }
 
 type core_ops_range_Range (a : Type0) = {
@@ -502,8 +499,8 @@ type core_ops_range_Range (a : Type0) = {
 (*** [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
+let alloc_boxed_Box_deref_mut (t : Type0) (x : t) : result (t & (t -> result t)) =
+  Return (x, (fun x -> Return x))
 
 // Trait instance
 let alloc_boxed_Box_coreopsDerefInst (self : Type0) : core_ops_deref_Deref self = {
@@ -515,7 +512,6 @@ let alloc_boxed_Box_coreopsDerefInst (self : Type0) : core_ops_deref_Deref self
 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 *)
@@ -535,10 +531,18 @@ let array_index_usize (a : Type0) (n : usize) (x : array a n) (i : usize) : resu
   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) =
+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
 
+let array_index_mut_usize (a : Type0) (n : usize) (x : array a n) (i : usize) :
+  result (a & (a -> result (array a n))) =
+  match array_index_usize a n x i with
+  | Fail e -> Fail e
+  | Return v ->
+    Return (v, array_update_usize a n x i)
+
 (*** Slice *)
 type slice (a : Type0) = s:list a{length s <= usize_max}
 
@@ -552,6 +556,13 @@ let slice_update_usize (a : Type0) (x : slice a) (i : usize) (nx : a) : result (
   if i < length x then Return (list_update x i nx)
   else Fail Failure
 
+let slice_index_mut_usize (a : Type0) (s : slice a) (i : usize) :
+  result (a & (a -> result (slice a))) =
+  match slice_index_usize a s i with
+  | Fail e -> Fail e
+  | Return x ->
+    Return (x, slice_update_usize a s i)
+
 (*** Subslices *)
 
 let array_to_slice (a : Type0) (n : usize) (x : array a n) : result (slice a) = Return x
@@ -559,6 +570,10 @@ let array_from_slice (a : Type0) (n : usize) (x : array a n) (s : slice a) : res
   if length s = n then Return s
   else Fail Failure
 
+let array_to_slice_mut (a : Type0) (n : usize) (x : array a n) :
+  result (slice a & (slice a -> result (array a n))) =
+  Return (x, array_from_slice a n x)
+
 // 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()
@@ -588,8 +603,13 @@ let alloc_vec_Vec_index_usize (#a : Type0) (v : alloc_vec_Vec a) (i : usize) : r
 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_index_mut_usize (#a : Type0) (v: alloc_vec_Vec a) (i: usize) :
+  result (a & (a → result (alloc_vec_Vec a))) =
+  match alloc_vec_Vec_index_usize v i with
+  | Return x ->
+    Return (x, alloc_vec_Vec_update_usize v i)
+  | Fail e -> Fail e
+
 let alloc_vec_Vec_push (a  : Type0) (v : alloc_vec_Vec a) (x : a) :
   Pure (result (alloc_vec_Vec a))
   (requires True)
@@ -605,9 +625,6 @@ let alloc_vec_Vec_push (a  : Type0) (v : alloc_vec_Vec a) (x : a) :
     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
 
@@ -619,13 +636,11 @@ 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_mut : self → t → result (option output & (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;
+  index_mut : self → t → result (output & (output -> result t));
 }
 
 // [core::slice::index::[T]::index]: forward function
@@ -643,14 +658,8 @@ let core_slice_index_RangeUsize_get (t : Type0) (i : core_ops_range_Range usize)
   admit () // TODO
 
 // [core::slice::index::Range::get_mut]: forward function
-let core_slice_index_RangeUsize_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_RangeUsize_get_mut_back
-  (t : Type0) :
-  core_ops_range_Range usize → slice t → option (slice t) → result (slice t) =
+let core_slice_index_RangeUsize_get_mut (t : Type0) :
+  core_ops_range_Range usize → slice t → result (option (slice t) & (option (slice t) -> result (slice t))) =
   admit () // TODO
 
 // [core::slice::index::Range::get_unchecked]: forward function
@@ -675,27 +684,16 @@ let core_slice_index_RangeUsize_index
   admit () // TODO
 
 // [core::slice::index::Range::index_mut]: forward function
-let core_slice_index_RangeUsize_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_RangeUsize_index_mut_back
-  (t : Type0) : core_ops_range_Range usize → slice t → slice t → result (slice t) =
+let core_slice_index_RangeUsize_index_mut (t : Type0) :
+  core_ops_range_Range usize → slice t → result (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 =
+  slice t → idx → result (inst.output & (inst.output -> result (slice t))) =
   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)
@@ -705,13 +703,8 @@ let core_array_Array_index
 // [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) =
+  (a : array t n) (i : idx) :
+  result (inst.indexInst.output & (inst.indexInst.output -> result (array t n))) =
   admit () // TODO
 
 // Trait implementation: [core::slice::index::private_slice_index::Range]
@@ -725,12 +718,10 @@ let core_slice_index_SliceIndexRangeUsizeSliceTInst (t : Type0) :
   output = slice t;
   get = core_slice_index_RangeUsize_get t;
   get_mut = core_slice_index_RangeUsize_get_mut t;
-  get_mut_back = core_slice_index_RangeUsize_get_mut_back t;
   get_unchecked = core_slice_index_RangeUsize_get_unchecked t;
   get_unchecked_mut = core_slice_index_RangeUsize_get_unchecked_mut t;
   index = core_slice_index_RangeUsize_index t;
   index_mut = core_slice_index_RangeUsize_index_mut t;
-  index_mut_back = core_slice_index_RangeUsize_index_mut_back t;
 }
 
 // Trait implementation: [core::slice::index::[T]]
@@ -747,7 +738,6 @@ let core_ops_index_IndexMutSliceTIInst (t idx : Type0)
   core_ops_index_IndexMut (slice t) idx = {
   indexInst = core_ops_index_IndexSliceTIInst 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]]
@@ -764,7 +754,6 @@ let core_ops_index_IndexMutArrayIInst (t idx : Type0) (n : usize)
   core_ops_index_IndexMut (array t n) idx = {
   indexInst = core_ops_index_IndexArrayInst 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
@@ -773,13 +762,8 @@ let core_slice_index_usize_get
   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) =
+let core_slice_index_usize_get_mut (t : Type0) :
+  usize → slice t → result (option t & (option t -> result (slice t))) =
   admit () // TODO
 
 // [core::slice::index::usize::get_unchecked]: forward function
@@ -797,12 +781,8 @@ 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) =
+let core_slice_index_usize_index_mut (t : Type0) :
+  usize → slice t → result (t & (t -> result (slice t))) =
   admit () // TODO
 
 // Trait implementation: [core::slice::index::private_slice_index::usize]
@@ -816,12 +796,10 @@ let core_slice_index_SliceIndexUsizeSliceTInst (t : Type0) :
   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
@@ -831,13 +809,8 @@ let alloc_vec_Vec_index (t idx : Type0) (inst : core_slice_index_SliceIndex idx
 
 // [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) =
+  (self : alloc_vec_Vec t) (i : idx) :
+  result (inst.output & (inst.output -> result (alloc_vec_Vec t))) =
   admit () // TODO
 
 // Trait implementation: [alloc::vec::Vec]
@@ -854,7 +827,6 @@ let alloc_vec_Vec_coreopsindexIndexMutInst (t idx : Type0)
   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 *)
@@ -870,15 +842,7 @@ let alloc_vec_Vec_index_eq (#a : Type0) (v : alloc_vec_Vec a) (i : usize) :
 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_SliceIndexUsizeSliceTInst a) v i ==
-      alloc_vec_Vec_index_usize v i)
+      alloc_vec_Vec_index_mut_usize v i)
   [SMTPat (alloc_vec_Vec_index_mut a usize (core_slice_index_SliceIndexUsizeSliceTInst 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_SliceIndexUsizeSliceTInst a) v i x ==
-      alloc_vec_Vec_update_usize v i x)
-  [SMTPat (alloc_vec_Vec_index_mut_back a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i x)]
-  =
-  admit()
diff --git a/tests/fstar/betree_back_stateful/BetreeMain.Funs.fst b/tests/fstar/betree_back_stateful/BetreeMain.Funs.fst
index 6c3c2161..196f120c 100644
--- a/tests/fstar/betree_back_stateful/BetreeMain.Funs.fst
+++ b/tests/fstar/betree_back_stateful/BetreeMain.Funs.fst
@@ -8,7 +8,7 @@ include BetreeMain.Clauses
 
 #set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
 
-(** [betree_main::betree::load_internal_node]: forward function
+(** [betree_main::betree::load_internal_node]:
     Source: 'src/betree.rs', lines 36:0-36:52 *)
 let betree_load_internal_node
   (id : u64) (st : state) :
@@ -16,58 +16,48 @@ let betree_load_internal_node
   =
   betree_utils_load_internal_node id st
 
-(** [betree_main::betree::store_internal_node]: forward function
+(** [betree_main::betree::store_internal_node]:
     Source: 'src/betree.rs', lines 41:0-41:60 *)
 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 id content st in
-  Return (st0, ())
+  let* (st1, _) = betree_utils_store_internal_node id content st in
+  Return (st1, ())
 
-(** [betree_main::betree::load_leaf_node]: forward function
+(** [betree_main::betree::load_leaf_node]:
     Source: 'src/betree.rs', lines 46:0-46:44 *)
 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
+(** [betree_main::betree::store_leaf_node]:
     Source: 'src/betree.rs', lines 51:0-51:52 *)
 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 id content st in
-  Return (st0, ())
-
-(** [betree_main::betree::fresh_node_id]: forward function
-    Source: 'src/betree.rs', lines 55:0-55:48 *)
-let betree_fresh_node_id (counter : u64) : result u64 =
-  let* _ = u64_add counter 1 in Return counter
+  let* (st1, _) = betree_utils_store_leaf_node id content st in
+  Return (st1, ())
 
-(** [betree_main::betree::fresh_node_id]: backward function 0
+(** [betree_main::betree::fresh_node_id]:
     Source: 'src/betree.rs', lines 55:0-55:48 *)
-let betree_fresh_node_id_back (counter : u64) : result u64 =
-  u64_add counter 1
+let betree_fresh_node_id (counter : u64) : result (u64 & u64) =
+  let* counter1 = u64_add counter 1 in Return (counter, counter1)
 
-(** [betree_main::betree::{betree_main::betree::NodeIdCounter}::new]: forward function
+(** [betree_main::betree::{betree_main::betree::NodeIdCounter}::new]:
     Source: 'src/betree.rs', lines 206:4-206:20 *)
 let betree_NodeIdCounter_new : result betree_NodeIdCounter_t =
   Return { next_node_id = 0 }
 
-(** [betree_main::betree::{betree_main::betree::NodeIdCounter}::fresh_id]: forward function
+(** [betree_main::betree::{betree_main::betree::NodeIdCounter}::fresh_id]:
     Source: 'src/betree.rs', lines 210:4-210:36 *)
 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
+  (self : betree_NodeIdCounter_t) : result (u64 & betree_NodeIdCounter_t) =
+  let* i = u64_add self.next_node_id 1 in
+  Return (self.next_node_id, { next_node_id = i })
 
-(** [betree_main::betree::{betree_main::betree::NodeIdCounter}::fresh_id]: backward function 0
-    Source: 'src/betree.rs', lines 210:4-210:36 *)
-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
+(** [betree_main::betree::upsert_update]:
     Source: 'src/betree.rs', lines 234:0-234:70 *)
 let betree_upsert_update
   (prev : option u64) (st : betree_UpsertFunState_t) : result u64 =
@@ -75,30 +65,30 @@ let betree_upsert_update
   | None ->
     begin match st with
     | Betree_UpsertFunState_Add v -> Return v
-    | Betree_UpsertFunState_Sub i -> Return 0
+    | Betree_UpsertFunState_Sub _ -> Return 0
     end
-  | Some prev0 ->
+  | Some prev1 ->
     begin match st with
     | 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
+      let* margin = u64_sub core_u64_max prev1 in
+      if margin >= v then u64_add prev1 v else Return core_u64_max
     | Betree_UpsertFunState_Sub v ->
-      if prev0 >= v then u64_sub prev0 v else Return 0
+      if prev1 >= v then u64_sub prev1 v else Return 0
     end
   end
 
-(** [betree_main::betree::{betree_main::betree::List<T>#1}::len]: forward function
+(** [betree_main::betree::{betree_main::betree::List<T>#1}::len]:
     Source: 'src/betree.rs', lines 276:4-276:24 *)
 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
-  | Betree_List_Cons x tl -> let* i = betree_List_len t tl in u64_add 1 i
+  | Betree_List_Cons _ tl -> let* i = betree_List_len t tl in u64_add 1 i
   | Betree_List_Nil -> Return 0
   end
 
-(** [betree_main::betree::{betree_main::betree::List<T>#1}::split_at]: forward function
+(** [betree_main::betree::{betree_main::betree::List<T>#1}::split_at]:
     Source: 'src/betree.rs', lines 284:4-284:51 *)
 let rec betree_List_split_at
   (t : Type0) (self : betree_List_t t) (n : u64) :
@@ -113,57 +103,45 @@ let rec betree_List_split_at
       let* i = u64_sub n 1 in
       let* p = betree_List_split_at t tl i in
       let (ls0, ls1) = p in
-      let l = ls0 in
-      Return (Betree_List_Cons hd l, ls1)
+      Return (Betree_List_Cons hd ls0, ls1)
     | Betree_List_Nil -> Fail Failure
     end
 
-(** [betree_main::betree::{betree_main::betree::List<T>#1}::push_front]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ())
+(** [betree_main::betree::{betree_main::betree::List<T>#1}::push_front]:
     Source: 'src/betree.rs', lines 299:4-299:34 *)
 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 (Betree_List_Cons x l)
-
-(** [betree_main::betree::{betree_main::betree::List<T>#1}::pop_front]: forward function
-    Source: 'src/betree.rs', lines 306:4-306:32 *)
-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
-  | Betree_List_Cons x tl -> Return x
-  | Betree_List_Nil -> Fail Failure
-  end
+  let (tl, _) = core_mem_replace (betree_List_t t) self Betree_List_Nil in
+  Return (Betree_List_Cons x tl)
 
-(** [betree_main::betree::{betree_main::betree::List<T>#1}::pop_front]: backward function 0
+(** [betree_main::betree::{betree_main::betree::List<T>#1}::pop_front]:
     Source: 'src/betree.rs', lines 306:4-306:32 *)
-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
+let betree_List_pop_front
+  (t : Type0) (self : betree_List_t t) : result (t & (betree_List_t t)) =
+  let (ls, _) = core_mem_replace (betree_List_t t) self Betree_List_Nil in
   begin match ls with
-  | Betree_List_Cons x tl -> Return tl
+  | Betree_List_Cons x tl -> Return (x, tl)
   | Betree_List_Nil -> Fail Failure
   end
 
-(** [betree_main::betree::{betree_main::betree::List<T>#1}::hd]: forward function
+(** [betree_main::betree::{betree_main::betree::List<T>#1}::hd]:
     Source: 'src/betree.rs', lines 318:4-318:22 *)
 let betree_List_hd (t : Type0) (self : betree_List_t t) : result t =
   begin match self with
-  | Betree_List_Cons hd l -> Return hd
+  | Betree_List_Cons hd _ -> Return hd
   | Betree_List_Nil -> Fail Failure
   end
 
-(** [betree_main::betree::{betree_main::betree::List<(u64, T)>#2}::head_has_key]: forward function
+(** [betree_main::betree::{betree_main::betree::List<(u64, T)>#2}::head_has_key]:
     Source: 'src/betree.rs', lines 327:4-327:44 *)
 let betree_ListTupleU64T_head_has_key
   (t : Type0) (self : betree_List_t (u64 & t)) (key : u64) : result bool =
   begin match self with
-  | Betree_List_Cons hd l -> let (i, _) = hd in Return (i = key)
+  | Betree_List_Cons hd _ -> let (i, _) = hd in Return (i = key)
   | Betree_List_Nil -> Return false
   end
 
-(** [betree_main::betree::{betree_main::betree::List<(u64, T)>#2}::partition_at_pivot]: forward function
+(** [betree_main::betree::{betree_main::betree::List<(u64, T)>#2}::partition_at_pivot]:
     Source: 'src/betree.rs', lines 339:4-339:73 *)
 let rec betree_ListTupleU64T_partition_at_pivot
   (t : Type0) (self : betree_List_t (u64 & t)) (pivot : u64) :
@@ -178,124 +156,55 @@ let rec betree_ListTupleU64T_partition_at_pivot
     else
       let* p = betree_ListTupleU64T_partition_at_pivot t tl pivot in
       let (ls0, ls1) = p in
-      let l = ls0 in
-      Return (Betree_List_Cons (i, x) l, ls1)
+      Return (Betree_List_Cons (i, x) ls0, ls1)
   | Betree_List_Nil -> Return (Betree_List_Nil, Betree_List_Nil)
   end
 
-(** [betree_main::betree::{betree_main::betree::Leaf#3}::split]: forward function
+(** [betree_main::betree::{betree_main::betree::Leaf#3}::split]:
     Source: 'src/betree.rs', lines 359:4-364:17 *)
 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)
-  =
-  let* p = betree_List_split_at (u64 & u64) content params.split_size in
-  let (content0, content1) = p in
-  let* p0 = betree_List_hd (u64 & u64) content1 in
-  let (pivot, _) = p0 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* (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::{betree_main::betree::Leaf#3}::split]: backward function 0
-    Source: 'src/betree.rs', lines 359:4-364:17 *)
-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 (u64 & u64) content params.split_size in
-  let (content0, content1) = p 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::{betree_main::betree::Leaf#3}::split]: backward function 1
-    Source: 'src/betree.rs', lines 359:4-364:17 *)
-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 (u64 & u64) content params.split_size in
-  let (content0, content1) = p 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::{betree_main::betree::Leaf#3}::split]: backward function 2
-    Source: 'src/betree.rs', lines 359:4-364:17 *)
-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_NodeIdCounter_t)
+  result (state & (betree_Internal_t & betree_NodeIdCounter_t))
   =
   let* p = betree_List_split_at (u64 & u64) content params.split_size in
   let (content0, content1) = p 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* p1 = betree_List_hd (u64 & u64) content1 in
+  let (pivot, _) = p1 in
+  let* (id0, nic) = betree_NodeIdCounter_fresh_id node_id_cnt in
+  let* (id1, nic1) = betree_NodeIdCounter_fresh_id nic 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)
+  let* (st2, _) = betree_store_leaf_node id1 content1 st1 in
+  let n = Betree_Node_Leaf { id = id0; size = params.split_size } in
+  let n1 = Betree_Node_Leaf { id = id1; size = params.split_size } in
+  Return (st2, ({ id = self.id; pivot = pivot; left = n; right = n1 }, nic1))
 
-(** [betree_main::betree::{betree_main::betree::Node#5}::lookup_first_message_for_key]: forward function
+(** [betree_main::betree::{betree_main::betree::Node#5}::lookup_first_message_for_key]:
     Source: 'src/betree.rs', lines 789:4-792:34 *)
 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)))
+  Tot (result ((betree_List_t (u64 & betree_Message_t)) & (betree_List_t (u64 &
+    betree_Message_t) -> result (betree_List_t (u64 & betree_Message_t)))))
   (decreases (betree_Node_lookup_first_message_for_key_decreases key msgs))
   =
   begin match msgs with
   | Betree_List_Cons x next_msgs ->
     let (i, m) = x in
     if i >= key
-    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::{betree_main::betree::Node#5}::lookup_first_message_for_key]: backward function 0
-    Source: 'src/betree.rs', lines 789:4-792:34 *)
-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
-  | Betree_List_Cons x next_msgs ->
-    let (i, m) = x in
-    if i >= key
-    then Return ret
+    then Return (Betree_List_Cons (i, m) next_msgs, Return)
     else
-      let* next_msgs0 =
-        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
+      let* (l, lookup_first_message_for_key_back) =
+        betree_Node_lookup_first_message_for_key key next_msgs in
+      let back_'a =
+        fun ret ->
+          let* next_msgs1 = lookup_first_message_for_key_back ret in
+          Return (Betree_List_Cons (i, m) next_msgs1) in
+      Return (l, back_'a)
+  | Betree_List_Nil -> Return (Betree_List_Nil, Return)
   end
 
-(** [betree_main::betree::{betree_main::betree::Node#5}::lookup_in_bindings]: forward function
+(** [betree_main::betree::{betree_main::betree::Node#5}::lookup_in_bindings]:
     Source: 'src/betree.rs', lines 636:4-636:80 *)
 let rec betree_Node_lookup_in_bindings
   (key : u64) (bindings : betree_List_t (u64 & u64)) :
@@ -304,221 +213,110 @@ let rec betree_Node_lookup_in_bindings
   =
   begin match bindings with
   | Betree_List_Cons hd tl ->
-    let (i, i0) = hd in
+    let (i, i1) = hd in
     if i = key
-    then Return (Some i0)
+    then Return (Some i1)
     else if i > key then Return None else betree_Node_lookup_in_bindings key tl
   | Betree_List_Nil -> Return None
   end
 
-(** [betree_main::betree::{betree_main::betree::Node#5}::apply_upserts]: forward function
+(** [betree_main::betree::{betree_main::betree::Node#5}::apply_upserts]:
     Source: 'src/betree.rs', lines 819:4-819:90 *)
 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))
+  Tot (result (state & (u64 & (betree_List_t (u64 & betree_Message_t)))))
   (decreases (betree_Node_apply_upserts_decreases msgs prev key st))
   =
   let* b = betree_ListTupleU64T_head_has_key betree_Message_t msgs key in
   if b
   then
-    let* msg = betree_List_pop_front (u64 & betree_Message_t) msgs in
+    let* (msg, l) = betree_List_pop_front (u64 & betree_Message_t) msgs in
     let (_, m) = msg in
     begin match m with
-    | Betree_Message_Insert i -> Fail Failure
+    | Betree_Message_Insert _ -> 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
+      betree_Node_apply_upserts l (Some v) key st
     end
   else
-    let* (st0, v) = core_option_Option_unwrap u64 prev st in
-    let* _ =
+    let* (st1, v) = core_option_Option_unwrap u64 prev st in
+    let* l =
       betree_List_push_front (u64 & betree_Message_t) msgs (key,
         Betree_Message_Insert v) in
-    Return (st0, v)
+    Return (st1, (v, l))
 
-(** [betree_main::betree::{betree_main::betree::Node#5}::apply_upserts]: backward function 0
-    Source: 'src/betree.rs', lines 819:4-819:90 *)
-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))
-  =
-  let* b = betree_ListTupleU64T_head_has_key betree_Message_t msgs key in
-  if b
-  then
-    let* msg = betree_List_pop_front (u64 & betree_Message_t) msgs in
-    let (_, m) = msg in
-    begin match m with
-    | 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 u64 prev st in
-    let* msgs0 =
-      betree_List_push_front (u64 & betree_Message_t) msgs (key,
-        Betree_Message_Insert v) in
-    Return (st0, msgs0)
-
-(** [betree_main::betree::{betree_main::betree::Internal#4}::lookup_in_children]: forward function
+(** [betree_main::betree::{betree_main::betree::Internal#4}::lookup_in_children]:
     Source: 'src/betree.rs', lines 395:4-395:63 *)
 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))
-  =
-  if key < self.pivot
-  then betree_Node_lookup self.left key st
-  else betree_Node_lookup self.right key st
-
-(** [betree_main::betree::{betree_main::betree::Internal#4}::lookup_in_children]: backward function 0
-    Source: 'src/betree.rs', lines 395:4-395:63 *)
-and betree_Internal_lookup_in_children_back
-  (self : betree_Internal_t) (key : u64) (st : state) (st0 : state) :
-  Tot (result (state & betree_Internal_t))
+  Tot (result (state & ((option u64) & betree_Internal_t)))
   (decreases (betree_Internal_lookup_in_children_decreases self key st))
   =
   if key < self.pivot
   then
-    let* (st1, n) = betree_Node_lookup_back self.left key st st0 in
-    Return (st1, { self with left = n })
+    let* (st1, (o, n)) = betree_Node_lookup self.left key st in
+    Return (st1, (o, { self with left = n }))
   else
-    let* (st1, n) = betree_Node_lookup_back self.right key st st0 in
-    Return (st1, { self with right = n })
+    let* (st1, (o, n)) = betree_Node_lookup self.right key st in
+    Return (st1, (o, { self with right = n }))
 
-(** [betree_main::betree::{betree_main::betree::Node#5}::lookup]: forward function
+(** [betree_main::betree::{betree_main::betree::Node#5}::lookup]:
     Source: 'src/betree.rs', lines 709:4-709:58 *)
 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))
-  =
-  begin match self with
-  | 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
-    | Betree_List_Cons p l ->
-      let (k, msg) = p in
-      if k <> key
-      then
-        let* (st1, o) = betree_Internal_lookup_in_children node key st0 in
-        let* _ =
-          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
-        | Betree_Message_Insert v ->
-          let* _ =
-            betree_Node_lookup_first_message_for_key_back key msgs
-              (Betree_List_Cons (k, Betree_Message_Insert v) l) in
-          Return (st0, Some v)
-        | Betree_Message_Delete ->
-          let* _ =
-            betree_Node_lookup_first_message_for_key_back key msgs
-              (Betree_List_Cons (k, Betree_Message_Delete) l) in
-          Return (st0, None)
-        | Betree_Message_Upsert ufs ->
-          let* (st1, v) = betree_Internal_lookup_in_children node key st0 in
-          let* (st2, v0) =
-            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
-          let* (st4, pending0) =
-            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 node0.id msgs0 st4 in
-          Return (st5, Some v0)
-        end
-    | 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 Betree_List_Nil
-        in
-      Return (st1, o)
-    end
-  | 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::{betree_main::betree::Node#5}::lookup]: backward function 0
-    Source: 'src/betree.rs', lines 709:4-709:58 *)
-and betree_Node_lookup_back
-  (self : betree_Node_t) (key : u64) (st : state) (st0 : state) :
-  Tot (result (state & betree_Node_t))
+  Tot (result (state & ((option u64) & betree_Node_t)))
   (decreases (betree_Node_lookup_decreases self key st))
   =
   begin match self with
   | 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
+    let* (pending, lookup_first_message_for_key_back) =
+      betree_Node_lookup_first_message_for_key key msgs in
     begin match pending with
     | Betree_List_Cons p l ->
       let (k, msg) = p in
       if k <> key
       then
+        let* (st2, (o, i)) = betree_Internal_lookup_in_children node key st1 in
         let* _ =
-          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, Betree_Node_Internal node0)
+          lookup_first_message_for_key_back (Betree_List_Cons (k, msg) l) in
+        Return (st2, (o, Betree_Node_Internal i))
       else
         begin match msg with
         | Betree_Message_Insert v ->
           let* _ =
-            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)
+            lookup_first_message_for_key_back (Betree_List_Cons (k,
+              Betree_Message_Insert v) l) in
+          Return (st1, (Some v, Betree_Node_Internal node))
         | Betree_Message_Delete ->
           let* _ =
-            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)
+            lookup_first_message_for_key_back (Betree_List_Cons (k,
+              Betree_Message_Delete) l) in
+          Return (st1, (None, Betree_Node_Internal node))
         | Betree_Message_Upsert ufs ->
-          let* (st2, v) = betree_Internal_lookup_in_children node key st1 in
-          let* (st3, _) =
+          let* (st2, (v, i)) = betree_Internal_lookup_in_children node key st1
+            in
+          let* (st3, (v1, l1)) =
             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
-          let* (st5, pending0) =
-            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 node0.id msgs0 st5 in
-          Return (st0, Betree_Node_Internal node0)
+          let* msgs1 = lookup_first_message_for_key_back l1 in
+          let* (st4, _) = betree_store_internal_node i.id msgs1 st3 in
+          Return (st4, (Some v1, Betree_Node_Internal i))
         end
     | Betree_List_Nil ->
-      let* _ =
-        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, Betree_Node_Internal node0)
+      let* (st2, (o, i)) = betree_Internal_lookup_in_children node key st1 in
+      let* _ = lookup_first_message_for_key_back Betree_List_Nil in
+      Return (st2, (o, Betree_Node_Internal i))
     end
   | 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)
+    let* (st1, bindings) = betree_load_leaf_node node.id st in
+    let* o = betree_Node_lookup_in_bindings key bindings in
+    Return (st1, (o, Betree_Node_Leaf node))
   end
 
-(** [betree_main::betree::{betree_main::betree::Node#5}::filter_messages_for_key]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ())
+(** [betree_main::betree::{betree_main::betree::Node#5}::filter_messages_for_key]:
     Source: 'src/betree.rs', lines 674:4-674:77 *)
 let rec betree_Node_filter_messages_for_key
   (key : u64) (msgs : betree_List_t (u64 & betree_Message_t)) :
@@ -530,36 +328,20 @@ let rec betree_Node_filter_messages_for_key
     let (k, m) = p in
     if k = key
     then
-      let* msgs0 =
-        betree_List_pop_front_back (u64 & betree_Message_t) (Betree_List_Cons
-          (k, m) l) in
-      betree_Node_filter_messages_for_key key msgs0
+      let* (_, l1) =
+        betree_List_pop_front (u64 & betree_Message_t) (Betree_List_Cons (k, m)
+          l) in
+      betree_Node_filter_messages_for_key key l1
     else Return (Betree_List_Cons (k, m) l)
   | Betree_List_Nil -> Return Betree_List_Nil
   end
 
-(** [betree_main::betree::{betree_main::betree::Node#5}::lookup_first_message_after_key]: forward function
+(** [betree_main::betree::{betree_main::betree::Node#5}::lookup_first_message_after_key]:
     Source: 'src/betree.rs', lines 689:4-692:34 *)
 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
-  | Betree_List_Cons p next_msgs ->
-    let (k, m) = p in
-    if k = key
-    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::{betree_main::betree::Node#5}::lookup_first_message_after_key]: backward function 0
-    Source: 'src/betree.rs', lines 689:4-692:34 *)
-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)))
+  Tot (result ((betree_List_t (u64 & betree_Message_t)) & (betree_List_t (u64 &
+    betree_Message_t) -> result (betree_List_t (u64 & betree_Message_t)))))
   (decreases (betree_Node_lookup_first_message_after_key_decreases key msgs))
   =
   begin match msgs with
@@ -567,75 +349,76 @@ let rec betree_Node_lookup_first_message_after_key_back
     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 (Betree_List_Cons (k, m) next_msgs0)
-    else Return ret
-  | Betree_List_Nil -> Return ret
+      let* (l, lookup_first_message_after_key_back) =
+        betree_Node_lookup_first_message_after_key key next_msgs in
+      let back_'a =
+        fun ret ->
+          let* next_msgs1 = lookup_first_message_after_key_back ret in
+          Return (Betree_List_Cons (k, m) next_msgs1) in
+      Return (l, back_'a)
+    else Return (Betree_List_Cons (k, m) next_msgs, Return)
+  | Betree_List_Nil -> Return (Betree_List_Nil, Return)
   end
 
-(** [betree_main::betree::{betree_main::betree::Node#5}::apply_to_internal]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ())
+(** [betree_main::betree::{betree_main::betree::Node#5}::apply_to_internal]:
     Source: 'src/betree.rs', lines 521:4-521:89 *)
 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 key msgs in
-  let* b = betree_ListTupleU64T_head_has_key betree_Message_t msgs0 key in
+  let* (msgs1, lookup_first_message_for_key_back) =
+    betree_Node_lookup_first_message_for_key key msgs in
+  let* b = betree_ListTupleU64T_head_has_key betree_Message_t msgs1 key in
   if b
   then
     begin match new_msg with
     | Betree_Message_Insert i ->
-      let* msgs1 = betree_Node_filter_messages_for_key key msgs0 in
-      let* msgs2 =
-        betree_List_push_front (u64 & betree_Message_t) msgs1 (key,
+      let* l = betree_Node_filter_messages_for_key key msgs1 in
+      let* l1 =
+        betree_List_push_front (u64 & betree_Message_t) l (key,
           Betree_Message_Insert i) in
-      betree_Node_lookup_first_message_for_key_back key msgs msgs2
+      lookup_first_message_for_key_back l1
     | Betree_Message_Delete ->
-      let* msgs1 = betree_Node_filter_messages_for_key key msgs0 in
-      let* msgs2 =
-        betree_List_push_front (u64 & betree_Message_t) msgs1 (key,
+      let* l = betree_Node_filter_messages_for_key key msgs1 in
+      let* l1 =
+        betree_List_push_front (u64 & betree_Message_t) l (key,
           Betree_Message_Delete) in
-      betree_Node_lookup_first_message_for_key_back key msgs msgs2
+      lookup_first_message_for_key_back l1
     | Betree_Message_Upsert s ->
-      let* p = betree_List_hd (u64 & betree_Message_t) msgs0 in
+      let* p = betree_List_hd (u64 & betree_Message_t) msgs1 in
       let (_, m) = p in
       begin match m with
       | 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 (u64 & betree_Message_t) msgs1 (key,
+        let* (_, l) = betree_List_pop_front (u64 & betree_Message_t) msgs1 in
+        let* l1 =
+          betree_List_push_front (u64 & betree_Message_t) l (key,
             Betree_Message_Insert v) in
-        betree_Node_lookup_first_message_for_key_back key msgs msgs2
+        lookup_first_message_for_key_back l1
       | Betree_Message_Delete ->
+        let* (_, l) = betree_List_pop_front (u64 & betree_Message_t) msgs1 in
         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 (u64 & betree_Message_t) msgs1 (key,
+        let* l1 =
+          betree_List_push_front (u64 & betree_Message_t) l (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 (u64 & betree_Message_t) msgs1 (key,
+        lookup_first_message_for_key_back l1
+      | Betree_Message_Upsert _ ->
+        let* (msgs2, lookup_first_message_after_key_back) =
+          betree_Node_lookup_first_message_after_key key msgs1 in
+        let* l =
+          betree_List_push_front (u64 & betree_Message_t) msgs2 (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
+        let* msgs3 = lookup_first_message_after_key_back l in
+        lookup_first_message_for_key_back msgs3
       end
     end
   else
-    let* 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
+    let* l =
+      betree_List_push_front (u64 & betree_Message_t) msgs1 (key, new_msg) in
+    lookup_first_message_for_key_back l
 
-(** [betree_main::betree::{betree_main::betree::Node#5}::apply_messages_to_internal]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ())
+(** [betree_main::betree::{betree_main::betree::Node#5}::apply_messages_to_internal]:
     Source: 'src/betree.rs', lines 502:4-505:5 *)
 let rec betree_Node_apply_messages_to_internal
   (msgs : betree_List_t (u64 & betree_Message_t))
@@ -646,89 +429,72 @@ let rec betree_Node_apply_messages_to_internal
   begin match new_msgs with
   | Betree_List_Cons new_msg new_msgs_tl ->
     let (i, m) = new_msg in
-    let* msgs0 = betree_Node_apply_to_internal msgs i m in
-    betree_Node_apply_messages_to_internal msgs0 new_msgs_tl
+    let* l = betree_Node_apply_to_internal msgs i m in
+    betree_Node_apply_messages_to_internal l new_msgs_tl
   | Betree_List_Nil -> Return msgs
   end
 
-(** [betree_main::betree::{betree_main::betree::Node#5}::lookup_mut_in_bindings]: forward function
+(** [betree_main::betree::{betree_main::betree::Node#5}::lookup_mut_in_bindings]:
     Source: 'src/betree.rs', lines 653:4-656:32 *)
 let rec betree_Node_lookup_mut_in_bindings
   (key : u64) (bindings : betree_List_t (u64 & u64)) :
-  Tot (result (betree_List_t (u64 & u64)))
+  Tot (result ((betree_List_t (u64 & u64)) & (betree_List_t (u64 & u64) ->
+    result (betree_List_t (u64 & u64)))))
   (decreases (betree_Node_lookup_mut_in_bindings_decreases key bindings))
   =
   begin match bindings with
   | Betree_List_Cons hd tl ->
-    let (i, i0) = hd in
+    let (i, i1) = hd in
     if i >= key
-    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::{betree_main::betree::Node#5}::lookup_mut_in_bindings]: backward function 0
-    Source: 'src/betree.rs', lines 653:4-656:32 *)
-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
-  | Betree_List_Cons hd tl ->
-    let (i, i0) = hd in
-    if i >= key
-    then Return ret
+    then Return (Betree_List_Cons (i, i1) tl, Return)
     else
-      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
+      let* (l, lookup_mut_in_bindings_back) =
+        betree_Node_lookup_mut_in_bindings key tl in
+      let back_'a =
+        fun ret ->
+          let* tl1 = lookup_mut_in_bindings_back ret in
+          Return (Betree_List_Cons (i, i1) tl1) in
+      Return (l, back_'a)
+  | Betree_List_Nil -> Return (Betree_List_Nil, Return)
   end
 
-(** [betree_main::betree::{betree_main::betree::Node#5}::apply_to_leaf]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ())
+(** [betree_main::betree::{betree_main::betree::Node#5}::apply_to_leaf]:
     Source: 'src/betree.rs', lines 460:4-460:87 *)
 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 key bindings in
-  let* b = betree_ListTupleU64T_head_has_key u64 bindings0 key in
+  let* (bindings1, lookup_mut_in_bindings_back) =
+    betree_Node_lookup_mut_in_bindings key bindings in
+  let* b = betree_ListTupleU64T_head_has_key u64 bindings1 key in
   if b
   then
-    let* hd = betree_List_pop_front (u64 & u64) bindings0 in
+    let* (hd, l) = betree_List_pop_front (u64 & u64) bindings1 in
     begin match new_msg with
     | 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
+      let* l1 = betree_List_push_front (u64 & u64) l (key, v) in
+      lookup_mut_in_bindings_back l1
+    | Betree_Message_Delete -> lookup_mut_in_bindings_back l
     | Betree_Message_Upsert s ->
       let (_, i) = hd in
       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
+      let* l1 = betree_List_push_front (u64 & u64) l (key, v) in
+      lookup_mut_in_bindings_back l1
     end
   else
     begin match new_msg with
     | 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
+      let* l = betree_List_push_front (u64 & u64) bindings1 (key, v) in
+      lookup_mut_in_bindings_back l
+    | Betree_Message_Delete -> lookup_mut_in_bindings_back bindings1
     | 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
+      let* l = betree_List_push_front (u64 & u64) bindings1 (key, v) in
+      lookup_mut_in_bindings_back l
     end
 
-(** [betree_main::betree::{betree_main::betree::Node#5}::apply_messages_to_leaf]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ())
+(** [betree_main::betree::{betree_main::betree::Node#5}::apply_messages_to_leaf]:
     Source: 'src/betree.rs', lines 444:4-447:5 *)
 let rec betree_Node_apply_messages_to_leaf
   (bindings : betree_List_t (u64 & u64))
@@ -739,18 +505,19 @@ let rec betree_Node_apply_messages_to_leaf
   begin match new_msgs with
   | Betree_List_Cons new_msg new_msgs_tl ->
     let (i, m) = new_msg in
-    let* bindings0 = betree_Node_apply_to_leaf bindings i m in
-    betree_Node_apply_messages_to_leaf bindings0 new_msgs_tl
+    let* l = betree_Node_apply_to_leaf bindings i m in
+    betree_Node_apply_messages_to_leaf l new_msgs_tl
   | Betree_List_Nil -> Return bindings
   end
 
-(** [betree_main::betree::{betree_main::betree::Internal#4}::flush]: forward function
+(** [betree_main::betree::{betree_main::betree::Internal#4}::flush]:
     Source: 'src/betree.rs', lines 410:4-415:26 *)
 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))))
+  Tot (result (state & ((betree_List_t (u64 & betree_Message_t)) &
+    (betree_Internal_t & betree_NodeIdCounter_t))))
   (decreases (
     betree_Internal_flush_decreases self params node_id_cnt content st))
   =
@@ -761,189 +528,31 @@ let rec betree_Internal_flush
   let* len_left = betree_List_len (u64 & betree_Message_t) msgs_left in
   if len_left >= params.min_flush_size
   then
-    let* (st0, _) =
+    let* (st1, p1) =
       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.left params node_id_cnt msgs_left
-        st st0 in
-    let* (st2, ()) =
-      betree_Node_apply_messages_back1 self.left params node_id_cnt msgs_left
-        st st1 in
+    let (n, node_id_cnt1) = p1 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 self.right params node_id_cnt0 msgs_right
-          st2 in
-      let* (st4, (_, _)) =
-        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.right params node_id_cnt0
-          msgs_right st2 st4 in
-      Return (st5, Betree_List_Nil)
-    else Return (st2, msgs_right)
+      let* (st2, p2) =
+        betree_Node_apply_messages self.right params node_id_cnt1 msgs_right
+          st1 in
+      let (n1, node_id_cnt2) = p2 in
+      Return (st2, (Betree_List_Nil, ({ self with left = n; right = n1 },
+        node_id_cnt2)))
+    else Return (st1, (msgs_right, ({ self with left = n }, node_id_cnt1)))
   else
-    let* (st0, _) =
+    let* (st1, p1) =
       betree_Node_apply_messages self.right params node_id_cnt msgs_right st in
-    let* (st1, (_, _)) =
-      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.right params node_id_cnt msgs_right
-        st st1 in
-    Return (st2, msgs_left)
+    let (n, node_id_cnt1) = p1 in
+    Return (st1, (msgs_left, ({ self with right = n }, node_id_cnt1)))
 
-(** [betree_main::betree::{betree_main::betree::Internal#4}::flush]: backward function 0
-    Source: 'src/betree.rs', lines 410:4-415:26 *)
-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_NodeIdCounter_t)))
-  (decreases (
-    betree_Internal_flush_decreases self params node_id_cnt content st))
-  =
-  let* p =
-    betree_ListTupleU64T_partition_at_pivot betree_Message_t content self.pivot
-    in
-  let (msgs_left, msgs_right) = p in
-  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 self.left params node_id_cnt msgs_left st in
-    let* (st2, (n, node_id_cnt0)) =
-      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.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 self.right params node_id_cnt0 msgs_right
-          st3 in
-      let* (st5, (n0, node_id_cnt1)) =
-        betree_Node_apply_messages_back'a self.right params node_id_cnt0
-          msgs_right st3 st4 in
-      let* _ =
-        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 self.right params node_id_cnt msgs_right st in
-    let* (st2, (n, node_id_cnt0)) =
-      betree_Node_apply_messages_back'a self.right params node_id_cnt
-        msgs_right st st1 in
-    let* _ =
-      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::{betree_main::betree::Internal#4}::flush]: backward function 1
-    Source: 'src/betree.rs', lines 410:4-415:26 *)
-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))
-  =
-  let* p =
-    betree_ListTupleU64T_partition_at_pivot betree_Message_t content self.pivot
-    in
-  let (msgs_left, msgs_right) = p in
-  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 self.left params node_id_cnt msgs_left st in
-    let* (st2, (_, node_id_cnt0)) =
-      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.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 self.right params node_id_cnt0 msgs_right
-          st3 in
-      let* (st5, (_, _)) =
-        betree_Node_apply_messages_back'a self.right params node_id_cnt0
-          msgs_right st3 st4 in
-      let* _ =
-        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 self.right params node_id_cnt msgs_right st in
-    let* (st2, (_, _)) =
-      betree_Node_apply_messages_back'a self.right params node_id_cnt
-        msgs_right st st1 in
-    let* _ =
-      betree_Node_apply_messages_back1 self.right params node_id_cnt msgs_right
-        st st2 in
-    Return (st0, ())
-
-(** [betree_main::betree::{betree_main::betree::Node#5}::apply_messages]: forward function
+(** [betree_main::betree::{betree_main::betree::Node#5}::apply_messages]:
     Source: 'src/betree.rs', lines 588:4-593:5 *)
 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))
-  =
-  begin match self with
-  | 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 node params node_id_cnt content0 st0 in
-      let* (st2, (node0, _)) =
-        betree_Internal_flush_back'a node params node_id_cnt content0 st0 st1
-        in
-      let* (st3, _) = betree_store_internal_node node0.id content1 st2 in
-      Return (st3, ())
-    else
-      let* (st1, _) = betree_store_internal_node node.id content0 st0 in
-      Return (st1, ())
-  | 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 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 node.id content0 st0 in
-      Return (st1, ())
-  end
-
-(** [betree_main::betree::{betree_main::betree::Node#5}::apply_messages]: backward function 0
-    Source: 'src/betree.rs', lines 588:4-593:5 *)
-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))
@@ -951,277 +560,110 @@ and betree_Node_apply_messages_back'a
   begin match self with
   | 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 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
-        in
-      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 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 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, (Betree_Node_Internal new_node, node_id_cnt0))
-    else
-      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::{betree_main::betree::Node#5}::apply_messages]: backward function 1
-    Source: 'src/betree.rs', lines 588:4-593:5 *)
-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))
-  =
-  begin match self with
-  | 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
+    let* l = betree_Node_apply_messages_to_internal content msgs in
+    let* num_msgs = betree_List_len (u64 & betree_Message_t) l in
     if num_msgs >= params.min_flush_size
     then
-      let* (st2, content1) =
-        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
-        in
-      let* _ = betree_store_internal_node node0.id content1 st3 in
-      betree_Internal_flush_back1 node params node_id_cnt content0 st1 st0
+      let* (st2, (content1, p)) =
+        betree_Internal_flush node params node_id_cnt l st1 in
+      let (node1, node_id_cnt1) = p in
+      let* (st3, _) = betree_store_internal_node node1.id content1 st2 in
+      Return (st3, (Betree_Node_Internal node1, node_id_cnt1))
     else
-      let* _ = betree_store_internal_node node.id content0 st1 in
-      Return (st0, ())
+      let* (st2, _) = betree_store_internal_node node.id l st1 in
+      Return (st2, (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* l = betree_Node_apply_messages_to_leaf content msgs in
+    let* len = betree_List_len (u64 & u64) l in
     let* i = u64_mul 2 params.split_size in
     if len >= i
     then
-      let* (st2, _) = betree_Leaf_split node content0 params node_id_cnt st1 in
+      let* (st2, (new_node, nic)) =
+        betree_Leaf_split node l 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
+      Return (st3, (Betree_Node_Internal new_node, nic))
     else
-      let* _ = betree_store_leaf_node node.id content0 st1 in Return (st0, ())
+      let* (st2, _) = betree_store_leaf_node node.id l st1 in
+      Return (st2, (Betree_Node_Leaf { node with size = len }, node_id_cnt))
   end
 
-(** [betree_main::betree::{betree_main::betree::Node#5}::apply]: forward function
+(** [betree_main::betree::{betree_main::betree::Node#5}::apply]:
     Source: 'src/betree.rs', lines 576:4-582:5 *)
 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 = Betree_List_Nil in
-  let* (st0, _) =
-    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 (Betree_List_Cons
-      (key, new_msg) l) st st0 in
-  betree_Node_apply_messages_back1 self params node_id_cnt (Betree_List_Cons
-    (key, new_msg) l) st st1
-
-(** [betree_main::betree::{betree_main::betree::Node#5}::apply]: backward function 0
-    Source: 'src/betree.rs', lines 576:4-582:5 *)
-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 = Betree_List_Nil in
-  let* (st1, _) =
+  let* (st1, p) =
     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 (Betree_List_Cons
-      (key, new_msg) l) st st1 in
-  let* _ =
-    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))
+      new_msg) Betree_List_Nil) st in
+  let (self1, node_id_cnt1) = p in
+  Return (st1, (self1, node_id_cnt1))
 
-(** [betree_main::betree::{betree_main::betree::Node#5}::apply]: backward function 1
-    Source: 'src/betree.rs', lines 576:4-582:5 *)
-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 = Betree_List_Nil in
-  let* (st1, _) =
-    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 (Betree_List_Cons
-      (key, new_msg) l) st st1 in
-  let* _ =
-    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_main::betree::BeTree#6}::new]: forward function
+(** [betree_main::betree::{betree_main::betree::BeTree#6}::new]:
     Source: 'src/betree.rs', lines 849:4-849:60 *)
 let betree_BeTree_new
   (min_flush_size : u64) (split_size : u64) (st : state) :
   result (state & betree_BeTree_t)
   =
   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,
+  let* (id, nic) = betree_NodeIdCounter_fresh_id node_id_cnt in
+  let* (st1, _) = betree_store_leaf_node id Betree_List_Nil st in
+  Return (st1,
     {
       params = { min_flush_size = min_flush_size; split_size = split_size };
-      node_id_cnt = node_id_cnt0;
+      node_id_cnt = nic;
       root = (Betree_Node_Leaf { id = id; size = 0 })
     })
 
-(** [betree_main::betree::{betree_main::betree::BeTree#6}::apply]: forward function
+(** [betree_main::betree::{betree_main::betree::BeTree#6}::apply]:
     Source: 'src/betree.rs', lines 868:4-868:47 *)
 let betree_BeTree_apply
   (self : betree_BeTree_t) (key : u64) (msg : betree_Message_t) (st : state) :
-  result (state & unit)
-  =
-  let* (st0, _) =
-    betree_Node_apply self.root self.params self.node_id_cnt key msg st in
-  let* (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_main::betree::BeTree#6}::apply]: backward function 0
-    Source: 'src/betree.rs', lines 868:4-868:47 *)
-let betree_BeTree_apply_back
-  (self : betree_BeTree_t) (key : u64) (msg : betree_Message_t) (st : state)
-  (st0 : state) :
   result (state & betree_BeTree_t)
   =
-  let* (st1, _) =
+  let* (st1, p) =
     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.root self.params self.node_id_cnt key msg st
-      st1 in
-  let* _ =
-    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 })
+  let (n, nic) = p in
+  Return (st1, { self with node_id_cnt = nic; root = n })
 
-(** [betree_main::betree::{betree_main::betree::BeTree#6}::insert]: forward function
+(** [betree_main::betree::{betree_main::betree::BeTree#6}::insert]:
     Source: 'src/betree.rs', lines 874:4-874:52 *)
 let betree_BeTree_insert
   (self : betree_BeTree_t) (key : u64) (value : u64) (st : state) :
-  result (state & unit)
-  =
-  let* (st0, _) = betree_BeTree_apply self key (Betree_Message_Insert value) st
-    in
-  let* (st1, _) =
-    betree_BeTree_apply_back self key (Betree_Message_Insert value) st st0 in
-  Return (st1, ())
-
-(** [betree_main::betree::{betree_main::betree::BeTree#6}::insert]: backward function 0
-    Source: 'src/betree.rs', lines 874:4-874:52 *)
-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_BeTree_apply self key (Betree_Message_Insert value) st
-    in
-  let* (_, self0) =
-    betree_BeTree_apply_back self key (Betree_Message_Insert value) st st1 in
-  Return (st0, self0)
+  betree_BeTree_apply self key (Betree_Message_Insert value) st
 
-(** [betree_main::betree::{betree_main::betree::BeTree#6}::delete]: forward function
+(** [betree_main::betree::{betree_main::betree::BeTree#6}::delete]:
     Source: 'src/betree.rs', lines 880:4-880:38 *)
 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_main::betree::BeTree#6}::delete]: backward function 0
-    Source: 'src/betree.rs', lines 880:4-880:38 *)
-let betree_BeTree_delete_back
-  (self : betree_BeTree_t) (key : u64) (st : state) (st0 : state) :
+  (self : betree_BeTree_t) (key : u64) (st : state) :
   result (state & betree_BeTree_t)
   =
-  let* (st1, _) = betree_BeTree_apply self key Betree_Message_Delete st in
-  let* (_, self0) =
-    betree_BeTree_apply_back self key Betree_Message_Delete st st1 in
-  Return (st0, self0)
+  betree_BeTree_apply self key Betree_Message_Delete st
 
-(** [betree_main::betree::{betree_main::betree::BeTree#6}::upsert]: forward function
+(** [betree_main::betree::{betree_main::betree::BeTree#6}::upsert]:
     Source: 'src/betree.rs', lines 886:4-886:59 *)
 let betree_BeTree_upsert
   (self : betree_BeTree_t) (key : u64) (upd : betree_UpsertFunState_t)
   (st : state) :
-  result (state & unit)
-  =
-  let* (st0, _) = betree_BeTree_apply self key (Betree_Message_Upsert upd) st
-    in
-  let* (st1, _) =
-    betree_BeTree_apply_back self key (Betree_Message_Upsert upd) st st0 in
-  Return (st1, ())
-
-(** [betree_main::betree::{betree_main::betree::BeTree#6}::upsert]: backward function 0
-    Source: 'src/betree.rs', lines 886:4-886:59 *)
-let betree_BeTree_upsert_back
-  (self : betree_BeTree_t) (key : u64) (upd : betree_UpsertFunState_t)
-  (st : state) (st0 : state) :
   result (state & betree_BeTree_t)
   =
-  let* (st1, _) = betree_BeTree_apply self key (Betree_Message_Upsert upd) st
-    in
-  let* (_, self0) =
-    betree_BeTree_apply_back self key (Betree_Message_Upsert upd) st st1 in
-  Return (st0, self0)
+  betree_BeTree_apply self key (Betree_Message_Upsert upd) st
 
-(** [betree_main::betree::{betree_main::betree::BeTree#6}::lookup]: forward function
+(** [betree_main::betree::{betree_main::betree::BeTree#6}::lookup]:
     Source: 'src/betree.rs', lines 895:4-895:62 *)
 let betree_BeTree_lookup
   (self : betree_BeTree_t) (key : u64) (st : state) :
-  result (state & (option u64))
-  =
-  betree_Node_lookup self.root key st
-
-(** [betree_main::betree::{betree_main::betree::BeTree#6}::lookup]: backward function 0
-    Source: 'src/betree.rs', lines 895:4-895:62 *)
-let betree_BeTree_lookup_back
-  (self : betree_BeTree_t) (key : u64) (st : state) (st0 : state) :
-  result (state & betree_BeTree_t)
+  result (state & ((option u64) & betree_BeTree_t))
   =
-  let* (st1, n) = betree_Node_lookup_back self.root key st st0 in
-  Return (st1, { self with root = n })
+  let* (st1, (o, n)) = betree_Node_lookup self.root key st in
+  Return (st1, (o, { self with root = n }))
 
-(** [betree_main::main]: forward function
+(** [betree_main::main]:
     Source: 'src/betree_main.rs', lines 5:0-5:9 *)
 let main : result unit =
   Return ()
diff --git a/tests/fstar/betree_back_stateful/BetreeMain.FunsExternal.fsti b/tests/fstar/betree_back_stateful/BetreeMain.FunsExternal.fsti
index cd2f956f..de9b96fd 100644
--- a/tests/fstar/betree_back_stateful/BetreeMain.FunsExternal.fsti
+++ b/tests/fstar/betree_back_stateful/BetreeMain.FunsExternal.fsti
@@ -6,29 +6,29 @@ include BetreeMain.Types
 
 #set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
 
-(** [betree_main::betree_utils::load_internal_node]: forward function
+(** [betree_main::betree_utils::load_internal_node]:
     Source: 'src/betree_utils.rs', lines 98:0-98:63 *)
 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
+(** [betree_main::betree_utils::store_internal_node]:
     Source: 'src/betree_utils.rs', lines 115:0-115:71 *)
 val betree_utils_store_internal_node
   :
   u64 -> betree_List_t (u64 & betree_Message_t) -> state -> result (state &
     unit)
 
-(** [betree_main::betree_utils::load_leaf_node]: forward function
+(** [betree_main::betree_utils::load_leaf_node]:
     Source: 'src/betree_utils.rs', lines 132:0-132:55 *)
 val betree_utils_load_leaf_node
   : u64 -> state -> result (state & (betree_List_t (u64 & u64)))
 
-(** [betree_main::betree_utils::store_leaf_node]: forward function
+(** [betree_main::betree_utils::store_leaf_node]:
     Source: 'src/betree_utils.rs', lines 145:0-145:63 *)
 val betree_utils_store_leaf_node
   : u64 -> betree_List_t (u64 & u64) -> state -> result (state & unit)
 
-(** [core::option::{core::option::Option<T>}::unwrap]: forward function
+(** [core::option::{core::option::Option<T>}::unwrap]:
     Source: '/rustc/d59363ad0b6391b7fc5bbb02c9ccf9300eef3753/library/core/src/option.rs', lines 932:4-932:34 *)
 val core_option_Option_unwrap
   (t : Type0) : option t -> state -> result (state & t)
diff --git a/tests/fstar/betree_back_stateful/Primitives.fst b/tests/fstar/betree_back_stateful/Primitives.fst
index a3ffbde4..fca80829 100644
--- a/tests/fstar/betree_back_stateful/Primitives.fst
+++ b/tests/fstar/betree_back_stateful/Primitives.fst
@@ -55,8 +55,7 @@ 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
+let core_mem_replace (a : Type0) (x : a) (y : a) : a & a = (x, x)
 
 // We don't really use raw pointers for now
 type mut_raw_ptr (t : Type0) = { v : t }
@@ -477,8 +476,7 @@ noeq type core_ops_index_Index (self idx : Type0) = {
 // 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;
+  index_mut : self → idx → result (indexInst.output & (indexInst.output → result self));
 }
 
 // Trait declaration [core::ops::deref::Deref]
@@ -490,8 +488,7 @@ noeq type core_ops_deref_Deref (self : Type0) = {
 // 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;
+  deref_mut : self → result (derefInst.target & (derefInst.target → result self));
 }
 
 type core_ops_range_Range (a : Type0) = {
@@ -502,8 +499,8 @@ type core_ops_range_Range (a : Type0) = {
 (*** [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
+let alloc_boxed_Box_deref_mut (t : Type0) (x : t) : result (t & (t -> result t)) =
+  Return (x, (fun x -> Return x))
 
 // Trait instance
 let alloc_boxed_Box_coreopsDerefInst (self : Type0) : core_ops_deref_Deref self = {
@@ -515,7 +512,6 @@ let alloc_boxed_Box_coreopsDerefInst (self : Type0) : core_ops_deref_Deref self
 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 *)
@@ -535,10 +531,18 @@ let array_index_usize (a : Type0) (n : usize) (x : array a n) (i : usize) : resu
   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) =
+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
 
+let array_index_mut_usize (a : Type0) (n : usize) (x : array a n) (i : usize) :
+  result (a & (a -> result (array a n))) =
+  match array_index_usize a n x i with
+  | Fail e -> Fail e
+  | Return v ->
+    Return (v, array_update_usize a n x i)
+
 (*** Slice *)
 type slice (a : Type0) = s:list a{length s <= usize_max}
 
@@ -552,6 +556,13 @@ let slice_update_usize (a : Type0) (x : slice a) (i : usize) (nx : a) : result (
   if i < length x then Return (list_update x i nx)
   else Fail Failure
 
+let slice_index_mut_usize (a : Type0) (s : slice a) (i : usize) :
+  result (a & (a -> result (slice a))) =
+  match slice_index_usize a s i with
+  | Fail e -> Fail e
+  | Return x ->
+    Return (x, slice_update_usize a s i)
+
 (*** Subslices *)
 
 let array_to_slice (a : Type0) (n : usize) (x : array a n) : result (slice a) = Return x
@@ -559,6 +570,10 @@ let array_from_slice (a : Type0) (n : usize) (x : array a n) (s : slice a) : res
   if length s = n then Return s
   else Fail Failure
 
+let array_to_slice_mut (a : Type0) (n : usize) (x : array a n) :
+  result (slice a & (slice a -> result (array a n))) =
+  Return (x, array_from_slice a n x)
+
 // 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()
@@ -588,8 +603,13 @@ let alloc_vec_Vec_index_usize (#a : Type0) (v : alloc_vec_Vec a) (i : usize) : r
 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_index_mut_usize (#a : Type0) (v: alloc_vec_Vec a) (i: usize) :
+  result (a & (a → result (alloc_vec_Vec a))) =
+  match alloc_vec_Vec_index_usize v i with
+  | Return x ->
+    Return (x, alloc_vec_Vec_update_usize v i)
+  | Fail e -> Fail e
+
 let alloc_vec_Vec_push (a  : Type0) (v : alloc_vec_Vec a) (x : a) :
   Pure (result (alloc_vec_Vec a))
   (requires True)
@@ -605,9 +625,6 @@ let alloc_vec_Vec_push (a  : Type0) (v : alloc_vec_Vec a) (x : a) :
     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
 
@@ -619,13 +636,11 @@ 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_mut : self → t → result (option output & (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;
+  index_mut : self → t → result (output & (output -> result t));
 }
 
 // [core::slice::index::[T]::index]: forward function
@@ -643,14 +658,8 @@ let core_slice_index_RangeUsize_get (t : Type0) (i : core_ops_range_Range usize)
   admit () // TODO
 
 // [core::slice::index::Range::get_mut]: forward function
-let core_slice_index_RangeUsize_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_RangeUsize_get_mut_back
-  (t : Type0) :
-  core_ops_range_Range usize → slice t → option (slice t) → result (slice t) =
+let core_slice_index_RangeUsize_get_mut (t : Type0) :
+  core_ops_range_Range usize → slice t → result (option (slice t) & (option (slice t) -> result (slice t))) =
   admit () // TODO
 
 // [core::slice::index::Range::get_unchecked]: forward function
@@ -675,27 +684,16 @@ let core_slice_index_RangeUsize_index
   admit () // TODO
 
 // [core::slice::index::Range::index_mut]: forward function
-let core_slice_index_RangeUsize_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_RangeUsize_index_mut_back
-  (t : Type0) : core_ops_range_Range usize → slice t → slice t → result (slice t) =
+let core_slice_index_RangeUsize_index_mut (t : Type0) :
+  core_ops_range_Range usize → slice t → result (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 =
+  slice t → idx → result (inst.output & (inst.output -> result (slice t))) =
   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)
@@ -705,13 +703,8 @@ let core_array_Array_index
 // [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) =
+  (a : array t n) (i : idx) :
+  result (inst.indexInst.output & (inst.indexInst.output -> result (array t n))) =
   admit () // TODO
 
 // Trait implementation: [core::slice::index::private_slice_index::Range]
@@ -725,12 +718,10 @@ let core_slice_index_SliceIndexRangeUsizeSliceTInst (t : Type0) :
   output = slice t;
   get = core_slice_index_RangeUsize_get t;
   get_mut = core_slice_index_RangeUsize_get_mut t;
-  get_mut_back = core_slice_index_RangeUsize_get_mut_back t;
   get_unchecked = core_slice_index_RangeUsize_get_unchecked t;
   get_unchecked_mut = core_slice_index_RangeUsize_get_unchecked_mut t;
   index = core_slice_index_RangeUsize_index t;
   index_mut = core_slice_index_RangeUsize_index_mut t;
-  index_mut_back = core_slice_index_RangeUsize_index_mut_back t;
 }
 
 // Trait implementation: [core::slice::index::[T]]
@@ -747,7 +738,6 @@ let core_ops_index_IndexMutSliceTIInst (t idx : Type0)
   core_ops_index_IndexMut (slice t) idx = {
   indexInst = core_ops_index_IndexSliceTIInst 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]]
@@ -764,7 +754,6 @@ let core_ops_index_IndexMutArrayIInst (t idx : Type0) (n : usize)
   core_ops_index_IndexMut (array t n) idx = {
   indexInst = core_ops_index_IndexArrayInst 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
@@ -773,13 +762,8 @@ let core_slice_index_usize_get
   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) =
+let core_slice_index_usize_get_mut (t : Type0) :
+  usize → slice t → result (option t & (option t -> result (slice t))) =
   admit () // TODO
 
 // [core::slice::index::usize::get_unchecked]: forward function
@@ -797,12 +781,8 @@ 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) =
+let core_slice_index_usize_index_mut (t : Type0) :
+  usize → slice t → result (t & (t -> result (slice t))) =
   admit () // TODO
 
 // Trait implementation: [core::slice::index::private_slice_index::usize]
@@ -816,12 +796,10 @@ let core_slice_index_SliceIndexUsizeSliceTInst (t : Type0) :
   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
@@ -831,13 +809,8 @@ let alloc_vec_Vec_index (t idx : Type0) (inst : core_slice_index_SliceIndex idx
 
 // [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) =
+  (self : alloc_vec_Vec t) (i : idx) :
+  result (inst.output & (inst.output -> result (alloc_vec_Vec t))) =
   admit () // TODO
 
 // Trait implementation: [alloc::vec::Vec]
@@ -854,7 +827,6 @@ let alloc_vec_Vec_coreopsindexIndexMutInst (t idx : Type0)
   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 *)
@@ -870,15 +842,7 @@ let alloc_vec_Vec_index_eq (#a : Type0) (v : alloc_vec_Vec a) (i : usize) :
 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_SliceIndexUsizeSliceTInst a) v i ==
-      alloc_vec_Vec_index_usize v i)
+      alloc_vec_Vec_index_mut_usize v i)
   [SMTPat (alloc_vec_Vec_index_mut a usize (core_slice_index_SliceIndexUsizeSliceTInst 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_SliceIndexUsizeSliceTInst a) v i x ==
-      alloc_vec_Vec_update_usize v i x)
-  [SMTPat (alloc_vec_Vec_index_mut_back a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i x)]
-  =
-  admit()
diff --git a/tests/fstar/hashmap/Hashmap.Funs.fst b/tests/fstar/hashmap/Hashmap.Funs.fst
index e6cd1411..447f9b49 100644
--- a/tests/fstar/hashmap/Hashmap.Funs.fst
+++ b/tests/fstar/hashmap/Hashmap.Funs.fst
@@ -7,12 +7,12 @@ include Hashmap.Clauses
 
 #set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
 
-(** [hashmap::hash_key]: forward function
+(** [hashmap::hash_key]:
     Source: 'src/hashmap.rs', lines 27:0-27:32 *)
 let hash_key (k : usize) : result usize =
   Return k
 
-(** [hashmap::{hashmap::HashMap<T>}::allocate_slots]: loop 0: forward function
+(** [hashmap::{hashmap::HashMap<T>}::allocate_slots]: loop 0:
     Source: 'src/hashmap.rs', lines 50:4-56:5 *)
 let rec hashMap_allocate_slots_loop
   (t : Type0) (slots : alloc_vec_Vec (list_t t)) (n : usize) :
@@ -21,12 +21,12 @@ let rec hashMap_allocate_slots_loop
   =
   if n > 0
   then
-    let* slots0 = alloc_vec_Vec_push (list_t t) slots List_Nil in
-    let* n0 = usize_sub n 1 in
-    hashMap_allocate_slots_loop t slots0 n0
+    let* v = alloc_vec_Vec_push (list_t t) slots List_Nil in
+    let* n1 = usize_sub n 1 in
+    hashMap_allocate_slots_loop t v n1
   else Return slots
 
-(** [hashmap::{hashmap::HashMap<T>}::allocate_slots]: forward function
+(** [hashmap::{hashmap::HashMap<T>}::allocate_slots]:
     Source: 'src/hashmap.rs', lines 50:4-50:76 *)
 let hashMap_allocate_slots
   (t : Type0) (slots : alloc_vec_Vec (list_t t)) (n : usize) :
@@ -34,107 +34,85 @@ let hashMap_allocate_slots
   =
   hashMap_allocate_slots_loop t slots n
 
-(** [hashmap::{hashmap::HashMap<T>}::new_with_capacity]: forward function
+(** [hashmap::{hashmap::HashMap<T>}::new_with_capacity]:
     Source: 'src/hashmap.rs', lines 59:4-63:13 *)
 let hashMap_new_with_capacity
   (t : Type0) (capacity : usize) (max_load_dividend : usize)
   (max_load_divisor : usize) :
   result (hashMap_t t)
   =
-  let v = alloc_vec_Vec_new (list_t t) in
-  let* slots = hashMap_allocate_slots t v capacity in
+  let* slots = hashMap_allocate_slots t (alloc_vec_Vec_new (list_t t)) capacity
+    in
   let* i = usize_mul capacity max_load_dividend in
-  let* i0 = usize_div i max_load_divisor in
+  let* i1 = usize_div i max_load_divisor in
   Return
     {
       num_entries = 0;
       max_load_factor = (max_load_dividend, max_load_divisor);
-      max_load = i0;
+      max_load = i1;
       slots = slots
     }
 
-(** [hashmap::{hashmap::HashMap<T>}::new]: forward function
+(** [hashmap::{hashmap::HashMap<T>}::new]:
     Source: 'src/hashmap.rs', lines 75:4-75:24 *)
 let hashMap_new (t : Type0) : result (hashMap_t t) =
   hashMap_new_with_capacity t 32 4 5
 
-(** [hashmap::{hashmap::HashMap<T>}::clear]: loop 0: merged forward/backward function
-    (there is a single backward function, and the forward function returns ())
+(** [hashmap::{hashmap::HashMap<T>}::clear]: loop 0:
     Source: 'src/hashmap.rs', lines 80:4-88:5 *)
 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 = alloc_vec_Vec_len (list_t t) slots in
-  if i < i0
+  let i1 = alloc_vec_Vec_len (list_t t) slots in
+  if i < i1
   then
-    let* i1 = usize_add i 1 in
-    let* slots0 =
-      alloc_vec_Vec_index_mut_back (list_t t) usize
-        (core_slice_index_SliceIndexUsizeSliceTInst (list_t t)) slots i
-        List_Nil in
-    hashMap_clear_loop t slots0 i1
+    let* (_, index_mut_back) =
+      alloc_vec_Vec_index_mut (list_t t) usize
+        (core_slice_index_SliceIndexUsizeSliceTInst (list_t t)) slots i in
+    let* i2 = usize_add i 1 in
+    let* slots1 = index_mut_back List_Nil in
+    hashMap_clear_loop t slots1 i2
   else Return slots
 
-(** [hashmap::{hashmap::HashMap<T>}::clear]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ())
+(** [hashmap::{hashmap::HashMap<T>}::clear]:
     Source: 'src/hashmap.rs', lines 80:4-80:27 *)
 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 }
+  let* back = hashMap_clear_loop t self.slots 0 in
+  Return { self with num_entries = 0; slots = back }
 
-(** [hashmap::{hashmap::HashMap<T>}::len]: forward function
+(** [hashmap::{hashmap::HashMap<T>}::len]:
     Source: 'src/hashmap.rs', lines 90:4-90:30 *)
 let hashMap_len (t : Type0) (self : hashMap_t t) : result usize =
   Return self.num_entries
 
-(** [hashmap::{hashmap::HashMap<T>}::insert_in_list]: loop 0: forward function
+(** [hashmap::{hashmap::HashMap<T>}::insert_in_list]: loop 0:
     Source: 'src/hashmap.rs', lines 97:4-114:5 *)
 let rec hashMap_insert_in_list_loop
   (t : Type0) (key : usize) (value : t) (ls : list_t t) :
-  Tot (result bool)
+  Tot (result (bool & (list_t t)))
   (decreases (hashMap_insert_in_list_loop_decreases t key value ls))
   =
   begin match ls with
   | List_Cons ckey cvalue tl ->
     if ckey = key
-    then Return false
-    else hashMap_insert_in_list_loop t key value tl
-  | List_Nil -> Return true
+    then Return (false, List_Cons ckey value tl)
+    else
+      let* (b, back) = hashMap_insert_in_list_loop t key value tl in
+      Return (b, List_Cons ckey cvalue back)
+  | List_Nil -> Return (true, List_Cons key value List_Nil)
   end
 
-(** [hashmap::{hashmap::HashMap<T>}::insert_in_list]: forward function
+(** [hashmap::{hashmap::HashMap<T>}::insert_in_list]:
     Source: 'src/hashmap.rs', lines 97:4-97:71 *)
 let hashMap_insert_in_list
-  (t : Type0) (key : usize) (value : t) (ls : list_t t) : result bool =
-  hashMap_insert_in_list_loop t key value ls
-
-(** [hashmap::{hashmap::HashMap<T>}::insert_in_list]: loop 0: backward function 0
-    Source: 'src/hashmap.rs', lines 97:4-114:5 *)
-let rec hashMap_insert_in_list_loop_back
   (t : Type0) (key : usize) (value : t) (ls : list_t t) :
-  Tot (result (list_t t))
-  (decreases (hashMap_insert_in_list_loop_decreases t key value ls))
+  result (bool & (list_t t))
   =
-  begin match ls with
-  | List_Cons ckey cvalue tl ->
-    if ckey = key
-    then Return (List_Cons ckey value tl)
-    else
-      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::HashMap<T>}::insert_in_list]: backward function 0
-    Source: 'src/hashmap.rs', lines 97:4-97:71 *)
-let hashMap_insert_in_list_back
-  (t : Type0) (key : usize) (value : t) (ls : list_t t) : result (list_t t) =
-  hashMap_insert_in_list_loop_back t key value ls
+  hashMap_insert_in_list_loop t key value ls
 
-(** [hashmap::{hashmap::HashMap<T>}::insert_no_resize]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ())
+(** [hashmap::{hashmap::HashMap<T>}::insert_no_resize]:
     Source: 'src/hashmap.rs', lines 117:4-117:54 *)
 let hashMap_insert_no_resize
   (t : Type0) (self : hashMap_t t) (key : usize) (value : t) :
@@ -143,30 +121,19 @@ let hashMap_insert_no_resize
   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 =
+  let* (l, index_mut_back) =
     alloc_vec_Vec_index_mut (list_t t) usize
       (core_slice_index_SliceIndexUsizeSliceTInst (list_t t)) self.slots
       hash_mod in
-  let* inserted = hashMap_insert_in_list t key value l in
+  let* (inserted, l1) = hashMap_insert_in_list t key value l in
   if inserted
   then
-    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_SliceIndexUsizeSliceTInst (list_t t)) self.slots
-        hash_mod l0 in
-    Return { self with num_entries = i0; slots = v }
-  else
-    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_SliceIndexUsizeSliceTInst (list_t t)) self.slots
-        hash_mod l0 in
-    Return { self with slots = v }
-
-(** [hashmap::{hashmap::HashMap<T>}::move_elements_from_list]: loop 0: merged forward/backward function
-    (there is a single backward function, and the forward function returns ())
+    let* i1 = usize_add self.num_entries 1 in
+    let* v = index_mut_back l1 in
+    Return { self with num_entries = i1; slots = v }
+  else let* v = index_mut_back l1 in Return { self with slots = v }
+
+(** [hashmap::{hashmap::HashMap<T>}::move_elements_from_list]: loop 0:
     Source: 'src/hashmap.rs', lines 183:4-196:5 *)
 let rec hashMap_move_elements_from_list_loop
   (t : Type0) (ntable : hashMap_t t) (ls : list_t t) :
@@ -175,20 +142,18 @@ let rec hashMap_move_elements_from_list_loop
   =
   begin match ls with
   | 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
+    let* hm = hashMap_insert_no_resize t ntable k v in
+    hashMap_move_elements_from_list_loop t hm tl
   | List_Nil -> Return ntable
   end
 
-(** [hashmap::{hashmap::HashMap<T>}::move_elements_from_list]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ())
+(** [hashmap::{hashmap::HashMap<T>}::move_elements_from_list]:
     Source: 'src/hashmap.rs', lines 183:4-183:72 *)
 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::HashMap<T>}::move_elements]: loop 0: merged forward/backward function
-    (there is a single backward function, and the forward function returns ())
+(** [hashmap::{hashmap::HashMap<T>}::move_elements]: loop 0:
     Source: 'src/hashmap.rs', lines 171:4-180:5 *)
 let rec hashMap_move_elements_loop
   (t : Type0) (ntable : hashMap_t t) (slots : alloc_vec_Vec (list_t t))
@@ -196,64 +161,63 @@ let rec hashMap_move_elements_loop
   Tot (result ((hashMap_t t) & (alloc_vec_Vec (list_t t))))
   (decreases (hashMap_move_elements_loop_decreases t ntable slots i))
   =
-  let i0 = alloc_vec_Vec_len (list_t t) slots in
-  if i < i0
+  let i1 = alloc_vec_Vec_len (list_t t) slots in
+  if i < i1
   then
-    let* l =
+    let* (l, index_mut_back) =
       alloc_vec_Vec_index_mut (list_t t) usize
         (core_slice_index_SliceIndexUsizeSliceTInst (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 = 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_SliceIndexUsizeSliceTInst (list_t t)) slots i l0 in
-    hashMap_move_elements_loop t ntable0 slots0 i1
+    let (ls, l1) = core_mem_replace (list_t t) l List_Nil in
+    let* hm = hashMap_move_elements_from_list t ntable ls in
+    let* i2 = usize_add i 1 in
+    let* slots1 = index_mut_back l1 in
+    let* back_'a = hashMap_move_elements_loop t hm slots1 i2 in
+    let (hm1, v) = back_'a in
+    Return (hm1, v)
   else Return (ntable, slots)
 
-(** [hashmap::{hashmap::HashMap<T>}::move_elements]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ())
+(** [hashmap::{hashmap::HashMap<T>}::move_elements]:
     Source: 'src/hashmap.rs', lines 171:4-171:95 *)
 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)))
   =
-  hashMap_move_elements_loop t ntable slots i
+  let* back_'a = hashMap_move_elements_loop t ntable slots i in
+  let (hm, v) = back_'a in
+  Return (hm, v)
 
-(** [hashmap::{hashmap::HashMap<T>}::try_resize]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ())
+(** [hashmap::{hashmap::HashMap<T>}::try_resize]:
     Source: 'src/hashmap.rs', lines 140:4-140:28 *)
 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.max_load_factor in
-  let* i1 = usize_div n1 i in
-  if capacity <= i1
+  let (i, i1) = self.max_load_factor in
+  let* i2 = usize_div n1 i in
+  if capacity <= i2
   then
-    let* i2 = usize_mul capacity 2 in
-    let* ntable = hashMap_new_with_capacity t i2 i i0 in
-    let* (ntable0, _) = hashMap_move_elements t ntable self.slots 0 in
+    let* i3 = usize_mul capacity 2 in
+    let* ntable = hashMap_new_with_capacity t i3 i i1 in
+    let* p = hashMap_move_elements t ntable self.slots 0 in
+    let (ntable1, _) = p in
     Return
-      { ntable0 with num_entries = self.num_entries; max_load_factor = (i, i0)
+      { ntable1 with num_entries = self.num_entries; max_load_factor = (i, i1)
       }
-  else Return { self with max_load_factor = (i, i0) }
+  else Return { self with max_load_factor = (i, i1) }
 
-(** [hashmap::{hashmap::HashMap<T>}::insert]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ())
+(** [hashmap::{hashmap::HashMap<T>}::insert]:
     Source: 'src/hashmap.rs', lines 129:4-129:48 *)
 let hashMap_insert
   (t : Type0) (self : hashMap_t t) (key : usize) (value : t) :
   result (hashMap_t t)
   =
-  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
+  let* hm = hashMap_insert_no_resize t self key value in
+  let* i = hashMap_len t hm in
+  if i > hm.max_load then hashMap_try_resize t hm else Return hm
 
-(** [hashmap::{hashmap::HashMap<T>}::contains_key_in_list]: loop 0: forward function
+(** [hashmap::{hashmap::HashMap<T>}::contains_key_in_list]: loop 0:
     Source: 'src/hashmap.rs', lines 206:4-219:5 *)
 let rec hashMap_contains_key_in_list_loop
   (t : Type0) (key : usize) (ls : list_t t) :
@@ -261,20 +225,20 @@ let rec hashMap_contains_key_in_list_loop
   (decreases (hashMap_contains_key_in_list_loop_decreases t key ls))
   =
   begin match ls with
-  | List_Cons ckey x tl ->
+  | List_Cons ckey _ tl ->
     if ckey = key
     then Return true
     else hashMap_contains_key_in_list_loop t key tl
   | List_Nil -> Return false
   end
 
-(** [hashmap::{hashmap::HashMap<T>}::contains_key_in_list]: forward function
+(** [hashmap::{hashmap::HashMap<T>}::contains_key_in_list]:
     Source: 'src/hashmap.rs', lines 206:4-206:68 *)
 let hashMap_contains_key_in_list
   (t : Type0) (key : usize) (ls : list_t t) : result bool =
   hashMap_contains_key_in_list_loop t key ls
 
-(** [hashmap::{hashmap::HashMap<T>}::contains_key]: forward function
+(** [hashmap::{hashmap::HashMap<T>}::contains_key]:
     Source: 'src/hashmap.rs', lines 199:4-199:49 *)
 let hashMap_contains_key
   (t : Type0) (self : hashMap_t t) (key : usize) : result bool =
@@ -287,7 +251,7 @@ let hashMap_contains_key
       hash_mod in
   hashMap_contains_key_in_list t key l
 
-(** [hashmap::{hashmap::HashMap<T>}::get_in_list]: loop 0: forward function
+(** [hashmap::{hashmap::HashMap<T>}::get_in_list]: loop 0:
     Source: 'src/hashmap.rs', lines 224:4-237:5 *)
 let rec hashMap_get_in_list_loop
   (t : Type0) (key : usize) (ls : list_t t) :
@@ -299,12 +263,12 @@ let rec hashMap_get_in_list_loop
   | List_Nil -> Fail Failure
   end
 
-(** [hashmap::{hashmap::HashMap<T>}::get_in_list]: forward function
+(** [hashmap::{hashmap::HashMap<T>}::get_in_list]:
     Source: 'src/hashmap.rs', lines 224:4-224:70 *)
 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::HashMap<T>}::get]: forward function
+(** [hashmap::{hashmap::HashMap<T>}::get]:
     Source: 'src/hashmap.rs', lines 239:4-239:55 *)
 let hashMap_get (t : Type0) (self : hashMap_t t) (key : usize) : result t =
   let* hash = hash_key key in
@@ -316,214 +280,146 @@ let hashMap_get (t : Type0) (self : hashMap_t t) (key : usize) : result t =
       hash_mod in
   hashMap_get_in_list t key l
 
-(** [hashmap::{hashmap::HashMap<T>}::get_mut_in_list]: loop 0: forward function
+(** [hashmap::{hashmap::HashMap<T>}::get_mut_in_list]: loop 0:
     Source: 'src/hashmap.rs', lines 245:4-254:5 *)
 let rec hashMap_get_mut_in_list_loop
   (t : Type0) (ls : list_t t) (key : usize) :
-  Tot (result t) (decreases (hashMap_get_mut_in_list_loop_decreases t ls key))
-  =
-  begin match ls with
-  | 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::HashMap<T>}::get_mut_in_list]: forward function
-    Source: 'src/hashmap.rs', lines 245:4-245:86 *)
-let hashMap_get_mut_in_list
-  (t : Type0) (ls : list_t t) (key : usize) : result t =
-  hashMap_get_mut_in_list_loop t ls key
-
-(** [hashmap::{hashmap::HashMap<T>}::get_mut_in_list]: loop 0: backward function 0
-    Source: 'src/hashmap.rs', lines 245:4-254:5 *)
-let rec hashMap_get_mut_in_list_loop_back
-  (t : Type0) (ls : list_t t) (key : usize) (ret : t) :
-  Tot (result (list_t t))
+  Tot (result (t & (t -> result (list_t t))))
   (decreases (hashMap_get_mut_in_list_loop_decreases t ls key))
   =
   begin match ls with
   | List_Cons ckey cvalue tl ->
     if ckey = key
-    then Return (List_Cons ckey ret tl)
+    then
+      let back_'a = fun ret -> Return (List_Cons ckey ret tl) in
+      Return (cvalue, back_'a)
     else
-      let* tl0 = hashMap_get_mut_in_list_loop_back t tl key ret in
-      Return (List_Cons ckey cvalue tl0)
+      let* (x, back_'a) = hashMap_get_mut_in_list_loop t tl key in
+      let back_'a1 =
+        fun ret -> let* tl1 = back_'a ret in Return (List_Cons ckey cvalue tl1)
+        in
+      Return (x, back_'a1)
   | List_Nil -> Fail Failure
   end
 
-(** [hashmap::{hashmap::HashMap<T>}::get_mut_in_list]: backward function 0
+(** [hashmap::{hashmap::HashMap<T>}::get_mut_in_list]:
     Source: 'src/hashmap.rs', lines 245:4-245:86 *)
-let hashMap_get_mut_in_list_back
-  (t : Type0) (ls : list_t t) (key : usize) (ret : t) : result (list_t t) =
-  hashMap_get_mut_in_list_loop_back t ls key ret
-
-(** [hashmap::{hashmap::HashMap<T>}::get_mut]: forward function
-    Source: 'src/hashmap.rs', lines 257:4-257:67 *)
-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 =
-    alloc_vec_Vec_index_mut (list_t t) usize
-      (core_slice_index_SliceIndexUsizeSliceTInst (list_t t)) self.slots
-      hash_mod in
-  hashMap_get_mut_in_list t l key
+let hashMap_get_mut_in_list
+  (t : Type0) (ls : list_t t) (key : usize) :
+  result (t & (t -> result (list_t t)))
+  =
+  let* (x, back_'a) = hashMap_get_mut_in_list_loop t ls key in
+  Return (x, back_'a)
 
-(** [hashmap::{hashmap::HashMap<T>}::get_mut]: backward function 0
+(** [hashmap::{hashmap::HashMap<T>}::get_mut]:
     Source: 'src/hashmap.rs', lines 257:4-257:67 *)
-let hashMap_get_mut_back
-  (t : Type0) (self : hashMap_t t) (key : usize) (ret : t) :
-  result (hashMap_t t)
+let hashMap_get_mut
+  (t : Type0) (self : hashMap_t t) (key : usize) :
+  result (t & (t -> 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 =
+  let* (l, index_mut_back) =
     alloc_vec_Vec_index_mut (list_t t) usize
       (core_slice_index_SliceIndexUsizeSliceTInst (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_SliceIndexUsizeSliceTInst (list_t t)) self.slots
-      hash_mod l0 in
-  Return { self with slots = v }
-
-(** [hashmap::{hashmap::HashMap<T>}::remove_from_list]: loop 0: forward function
+  let* (x, get_mut_in_list_back) = hashMap_get_mut_in_list t l key in
+  let back_'a =
+    fun ret ->
+      let* l1 = get_mut_in_list_back ret in
+      let* v = index_mut_back l1 in
+      Return { self with slots = v } in
+  Return (x, back_'a)
+
+(** [hashmap::{hashmap::HashMap<T>}::remove_from_list]: loop 0:
     Source: 'src/hashmap.rs', lines 265:4-291:5 *)
 let rec hashMap_remove_from_list_loop
   (t : Type0) (key : usize) (ls : list_t t) :
-  Tot (result (option t))
+  Tot (result ((option t) & (list_t t)))
   (decreases (hashMap_remove_from_list_loop_decreases t key ls))
   =
   begin match ls with
   | List_Cons ckey x tl ->
     if ckey = key
     then
-      let mv_ls = core_mem_replace (list_t t) (List_Cons ckey x tl) List_Nil in
+      let (mv_ls, _) =
+        core_mem_replace (list_t t) (List_Cons ckey x tl) List_Nil in
       begin match mv_ls with
-      | List_Cons i cvalue tl0 -> Return (Some cvalue)
+      | List_Cons _ cvalue tl1 -> Return (Some cvalue, tl1)
       | List_Nil -> Fail Failure
       end
-    else hashMap_remove_from_list_loop t key tl
-  | List_Nil -> Return None
+    else
+      let* (o, back) = hashMap_remove_from_list_loop t key tl in
+      Return (o, List_Cons ckey x back)
+  | List_Nil -> Return (None, List_Nil)
   end
 
-(** [hashmap::{hashmap::HashMap<T>}::remove_from_list]: forward function
+(** [hashmap::{hashmap::HashMap<T>}::remove_from_list]:
     Source: 'src/hashmap.rs', lines 265:4-265:69 *)
 let hashMap_remove_from_list
-  (t : Type0) (key : usize) (ls : list_t t) : result (option t) =
-  hashMap_remove_from_list_loop t key ls
-
-(** [hashmap::{hashmap::HashMap<T>}::remove_from_list]: loop 0: backward function 1
-    Source: 'src/hashmap.rs', lines 265:4-291:5 *)
-let rec hashMap_remove_from_list_loop_back
   (t : Type0) (key : usize) (ls : list_t t) :
-  Tot (result (list_t t))
-  (decreases (hashMap_remove_from_list_loop_decreases t key ls))
+  result ((option t) & (list_t t))
   =
-  begin match ls with
-  | List_Cons ckey x tl ->
-    if ckey = key
-    then
-      let mv_ls = core_mem_replace (list_t t) (List_Cons ckey x tl) List_Nil in
-      begin match mv_ls with
-      | List_Cons i cvalue tl0 -> Return tl0
-      | List_Nil -> Fail Failure
-      end
-    else
-      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::HashMap<T>}::remove_from_list]: backward function 1
-    Source: 'src/hashmap.rs', lines 265:4-265:69 *)
-let hashMap_remove_from_list_back
-  (t : Type0) (key : usize) (ls : list_t t) : result (list_t t) =
-  hashMap_remove_from_list_loop_back t key ls
+  hashMap_remove_from_list_loop t key ls
 
-(** [hashmap::{hashmap::HashMap<T>}::remove]: forward function
+(** [hashmap::{hashmap::HashMap<T>}::remove]:
     Source: 'src/hashmap.rs', lines 294:4-294:52 *)
 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 =
-    alloc_vec_Vec_index_mut (list_t t) usize
-      (core_slice_index_SliceIndexUsizeSliceTInst (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.num_entries 1 in Return (Some x0)
-  end
-
-(** [hashmap::{hashmap::HashMap<T>}::remove]: backward function 0
-    Source: 'src/hashmap.rs', lines 294:4-294:52 *)
-let hashMap_remove_back
-  (t : Type0) (self : hashMap_t t) (key : usize) : result (hashMap_t t) =
+  (t : Type0) (self : hashMap_t t) (key : usize) :
+  result ((option t) & (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 =
+  let* (l, index_mut_back) =
     alloc_vec_Vec_index_mut (list_t t) usize
       (core_slice_index_SliceIndexUsizeSliceTInst (list_t t)) self.slots
       hash_mod in
-  let* x = hashMap_remove_from_list t key l in
+  let* (x, l1) = hashMap_remove_from_list t key l in
   begin match x with
   | None ->
-    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_SliceIndexUsizeSliceTInst (list_t t)) self.slots
-        hash_mod l0 in
-    Return { self with slots = v }
-  | Some x0 ->
-    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_SliceIndexUsizeSliceTInst (list_t t)) self.slots
-        hash_mod l0 in
-    Return { self with num_entries = i0; slots = v }
+    let* v = index_mut_back l1 in Return (None, { self with slots = v })
+  | Some x1 ->
+    let* i1 = usize_sub self.num_entries 1 in
+    let* v = index_mut_back l1 in
+    Return (Some x1, { self with num_entries = i1; slots = v })
   end
 
-(** [hashmap::test1]: forward function
+(** [hashmap::test1]:
     Source: 'src/hashmap.rs', lines 315:0-315:10 *)
 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
+  let* hm1 = hashMap_insert u64 hm 0 42 in
+  let* hm2 = hashMap_insert u64 hm1 128 18 in
+  let* hm3 = hashMap_insert u64 hm2 1024 138 in
+  let* hm4 = hashMap_insert u64 hm3 1056 256 in
+  let* i = hashMap_get u64 hm4 128 in
   if not (i = 18)
   then Fail Failure
   else
-    let* hm4 = hashMap_get_mut_back u64 hm3 1024 56 in
-    let* i0 = hashMap_get u64 hm4 1024 in
-    if not (i0 = 56)
+    let* (_, get_mut_back) = hashMap_get_mut u64 hm4 1024 in
+    let* hm5 = get_mut_back 56 in
+    let* i1 = hashMap_get u64 hm5 1024 in
+    if not (i1 = 56)
     then Fail Failure
     else
-      let* x = hashMap_remove u64 hm4 1024 in
+      let* (x, hm6) = hashMap_remove u64 hm5 1024 in
       begin match x with
       | None -> Fail Failure
-      | Some x0 ->
-        if not (x0 = 56)
+      | Some x1 ->
+        if not (x1 = 56)
         then Fail Failure
         else
-          let* hm5 = hashMap_remove_back u64 hm4 1024 in
-          let* i1 = hashMap_get u64 hm5 0 in
-          if not (i1 = 42)
+          let* i2 = hashMap_get u64 hm6 0 in
+          if not (i2 = 42)
           then Fail Failure
           else
-            let* i2 = hashMap_get u64 hm5 128 in
-            if not (i2 = 18)
+            let* i3 = hashMap_get u64 hm6 128 in
+            if not (i3 = 18)
             then Fail Failure
             else
-              let* i3 = hashMap_get u64 hm5 1056 in
-              if not (i3 = 256) then Fail Failure else Return ()
+              let* i4 = hashMap_get u64 hm6 1056 in
+              if not (i4 = 256) then Fail Failure else Return ()
       end
 
diff --git a/tests/fstar/hashmap/Primitives.fst b/tests/fstar/hashmap/Primitives.fst
index a3ffbde4..fca80829 100644
--- a/tests/fstar/hashmap/Primitives.fst
+++ b/tests/fstar/hashmap/Primitives.fst
@@ -55,8 +55,7 @@ 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
+let core_mem_replace (a : Type0) (x : a) (y : a) : a & a = (x, x)
 
 // We don't really use raw pointers for now
 type mut_raw_ptr (t : Type0) = { v : t }
@@ -477,8 +476,7 @@ noeq type core_ops_index_Index (self idx : Type0) = {
 // 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;
+  index_mut : self → idx → result (indexInst.output & (indexInst.output → result self));
 }
 
 // Trait declaration [core::ops::deref::Deref]
@@ -490,8 +488,7 @@ noeq type core_ops_deref_Deref (self : Type0) = {
 // 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;
+  deref_mut : self → result (derefInst.target & (derefInst.target → result self));
 }
 
 type core_ops_range_Range (a : Type0) = {
@@ -502,8 +499,8 @@ type core_ops_range_Range (a : Type0) = {
 (*** [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
+let alloc_boxed_Box_deref_mut (t : Type0) (x : t) : result (t & (t -> result t)) =
+  Return (x, (fun x -> Return x))
 
 // Trait instance
 let alloc_boxed_Box_coreopsDerefInst (self : Type0) : core_ops_deref_Deref self = {
@@ -515,7 +512,6 @@ let alloc_boxed_Box_coreopsDerefInst (self : Type0) : core_ops_deref_Deref self
 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 *)
@@ -535,10 +531,18 @@ let array_index_usize (a : Type0) (n : usize) (x : array a n) (i : usize) : resu
   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) =
+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
 
+let array_index_mut_usize (a : Type0) (n : usize) (x : array a n) (i : usize) :
+  result (a & (a -> result (array a n))) =
+  match array_index_usize a n x i with
+  | Fail e -> Fail e
+  | Return v ->
+    Return (v, array_update_usize a n x i)
+
 (*** Slice *)
 type slice (a : Type0) = s:list a{length s <= usize_max}
 
@@ -552,6 +556,13 @@ let slice_update_usize (a : Type0) (x : slice a) (i : usize) (nx : a) : result (
   if i < length x then Return (list_update x i nx)
   else Fail Failure
 
+let slice_index_mut_usize (a : Type0) (s : slice a) (i : usize) :
+  result (a & (a -> result (slice a))) =
+  match slice_index_usize a s i with
+  | Fail e -> Fail e
+  | Return x ->
+    Return (x, slice_update_usize a s i)
+
 (*** Subslices *)
 
 let array_to_slice (a : Type0) (n : usize) (x : array a n) : result (slice a) = Return x
@@ -559,6 +570,10 @@ let array_from_slice (a : Type0) (n : usize) (x : array a n) (s : slice a) : res
   if length s = n then Return s
   else Fail Failure
 
+let array_to_slice_mut (a : Type0) (n : usize) (x : array a n) :
+  result (slice a & (slice a -> result (array a n))) =
+  Return (x, array_from_slice a n x)
+
 // 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()
@@ -588,8 +603,13 @@ let alloc_vec_Vec_index_usize (#a : Type0) (v : alloc_vec_Vec a) (i : usize) : r
 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_index_mut_usize (#a : Type0) (v: alloc_vec_Vec a) (i: usize) :
+  result (a & (a → result (alloc_vec_Vec a))) =
+  match alloc_vec_Vec_index_usize v i with
+  | Return x ->
+    Return (x, alloc_vec_Vec_update_usize v i)
+  | Fail e -> Fail e
+
 let alloc_vec_Vec_push (a  : Type0) (v : alloc_vec_Vec a) (x : a) :
   Pure (result (alloc_vec_Vec a))
   (requires True)
@@ -605,9 +625,6 @@ let alloc_vec_Vec_push (a  : Type0) (v : alloc_vec_Vec a) (x : a) :
     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
 
@@ -619,13 +636,11 @@ 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_mut : self → t → result (option output & (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;
+  index_mut : self → t → result (output & (output -> result t));
 }
 
 // [core::slice::index::[T]::index]: forward function
@@ -643,14 +658,8 @@ let core_slice_index_RangeUsize_get (t : Type0) (i : core_ops_range_Range usize)
   admit () // TODO
 
 // [core::slice::index::Range::get_mut]: forward function
-let core_slice_index_RangeUsize_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_RangeUsize_get_mut_back
-  (t : Type0) :
-  core_ops_range_Range usize → slice t → option (slice t) → result (slice t) =
+let core_slice_index_RangeUsize_get_mut (t : Type0) :
+  core_ops_range_Range usize → slice t → result (option (slice t) & (option (slice t) -> result (slice t))) =
   admit () // TODO
 
 // [core::slice::index::Range::get_unchecked]: forward function
@@ -675,27 +684,16 @@ let core_slice_index_RangeUsize_index
   admit () // TODO
 
 // [core::slice::index::Range::index_mut]: forward function
-let core_slice_index_RangeUsize_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_RangeUsize_index_mut_back
-  (t : Type0) : core_ops_range_Range usize → slice t → slice t → result (slice t) =
+let core_slice_index_RangeUsize_index_mut (t : Type0) :
+  core_ops_range_Range usize → slice t → result (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 =
+  slice t → idx → result (inst.output & (inst.output -> result (slice t))) =
   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)
@@ -705,13 +703,8 @@ let core_array_Array_index
 // [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) =
+  (a : array t n) (i : idx) :
+  result (inst.indexInst.output & (inst.indexInst.output -> result (array t n))) =
   admit () // TODO
 
 // Trait implementation: [core::slice::index::private_slice_index::Range]
@@ -725,12 +718,10 @@ let core_slice_index_SliceIndexRangeUsizeSliceTInst (t : Type0) :
   output = slice t;
   get = core_slice_index_RangeUsize_get t;
   get_mut = core_slice_index_RangeUsize_get_mut t;
-  get_mut_back = core_slice_index_RangeUsize_get_mut_back t;
   get_unchecked = core_slice_index_RangeUsize_get_unchecked t;
   get_unchecked_mut = core_slice_index_RangeUsize_get_unchecked_mut t;
   index = core_slice_index_RangeUsize_index t;
   index_mut = core_slice_index_RangeUsize_index_mut t;
-  index_mut_back = core_slice_index_RangeUsize_index_mut_back t;
 }
 
 // Trait implementation: [core::slice::index::[T]]
@@ -747,7 +738,6 @@ let core_ops_index_IndexMutSliceTIInst (t idx : Type0)
   core_ops_index_IndexMut (slice t) idx = {
   indexInst = core_ops_index_IndexSliceTIInst 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]]
@@ -764,7 +754,6 @@ let core_ops_index_IndexMutArrayIInst (t idx : Type0) (n : usize)
   core_ops_index_IndexMut (array t n) idx = {
   indexInst = core_ops_index_IndexArrayInst 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
@@ -773,13 +762,8 @@ let core_slice_index_usize_get
   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) =
+let core_slice_index_usize_get_mut (t : Type0) :
+  usize → slice t → result (option t & (option t -> result (slice t))) =
   admit () // TODO
 
 // [core::slice::index::usize::get_unchecked]: forward function
@@ -797,12 +781,8 @@ 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) =
+let core_slice_index_usize_index_mut (t : Type0) :
+  usize → slice t → result (t & (t -> result (slice t))) =
   admit () // TODO
 
 // Trait implementation: [core::slice::index::private_slice_index::usize]
@@ -816,12 +796,10 @@ let core_slice_index_SliceIndexUsizeSliceTInst (t : Type0) :
   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
@@ -831,13 +809,8 @@ let alloc_vec_Vec_index (t idx : Type0) (inst : core_slice_index_SliceIndex idx
 
 // [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) =
+  (self : alloc_vec_Vec t) (i : idx) :
+  result (inst.output & (inst.output -> result (alloc_vec_Vec t))) =
   admit () // TODO
 
 // Trait implementation: [alloc::vec::Vec]
@@ -854,7 +827,6 @@ let alloc_vec_Vec_coreopsindexIndexMutInst (t idx : Type0)
   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 *)
@@ -870,15 +842,7 @@ let alloc_vec_Vec_index_eq (#a : Type0) (v : alloc_vec_Vec a) (i : usize) :
 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_SliceIndexUsizeSliceTInst a) v i ==
-      alloc_vec_Vec_index_usize v i)
+      alloc_vec_Vec_index_mut_usize v i)
   [SMTPat (alloc_vec_Vec_index_mut a usize (core_slice_index_SliceIndexUsizeSliceTInst 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_SliceIndexUsizeSliceTInst a) v i x ==
-      alloc_vec_Vec_update_usize v i x)
-  [SMTPat (alloc_vec_Vec_index_mut_back a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i x)]
-  =
-  admit()
diff --git a/tests/fstar/hashmap_on_disk/HashmapMain.Funs.fst b/tests/fstar/hashmap_on_disk/HashmapMain.Funs.fst
index f2d09a38..b16dcada 100644
--- a/tests/fstar/hashmap_on_disk/HashmapMain.Funs.fst
+++ b/tests/fstar/hashmap_on_disk/HashmapMain.Funs.fst
@@ -8,12 +8,12 @@ include HashmapMain.Clauses
 
 #set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
 
-(** [hashmap_main::hashmap::hash_key]: forward function
+(** [hashmap_main::hashmap::hash_key]:
     Source: 'src/hashmap.rs', lines 27:0-27:32 *)
 let hashmap_hash_key (k : usize) : result usize =
   Return k
 
-(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::allocate_slots]: loop 0: forward function
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::allocate_slots]: loop 0:
     Source: 'src/hashmap.rs', lines 50:4-56:5 *)
 let rec hashmap_HashMap_allocate_slots_loop
   (t : Type0) (slots : alloc_vec_Vec (hashmap_List_t t)) (n : usize) :
@@ -22,13 +22,12 @@ let rec hashmap_HashMap_allocate_slots_loop
   =
   if n > 0
   then
-    let* slots0 = alloc_vec_Vec_push (hashmap_List_t t) slots Hashmap_List_Nil
-      in
-    let* n0 = usize_sub n 1 in
-    hashmap_HashMap_allocate_slots_loop t slots0 n0
+    let* v = alloc_vec_Vec_push (hashmap_List_t t) slots Hashmap_List_Nil in
+    let* n1 = usize_sub n 1 in
+    hashmap_HashMap_allocate_slots_loop t v n1
   else Return slots
 
-(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::allocate_slots]: forward function
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::allocate_slots]:
     Source: 'src/hashmap.rs', lines 50:4-50:76 *)
 let hashmap_HashMap_allocate_slots
   (t : Type0) (slots : alloc_vec_Vec (hashmap_List_t t)) (n : usize) :
@@ -36,112 +35,90 @@ let hashmap_HashMap_allocate_slots
   =
   hashmap_HashMap_allocate_slots_loop t slots n
 
-(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::new_with_capacity]: forward function
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::new_with_capacity]:
     Source: 'src/hashmap.rs', lines 59:4-63:13 *)
 let hashmap_HashMap_new_with_capacity
   (t : Type0) (capacity : usize) (max_load_dividend : usize)
   (max_load_divisor : usize) :
   result (hashmap_HashMap_t t)
   =
-  let v = alloc_vec_Vec_new (hashmap_List_t t) in
-  let* slots = hashmap_HashMap_allocate_slots t v capacity in
+  let* slots =
+    hashmap_HashMap_allocate_slots t (alloc_vec_Vec_new (hashmap_List_t t))
+      capacity in
   let* i = usize_mul capacity max_load_dividend in
-  let* i0 = usize_div i max_load_divisor in
+  let* i1 = usize_div i max_load_divisor in
   Return
     {
       num_entries = 0;
       max_load_factor = (max_load_dividend, max_load_divisor);
-      max_load = i0;
+      max_load = i1;
       slots = slots
     }
 
-(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::new]: forward function
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::new]:
     Source: 'src/hashmap.rs', lines 75:4-75:24 *)
 let hashmap_HashMap_new (t : Type0) : result (hashmap_HashMap_t t) =
   hashmap_HashMap_new_with_capacity t 32 4 5
 
-(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::clear]: loop 0: merged forward/backward function
-    (there is a single backward function, and the forward function returns ())
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::clear]: loop 0:
     Source: 'src/hashmap.rs', lines 80:4-88:5 *)
 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 = alloc_vec_Vec_len (hashmap_List_t t) slots in
-  if i < i0
+  let i1 = alloc_vec_Vec_len (hashmap_List_t t) slots in
+  if i < i1
   then
-    let* i1 = usize_add i 1 in
-    let* slots0 =
-      alloc_vec_Vec_index_mut_back (hashmap_List_t t) usize
+    let* (_, index_mut_back) =
+      alloc_vec_Vec_index_mut (hashmap_List_t t) usize
         (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t t)) slots i
-        Hashmap_List_Nil in
-    hashmap_HashMap_clear_loop t slots0 i1
+      in
+    let* i2 = usize_add i 1 in
+    let* slots1 = index_mut_back Hashmap_List_Nil in
+    hashmap_HashMap_clear_loop t slots1 i2
   else Return slots
 
-(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::clear]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ())
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::clear]:
     Source: 'src/hashmap.rs', lines 80:4-80:27 *)
 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 }
+  let* back = hashmap_HashMap_clear_loop t self.slots 0 in
+  Return { self with num_entries = 0; slots = back }
 
-(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::len]: forward function
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::len]:
     Source: 'src/hashmap.rs', lines 90:4-90:30 *)
 let hashmap_HashMap_len
   (t : Type0) (self : hashmap_HashMap_t t) : result usize =
   Return self.num_entries
 
-(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::insert_in_list]: loop 0: forward function
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::insert_in_list]: loop 0:
     Source: 'src/hashmap.rs', lines 97:4-114:5 *)
 let rec hashmap_HashMap_insert_in_list_loop
   (t : Type0) (key : usize) (value : t) (ls : hashmap_List_t t) :
-  Tot (result bool)
+  Tot (result (bool & (hashmap_List_t t)))
   (decreases (hashmap_HashMap_insert_in_list_loop_decreases t key value ls))
   =
   begin match ls with
   | Hashmap_List_Cons ckey cvalue tl ->
     if ckey = key
-    then Return false
-    else hashmap_HashMap_insert_in_list_loop t key value tl
-  | Hashmap_List_Nil -> Return true
-  end
-
-(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::insert_in_list]: forward function
-    Source: 'src/hashmap.rs', lines 97:4-97:71 *)
-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_main::hashmap::HashMap<T>}::insert_in_list]: loop 0: backward function 0
-    Source: 'src/hashmap.rs', lines 97:4-114:5 *)
-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
-  | Hashmap_List_Cons ckey cvalue tl ->
-    if ckey = key
-    then Return (Hashmap_List_Cons ckey value tl)
+    then Return (false, Hashmap_List_Cons ckey value tl)
     else
-      let* tl0 = hashmap_HashMap_insert_in_list_loop_back t key value tl in
-      Return (Hashmap_List_Cons ckey cvalue tl0)
+      let* (b, back) = hashmap_HashMap_insert_in_list_loop t key value tl in
+      Return (b, Hashmap_List_Cons ckey cvalue back)
   | Hashmap_List_Nil ->
-    let l = Hashmap_List_Nil in Return (Hashmap_List_Cons key value l)
+    Return (true, Hashmap_List_Cons key value Hashmap_List_Nil)
   end
 
-(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::insert_in_list]: backward function 0
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::insert_in_list]:
     Source: 'src/hashmap.rs', lines 97:4-97:71 *)
-let hashmap_HashMap_insert_in_list_back
+let hashmap_HashMap_insert_in_list
   (t : Type0) (key : usize) (value : t) (ls : hashmap_List_t t) :
-  result (hashmap_List_t t)
+  result (bool & (hashmap_List_t t))
   =
-  hashmap_HashMap_insert_in_list_loop_back t key value ls
+  hashmap_HashMap_insert_in_list_loop t key value ls
 
-(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::insert_no_resize]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ())
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::insert_no_resize]:
     Source: 'src/hashmap.rs', lines 117:4-117:54 *)
 let hashmap_HashMap_insert_no_resize
   (t : Type0) (self : hashmap_HashMap_t t) (key : usize) (value : t) :
@@ -150,30 +127,19 @@ let hashmap_HashMap_insert_no_resize
   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 =
+  let* (l, index_mut_back) =
     alloc_vec_Vec_index_mut (hashmap_List_t t) usize
       (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t t))
       self.slots hash_mod in
-  let* inserted = hashmap_HashMap_insert_in_list t key value l in
+  let* (inserted, l1) = hashmap_HashMap_insert_in_list t key value l in
   if inserted
   then
-    let* i0 = usize_add self.num_entries 1 in
-    let* l0 = hashmap_HashMap_insert_in_list_back t key value l in
-    let* v =
-      alloc_vec_Vec_index_mut_back (hashmap_List_t t) usize
-        (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t t))
-        self.slots hash_mod l0 in
-    Return { self with num_entries = i0; slots = v }
-  else
-    let* l0 = hashmap_HashMap_insert_in_list_back t key value l in
-    let* v =
-      alloc_vec_Vec_index_mut_back (hashmap_List_t t) usize
-        (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t t))
-        self.slots hash_mod l0 in
-    Return { self with slots = v }
-
-(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::move_elements_from_list]: loop 0: merged forward/backward function
-    (there is a single backward function, and the forward function returns ())
+    let* i1 = usize_add self.num_entries 1 in
+    let* v = index_mut_back l1 in
+    Return { self with num_entries = i1; slots = v }
+  else let* v = index_mut_back l1 in Return { self with slots = v }
+
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::move_elements_from_list]: loop 0:
     Source: 'src/hashmap.rs', lines 183:4-196:5 *)
 let rec hashmap_HashMap_move_elements_from_list_loop
   (t : Type0) (ntable : hashmap_HashMap_t t) (ls : hashmap_List_t t) :
@@ -183,13 +149,12 @@ let rec hashmap_HashMap_move_elements_from_list_loop
   =
   begin match ls with
   | 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
+    let* hm = hashmap_HashMap_insert_no_resize t ntable k v in
+    hashmap_HashMap_move_elements_from_list_loop t hm tl
   | Hashmap_List_Nil -> Return ntable
   end
 
-(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::move_elements_from_list]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ())
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::move_elements_from_list]:
     Source: 'src/hashmap.rs', lines 183:4-183:72 *)
 let hashmap_HashMap_move_elements_from_list
   (t : Type0) (ntable : hashmap_HashMap_t t) (ls : hashmap_List_t t) :
@@ -197,8 +162,7 @@ let hashmap_HashMap_move_elements_from_list
   =
   hashmap_HashMap_move_elements_from_list_loop t ntable ls
 
-(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::move_elements]: loop 0: merged forward/backward function
-    (there is a single backward function, and the forward function returns ())
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::move_elements]: loop 0:
     Source: 'src/hashmap.rs', lines 171:4-180:5 *)
 let rec hashmap_HashMap_move_elements_loop
   (t : Type0) (ntable : hashmap_HashMap_t t)
@@ -206,68 +170,64 @@ let rec hashmap_HashMap_move_elements_loop
   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 = alloc_vec_Vec_len (hashmap_List_t t) slots in
-  if i < i0
+  let i1 = alloc_vec_Vec_len (hashmap_List_t t) slots in
+  if i < i1
   then
-    let* l =
+    let* (l, index_mut_back) =
       alloc_vec_Vec_index_mut (hashmap_List_t t) usize
         (core_slice_index_SliceIndexUsizeSliceTInst (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 = 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_SliceIndexUsizeSliceTInst (hashmap_List_t t)) slots i
-        l0 in
-    hashmap_HashMap_move_elements_loop t ntable0 slots0 i1
+    let (ls, l1) = core_mem_replace (hashmap_List_t t) l Hashmap_List_Nil in
+    let* hm = hashmap_HashMap_move_elements_from_list t ntable ls in
+    let* i2 = usize_add i 1 in
+    let* slots1 = index_mut_back l1 in
+    let* back_'a = hashmap_HashMap_move_elements_loop t hm slots1 i2 in
+    let (hm1, v) = back_'a in
+    Return (hm1, v)
   else Return (ntable, slots)
 
-(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::move_elements]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ())
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::move_elements]:
     Source: 'src/hashmap.rs', lines 171:4-171:95 *)
 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_HashMap_move_elements_loop t ntable slots i
+  let* back_'a = hashmap_HashMap_move_elements_loop t ntable slots i in
+  let (hm, v) = back_'a in
+  Return (hm, v)
 
-(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::try_resize]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ())
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::try_resize]:
     Source: 'src/hashmap.rs', lines 140:4-140:28 *)
 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.max_load_factor in
-  let* i1 = usize_div n1 i in
-  if capacity <= i1
+  let (i, i1) = self.max_load_factor in
+  let* i2 = usize_div n1 i in
+  if capacity <= i2
   then
-    let* i2 = usize_mul capacity 2 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
+    let* i3 = usize_mul capacity 2 in
+    let* ntable = hashmap_HashMap_new_with_capacity t i3 i i1 in
+    let* p = hashmap_HashMap_move_elements t ntable self.slots 0 in
+    let (ntable1, _) = p in
     Return
-      { ntable0 with num_entries = self.num_entries; max_load_factor = (i, i0)
+      { ntable1 with num_entries = self.num_entries; max_load_factor = (i, i1)
       }
-  else Return { self with max_load_factor = (i, i0) }
+  else Return { self with max_load_factor = (i, i1) }
 
-(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::insert]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ())
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::insert]:
     Source: 'src/hashmap.rs', lines 129:4-129:48 *)
 let hashmap_HashMap_insert
   (t : Type0) (self : hashmap_HashMap_t t) (key : usize) (value : t) :
   result (hashmap_HashMap_t t)
   =
-  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
+  let* hm = hashmap_HashMap_insert_no_resize t self key value in
+  let* i = hashmap_HashMap_len t hm in
+  if i > hm.max_load then hashmap_HashMap_try_resize t hm else Return hm
 
-(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::contains_key_in_list]: loop 0: forward function
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::contains_key_in_list]: loop 0:
     Source: 'src/hashmap.rs', lines 206:4-219:5 *)
 let rec hashmap_HashMap_contains_key_in_list_loop
   (t : Type0) (key : usize) (ls : hashmap_List_t t) :
@@ -275,20 +235,20 @@ let rec hashmap_HashMap_contains_key_in_list_loop
   (decreases (hashmap_HashMap_contains_key_in_list_loop_decreases t key ls))
   =
   begin match ls with
-  | Hashmap_List_Cons ckey x tl ->
+  | Hashmap_List_Cons ckey _ tl ->
     if ckey = key
     then Return true
     else hashmap_HashMap_contains_key_in_list_loop t key tl
   | Hashmap_List_Nil -> Return false
   end
 
-(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::contains_key_in_list]: forward function
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::contains_key_in_list]:
     Source: 'src/hashmap.rs', lines 206:4-206:68 *)
 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_main::hashmap::HashMap<T>}::contains_key]: forward function
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::contains_key]:
     Source: 'src/hashmap.rs', lines 199:4-199:49 *)
 let hashmap_HashMap_contains_key
   (t : Type0) (self : hashmap_HashMap_t t) (key : usize) : result bool =
@@ -301,7 +261,7 @@ let hashmap_HashMap_contains_key
       self.slots hash_mod in
   hashmap_HashMap_contains_key_in_list t key l
 
-(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_in_list]: loop 0: forward function
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_in_list]: loop 0:
     Source: 'src/hashmap.rs', lines 224:4-237:5 *)
 let rec hashmap_HashMap_get_in_list_loop
   (t : Type0) (key : usize) (ls : hashmap_List_t t) :
@@ -316,13 +276,13 @@ let rec hashmap_HashMap_get_in_list_loop
   | Hashmap_List_Nil -> Fail Failure
   end
 
-(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_in_list]: forward function
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_in_list]:
     Source: 'src/hashmap.rs', lines 224:4-224:70 *)
 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_main::hashmap::HashMap<T>}::get]: forward function
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get]:
     Source: 'src/hashmap.rs', lines 239:4-239:55 *)
 let hashmap_HashMap_get
   (t : Type0) (self : hashmap_HashMap_t t) (key : usize) : result t =
@@ -335,241 +295,161 @@ let hashmap_HashMap_get
       self.slots hash_mod in
   hashmap_HashMap_get_in_list t key l
 
-(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_mut_in_list]: loop 0: forward function
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_mut_in_list]: loop 0:
     Source: 'src/hashmap.rs', lines 245:4-254:5 *)
 let rec hashmap_HashMap_get_mut_in_list_loop
   (t : Type0) (ls : hashmap_List_t t) (key : usize) :
-  Tot (result t)
-  (decreases (hashmap_HashMap_get_mut_in_list_loop_decreases t ls key))
-  =
-  begin match ls with
-  | Hashmap_List_Cons ckey cvalue tl ->
-    if ckey = key
-    then Return cvalue
-    else hashmap_HashMap_get_mut_in_list_loop t tl key
-  | Hashmap_List_Nil -> Fail Failure
-  end
-
-(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_mut_in_list]: forward function
-    Source: 'src/hashmap.rs', lines 245:4-245:86 *)
-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_main::hashmap::HashMap<T>}::get_mut_in_list]: loop 0: backward function 0
-    Source: 'src/hashmap.rs', lines 245:4-254:5 *)
-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))
+  Tot (result (t & (t -> result (hashmap_List_t t))))
   (decreases (hashmap_HashMap_get_mut_in_list_loop_decreases t ls key))
   =
   begin match ls with
   | Hashmap_List_Cons ckey cvalue tl ->
     if ckey = key
-    then Return (Hashmap_List_Cons ckey ret tl)
+    then
+      let back_'a = fun ret -> Return (Hashmap_List_Cons ckey ret tl) in
+      Return (cvalue, back_'a)
     else
-      let* tl0 = hashmap_HashMap_get_mut_in_list_loop_back t tl key ret in
-      Return (Hashmap_List_Cons ckey cvalue tl0)
+      let* (x, back_'a) = hashmap_HashMap_get_mut_in_list_loop t tl key in
+      let back_'a1 =
+        fun ret ->
+          let* tl1 = back_'a ret in Return (Hashmap_List_Cons ckey cvalue tl1)
+        in
+      Return (x, back_'a1)
   | Hashmap_List_Nil -> Fail Failure
   end
 
-(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_mut_in_list]: backward function 0
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_mut_in_list]:
     Source: 'src/hashmap.rs', lines 245:4-245:86 *)
-let hashmap_HashMap_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
+  (t : Type0) (ls : hashmap_List_t t) (key : usize) :
+  result (t & (t -> result (hashmap_List_t t)))
   =
-  hashmap_HashMap_get_mut_in_list_loop_back t ls key ret
+  let* (x, back_'a) = hashmap_HashMap_get_mut_in_list_loop t ls key in
+  Return (x, back_'a)
 
-(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_mut]: forward function
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_mut]:
     Source: 'src/hashmap.rs', lines 257:4-257:67 *)
 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 =
-    alloc_vec_Vec_index_mut (hashmap_List_t t) usize
-      (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t t))
-      self.slots hash_mod in
-  hashmap_HashMap_get_mut_in_list t l key
-
-(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_mut]: backward function 0
-    Source: 'src/hashmap.rs', lines 257:4-257:67 *)
-let hashmap_HashMap_get_mut_back
-  (t : Type0) (self : hashmap_HashMap_t t) (key : usize) (ret : t) :
-  result (hashmap_HashMap_t t)
+  (t : Type0) (self : hashmap_HashMap_t t) (key : usize) :
+  result (t & (t -> result (hashmap_HashMap_t 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 =
+  let* (l, index_mut_back) =
     alloc_vec_Vec_index_mut (hashmap_List_t t) usize
       (core_slice_index_SliceIndexUsizeSliceTInst (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 =
-    alloc_vec_Vec_index_mut_back (hashmap_List_t t) usize
-      (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t t))
-      self.slots hash_mod l0 in
-  Return { self with slots = v }
-
-(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::remove_from_list]: loop 0: forward function
+  let* (x, get_mut_in_list_back) = hashmap_HashMap_get_mut_in_list t l key in
+  let back_'a =
+    fun ret ->
+      let* l1 = get_mut_in_list_back ret in
+      let* v = index_mut_back l1 in
+      Return { self with slots = v } in
+  Return (x, back_'a)
+
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::remove_from_list]: loop 0:
     Source: 'src/hashmap.rs', lines 265:4-291:5 *)
 let rec hashmap_HashMap_remove_from_list_loop
   (t : Type0) (key : usize) (ls : hashmap_List_t t) :
-  Tot (result (option t))
+  Tot (result ((option t) & (hashmap_List_t t)))
   (decreases (hashmap_HashMap_remove_from_list_loop_decreases t key ls))
   =
   begin match ls with
   | Hashmap_List_Cons ckey x tl ->
     if ckey = key
     then
-      let mv_ls =
+      let (mv_ls, _) =
         core_mem_replace (hashmap_List_t t) (Hashmap_List_Cons ckey x tl)
           Hashmap_List_Nil in
       begin match mv_ls with
-      | Hashmap_List_Cons i cvalue tl0 -> Return (Some cvalue)
-      | Hashmap_List_Nil -> Fail Failure
-      end
-    else hashmap_HashMap_remove_from_list_loop t key tl
-  | Hashmap_List_Nil -> Return None
-  end
-
-(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::remove_from_list]: forward function
-    Source: 'src/hashmap.rs', lines 265:4-265:69 *)
-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_main::hashmap::HashMap<T>}::remove_from_list]: loop 0: backward function 1
-    Source: 'src/hashmap.rs', lines 265:4-291:5 *)
-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
-  | Hashmap_List_Cons ckey x tl ->
-    if ckey = key
-    then
-      let mv_ls =
-        core_mem_replace (hashmap_List_t t) (Hashmap_List_Cons ckey x tl)
-          Hashmap_List_Nil in
-      begin match mv_ls with
-      | Hashmap_List_Cons i cvalue tl0 -> Return tl0
+      | Hashmap_List_Cons _ cvalue tl1 -> Return (Some cvalue, tl1)
       | Hashmap_List_Nil -> Fail Failure
       end
     else
-      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
+      let* (o, back) = hashmap_HashMap_remove_from_list_loop t key tl in
+      Return (o, Hashmap_List_Cons ckey x back)
+  | Hashmap_List_Nil -> Return (None, Hashmap_List_Nil)
   end
 
-(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::remove_from_list]: backward function 1
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::remove_from_list]:
     Source: 'src/hashmap.rs', lines 265:4-265:69 *)
-let hashmap_HashMap_remove_from_list_back
+let hashmap_HashMap_remove_from_list
   (t : Type0) (key : usize) (ls : hashmap_List_t t) :
-  result (hashmap_List_t t)
+  result ((option t) & (hashmap_List_t t))
   =
-  hashmap_HashMap_remove_from_list_loop_back t key ls
+  hashmap_HashMap_remove_from_list_loop t key ls
 
-(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::remove]: forward function
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::remove]:
     Source: 'src/hashmap.rs', lines 294:4-294:52 *)
 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 =
-    alloc_vec_Vec_index_mut (hashmap_List_t t) usize
-      (core_slice_index_SliceIndexUsizeSliceTInst (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.num_entries 1 in Return (Some x0)
-  end
-
-(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::remove]: backward function 0
-    Source: 'src/hashmap.rs', lines 294:4-294:52 *)
-let hashmap_HashMap_remove_back
   (t : Type0) (self : hashmap_HashMap_t t) (key : usize) :
-  result (hashmap_HashMap_t t)
+  result ((option t) & (hashmap_HashMap_t 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 =
+  let* (l, index_mut_back) =
     alloc_vec_Vec_index_mut (hashmap_List_t t) usize
       (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t t))
       self.slots hash_mod in
-  let* x = hashmap_HashMap_remove_from_list t key l in
+  let* (x, l1) = hashmap_HashMap_remove_from_list t key l in
   begin match x with
   | None ->
-    let* l0 = hashmap_HashMap_remove_from_list_back t key l in
-    let* v =
-      alloc_vec_Vec_index_mut_back (hashmap_List_t t) usize
-        (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t t))
-        self.slots hash_mod l0 in
-    Return { self with slots = v }
-  | Some x0 ->
-    let* i0 = usize_sub self.num_entries 1 in
-    let* l0 = hashmap_HashMap_remove_from_list_back t key l in
-    let* v =
-      alloc_vec_Vec_index_mut_back (hashmap_List_t t) usize
-        (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t t))
-        self.slots hash_mod l0 in
-    Return { self with num_entries = i0; slots = v }
+    let* v = index_mut_back l1 in Return (None, { self with slots = v })
+  | Some x1 ->
+    let* i1 = usize_sub self.num_entries 1 in
+    let* v = index_mut_back l1 in
+    Return (Some x1, { self with num_entries = i1; slots = v })
   end
 
-(** [hashmap_main::hashmap::test1]: forward function
+(** [hashmap_main::hashmap::test1]:
     Source: 'src/hashmap.rs', lines 315:0-315:10 *)
 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
+  let* hm1 = hashmap_HashMap_insert u64 hm 0 42 in
+  let* hm2 = hashmap_HashMap_insert u64 hm1 128 18 in
+  let* hm3 = hashmap_HashMap_insert u64 hm2 1024 138 in
+  let* hm4 = hashmap_HashMap_insert u64 hm3 1056 256 in
+  let* i = hashmap_HashMap_get u64 hm4 128 in
   if not (i = 18)
   then Fail Failure
   else
-    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)
+    let* (_, get_mut_back) = hashmap_HashMap_get_mut u64 hm4 1024 in
+    let* hm5 = get_mut_back 56 in
+    let* i1 = hashmap_HashMap_get u64 hm5 1024 in
+    if not (i1 = 56)
     then Fail Failure
     else
-      let* x = hashmap_HashMap_remove u64 hm4 1024 in
+      let* (x, hm6) = hashmap_HashMap_remove u64 hm5 1024 in
       begin match x with
       | None -> Fail Failure
-      | Some x0 ->
-        if not (x0 = 56)
+      | Some x1 ->
+        if not (x1 = 56)
         then Fail Failure
         else
-          let* hm5 = hashmap_HashMap_remove_back u64 hm4 1024 in
-          let* i1 = hashmap_HashMap_get u64 hm5 0 in
-          if not (i1 = 42)
+          let* i2 = hashmap_HashMap_get u64 hm6 0 in
+          if not (i2 = 42)
           then Fail Failure
           else
-            let* i2 = hashmap_HashMap_get u64 hm5 128 in
-            if not (i2 = 18)
+            let* i3 = hashmap_HashMap_get u64 hm6 128 in
+            if not (i3 = 18)
             then Fail Failure
             else
-              let* i3 = hashmap_HashMap_get u64 hm5 1056 in
-              if not (i3 = 256) then Fail Failure else Return ()
+              let* i4 = hashmap_HashMap_get u64 hm6 1056 in
+              if not (i4 = 256) then Fail Failure else Return ()
       end
 
-(** [hashmap_main::insert_on_disk]: forward function
+(** [hashmap_main::insert_on_disk]:
     Source: 'src/hashmap_main.rs', lines 7:0-7:43 *)
 let insert_on_disk
   (key : usize) (value : u64) (st : state) : result (state & unit) =
-  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, ())
+  let* (st1, hm) = hashmap_utils_deserialize st in
+  let* hm1 = hashmap_HashMap_insert u64 hm key value in
+  let* (st2, _) = hashmap_utils_serialize hm1 st1 in
+  Return (st2, ())
 
-(** [hashmap_main::main]: forward function
+(** [hashmap_main::main]:
     Source: 'src/hashmap_main.rs', lines 16:0-16:13 *)
 let main : result unit =
   Return ()
diff --git a/tests/fstar/hashmap_on_disk/HashmapMain.FunsExternal.fsti b/tests/fstar/hashmap_on_disk/HashmapMain.FunsExternal.fsti
index b00bbcde..50a6509f 100644
--- a/tests/fstar/hashmap_on_disk/HashmapMain.FunsExternal.fsti
+++ b/tests/fstar/hashmap_on_disk/HashmapMain.FunsExternal.fsti
@@ -6,12 +6,12 @@ include HashmapMain.Types
 
 #set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
 
-(** [hashmap_main::hashmap_utils::deserialize]: forward function
+(** [hashmap_main::hashmap_utils::deserialize]:
     Source: 'src/hashmap_utils.rs', lines 10:0-10:43 *)
 val hashmap_utils_deserialize
   : state -> result (state & (hashmap_HashMap_t u64))
 
-(** [hashmap_main::hashmap_utils::serialize]: forward function
+(** [hashmap_main::hashmap_utils::serialize]:
     Source: 'src/hashmap_utils.rs', lines 5:0-5:42 *)
 val hashmap_utils_serialize
   : hashmap_HashMap_t u64 -> state -> result (state & unit)
diff --git a/tests/fstar/hashmap_on_disk/Primitives.fst b/tests/fstar/hashmap_on_disk/Primitives.fst
index a3ffbde4..fca80829 100644
--- a/tests/fstar/hashmap_on_disk/Primitives.fst
+++ b/tests/fstar/hashmap_on_disk/Primitives.fst
@@ -55,8 +55,7 @@ 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
+let core_mem_replace (a : Type0) (x : a) (y : a) : a & a = (x, x)
 
 // We don't really use raw pointers for now
 type mut_raw_ptr (t : Type0) = { v : t }
@@ -477,8 +476,7 @@ noeq type core_ops_index_Index (self idx : Type0) = {
 // 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;
+  index_mut : self → idx → result (indexInst.output & (indexInst.output → result self));
 }
 
 // Trait declaration [core::ops::deref::Deref]
@@ -490,8 +488,7 @@ noeq type core_ops_deref_Deref (self : Type0) = {
 // 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;
+  deref_mut : self → result (derefInst.target & (derefInst.target → result self));
 }
 
 type core_ops_range_Range (a : Type0) = {
@@ -502,8 +499,8 @@ type core_ops_range_Range (a : Type0) = {
 (*** [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
+let alloc_boxed_Box_deref_mut (t : Type0) (x : t) : result (t & (t -> result t)) =
+  Return (x, (fun x -> Return x))
 
 // Trait instance
 let alloc_boxed_Box_coreopsDerefInst (self : Type0) : core_ops_deref_Deref self = {
@@ -515,7 +512,6 @@ let alloc_boxed_Box_coreopsDerefInst (self : Type0) : core_ops_deref_Deref self
 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 *)
@@ -535,10 +531,18 @@ let array_index_usize (a : Type0) (n : usize) (x : array a n) (i : usize) : resu
   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) =
+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
 
+let array_index_mut_usize (a : Type0) (n : usize) (x : array a n) (i : usize) :
+  result (a & (a -> result (array a n))) =
+  match array_index_usize a n x i with
+  | Fail e -> Fail e
+  | Return v ->
+    Return (v, array_update_usize a n x i)
+
 (*** Slice *)
 type slice (a : Type0) = s:list a{length s <= usize_max}
 
@@ -552,6 +556,13 @@ let slice_update_usize (a : Type0) (x : slice a) (i : usize) (nx : a) : result (
   if i < length x then Return (list_update x i nx)
   else Fail Failure
 
+let slice_index_mut_usize (a : Type0) (s : slice a) (i : usize) :
+  result (a & (a -> result (slice a))) =
+  match slice_index_usize a s i with
+  | Fail e -> Fail e
+  | Return x ->
+    Return (x, slice_update_usize a s i)
+
 (*** Subslices *)
 
 let array_to_slice (a : Type0) (n : usize) (x : array a n) : result (slice a) = Return x
@@ -559,6 +570,10 @@ let array_from_slice (a : Type0) (n : usize) (x : array a n) (s : slice a) : res
   if length s = n then Return s
   else Fail Failure
 
+let array_to_slice_mut (a : Type0) (n : usize) (x : array a n) :
+  result (slice a & (slice a -> result (array a n))) =
+  Return (x, array_from_slice a n x)
+
 // 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()
@@ -588,8 +603,13 @@ let alloc_vec_Vec_index_usize (#a : Type0) (v : alloc_vec_Vec a) (i : usize) : r
 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_index_mut_usize (#a : Type0) (v: alloc_vec_Vec a) (i: usize) :
+  result (a & (a → result (alloc_vec_Vec a))) =
+  match alloc_vec_Vec_index_usize v i with
+  | Return x ->
+    Return (x, alloc_vec_Vec_update_usize v i)
+  | Fail e -> Fail e
+
 let alloc_vec_Vec_push (a  : Type0) (v : alloc_vec_Vec a) (x : a) :
   Pure (result (alloc_vec_Vec a))
   (requires True)
@@ -605,9 +625,6 @@ let alloc_vec_Vec_push (a  : Type0) (v : alloc_vec_Vec a) (x : a) :
     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
 
@@ -619,13 +636,11 @@ 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_mut : self → t → result (option output & (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;
+  index_mut : self → t → result (output & (output -> result t));
 }
 
 // [core::slice::index::[T]::index]: forward function
@@ -643,14 +658,8 @@ let core_slice_index_RangeUsize_get (t : Type0) (i : core_ops_range_Range usize)
   admit () // TODO
 
 // [core::slice::index::Range::get_mut]: forward function
-let core_slice_index_RangeUsize_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_RangeUsize_get_mut_back
-  (t : Type0) :
-  core_ops_range_Range usize → slice t → option (slice t) → result (slice t) =
+let core_slice_index_RangeUsize_get_mut (t : Type0) :
+  core_ops_range_Range usize → slice t → result (option (slice t) & (option (slice t) -> result (slice t))) =
   admit () // TODO
 
 // [core::slice::index::Range::get_unchecked]: forward function
@@ -675,27 +684,16 @@ let core_slice_index_RangeUsize_index
   admit () // TODO
 
 // [core::slice::index::Range::index_mut]: forward function
-let core_slice_index_RangeUsize_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_RangeUsize_index_mut_back
-  (t : Type0) : core_ops_range_Range usize → slice t → slice t → result (slice t) =
+let core_slice_index_RangeUsize_index_mut (t : Type0) :
+  core_ops_range_Range usize → slice t → result (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 =
+  slice t → idx → result (inst.output & (inst.output -> result (slice t))) =
   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)
@@ -705,13 +703,8 @@ let core_array_Array_index
 // [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) =
+  (a : array t n) (i : idx) :
+  result (inst.indexInst.output & (inst.indexInst.output -> result (array t n))) =
   admit () // TODO
 
 // Trait implementation: [core::slice::index::private_slice_index::Range]
@@ -725,12 +718,10 @@ let core_slice_index_SliceIndexRangeUsizeSliceTInst (t : Type0) :
   output = slice t;
   get = core_slice_index_RangeUsize_get t;
   get_mut = core_slice_index_RangeUsize_get_mut t;
-  get_mut_back = core_slice_index_RangeUsize_get_mut_back t;
   get_unchecked = core_slice_index_RangeUsize_get_unchecked t;
   get_unchecked_mut = core_slice_index_RangeUsize_get_unchecked_mut t;
   index = core_slice_index_RangeUsize_index t;
   index_mut = core_slice_index_RangeUsize_index_mut t;
-  index_mut_back = core_slice_index_RangeUsize_index_mut_back t;
 }
 
 // Trait implementation: [core::slice::index::[T]]
@@ -747,7 +738,6 @@ let core_ops_index_IndexMutSliceTIInst (t idx : Type0)
   core_ops_index_IndexMut (slice t) idx = {
   indexInst = core_ops_index_IndexSliceTIInst 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]]
@@ -764,7 +754,6 @@ let core_ops_index_IndexMutArrayIInst (t idx : Type0) (n : usize)
   core_ops_index_IndexMut (array t n) idx = {
   indexInst = core_ops_index_IndexArrayInst 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
@@ -773,13 +762,8 @@ let core_slice_index_usize_get
   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) =
+let core_slice_index_usize_get_mut (t : Type0) :
+  usize → slice t → result (option t & (option t -> result (slice t))) =
   admit () // TODO
 
 // [core::slice::index::usize::get_unchecked]: forward function
@@ -797,12 +781,8 @@ 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) =
+let core_slice_index_usize_index_mut (t : Type0) :
+  usize → slice t → result (t & (t -> result (slice t))) =
   admit () // TODO
 
 // Trait implementation: [core::slice::index::private_slice_index::usize]
@@ -816,12 +796,10 @@ let core_slice_index_SliceIndexUsizeSliceTInst (t : Type0) :
   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
@@ -831,13 +809,8 @@ let alloc_vec_Vec_index (t idx : Type0) (inst : core_slice_index_SliceIndex idx
 
 // [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) =
+  (self : alloc_vec_Vec t) (i : idx) :
+  result (inst.output & (inst.output -> result (alloc_vec_Vec t))) =
   admit () // TODO
 
 // Trait implementation: [alloc::vec::Vec]
@@ -854,7 +827,6 @@ let alloc_vec_Vec_coreopsindexIndexMutInst (t idx : Type0)
   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 *)
@@ -870,15 +842,7 @@ let alloc_vec_Vec_index_eq (#a : Type0) (v : alloc_vec_Vec a) (i : usize) :
 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_SliceIndexUsizeSliceTInst a) v i ==
-      alloc_vec_Vec_index_usize v i)
+      alloc_vec_Vec_index_mut_usize v i)
   [SMTPat (alloc_vec_Vec_index_mut a usize (core_slice_index_SliceIndexUsizeSliceTInst 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_SliceIndexUsizeSliceTInst a) v i x ==
-      alloc_vec_Vec_update_usize v i x)
-  [SMTPat (alloc_vec_Vec_index_mut_back a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i x)]
-  =
-  admit()
diff --git a/tests/fstar/misc/Bitwise.fst b/tests/fstar/misc/Bitwise.fst
index d7ba2c57..7330f07a 100644
--- a/tests/fstar/misc/Bitwise.fst
+++ b/tests/fstar/misc/Bitwise.fst
@@ -5,27 +5,27 @@ open Primitives
 
 #set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
 
-(** [bitwise::shift_u32]: forward function
+(** [bitwise::shift_u32]:
     Source: 'src/bitwise.rs', lines 3:0-3:31 *)
 let shift_u32 (a : u32) : result u32 =
   let* t = u32_shr #Usize a 16 in u32_shl #Usize t 16
 
-(** [bitwise::shift_i32]: forward function
+(** [bitwise::shift_i32]:
     Source: 'src/bitwise.rs', lines 10:0-10:31 *)
 let shift_i32 (a : i32) : result i32 =
   let* t = i32_shr #Isize a 16 in i32_shl #Isize t 16
 
-(** [bitwise::xor_u32]: forward function
+(** [bitwise::xor_u32]:
     Source: 'src/bitwise.rs', lines 17:0-17:37 *)
 let xor_u32 (a : u32) (b : u32) : result u32 =
   Return (u32_xor a b)
 
-(** [bitwise::or_u32]: forward function
+(** [bitwise::or_u32]:
     Source: 'src/bitwise.rs', lines 21:0-21:36 *)
 let or_u32 (a : u32) (b : u32) : result u32 =
   Return (u32_or a b)
 
-(** [bitwise::and_u32]: forward function
+(** [bitwise::and_u32]:
     Source: 'src/bitwise.rs', lines 25:0-25:37 *)
 let and_u32 (a : u32) (b : u32) : result u32 =
   Return (u32_and a b)
diff --git a/tests/fstar/misc/Constants.fst b/tests/fstar/misc/Constants.fst
index daeefbb0..7bf42b46 100644
--- a/tests/fstar/misc/Constants.fst
+++ b/tests/fstar/misc/Constants.fst
@@ -20,7 +20,7 @@ let x1_c : u32 = eval_global x1_body
 let x2_body : result u32 = Return 3
 let x2_c : u32 = eval_global x2_body
 
-(** [constants::incr]: forward function
+(** [constants::incr]:
     Source: 'src/constants.rs', lines 17:0-17:32 *)
 let incr (n : u32) : result u32 =
   u32_add n 1
@@ -30,7 +30,7 @@ let incr (n : u32) : result u32 =
 let x3_body : result u32 = incr 32
 let x3_c : u32 = eval_global x3_body
 
-(** [constants::mk_pair0]: forward function
+(** [constants::mk_pair0]:
     Source: 'src/constants.rs', lines 23:0-23:51 *)
 let mk_pair0 (x : u32) (y : u32) : result (u32 & u32) =
   Return (x, y)
@@ -39,7 +39,7 @@ let mk_pair0 (x : u32) (y : u32) : result (u32 & u32) =
     Source: 'src/constants.rs', lines 36:0-36:23 *)
 type pair_t (t1 t2 : Type0) = { x : t1; y : t2; }
 
-(** [constants::mk_pair1]: forward function
+(** [constants::mk_pair1]:
     Source: 'src/constants.rs', lines 27:0-27:55 *)
 let mk_pair1 (x : u32) (y : u32) : result (pair_t u32 u32) =
   Return { x = x; y = y }
@@ -68,7 +68,7 @@ let p3_c : pair_t u32 u32 = eval_global p3_body
     Source: 'src/constants.rs', lines 49:0-49:18 *)
 type wrap_t (t : Type0) = { value : t; }
 
-(** [constants::{constants::Wrap<T>}::new]: forward function
+(** [constants::{constants::Wrap<T>}::new]:
     Source: 'src/constants.rs', lines 54:4-54:41 *)
 let wrap_new (t : Type0) (value : t) : result (wrap_t t) =
   Return { value = value }
@@ -78,7 +78,7 @@ let wrap_new (t : Type0) (value : t) : result (wrap_t t) =
 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
+(** [constants::unwrap_y]:
     Source: 'src/constants.rs', lines 43:0-43:30 *)
 let unwrap_y : result i32 =
   Return y_c.value
@@ -93,12 +93,12 @@ let yval_c : i32 = eval_global yval_body
 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
+(** [constants::get_z1]:
     Source: 'src/constants.rs', lines 61:0-61:28 *)
 let get_z1 : result i32 =
   Return get_z1_z1_c
 
-(** [constants::add]: forward function
+(** [constants::add]:
     Source: 'src/constants.rs', lines 66:0-66:39 *)
 let add (a : i32) (b : i32) : result i32 =
   i32_add a b
@@ -118,10 +118,10 @@ let q2_c : i32 = eval_global q2_body
 let q3_body : result i32 = add q2_c 3
 let q3_c : i32 = eval_global q3_body
 
-(** [constants::get_z2]: forward function
+(** [constants::get_z2]:
     Source: 'src/constants.rs', lines 70:0-70:28 *)
 let get_z2 : result i32 =
-  let* i = get_z1 in let* i0 = add i q3_c in add q1_c i0
+  let* i = get_z1 in let* i1 = add i q3_c in add q1_c i1
 
 (** [constants::S1]
     Source: 'src/constants.rs', lines 80:0-80:18 *)
diff --git a/tests/fstar/misc/External.Funs.fst b/tests/fstar/misc/External.Funs.fst
index 00995634..6672b523 100644
--- a/tests/fstar/misc/External.Funs.fst
+++ b/tests/fstar/misc/External.Funs.fst
@@ -7,78 +7,48 @@ include External.FunsExternal
 
 #set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
 
-(** [external::swap]: forward function
+(** [external::swap]:
     Source: 'src/external.rs', lines 6:0-6:46 *)
-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, ())
+let swap (t : Type0) (x : t) (y : t) (st : state) : result (state & (t & t)) =
+  core_mem_swap t x y st
 
-(** [external::swap]: backward function 0
-    Source: 'src/external.rs', lines 6:0-6:46 *)
-let swap_back
-  (t : Type0) (x : t) (y : t) (st : state) (st0 : state) :
-  result (state & (t & t))
-  =
-  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
+(** [external::test_new_non_zero_u32]:
     Source: 'src/external.rs', lines 11:0-11:60 *)
 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
+  let* (st1, o) = core_num_nonzero_NonZeroU32_new x st in
+  core_option_Option_unwrap core_num_nonzero_NonZeroU32_t o st1
 
-(** [external::test_vec]: forward function
+(** [external::test_vec]:
     Source: 'src/external.rs', lines 17:0-17:17 *)
 let test_vec : result unit =
-  let v = alloc_vec_Vec_new u32 in
-  let* _ = alloc_vec_Vec_push u32 v 0 in
-  Return ()
+  let* _ = alloc_vec_Vec_push u32 (alloc_vec_Vec_new u32) 0 in Return ()
 
 (** Unit test for [external::test_vec] *)
 let _ = assert_norm (test_vec = Return ())
 
-(** [external::custom_swap]: forward function
-    Source: 'src/external.rs', lines 24:0-24:66 *)
-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)
-
-(** [external::custom_swap]: backward function 0
+(** [external::custom_swap]:
     Source: 'src/external.rs', lines 24:0-24:66 *)
-let custom_swap_back
-  (t : Type0) (x : t) (y : t) (st : state) (ret : t) (st0 : state) :
-  result (state & (t & t))
+let custom_swap
+  (t : Type0) (x : t) (y : t) (st : state) :
+  result (state & (t & (t -> state -> result (state & (t & t)))))
   =
-  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
-    Source: 'src/external.rs', lines 29:0-29:59 *)
-let test_custom_swap (x : u32) (y : u32) (st : state) : result (state & unit) =
-  let* (st0, _) = custom_swap u32 x y st in Return (st0, ())
+  let* (st1, (x1, x2)) = core_mem_swap t x y st in
+  let back_'a = fun ret st2 -> Return (st2, (ret, x2)) in
+  Return (st1, (x1, back_'a))
 
-(** [external::test_custom_swap]: backward function 0
+(** [external::test_custom_swap]:
     Source: 'src/external.rs', lines 29:0-29:59 *)
-let test_custom_swap_back
-  (x : u32) (y : u32) (st : state) (st0 : state) :
-  result (state & (u32 & u32))
-  =
-  custom_swap_back u32 x y st 1 st0
+let test_custom_swap
+  (x : u32) (y : u32) (st : state) : result (state & (u32 & u32)) =
+  let* (st1, (_, custom_swap_back)) = custom_swap u32 x y st in
+  let* (_, (x1, y1)) = custom_swap_back 1 st1 in
+  Return (st1, (x1, y1))
 
-(** [external::test_swap_non_zero]: forward function
+(** [external::test_swap_non_zero]:
     Source: 'src/external.rs', lines 35:0-35:44 *)
 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)
+  let* (st1, p) = swap u32 x 0 st in
+  let (x1, _) = p in
+  if x1 = 0 then Fail Failure else Return (st1, x1)
 
diff --git a/tests/fstar/misc/External.FunsExternal.fsti b/tests/fstar/misc/External.FunsExternal.fsti
index 923a1101..a412aea9 100644
--- a/tests/fstar/misc/External.FunsExternal.fsti
+++ b/tests/fstar/misc/External.FunsExternal.fsti
@@ -6,26 +6,16 @@ include External.Types
 
 #set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
 
-(** [core::mem::swap]: forward function
+(** [core::mem::swap]:
     Source: '/rustc/d59363ad0b6391b7fc5bbb02c9ccf9300eef3753/library/core/src/mem/mod.rs', lines 726:0-726:42 *)
-val core_mem_swap (t : Type0) : t -> t -> state -> result (state & unit)
+val core_mem_swap (t : Type0) : t -> t -> state -> result (state & (t & t))
 
-(** [core::mem::swap]: backward function 0
-    Source: '/rustc/d59363ad0b6391b7fc5bbb02c9ccf9300eef3753/library/core/src/mem/mod.rs', lines 726:0-726:42 *)
-val core_mem_swap_back0
-  (t : Type0) : t -> t -> state -> state -> result (state & t)
-
-(** [core::mem::swap]: backward function 1
-    Source: '/rustc/d59363ad0b6391b7fc5bbb02c9ccf9300eef3753/library/core/src/mem/mod.rs', lines 726:0-726:42 *)
-val core_mem_swap_back1
-  (t : Type0) : t -> t -> state -> state -> result (state & t)
-
-(** [core::num::nonzero::{core::num::nonzero::NonZeroU32#14}::new]: forward function
+(** [core::num::nonzero::{core::num::nonzero::NonZeroU32#14}::new]:
     Source: '/rustc/d59363ad0b6391b7fc5bbb02c9ccf9300eef3753/library/core/src/num/nonzero.rs', lines 79:16-79:57 *)
 val core_num_nonzero_NonZeroU32_new
   : u32 -> state -> result (state & (option core_num_nonzero_NonZeroU32_t))
 
-(** [core::option::{core::option::Option<T>}::unwrap]: forward function
+(** [core::option::{core::option::Option<T>}::unwrap]:
     Source: '/rustc/d59363ad0b6391b7fc5bbb02c9ccf9300eef3753/library/core/src/option.rs', lines 932:4-932:34 *)
 val core_option_Option_unwrap
   (t : Type0) : option t -> state -> result (state & t)
diff --git a/tests/fstar/misc/Loops.Funs.fst b/tests/fstar/misc/Loops.Funs.fst
index d2ac5561..88389300 100644
--- a/tests/fstar/misc/Loops.Funs.fst
+++ b/tests/fstar/misc/Loops.Funs.fst
@@ -7,22 +7,22 @@ include Loops.Clauses
 
 #set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
 
-(** [loops::sum]: loop 0: forward function
+(** [loops::sum]: loop 0:
     Source: 'src/loops.rs', lines 4:0-14:1 *)
 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 max i0 s0
+  then let* s1 = u32_add s i in let* i1 = u32_add i 1 in sum_loop max i1 s1
   else u32_mul s 2
 
-(** [loops::sum]: forward function
+(** [loops::sum]:
     Source: 'src/loops.rs', lines 4:0-4:27 *)
 let sum (max : u32) : result u32 =
   sum_loop max 0 0
 
-(** [loops::sum_with_mut_borrows]: loop 0: forward function
+(** [loops::sum_with_mut_borrows]: loop 0:
     Source: 'src/loops.rs', lines 19:0-31:1 *)
 let rec sum_with_mut_borrows_loop
   (max : u32) (mi : u32) (ms : u32) :
@@ -30,17 +30,17 @@ let rec sum_with_mut_borrows_loop
   =
   if mi < max
   then
-    let* ms0 = u32_add ms mi in
-    let* mi0 = u32_add mi 1 in
-    sum_with_mut_borrows_loop max mi0 ms0
+    let* ms1 = u32_add ms mi in
+    let* mi1 = u32_add mi 1 in
+    sum_with_mut_borrows_loop max mi1 ms1
   else u32_mul ms 2
 
-(** [loops::sum_with_mut_borrows]: forward function
+(** [loops::sum_with_mut_borrows]:
     Source: 'src/loops.rs', lines 19:0-19:44 *)
 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
+(** [loops::sum_with_shared_borrows]: loop 0:
     Source: 'src/loops.rs', lines 34:0-48:1 *)
 let rec sum_with_shared_borrows_loop
   (max : u32) (i : u32) (s : u32) :
@@ -48,40 +48,39 @@ let rec sum_with_shared_borrows_loop
   =
   if i < max
   then
-    let* i0 = u32_add i 1 in
-    let* s0 = u32_add s i0 in
-    sum_with_shared_borrows_loop max i0 s0
+    let* i1 = u32_add i 1 in
+    let* s1 = u32_add s i1 in
+    sum_with_shared_borrows_loop max i1 s1
   else u32_mul s 2
 
-(** [loops::sum_with_shared_borrows]: forward function
+(** [loops::sum_with_shared_borrows]:
     Source: 'src/loops.rs', lines 34:0-34:47 *)
 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 ())
+(** [loops::clear]: loop 0:
     Source: 'src/loops.rs', lines 52:0-58:1 *)
 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 = alloc_vec_Vec_len u32 v in
-  if i < i0
+  let i1 = alloc_vec_Vec_len u32 v in
+  if i < i1
   then
-    let* i1 = usize_add i 1 in
-    let* v0 =
-      alloc_vec_Vec_index_mut_back u32 usize
-        (core_slice_index_SliceIndexUsizeSliceTInst u32) v i 0 in
-    clear_loop v0 i1
+    let* (_, index_mut_back) =
+      alloc_vec_Vec_index_mut u32 usize
+        (core_slice_index_SliceIndexUsizeSliceTInst u32) v i in
+    let* i2 = usize_add i 1 in
+    let* v1 = index_mut_back 0 in
+    clear_loop v1 i2
   else Return v
 
-(** [loops::clear]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ())
+(** [loops::clear]:
     Source: 'src/loops.rs', lines 52:0-52:30 *)
 let clear (v : alloc_vec_Vec u32) : result (alloc_vec_Vec u32) =
   clear_loop v 0
 
-(** [loops::list_mem]: loop 0: forward function
+(** [loops::list_mem]: loop 0:
     Source: 'src/loops.rs', lines 66:0-75:1 *)
 let rec list_mem_loop
   (x : u32) (ls : list_t u32) :
@@ -92,54 +91,39 @@ let rec list_mem_loop
   | List_Nil -> Return false
   end
 
-(** [loops::list_mem]: forward function
+(** [loops::list_mem]:
     Source: 'src/loops.rs', lines 66:0-66:52 *)
 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
+(** [loops::list_nth_mut_loop]: loop 0:
     Source: 'src/loops.rs', lines 78:0-88:1 *)
 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))
+  Tot (result (t & (t -> result (list_t t))))
+  (decreases (list_nth_mut_loop_loop_decreases t ls i))
   =
   begin match ls with
   | List_Cons x tl ->
     if i = 0
-    then Return x
-    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
-    Source: 'src/loops.rs', lines 78:0-78:71 *)
-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
-    Source: 'src/loops.rs', lines 78:0-88:1 *)
-let rec list_nth_mut_loop_loop_back
-  (t : Type0) (ls : list_t t) (i : u32) (ret : t) :
-  Tot (result (list_t t)) (decreases (list_nth_mut_loop_loop_decreases t ls i))
-  =
-  begin match ls with
-  | List_Cons x tl ->
-    if i = 0
-    then Return (List_Cons ret tl)
+    then let back = fun ret -> Return (List_Cons ret tl) in Return (x, back)
     else
-      let* i0 = u32_sub i 1 in
-      let* tl0 = list_nth_mut_loop_loop_back t tl i0 ret in
-      Return (List_Cons x tl0)
+      let* i1 = u32_sub i 1 in
+      let* (x1, back) = list_nth_mut_loop_loop t tl i1 in
+      let back1 = fun ret -> let* tl1 = back ret in Return (List_Cons x tl1) in
+      Return (x1, back1)
   | List_Nil -> Fail Failure
   end
 
-(** [loops::list_nth_mut_loop]: backward function 0
+(** [loops::list_nth_mut_loop]:
     Source: 'src/loops.rs', lines 78:0-78:71 *)
-let list_nth_mut_loop_back
-  (t : Type0) (ls : list_t t) (i : u32) (ret : t) : result (list_t t) =
-  list_nth_mut_loop_loop_back t ls i ret
+let list_nth_mut_loop
+  (t : Type0) (ls : list_t t) (i : u32) :
+  result (t & (t -> result (list_t t)))
+  =
+  let* (x, back) = list_nth_mut_loop_loop t ls i in Return (x, back)
 
-(** [loops::list_nth_shared_loop]: loop 0: forward function
+(** [loops::list_nth_shared_loop]: loop 0:
     Source: 'src/loops.rs', lines 91:0-101:1 *)
 let rec list_nth_shared_loop_loop
   (t : Type0) (ls : list_t t) (i : u32) :
@@ -149,63 +133,47 @@ let rec list_nth_shared_loop_loop
   | List_Cons x tl ->
     if i = 0
     then Return x
-    else let* i0 = u32_sub i 1 in list_nth_shared_loop_loop t tl i0
+    else let* i1 = u32_sub i 1 in list_nth_shared_loop_loop t tl i1
   | List_Nil -> Fail Failure
   end
 
-(** [loops::list_nth_shared_loop]: forward function
+(** [loops::list_nth_shared_loop]:
     Source: 'src/loops.rs', lines 91:0-91:66 *)
 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
+(** [loops::get_elem_mut]: loop 0:
     Source: 'src/loops.rs', lines 103:0-117:1 *)
 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
-  | 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
-    Source: 'src/loops.rs', lines 103:0-103:73 *)
-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_SliceIndexUsizeSliceTInst (list_t usize)) slots 0 in
-  get_elem_mut_loop x l
-
-(** [loops::get_elem_mut]: loop 0: backward function 0
-    Source: 'src/loops.rs', lines 103:0-117:1 *)
-let rec get_elem_mut_loop_back
-  (x : usize) (ls : list_t usize) (ret : usize) :
-  Tot (result (list_t usize)) (decreases (get_elem_mut_loop_decreases x ls))
+  Tot (result (usize & (usize -> result (list_t usize))))
+  (decreases (get_elem_mut_loop_decreases x ls))
   =
   begin match ls with
   | List_Cons y tl ->
     if y = x
-    then Return (List_Cons ret tl)
-    else let* tl0 = get_elem_mut_loop_back x tl ret in Return (List_Cons y tl0)
+    then let back = fun ret -> Return (List_Cons ret tl) in Return (y, back)
+    else
+      let* (i, back) = get_elem_mut_loop x tl in
+      let back1 = fun ret -> let* tl1 = back ret in Return (List_Cons y tl1) in
+      Return (i, back1)
   | List_Nil -> Fail Failure
   end
 
-(** [loops::get_elem_mut]: backward function 0
+(** [loops::get_elem_mut]:
     Source: 'src/loops.rs', lines 103:0-103:73 *)
-let get_elem_mut_back
-  (slots : alloc_vec_Vec (list_t usize)) (x : usize) (ret : usize) :
-  result (alloc_vec_Vec (list_t usize))
+let get_elem_mut
+  (slots : alloc_vec_Vec (list_t usize)) (x : usize) :
+  result (usize & (usize -> result (alloc_vec_Vec (list_t usize))))
   =
-  let* l =
+  let* (l, index_mut_back) =
     alloc_vec_Vec_index_mut (list_t usize) usize
       (core_slice_index_SliceIndexUsizeSliceTInst (list_t usize)) slots 0 in
-  let* l0 = get_elem_mut_loop_back x l ret in
-  alloc_vec_Vec_index_mut_back (list_t usize) usize
-    (core_slice_index_SliceIndexUsizeSliceTInst (list_t usize)) slots 0 l0
+  let* (i, back) = get_elem_mut_loop x l in
+  let back1 = fun ret -> let* l1 = back ret in index_mut_back l1 in
+  Return (i, back1)
 
-(** [loops::get_elem_shared]: loop 0: forward function
+(** [loops::get_elem_shared]: loop 0:
     Source: 'src/loops.rs', lines 119:0-133:1 *)
 let rec get_elem_shared_loop
   (x : usize) (ls : list_t usize) :
@@ -216,7 +184,7 @@ let rec get_elem_shared_loop
   | List_Nil -> Fail Failure
   end
 
-(** [loops::get_elem_shared]: forward function
+(** [loops::get_elem_shared]:
     Source: 'src/loops.rs', lines 119:0-119:68 *)
 let get_elem_shared
   (slots : alloc_vec_Vec (list_t usize)) (x : usize) : result usize =
@@ -225,69 +193,50 @@ let get_elem_shared
       (core_slice_index_SliceIndexUsizeSliceTInst (list_t usize)) slots 0 in
   get_elem_shared_loop x l
 
-(** [loops::id_mut]: forward function
-    Source: 'src/loops.rs', lines 135:0-135:50 *)
-let id_mut (t : Type0) (ls : list_t t) : result (list_t t) =
-  Return ls
-
-(** [loops::id_mut]: backward function 0
+(** [loops::id_mut]:
     Source: 'src/loops.rs', lines 135:0-135:50 *)
-let id_mut_back
-  (t : Type0) (ls : list_t t) (ret : list_t t) : result (list_t t) =
-  Return ret
+let id_mut
+  (t : Type0) (ls : list_t t) :
+  result ((list_t t) & (list_t t -> result (list_t t)))
+  =
+  Return (ls, Return)
 
-(** [loops::id_shared]: forward function
+(** [loops::id_shared]:
     Source: 'src/loops.rs', lines 139:0-139:45 *)
 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
+(** [loops::list_nth_mut_loop_with_id]: loop 0:
     Source: 'src/loops.rs', lines 144:0-155:1 *)
 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
-  | 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 t i0 tl
-  | List_Nil -> Fail Failure
-  end
-
-(** [loops::list_nth_mut_loop_with_id]: forward function
-    Source: 'src/loops.rs', lines 144:0-144:75 *)
-let list_nth_mut_loop_with_id
-  (t : Type0) (ls : list_t t) (i : u32) : result t =
-  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
-    Source: 'src/loops.rs', lines 144:0-155:1 *)
-let rec list_nth_mut_loop_with_id_loop_back
-  (t : Type0) (i : u32) (ls : list_t t) (ret : t) :
-  Tot (result (list_t t))
+  Tot (result (t & (t -> result (list_t t))))
   (decreases (list_nth_mut_loop_with_id_loop_decreases t i ls))
   =
   begin match ls with
   | List_Cons x tl ->
     if i = 0
-    then Return (List_Cons ret tl)
+    then let back = fun ret -> Return (List_Cons ret tl) in Return (x, back)
     else
-      let* i0 = u32_sub i 1 in
-      let* tl0 = list_nth_mut_loop_with_id_loop_back t i0 tl ret in
-      Return (List_Cons x tl0)
+      let* i1 = u32_sub i 1 in
+      let* (x1, back) = list_nth_mut_loop_with_id_loop t i1 tl in
+      let back1 = fun ret -> let* tl1 = back ret in Return (List_Cons x tl1) in
+      Return (x1, back1)
   | List_Nil -> Fail Failure
   end
 
-(** [loops::list_nth_mut_loop_with_id]: backward function 0
+(** [loops::list_nth_mut_loop_with_id]:
     Source: 'src/loops.rs', lines 144:0-144:75 *)
-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 t ls in
-  let* l = list_nth_mut_loop_with_id_loop_back t i ls0 ret in
-  id_mut_back t ls l
+let list_nth_mut_loop_with_id
+  (t : Type0) (ls : list_t t) (i : u32) :
+  result (t & (t -> result (list_t t)))
+  =
+  let* (ls1, id_mut_back) = id_mut t ls in
+  let* (x, back) = list_nth_mut_loop_with_id_loop t i ls1 in
+  let back1 = fun ret -> let* l = back ret in id_mut_back l in
+  Return (x, back1)
 
-(** [loops::list_nth_shared_loop_with_id]: loop 0: forward function
+(** [loops::list_nth_shared_loop_with_id]: loop 0:
     Source: 'src/loops.rs', lines 158:0-169:1 *)
 let rec list_nth_shared_loop_with_id_loop
   (t : Type0) (i : u32) (ls : list_t t) :
@@ -298,46 +247,21 @@ let rec list_nth_shared_loop_with_id_loop
   | 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 t i0 tl
+    else let* i1 = u32_sub i 1 in list_nth_shared_loop_with_id_loop t i1 tl
   | List_Nil -> Fail Failure
   end
 
-(** [loops::list_nth_shared_loop_with_id]: forward function
+(** [loops::list_nth_shared_loop_with_id]:
     Source: 'src/loops.rs', lines 158:0-158:70 *)
 let list_nth_shared_loop_with_id
   (t : Type0) (ls : list_t t) (i : u32) : result t =
-  let* ls0 = id_shared t ls in list_nth_shared_loop_with_id_loop t i ls0
+  let* ls1 = id_shared t ls in list_nth_shared_loop_with_id_loop t i ls1
 
-(** [loops::list_nth_mut_loop_pair]: loop 0: forward function
+(** [loops::list_nth_mut_loop_pair]: loop 0:
     Source: 'src/loops.rs', lines 174:0-195:1 *)
 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
-  | List_Cons x0 tl0 ->
-    begin match ls1 with
-    | 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 t tl0 tl1 i0
-    | List_Nil -> Fail Failure
-    end
-  | List_Nil -> Fail Failure
-  end
-
-(** [loops::list_nth_mut_loop_pair]: forward function
-    Source: 'src/loops.rs', lines 174:0-178:27 *)
-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 t ls0 ls1 i
-
-(** [loops::list_nth_mut_loop_pair]: loop 0: backward function 0
-    Source: 'src/loops.rs', lines 174:0-195:1 *)
-let rec list_nth_mut_loop_pair_loop_back'a
-  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : t) :
-  Tot (result (list_t t))
+  Tot (result ((t & t) & (t -> result (list_t t)) & (t -> result (list_t t))))
   (decreases (list_nth_mut_loop_pair_loop_decreases t ls0 ls1 i))
   =
   begin match ls0 with
@@ -345,55 +269,34 @@ let rec list_nth_mut_loop_pair_loop_back'a
     begin match ls1 with
     | List_Cons x1 tl1 ->
       if i = 0
-      then Return (List_Cons ret tl0)
+      then
+        let back_'a = fun ret -> Return (List_Cons ret tl0) in
+        let back_'b = fun ret -> Return (List_Cons ret tl1) in
+        Return ((x0, x1), back_'a, back_'b)
       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 (List_Cons x0 tl00)
+        let* i1 = u32_sub i 1 in
+        let* (p, back_'a, back_'b) = list_nth_mut_loop_pair_loop t tl0 tl1 i1
+          in
+        let back_'a1 =
+          fun ret -> let* tl01 = back_'a ret in Return (List_Cons x0 tl01) in
+        let back_'b1 =
+          fun ret -> let* tl11 = back_'b ret in Return (List_Cons x1 tl11) in
+        Return (p, back_'a1, back_'b1)
     | List_Nil -> Fail Failure
     end
   | List_Nil -> Fail Failure
   end
 
-(** [loops::list_nth_mut_loop_pair]: backward function 0
+(** [loops::list_nth_mut_loop_pair]:
     Source: 'src/loops.rs', lines 174:0-178:27 *)
-let list_nth_mut_loop_pair_back'a
-  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : t) :
-  result (list_t t)
-  =
-  list_nth_mut_loop_pair_loop_back'a t ls0 ls1 i ret
-
-(** [loops::list_nth_mut_loop_pair]: loop 0: backward function 1
-    Source: 'src/loops.rs', lines 174:0-195:1 *)
-let rec list_nth_mut_loop_pair_loop_back'b
-  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : t) :
-  Tot (result (list_t t))
-  (decreases (list_nth_mut_loop_pair_loop_decreases t ls0 ls1 i))
-  =
-  begin match ls0 with
-  | List_Cons x0 tl0 ->
-    begin match ls1 with
-    | List_Cons x1 tl1 ->
-      if i = 0
-      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 (List_Cons x1 tl10)
-    | List_Nil -> Fail Failure
-    end
-  | List_Nil -> Fail Failure
-  end
-
-(** [loops::list_nth_mut_loop_pair]: backward function 1
-    Source: 'src/loops.rs', lines 174:0-178:27 *)
-let list_nth_mut_loop_pair_back'b
-  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : t) :
-  result (list_t t)
+let list_nth_mut_loop_pair
+  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) :
+  result ((t & t) & (t -> result (list_t t)) & (t -> result (list_t t)))
   =
-  list_nth_mut_loop_pair_loop_back'b t ls0 ls1 i ret
+  let* (p, back_'a, back_'b) = list_nth_mut_loop_pair_loop t ls0 ls1 i in
+  Return (p, back_'a, back_'b)
 
-(** [loops::list_nth_shared_loop_pair]: loop 0: forward function
+(** [loops::list_nth_shared_loop_pair]: loop 0:
     Source: 'src/loops.rs', lines 198:0-219:1 *)
 let rec list_nth_shared_loop_pair_loop
   (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) :
@@ -406,23 +309,23 @@ let rec list_nth_shared_loop_pair_loop
     | 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 t tl0 tl1 i0
+      else let* i1 = u32_sub i 1 in list_nth_shared_loop_pair_loop t tl0 tl1 i1
     | List_Nil -> Fail Failure
     end
   | List_Nil -> Fail Failure
   end
 
-(** [loops::list_nth_shared_loop_pair]: forward function
+(** [loops::list_nth_shared_loop_pair]:
     Source: 'src/loops.rs', lines 198:0-202:19 *)
 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 t ls0 ls1 i
 
-(** [loops::list_nth_mut_loop_pair_merge]: loop 0: forward function
+(** [loops::list_nth_mut_loop_pair_merge]: loop 0:
     Source: 'src/loops.rs', lines 223:0-238:1 *)
 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))
+  Tot (result ((t & t) & ((t & t) -> result ((list_t t) & (list_t t)))))
   (decreases (list_nth_mut_loop_pair_merge_loop_decreases t ls0 ls1 i))
   =
   begin match ls0 with
@@ -430,52 +333,34 @@ let rec list_nth_mut_loop_pair_merge_loop
     begin match ls1 with
     | List_Cons x1 tl1 ->
       if i = 0
-      then Return (x0, x1)
+      then
+        let back_'a =
+          fun ret ->
+            let (x, x2) = ret in Return (List_Cons x tl0, List_Cons x2 tl1) in
+        Return ((x0, x1), back_'a)
       else
-        let* i0 = u32_sub i 1 in list_nth_mut_loop_pair_merge_loop t tl0 tl1 i0
+        let* i1 = u32_sub i 1 in
+        let* (p, back_'a) = list_nth_mut_loop_pair_merge_loop t tl0 tl1 i1 in
+        let back_'a1 =
+          fun ret ->
+            let* (tl01, tl11) = back_'a ret in
+            Return (List_Cons x0 tl01, List_Cons x1 tl11) in
+        Return (p, back_'a1)
     | List_Nil -> Fail Failure
     end
   | List_Nil -> Fail Failure
   end
 
-(** [loops::list_nth_mut_loop_pair_merge]: forward function
+(** [loops::list_nth_mut_loop_pair_merge]:
     Source: 'src/loops.rs', lines 223:0-227:27 *)
 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 t ls0 ls1 i
-
-(** [loops::list_nth_mut_loop_pair_merge]: loop 0: backward function 0
-    Source: 'src/loops.rs', lines 223:0-238:1 *)
-let rec list_nth_mut_loop_pair_merge_loop_back
-  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : (t & t)) :
-  Tot (result ((list_t t) & (list_t t)))
-  (decreases (list_nth_mut_loop_pair_merge_loop_decreases t ls0 ls1 i))
-  =
-  begin match ls0 with
-  | List_Cons x0 tl0 ->
-    begin match ls1 with
-    | List_Cons x1 tl1 ->
-      if i = 0
-      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 (List_Cons x0 tl00, List_Cons x1 tl10)
-    | List_Nil -> Fail Failure
-    end
-  | List_Nil -> Fail Failure
-  end
-
-(** [loops::list_nth_mut_loop_pair_merge]: backward function 0
-    Source: 'src/loops.rs', lines 223:0-227:27 *)
-let list_nth_mut_loop_pair_merge_back
-  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : (t & t)) :
-  result ((list_t t) & (list_t t))
+  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) :
+  result ((t & t) & ((t & t) -> result ((list_t t) & (list_t t))))
   =
-  list_nth_mut_loop_pair_merge_loop_back t ls0 ls1 i ret
+  let* (p, back_'a) = list_nth_mut_loop_pair_merge_loop t ls0 ls1 i in
+  Return (p, back_'a)
 
-(** [loops::list_nth_shared_loop_pair_merge]: loop 0: forward function
+(** [loops::list_nth_shared_loop_pair_merge]: loop 0:
     Source: 'src/loops.rs', lines 241:0-256:1 *)
 let rec list_nth_shared_loop_pair_merge_loop
   (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) :
@@ -489,24 +374,24 @@ let rec list_nth_shared_loop_pair_merge_loop
       if i = 0
       then Return (x0, x1)
       else
-        let* i0 = u32_sub i 1 in
-        list_nth_shared_loop_pair_merge_loop t tl0 tl1 i0
+        let* i1 = u32_sub i 1 in
+        list_nth_shared_loop_pair_merge_loop t tl0 tl1 i1
     | List_Nil -> Fail Failure
     end
   | List_Nil -> Fail Failure
   end
 
-(** [loops::list_nth_shared_loop_pair_merge]: forward function
+(** [loops::list_nth_shared_loop_pair_merge]:
     Source: 'src/loops.rs', lines 241:0-245:19 *)
 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 t ls0 ls1 i
 
-(** [loops::list_nth_mut_shared_loop_pair]: loop 0: forward function
+(** [loops::list_nth_mut_shared_loop_pair]: loop 0:
     Source: 'src/loops.rs', lines 259:0-274:1 *)
 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))
+  Tot (result ((t & t) & (t -> result (list_t t))))
   (decreases (list_nth_mut_shared_loop_pair_loop_decreases t ls0 ls1 i))
   =
   begin match ls0 with
@@ -514,56 +399,34 @@ let rec list_nth_mut_shared_loop_pair_loop
     begin match ls1 with
     | List_Cons x1 tl1 ->
       if i = 0
-      then Return (x0, x1)
+      then
+        let back_'a = fun ret -> Return (List_Cons ret tl0) in
+        Return ((x0, x1), back_'a)
       else
-        let* i0 = u32_sub i 1 in
-        list_nth_mut_shared_loop_pair_loop t tl0 tl1 i0
+        let* i1 = u32_sub i 1 in
+        let* (p, back_'a) = list_nth_mut_shared_loop_pair_loop t tl0 tl1 i1 in
+        let back_'a1 =
+          fun ret -> let* tl01 = back_'a ret in Return (List_Cons x0 tl01) in
+        Return (p, back_'a1)
     | List_Nil -> Fail Failure
     end
   | List_Nil -> Fail Failure
   end
 
-(** [loops::list_nth_mut_shared_loop_pair]: forward function
+(** [loops::list_nth_mut_shared_loop_pair]:
     Source: 'src/loops.rs', lines 259:0-263:23 *)
 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 t ls0 ls1 i
-
-(** [loops::list_nth_mut_shared_loop_pair]: loop 0: backward function 0
-    Source: 'src/loops.rs', lines 259:0-274:1 *)
-let rec list_nth_mut_shared_loop_pair_loop_back
-  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : t) :
-  Tot (result (list_t t))
-  (decreases (list_nth_mut_shared_loop_pair_loop_decreases t ls0 ls1 i))
-  =
-  begin match ls0 with
-  | List_Cons x0 tl0 ->
-    begin match ls1 with
-    | List_Cons x1 tl1 ->
-      if i = 0
-      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 (List_Cons x0 tl00)
-    | List_Nil -> Fail Failure
-    end
-  | List_Nil -> Fail Failure
-  end
-
-(** [loops::list_nth_mut_shared_loop_pair]: backward function 0
-    Source: 'src/loops.rs', lines 259:0-263:23 *)
-let list_nth_mut_shared_loop_pair_back
-  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : t) :
-  result (list_t t)
+  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) :
+  result ((t & t) & (t -> result (list_t t)))
   =
-  list_nth_mut_shared_loop_pair_loop_back t ls0 ls1 i ret
+  let* (p, back_'a) = list_nth_mut_shared_loop_pair_loop t ls0 ls1 i in
+  Return (p, back_'a)
 
-(** [loops::list_nth_mut_shared_loop_pair_merge]: loop 0: forward function
+(** [loops::list_nth_mut_shared_loop_pair_merge]: loop 0:
     Source: 'src/loops.rs', lines 278:0-293:1 *)
 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))
+  Tot (result ((t & t) & (t -> result (list_t t))))
   (decreases (list_nth_mut_shared_loop_pair_merge_loop_decreases t ls0 ls1 i))
   =
   begin match ls0 with
@@ -571,57 +434,35 @@ let rec list_nth_mut_shared_loop_pair_merge_loop
     begin match ls1 with
     | List_Cons x1 tl1 ->
       if i = 0
-      then Return (x0, x1)
+      then
+        let back_'a = fun ret -> Return (List_Cons ret tl0) in
+        Return ((x0, x1), back_'a)
       else
-        let* i0 = u32_sub i 1 in
-        list_nth_mut_shared_loop_pair_merge_loop t tl0 tl1 i0
+        let* i1 = u32_sub i 1 in
+        let* (p, back_'a) =
+          list_nth_mut_shared_loop_pair_merge_loop t tl0 tl1 i1 in
+        let back_'a1 =
+          fun ret -> let* tl01 = back_'a ret in Return (List_Cons x0 tl01) in
+        Return (p, back_'a1)
     | List_Nil -> Fail Failure
     end
   | List_Nil -> Fail Failure
   end
 
-(** [loops::list_nth_mut_shared_loop_pair_merge]: forward function
+(** [loops::list_nth_mut_shared_loop_pair_merge]:
     Source: 'src/loops.rs', lines 278:0-282:23 *)
 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 t ls0 ls1 i
-
-(** [loops::list_nth_mut_shared_loop_pair_merge]: loop 0: backward function 0
-    Source: 'src/loops.rs', lines 278:0-293:1 *)
-let rec list_nth_mut_shared_loop_pair_merge_loop_back
-  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : t) :
-  Tot (result (list_t t))
-  (decreases (list_nth_mut_shared_loop_pair_merge_loop_decreases t ls0 ls1 i))
-  =
-  begin match ls0 with
-  | List_Cons x0 tl0 ->
-    begin match ls1 with
-    | List_Cons x1 tl1 ->
-      if i = 0
-      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 (List_Cons x0 tl00)
-    | List_Nil -> Fail Failure
-    end
-  | List_Nil -> Fail Failure
-  end
-
-(** [loops::list_nth_mut_shared_loop_pair_merge]: backward function 0
-    Source: 'src/loops.rs', lines 278:0-282:23 *)
-let list_nth_mut_shared_loop_pair_merge_back
-  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : t) :
-  result (list_t t)
+  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) :
+  result ((t & t) & (t -> result (list_t t)))
   =
-  list_nth_mut_shared_loop_pair_merge_loop_back t ls0 ls1 i ret
+  let* (p, back_'a) = list_nth_mut_shared_loop_pair_merge_loop t ls0 ls1 i in
+  Return (p, back_'a)
 
-(** [loops::list_nth_shared_mut_loop_pair]: loop 0: forward function
+(** [loops::list_nth_shared_mut_loop_pair]: loop 0:
     Source: 'src/loops.rs', lines 297:0-312:1 *)
 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))
+  Tot (result ((t & t) & (t -> result (list_t t))))
   (decreases (list_nth_shared_mut_loop_pair_loop_decreases t ls0 ls1 i))
   =
   begin match ls0 with
@@ -629,56 +470,34 @@ let rec list_nth_shared_mut_loop_pair_loop
     begin match ls1 with
     | List_Cons x1 tl1 ->
       if i = 0
-      then Return (x0, x1)
+      then
+        let back_'b = fun ret -> Return (List_Cons ret tl1) in
+        Return ((x0, x1), back_'b)
       else
-        let* i0 = u32_sub i 1 in
-        list_nth_shared_mut_loop_pair_loop t tl0 tl1 i0
+        let* i1 = u32_sub i 1 in
+        let* (p, back_'b) = list_nth_shared_mut_loop_pair_loop t tl0 tl1 i1 in
+        let back_'b1 =
+          fun ret -> let* tl11 = back_'b ret in Return (List_Cons x1 tl11) in
+        Return (p, back_'b1)
     | List_Nil -> Fail Failure
     end
   | List_Nil -> Fail Failure
   end
 
-(** [loops::list_nth_shared_mut_loop_pair]: forward function
+(** [loops::list_nth_shared_mut_loop_pair]:
     Source: 'src/loops.rs', lines 297:0-301:23 *)
 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 t ls0 ls1 i
-
-(** [loops::list_nth_shared_mut_loop_pair]: loop 0: backward function 1
-    Source: 'src/loops.rs', lines 297:0-312:1 *)
-let rec list_nth_shared_mut_loop_pair_loop_back
-  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : t) :
-  Tot (result (list_t t))
-  (decreases (list_nth_shared_mut_loop_pair_loop_decreases t ls0 ls1 i))
-  =
-  begin match ls0 with
-  | List_Cons x0 tl0 ->
-    begin match ls1 with
-    | List_Cons x1 tl1 ->
-      if i = 0
-      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 (List_Cons x1 tl10)
-    | List_Nil -> Fail Failure
-    end
-  | List_Nil -> Fail Failure
-  end
-
-(** [loops::list_nth_shared_mut_loop_pair]: backward function 1
-    Source: 'src/loops.rs', lines 297:0-301:23 *)
-let list_nth_shared_mut_loop_pair_back
-  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : t) :
-  result (list_t t)
+  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) :
+  result ((t & t) & (t -> result (list_t t)))
   =
-  list_nth_shared_mut_loop_pair_loop_back t ls0 ls1 i ret
+  let* (p, back_'b) = list_nth_shared_mut_loop_pair_loop t ls0 ls1 i in
+  Return (p, back_'b)
 
-(** [loops::list_nth_shared_mut_loop_pair_merge]: loop 0: forward function
+(** [loops::list_nth_shared_mut_loop_pair_merge]: loop 0:
     Source: 'src/loops.rs', lines 316:0-331:1 *)
 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))
+  Tot (result ((t & t) & (t -> result (list_t t))))
   (decreases (list_nth_shared_mut_loop_pair_merge_loop_decreases t ls0 ls1 i))
   =
   begin match ls0 with
@@ -686,49 +505,27 @@ let rec list_nth_shared_mut_loop_pair_merge_loop
     begin match ls1 with
     | List_Cons x1 tl1 ->
       if i = 0
-      then Return (x0, x1)
+      then
+        let back_'a = fun ret -> Return (List_Cons ret tl1) in
+        Return ((x0, x1), back_'a)
       else
-        let* i0 = u32_sub i 1 in
-        list_nth_shared_mut_loop_pair_merge_loop t tl0 tl1 i0
+        let* i1 = u32_sub i 1 in
+        let* (p, back_'a) =
+          list_nth_shared_mut_loop_pair_merge_loop t tl0 tl1 i1 in
+        let back_'a1 =
+          fun ret -> let* tl11 = back_'a ret in Return (List_Cons x1 tl11) in
+        Return (p, back_'a1)
     | List_Nil -> Fail Failure
     end
   | List_Nil -> Fail Failure
   end
 
-(** [loops::list_nth_shared_mut_loop_pair_merge]: forward function
+(** [loops::list_nth_shared_mut_loop_pair_merge]:
     Source: 'src/loops.rs', lines 316:0-320:23 *)
 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 t ls0 ls1 i
-
-(** [loops::list_nth_shared_mut_loop_pair_merge]: loop 0: backward function 0
-    Source: 'src/loops.rs', lines 316:0-331:1 *)
-let rec list_nth_shared_mut_loop_pair_merge_loop_back
-  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : t) :
-  Tot (result (list_t t))
-  (decreases (list_nth_shared_mut_loop_pair_merge_loop_decreases t ls0 ls1 i))
-  =
-  begin match ls0 with
-  | List_Cons x0 tl0 ->
-    begin match ls1 with
-    | List_Cons x1 tl1 ->
-      if i = 0
-      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 (List_Cons x1 tl10)
-    | List_Nil -> Fail Failure
-    end
-  | List_Nil -> Fail Failure
-  end
-
-(** [loops::list_nth_shared_mut_loop_pair_merge]: backward function 0
-    Source: 'src/loops.rs', lines 316:0-320:23 *)
-let list_nth_shared_mut_loop_pair_merge_back
-  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : t) :
-  result (list_t t)
+  (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) :
+  result ((t & t) & (t -> result (list_t t)))
   =
-  list_nth_shared_mut_loop_pair_merge_loop_back t ls0 ls1 i ret
+  let* (p, back_'a) = list_nth_shared_mut_loop_pair_merge_loop t ls0 ls1 i in
+  Return (p, back_'a)
 
diff --git a/tests/fstar/misc/NoNestedBorrows.fst b/tests/fstar/misc/NoNestedBorrows.fst
index 1386b02c..ffcc32f3 100644
--- a/tests/fstar/misc/NoNestedBorrows.fst
+++ b/tests/fstar/misc/NoNestedBorrows.fst
@@ -37,96 +37,96 @@ type sum_t (t1 t2 : Type0) =
 | Sum_Left : t1 -> sum_t t1 t2
 | Sum_Right : t2 -> sum_t t1 t2
 
-(** [no_nested_borrows::neg_test]: forward function
+(** [no_nested_borrows::neg_test]:
     Source: 'src/no_nested_borrows.rs', lines 48:0-48:30 *)
 let neg_test (x : i32) : result i32 =
   i32_neg x
 
-(** [no_nested_borrows::add_u32]: forward function
+(** [no_nested_borrows::add_u32]:
     Source: 'src/no_nested_borrows.rs', lines 54:0-54:37 *)
 let add_u32 (x : u32) (y : u32) : result u32 =
   u32_add x y
 
-(** [no_nested_borrows::subs_u32]: forward function
+(** [no_nested_borrows::subs_u32]:
     Source: 'src/no_nested_borrows.rs', lines 60:0-60:38 *)
 let subs_u32 (x : u32) (y : u32) : result u32 =
   u32_sub x y
 
-(** [no_nested_borrows::div_u32]: forward function
+(** [no_nested_borrows::div_u32]:
     Source: 'src/no_nested_borrows.rs', lines 66:0-66:37 *)
 let div_u32 (x : u32) (y : u32) : result u32 =
   u32_div x y
 
-(** [no_nested_borrows::div_u32_const]: forward function
+(** [no_nested_borrows::div_u32_const]:
     Source: 'src/no_nested_borrows.rs', lines 73:0-73:35 *)
 let div_u32_const (x : u32) : result u32 =
   u32_div x 2
 
-(** [no_nested_borrows::rem_u32]: forward function
+(** [no_nested_borrows::rem_u32]:
     Source: 'src/no_nested_borrows.rs', lines 78:0-78:37 *)
 let rem_u32 (x : u32) (y : u32) : result u32 =
   u32_rem x y
 
-(** [no_nested_borrows::mul_u32]: forward function
+(** [no_nested_borrows::mul_u32]:
     Source: 'src/no_nested_borrows.rs', lines 82:0-82:37 *)
 let mul_u32 (x : u32) (y : u32) : result u32 =
   u32_mul x y
 
-(** [no_nested_borrows::add_i32]: forward function
+(** [no_nested_borrows::add_i32]:
     Source: 'src/no_nested_borrows.rs', lines 88:0-88:37 *)
 let add_i32 (x : i32) (y : i32) : result i32 =
   i32_add x y
 
-(** [no_nested_borrows::subs_i32]: forward function
+(** [no_nested_borrows::subs_i32]:
     Source: 'src/no_nested_borrows.rs', lines 92:0-92:38 *)
 let subs_i32 (x : i32) (y : i32) : result i32 =
   i32_sub x y
 
-(** [no_nested_borrows::div_i32]: forward function
+(** [no_nested_borrows::div_i32]:
     Source: 'src/no_nested_borrows.rs', lines 96:0-96:37 *)
 let div_i32 (x : i32) (y : i32) : result i32 =
   i32_div x y
 
-(** [no_nested_borrows::div_i32_const]: forward function
+(** [no_nested_borrows::div_i32_const]:
     Source: 'src/no_nested_borrows.rs', lines 100:0-100:35 *)
 let div_i32_const (x : i32) : result i32 =
   i32_div x 2
 
-(** [no_nested_borrows::rem_i32]: forward function
+(** [no_nested_borrows::rem_i32]:
     Source: 'src/no_nested_borrows.rs', lines 104:0-104:37 *)
 let rem_i32 (x : i32) (y : i32) : result i32 =
   i32_rem x y
 
-(** [no_nested_borrows::mul_i32]: forward function
+(** [no_nested_borrows::mul_i32]:
     Source: 'src/no_nested_borrows.rs', lines 108:0-108:37 *)
 let mul_i32 (x : i32) (y : i32) : result i32 =
   i32_mul x y
 
-(** [no_nested_borrows::mix_arith_u32]: forward function
+(** [no_nested_borrows::mix_arith_u32]:
     Source: 'src/no_nested_borrows.rs', lines 112:0-112:51 *)
 let mix_arith_u32 (x : u32) (y : u32) (z : u32) : result u32 =
   let* i = u32_add x y in
-  let* i0 = u32_div x y in
-  let* i1 = u32_mul i i0 in
-  let* i2 = u32_rem z y in
-  let* i3 = u32_sub x i2 in
-  let* i4 = u32_add i1 i3 in
-  let* i5 = u32_add x y in
-  let* i6 = u32_add i5 z in
-  u32_rem i4 i6
-
-(** [no_nested_borrows::mix_arith_i32]: forward function
+  let* i1 = u32_div x y in
+  let* i2 = u32_mul i i1 in
+  let* i3 = u32_rem z y in
+  let* i4 = u32_sub x i3 in
+  let* i5 = u32_add i2 i4 in
+  let* i6 = u32_add x y in
+  let* i7 = u32_add i6 z in
+  u32_rem i5 i7
+
+(** [no_nested_borrows::mix_arith_i32]:
     Source: 'src/no_nested_borrows.rs', lines 116:0-116:51 *)
 let mix_arith_i32 (x : i32) (y : i32) (z : i32) : result i32 =
   let* i = i32_add x y in
-  let* i0 = i32_div x y in
-  let* i1 = i32_mul i i0 in
-  let* i2 = i32_rem z y in
-  let* i3 = i32_sub x i2 in
-  let* i4 = i32_add i1 i3 in
-  let* i5 = i32_add x y in
-  let* i6 = i32_add i5 z in
-  i32_rem i4 i6
+  let* i1 = i32_div x y in
+  let* i2 = i32_mul i i1 in
+  let* i3 = i32_rem z y in
+  let* i4 = i32_sub x i3 in
+  let* i5 = i32_add i2 i4 in
+  let* i6 = i32_add x y in
+  let* i7 = i32_add i6 z in
+  i32_rem i5 i7
 
 (** [no_nested_borrows::CONST0]
     Source: 'src/no_nested_borrows.rs', lines 125:0-125:23 *)
@@ -138,22 +138,22 @@ let const0_c : usize = eval_global const0_body
 let const1_body : result usize = usize_mul 2 2
 let const1_c : usize = eval_global const1_body
 
-(** [no_nested_borrows::cast_u32_to_i32]: forward function
+(** [no_nested_borrows::cast_u32_to_i32]:
     Source: 'src/no_nested_borrows.rs', lines 128:0-128:37 *)
 let cast_u32_to_i32 (x : u32) : result i32 =
   scalar_cast U32 I32 x
 
-(** [no_nested_borrows::cast_bool_to_i32]: forward function
+(** [no_nested_borrows::cast_bool_to_i32]:
     Source: 'src/no_nested_borrows.rs', lines 132:0-132:39 *)
 let cast_bool_to_i32 (x : bool) : result i32 =
   scalar_cast_bool I32 x
 
-(** [no_nested_borrows::cast_bool_to_bool]: forward function
+(** [no_nested_borrows::cast_bool_to_bool]:
     Source: 'src/no_nested_borrows.rs', lines 137:0-137:41 *)
 let cast_bool_to_bool (x : bool) : result bool =
   Return x
 
-(** [no_nested_borrows::test2]: forward function
+(** [no_nested_borrows::test2]:
     Source: 'src/no_nested_borrows.rs', lines 142:0-142:14 *)
 let test2 : result unit =
   let* _ = u32_add 23 44 in Return ()
@@ -161,12 +161,12 @@ let test2 : result unit =
 (** Unit test for [no_nested_borrows::test2] *)
 let _ = assert_norm (test2 = Return ())
 
-(** [no_nested_borrows::get_max]: forward function
+(** [no_nested_borrows::get_max]:
     Source: 'src/no_nested_borrows.rs', lines 154:0-154:37 *)
 let get_max (x : u32) (y : u32) : result u32 =
   if x >= y then Return x else Return y
 
-(** [no_nested_borrows::test3]: forward function
+(** [no_nested_borrows::test3]:
     Source: 'src/no_nested_borrows.rs', lines 162:0-162:14 *)
 let test3 : result unit =
   let* x = get_max 4 3 in
@@ -177,7 +177,7 @@ let test3 : result unit =
 (** Unit test for [no_nested_borrows::test3] *)
 let _ = assert_norm (test3 = Return ())
 
-(** [no_nested_borrows::test_neg1]: forward function
+(** [no_nested_borrows::test_neg1]:
     Source: 'src/no_nested_borrows.rs', lines 169:0-169:18 *)
 let test_neg1 : result unit =
   let* y = i32_neg 3 in if not (y = -3) then Fail Failure else Return ()
@@ -185,7 +185,7 @@ let test_neg1 : result unit =
 (** Unit test for [no_nested_borrows::test_neg1] *)
 let _ = assert_norm (test_neg1 = Return ())
 
-(** [no_nested_borrows::refs_test1]: forward function
+(** [no_nested_borrows::refs_test1]:
     Source: 'src/no_nested_borrows.rs', lines 176:0-176:19 *)
 let refs_test1 : result unit =
   if not (1 = 1) then Fail Failure else Return ()
@@ -193,7 +193,7 @@ let refs_test1 : result unit =
 (** Unit test for [no_nested_borrows::refs_test1] *)
 let _ = assert_norm (refs_test1 = Return ())
 
-(** [no_nested_borrows::refs_test2]: forward function
+(** [no_nested_borrows::refs_test2]:
     Source: 'src/no_nested_borrows.rs', lines 187:0-187:19 *)
 let refs_test2 : result unit =
   if not (2 = 2)
@@ -209,7 +209,7 @@ let refs_test2 : result unit =
 (** Unit test for [no_nested_borrows::refs_test2] *)
 let _ = assert_norm (refs_test2 = Return ())
 
-(** [no_nested_borrows::test_list1]: forward function
+(** [no_nested_borrows::test_list1]:
     Source: 'src/no_nested_borrows.rs', lines 203:0-203:19 *)
 let test_list1 : result unit =
   Return ()
@@ -217,33 +217,33 @@ let test_list1 : result unit =
 (** Unit test for [no_nested_borrows::test_list1] *)
 let _ = assert_norm (test_list1 = Return ())
 
-(** [no_nested_borrows::test_box1]: forward function
+(** [no_nested_borrows::test_box1]:
     Source: 'src/no_nested_borrows.rs', lines 208:0-208:18 *)
 let test_box1 : result unit =
-  let b = 0 in
-  let* b0 = alloc_boxed_Box_deref_mut_back i32 b 1 in
-  let* x = alloc_boxed_Box_deref i32 b0 in
+  let* (_, deref_mut_back) = alloc_boxed_Box_deref_mut i32 0 in
+  let* b = deref_mut_back 1 in
+  let* x = alloc_boxed_Box_deref i32 b in
   if not (x = 1) then Fail Failure else Return ()
 
 (** Unit test for [no_nested_borrows::test_box1] *)
 let _ = assert_norm (test_box1 = Return ())
 
-(** [no_nested_borrows::copy_int]: forward function
+(** [no_nested_borrows::copy_int]:
     Source: 'src/no_nested_borrows.rs', lines 218:0-218:30 *)
 let copy_int (x : i32) : result i32 =
   Return x
 
-(** [no_nested_borrows::test_unreachable]: forward function
+(** [no_nested_borrows::test_unreachable]:
     Source: 'src/no_nested_borrows.rs', lines 224:0-224:32 *)
 let test_unreachable (b : bool) : result unit =
   if b then Fail Failure else Return ()
 
-(** [no_nested_borrows::test_panic]: forward function
+(** [no_nested_borrows::test_panic]:
     Source: 'src/no_nested_borrows.rs', lines 232:0-232:26 *)
 let test_panic (b : bool) : result unit =
   if b then Fail Failure else Return ()
 
-(** [no_nested_borrows::test_copy_int]: forward function
+(** [no_nested_borrows::test_copy_int]:
     Source: 'src/no_nested_borrows.rs', lines 239:0-239:22 *)
 let test_copy_int : result unit =
   let* y = copy_int 0 in if not (0 = y) then Fail Failure else Return ()
@@ -251,25 +251,24 @@ let test_copy_int : result unit =
 (** Unit test for [no_nested_borrows::test_copy_int] *)
 let _ = assert_norm (test_copy_int = Return ())
 
-(** [no_nested_borrows::is_cons]: forward function
+(** [no_nested_borrows::is_cons]:
     Source: 'src/no_nested_borrows.rs', lines 246:0-246:38 *)
 let is_cons (t : Type0) (l : list_t t) : result bool =
   begin match l with
-  | List_Cons x l0 -> Return true
+  | List_Cons _ _ -> Return true
   | List_Nil -> Return false
   end
 
-(** [no_nested_borrows::test_is_cons]: forward function
+(** [no_nested_borrows::test_is_cons]:
     Source: 'src/no_nested_borrows.rs', lines 253:0-253:21 *)
 let test_is_cons : result unit =
-  let l = List_Nil in
-  let* b = is_cons i32 (List_Cons 0 l) in
+  let* b = is_cons i32 (List_Cons 0 List_Nil) in
   if not b then Fail Failure else Return ()
 
 (** Unit test for [no_nested_borrows::test_is_cons] *)
 let _ = assert_norm (test_is_cons = Return ())
 
-(** [no_nested_borrows::split_list]: forward function
+(** [no_nested_borrows::split_list]:
     Source: 'src/no_nested_borrows.rs', lines 259:0-259:48 *)
 let split_list (t : Type0) (l : list_t t) : result (t & (list_t t)) =
   begin match l with
@@ -277,37 +276,33 @@ let split_list (t : Type0) (l : list_t t) : result (t & (list_t t)) =
   | List_Nil -> Fail Failure
   end
 
-(** [no_nested_borrows::test_split_list]: forward function
+(** [no_nested_borrows::test_split_list]:
     Source: 'src/no_nested_borrows.rs', lines 267:0-267:24 *)
 let test_split_list : result unit =
-  let l = List_Nil in
-  let* p = split_list i32 (List_Cons 0 l) in
+  let* p = split_list i32 (List_Cons 0 List_Nil) 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 = Return ())
 
-(** [no_nested_borrows::choose]: forward function
+(** [no_nested_borrows::choose]:
     Source: 'src/no_nested_borrows.rs', lines 274:0-274:70 *)
-let choose (t : Type0) (b : bool) (x : t) (y : t) : result t =
-  if b then Return x else Return y
+let choose
+  (t : Type0) (b : bool) (x : t) (y : t) : result (t & (t -> result (t & t))) =
+  if b
+  then let back_'a = fun ret -> Return (ret, y) in Return (x, back_'a)
+  else let back_'a = fun ret -> Return (x, ret) in Return (y, back_'a)
 
-(** [no_nested_borrows::choose]: backward function 0
-    Source: 'src/no_nested_borrows.rs', lines 274:0-274:70 *)
-let choose_back
-  (t : Type0) (b : bool) (x : t) (y : t) (ret : t) : result (t & t) =
-  if b then Return (ret, y) else Return (x, ret)
-
-(** [no_nested_borrows::choose_test]: forward function
+(** [no_nested_borrows::choose_test]:
     Source: 'src/no_nested_borrows.rs', lines 282:0-282:20 *)
 let choose_test : result unit =
-  let* z = choose i32 true 0 0 in
-  let* z0 = i32_add z 1 in
-  if not (z0 = 1)
+  let* (z, choose_back) = choose i32 true 0 0 in
+  let* z1 = i32_add z 1 in
+  if not (z1 = 1)
   then Fail Failure
   else
-    let* (x, y) = choose_back i32 true 0 0 z0 in
+    let* (x, y) = choose_back z1 in
     if not (x = 1)
     then Fail Failure
     else if not (y = 0) then Fail Failure else Return ()
@@ -315,7 +310,7 @@ let choose_test : result unit =
 (** Unit test for [no_nested_borrows::choose_test] *)
 let _ = assert_norm (choose_test = Return ())
 
-(** [no_nested_borrows::test_char]: forward function
+(** [no_nested_borrows::test_char]:
     Source: 'src/no_nested_borrows.rs', lines 294:0-294:26 *)
 let test_char : result char =
   Return 'a'
@@ -332,50 +327,47 @@ 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
+(** [no_nested_borrows::list_length]:
     Source: 'src/no_nested_borrows.rs', lines 339:0-339:48 *)
 let rec list_length (t : Type0) (l : list_t t) : result u32 =
   begin match l with
-  | List_Cons x l1 -> let* i = list_length t l1 in u32_add 1 i
+  | List_Cons _ 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
+(** [no_nested_borrows::list_nth_shared]:
     Source: 'src/no_nested_borrows.rs', lines 347:0-347:62 *)
 let rec list_nth_shared (t : Type0) (l : list_t t) (i : u32) : result t =
   begin match l with
   | List_Cons x tl ->
     if i = 0
     then Return x
-    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
-    Source: 'src/no_nested_borrows.rs', lines 363:0-363:67 *)
-let rec list_nth_mut (t : Type0) (l : list_t t) (i : u32) : result t =
-  begin match l with
-  | List_Cons x tl ->
-    if i = 0 then Return x else let* i0 = u32_sub i 1 in list_nth_mut t tl i0
+    else let* i1 = u32_sub i 1 in list_nth_shared t tl i1
   | List_Nil -> Fail Failure
   end
 
-(** [no_nested_borrows::list_nth_mut]: backward function 0
+(** [no_nested_borrows::list_nth_mut]:
     Source: 'src/no_nested_borrows.rs', lines 363:0-363:67 *)
-let rec list_nth_mut_back
-  (t : Type0) (l : list_t t) (i : u32) (ret : t) : result (list_t t) =
+let rec list_nth_mut
+  (t : Type0) (l : list_t t) (i : u32) :
+  result (t & (t -> result (list_t t)))
+  =
   begin match l with
   | List_Cons x tl ->
     if i = 0
-    then Return (List_Cons ret tl)
+    then
+      let back_'a = fun ret -> Return (List_Cons ret tl) in Return (x, back_'a)
     else
-      let* i0 = u32_sub i 1 in
-      let* tl0 = list_nth_mut_back t tl i0 ret in
-      Return (List_Cons x tl0)
+      let* i1 = u32_sub i 1 in
+      let* (x1, list_nth_mut_back) = list_nth_mut t tl i1 in
+      let back_'a =
+        fun ret -> let* tl1 = list_nth_mut_back ret in Return (List_Cons x tl1)
+        in
+      Return (x1, back_'a)
   | List_Nil -> Fail Failure
   end
 
-(** [no_nested_borrows::list_rev_aux]: forward function
+(** [no_nested_borrows::list_rev_aux]:
     Source: 'src/no_nested_borrows.rs', lines 379:0-379:63 *)
 let rec list_rev_aux
   (t : Type0) (li : list_t t) (lo : list_t t) : result (list_t t) =
@@ -384,120 +376,99 @@ let rec list_rev_aux
   | 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 ())
+(** [no_nested_borrows::list_rev]:
     Source: 'src/no_nested_borrows.rs', lines 393:0-393:42 *)
 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
+  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
+(** [no_nested_borrows::test_list_functions]:
     Source: 'src/no_nested_borrows.rs', lines 398:0-398:28 *)
 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 l = List_Cons 2 List_Nil in
+  let l1 = List_Cons 1 l in
   let* i = list_length i32 (List_Cons 0 l1) in
   if not (i = 3)
   then Fail Failure
   else
-    let* i0 = list_nth_shared i32 (List_Cons 0 l1) 0 in
-    if not (i0 = 0)
+    let* i1 = list_nth_shared i32 (List_Cons 0 l1) 0 in
+    if not (i1 = 0)
     then Fail Failure
     else
-      let* i1 = list_nth_shared i32 (List_Cons 0 l1) 1 in
-      if not (i1 = 1)
+      let* i2 = list_nth_shared i32 (List_Cons 0 l1) 1 in
+      if not (i2 = 1)
       then Fail Failure
       else
-        let* i2 = list_nth_shared i32 (List_Cons 0 l1) 2 in
-        if not (i2 = 2)
+        let* i3 = list_nth_shared i32 (List_Cons 0 l1) 2 in
+        if not (i3 = 2)
         then Fail Failure
         else
-          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)
+          let* (_, list_nth_mut_back) = list_nth_mut i32 (List_Cons 0 l1) 1 in
+          let* ls = list_nth_mut_back 3 in
+          let* i4 = list_nth_shared i32 ls 0 in
+          if not (i4 = 0)
           then Fail Failure
           else
-            let* i4 = list_nth_shared i32 ls 1 in
-            if not (i4 = 3)
+            let* i5 = list_nth_shared i32 ls 1 in
+            if not (i5 = 3)
             then Fail Failure
             else
-              let* i5 = list_nth_shared i32 ls 2 in
-              if not (i5 = 2) then Fail Failure else Return ()
+              let* i6 = list_nth_shared i32 ls 2 in
+              if not (i6 = 2) then Fail Failure else Return ()
 
 (** Unit test for [no_nested_borrows::test_list_functions] *)
 let _ = assert_norm (test_list_functions = Return ())
 
-(** [no_nested_borrows::id_mut_pair1]: forward function
+(** [no_nested_borrows::id_mut_pair1]:
     Source: 'src/no_nested_borrows.rs', lines 414:0-414:89 *)
-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
-    Source: 'src/no_nested_borrows.rs', lines 414:0-414:89 *)
-let id_mut_pair1_back
-  (t1 t2 : Type0) (x : t1) (y : t2) (ret : (t1 & t2)) : result (t1 & t2) =
-  let (x0, x1) = ret in Return (x0, x1)
-
-(** [no_nested_borrows::id_mut_pair2]: forward function
+let id_mut_pair1
+  (t1 t2 : Type0) (x : t1) (y : t2) :
+  result ((t1 & t2) & ((t1 & t2) -> result (t1 & t2)))
+  =
+  let back_'a = fun ret -> let (x1, x2) = ret in Return (x1, x2) in
+  Return ((x, y), back_'a)
+
+(** [no_nested_borrows::id_mut_pair2]:
     Source: 'src/no_nested_borrows.rs', lines 418:0-418:88 *)
-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
-    Source: 'src/no_nested_borrows.rs', lines 418:0-418:88 *)
-let id_mut_pair2_back
-  (t1 t2 : Type0) (p : (t1 & t2)) (ret : (t1 & t2)) : result (t1 & t2) =
-  let (x, x0) = ret in Return (x, x0)
-
-(** [no_nested_borrows::id_mut_pair3]: forward function
+let id_mut_pair2
+  (t1 t2 : Type0) (p : (t1 & t2)) :
+  result ((t1 & t2) & ((t1 & t2) -> result (t1 & t2)))
+  =
+  let (x, x1) = p in
+  let back_'a = fun ret -> let (x2, x3) = ret in Return (x2, x3) in
+  Return ((x, x1), back_'a)
+
+(** [no_nested_borrows::id_mut_pair3]:
     Source: 'src/no_nested_borrows.rs', lines 422:0-422:93 *)
-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
-    Source: 'src/no_nested_borrows.rs', lines 422:0-422:93 *)
-let id_mut_pair3_back'a
-  (t1 t2 : Type0) (x : t1) (y : t2) (ret : t1) : result t1 =
-  Return ret
-
-(** [no_nested_borrows::id_mut_pair3]: backward function 1
-    Source: 'src/no_nested_borrows.rs', lines 422:0-422:93 *)
-let id_mut_pair3_back'b
-  (t1 t2 : Type0) (x : t1) (y : t2) (ret : t2) : result t2 =
-  Return ret
-
-(** [no_nested_borrows::id_mut_pair4]: forward function
-    Source: 'src/no_nested_borrows.rs', lines 426:0-426:92 *)
-let id_mut_pair4 (t1 t2 : Type0) (p : (t1 & t2)) : result (t1 & t2) =
-  let (x, x0) = p in Return (x, x0)
+let id_mut_pair3
+  (t1 t2 : Type0) (x : t1) (y : t2) :
+  result ((t1 & t2) & (t1 -> result t1) & (t2 -> result t2))
+  =
+  Return ((x, y), Return, Return)
 
-(** [no_nested_borrows::id_mut_pair4]: backward function 0
+(** [no_nested_borrows::id_mut_pair4]:
     Source: 'src/no_nested_borrows.rs', lines 426:0-426:92 *)
-let id_mut_pair4_back'a
-  (t1 t2 : Type0) (p : (t1 & t2)) (ret : t1) : result t1 =
-  Return ret
-
-(** [no_nested_borrows::id_mut_pair4]: backward function 1
-    Source: 'src/no_nested_borrows.rs', lines 426:0-426:92 *)
-let id_mut_pair4_back'b
-  (t1 t2 : Type0) (p : (t1 & t2)) (ret : t2) : result t2 =
-  Return ret
+let id_mut_pair4
+  (t1 t2 : Type0) (p : (t1 & t2)) :
+  result ((t1 & t2) & (t1 -> result t1) & (t2 -> result t2))
+  =
+  let (x, x1) = p in Return ((x, x1), Return, Return)
 
 (** [no_nested_borrows::StructWithTuple]
     Source: 'src/no_nested_borrows.rs', lines 433:0-433:34 *)
 type structWithTuple_t (t1 t2 : Type0) = { p : (t1 & t2); }
 
-(** [no_nested_borrows::new_tuple1]: forward function
+(** [no_nested_borrows::new_tuple1]:
     Source: 'src/no_nested_borrows.rs', lines 437:0-437:48 *)
 let new_tuple1 : result (structWithTuple_t u32 u32) =
   Return { p = (1, 2) }
 
-(** [no_nested_borrows::new_tuple2]: forward function
+(** [no_nested_borrows::new_tuple2]:
     Source: 'src/no_nested_borrows.rs', lines 441:0-441:48 *)
 let new_tuple2 : result (structWithTuple_t i16 i16) =
   Return { p = (1, 2) }
 
-(** [no_nested_borrows::new_tuple3]: forward function
+(** [no_nested_borrows::new_tuple3]:
     Source: 'src/no_nested_borrows.rs', lines 445:0-445:48 *)
 let new_tuple3 : result (structWithTuple_t u64 i64) =
   Return { p = (1, 2) }
@@ -506,12 +477,12 @@ let new_tuple3 : result (structWithTuple_t u64 i64) =
     Source: 'src/no_nested_borrows.rs', lines 450:0-450:33 *)
 type structWithPair_t (t1 t2 : Type0) = { p : pair_t t1 t2; }
 
-(** [no_nested_borrows::new_pair1]: forward function
+(** [no_nested_borrows::new_pair1]:
     Source: 'src/no_nested_borrows.rs', lines 454:0-454:46 *)
 let new_pair1 : result (structWithPair_t u32 u32) =
   Return { p = { x = 1; y = 2 } }
 
-(** [no_nested_borrows::test_constants]: forward function
+(** [no_nested_borrows::test_constants]:
     Source: 'src/no_nested_borrows.rs', lines 462:0-462:23 *)
 let test_constants : result unit =
   let* swt = new_tuple1 in
@@ -519,14 +490,14 @@ let test_constants : result unit =
   if not (i = 1)
   then Fail Failure
   else
-    let* swt0 = new_tuple2 in
-    let (i0, _) = swt0.p in
-    if not (i0 = 1)
+    let* swt1 = new_tuple2 in
+    let (i1, _) = swt1.p in
+    if not (i1 = 1)
     then Fail Failure
     else
-      let* swt1 = new_tuple3 in
-      let (i1, _) = swt1.p in
-      if not (i1 = 1)
+      let* swt2 = new_tuple3 in
+      let (i2, _) = swt2.p in
+      if not (i2 = 1)
       then Fail Failure
       else
         let* swp = new_pair1 in
@@ -535,7 +506,7 @@ let test_constants : result unit =
 (** Unit test for [no_nested_borrows::test_constants] *)
 let _ = assert_norm (test_constants = Return ())
 
-(** [no_nested_borrows::test_weird_borrows1]: forward function
+(** [no_nested_borrows::test_weird_borrows1]:
     Source: 'src/no_nested_borrows.rs', lines 471:0-471:28 *)
 let test_weird_borrows1 : result unit =
   Return ()
@@ -543,59 +514,72 @@ let test_weird_borrows1 : result unit =
 (** Unit test for [no_nested_borrows::test_weird_borrows1] *)
 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 ())
+(** [no_nested_borrows::test_mem_replace]:
     Source: 'src/no_nested_borrows.rs', lines 481:0-481:37 *)
 let test_mem_replace (px : u32) : result u32 =
-  let y = core_mem_replace u32 px 1 in
+  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
+(** [no_nested_borrows::test_shared_borrow_bool1]:
     Source: 'src/no_nested_borrows.rs', lines 488:0-488:47 *)
 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
+(** [no_nested_borrows::test_shared_borrow_bool2]:
     Source: 'src/no_nested_borrows.rs', lines 501:0-501:40 *)
 let test_shared_borrow_bool2 : result u32 =
   Return 0
 
-(** [no_nested_borrows::test_shared_borrow_enum1]: forward function
+(** [no_nested_borrows::test_shared_borrow_enum1]:
     Source: 'src/no_nested_borrows.rs', lines 516:0-516:52 *)
 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
+  begin match l with | List_Cons _ _ -> Return 1 | List_Nil -> Return 0 end
 
-(** [no_nested_borrows::test_shared_borrow_enum2]: forward function
+(** [no_nested_borrows::test_shared_borrow_enum2]:
     Source: 'src/no_nested_borrows.rs', lines 528:0-528:40 *)
 let test_shared_borrow_enum2 : result u32 =
   Return 0
 
-(** [no_nested_borrows::Tuple]
+(** [no_nested_borrows::incr]:
     Source: 'src/no_nested_borrows.rs', lines 539:0-539:24 *)
+let incr (x : u32) : result u32 =
+  u32_add x 1
+
+(** [no_nested_borrows::call_incr]:
+    Source: 'src/no_nested_borrows.rs', lines 543:0-543:35 *)
+let call_incr (x : u32) : result u32 =
+  incr x
+
+(** [no_nested_borrows::read_then_incr]:
+    Source: 'src/no_nested_borrows.rs', lines 548:0-548:41 *)
+let read_then_incr (x : u32) : result (u32 & u32) =
+  let* x1 = u32_add x 1 in Return (x, x1)
+
+(** [no_nested_borrows::Tuple]
+    Source: 'src/no_nested_borrows.rs', lines 554:0-554:24 *)
 type tuple_t (t1 t2 : Type0) = t1 * t2
 
-(** [no_nested_borrows::use_tuple_struct]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ())
-    Source: 'src/no_nested_borrows.rs', lines 541:0-541:48 *)
+(** [no_nested_borrows::use_tuple_struct]:
+    Source: 'src/no_nested_borrows.rs', lines 556:0-556:48 *)
 let use_tuple_struct (x : tuple_t u32 u32) : result (tuple_t u32 u32) =
   let (_, i) = x in Return (1, i)
 
-(** [no_nested_borrows::create_tuple_struct]: forward function
-    Source: 'src/no_nested_borrows.rs', lines 545:0-545:61 *)
+(** [no_nested_borrows::create_tuple_struct]:
+    Source: 'src/no_nested_borrows.rs', lines 560:0-560:61 *)
 let create_tuple_struct (x : u32) (y : u64) : result (tuple_t u32 u64) =
   Return (x, y)
 
 (** [no_nested_borrows::IdType]
-    Source: 'src/no_nested_borrows.rs', lines 550:0-550:20 *)
+    Source: 'src/no_nested_borrows.rs', lines 565:0-565:20 *)
 type idType_t (t : Type0) = t
 
-(** [no_nested_borrows::use_id_type]: forward function
-    Source: 'src/no_nested_borrows.rs', lines 552:0-552:40 *)
+(** [no_nested_borrows::use_id_type]:
+    Source: 'src/no_nested_borrows.rs', lines 567:0-567:40 *)
 let use_id_type (t : Type0) (x : idType_t t) : result t =
   Return x
 
-(** [no_nested_borrows::create_id_type]: forward function
-    Source: 'src/no_nested_borrows.rs', lines 556:0-556:43 *)
+(** [no_nested_borrows::create_id_type]:
+    Source: 'src/no_nested_borrows.rs', lines 571:0-571:43 *)
 let create_id_type (t : Type0) (x : t) : result (idType_t t) =
   Return x
 
diff --git a/tests/fstar/misc/Paper.fst b/tests/fstar/misc/Paper.fst
index 14bc59e8..cf4dc454 100644
--- a/tests/fstar/misc/Paper.fst
+++ b/tests/fstar/misc/Paper.fst
@@ -5,40 +5,36 @@ open Primitives
 
 #set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
 
-(** [paper::ref_incr]: merged forward/backward function
-    (there is a single backward function, and the forward function returns ())
+(** [paper::ref_incr]:
     Source: 'src/paper.rs', lines 4:0-4:28 *)
 let ref_incr (x : i32) : result i32 =
   i32_add x 1
 
-(** [paper::test_incr]: forward function
+(** [paper::test_incr]:
     Source: 'src/paper.rs', lines 8:0-8:18 *)
 let test_incr : result unit =
-  let* x = ref_incr 0 in if not (x = 1) then Fail Failure else Return ()
+  let* i = ref_incr 0 in if not (i = 1) then Fail Failure else Return ()
 
 (** Unit test for [paper::test_incr] *)
 let _ = assert_norm (test_incr = Return ())
 
-(** [paper::choose]: forward function
+(** [paper::choose]:
     Source: 'src/paper.rs', lines 15:0-15:70 *)
-let choose (t : Type0) (b : bool) (x : t) (y : t) : result t =
-  if b then Return x else Return y
+let choose
+  (t : Type0) (b : bool) (x : t) (y : t) : result (t & (t -> result (t & t))) =
+  if b
+  then let back_'a = fun ret -> Return (ret, y) in Return (x, back_'a)
+  else let back_'a = fun ret -> Return (x, ret) in Return (y, back_'a)
 
-(** [paper::choose]: backward function 0
-    Source: 'src/paper.rs', lines 15:0-15:70 *)
-let choose_back
-  (t : Type0) (b : bool) (x : t) (y : t) (ret : t) : result (t & t) =
-  if b then Return (ret, y) else Return (x, ret)
-
-(** [paper::test_choose]: forward function
+(** [paper::test_choose]:
     Source: 'src/paper.rs', lines 23:0-23:20 *)
 let test_choose : result unit =
-  let* z = choose i32 true 0 0 in
-  let* z0 = i32_add z 1 in
-  if not (z0 = 1)
+  let* (z, choose_back) = choose i32 true 0 0 in
+  let* z1 = i32_add z 1 in
+  if not (z1 = 1)
   then Fail Failure
   else
-    let* (x, y) = choose_back i32 true 0 0 z0 in
+    let* (x, y) = choose_back z1 in
     if not (x = 1)
     then Fail Failure
     else if not (y = 0) then Fail Failure else Return ()
@@ -52,31 +48,28 @@ type list_t (t : Type0) =
 | List_Cons : t -> list_t t -> list_t t
 | List_Nil : list_t t
 
-(** [paper::list_nth_mut]: forward function
-    Source: 'src/paper.rs', lines 42:0-42:67 *)
-let rec list_nth_mut (t : Type0) (l : list_t t) (i : u32) : result t =
-  begin match l with
-  | 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
+(** [paper::list_nth_mut]:
     Source: 'src/paper.rs', lines 42:0-42:67 *)
-let rec list_nth_mut_back
-  (t : Type0) (l : list_t t) (i : u32) (ret : t) : result (list_t t) =
+let rec list_nth_mut
+  (t : Type0) (l : list_t t) (i : u32) :
+  result (t & (t -> result (list_t t)))
+  =
   begin match l with
   | List_Cons x tl ->
     if i = 0
-    then Return (List_Cons ret tl)
+    then
+      let back_'a = fun ret -> Return (List_Cons ret tl) in Return (x, back_'a)
     else
-      let* i0 = u32_sub i 1 in
-      let* tl0 = list_nth_mut_back t tl i0 ret in
-      Return (List_Cons x tl0)
+      let* i1 = u32_sub i 1 in
+      let* (x1, list_nth_mut_back) = list_nth_mut t tl i1 in
+      let back_'a =
+        fun ret -> let* tl1 = list_nth_mut_back ret in Return (List_Cons x tl1)
+        in
+      Return (x1, back_'a)
   | List_Nil -> Fail Failure
   end
 
-(** [paper::sum]: forward function
+(** [paper::sum]:
     Source: 'src/paper.rs', lines 57:0-57:32 *)
 let rec sum (l : list_t i32) : result i32 =
   begin match l with
@@ -84,27 +77,26 @@ let rec sum (l : list_t i32) : result i32 =
   | List_Nil -> Return 0
   end
 
-(** [paper::test_nth]: forward function
+(** [paper::test_nth]:
     Source: 'src/paper.rs', lines 68:0-68:17 *)
 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 (List_Cons 1 l1) 2 x0 in
+  let l = List_Cons 3 List_Nil in
+  let l1 = List_Cons 2 l in
+  let* (x, list_nth_mut_back) = list_nth_mut i32 (List_Cons 1 l1) 2 in
+  let* x1 = i32_add x 1 in
+  let* l2 = list_nth_mut_back x1 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 = Return ())
 
-(** [paper::call_choose]: forward function
+(** [paper::call_choose]:
     Source: 'src/paper.rs', lines 76:0-76:44 *)
 let call_choose (p : (u32 & u32)) : result u32 =
   let (px, py) = p 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
+  let* (pz, choose_back) = choose u32 true px py in
+  let* pz1 = u32_add pz 1 in
+  let* (px1, _) = choose_back pz1 in
+  Return px1
 
diff --git a/tests/fstar/misc/PoloniusList.fst b/tests/fstar/misc/PoloniusList.fst
index 188b22d8..b477802b 100644
--- a/tests/fstar/misc/PoloniusList.fst
+++ b/tests/fstar/misc/PoloniusList.fst
@@ -11,24 +11,22 @@ type list_t (t : Type0) =
 | List_Cons : t -> list_t t -> list_t t
 | List_Nil : list_t t
 
-(** [polonius_list::get_list_at_x]: forward function
+(** [polonius_list::get_list_at_x]:
     Source: 'src/polonius_list.rs', lines 13:0-13:76 *)
-let rec get_list_at_x (ls : list_t u32) (x : u32) : result (list_t u32) =
-  begin match ls with
-  | 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
-    Source: 'src/polonius_list.rs', lines 13:0-13:76 *)
-let rec get_list_at_x_back
-  (ls : list_t u32) (x : u32) (ret : list_t u32) : result (list_t u32) =
+let rec get_list_at_x
+  (ls : list_t u32) (x : u32) :
+  result ((list_t u32) & (list_t u32 -> result (list_t u32)))
+  =
   begin match ls with
   | List_Cons hd tl ->
     if hd = x
-    then Return ret
-    else let* tl0 = get_list_at_x_back tl x ret in Return (List_Cons hd tl0)
-  | List_Nil -> Return ret
+    then Return (List_Cons hd tl, Return)
+    else
+      let* (l, get_list_at_x_back) = get_list_at_x tl x in
+      let back_'a =
+        fun ret ->
+          let* tl1 = get_list_at_x_back ret in Return (List_Cons hd tl1) in
+      Return (l, back_'a)
+  | List_Nil -> Return (List_Nil, Return)
   end
 
diff --git a/tests/fstar/misc/Primitives.fst b/tests/fstar/misc/Primitives.fst
index a3ffbde4..fca80829 100644
--- a/tests/fstar/misc/Primitives.fst
+++ b/tests/fstar/misc/Primitives.fst
@@ -55,8 +55,7 @@ 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
+let core_mem_replace (a : Type0) (x : a) (y : a) : a & a = (x, x)
 
 // We don't really use raw pointers for now
 type mut_raw_ptr (t : Type0) = { v : t }
@@ -477,8 +476,7 @@ noeq type core_ops_index_Index (self idx : Type0) = {
 // 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;
+  index_mut : self → idx → result (indexInst.output & (indexInst.output → result self));
 }
 
 // Trait declaration [core::ops::deref::Deref]
@@ -490,8 +488,7 @@ noeq type core_ops_deref_Deref (self : Type0) = {
 // 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;
+  deref_mut : self → result (derefInst.target & (derefInst.target → result self));
 }
 
 type core_ops_range_Range (a : Type0) = {
@@ -502,8 +499,8 @@ type core_ops_range_Range (a : Type0) = {
 (*** [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
+let alloc_boxed_Box_deref_mut (t : Type0) (x : t) : result (t & (t -> result t)) =
+  Return (x, (fun x -> Return x))
 
 // Trait instance
 let alloc_boxed_Box_coreopsDerefInst (self : Type0) : core_ops_deref_Deref self = {
@@ -515,7 +512,6 @@ let alloc_boxed_Box_coreopsDerefInst (self : Type0) : core_ops_deref_Deref self
 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 *)
@@ -535,10 +531,18 @@ let array_index_usize (a : Type0) (n : usize) (x : array a n) (i : usize) : resu
   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) =
+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
 
+let array_index_mut_usize (a : Type0) (n : usize) (x : array a n) (i : usize) :
+  result (a & (a -> result (array a n))) =
+  match array_index_usize a n x i with
+  | Fail e -> Fail e
+  | Return v ->
+    Return (v, array_update_usize a n x i)
+
 (*** Slice *)
 type slice (a : Type0) = s:list a{length s <= usize_max}
 
@@ -552,6 +556,13 @@ let slice_update_usize (a : Type0) (x : slice a) (i : usize) (nx : a) : result (
   if i < length x then Return (list_update x i nx)
   else Fail Failure
 
+let slice_index_mut_usize (a : Type0) (s : slice a) (i : usize) :
+  result (a & (a -> result (slice a))) =
+  match slice_index_usize a s i with
+  | Fail e -> Fail e
+  | Return x ->
+    Return (x, slice_update_usize a s i)
+
 (*** Subslices *)
 
 let array_to_slice (a : Type0) (n : usize) (x : array a n) : result (slice a) = Return x
@@ -559,6 +570,10 @@ let array_from_slice (a : Type0) (n : usize) (x : array a n) (s : slice a) : res
   if length s = n then Return s
   else Fail Failure
 
+let array_to_slice_mut (a : Type0) (n : usize) (x : array a n) :
+  result (slice a & (slice a -> result (array a n))) =
+  Return (x, array_from_slice a n x)
+
 // 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()
@@ -588,8 +603,13 @@ let alloc_vec_Vec_index_usize (#a : Type0) (v : alloc_vec_Vec a) (i : usize) : r
 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_index_mut_usize (#a : Type0) (v: alloc_vec_Vec a) (i: usize) :
+  result (a & (a → result (alloc_vec_Vec a))) =
+  match alloc_vec_Vec_index_usize v i with
+  | Return x ->
+    Return (x, alloc_vec_Vec_update_usize v i)
+  | Fail e -> Fail e
+
 let alloc_vec_Vec_push (a  : Type0) (v : alloc_vec_Vec a) (x : a) :
   Pure (result (alloc_vec_Vec a))
   (requires True)
@@ -605,9 +625,6 @@ let alloc_vec_Vec_push (a  : Type0) (v : alloc_vec_Vec a) (x : a) :
     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
 
@@ -619,13 +636,11 @@ 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_mut : self → t → result (option output & (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;
+  index_mut : self → t → result (output & (output -> result t));
 }
 
 // [core::slice::index::[T]::index]: forward function
@@ -643,14 +658,8 @@ let core_slice_index_RangeUsize_get (t : Type0) (i : core_ops_range_Range usize)
   admit () // TODO
 
 // [core::slice::index::Range::get_mut]: forward function
-let core_slice_index_RangeUsize_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_RangeUsize_get_mut_back
-  (t : Type0) :
-  core_ops_range_Range usize → slice t → option (slice t) → result (slice t) =
+let core_slice_index_RangeUsize_get_mut (t : Type0) :
+  core_ops_range_Range usize → slice t → result (option (slice t) & (option (slice t) -> result (slice t))) =
   admit () // TODO
 
 // [core::slice::index::Range::get_unchecked]: forward function
@@ -675,27 +684,16 @@ let core_slice_index_RangeUsize_index
   admit () // TODO
 
 // [core::slice::index::Range::index_mut]: forward function
-let core_slice_index_RangeUsize_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_RangeUsize_index_mut_back
-  (t : Type0) : core_ops_range_Range usize → slice t → slice t → result (slice t) =
+let core_slice_index_RangeUsize_index_mut (t : Type0) :
+  core_ops_range_Range usize → slice t → result (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 =
+  slice t → idx → result (inst.output & (inst.output -> result (slice t))) =
   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)
@@ -705,13 +703,8 @@ let core_array_Array_index
 // [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) =
+  (a : array t n) (i : idx) :
+  result (inst.indexInst.output & (inst.indexInst.output -> result (array t n))) =
   admit () // TODO
 
 // Trait implementation: [core::slice::index::private_slice_index::Range]
@@ -725,12 +718,10 @@ let core_slice_index_SliceIndexRangeUsizeSliceTInst (t : Type0) :
   output = slice t;
   get = core_slice_index_RangeUsize_get t;
   get_mut = core_slice_index_RangeUsize_get_mut t;
-  get_mut_back = core_slice_index_RangeUsize_get_mut_back t;
   get_unchecked = core_slice_index_RangeUsize_get_unchecked t;
   get_unchecked_mut = core_slice_index_RangeUsize_get_unchecked_mut t;
   index = core_slice_index_RangeUsize_index t;
   index_mut = core_slice_index_RangeUsize_index_mut t;
-  index_mut_back = core_slice_index_RangeUsize_index_mut_back t;
 }
 
 // Trait implementation: [core::slice::index::[T]]
@@ -747,7 +738,6 @@ let core_ops_index_IndexMutSliceTIInst (t idx : Type0)
   core_ops_index_IndexMut (slice t) idx = {
   indexInst = core_ops_index_IndexSliceTIInst 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]]
@@ -764,7 +754,6 @@ let core_ops_index_IndexMutArrayIInst (t idx : Type0) (n : usize)
   core_ops_index_IndexMut (array t n) idx = {
   indexInst = core_ops_index_IndexArrayInst 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
@@ -773,13 +762,8 @@ let core_slice_index_usize_get
   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) =
+let core_slice_index_usize_get_mut (t : Type0) :
+  usize → slice t → result (option t & (option t -> result (slice t))) =
   admit () // TODO
 
 // [core::slice::index::usize::get_unchecked]: forward function
@@ -797,12 +781,8 @@ 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) =
+let core_slice_index_usize_index_mut (t : Type0) :
+  usize → slice t → result (t & (t -> result (slice t))) =
   admit () // TODO
 
 // Trait implementation: [core::slice::index::private_slice_index::usize]
@@ -816,12 +796,10 @@ let core_slice_index_SliceIndexUsizeSliceTInst (t : Type0) :
   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
@@ -831,13 +809,8 @@ let alloc_vec_Vec_index (t idx : Type0) (inst : core_slice_index_SliceIndex idx
 
 // [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) =
+  (self : alloc_vec_Vec t) (i : idx) :
+  result (inst.output & (inst.output -> result (alloc_vec_Vec t))) =
   admit () // TODO
 
 // Trait implementation: [alloc::vec::Vec]
@@ -854,7 +827,6 @@ let alloc_vec_Vec_coreopsindexIndexMutInst (t idx : Type0)
   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 *)
@@ -870,15 +842,7 @@ let alloc_vec_Vec_index_eq (#a : Type0) (v : alloc_vec_Vec a) (i : usize) :
 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_SliceIndexUsizeSliceTInst a) v i ==
-      alloc_vec_Vec_index_usize v i)
+      alloc_vec_Vec_index_mut_usize v i)
   [SMTPat (alloc_vec_Vec_index_mut a usize (core_slice_index_SliceIndexUsizeSliceTInst 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_SliceIndexUsizeSliceTInst a) v i x ==
-      alloc_vec_Vec_update_usize v i x)
-  [SMTPat (alloc_vec_Vec_index_mut_back a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i x)]
-  =
-  admit()
diff --git a/tests/fstar/traits/Primitives.fst b/tests/fstar/traits/Primitives.fst
index a3ffbde4..fca80829 100644
--- a/tests/fstar/traits/Primitives.fst
+++ b/tests/fstar/traits/Primitives.fst
@@ -55,8 +55,7 @@ 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
+let core_mem_replace (a : Type0) (x : a) (y : a) : a & a = (x, x)
 
 // We don't really use raw pointers for now
 type mut_raw_ptr (t : Type0) = { v : t }
@@ -477,8 +476,7 @@ noeq type core_ops_index_Index (self idx : Type0) = {
 // 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;
+  index_mut : self → idx → result (indexInst.output & (indexInst.output → result self));
 }
 
 // Trait declaration [core::ops::deref::Deref]
@@ -490,8 +488,7 @@ noeq type core_ops_deref_Deref (self : Type0) = {
 // 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;
+  deref_mut : self → result (derefInst.target & (derefInst.target → result self));
 }
 
 type core_ops_range_Range (a : Type0) = {
@@ -502,8 +499,8 @@ type core_ops_range_Range (a : Type0) = {
 (*** [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
+let alloc_boxed_Box_deref_mut (t : Type0) (x : t) : result (t & (t -> result t)) =
+  Return (x, (fun x -> Return x))
 
 // Trait instance
 let alloc_boxed_Box_coreopsDerefInst (self : Type0) : core_ops_deref_Deref self = {
@@ -515,7 +512,6 @@ let alloc_boxed_Box_coreopsDerefInst (self : Type0) : core_ops_deref_Deref self
 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 *)
@@ -535,10 +531,18 @@ let array_index_usize (a : Type0) (n : usize) (x : array a n) (i : usize) : resu
   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) =
+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
 
+let array_index_mut_usize (a : Type0) (n : usize) (x : array a n) (i : usize) :
+  result (a & (a -> result (array a n))) =
+  match array_index_usize a n x i with
+  | Fail e -> Fail e
+  | Return v ->
+    Return (v, array_update_usize a n x i)
+
 (*** Slice *)
 type slice (a : Type0) = s:list a{length s <= usize_max}
 
@@ -552,6 +556,13 @@ let slice_update_usize (a : Type0) (x : slice a) (i : usize) (nx : a) : result (
   if i < length x then Return (list_update x i nx)
   else Fail Failure
 
+let slice_index_mut_usize (a : Type0) (s : slice a) (i : usize) :
+  result (a & (a -> result (slice a))) =
+  match slice_index_usize a s i with
+  | Fail e -> Fail e
+  | Return x ->
+    Return (x, slice_update_usize a s i)
+
 (*** Subslices *)
 
 let array_to_slice (a : Type0) (n : usize) (x : array a n) : result (slice a) = Return x
@@ -559,6 +570,10 @@ let array_from_slice (a : Type0) (n : usize) (x : array a n) (s : slice a) : res
   if length s = n then Return s
   else Fail Failure
 
+let array_to_slice_mut (a : Type0) (n : usize) (x : array a n) :
+  result (slice a & (slice a -> result (array a n))) =
+  Return (x, array_from_slice a n x)
+
 // 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()
@@ -588,8 +603,13 @@ let alloc_vec_Vec_index_usize (#a : Type0) (v : alloc_vec_Vec a) (i : usize) : r
 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_index_mut_usize (#a : Type0) (v: alloc_vec_Vec a) (i: usize) :
+  result (a & (a → result (alloc_vec_Vec a))) =
+  match alloc_vec_Vec_index_usize v i with
+  | Return x ->
+    Return (x, alloc_vec_Vec_update_usize v i)
+  | Fail e -> Fail e
+
 let alloc_vec_Vec_push (a  : Type0) (v : alloc_vec_Vec a) (x : a) :
   Pure (result (alloc_vec_Vec a))
   (requires True)
@@ -605,9 +625,6 @@ let alloc_vec_Vec_push (a  : Type0) (v : alloc_vec_Vec a) (x : a) :
     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
 
@@ -619,13 +636,11 @@ 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_mut : self → t → result (option output & (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;
+  index_mut : self → t → result (output & (output -> result t));
 }
 
 // [core::slice::index::[T]::index]: forward function
@@ -643,14 +658,8 @@ let core_slice_index_RangeUsize_get (t : Type0) (i : core_ops_range_Range usize)
   admit () // TODO
 
 // [core::slice::index::Range::get_mut]: forward function
-let core_slice_index_RangeUsize_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_RangeUsize_get_mut_back
-  (t : Type0) :
-  core_ops_range_Range usize → slice t → option (slice t) → result (slice t) =
+let core_slice_index_RangeUsize_get_mut (t : Type0) :
+  core_ops_range_Range usize → slice t → result (option (slice t) & (option (slice t) -> result (slice t))) =
   admit () // TODO
 
 // [core::slice::index::Range::get_unchecked]: forward function
@@ -675,27 +684,16 @@ let core_slice_index_RangeUsize_index
   admit () // TODO
 
 // [core::slice::index::Range::index_mut]: forward function
-let core_slice_index_RangeUsize_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_RangeUsize_index_mut_back
-  (t : Type0) : core_ops_range_Range usize → slice t → slice t → result (slice t) =
+let core_slice_index_RangeUsize_index_mut (t : Type0) :
+  core_ops_range_Range usize → slice t → result (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 =
+  slice t → idx → result (inst.output & (inst.output -> result (slice t))) =
   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)
@@ -705,13 +703,8 @@ let core_array_Array_index
 // [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) =
+  (a : array t n) (i : idx) :
+  result (inst.indexInst.output & (inst.indexInst.output -> result (array t n))) =
   admit () // TODO
 
 // Trait implementation: [core::slice::index::private_slice_index::Range]
@@ -725,12 +718,10 @@ let core_slice_index_SliceIndexRangeUsizeSliceTInst (t : Type0) :
   output = slice t;
   get = core_slice_index_RangeUsize_get t;
   get_mut = core_slice_index_RangeUsize_get_mut t;
-  get_mut_back = core_slice_index_RangeUsize_get_mut_back t;
   get_unchecked = core_slice_index_RangeUsize_get_unchecked t;
   get_unchecked_mut = core_slice_index_RangeUsize_get_unchecked_mut t;
   index = core_slice_index_RangeUsize_index t;
   index_mut = core_slice_index_RangeUsize_index_mut t;
-  index_mut_back = core_slice_index_RangeUsize_index_mut_back t;
 }
 
 // Trait implementation: [core::slice::index::[T]]
@@ -747,7 +738,6 @@ let core_ops_index_IndexMutSliceTIInst (t idx : Type0)
   core_ops_index_IndexMut (slice t) idx = {
   indexInst = core_ops_index_IndexSliceTIInst 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]]
@@ -764,7 +754,6 @@ let core_ops_index_IndexMutArrayIInst (t idx : Type0) (n : usize)
   core_ops_index_IndexMut (array t n) idx = {
   indexInst = core_ops_index_IndexArrayInst 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
@@ -773,13 +762,8 @@ let core_slice_index_usize_get
   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) =
+let core_slice_index_usize_get_mut (t : Type0) :
+  usize → slice t → result (option t & (option t -> result (slice t))) =
   admit () // TODO
 
 // [core::slice::index::usize::get_unchecked]: forward function
@@ -797,12 +781,8 @@ 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) =
+let core_slice_index_usize_index_mut (t : Type0) :
+  usize → slice t → result (t & (t -> result (slice t))) =
   admit () // TODO
 
 // Trait implementation: [core::slice::index::private_slice_index::usize]
@@ -816,12 +796,10 @@ let core_slice_index_SliceIndexUsizeSliceTInst (t : Type0) :
   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
@@ -831,13 +809,8 @@ let alloc_vec_Vec_index (t idx : Type0) (inst : core_slice_index_SliceIndex idx
 
 // [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) =
+  (self : alloc_vec_Vec t) (i : idx) :
+  result (inst.output & (inst.output -> result (alloc_vec_Vec t))) =
   admit () // TODO
 
 // Trait implementation: [alloc::vec::Vec]
@@ -854,7 +827,6 @@ let alloc_vec_Vec_coreopsindexIndexMutInst (t idx : Type0)
   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 *)
@@ -870,15 +842,7 @@ let alloc_vec_Vec_index_eq (#a : Type0) (v : alloc_vec_Vec a) (i : usize) :
 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_SliceIndexUsizeSliceTInst a) v i ==
-      alloc_vec_Vec_index_usize v i)
+      alloc_vec_Vec_index_mut_usize v i)
   [SMTPat (alloc_vec_Vec_index_mut a usize (core_slice_index_SliceIndexUsizeSliceTInst 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_SliceIndexUsizeSliceTInst a) v i x ==
-      alloc_vec_Vec_update_usize v i x)
-  [SMTPat (alloc_vec_Vec_index_mut_back a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i x)]
-  =
-  admit()
diff --git a/tests/fstar/traits/Traits.fst b/tests/fstar/traits/Traits.fst
index 7d504cb5..cb9c1654 100644
--- a/tests/fstar/traits/Traits.fst
+++ b/tests/fstar/traits/Traits.fst
@@ -9,7 +9,7 @@ open Primitives
     Source: 'src/traits.rs', lines 1:0-1:19 *)
 noeq type boolTrait_t (self : Type0) = { get_bool : self -> result bool; }
 
-(** [traits::{bool}::get_bool]: forward function
+(** [traits::{bool}::get_bool]:
     Source: 'src/traits.rs', lines 12:4-12:30 *)
 let bool_get_bool (self : bool) : result bool =
   Return self
@@ -18,24 +18,24 @@ let bool_get_bool (self : bool) : result bool =
     Source: 'src/traits.rs', lines 11:0-11:23 *)
 let traits_BoolTraitBoolInst : boolTrait_t bool = { get_bool = bool_get_bool; }
 
-(** [traits::BoolTrait::ret_true]: forward function
+(** [traits::BoolTrait::ret_true]:
     Source: 'src/traits.rs', lines 6:4-6:30 *)
 let boolTrait_ret_true
-  (#self : Type0) (self_clause : boolTrait_t self) (self0 : self) :
+  (#self : Type0) (self_clause : boolTrait_t self) (self1 : self) :
   result bool
   =
   Return true
 
-(** [traits::test_bool_trait_bool]: forward function
+(** [traits::test_bool_trait_bool]:
     Source: 'src/traits.rs', lines 17:0-17:44 *)
 let test_bool_trait_bool (x : bool) : result bool =
   let* b = bool_get_bool x in
   if b then boolTrait_ret_true traits_BoolTraitBoolInst x else Return false
 
-(** [traits::{core::option::Option<T>#1}::get_bool]: forward function
+(** [traits::{core::option::Option<T>#1}::get_bool]:
     Source: 'src/traits.rs', lines 23:4-23:30 *)
 let option_get_bool (t : Type0) (self : option t) : result bool =
-  begin match self with | None -> Return false | Some x -> Return true end
+  begin match self with | None -> Return false | Some _ -> Return true end
 
 (** Trait implementation: [traits::{core::option::Option<T>#1}]
     Source: 'src/traits.rs', lines 22:0-22:31 *)
@@ -44,7 +44,7 @@ let traits_BoolTraitcoreoptionOptionTInst (t : Type0) : boolTrait_t (option t)
   get_bool = option_get_bool t;
 }
 
-(** [traits::test_bool_trait_option]: forward function
+(** [traits::test_bool_trait_option]:
     Source: 'src/traits.rs', lines 31:0-31:54 *)
 let test_bool_trait_option (t : Type0) (x : option t) : result bool =
   let* b = option_get_bool t x in
@@ -52,7 +52,7 @@ let test_bool_trait_option (t : Type0) (x : option t) : result bool =
   then boolTrait_ret_true (traits_BoolTraitcoreoptionOptionTInst t) x
   else Return false
 
-(** [traits::test_bool_trait]: forward function
+(** [traits::test_bool_trait]:
     Source: 'src/traits.rs', lines 35:0-35:50 *)
 let test_bool_trait
   (t : Type0) (boolTraitTInst : boolTrait_t t) (x : t) : result bool =
@@ -62,7 +62,7 @@ let test_bool_trait
     Source: 'src/traits.rs', lines 39:0-39:15 *)
 noeq type toU64_t (self : Type0) = { to_u64 : self -> result u64; }
 
-(** [traits::{u64#2}::to_u64]: forward function
+(** [traits::{u64#2}::to_u64]:
     Source: 'src/traits.rs', lines 44:4-44:26 *)
 let u64_to_u64 (self : u64) : result u64 =
   Return self
@@ -71,14 +71,14 @@ let u64_to_u64 (self : u64) : result u64 =
     Source: 'src/traits.rs', lines 43:0-43:18 *)
 let traits_ToU64U64Inst : toU64_t u64 = { to_u64 = u64_to_u64; }
 
-(** [traits::{(A, A)#3}::to_u64]: forward function
+(** [traits::{(A, A)#3}::to_u64]:
     Source: 'src/traits.rs', lines 50:4-50:26 *)
 let pair_to_u64
   (a : Type0) (toU64AInst : toU64_t a) (self : (a & a)) : result u64 =
-  let (x, x0) = self in
+  let (x, x1) = self in
   let* i = toU64AInst.to_u64 x in
-  let* i0 = toU64AInst.to_u64 x0 in
-  u64_add i i0
+  let* i1 = toU64AInst.to_u64 x1 in
+  u64_add i i1
 
 (** Trait implementation: [traits::{(A, A)#3}]
     Source: 'src/traits.rs', lines 49:0-49:31 *)
@@ -87,18 +87,18 @@ let traits_ToU64TupleAAInst (a : Type0) (toU64AInst : toU64_t a) : toU64_t (a &
   to_u64 = pair_to_u64 a toU64AInst;
 }
 
-(** [traits::f]: forward function
+(** [traits::f]:
     Source: 'src/traits.rs', lines 55:0-55:36 *)
 let f (t : Type0) (toU64TInst : toU64_t t) (x : (t & t)) : result u64 =
   pair_to_u64 t toU64TInst x
 
-(** [traits::g]: forward function
+(** [traits::g]:
     Source: 'src/traits.rs', lines 59:0-61:18 *)
 let g
   (t : Type0) (toU64TupleTTInst : toU64_t (t & t)) (x : (t & t)) : result u64 =
   toU64TupleTTInst.to_u64 x
 
-(** [traits::h0]: forward function
+(** [traits::h0]:
     Source: 'src/traits.rs', lines 66:0-66:24 *)
 let h0 (x : u64) : result u64 =
   u64_to_u64 x
@@ -107,7 +107,7 @@ let h0 (x : u64) : result u64 =
     Source: 'src/traits.rs', lines 70:0-70:21 *)
 type wrapper_t (t : Type0) = { x : t; }
 
-(** [traits::{traits::Wrapper<T>#4}::to_u64]: forward function
+(** [traits::{traits::Wrapper<T>#4}::to_u64]:
     Source: 'src/traits.rs', lines 75:4-75:26 *)
 let wrapper_to_u64
   (t : Type0) (toU64TInst : toU64_t t) (self : wrapper_t t) : result u64 =
@@ -120,12 +120,12 @@ let traits_ToU64traitsWrapperTInst (t : Type0) (toU64TInst : toU64_t t) :
   to_u64 = wrapper_to_u64 t toU64TInst;
 }
 
-(** [traits::h1]: forward function
+(** [traits::h1]:
     Source: 'src/traits.rs', lines 80:0-80:33 *)
 let h1 (x : wrapper_t u64) : result u64 =
   wrapper_to_u64 u64 traits_ToU64U64Inst x
 
-(** [traits::h2]: forward function
+(** [traits::h2]:
     Source: 'src/traits.rs', lines 84:0-84:41 *)
 let h2 (t : Type0) (toU64TInst : toU64_t t) (x : wrapper_t t) : result u64 =
   wrapper_to_u64 t toU64TInst x
@@ -134,7 +134,7 @@ let h2 (t : Type0) (toU64TInst : toU64_t t) (x : wrapper_t t) : result u64 =
     Source: 'src/traits.rs', lines 88:0-88:19 *)
 noeq type toType_t (self t : Type0) = { to_type : self -> result t; }
 
-(** [traits::{u64#5}::to_type]: forward function
+(** [traits::{u64#5}::to_type]:
     Source: 'src/traits.rs', lines 93:4-93:28 *)
 let u64_to_type (self : u64) : result bool =
   Return (self > 0)
@@ -150,7 +150,7 @@ noeq type ofType_t (self : Type0) = {
     self;
 }
 
-(** [traits::h3]: forward function
+(** [traits::h3]:
     Source: 'src/traits.rs', lines 104:0-104:50 *)
 let h3
   (t1 t2 : Type0) (ofTypeT1Inst : ofType_t t1) (toTypeT2T1Inst : toType_t t2
@@ -166,7 +166,7 @@ noeq type ofTypeBis_t (self t : Type0) = {
   of_type : t -> result self;
 }
 
-(** [traits::h4]: forward function
+(** [traits::h4]:
     Source: 'src/traits.rs', lines 118:0-118:57 *)
 let h4
   (t1 t2 : Type0) (ofTypeBisT1T2Inst : ofTypeBis_t t1 t2) (toTypeT2T1Inst :
@@ -189,7 +189,7 @@ noeq type testType_test_TestTrait_t (self : Type0) = {
   test : self -> result bool;
 }
 
-(** [traits::{traits::TestType<T>#6}::test::{traits::{traits::TestType<T>#6}::test::TestType1}::test]: forward function
+(** [traits::{traits::TestType<T>#6}::test::{traits::{traits::TestType<T>#6}::test::TestType1}::test]:
     Source: 'src/traits.rs', lines 139:12-139:34 *)
 let testType_test_TestType1_test
   (self : testType_test_TestType1_t) : result bool =
@@ -202,20 +202,20 @@ let traits_TestType_test_TestTraittraitstraitsTestTypeTtestTestType1Inst :
   test = testType_test_TestType1_test;
 }
 
-(** [traits::{traits::TestType<T>#6}::test]: forward function
+(** [traits::{traits::TestType<T>#6}::test]:
     Source: 'src/traits.rs', lines 126:4-126:36 *)
 let testType_test
   (t : Type0) (toU64TInst : toU64_t t) (self : testType_t t) (x : t) :
   result bool
   =
-  let* x0 = toU64TInst.to_u64 x in
-  if x0 > 0 then testType_test_TestType1_test 0 else Return false
+  let* x1 = toU64TInst.to_u64 x in
+  if x1 > 0 then testType_test_TestType1_test 0 else Return false
 
 (** [traits::BoolWrapper]
     Source: 'src/traits.rs', lines 150:0-150:22 *)
 type boolWrapper_t = bool
 
-(** [traits::{traits::BoolWrapper#7}::to_type]: forward function
+(** [traits::{traits::BoolWrapper#7}::to_type]:
     Source: 'src/traits.rs', lines 156:4-156:25 *)
 let boolWrapper_to_type
   (t : Type0) (toTypeBoolTInst : toType_t bool t) (self : boolWrapper_t) :
@@ -251,8 +251,7 @@ noeq type withConstTy_t (self : Type0) (len : usize) = {
 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 ())
+(** [traits::{bool#8}::f]:
     Source: 'src/traits.rs', lines 180:4-180:39 *)
 let bool_f (i : u64) (a : array u8 32) : result u64 =
   Return i
@@ -268,15 +267,15 @@ let traits_WithConstTyBool32Inst : withConstTy_t bool 32 = {
   f = bool_f;
 }
 
-(** [traits::use_with_const_ty1]: forward function
+(** [traits::use_with_const_ty1]:
     Source: 'src/traits.rs', lines 183:0-183:75 *)
 let use_with_const_ty1
   (h : Type0) (len : usize) (withConstTyHLENInst : withConstTy_t h len) :
   result usize
   =
-  let i = withConstTyHLENInst.cLEN1 in Return i
+  Return withConstTyHLENInst.cLEN1
 
-(** [traits::use_with_const_ty2]: forward function
+(** [traits::use_with_const_ty2]:
     Source: 'src/traits.rs', lines 187:0-187:73 *)
 let use_with_const_ty2
   (h : Type0) (len : usize) (withConstTyHLENInst : withConstTy_t h len)
@@ -285,7 +284,7 @@ let use_with_const_ty2
   =
   Return ()
 
-(** [traits::use_with_const_ty3]: forward function
+(** [traits::use_with_const_ty3]:
     Source: 'src/traits.rs', lines 189:0-189:80 *)
 let use_with_const_ty3
   (h : Type0) (len : usize) (withConstTyHLENInst : withConstTy_t h len)
@@ -294,12 +293,12 @@ let use_with_const_ty3
   =
   withConstTyHLENInst.tW_clause_0.to_u64 x
 
-(** [traits::test_where1]: forward function
+(** [traits::test_where1]:
     Source: 'src/traits.rs', lines 193:0-193:40 *)
 let test_where1 (t : Type0) (_x : t) : result unit =
   Return ()
 
-(** [traits::test_where2]: forward function
+(** [traits::test_where2]:
     Source: 'src/traits.rs', lines 194:0-194:57 *)
 let test_where2
   (t : Type0) (withConstTyT32Inst : withConstTy_t t 32) (_x : u32) :
@@ -326,22 +325,30 @@ noeq type childTrait_t (self : Type0) = {
   parentTrait1SelfInst : parentTrait1_t self;
 }
 
-(** [traits::test_child_trait1]: forward function
-    Source: 'src/traits.rs', lines 209:0-209:56 *)
+(** [traits::test_parent_trait0]:
+    Source: 'src/traits.rs', lines 208:0-208:57 *)
+let test_parent_trait0
+  (t : Type0) (parentTrait0TInst : parentTrait0_t t) (x : t) :
+  result parentTrait0TInst.tW
+  =
+  parentTrait0TInst.get_w x
+
+(** [traits::test_child_trait1]:
+    Source: 'src/traits.rs', lines 213:0-213:56 *)
 let test_child_trait1
   (t : Type0) (childTraitTInst : childTrait_t t) (x : t) : result string =
   childTraitTInst.parentTrait0SelfInst.get_name x
 
-(** [traits::test_child_trait2]: forward function
-    Source: 'src/traits.rs', lines 213:0-213:54 *)
+(** [traits::test_child_trait2]:
+    Source: 'src/traits.rs', lines 217:0-217:54 *)
 let test_child_trait2
   (t : Type0) (childTraitTInst : childTrait_t t) (x : t) :
   result childTraitTInst.parentTrait0SelfInst.tW
   =
   childTraitTInst.parentTrait0SelfInst.get_w x
 
-(** [traits::order1]: forward function
-    Source: 'src/traits.rs', lines 219:0-219:59 *)
+(** [traits::order1]:
+    Source: 'src/traits.rs', lines 223:0-223:59 *)
 let order1
   (t u : Type0) (parentTrait0TInst : parentTrait0_t t) (parentTrait0UInst :
   parentTrait0_t u) :
@@ -350,27 +357,27 @@ let order1
   Return ()
 
 (** Trait declaration: [traits::ChildTrait1]
-    Source: 'src/traits.rs', lines 222:0-222:35 *)
+    Source: 'src/traits.rs', lines 226:0-226:35 *)
 noeq type childTrait1_t (self : Type0) = {
   parentTrait1SelfInst : parentTrait1_t self;
 }
 
 (** Trait implementation: [traits::{usize#9}]
-    Source: 'src/traits.rs', lines 224:0-224:27 *)
+    Source: 'src/traits.rs', lines 228:0-228:27 *)
 let traits_ParentTrait1UsizeInst : parentTrait1_t usize = ()
 
 (** Trait implementation: [traits::{usize#10}]
-    Source: 'src/traits.rs', lines 225:0-225:26 *)
+    Source: 'src/traits.rs', lines 229:0-229:26 *)
 let traits_ChildTrait1UsizeInst : childTrait1_t usize = {
   parentTrait1SelfInst = traits_ParentTrait1UsizeInst;
 }
 
 (** Trait declaration: [traits::Iterator]
-    Source: 'src/traits.rs', lines 229:0-229:18 *)
+    Source: 'src/traits.rs', lines 233:0-233:18 *)
 noeq type iterator_t (self : Type0) = { tItem : Type0; }
 
 (** Trait declaration: [traits::IntoIterator]
-    Source: 'src/traits.rs', lines 233:0-233:22 *)
+    Source: 'src/traits.rs', lines 237:0-237:22 *)
 noeq type intoIterator_t (self : Type0) = {
   tItem : Type0;
   tIntoIter : Type0;
@@ -379,29 +386,29 @@ noeq type intoIterator_t (self : Type0) = {
 }
 
 (** Trait declaration: [traits::FromResidual]
-    Source: 'src/traits.rs', lines 250:0-250:21 *)
+    Source: 'src/traits.rs', lines 254:0-254:21 *)
 type fromResidual_t (self t : Type0) = unit
 
 (** Trait declaration: [traits::Try]
-    Source: 'src/traits.rs', lines 246:0-246:48 *)
+    Source: 'src/traits.rs', lines 250:0-250:48 *)
 noeq type try_t (self : Type0) = {
   tResidual : Type0;
   fromResidualSelftraitsTrySelfResidualInst : fromResidual_t self tResidual;
 }
 
 (** Trait declaration: [traits::WithTarget]
-    Source: 'src/traits.rs', lines 252:0-252:20 *)
+    Source: 'src/traits.rs', lines 256:0-256:20 *)
 noeq type withTarget_t (self : Type0) = { tTarget : Type0; }
 
 (** Trait declaration: [traits::ParentTrait2]
-    Source: 'src/traits.rs', lines 256:0-256:22 *)
+    Source: 'src/traits.rs', lines 260:0-260:22 *)
 noeq type parentTrait2_t (self : Type0) = {
   tU : Type0;
   tU_clause_0 : withTarget_t tU;
 }
 
 (** Trait declaration: [traits::ChildTrait2]
-    Source: 'src/traits.rs', lines 260:0-260:35 *)
+    Source: 'src/traits.rs', lines 264:0-264:35 *)
 noeq type childTrait2_t (self : Type0) = {
   parentTrait2SelfInst : parentTrait2_t self;
   convert : parentTrait2SelfInst.tU -> result
@@ -409,48 +416,59 @@ noeq type childTrait2_t (self : Type0) = {
 }
 
 (** Trait implementation: [traits::{u32#11}]
-    Source: 'src/traits.rs', lines 264:0-264:23 *)
+    Source: 'src/traits.rs', lines 268:0-268:23 *)
 let traits_WithTargetU32Inst : withTarget_t u32 = { tTarget = u32; }
 
 (** Trait implementation: [traits::{u32#12}]
-    Source: 'src/traits.rs', lines 268:0-268:25 *)
+    Source: 'src/traits.rs', lines 272:0-272:25 *)
 let traits_ParentTrait2U32Inst : parentTrait2_t u32 = {
   tU = u32;
   tU_clause_0 = traits_WithTargetU32Inst;
 }
 
-(** [traits::{u32#13}::convert]: forward function
-    Source: 'src/traits.rs', lines 273:4-273:29 *)
+(** [traits::{u32#13}::convert]:
+    Source: 'src/traits.rs', lines 277:4-277:29 *)
 let u32_convert (x : u32) : result u32 =
   Return x
 
 (** Trait implementation: [traits::{u32#13}]
-    Source: 'src/traits.rs', lines 272:0-272:24 *)
+    Source: 'src/traits.rs', lines 276:0-276:24 *)
 let traits_ChildTrait2U32Inst : childTrait2_t u32 = {
   parentTrait2SelfInst = traits_ParentTrait2U32Inst;
   convert = u32_convert;
 }
 
 (** Trait declaration: [traits::CFnOnce]
-    Source: 'src/traits.rs', lines 286:0-286:23 *)
+    Source: 'src/traits.rs', lines 290:0-290:23 *)
 noeq type cFnOnce_t (self args : Type0) = {
   tOutput : Type0;
   call_once : self -> args -> result tOutput;
 }
 
 (** Trait declaration: [traits::CFnMut]
-    Source: 'src/traits.rs', lines 292:0-292:37 *)
+    Source: 'src/traits.rs', lines 296:0-296:37 *)
 noeq type cFnMut_t (self args : Type0) = {
   cFnOnceSelfArgsInst : cFnOnce_t self args;
-  call_mut : self -> args -> result cFnOnceSelfArgsInst.tOutput;
-  call_mut_back : self -> args -> cFnOnceSelfArgsInst.tOutput -> result self;
+  call_mut : self -> args -> result (cFnOnceSelfArgsInst.tOutput & self);
 }
 
 (** Trait declaration: [traits::CFn]
-    Source: 'src/traits.rs', lines 296:0-296:33 *)
+    Source: 'src/traits.rs', lines 300:0-300:33 *)
 noeq type cFn_t (self args : Type0) = {
   cFnMutSelfArgsInst : cFnMut_t self args;
-  call_mut : self -> args -> result
-    cFnMutSelfArgsInst.cFnOnceSelfArgsInst.tOutput;
+  call : self -> args -> result cFnMutSelfArgsInst.cFnOnceSelfArgsInst.tOutput;
+}
+
+(** Trait declaration: [traits::GetTrait]
+    Source: 'src/traits.rs', lines 304:0-304:18 *)
+noeq type getTrait_t (self : Type0) = { tW : Type0; get_w : self -> result tW;
 }
 
+(** [traits::test_get_trait]:
+    Source: 'src/traits.rs', lines 309:0-309:49 *)
+let test_get_trait
+  (t : Type0) (getTraitTInst : getTrait_t t) (x : t) :
+  result getTraitTInst.tW
+  =
+  getTraitTInst.get_w x
+
diff --git a/tests/lean/Array.lean b/tests/lean/Array.lean
index 25dad3cf..7785a208 100644
--- a/tests/lean/Array.lean
+++ b/tests/lean/Array.lean
@@ -11,99 +11,91 @@ inductive AB :=
 | A : AB
 | B : AB
 
-/- [array::incr]: merged forward/backward function
-   (there is a single backward function, and the forward function returns ())
+/- [array::incr]:
    Source: 'src/array.rs', lines 8:0-8:24 -/
 def incr (x : U32) : Result U32 :=
   x + 1#u32
 
-/- [array::array_to_shared_slice_]: forward function
+/- [array::array_to_shared_slice_]:
    Source: 'src/array.rs', lines 16:0-16:53 -/
 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
+/- [array::array_to_mut_slice_]:
    Source: 'src/array.rs', lines 21:0-21:58 -/
-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
-   Source: 'src/array.rs', lines 21:0-21:58 -/
-def array_to_mut_slice__back
-  (T : Type) (s : Array T 32#usize) (ret : Slice T) :
-  Result (Array T 32#usize)
+def array_to_mut_slice_
+  (T : Type) (s : Array T 32#usize) :
+  Result ((Slice T) × (Slice T → Result (Array T 32#usize)))
   :=
-  Array.from_slice T 32#usize s ret
+  do
+  let (s1, to_slice_mut_back) ← Array.to_slice_mut T 32#usize s
+  Result.ret (s1, to_slice_mut_back)
 
-/- [array::array_len]: forward function
+/- [array::array_len]:
    Source: 'src/array.rs', lines 25:0-25:40 -/
 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
+  let s1 ← Array.to_slice T 32#usize s
+  let i := Slice.len T s1
+  Result.ret i
 
-/- [array::shared_array_len]: forward function
+/- [array::shared_array_len]:
    Source: 'src/array.rs', lines 29:0-29:48 -/
 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
+  let s1 ← Array.to_slice T 32#usize s
+  let i := Slice.len T s1
+  Result.ret i
 
-/- [array::shared_slice_len]: forward function
+/- [array::shared_slice_len]:
    Source: 'src/array.rs', lines 33:0-33:44 -/
 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
+/- [array::index_array_shared]:
    Source: 'src/array.rs', lines 37:0-37:57 -/
 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
+/- [array::index_array_u32]:
    Source: 'src/array.rs', lines 44:0-44:53 -/
 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
+/- [array::index_array_copy]:
    Source: 'src/array.rs', lines 48:0-48:45 -/
 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
+/- [array::index_mut_array]:
    Source: 'src/array.rs', lines 52:0-52:62 -/
-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
-   Source: 'src/array.rs', lines 52:0-52:62 -/
-def index_mut_array_back
-  (T : Type) (s : Array T 32#usize) (i : Usize) (ret : T) :
-  Result (Array T 32#usize)
+def index_mut_array
+  (T : Type) (s : Array T 32#usize) (i : Usize) :
+  Result (T × (T → Result (Array T 32#usize)))
   :=
-  Array.update_usize T 32#usize s i ret
+  do
+  let (t, index_mut_back) ← Array.index_mut_usize T 32#usize s i
+  Result.ret (t, index_mut_back)
 
-/- [array::index_slice]: forward function
+/- [array::index_slice]:
    Source: 'src/array.rs', lines 56:0-56:46 -/
 def index_slice (T : Type) (s : Slice T) (i : Usize) : Result T :=
   Slice.index_usize T s i
 
-/- [array::index_mut_slice]: forward function
+/- [array::index_mut_slice]:
    Source: 'src/array.rs', lines 60:0-60:58 -/
-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
-   Source: 'src/array.rs', lines 60:0-60:58 -/
-def index_mut_slice_back
-  (T : Type) (s : Slice T) (i : Usize) (ret : T) : Result (Slice T) :=
-  Slice.update_usize T s i ret
+def index_mut_slice
+  (T : Type) (s : Slice T) (i : Usize) :
+  Result (T × (T → Result (Slice T)))
+  :=
+  do
+  let (t, index_mut_back) ← Slice.index_mut_usize T s i
+  Result.ret (t, index_mut_back)
 
-/- [array::slice_subslice_shared_]: forward function
+/- [array::slice_subslice_shared_]:
    Source: 'src/array.rs', lines 64:0-64:70 -/
 def slice_subslice_shared_
   (x : Slice U32) (y : Usize) (z : Usize) : Result (Slice U32) :=
@@ -111,41 +103,35 @@ def slice_subslice_shared_
     (core.slice.index.SliceIndexRangeUsizeSliceTInst U32) x
     { start := y, end_ := z }
 
-/- [array::slice_subslice_mut_]: forward function
+/- [array::slice_subslice_mut_]:
    Source: 'src/array.rs', lines 68:0-68:75 -/
 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.SliceIndexRangeUsizeSliceTInst U32) x
-    { start := y, end_ := z }
-
-/- [array::slice_subslice_mut_]: backward function 0
-   Source: 'src/array.rs', lines 68:0-68:75 -/
-def slice_subslice_mut__back
-  (x : Slice U32) (y : Usize) (z : Usize) (ret : Slice U32) :
-  Result (Slice U32)
+  (x : Slice U32) (y : Usize) (z : Usize) :
+  Result ((Slice U32) × (Slice U32 → Result (Slice U32)))
   :=
-  core.slice.index.Slice.index_mut_back U32 (core.ops.range.Range Usize)
-    (core.slice.index.SliceIndexRangeUsizeSliceTInst U32) x
-    { start := y, end_ := z } ret
+  do
+  let (s, index_mut_back) ←
+    core.slice.index.Slice.index_mut U32 (core.ops.range.Range Usize)
+      (core.slice.index.SliceIndexRangeUsizeSliceTInst U32) x
+      { start := y, end_ := z }
+  Result.ret (s, index_mut_back)
 
-/- [array::array_to_slice_shared_]: forward function
+/- [array::array_to_slice_shared_]:
    Source: 'src/array.rs', lines 72:0-72:54 -/
 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
+/- [array::array_to_slice_mut_]:
    Source: 'src/array.rs', lines 76:0-76:59 -/
-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
-   Source: 'src/array.rs', lines 76:0-76:59 -/
-def 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
+def array_to_slice_mut_
+  (x : Array U32 32#usize) :
+  Result ((Slice U32) × (Slice U32 → Result (Array U32 32#usize)))
+  :=
+  do
+  let (s, to_slice_mut_back) ← Array.to_slice_mut U32 32#usize x
+  Result.ret (s, to_slice_mut_back)
 
-/- [array::array_subslice_shared_]: forward function
+/- [array::array_subslice_shared_]:
    Source: 'src/array.rs', lines 80:0-80:74 -/
 def array_subslice_shared_
   (x : Array U32 32#usize) (y : Usize) (z : Usize) : Result (Slice U32) :=
@@ -154,311 +140,294 @@ def array_subslice_shared_
     (core.slice.index.SliceIndexRangeUsizeSliceTInst U32)) x
     { start := y, end_ := z }
 
-/- [array::array_subslice_mut_]: forward function
+/- [array::array_subslice_mut_]:
    Source: 'src/array.rs', lines 84:0-84:79 -/
 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.ops.index.IndexMutSliceTIInst U32 (core.ops.range.Range Usize)
-    (core.slice.index.SliceIndexRangeUsizeSliceTInst U32)) x
-    { start := y, end_ := z }
-
-/- [array::array_subslice_mut_]: backward function 0
-   Source: 'src/array.rs', lines 84:0-84:79 -/
-def array_subslice_mut__back
-  (x : Array U32 32#usize) (y : Usize) (z : Usize) (ret : Slice U32) :
-  Result (Array U32 32#usize)
+  (x : Array U32 32#usize) (y : Usize) (z : Usize) :
+  Result ((Slice U32) × (Slice U32 → Result (Array U32 32#usize)))
   :=
-  core.array.Array.index_mut_back U32 (core.ops.range.Range Usize) 32#usize
-    (core.ops.index.IndexMutSliceTIInst U32 (core.ops.range.Range Usize)
-    (core.slice.index.SliceIndexRangeUsizeSliceTInst U32)) x
-    { start := y, end_ := z } ret
-
-/- [array::index_slice_0]: forward function
+  do
+  let (s, index_mut_back) ←
+    core.array.Array.index_mut U32 (core.ops.range.Range Usize) 32#usize
+      (core.ops.index.IndexMutSliceTIInst U32 (core.ops.range.Range Usize)
+      (core.slice.index.SliceIndexRangeUsizeSliceTInst U32)) x
+      { start := y, end_ := z }
+  Result.ret (s, index_mut_back)
+
+/- [array::index_slice_0]:
    Source: 'src/array.rs', lines 88:0-88:38 -/
 def index_slice_0 (T : Type) (s : Slice T) : Result T :=
   Slice.index_usize T s 0#usize
 
-/- [array::index_array_0]: forward function
+/- [array::index_array_0]:
    Source: 'src/array.rs', lines 92:0-92:42 -/
 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
+/- [array::index_index_array]:
    Source: 'src/array.rs', lines 103:0-103:71 -/
 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
+  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
+/- [array::update_update_array]:
    Source: 'src/array.rs', lines 114:0-114:70 -/
 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 ()
+  let (a, index_mut_back) ←
+    Array.index_mut_usize (Array U32 32#usize) 32#usize s i
+  let (_, index_mut_back1) ← Array.index_mut_usize U32 32#usize a j
+  let a1 ← index_mut_back1 0#u32
+  let _ ← index_mut_back a1
+  Result.ret ()
 
-/- [array::array_local_deep_copy]: forward function
+/- [array::array_local_deep_copy]:
    Source: 'src/array.rs', lines 118:0-118:43 -/
 def array_local_deep_copy (x : Array U32 32#usize) : Result Unit :=
   Result.ret ()
 
-/- [array::take_array]: forward function
+/- [array::take_array]:
    Source: 'src/array.rs', lines 122:0-122:30 -/
 def take_array (a : Array U32 2#usize) : Result Unit :=
   Result.ret ()
 
-/- [array::take_array_borrow]: forward function
+/- [array::take_array_borrow]:
    Source: 'src/array.rs', lines 123:0-123:38 -/
 def take_array_borrow (a : Array U32 2#usize) : Result Unit :=
   Result.ret ()
 
-/- [array::take_slice]: forward function
+/- [array::take_slice]:
    Source: 'src/array.rs', lines 124:0-124:28 -/
 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 ())
+/- [array::take_mut_slice]:
    Source: 'src/array.rs', lines 125:0-125:36 -/
 def take_mut_slice (s : Slice U32) : Result (Slice U32) :=
   Result.ret s
 
-/- [array::const_array]: forward function
+/- [array::const_array]:
    Source: 'src/array.rs', lines 127:0-127:32 -/
 def const_array : Result (Array U32 2#usize) :=
   Result.ret (Array.make U32 2#usize [ 0#u32, 0#u32 ])
 
-/- [array::const_slice]: forward function
+/- [array::const_slice]:
    Source: 'src/array.rs', lines 131:0-131:20 -/
 def const_slice : Result Unit :=
   do
-    let _ ←
-      Array.to_slice U32 2#usize (Array.make U32 2#usize [ 0#u32, 0#u32 ])
-    Result.ret ()
+  let _ ←
+    Array.to_slice U32 2#usize (Array.make U32 2#usize [ 0#u32, 0#u32 ])
+  Result.ret ()
 
-/- [array::take_all]: forward function
+/- [array::take_all]:
    Source: 'src/array.rs', lines 141:0-141:17 -/
 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
+  let _ ← take_array (Array.make U32 2#usize [ 0#u32, 0#u32 ])
+  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 (s1, to_slice_mut_back) ←
+    Array.to_slice_mut U32 2#usize (Array.make U32 2#usize [ 0#u32, 0#u32 ])
+  let s2 ← take_mut_slice s1
+  let _ ← to_slice_mut_back s2
+  Result.ret ()
+
+/- [array::index_array]:
    Source: 'src/array.rs', lines 155:0-155:38 -/
 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
+/- [array::index_array_borrow]:
    Source: 'src/array.rs', lines 158:0-158:46 -/
 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
+/- [array::index_slice_u32_0]:
    Source: 'src/array.rs', lines 162:0-162:42 -/
 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
+/- [array::index_mut_slice_u32_0]:
    Source: 'src/array.rs', lines 166:0-166:50 -/
-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
-   Source: 'src/array.rs', lines 166:0-166:50 -/
-def index_mut_slice_u32_0_back (x : Slice U32) : Result (Slice U32) :=
+def index_mut_slice_u32_0 (x : Slice U32) : Result (U32 × (Slice U32)) :=
   do
-    let _ ← Slice.index_usize U32 x 0#usize
-    Result.ret x
+  let i ← Slice.index_usize U32 x 0#usize
+  Result.ret (i, x)
 
-/- [array::index_all]: forward function
+/- [array::index_all]:
    Source: 'src/array.rs', lines 170:0-170:25 -/
 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
+  let i ← index_array (Array.make U32 2#usize [ 0#u32, 0#u32 ])
+  let i1 ← index_array (Array.make U32 2#usize [ 0#u32, 0#u32 ])
+  let i2 ← i + i1
+  let i3 ← index_array_borrow (Array.make U32 2#usize [ 0#u32, 0#u32 ])
+  let i4 ← i2 + i3
+  let s ←
+    Array.to_slice U32 2#usize (Array.make U32 2#usize [ 0#u32, 0#u32 ])
+  let i5 ← index_slice_u32_0 s
+  let i6 ← i4 + i5
+  let (s1, to_slice_mut_back) ←
+    Array.to_slice_mut U32 2#usize (Array.make U32 2#usize [ 0#u32, 0#u32 ])
+  let (i7, s2) ← index_mut_slice_u32_0 s1
+  let i8 ← i6 + i7
+  let _ ← to_slice_mut_back s2
+  Result.ret i8
+
+/- [array::update_array]:
    Source: 'src/array.rs', lines 184:0-184:36 -/
 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 ()
+  let (_, index_mut_back) ← Array.index_mut_usize U32 2#usize x 0#usize
+  let _ ← index_mut_back 1#u32
+  Result.ret ()
 
-/- [array::update_array_mut_borrow]: merged forward/backward function
-   (there is a single backward function, and the forward function returns ())
+/- [array::update_array_mut_borrow]:
    Source: 'src/array.rs', lines 187:0-187:48 -/
 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
+  do
+  let (_, index_mut_back) ← Array.index_mut_usize U32 2#usize x 0#usize
+  index_mut_back 1#u32
 
-/- [array::update_mut_slice]: merged forward/backward function
-   (there is a single backward function, and the forward function returns ())
+/- [array::update_mut_slice]:
    Source: 'src/array.rs', lines 190:0-190:38 -/
 def update_mut_slice (x : Slice U32) : Result (Slice U32) :=
-  Slice.update_usize U32 x 0#usize 1#u32
+  do
+  let (_, index_mut_back) ← Slice.index_mut_usize U32 x 0#usize
+  index_mut_back 1#u32
 
-/- [array::update_all]: forward function
+/- [array::update_all]:
    Source: 'src/array.rs', lines 194:0-194:19 -/
 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
+  let _ ← update_array (Array.make U32 2#usize [ 0#u32, 0#u32 ])
+  let _ ← update_array (Array.make U32 2#usize [ 0#u32, 0#u32 ])
+  let a ← update_array_mut_borrow (Array.make U32 2#usize [ 0#u32, 0#u32 ])
+  let (s, to_slice_mut_back) ← Array.to_slice_mut U32 2#usize a
+  let s1 ← update_mut_slice s
+  let _ ← to_slice_mut_back s1
+  Result.ret ()
+
+/- [array::range_all]:
    Source: 'src/array.rs', lines 205:0-205:18 -/
 def range_all : Result Unit :=
   do
-    let s ←
-      core.array.Array.index_mut U32 (core.ops.range.Range Usize) 4#usize
-        (core.ops.index.IndexMutSliceTIInst U32 (core.ops.range.Range Usize)
-        (core.slice.index.SliceIndexRangeUsizeSliceTInst 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.ops.index.IndexMutSliceTIInst U32 (core.ops.range.Range Usize)
-        (core.slice.index.SliceIndexRangeUsizeSliceTInst 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
+  let (s, index_mut_back) ←
+    core.array.Array.index_mut U32 (core.ops.range.Range Usize) 4#usize
+      (core.ops.index.IndexMutSliceTIInst U32 (core.ops.range.Range Usize)
+      (core.slice.index.SliceIndexRangeUsizeSliceTInst U32))
+      (Array.make U32 4#usize [ 0#u32, 0#u32, 0#u32, 0#u32 ])
+      { start := 1#usize, end_ := 3#usize }
+  let s1 ← update_mut_slice s
+  let _ ← index_mut_back s1
+  Result.ret ()
+
+/- [array::deref_array_borrow]:
    Source: 'src/array.rs', lines 214:0-214:46 -/
 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
-   Source: 'src/array.rs', lines 219:0-219:54 -/
-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
+/- [array::deref_array_mut_borrow]:
    Source: 'src/array.rs', lines 219:0-219:54 -/
-def deref_array_mut_borrow_back
-  (x : Array U32 2#usize) : Result (Array U32 2#usize) :=
+def deref_array_mut_borrow
+  (x : Array U32 2#usize) : Result (U32 × (Array U32 2#usize)) :=
   do
-    let _ ← Array.index_usize U32 2#usize x 0#usize
-    Result.ret x
+  let i ← Array.index_usize U32 2#usize x 0#usize
+  Result.ret (i, x)
 
-/- [array::take_array_t]: forward function
+/- [array::take_array_t]:
    Source: 'src/array.rs', lines 227:0-227:31 -/
 def take_array_t (a : Array AB 2#usize) : Result Unit :=
   Result.ret ()
 
-/- [array::non_copyable_array]: forward function
+/- [array::non_copyable_array]:
    Source: 'src/array.rs', lines 229:0-229:27 -/
 def non_copyable_array : Result Unit :=
   do
-    let _ ← take_array_t (Array.make AB 2#usize [ AB.A, AB.B ])
-    Result.ret ()
+  let _ ← take_array_t (Array.make AB 2#usize [ AB.A, AB.B ])
+  Result.ret ()
 
-/- [array::sum]: loop 0: forward function
+/- [array::sum]: loop 0:
    Source: 'src/array.rs', lines 242:0-250:1 -/
-divergent def sum_loop (s : Slice U32) (sum0 : U32) (i : Usize) : Result U32 :=
-  let i0 := Slice.len U32 s
-  if i < i0
+divergent def sum_loop (s : Slice U32) (sum1 : U32) (i : Usize) : Result U32 :=
+  let i1 := Slice.len U32 s
+  if i < i1
   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
+    let i2 ← Slice.index_usize U32 s i
+    let sum3 ← sum1 + i2
+    let i3 ← i + 1#usize
+    sum_loop s sum3 i3
+  else Result.ret sum1
 
-/- [array::sum]: forward function
+/- [array::sum]:
    Source: 'src/array.rs', lines 242:0-242:28 -/
 def sum (s : Slice U32) : Result U32 :=
   sum_loop s 0#u32 0#usize
 
-/- [array::sum2]: loop 0: forward function
+/- [array::sum2]: loop 0:
    Source: 'src/array.rs', lines 252:0-261:1 -/
 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
+  (s : Slice U32) (s2 : Slice U32) (sum1 : U32) (i : Usize) : Result U32 :=
+  let i1 := Slice.len U32 s
+  if i < i1
   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
+    let i2 ← Slice.index_usize U32 s i
+    let i3 ← Slice.index_usize U32 s2 i
+    let i4 ← i2 + i3
+    let sum3 ← sum1 + i4
+    let i5 ← i + 1#usize
+    sum2_loop s s2 sum3 i5
+  else Result.ret sum1
+
+/- [array::sum2]:
    Source: 'src/array.rs', lines 252:0-252:41 -/
 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)
+  let i1 := Slice.len U32 s2
+  if not (i = i1)
   then Result.fail .panic
   else sum2_loop s s2 0#u32 0#usize
 
-/- [array::f0]: forward function
+/- [array::f0]:
    Source: 'src/array.rs', lines 263:0-263:11 -/
 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
+  let (s, to_slice_mut_back) ←
+    Array.to_slice_mut U32 2#usize (Array.make U32 2#usize [ 1#u32, 2#u32 ])
+  let (_, index_mut_back) ← Slice.index_mut_usize U32 s 0#usize
+  let s1 ← index_mut_back 1#u32
+  let _ ← to_slice_mut_back s1
+  Result.ret ()
+
+/- [array::f1]:
    Source: 'src/array.rs', lines 268:0-268:11 -/
 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 ()
+  let (_, index_mut_back) ←
+    Array.index_mut_usize U32 2#usize (Array.make U32 2#usize [ 1#u32, 2#u32 ])
+      0#usize
+  let _ ← index_mut_back 1#u32
+  Result.ret ()
 
-/- [array::f2]: forward function
+/- [array::f2]:
    Source: 'src/array.rs', lines 273:0-273:17 -/
 def f2 (i : U32) : Result Unit :=
   Result.ret ()
 
-/- [array::f4]: forward function
+/- [array::f4]:
    Source: 'src/array.rs', lines 282:0-282:54 -/
 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
@@ -466,44 +435,42 @@ def f4 (x : Array U32 32#usize) (y : Usize) (z : Usize) : Result (Slice U32) :=
     (core.slice.index.SliceIndexRangeUsizeSliceTInst U32)) x
     { start := y, end_ := z }
 
-/- [array::f3]: forward function
+/- [array::f3]:
    Source: 'src/array.rs', lines 275:0-275:18 -/
 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
+  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 s1 ← f4 b 16#usize 18#usize
+  sum2 s s1
 
 /- [array::SZ]
    Source: 'src/array.rs', lines 286:0-286:19 -/
 def sz_body : Result Usize := Result.ret 32#usize
 def sz_c : Usize := eval_global sz_body (by simp)
 
-/- [array::f5]: forward function
+/- [array::f5]:
    Source: 'src/array.rs', lines 289:0-289:31 -/
 def f5 (x : Array U32 32#usize) : Result U32 :=
   Array.index_usize U32 32#usize x 0#usize
 
-/- [array::ite]: forward function
+/- [array::ite]:
    Source: 'src/array.rs', lines 294:0-294:12 -/
 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 ()
+  let (s, to_slice_mut_back) ←
+    Array.to_slice_mut U32 2#usize (Array.make U32 2#usize [ 0#u32, 0#u32 ])
+  let (_, s1) ← index_mut_slice_u32_0 s
+  let (s2, to_slice_mut_back1) ←
+    Array.to_slice_mut U32 2#usize (Array.make U32 2#usize [ 0#u32, 0#u32 ])
+  let (_, s3) ← index_mut_slice_u32_0 s2
+  let _ ← to_slice_mut_back1 s3
+  let _ ← to_slice_mut_back s1
+  Result.ret ()
 
 end array
diff --git a/tests/lean/BetreeMain/Funs.lean b/tests/lean/BetreeMain/Funs.lean
index 0d7cb984..96daa197 100644
--- a/tests/lean/BetreeMain/Funs.lean
+++ b/tests/lean/BetreeMain/Funs.lean
@@ -7,7 +7,7 @@ open Primitives
 
 namespace betree_main
 
-/- [betree_main::betree::load_internal_node]: forward function
+/- [betree_main::betree::load_internal_node]:
    Source: 'src/betree.rs', lines 36:0-36:52 -/
 def betree.load_internal_node
   (id : U64) (st : State) :
@@ -15,65 +15,53 @@ def betree.load_internal_node
   :=
   betree_utils.load_internal_node id st
 
-/- [betree_main::betree::store_internal_node]: forward function
+/- [betree_main::betree::store_internal_node]:
    Source: 'src/betree.rs', lines 41:0-41:60 -/
 def betree.store_internal_node
   (id : U64) (content : betree.List (U64 × betree.Message)) (st : State) :
   Result (State × Unit)
   :=
   do
-    let (st0, _) ← betree_utils.store_internal_node id content st
-    Result.ret (st0, ())
+  let (st1, _) ← betree_utils.store_internal_node id content st
+  Result.ret (st1, ())
 
-/- [betree_main::betree::load_leaf_node]: forward function
+/- [betree_main::betree::load_leaf_node]:
    Source: 'src/betree.rs', lines 46:0-46:44 -/
 def betree.load_leaf_node
   (id : U64) (st : State) : Result (State × (betree.List (U64 × U64))) :=
   betree_utils.load_leaf_node id st
 
-/- [betree_main::betree::store_leaf_node]: forward function
+/- [betree_main::betree::store_leaf_node]:
    Source: 'src/betree.rs', lines 51:0-51:52 -/
 def betree.store_leaf_node
   (id : U64) (content : betree.List (U64 × U64)) (st : State) :
   Result (State × Unit)
   :=
   do
-    let (st0, _) ← betree_utils.store_leaf_node id content st
-    Result.ret (st0, ())
+  let (st1, _) ← betree_utils.store_leaf_node id content st
+  Result.ret (st1, ())
 
-/- [betree_main::betree::fresh_node_id]: forward function
+/- [betree_main::betree::fresh_node_id]:
    Source: 'src/betree.rs', lines 55:0-55:48 -/
-def betree.fresh_node_id (counter : U64) : Result U64 :=
+def betree.fresh_node_id (counter : U64) : Result (U64 × U64) :=
   do
-    let _ ← counter + 1#u64
-    Result.ret counter
+  let counter1 ← counter + 1#u64
+  Result.ret (counter, counter1)
 
-/- [betree_main::betree::fresh_node_id]: backward function 0
-   Source: 'src/betree.rs', lines 55:0-55:48 -/
-def betree.fresh_node_id_back (counter : U64) : Result U64 :=
-  counter + 1#u64
-
-/- [betree_main::betree::{betree_main::betree::NodeIdCounter}::new]: forward function
+/- [betree_main::betree::{betree_main::betree::NodeIdCounter}::new]:
    Source: 'src/betree.rs', lines 206:4-206:20 -/
 def betree.NodeIdCounter.new : Result betree.NodeIdCounter :=
   Result.ret { next_node_id := 0#u64 }
 
-/- [betree_main::betree::{betree_main::betree::NodeIdCounter}::fresh_id]: forward function
+/- [betree_main::betree::{betree_main::betree::NodeIdCounter}::fresh_id]:
    Source: 'src/betree.rs', lines 210:4-210:36 -/
-def betree.NodeIdCounter.fresh_id (self : betree.NodeIdCounter) : Result U64 :=
+def betree.NodeIdCounter.fresh_id
+  (self : betree.NodeIdCounter) : Result (U64 × betree.NodeIdCounter) :=
   do
-    let _ ← self.next_node_id + 1#u64
-    Result.ret self.next_node_id
+  let i ← self.next_node_id + 1#u64
+  Result.ret (self.next_node_id, { next_node_id := i })
 
-/- [betree_main::betree::{betree_main::betree::NodeIdCounter}::fresh_id]: backward function 0
-   Source: 'src/betree.rs', lines 210:4-210:36 -/
-def betree.NodeIdCounter.fresh_id_back
-  (self : betree.NodeIdCounter) : Result betree.NodeIdCounter :=
-  do
-    let i ← self.next_node_id + 1#u64
-    Result.ret { next_node_id := i }
-
-/- [betree_main::betree::upsert_update]: forward function
+/- [betree_main::betree::upsert_update]:
    Source: 'src/betree.rs', lines 234:0-234:70 -/
 def betree.upsert_update
   (prev : Option U64) (st : betree.UpsertFunState) : Result U64 :=
@@ -81,30 +69,30 @@ def betree.upsert_update
   | none =>
     match st with
     | betree.UpsertFunState.Add v => Result.ret v
-    | betree.UpsertFunState.Sub i => Result.ret 0#u64
-  | some prev0 =>
+    | betree.UpsertFunState.Sub _ => Result.ret 0#u64
+  | some prev1 =>
     match st with
     | betree.UpsertFunState.Add v =>
       do
-        let margin ← core_u64_max - prev0
-        if margin >= v
-        then prev0 + v
-        else Result.ret core_u64_max
+      let margin ← core_u64_max - prev1
+      if margin >= v
+      then prev1 + v
+      else Result.ret core_u64_max
     | betree.UpsertFunState.Sub v =>
-      if prev0 >= v
-      then prev0 - v
+      if prev1 >= v
+      then prev1 - v
       else Result.ret 0#u64
 
-/- [betree_main::betree::{betree_main::betree::List<T>#1}::len]: forward function
+/- [betree_main::betree::{betree_main::betree::List<T>#1}::len]:
    Source: 'src/betree.rs', lines 276:4-276:24 -/
 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
-                               1#u64 + i
+  | betree.List.Cons _ tl => do
+                             let i ← betree.List.len T tl
+                             1#u64 + i
   | betree.List.Nil => Result.ret 0#u64
 
-/- [betree_main::betree::{betree_main::betree::List<T>#1}::split_at]: forward function
+/- [betree_main::betree::{betree_main::betree::List<T>#1}::split_at]:
    Source: 'src/betree.rs', lines 284:4-284:51 -/
 divergent def betree.List.split_at
   (T : Type) (self : betree.List T) (n : U64) :
@@ -116,56 +104,45 @@ divergent def betree.List.split_at
     match self with
     | betree.List.Cons hd tl =>
       do
-        let i ← n - 1#u64
-        let p ← betree.List.split_at T tl i
-        let (ls0, ls1) := p
-        let l := ls0
-        Result.ret (betree.List.Cons hd l, ls1)
+      let i ← n - 1#u64
+      let p ← betree.List.split_at T tl i
+      let (ls0, ls1) := p
+      Result.ret (betree.List.Cons hd ls0, ls1)
     | betree.List.Nil => Result.fail .panic
 
-/- [betree_main::betree::{betree_main::betree::List<T>#1}::push_front]: merged forward/backward function
-   (there is a single backward function, and the forward function returns ())
+/- [betree_main::betree::{betree_main::betree::List<T>#1}::push_front]:
    Source: 'src/betree.rs', lines 299:4-299:34 -/
 def betree.List.push_front
   (T : Type) (self : betree.List T) (x : T) : Result (betree.List T) :=
-  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::{betree_main::betree::List<T>#1}::pop_front]: forward function
-   Source: 'src/betree.rs', lines 306:4-306:32 -/
-def betree.List.pop_front (T : Type) (self : betree.List T) : Result T :=
-  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 .panic
+  let (tl, _) := core.mem.replace (betree.List T) self betree.List.Nil
+  Result.ret (betree.List.Cons x tl)
 
-/- [betree_main::betree::{betree_main::betree::List<T>#1}::pop_front]: backward function 0
+/- [betree_main::betree::{betree_main::betree::List<T>#1}::pop_front]:
    Source: 'src/betree.rs', lines 306:4-306:32 -/
-def betree.List.pop_front_back
-  (T : Type) (self : betree.List T) : Result (betree.List T) :=
-  let ls := core.mem.replace (betree.List T) self betree.List.Nil
+def betree.List.pop_front
+  (T : Type) (self : betree.List T) : Result (T × (betree.List T)) :=
+  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.Cons x tl => Result.ret (x, tl)
   | betree.List.Nil => Result.fail .panic
 
-/- [betree_main::betree::{betree_main::betree::List<T>#1}::hd]: forward function
+/- [betree_main::betree::{betree_main::betree::List<T>#1}::hd]:
    Source: 'src/betree.rs', lines 318:4-318:22 -/
 def betree.List.hd (T : Type) (self : betree.List T) : Result T :=
   match self with
-  | betree.List.Cons hd l => Result.ret hd
+  | betree.List.Cons hd _ => Result.ret hd
   | betree.List.Nil => Result.fail .panic
 
-/- [betree_main::betree::{betree_main::betree::List<(u64, T)>#2}::head_has_key]: forward function
+/- [betree_main::betree::{betree_main::betree::List<(u64, T)>#2}::head_has_key]:
    Source: 'src/betree.rs', lines 327:4-327:44 -/
 def betree.ListTupleU64T.head_has_key
   (T : Type) (self : betree.List (U64 × T)) (key : U64) : Result Bool :=
   match self with
-  | betree.List.Cons hd l => let (i, _) := hd
+  | betree.List.Cons hd _ => let (i, _) := hd
                              Result.ret (i = key)
   | betree.List.Nil => Result.ret false
 
-/- [betree_main::betree::{betree_main::betree::List<(u64, T)>#2}::partition_at_pivot]: forward function
+/- [betree_main::betree::{betree_main::betree::List<(u64, T)>#2}::partition_at_pivot]:
    Source: 'src/betree.rs', lines 339:4-339:73 -/
 divergent def betree.ListTupleU64T.partition_at_pivot
   (T : Type) (self : betree.List (U64 × T)) (pivot : U64) :
@@ -178,334 +155,186 @@ divergent def betree.ListTupleU64T.partition_at_pivot
     then Result.ret (betree.List.Nil, betree.List.Cons (i, t) tl)
     else
       do
-        let p ← betree.ListTupleU64T.partition_at_pivot T tl pivot
-        let (ls0, ls1) := p
-        let l := ls0
-        Result.ret (betree.List.Cons (i, t) l, ls1)
+      let p ← betree.ListTupleU64T.partition_at_pivot T tl pivot
+      let (ls0, ls1) := p
+      Result.ret (betree.List.Cons (i, t) ls0, ls1)
   | betree.List.Nil => Result.ret (betree.List.Nil, betree.List.Nil)
 
-/- [betree_main::betree::{betree_main::betree::Leaf#3}::split]: forward function
+/- [betree_main::betree::{betree_main::betree::Leaf#3}::split]:
    Source: 'src/betree.rs', lines 359:4-364:17 -/
 def betree.Leaf.split
   (self : betree.Leaf) (content : betree.List (U64 × U64))
   (params : betree.Params) (node_id_cnt : betree.NodeIdCounter) (st : State) :
-  Result (State × betree.Internal)
+  Result (State × (betree.Internal × betree.NodeIdCounter))
   :=
   do
-    let p ← betree.List.split_at (U64 × U64) content params.split_size
-    let (content0, content1) := p
-    let p0 ← betree.List.hd (U64 × U64) content1
-    let (pivot, _) := p0
-    let id0 ← betree.NodeIdCounter.fresh_id node_id_cnt
-    let node_id_cnt0 ← betree.NodeIdCounter.fresh_id_back node_id_cnt
-    let id1 ← betree.NodeIdCounter.fresh_id node_id_cnt0
-    let (st0, _) ← betree.store_leaf_node id0 content0 st
-    let (st1, _) ← betree.store_leaf_node id1 content1 st0
-    let n := betree.Node.Leaf { id := id0, size := params.split_size }
-    let n0 := betree.Node.Leaf { id := id1, size := params.split_size }
-    Result.ret (st1, betree.Internal.mk self.id pivot n n0)
-
-/- [betree_main::betree::{betree_main::betree::Leaf#3}::split]: backward function 2
-   Source: 'src/betree.rs', lines 359:4-364:17 -/
-def betree.Leaf.split_back
-  (self : betree.Leaf) (content : betree.List (U64 × U64))
-  (params : betree.Params) (node_id_cnt : betree.NodeIdCounter) (st : State) :
-  Result betree.NodeIdCounter
-  :=
-  do
-    let p ← betree.List.split_at (U64 × U64) content params.split_size
-    let (content0, content1) := p
-    let _ ← betree.List.hd (U64 × U64) content1
-    let id0 ← betree.NodeIdCounter.fresh_id node_id_cnt
-    let node_id_cnt0 ← betree.NodeIdCounter.fresh_id_back node_id_cnt
-    let id1 ← betree.NodeIdCounter.fresh_id node_id_cnt0
-    let (st0, _) ← betree.store_leaf_node id0 content0 st
-    let _ ← betree.store_leaf_node id1 content1 st0
-    betree.NodeIdCounter.fresh_id_back node_id_cnt0
-
-/- [betree_main::betree::{betree_main::betree::Node#5}::lookup_first_message_for_key]: forward function
+  let p ← betree.List.split_at (U64 × U64) content params.split_size
+  let (content0, content1) := p
+  let p1 ← betree.List.hd (U64 × U64) content1
+  let (pivot, _) := p1
+  let (id0, nic) ← betree.NodeIdCounter.fresh_id node_id_cnt
+  let (id1, nic1) ← betree.NodeIdCounter.fresh_id nic
+  let (st1, _) ← betree.store_leaf_node id0 content0 st
+  let (st2, _) ← betree.store_leaf_node id1 content1 st1
+  let n := betree.Node.Leaf { id := id0, size := params.split_size }
+  let n1 := betree.Node.Leaf { id := id1, size := params.split_size }
+  Result.ret (st2, (betree.Internal.mk self.id pivot n n1, nic1))
+
+/- [betree_main::betree::{betree_main::betree::Node#5}::lookup_first_message_for_key]:
    Source: 'src/betree.rs', lines 789:4-792:34 -/
 divergent def betree.Node.lookup_first_message_for_key
   (key : U64) (msgs : betree.List (U64 × betree.Message)) :
-  Result (betree.List (U64 × betree.Message))
+  Result ((betree.List (U64 × betree.Message)) × (betree.List (U64 ×
+    betree.Message) → Result (betree.List (U64 × betree.Message))))
   :=
   match msgs with
   | betree.List.Cons x next_msgs =>
     let (i, m) := x
     if i >= key
-    then Result.ret (betree.List.Cons (i, m) next_msgs)
-    else betree.Node.lookup_first_message_for_key key next_msgs
-  | betree.List.Nil => Result.ret betree.List.Nil
-
-/- [betree_main::betree::{betree_main::betree::Node#5}::lookup_first_message_for_key]: backward function 0
-   Source: 'src/betree.rs', lines 789:4-792:34 -/
-divergent def betree.Node.lookup_first_message_for_key_back
-  (key : U64) (msgs : betree.List (U64 × betree.Message))
-  (ret : betree.List (U64 × betree.Message)) :
-  Result (betree.List (U64 × betree.Message))
-  :=
-  match msgs with
-  | betree.List.Cons x next_msgs =>
-    let (i, m) := x
-    if i >= key
-    then Result.ret ret
+    then Result.ret (betree.List.Cons (i, m) next_msgs, Result.ret)
     else
       do
-        let next_msgs0 ←
-          betree.Node.lookup_first_message_for_key_back key next_msgs ret
-        Result.ret (betree.List.Cons (i, m) next_msgs0)
-  | betree.List.Nil => Result.ret ret
+      let (l, lookup_first_message_for_key_back) ←
+        betree.Node.lookup_first_message_for_key key next_msgs
+      let back_'a :=
+        fun ret =>
+          do
+          let next_msgs1 ← lookup_first_message_for_key_back ret
+          Result.ret (betree.List.Cons (i, m) next_msgs1)
+      Result.ret (l, back_'a)
+  | betree.List.Nil => Result.ret (betree.List.Nil, Result.ret)
 
-/- [betree_main::betree::{betree_main::betree::Node#5}::lookup_in_bindings]: forward function
+/- [betree_main::betree::{betree_main::betree::Node#5}::lookup_in_bindings]:
    Source: 'src/betree.rs', lines 636:4-636:80 -/
 divergent def betree.Node.lookup_in_bindings
   (key : U64) (bindings : betree.List (U64 × U64)) : Result (Option U64) :=
   match bindings with
   | betree.List.Cons hd tl =>
-    let (i, i0) := hd
+    let (i, i1) := hd
     if i = key
-    then Result.ret (some i0)
+    then Result.ret (some i1)
     else
       if i > key
       then Result.ret none
       else betree.Node.lookup_in_bindings key tl
   | betree.List.Nil => Result.ret none
 
-/- [betree_main::betree::{betree_main::betree::Node#5}::apply_upserts]: forward function
+/- [betree_main::betree::{betree_main::betree::Node#5}::apply_upserts]:
    Source: 'src/betree.rs', lines 819:4-819:90 -/
 divergent def betree.Node.apply_upserts
   (msgs : betree.List (U64 × betree.Message)) (prev : Option U64) (key : U64)
   (st : State) :
-  Result (State × U64)
+  Result (State × (U64 × (betree.List (U64 × betree.Message))))
   :=
   do
-    let b ← betree.ListTupleU64T.head_has_key betree.Message msgs key
-    if b
-    then
-      do
-        let msg ← betree.List.pop_front (U64 × betree.Message) msgs
-        let (_, m) := msg
-        match m with
-        | betree.Message.Insert i => Result.fail .panic
-        | betree.Message.Delete => Result.fail .panic
-        | betree.Message.Upsert s =>
-          do
-            let v ← betree.upsert_update prev s
-            let msgs0 ←
-              betree.List.pop_front_back (U64 × betree.Message) msgs
-            betree.Node.apply_upserts msgs0 (some v) key st
-    else
-      do
-        let (st0, v) ← core.option.Option.unwrap U64 prev st
-        let _ ←
-          betree.List.push_front (U64 × betree.Message) msgs (key,
-            betree.Message.Insert v)
-        Result.ret (st0, v)
-
-/- [betree_main::betree::{betree_main::betree::Node#5}::apply_upserts]: backward function 0
-   Source: 'src/betree.rs', lines 819:4-819:90 -/
-divergent def betree.Node.apply_upserts_back
-  (msgs : betree.List (U64 × betree.Message)) (prev : Option U64) (key : U64)
-  (st : State) :
-  Result (betree.List (U64 × betree.Message))
-  :=
-  do
-    let b ← betree.ListTupleU64T.head_has_key betree.Message msgs key
-    if b
-    then
-      do
-        let msg ← betree.List.pop_front (U64 × betree.Message) msgs
-        let (_, m) := msg
-        match m with
-        | betree.Message.Insert i => Result.fail .panic
-        | betree.Message.Delete => Result.fail .panic
-        | betree.Message.Upsert s =>
-          do
-            let v ← betree.upsert_update prev s
-            let msgs0 ←
-              betree.List.pop_front_back (U64 × betree.Message) msgs
-            betree.Node.apply_upserts_back msgs0 (some v) key st
-    else
+  let b ← betree.ListTupleU64T.head_has_key betree.Message msgs key
+  if b
+  then
+    do
+    let (msg, l) ← betree.List.pop_front (U64 × betree.Message) msgs
+    let (_, m) := msg
+    match m with
+    | betree.Message.Insert _ => Result.fail .panic
+    | betree.Message.Delete => Result.fail .panic
+    | betree.Message.Upsert s =>
       do
-        let (_, v) ← core.option.Option.unwrap U64 prev st
-        betree.List.push_front (U64 × betree.Message) msgs (key,
-          betree.Message.Insert v)
+      let v ← betree.upsert_update prev s
+      betree.Node.apply_upserts l (some v) key st
+  else
+    do
+    let (st1, v) ← core.option.Option.unwrap U64 prev st
+    let l ←
+      betree.List.push_front (U64 × betree.Message) msgs (key,
+        betree.Message.Insert v)
+    Result.ret (st1, (v, l))
 
-/- [betree_main::betree::{betree_main::betree::Internal#4}::lookup_in_children]: forward function
+/- [betree_main::betree::{betree_main::betree::Internal#4}::lookup_in_children]:
    Source: 'src/betree.rs', lines 395:4-395:63 -/
 mutual divergent def betree.Internal.lookup_in_children
   (self : betree.Internal) (key : U64) (st : State) :
-  Result (State × (Option U64))
+  Result (State × ((Option U64) × betree.Internal))
   :=
-  let ⟨ _, i, n, n0 ⟩ := self
-  if key < i
-  then betree.Node.lookup n key st
-  else betree.Node.lookup n0 key st
-
-/- [betree_main::betree::{betree_main::betree::Internal#4}::lookup_in_children]: backward function 0
-   Source: 'src/betree.rs', lines 395:4-395:63 -/
-divergent def betree.Internal.lookup_in_children_back
-  (self : betree.Internal) (key : U64) (st : State) : Result betree.Internal :=
-  let ⟨ i, i0, n, n0 ⟩ := self
-  if key < i0
+  let ⟨ i, i1, n, n1 ⟩ := self
+  if key < i1
   then
     do
-      let n1 ← betree.Node.lookup_back n key st
-      Result.ret (betree.Internal.mk i i0 n1 n0)
+    let (st1, (o, n2)) ← betree.Node.lookup n key st
+    Result.ret (st1, (o, betree.Internal.mk i i1 n2 n1))
   else
     do
-      let n1 ← betree.Node.lookup_back n0 key st
-      Result.ret (betree.Internal.mk i i0 n n1)
+    let (st1, (o, n2)) ← betree.Node.lookup n1 key st
+    Result.ret (st1, (o, betree.Internal.mk i i1 n n2))
 
-/- [betree_main::betree::{betree_main::betree::Node#5}::lookup]: forward function
+/- [betree_main::betree::{betree_main::betree::Node#5}::lookup]:
    Source: 'src/betree.rs', lines 709:4-709:58 -/
 divergent def betree.Node.lookup
   (self : betree.Node) (key : U64) (st : State) :
-  Result (State × (Option U64))
+  Result (State × ((Option U64) × betree.Node))
   :=
   match self with
   | betree.Node.Internal node =>
     do
-      let ⟨ i, i0, n, n0 ⟩ := node
-      let (st0, msgs) ← betree.load_internal_node i st
-      let pending ← betree.Node.lookup_first_message_for_key key msgs
-      match pending with
-      | betree.List.Cons p l =>
-        let (k, msg) := p
-        if k != key
-        then
-          do
-            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, o)
-        else
-          match msg with
-          | betree.Message.Insert v =>
-            do
-              let _ ←
-                betree.Node.lookup_first_message_for_key_back key msgs
-                  (betree.List.Cons (k, betree.Message.Insert v) l)
-              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, none)
-          | betree.Message.Upsert ufs =>
-            do
-              let (st1, v) ←
-                betree.Internal.lookup_in_children (betree.Internal.mk i i0 n
-                  n0) key st0
-              let (st2, v0) ←
-                betree.Node.apply_upserts (betree.List.Cons (k,
-                  betree.Message.Upsert ufs) l) v key st1
-              let node0 ←
-                betree.Internal.lookup_in_children_back (betree.Internal.mk i
-                  i0 n n0) key st0
-              let ⟨ i1, _, _, _ ⟩ := node0
-              let pending0 ←
-                betree.Node.apply_upserts_back (betree.List.Cons (k,
-                  betree.Message.Upsert ufs) l) v key st1
-              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, some v0)
-      | betree.List.Nil =>
+    let ⟨ i, i1, n, n1 ⟩ := node
+    let (st1, msgs) ← betree.load_internal_node i st
+    let (pending, lookup_first_message_for_key_back) ←
+      betree.Node.lookup_first_message_for_key key msgs
+    match pending with
+    | betree.List.Cons p l =>
+      let (k, msg) := p
+      if k != key
+      then
         do
-          let (st1, o) ←
-            betree.Internal.lookup_in_children (betree.Internal.mk i i0 n n0)
-              key st0
+        let (st2, (o, i2)) ←
+          betree.Internal.lookup_in_children (betree.Internal.mk i i1 n n1) key
+            st1
+        let _ ←
+          lookup_first_message_for_key_back (betree.List.Cons (k, msg) l)
+        Result.ret (st2, (o, betree.Node.Internal i2))
+      else
+        match msg with
+        | betree.Message.Insert v =>
+          do
           let _ ←
-            betree.Node.lookup_first_message_for_key_back key msgs
-              betree.List.Nil
-          Result.ret (st1, o)
-  | betree.Node.Leaf node =>
-    do
-      let (st0, bindings) ← betree.load_leaf_node node.id st
-      let o ← betree.Node.lookup_in_bindings key bindings
-      Result.ret (st0, o)
-
-/- [betree_main::betree::{betree_main::betree::Node#5}::lookup]: backward function 0
-   Source: 'src/betree.rs', lines 709:4-709:58 -/
-divergent def betree.Node.lookup_back
-  (self : betree.Node) (key : U64) (st : State) : Result betree.Node :=
-  match self with
-  | betree.Node.Internal node =>
-    do
-      let ⟨ i, i0, n, n0 ⟩ := node
-      let (st0, msgs) ← betree.load_internal_node i st
-      let pending ← betree.Node.lookup_first_message_for_key key msgs
-      match pending with
-      | betree.List.Cons p l =>
-        let (k, msg) := p
-        if k != key
-        then
+            lookup_first_message_for_key_back (betree.List.Cons (k,
+              betree.Message.Insert v) l)
+          Result.ret (st1, (some v, betree.Node.Internal (betree.Internal.mk i
+            i1 n n1)))
+        | betree.Message.Delete =>
           do
-            let _ ←
-              betree.Node.lookup_first_message_for_key_back key msgs
-                (betree.List.Cons (k, msg) l)
-            let node0 ←
-              betree.Internal.lookup_in_children_back (betree.Internal.mk i i0
-                n n0) key st0
-            Result.ret (betree.Node.Internal node0)
-        else
-          match msg with
-          | betree.Message.Insert v =>
-            do
-              let _ ←
-                betree.Node.lookup_first_message_for_key_back key msgs
-                  (betree.List.Cons (k, betree.Message.Insert v) l)
-              Result.ret (betree.Node.Internal (betree.Internal.mk i i0 n n0))
-          | 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 (betree.Node.Internal (betree.Internal.mk i i0 n n0))
-          | betree.Message.Upsert ufs =>
-            do
-              let (st1, v) ←
-                betree.Internal.lookup_in_children (betree.Internal.mk i i0 n
-                  n0) key st0
-              let (st2, _) ←
-                betree.Node.apply_upserts (betree.List.Cons (k,
-                  betree.Message.Upsert ufs) l) v key st1
-              let node0 ←
-                betree.Internal.lookup_in_children_back (betree.Internal.mk i
-                  i0 n n0) key st0
-              let ⟨ i1, i2, n1, n2 ⟩ := node0
-              let pending0 ←
-                betree.Node.apply_upserts_back (betree.List.Cons (k,
-                  betree.Message.Upsert ufs) l) v key st1
-              let msgs0 ←
-                betree.Node.lookup_first_message_for_key_back key msgs pending0
-              let _ ← betree.store_internal_node i1 msgs0 st2
-              Result.ret (betree.Node.Internal (betree.Internal.mk i1 i2 n1
-                n2))
-      | betree.List.Nil =>
-        do
           let _ ←
-            betree.Node.lookup_first_message_for_key_back key msgs
-              betree.List.Nil
-          let node0 ←
-            betree.Internal.lookup_in_children_back (betree.Internal.mk i i0 n
-              n0) key st0
-          Result.ret (betree.Node.Internal node0)
+            lookup_first_message_for_key_back (betree.List.Cons (k,
+              betree.Message.Delete) l)
+          Result.ret (st1, (none, betree.Node.Internal (betree.Internal.mk i i1
+            n n1)))
+        | betree.Message.Upsert ufs =>
+          do
+          let (st2, (v, i2)) ←
+            betree.Internal.lookup_in_children (betree.Internal.mk i i1 n n1)
+              key st1
+          let (st3, (v1, l1)) ←
+            betree.Node.apply_upserts (betree.List.Cons (k,
+              betree.Message.Upsert ufs) l) v key st2
+          let ⟨ i3, i4, n2, n3 ⟩ := i2
+          let msgs1 ← lookup_first_message_for_key_back l1
+          let (st4, _) ← betree.store_internal_node i3 msgs1 st3
+          Result.ret (st4, (some v1, betree.Node.Internal (betree.Internal.mk
+            i3 i4 n2 n3)))
+    | betree.List.Nil =>
+      do
+      let (st2, (o, i2)) ←
+        betree.Internal.lookup_in_children (betree.Internal.mk i i1 n n1) key
+          st1
+      let _ ← lookup_first_message_for_key_back betree.List.Nil
+      Result.ret (st2, (o, betree.Node.Internal i2))
   | betree.Node.Leaf node =>
     do
-      let (_, bindings) ← betree.load_leaf_node node.id st
-      let _ ← betree.Node.lookup_in_bindings key bindings
-      Result.ret (betree.Node.Leaf node)
+    let (st1, bindings) ← betree.load_leaf_node node.id st
+    let o ← betree.Node.lookup_in_bindings key bindings
+    Result.ret (st1, (o, betree.Node.Leaf node))
 
 end
 
-/- [betree_main::betree::{betree_main::betree::Node#5}::filter_messages_for_key]: merged forward/backward function
-   (there is a single backward function, and the forward function returns ())
+/- [betree_main::betree::{betree_main::betree::Node#5}::filter_messages_for_key]:
    Source: 'src/betree.rs', lines 674:4-674:77 -/
 divergent def betree.Node.filter_messages_for_key
   (key : U64) (msgs : betree.List (U64 × betree.Message)) :
@@ -517,33 +346,19 @@ divergent def betree.Node.filter_messages_for_key
     if k = key
     then
       do
-        let msgs0 ←
-          betree.List.pop_front_back (U64 × betree.Message) (betree.List.Cons
-            (k, m) l)
-        betree.Node.filter_messages_for_key key msgs0
+      let (_, l1) ←
+        betree.List.pop_front (U64 × betree.Message) (betree.List.Cons (k, m)
+          l)
+      betree.Node.filter_messages_for_key key l1
     else Result.ret (betree.List.Cons (k, m) l)
   | betree.List.Nil => Result.ret betree.List.Nil
 
-/- [betree_main::betree::{betree_main::betree::Node#5}::lookup_first_message_after_key]: forward function
+/- [betree_main::betree::{betree_main::betree::Node#5}::lookup_first_message_after_key]:
    Source: 'src/betree.rs', lines 689:4-692:34 -/
 divergent def betree.Node.lookup_first_message_after_key
   (key : U64) (msgs : betree.List (U64 × betree.Message)) :
-  Result (betree.List (U64 × betree.Message))
-  :=
-  match msgs with
-  | betree.List.Cons p next_msgs =>
-    let (k, m) := p
-    if k = key
-    then betree.Node.lookup_first_message_after_key key next_msgs
-    else Result.ret (betree.List.Cons (k, m) next_msgs)
-  | betree.List.Nil => Result.ret betree.List.Nil
-
-/- [betree_main::betree::{betree_main::betree::Node#5}::lookup_first_message_after_key]: backward function 0
-   Source: 'src/betree.rs', lines 689:4-692:34 -/
-divergent def betree.Node.lookup_first_message_after_key_back
-  (key : U64) (msgs : betree.List (U64 × betree.Message))
-  (ret : betree.List (U64 × betree.Message)) :
-  Result (betree.List (U64 × betree.Message))
+  Result ((betree.List (U64 × betree.Message)) × (betree.List (U64 ×
+    betree.Message) → Result (betree.List (U64 × betree.Message))))
   :=
   match msgs with
   | betree.List.Cons p next_msgs =>
@@ -551,14 +366,18 @@ divergent def betree.Node.lookup_first_message_after_key_back
     if k = key
     then
       do
-        let next_msgs0 ←
-          betree.Node.lookup_first_message_after_key_back key next_msgs ret
-        Result.ret (betree.List.Cons (k, m) next_msgs0)
-    else Result.ret ret
-  | betree.List.Nil => Result.ret ret
+      let (l, lookup_first_message_after_key_back) ←
+        betree.Node.lookup_first_message_after_key key next_msgs
+      let back_'a :=
+        fun ret =>
+          do
+          let next_msgs1 ← lookup_first_message_after_key_back ret
+          Result.ret (betree.List.Cons (k, m) next_msgs1)
+      Result.ret (l, back_'a)
+    else Result.ret (betree.List.Cons (k, m) next_msgs, Result.ret)
+  | betree.List.Nil => Result.ret (betree.List.Nil, Result.ret)
 
-/- [betree_main::betree::{betree_main::betree::Node#5}::apply_to_internal]: merged forward/backward function
-   (there is a single backward function, and the forward function returns ())
+/- [betree_main::betree::{betree_main::betree::Node#5}::apply_to_internal]:
    Source: 'src/betree.rs', lines 521:4-521:89 -/
 def betree.Node.apply_to_internal
   (msgs : betree.List (U64 × betree.Message)) (key : U64)
@@ -566,66 +385,63 @@ def betree.Node.apply_to_internal
   Result (betree.List (U64 × betree.Message))
   :=
   do
-    let msgs0 ← betree.Node.lookup_first_message_for_key key msgs
-    let b ← betree.ListTupleU64T.head_has_key betree.Message msgs0 key
-    if b
-    then
-      match new_msg with
-      | betree.Message.Insert i =>
+  let (msgs1, lookup_first_message_for_key_back) ←
+    betree.Node.lookup_first_message_for_key key msgs
+  let b ← betree.ListTupleU64T.head_has_key betree.Message msgs1 key
+  if b
+  then
+    match new_msg with
+    | betree.Message.Insert i =>
+      do
+      let l ← betree.Node.filter_messages_for_key key msgs1
+      let l1 ←
+        betree.List.push_front (U64 × betree.Message) l (key,
+          betree.Message.Insert i)
+      lookup_first_message_for_key_back l1
+    | betree.Message.Delete =>
+      do
+      let l ← betree.Node.filter_messages_for_key key msgs1
+      let l1 ←
+        betree.List.push_front (U64 × betree.Message) l (key,
+          betree.Message.Delete)
+      lookup_first_message_for_key_back l1
+    | betree.Message.Upsert s =>
+      do
+      let p ← betree.List.hd (U64 × betree.Message) msgs1
+      let (_, m) := p
+      match m with
+      | betree.Message.Insert prev =>
         do
-          let msgs1 ← betree.Node.filter_messages_for_key key msgs0
-          let msgs2 ←
-            betree.List.push_front (U64 × betree.Message) msgs1 (key,
-              betree.Message.Insert i)
-          betree.Node.lookup_first_message_for_key_back key msgs msgs2
+        let v ← betree.upsert_update (some prev) s
+        let (_, l) ← betree.List.pop_front (U64 × betree.Message) msgs1
+        let l1 ←
+          betree.List.push_front (U64 × betree.Message) l (key,
+            betree.Message.Insert v)
+        lookup_first_message_for_key_back l1
       | betree.Message.Delete =>
         do
-          let msgs1 ← betree.Node.filter_messages_for_key key msgs0
-          let msgs2 ←
-            betree.List.push_front (U64 × betree.Message) msgs1 (key,
-              betree.Message.Delete)
-          betree.Node.lookup_first_message_for_key_back key msgs msgs2
-      | betree.Message.Upsert s =>
+        let (_, l) ← betree.List.pop_front (U64 × betree.Message) msgs1
+        let v ← betree.upsert_update none s
+        let l1 ←
+          betree.List.push_front (U64 × betree.Message) l (key,
+            betree.Message.Insert v)
+        lookup_first_message_for_key_back l1
+      | betree.Message.Upsert _ =>
         do
-          let p ← betree.List.hd (U64 × betree.Message) msgs0
-          let (_, m) := p
-          match m with
-          | betree.Message.Insert prev =>
-            do
-              let v ← betree.upsert_update (some prev) s
-              let msgs1 ←
-                betree.List.pop_front_back (U64 × betree.Message) msgs0
-              let msgs2 ←
-                betree.List.push_front (U64 × betree.Message) msgs1 (key,
-                  betree.Message.Insert v)
-              betree.Node.lookup_first_message_for_key_back key msgs msgs2
-          | betree.Message.Delete =>
-            do
-              let v ← betree.upsert_update none s
-              let msgs1 ←
-                betree.List.pop_front_back (U64 × betree.Message) msgs0
-              let msgs2 ←
-                betree.List.push_front (U64 × betree.Message) msgs1 (key,
-                  betree.Message.Insert v)
-              betree.Node.lookup_first_message_for_key_back key msgs msgs2
-          | betree.Message.Upsert ufs =>
-            do
-              let msgs1 ←
-                betree.Node.lookup_first_message_after_key key msgs0
-              let msgs2 ←
-                betree.List.push_front (U64 × betree.Message) msgs1 (key,
-                  betree.Message.Upsert s)
-              let msgs3 ←
-                betree.Node.lookup_first_message_after_key_back key msgs0 msgs2
-              betree.Node.lookup_first_message_for_key_back key msgs msgs3
-    else
-      do
-        let msgs1 ←
-          betree.List.push_front (U64 × betree.Message) msgs0 (key, new_msg)
-        betree.Node.lookup_first_message_for_key_back key msgs msgs1
+        let (msgs2, lookup_first_message_after_key_back) ←
+          betree.Node.lookup_first_message_after_key key msgs1
+        let l ←
+          betree.List.push_front (U64 × betree.Message) msgs2 (key,
+            betree.Message.Upsert s)
+        let msgs3 ← lookup_first_message_after_key_back l
+        lookup_first_message_for_key_back msgs3
+  else
+    do
+    let l ←
+      betree.List.push_front (U64 × betree.Message) msgs1 (key, new_msg)
+    lookup_first_message_for_key_back l
 
-/- [betree_main::betree::{betree_main::betree::Node#5}::apply_messages_to_internal]: merged forward/backward function
-   (there is a single backward function, and the forward function returns ())
+/- [betree_main::betree::{betree_main::betree::Node#5}::apply_messages_to_internal]:
    Source: 'src/betree.rs', lines 502:4-505:5 -/
 divergent def betree.Node.apply_messages_to_internal
   (msgs : betree.List (U64 × betree.Message))
@@ -635,45 +451,36 @@ divergent def betree.Node.apply_messages_to_internal
   match new_msgs with
   | betree.List.Cons new_msg new_msgs_tl =>
     do
-      let (i, m) := new_msg
-      let msgs0 ← betree.Node.apply_to_internal msgs i m
-      betree.Node.apply_messages_to_internal msgs0 new_msgs_tl
+    let (i, m) := new_msg
+    let l ← betree.Node.apply_to_internal msgs i m
+    betree.Node.apply_messages_to_internal l new_msgs_tl
   | betree.List.Nil => Result.ret msgs
 
-/- [betree_main::betree::{betree_main::betree::Node#5}::lookup_mut_in_bindings]: forward function
+/- [betree_main::betree::{betree_main::betree::Node#5}::lookup_mut_in_bindings]:
    Source: 'src/betree.rs', lines 653:4-656:32 -/
 divergent def betree.Node.lookup_mut_in_bindings
   (key : U64) (bindings : betree.List (U64 × U64)) :
-  Result (betree.List (U64 × U64))
-  :=
-  match bindings with
-  | betree.List.Cons hd tl =>
-    let (i, i0) := hd
-    if i >= key
-    then Result.ret (betree.List.Cons (i, i0) tl)
-    else betree.Node.lookup_mut_in_bindings key tl
-  | betree.List.Nil => Result.ret betree.List.Nil
-
-/- [betree_main::betree::{betree_main::betree::Node#5}::lookup_mut_in_bindings]: backward function 0
-   Source: 'src/betree.rs', lines 653:4-656:32 -/
-divergent def betree.Node.lookup_mut_in_bindings_back
-  (key : U64) (bindings : betree.List (U64 × U64))
-  (ret : betree.List (U64 × U64)) :
-  Result (betree.List (U64 × U64))
+  Result ((betree.List (U64 × U64)) × (betree.List (U64 × U64) → Result
+    (betree.List (U64 × U64))))
   :=
   match bindings with
   | betree.List.Cons hd tl =>
-    let (i, i0) := hd
+    let (i, i1) := hd
     if i >= key
-    then Result.ret ret
+    then Result.ret (betree.List.Cons (i, i1) tl, Result.ret)
     else
       do
-        let tl0 ← betree.Node.lookup_mut_in_bindings_back key tl ret
-        Result.ret (betree.List.Cons (i, i0) tl0)
-  | betree.List.Nil => Result.ret ret
+      let (l, lookup_mut_in_bindings_back) ←
+        betree.Node.lookup_mut_in_bindings key tl
+      let back_'a :=
+        fun ret =>
+          do
+          let tl1 ← lookup_mut_in_bindings_back ret
+          Result.ret (betree.List.Cons (i, i1) tl1)
+      Result.ret (l, back_'a)
+  | betree.List.Nil => Result.ret (betree.List.Nil, Result.ret)
 
-/- [betree_main::betree::{betree_main::betree::Node#5}::apply_to_leaf]: merged forward/backward function
-   (there is a single backward function, and the forward function returns ())
+/- [betree_main::betree::{betree_main::betree::Node#5}::apply_to_leaf]:
    Source: 'src/betree.rs', lines 460:4-460:87 -/
 def betree.Node.apply_to_leaf
   (bindings : betree.List (U64 × U64)) (key : U64) (new_msg : betree.Message)
@@ -681,49 +488,39 @@ def betree.Node.apply_to_leaf
   Result (betree.List (U64 × U64))
   :=
   do
-    let bindings0 ← betree.Node.lookup_mut_in_bindings key bindings
-    let b ← betree.ListTupleU64T.head_has_key U64 bindings0 key
-    if b
-    then
+  let (bindings1, lookup_mut_in_bindings_back) ←
+    betree.Node.lookup_mut_in_bindings key bindings
+  let b ← betree.ListTupleU64T.head_has_key U64 bindings1 key
+  if b
+  then
+    do
+    let (hd, l) ← betree.List.pop_front (U64 × U64) bindings1
+    match new_msg with
+    | betree.Message.Insert v =>
       do
-        let hd ← betree.List.pop_front (U64 × U64) bindings0
-        match new_msg with
-        | betree.Message.Insert v =>
-          do
-            let bindings1 ← betree.List.pop_front_back (U64 × U64) bindings0
-            let bindings2 ←
-              betree.List.push_front (U64 × U64) bindings1 (key, v)
-            betree.Node.lookup_mut_in_bindings_back key bindings bindings2
-        | betree.Message.Delete =>
-          do
-            let bindings1 ← betree.List.pop_front_back (U64 × U64) bindings0
-            betree.Node.lookup_mut_in_bindings_back key bindings bindings1
-        | betree.Message.Upsert s =>
-          do
-            let (_, i) := hd
-            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)
-            betree.Node.lookup_mut_in_bindings_back key bindings bindings2
-    else
-      match new_msg with
-      | betree.Message.Insert v =>
-        do
-          let bindings1 ←
-            betree.List.push_front (U64 × U64) bindings0 (key, v)
-          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 =>
-        do
-          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
+      let l1 ← betree.List.push_front (U64 × U64) l (key, v)
+      lookup_mut_in_bindings_back l1
+    | betree.Message.Delete => lookup_mut_in_bindings_back l
+    | betree.Message.Upsert s =>
+      do
+      let (_, i) := hd
+      let v ← betree.upsert_update (some i) s
+      let l1 ← betree.List.push_front (U64 × U64) l (key, v)
+      lookup_mut_in_bindings_back l1
+  else
+    match new_msg with
+    | betree.Message.Insert v =>
+      do
+      let l ← betree.List.push_front (U64 × U64) bindings1 (key, v)
+      lookup_mut_in_bindings_back l
+    | betree.Message.Delete => lookup_mut_in_bindings_back bindings1
+    | betree.Message.Upsert s =>
+      do
+      let v ← betree.upsert_update none s
+      let l ← betree.List.push_front (U64 × U64) bindings1 (key, v)
+      lookup_mut_in_bindings_back l
 
-/- [betree_main::betree::{betree_main::betree::Node#5}::apply_messages_to_leaf]: merged forward/backward function
-   (there is a single backward function, and the forward function returns ())
+/- [betree_main::betree::{betree_main::betree::Node#5}::apply_messages_to_leaf]:
    Source: 'src/betree.rs', lines 444:4-447:5 -/
 divergent def betree.Node.apply_messages_to_leaf
   (bindings : betree.List (U64 × U64))
@@ -733,337 +530,182 @@ divergent def betree.Node.apply_messages_to_leaf
   match new_msgs with
   | betree.List.Cons new_msg new_msgs_tl =>
     do
-      let (i, m) := new_msg
-      let bindings0 ← betree.Node.apply_to_leaf bindings i m
-      betree.Node.apply_messages_to_leaf bindings0 new_msgs_tl
+    let (i, m) := new_msg
+    let l ← betree.Node.apply_to_leaf bindings i m
+    betree.Node.apply_messages_to_leaf l new_msgs_tl
   | betree.List.Nil => Result.ret bindings
 
-/- [betree_main::betree::{betree_main::betree::Internal#4}::flush]: forward function
+/- [betree_main::betree::{betree_main::betree::Internal#4}::flush]:
    Source: 'src/betree.rs', lines 410:4-415:26 -/
 mutual divergent def betree.Internal.flush
   (self : betree.Internal) (params : betree.Params)
   (node_id_cnt : betree.NodeIdCounter)
   (content : betree.List (U64 × betree.Message)) (st : State) :
-  Result (State × (betree.List (U64 × betree.Message)))
+  Result (State × ((betree.List (U64 × betree.Message)) × (betree.Internal
+    × betree.NodeIdCounter)))
   :=
   do
-    let ⟨ _, i, n, n0 ⟩ := self
-    let p ← betree.ListTupleU64T.partition_at_pivot betree.Message content i
-    let (msgs_left, msgs_right) := p
-    let len_left ← betree.List.len (U64 × betree.Message) msgs_left
-    if len_left >= params.min_flush_size
+  let ⟨ i, i1, n, n1 ⟩ := self
+  let p ← betree.ListTupleU64T.partition_at_pivot betree.Message content i1
+  let (msgs_left, msgs_right) := p
+  let len_left ← betree.List.len (U64 × betree.Message) msgs_left
+  if len_left >= params.min_flush_size
+  then
+    do
+    let (st1, p1) ←
+      betree.Node.apply_messages n params node_id_cnt msgs_left st
+    let (n2, node_id_cnt1) := p1
+    let len_right ← betree.List.len (U64 × betree.Message) msgs_right
+    if len_right >= params.min_flush_size
     then
       do
-        let (st0, _) ←
-          betree.Node.apply_messages n params node_id_cnt msgs_left st
-        let (_, node_id_cnt0) ←
-          betree.Node.apply_messages_back n params node_id_cnt msgs_left st
-        let len_right ← betree.List.len (U64 × betree.Message) msgs_right
-        if len_right >= params.min_flush_size
-        then
-          do
-            let (st1, _) ←
-              betree.Node.apply_messages n0 params node_id_cnt0 msgs_right st0
-            let _ ←
-              betree.Node.apply_messages_back n0 params node_id_cnt0 msgs_right
-                st0
-            Result.ret (st1, betree.List.Nil)
-        else Result.ret (st0, msgs_right)
+      let (st2, p2) ←
+        betree.Node.apply_messages n1 params node_id_cnt1 msgs_right st1
+      let (n3, node_id_cnt2) := p2
+      Result.ret (st2, (betree.List.Nil, (betree.Internal.mk i i1 n2 n3,
+        node_id_cnt2)))
     else
-      do
-        let (st0, _) ←
-          betree.Node.apply_messages n0 params node_id_cnt msgs_right st
-        let _ ←
-          betree.Node.apply_messages_back n0 params node_id_cnt msgs_right st
-        Result.ret (st0, msgs_left)
-
-/- [betree_main::betree::{betree_main::betree::Internal#4}::flush]: backward function 0
-   Source: 'src/betree.rs', lines 410:4-415:26 -/
-divergent def betree.Internal.flush_back
-  (self : betree.Internal) (params : betree.Params)
-  (node_id_cnt : betree.NodeIdCounter)
-  (content : betree.List (U64 × betree.Message)) (st : State) :
-  Result (betree.Internal × betree.NodeIdCounter)
-  :=
-  do
-    let ⟨ i, i0, n, n0 ⟩ := self
-    let p ← betree.ListTupleU64T.partition_at_pivot betree.Message content i0
-    let (msgs_left, msgs_right) := p
-    let len_left ← betree.List.len (U64 × betree.Message) msgs_left
-    if len_left >= params.min_flush_size
-    then
-      do
-        let (st0, _) ←
-          betree.Node.apply_messages n params node_id_cnt msgs_left st
-        let (n1, node_id_cnt0) ←
-          betree.Node.apply_messages_back n params node_id_cnt msgs_left st
-        let len_right ← betree.List.len (U64 × betree.Message) msgs_right
-        if len_right >= params.min_flush_size
-        then
-          do
-            let (n2, node_id_cnt1) ←
-              betree.Node.apply_messages_back n0 params node_id_cnt0 msgs_right
-                st0
-            Result.ret (betree.Internal.mk i i0 n1 n2, node_id_cnt1)
-        else Result.ret (betree.Internal.mk i i0 n1 n0, node_id_cnt0)
-    else
-      do
-        let (n1, node_id_cnt0) ←
-          betree.Node.apply_messages_back n0 params node_id_cnt msgs_right st
-        Result.ret (betree.Internal.mk i i0 n n1, node_id_cnt0)
-
-/- [betree_main::betree::{betree_main::betree::Node#5}::apply_messages]: forward function
-   Source: 'src/betree.rs', lines 588:4-593:5 -/
-divergent def betree.Node.apply_messages
-  (self : betree.Node) (params : betree.Params)
-  (node_id_cnt : betree.NodeIdCounter)
-  (msgs : betree.List (U64 × betree.Message)) (st : State) :
-  Result (State × Unit)
-  :=
-  match self with
-  | betree.Node.Internal node =>
-    do
-      let ⟨ i, i0, n, n0 ⟩ := node
-      let (st0, content) ← betree.load_internal_node i st
-      let content0 ← betree.Node.apply_messages_to_internal content msgs
-      let num_msgs ← betree.List.len (U64 × betree.Message) content0
-      if num_msgs >= params.min_flush_size
-      then
-        do
-          let (st1, content1) ←
-            betree.Internal.flush (betree.Internal.mk i i0 n n0) params
-              node_id_cnt content0 st0
-          let (node0, _) ←
-            betree.Internal.flush_back (betree.Internal.mk i i0 n n0) params
-              node_id_cnt content0 st0
-          let ⟨ i1, _, _, _ ⟩ := node0
-          let (st2, _) ← betree.store_internal_node i1 content1 st1
-          Result.ret (st2, ())
-      else
-        do
-          let (st1, _) ← betree.store_internal_node i content0 st0
-          Result.ret (st1, ())
-  | betree.Node.Leaf node =>
+      Result.ret (st1, (msgs_right, (betree.Internal.mk i i1 n2 n1,
+        node_id_cnt1)))
+  else
     do
-      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 ← 2#u64 * params.split_size
-      if len >= i
-      then
-        do
-          let (st1, _) ←
-            betree.Leaf.split node content0 params node_id_cnt st0
-          let (st2, _) ← betree.store_leaf_node node.id betree.List.Nil st1
-          Result.ret (st2, ())
-      else
-        do
-          let (st1, _) ← betree.store_leaf_node node.id content0 st0
-          Result.ret (st1, ())
+    let (st1, p1) ←
+      betree.Node.apply_messages n1 params node_id_cnt msgs_right st
+    let (n2, node_id_cnt1) := p1
+    Result.ret (st1, (msgs_left, (betree.Internal.mk i i1 n n2, node_id_cnt1)))
 
-/- [betree_main::betree::{betree_main::betree::Node#5}::apply_messages]: backward function 0
+/- [betree_main::betree::{betree_main::betree::Node#5}::apply_messages]:
    Source: 'src/betree.rs', lines 588:4-593:5 -/
-divergent def betree.Node.apply_messages_back
+divergent def betree.Node.apply_messages
   (self : betree.Node) (params : betree.Params)
   (node_id_cnt : betree.NodeIdCounter)
   (msgs : betree.List (U64 × betree.Message)) (st : State) :
-  Result (betree.Node × betree.NodeIdCounter)
+  Result (State × (betree.Node × betree.NodeIdCounter))
   :=
   match self with
   | betree.Node.Internal node =>
     do
-      let ⟨ i, i0, n, n0 ⟩ := node
-      let (st0, content) ← betree.load_internal_node i st
-      let content0 ← betree.Node.apply_messages_to_internal content msgs
-      let num_msgs ← betree.List.len (U64 × betree.Message) content0
-      if num_msgs >= params.min_flush_size
-      then
-        do
-          let (st1, content1) ←
-            betree.Internal.flush (betree.Internal.mk i i0 n n0) params
-              node_id_cnt content0 st0
-          let (node0, node_id_cnt0) ←
-            betree.Internal.flush_back (betree.Internal.mk i i0 n n0) params
-              node_id_cnt content0 st0
-          let ⟨ i1, i2, n1, n2 ⟩ := node0
-          let _ ← betree.store_internal_node i1 content1 st1
-          Result.ret (betree.Node.Internal (betree.Internal.mk i1 i2 n1 n2),
-            node_id_cnt0)
-      else
-        do
-          let _ ← betree.store_internal_node i content0 st0
-          Result.ret (betree.Node.Internal (betree.Internal.mk i i0 n n0),
-            node_id_cnt)
+    let ⟨ i, i1, n, n1 ⟩ := node
+    let (st1, content) ← betree.load_internal_node i st
+    let l ← betree.Node.apply_messages_to_internal content msgs
+    let num_msgs ← betree.List.len (U64 × betree.Message) l
+    if num_msgs >= params.min_flush_size
+    then
+      do
+      let (st2, (content1, p)) ←
+        betree.Internal.flush (betree.Internal.mk i i1 n n1) params node_id_cnt
+          l st1
+      let (node1, node_id_cnt1) := p
+      let ⟨ i2, i3, n2, n3 ⟩ := node1
+      let (st3, _) ← betree.store_internal_node i2 content1 st2
+      Result.ret (st3, (betree.Node.Internal (betree.Internal.mk i2 i3 n2 n3),
+        node_id_cnt1))
+    else
+      do
+      let (st2, _) ← betree.store_internal_node i l st1
+      Result.ret (st2, (betree.Node.Internal (betree.Internal.mk i i1 n n1),
+        node_id_cnt))
   | betree.Node.Leaf node =>
     do
-      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 ← 2#u64 * params.split_size
-      if len >= i
-      then
-        do
-          let (st1, new_node) ←
-            betree.Leaf.split node content0 params node_id_cnt st0
-          let _ ← betree.store_leaf_node node.id betree.List.Nil st1
-          let node_id_cnt0 ←
-            betree.Leaf.split_back node content0 params node_id_cnt st0
-          Result.ret (betree.Node.Internal new_node, node_id_cnt0)
-      else
-        do
-          let _ ← betree.store_leaf_node node.id content0 st0
-          Result.ret (betree.Node.Leaf { node with size := len }, node_id_cnt)
+    let (st1, content) ← betree.load_leaf_node node.id st
+    let l ← betree.Node.apply_messages_to_leaf content msgs
+    let len ← betree.List.len (U64 × U64) l
+    let i ← 2#u64 * params.split_size
+    if len >= i
+    then
+      do
+      let (st2, (new_node, nic)) ←
+        betree.Leaf.split node l params node_id_cnt st1
+      let (st3, _) ← betree.store_leaf_node node.id betree.List.Nil st2
+      Result.ret (st3, (betree.Node.Internal new_node, nic))
+    else
+      do
+      let (st2, _) ← betree.store_leaf_node node.id l st1
+      Result.ret (st2, (betree.Node.Leaf { node with size := len },
+        node_id_cnt))
 
 end
 
-/- [betree_main::betree::{betree_main::betree::Node#5}::apply]: forward function
+/- [betree_main::betree::{betree_main::betree::Node#5}::apply]:
    Source: 'src/betree.rs', lines 576:4-582:5 -/
 def betree.Node.apply
   (self : betree.Node) (params : betree.Params)
   (node_id_cnt : betree.NodeIdCounter) (key : U64) (new_msg : betree.Message)
   (st : State) :
-  Result (State × Unit)
+  Result (State × (betree.Node × betree.NodeIdCounter))
   :=
   do
-    let l := betree.List.Nil
-    let (st0, _) ←
-      betree.Node.apply_messages self params node_id_cnt (betree.List.Cons
-        (key, new_msg) l) st
-    let _ ←
-      betree.Node.apply_messages_back self params node_id_cnt (betree.List.Cons
-        (key, new_msg) l) st
-    Result.ret (st0, ())
+  let (st1, p) ←
+    betree.Node.apply_messages self params node_id_cnt (betree.List.Cons (key,
+      new_msg) betree.List.Nil) st
+  let (self1, node_id_cnt1) := p
+  Result.ret (st1, (self1, node_id_cnt1))
 
-/- [betree_main::betree::{betree_main::betree::Node#5}::apply]: backward function 0
-   Source: 'src/betree.rs', lines 576:4-582:5 -/
-def betree.Node.apply_back
-  (self : betree.Node) (params : betree.Params)
-  (node_id_cnt : betree.NodeIdCounter) (key : U64) (new_msg : betree.Message)
-  (st : State) :
-  Result (betree.Node × betree.NodeIdCounter)
-  :=
-  let l := betree.List.Nil
-  betree.Node.apply_messages_back self params node_id_cnt (betree.List.Cons
-    (key, new_msg) l) st
-
-/- [betree_main::betree::{betree_main::betree::BeTree#6}::new]: forward function
+/- [betree_main::betree::{betree_main::betree::BeTree#6}::new]:
    Source: 'src/betree.rs', lines 849:4-849:60 -/
 def betree.BeTree.new
   (min_flush_size : U64) (split_size : U64) (st : State) :
   Result (State × betree.BeTree)
   :=
   do
-    let node_id_cnt ← betree.NodeIdCounter.new
-    let id ← betree.NodeIdCounter.fresh_id node_id_cnt
-    let (st0, _) ← betree.store_leaf_node id betree.List.Nil st
-    let node_id_cnt0 ← betree.NodeIdCounter.fresh_id_back node_id_cnt
-    Result.ret (st0,
-      {
-        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#u64 })
-      })
-
-/- [betree_main::betree::{betree_main::betree::BeTree#6}::apply]: forward function
+  let node_id_cnt ← betree.NodeIdCounter.new
+  let (id, nic) ← betree.NodeIdCounter.fresh_id node_id_cnt
+  let (st1, _) ← betree.store_leaf_node id betree.List.Nil st
+  Result.ret (st1,
+    {
+      params := { min_flush_size := min_flush_size, split_size := split_size },
+      node_id_cnt := nic,
+      root := (betree.Node.Leaf { id := id, size := 0#u64 })
+    })
+
+/- [betree_main::betree::{betree_main::betree::BeTree#6}::apply]:
    Source: 'src/betree.rs', lines 868:4-868:47 -/
 def betree.BeTree.apply
   (self : betree.BeTree) (key : U64) (msg : betree.Message) (st : State) :
-  Result (State × Unit)
-  :=
-  do
-    let (st0, _) ←
-      betree.Node.apply self.root self.params self.node_id_cnt key msg st
-    let _ ←
-      betree.Node.apply_back self.root self.params self.node_id_cnt key msg st
-    Result.ret (st0, ())
-
-/- [betree_main::betree::{betree_main::betree::BeTree#6}::apply]: backward function 0
-   Source: 'src/betree.rs', lines 868:4-868:47 -/
-def betree.BeTree.apply_back
-  (self : betree.BeTree) (key : U64) (msg : betree.Message) (st : State) :
-  Result betree.BeTree
+  Result (State × betree.BeTree)
   :=
   do
-    let (n, nic) ←
-      betree.Node.apply_back self.root self.params self.node_id_cnt key msg st
-    Result.ret { self with node_id_cnt := nic, root := n }
+  let (st1, p) ←
+    betree.Node.apply self.root self.params self.node_id_cnt key msg st
+  let (n, nic) := p
+  Result.ret (st1, { self with node_id_cnt := nic, root := n })
 
-/- [betree_main::betree::{betree_main::betree::BeTree#6}::insert]: forward function
+/- [betree_main::betree::{betree_main::betree::BeTree#6}::insert]:
    Source: 'src/betree.rs', lines 874:4-874:52 -/
 def betree.BeTree.insert
   (self : betree.BeTree) (key : U64) (value : U64) (st : State) :
-  Result (State × Unit)
-  :=
-  do
-    let (st0, _) ←
-      betree.BeTree.apply self key (betree.Message.Insert value) st
-    let _ ←
-      betree.BeTree.apply_back self key (betree.Message.Insert value) st
-    Result.ret (st0, ())
-
-/- [betree_main::betree::{betree_main::betree::BeTree#6}::insert]: backward function 0
-   Source: 'src/betree.rs', lines 874:4-874:52 -/
-def betree.BeTree.insert_back
-  (self : betree.BeTree) (key : U64) (value : U64) (st : State) :
-  Result betree.BeTree
+  Result (State × betree.BeTree)
   :=
-  betree.BeTree.apply_back self key (betree.Message.Insert value) st
+  betree.BeTree.apply self key (betree.Message.Insert value) st
 
-/- [betree_main::betree::{betree_main::betree::BeTree#6}::delete]: forward function
+/- [betree_main::betree::{betree_main::betree::BeTree#6}::delete]:
    Source: 'src/betree.rs', lines 880:4-880:38 -/
 def betree.BeTree.delete
-  (self : betree.BeTree) (key : U64) (st : State) : Result (State × Unit) :=
-  do
-    let (st0, _) ← betree.BeTree.apply self key betree.Message.Delete st
-    let _ ← betree.BeTree.apply_back self key betree.Message.Delete st
-    Result.ret (st0, ())
-
-/- [betree_main::betree::{betree_main::betree::BeTree#6}::delete]: backward function 0
-   Source: 'src/betree.rs', lines 880:4-880:38 -/
-def betree.BeTree.delete_back
-  (self : betree.BeTree) (key : U64) (st : State) : Result betree.BeTree :=
-  betree.BeTree.apply_back self key betree.Message.Delete st
-
-/- [betree_main::betree::{betree_main::betree::BeTree#6}::upsert]: forward function
-   Source: 'src/betree.rs', lines 886:4-886:59 -/
-def betree.BeTree.upsert
-  (self : betree.BeTree) (key : U64) (upd : betree.UpsertFunState) (st : State)
-  :
-  Result (State × Unit)
+  (self : betree.BeTree) (key : U64) (st : State) :
+  Result (State × betree.BeTree)
   :=
-  do
-    let (st0, _) ←
-      betree.BeTree.apply self key (betree.Message.Upsert upd) st
-    let _ ← betree.BeTree.apply_back self key (betree.Message.Upsert upd) st
-    Result.ret (st0, ())
+  betree.BeTree.apply self key betree.Message.Delete st
 
-/- [betree_main::betree::{betree_main::betree::BeTree#6}::upsert]: backward function 0
+/- [betree_main::betree::{betree_main::betree::BeTree#6}::upsert]:
    Source: 'src/betree.rs', lines 886:4-886:59 -/
-def betree.BeTree.upsert_back
+def betree.BeTree.upsert
   (self : betree.BeTree) (key : U64) (upd : betree.UpsertFunState) (st : State)
   :
-  Result betree.BeTree
+  Result (State × betree.BeTree)
   :=
-  betree.BeTree.apply_back self key (betree.Message.Upsert upd) st
+  betree.BeTree.apply self key (betree.Message.Upsert upd) st
 
-/- [betree_main::betree::{betree_main::betree::BeTree#6}::lookup]: forward function
+/- [betree_main::betree::{betree_main::betree::BeTree#6}::lookup]:
    Source: 'src/betree.rs', lines 895:4-895:62 -/
 def betree.BeTree.lookup
   (self : betree.BeTree) (key : U64) (st : State) :
-  Result (State × (Option U64))
+  Result (State × ((Option U64) × betree.BeTree))
   :=
-  betree.Node.lookup self.root key st
-
-/- [betree_main::betree::{betree_main::betree::BeTree#6}::lookup]: backward function 0
-   Source: 'src/betree.rs', lines 895:4-895:62 -/
-def betree.BeTree.lookup_back
-  (self : betree.BeTree) (key : U64) (st : State) : Result betree.BeTree :=
   do
-    let n ← betree.Node.lookup_back self.root key st
-    Result.ret { self with root := n }
+  let (st1, (o, n)) ← betree.Node.lookup self.root key st
+  Result.ret (st1, (o, { self with root := n }))
 
-/- [betree_main::main]: forward function
+/- [betree_main::main]:
    Source: 'src/betree_main.rs', lines 5:0-5:9 -/
 def main : Result Unit :=
   Result.ret ()
diff --git a/tests/lean/BetreeMain/FunsExternal_Template.lean b/tests/lean/BetreeMain/FunsExternal_Template.lean
index 95f88873..eaa4b6c2 100644
--- a/tests/lean/BetreeMain/FunsExternal_Template.lean
+++ b/tests/lean/BetreeMain/FunsExternal_Template.lean
@@ -6,29 +6,29 @@ import BetreeMain.Types
 open Primitives
 open betree_main
 
-/- [betree_main::betree_utils::load_internal_node]: forward function
+/- [betree_main::betree_utils::load_internal_node]:
    Source: 'src/betree_utils.rs', lines 98:0-98:63 -/
 axiom betree_utils.load_internal_node
   : U64 → State → Result (State × (betree.List (U64 × betree.Message)))
 
-/- [betree_main::betree_utils::store_internal_node]: forward function
+/- [betree_main::betree_utils::store_internal_node]:
    Source: 'src/betree_utils.rs', lines 115:0-115:71 -/
 axiom betree_utils.store_internal_node
   :
   U64 → betree.List (U64 × betree.Message) → State → Result (State ×
     Unit)
 
-/- [betree_main::betree_utils::load_leaf_node]: forward function
+/- [betree_main::betree_utils::load_leaf_node]:
    Source: 'src/betree_utils.rs', lines 132:0-132:55 -/
 axiom betree_utils.load_leaf_node
   : U64 → State → Result (State × (betree.List (U64 × U64)))
 
-/- [betree_main::betree_utils::store_leaf_node]: forward function
+/- [betree_main::betree_utils::store_leaf_node]:
    Source: 'src/betree_utils.rs', lines 145:0-145:63 -/
 axiom betree_utils.store_leaf_node
   : U64 → betree.List (U64 × U64) → State → Result (State × Unit)
 
-/- [core::option::{core::option::Option<T>}::unwrap]: forward function
+/- [core::option::{core::option::Option<T>}::unwrap]:
    Source: '/rustc/d59363ad0b6391b7fc5bbb02c9ccf9300eef3753/library/core/src/option.rs', lines 932:4-932:34 -/
 axiom core.option.Option.unwrap
   (T : Type) : Option T → State → Result (State × T)
diff --git a/tests/lean/Bitwise.lean b/tests/lean/Bitwise.lean
index c8538aa2..7c47e3dd 100644
--- a/tests/lean/Bitwise.lean
+++ b/tests/lean/Bitwise.lean
@@ -5,31 +5,31 @@ open Primitives
 
 namespace bitwise
 
-/- [bitwise::shift_u32]: forward function
+/- [bitwise::shift_u32]:
    Source: 'src/bitwise.rs', lines 3:0-3:31 -/
 def shift_u32 (a : U32) : Result U32 :=
   do
-    let t ← a >>> 16#usize
-    t <<< 16#usize
+  let t ← a >>> 16#usize
+  t <<< 16#usize
 
-/- [bitwise::shift_i32]: forward function
+/- [bitwise::shift_i32]:
    Source: 'src/bitwise.rs', lines 10:0-10:31 -/
 def shift_i32 (a : I32) : Result I32 :=
   do
-    let t ← a >>> 16#isize
-    t <<< 16#isize
+  let t ← a >>> 16#isize
+  t <<< 16#isize
 
-/- [bitwise::xor_u32]: forward function
+/- [bitwise::xor_u32]:
    Source: 'src/bitwise.rs', lines 17:0-17:37 -/
 def xor_u32 (a : U32) (b : U32) : Result U32 :=
   Result.ret (a ^^^ b)
 
-/- [bitwise::or_u32]: forward function
+/- [bitwise::or_u32]:
    Source: 'src/bitwise.rs', lines 21:0-21:36 -/
 def or_u32 (a : U32) (b : U32) : Result U32 :=
   Result.ret (a ||| b)
 
-/- [bitwise::and_u32]: forward function
+/- [bitwise::and_u32]:
    Source: 'src/bitwise.rs', lines 25:0-25:37 -/
 def and_u32 (a : U32) (b : U32) : Result U32 :=
   Result.ret (a &&& b)
diff --git a/tests/lean/Constants.lean b/tests/lean/Constants.lean
index 80864427..2912805f 100644
--- a/tests/lean/Constants.lean
+++ b/tests/lean/Constants.lean
@@ -20,7 +20,7 @@ def x1_c : U32 := eval_global x1_body (by simp)
 def x2_body : Result U32 := Result.ret 3#u32
 def x2_c : U32 := eval_global x2_body (by simp)
 
-/- [constants::incr]: forward function
+/- [constants::incr]:
    Source: 'src/constants.rs', lines 17:0-17:32 -/
 def incr (n : U32) : Result U32 :=
   n + 1#u32
@@ -30,7 +30,7 @@ def incr (n : U32) : Result U32 :=
 def x3_body : Result U32 := incr 32#u32
 def x3_c : U32 := eval_global x3_body (by simp)
 
-/- [constants::mk_pair0]: forward function
+/- [constants::mk_pair0]:
    Source: 'src/constants.rs', lines 23:0-23:51 -/
 def mk_pair0 (x : U32) (y : U32) : Result (U32 × U32) :=
   Result.ret (x, y)
@@ -41,7 +41,7 @@ structure Pair (T1 T2 : Type) where
   x : T1
   y : T2
 
-/- [constants::mk_pair1]: forward function
+/- [constants::mk_pair1]:
    Source: 'src/constants.rs', lines 27:0-27:55 -/
 def mk_pair1 (x : U32) (y : U32) : Result (Pair U32 U32) :=
   Result.ret { x := x, y := y }
@@ -71,7 +71,7 @@ def p3_c : Pair U32 U32 := eval_global p3_body (by simp)
 structure Wrap (T : Type) where
   value : T
 
-/- [constants::{constants::Wrap<T>}::new]: forward function
+/- [constants::{constants::Wrap<T>}::new]:
    Source: 'src/constants.rs', lines 54:4-54:41 -/
 def Wrap.new (T : Type) (value : T) : Result (Wrap T) :=
   Result.ret { value := value }
@@ -81,7 +81,7 @@ def Wrap.new (T : Type) (value : T) : Result (Wrap T) :=
 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
+/- [constants::unwrap_y]:
    Source: 'src/constants.rs', lines 43:0-43:30 -/
 def unwrap_y : Result I32 :=
   Result.ret y_c.value
@@ -96,12 +96,12 @@ def yval_c : I32 := eval_global yval_body (by simp)
 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
+/- [constants::get_z1]:
    Source: 'src/constants.rs', lines 61:0-61:28 -/
 def get_z1 : Result I32 :=
   Result.ret get_z1_z1_c
 
-/- [constants::add]: forward function
+/- [constants::add]:
    Source: 'src/constants.rs', lines 66:0-66:39 -/
 def add (a : I32) (b : I32) : Result I32 :=
   a + b
@@ -121,13 +121,13 @@ def q2_c : I32 := eval_global q2_body (by simp)
 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
+/- [constants::get_z2]:
    Source: 'src/constants.rs', lines 70:0-70:28 -/
 def get_z2 : Result I32 :=
   do
-    let i ← get_z1
-    let i0 ← add i q3_c
-    add q1_c i0
+  let i ← get_z1
+  let i1 ← add i q3_c
+  add q1_c i1
 
 /- [constants::S1]
    Source: 'src/constants.rs', lines 80:0-80:18 -/
diff --git a/tests/lean/External/Funs.lean b/tests/lean/External/Funs.lean
index 48ec6ad5..db15aacc 100644
--- a/tests/lean/External/Funs.lean
+++ b/tests/lean/External/Funs.lean
@@ -7,92 +7,58 @@ open Primitives
 
 namespace external
 
-/- [external::swap]: forward function
+/- [external::swap]:
    Source: 'src/external.rs', lines 6:0-6:46 -/
-def swap (T : Type) (x : T) (y : T) (st : State) : Result (State × Unit) :=
-  do
-    let (st0, _) ← core.mem.swap T x y st
-    let (st1, _) ← core.mem.swap_back0 T x y st st0
-    let (st2, _) ← core.mem.swap_back1 T x y st st1
-    Result.ret (st2, ())
-
-/- [external::swap]: backward function 0
-   Source: 'src/external.rs', lines 6:0-6:46 -/
-def swap_back
-  (T : Type) (x : T) (y : T) (st : State) (st0 : State) :
-  Result (State × (T × T))
-  :=
-  do
-    let (st1, _) ← core.mem.swap T x y st
-    let (st2, x0) ← core.mem.swap_back0 T x y st st1
-    let (_, y0) ← core.mem.swap_back1 T x y st st2
-    Result.ret (st0, (x0, y0))
+def swap
+  (T : Type) (x : T) (y : T) (st : State) : Result (State × (T × T)) :=
+  core.mem.swap T x y st
 
-/- [external::test_new_non_zero_u32]: forward function
+/- [external::test_new_non_zero_u32]:
    Source: 'src/external.rs', lines 11:0-11:60 -/
 def test_new_non_zero_u32
   (x : U32) (st : State) : Result (State × core.num.nonzero.NonZeroU32) :=
   do
-    let (st0, o) ← core.num.nonzero.NonZeroU32.new x st
-    core.option.Option.unwrap core.num.nonzero.NonZeroU32 o st0
+  let (st1, o) ← core.num.nonzero.NonZeroU32.new x st
+  core.option.Option.unwrap core.num.nonzero.NonZeroU32 o st1
 
-/- [external::test_vec]: forward function
+/- [external::test_vec]:
    Source: 'src/external.rs', lines 17:0-17:17 -/
 def test_vec : Result Unit :=
   do
-    let v := alloc.vec.Vec.new U32
-    let _ ← alloc.vec.Vec.push U32 v 0#u32
-    Result.ret ()
+  let _ ← alloc.vec.Vec.push U32 (alloc.vec.Vec.new U32) 0#u32
+  Result.ret ()
 
 /- Unit test for [external::test_vec] -/
 #assert (test_vec == Result.ret ())
 
-/- [external::custom_swap]: forward function
+/- [external::custom_swap]:
    Source: 'src/external.rs', lines 24:0-24:66 -/
 def custom_swap
-  (T : Type) (x : T) (y : T) (st : State) : Result (State × T) :=
-  do
-    let (st0, _) ← core.mem.swap T x y st
-    let (st1, x0) ← core.mem.swap_back0 T x y st st0
-    let (st2, _) ← core.mem.swap_back1 T x y st st1
-    Result.ret (st2, x0)
-
-/- [external::custom_swap]: backward function 0
-   Source: 'src/external.rs', lines 24:0-24:66 -/
-def custom_swap_back
-  (T : Type) (x : T) (y : T) (st : State) (ret : T) (st0 : State) :
-  Result (State × (T × T))
+  (T : Type) (x : T) (y : T) (st : State) :
+  Result (State × (T × (T → State → Result (State × (T × T)))))
   :=
   do
-    let (st1, _) ← core.mem.swap T x y st
-    let (st2, _) ← core.mem.swap_back0 T x y st st1
-    let (_, y0) ← core.mem.swap_back1 T x y st st2
-    Result.ret (st0, (ret, y0))
+  let (st1, (t, t1)) ← core.mem.swap T x y st
+  let back_'a := fun ret st2 => Result.ret (st2, (ret, t1))
+  Result.ret (st1, (t, back_'a))
 
-/- [external::test_custom_swap]: forward function
+/- [external::test_custom_swap]:
    Source: 'src/external.rs', lines 29:0-29:59 -/
 def test_custom_swap
-  (x : U32) (y : U32) (st : State) : Result (State × Unit) :=
+  (x : U32) (y : U32) (st : State) : Result (State × (U32 × U32)) :=
   do
-    let (st0, _) ← custom_swap U32 x y st
-    Result.ret (st0, ())
-
-/- [external::test_custom_swap]: backward function 0
-   Source: 'src/external.rs', lines 29:0-29:59 -/
-def test_custom_swap_back
-  (x : U32) (y : U32) (st : State) (st0 : State) :
-  Result (State × (U32 × U32))
-  :=
-  custom_swap_back U32 x y st 1#u32 st0
+  let (st1, (_, custom_swap_back)) ← custom_swap U32 x y st
+  let (_, (x1, y1)) ← custom_swap_back 1#u32 st1
+  Result.ret (st1, (x1, y1))
 
-/- [external::test_swap_non_zero]: forward function
+/- [external::test_swap_non_zero]:
    Source: 'src/external.rs', lines 35:0-35:44 -/
 def test_swap_non_zero (x : U32) (st : State) : Result (State × U32) :=
   do
-    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 .panic
-    else Result.ret (st1, x0)
+  let (st1, p) ← swap U32 x 0#u32 st
+  let (x1, _) := p
+  if x1 = 0#u32
+  then Result.fail .panic
+  else Result.ret (st1, x1)
 
 end external
diff --git a/tests/lean/External/FunsExternal.lean b/tests/lean/External/FunsExternal.lean
index aae11ba1..63830abc 100644
--- a/tests/lean/External/FunsExternal.lean
+++ b/tests/lean/External/FunsExternal.lean
@@ -8,22 +8,11 @@ open external
 
 /- [core::mem::swap] -/
 def core.mem.swap
-  (T : Type) : T → T → State → Result (State × Unit) :=
-  fun _x _y s => .ret (s, ())
-
-/- [core::mem::swap] -/
-def core.mem.swap_back0
-  (T : Type) : T → T → State → State → Result (State × T) :=
-  fun _x y _s0 s1 => .ret (s1, y)
-
-/- [core::mem::swap] -/
-def core.mem.swap_back1
-  (T : Type) : T → T → State → State → Result (State × T) :=
-  fun x _y _s0 s1 => .ret (s1, x)
+  (T : Type) : T → T → State → Result (State × (T × T)) :=
+  fun x y s => .ret (s, (y, x))
 
 /- [core::num::nonzero::NonZeroU32::{14}::new] -/
-def core.num.nonzero.NonZeroU32.new
-  :
+def core.num.nonzero.NonZeroU32.new :
   U32 → State → Result (State × (Option core_num_nonzero_non_zero_u32_t)) :=
   fun _ _ => .fail .panic
 
diff --git a/tests/lean/External/FunsExternal_Template.lean b/tests/lean/External/FunsExternal_Template.lean
index 55cd6bb5..7e237369 100644
--- a/tests/lean/External/FunsExternal_Template.lean
+++ b/tests/lean/External/FunsExternal_Template.lean
@@ -6,26 +6,17 @@ import External.Types
 open Primitives
 open external
 
-/- [core::mem::swap]: forward function
+/- [core::mem::swap]:
    Source: '/rustc/d59363ad0b6391b7fc5bbb02c9ccf9300eef3753/library/core/src/mem/mod.rs', lines 726:0-726:42 -/
-axiom core.mem.swap (T : Type) : T → T → State → Result (State × Unit)
+axiom core.mem.swap
+  (T : Type) : T → T → State → Result (State × (T × T))
 
-/- [core::mem::swap]: backward function 0
-   Source: '/rustc/d59363ad0b6391b7fc5bbb02c9ccf9300eef3753/library/core/src/mem/mod.rs', lines 726:0-726:42 -/
-axiom core.mem.swap_back0
-  (T : Type) : T → T → State → State → Result (State × T)
-
-/- [core::mem::swap]: backward function 1
-   Source: '/rustc/d59363ad0b6391b7fc5bbb02c9ccf9300eef3753/library/core/src/mem/mod.rs', lines 726:0-726:42 -/
-axiom core.mem.swap_back1
-  (T : Type) : T → T → State → State → Result (State × T)
-
-/- [core::num::nonzero::{core::num::nonzero::NonZeroU32#14}::new]: forward function
+/- [core::num::nonzero::{core::num::nonzero::NonZeroU32#14}::new]:
    Source: '/rustc/d59363ad0b6391b7fc5bbb02c9ccf9300eef3753/library/core/src/num/nonzero.rs', lines 79:16-79:57 -/
 axiom core.num.nonzero.NonZeroU32.new
   : U32 → State → Result (State × (Option core.num.nonzero.NonZeroU32))
 
-/- [core::option::{core::option::Option<T>}::unwrap]: forward function
+/- [core::option::{core::option::Option<T>}::unwrap]:
    Source: '/rustc/d59363ad0b6391b7fc5bbb02c9ccf9300eef3753/library/core/src/option.rs', lines 932:4-932:34 -/
 axiom core.option.Option.unwrap
   (T : Type) : Option T → State → Result (State × T)
diff --git a/tests/lean/Hashmap/Funs.lean b/tests/lean/Hashmap/Funs.lean
index e03981a2..3978bfc7 100644
--- a/tests/lean/Hashmap/Funs.lean
+++ b/tests/lean/Hashmap/Funs.lean
@@ -6,12 +6,12 @@ open Primitives
 
 namespace hashmap
 
-/- [hashmap::hash_key]: forward function
+/- [hashmap::hash_key]:
    Source: 'src/hashmap.rs', lines 27:0-27:32 -/
 def hash_key (k : Usize) : Result Usize :=
   Result.ret k
 
-/- [hashmap::{hashmap::HashMap<T>}::allocate_slots]: loop 0: forward function
+/- [hashmap::{hashmap::HashMap<T>}::allocate_slots]: loop 0:
    Source: 'src/hashmap.rs', lines 50:4-56:5 -/
 divergent def HashMap.allocate_slots_loop
   (T : Type) (slots : alloc.vec.Vec (List T)) (n : Usize) :
@@ -20,12 +20,12 @@ divergent def HashMap.allocate_slots_loop
   if n > 0#usize
   then
     do
-      let slots0 ← alloc.vec.Vec.push (List T) slots List.Nil
-      let n0 ← n - 1#usize
-      HashMap.allocate_slots_loop T slots0 n0
+    let v ← alloc.vec.Vec.push (List T) slots List.Nil
+    let n1 ← n - 1#usize
+    HashMap.allocate_slots_loop T v n1
   else Result.ret slots
 
-/- [hashmap::{hashmap::HashMap<T>}::allocate_slots]: forward function
+/- [hashmap::{hashmap::HashMap<T>}::allocate_slots]:
    Source: 'src/hashmap.rs', lines 50:4-50:76 -/
 def HashMap.allocate_slots
   (T : Type) (slots : alloc.vec.Vec (List T)) (n : Usize) :
@@ -33,7 +33,7 @@ def HashMap.allocate_slots
   :=
   HashMap.allocate_slots_loop T slots n
 
-/- [hashmap::{hashmap::HashMap<T>}::new_with_capacity]: forward function
+/- [hashmap::{hashmap::HashMap<T>}::new_with_capacity]:
    Source: 'src/hashmap.rs', lines 59:4-63:13 -/
 def HashMap.new_with_capacity
   (T : Type) (capacity : Usize) (max_load_dividend : Usize)
@@ -41,252 +41,220 @@ def HashMap.new_with_capacity
   Result (HashMap T)
   :=
   do
-    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 := 0#usize,
-        max_load_factor := (max_load_dividend, max_load_divisor),
-        max_load := i0,
-        slots := slots
-      }
-
-/- [hashmap::{hashmap::HashMap<T>}::new]: forward function
+  let slots ← HashMap.allocate_slots T (alloc.vec.Vec.new (List T)) capacity
+  let i ← capacity * max_load_dividend
+  let i1 ← i / max_load_divisor
+  Result.ret
+    {
+      num_entries := 0#usize,
+      max_load_factor := (max_load_dividend, max_load_divisor),
+      max_load := i1,
+      slots := slots
+    }
+
+/- [hashmap::{hashmap::HashMap<T>}::new]:
    Source: 'src/hashmap.rs', lines 75:4-75:24 -/
 def HashMap.new (T : Type) : Result (HashMap T) :=
   HashMap.new_with_capacity T 32#usize 4#usize 5#usize
 
-/- [hashmap::{hashmap::HashMap<T>}::clear]: loop 0: merged forward/backward function
-   (there is a single backward function, and the forward function returns ())
+/- [hashmap::{hashmap::HashMap<T>}::clear]: loop 0:
    Source: 'src/hashmap.rs', lines 80:4-88:5 -/
 divergent def HashMap.clear_loop
   (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
+  let i1 := alloc.vec.Vec.len (List T) slots
+  if i < i1
   then
     do
-      let i1 ← i + 1#usize
-      let slots0 ←
-        alloc.vec.Vec.index_mut_back (List T) Usize
-          (core.slice.index.SliceIndexUsizeSliceTInst (List T)) slots i
-          List.Nil
-      HashMap.clear_loop T slots0 i1
+    let (_, index_mut_back) ←
+      alloc.vec.Vec.index_mut (List T) Usize
+        (core.slice.index.SliceIndexUsizeSliceTInst (List T)) slots i
+    let i2 ← i + 1#usize
+    let slots1 ← index_mut_back List.Nil
+    HashMap.clear_loop T slots1 i2
   else Result.ret slots
 
-/- [hashmap::{hashmap::HashMap<T>}::clear]: merged forward/backward function
-   (there is a single backward function, and the forward function returns ())
+/- [hashmap::{hashmap::HashMap<T>}::clear]:
    Source: 'src/hashmap.rs', lines 80:4-80:27 -/
 def HashMap.clear (T : Type) (self : HashMap T) : Result (HashMap T) :=
   do
-    let v ← HashMap.clear_loop T self.slots 0#usize
-    Result.ret { self with num_entries := 0#usize, slots := v }
+  let back ← HashMap.clear_loop T self.slots 0#usize
+  Result.ret { self with num_entries := 0#usize, slots := back }
 
-/- [hashmap::{hashmap::HashMap<T>}::len]: forward function
+/- [hashmap::{hashmap::HashMap<T>}::len]:
    Source: 'src/hashmap.rs', lines 90:4-90:30 -/
 def HashMap.len (T : Type) (self : HashMap T) : Result Usize :=
   Result.ret self.num_entries
 
-/- [hashmap::{hashmap::HashMap<T>}::insert_in_list]: loop 0: forward function
+/- [hashmap::{hashmap::HashMap<T>}::insert_in_list]: loop 0:
    Source: 'src/hashmap.rs', lines 97:4-114:5 -/
 divergent def HashMap.insert_in_list_loop
-  (T : Type) (key : Usize) (value : T) (ls : List T) : Result Bool :=
-  match ls with
-  | List.Cons ckey cvalue tl =>
-    if ckey = key
-    then Result.ret false
-    else HashMap.insert_in_list_loop T key value tl
-  | List.Nil => Result.ret true
-
-/- [hashmap::{hashmap::HashMap<T>}::insert_in_list]: forward function
-   Source: 'src/hashmap.rs', lines 97:4-97:71 -/
-def HashMap.insert_in_list
-  (T : Type) (key : Usize) (value : T) (ls : List T) : Result Bool :=
-  HashMap.insert_in_list_loop T key value ls
-
-/- [hashmap::{hashmap::HashMap<T>}::insert_in_list]: loop 0: backward function 0
-   Source: 'src/hashmap.rs', lines 97:4-114:5 -/
-divergent def HashMap.insert_in_list_loop_back
-  (T : Type) (key : Usize) (value : T) (ls : List T) : Result (List T) :=
+  (T : Type) (key : Usize) (value : T) (ls : List T) :
+  Result (Bool × (List T))
+  :=
   match ls with
   | List.Cons ckey cvalue tl =>
     if ckey = key
-    then Result.ret (List.Cons ckey value tl)
+    then Result.ret (false, List.Cons ckey value tl)
     else
       do
-        let tl0 ← HashMap.insert_in_list_loop_back T key value tl
-        Result.ret (List.Cons ckey cvalue tl0)
-  | List.Nil => let l := List.Nil
-                Result.ret (List.Cons key value l)
+      let (b, back) ← HashMap.insert_in_list_loop T key value tl
+      Result.ret (b, List.Cons ckey cvalue back)
+  | List.Nil => Result.ret (true, List.Cons key value List.Nil)
 
-/- [hashmap::{hashmap::HashMap<T>}::insert_in_list]: backward function 0
+/- [hashmap::{hashmap::HashMap<T>}::insert_in_list]:
    Source: 'src/hashmap.rs', lines 97:4-97:71 -/
-def HashMap.insert_in_list_back
-  (T : Type) (key : Usize) (value : T) (ls : List T) : Result (List T) :=
-  HashMap.insert_in_list_loop_back T key value ls
+def HashMap.insert_in_list
+  (T : Type) (key : Usize) (value : T) (ls : List T) :
+  Result (Bool × (List T))
+  :=
+  HashMap.insert_in_list_loop T key value ls
 
-/- [hashmap::{hashmap::HashMap<T>}::insert_no_resize]: merged forward/backward function
-   (there is a single backward function, and the forward function returns ())
+/- [hashmap::{hashmap::HashMap<T>}::insert_no_resize]:
    Source: 'src/hashmap.rs', lines 117:4-117:54 -/
 def HashMap.insert_no_resize
   (T : Type) (self : HashMap T) (key : Usize) (value : T) :
   Result (HashMap T)
   :=
   do
-    let hash ← hash_key key
-    let i := alloc.vec.Vec.len (List T) self.slots
-    let hash_mod ← hash % i
-    let l ←
-      alloc.vec.Vec.index_mut (List T) Usize
-        (core.slice.index.SliceIndexUsizeSliceTInst (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 + 1#usize
-        let l0 ← HashMap.insert_in_list_back T key value l
-        let v ←
-          alloc.vec.Vec.index_mut_back (List T) Usize
-            (core.slice.index.SliceIndexUsizeSliceTInst (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 ←
-          alloc.vec.Vec.index_mut_back (List T) Usize
-            (core.slice.index.SliceIndexUsizeSliceTInst (List T)) self.slots
-            hash_mod l0
-        Result.ret { self with slots := v }
-
-/- [hashmap::{hashmap::HashMap<T>}::move_elements_from_list]: loop 0: merged forward/backward function
-   (there is a single backward function, and the forward function returns ())
+  let hash ← hash_key key
+  let i := alloc.vec.Vec.len (List T) self.slots
+  let hash_mod ← hash % i
+  let (l, index_mut_back) ←
+    alloc.vec.Vec.index_mut (List T) Usize
+      (core.slice.index.SliceIndexUsizeSliceTInst (List T)) self.slots hash_mod
+  let (inserted, l1) ← HashMap.insert_in_list T key value l
+  if inserted
+  then
+    do
+    let i1 ← self.num_entries + 1#usize
+    let v ← index_mut_back l1
+    Result.ret { self with num_entries := i1, slots := v }
+  else do
+       let v ← index_mut_back l1
+       Result.ret { self with slots := v }
+
+/- [hashmap::{hashmap::HashMap<T>}::move_elements_from_list]: loop 0:
    Source: 'src/hashmap.rs', lines 183:4-196:5 -/
 divergent def HashMap.move_elements_from_list_loop
   (T : Type) (ntable : HashMap T) (ls : List T) : Result (HashMap T) :=
   match ls with
   | List.Cons k v tl =>
     do
-      let ntable0 ← HashMap.insert_no_resize T ntable k v
-      HashMap.move_elements_from_list_loop T ntable0 tl
+    let hm ← HashMap.insert_no_resize T ntable k v
+    HashMap.move_elements_from_list_loop T hm tl
   | List.Nil => Result.ret ntable
 
-/- [hashmap::{hashmap::HashMap<T>}::move_elements_from_list]: merged forward/backward function
-   (there is a single backward function, and the forward function returns ())
+/- [hashmap::{hashmap::HashMap<T>}::move_elements_from_list]:
    Source: 'src/hashmap.rs', lines 183:4-183:72 -/
 def HashMap.move_elements_from_list
   (T : Type) (ntable : HashMap T) (ls : List T) : Result (HashMap T) :=
   HashMap.move_elements_from_list_loop T ntable ls
 
-/- [hashmap::{hashmap::HashMap<T>}::move_elements]: loop 0: merged forward/backward function
-   (there is a single backward function, and the forward function returns ())
+/- [hashmap::{hashmap::HashMap<T>}::move_elements]: loop 0:
    Source: 'src/hashmap.rs', lines 171:4-180:5 -/
 divergent def HashMap.move_elements_loop
   (T : Type) (ntable : HashMap T) (slots : alloc.vec.Vec (List T)) (i : Usize)
   :
   Result ((HashMap T) × (alloc.vec.Vec (List T)))
   :=
-  let i0 := alloc.vec.Vec.len (List T) slots
-  if i < i0
+  let i1 := alloc.vec.Vec.len (List T) slots
+  if i < i1
   then
     do
-      let l ←
-        alloc.vec.Vec.index_mut (List T) Usize
-          (core.slice.index.SliceIndexUsizeSliceTInst (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 + 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.SliceIndexUsizeSliceTInst (List T)) slots i l0
-      HashMap.move_elements_loop T ntable0 slots0 i1
+    let (l, index_mut_back) ←
+      alloc.vec.Vec.index_mut (List T) Usize
+        (core.slice.index.SliceIndexUsizeSliceTInst (List T)) slots i
+    let (ls, l1) := core.mem.replace (List T) l List.Nil
+    let hm ← HashMap.move_elements_from_list T ntable ls
+    let i2 ← i + 1#usize
+    let slots1 ← index_mut_back l1
+    let back_'a ← HashMap.move_elements_loop T hm slots1 i2
+    let (hm1, v) := back_'a
+    Result.ret (hm1, v)
   else Result.ret (ntable, slots)
 
-/- [hashmap::{hashmap::HashMap<T>}::move_elements]: merged forward/backward function
-   (there is a single backward function, and the forward function returns ())
+/- [hashmap::{hashmap::HashMap<T>}::move_elements]:
    Source: 'src/hashmap.rs', lines 171:4-171:95 -/
 def HashMap.move_elements
   (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
+  do
+  let back_'a ← HashMap.move_elements_loop T ntable slots i
+  let (hm, v) := back_'a
+  Result.ret (hm, v)
 
-/- [hashmap::{hashmap::HashMap<T>}::try_resize]: merged forward/backward function
-   (there is a single backward function, and the forward function returns ())
+/- [hashmap::{hashmap::HashMap<T>}::try_resize]:
    Source: 'src/hashmap.rs', lines 140:4-140:28 -/
 def HashMap.try_resize (T : Type) (self : HashMap T) : Result (HashMap T) :=
   do
-    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 * 2#usize
-        let ntable ← HashMap.new_with_capacity T i2 i i0
-        let (ntable0, _) ← HashMap.move_elements T ntable self.slots 0#usize
-        Result.ret
-          {
-            ntable0
-              with
-              num_entries := self.num_entries, max_load_factor := (i, i0)
-          }
-    else Result.ret { self with max_load_factor := (i, i0) }
-
-/- [hashmap::{hashmap::HashMap<T>}::insert]: merged forward/backward function
-   (there is a single backward function, and the forward function returns ())
+  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, i1) := self.max_load_factor
+  let i2 ← n1 / i
+  if capacity <= i2
+  then
+    do
+    let i3 ← capacity * 2#usize
+    let ntable ← HashMap.new_with_capacity T i3 i i1
+    let p ← HashMap.move_elements T ntable self.slots 0#usize
+    let (ntable1, _) := p
+    Result.ret
+      {
+        ntable1
+          with
+          num_entries := self.num_entries, max_load_factor := (i, i1)
+      }
+  else Result.ret { self with max_load_factor := (i, i1) }
+
+/- [hashmap::{hashmap::HashMap<T>}::insert]:
    Source: 'src/hashmap.rs', lines 129:4-129:48 -/
 def HashMap.insert
   (T : Type) (self : HashMap T) (key : Usize) (value : T) :
   Result (HashMap T)
   :=
   do
-    let self0 ← HashMap.insert_no_resize T self key value
-    let i ← HashMap.len T self0
-    if i > self0.max_load
-    then HashMap.try_resize T self0
-    else Result.ret self0
+  let hm ← HashMap.insert_no_resize T self key value
+  let i ← HashMap.len T hm
+  if i > hm.max_load
+  then HashMap.try_resize T hm
+  else Result.ret hm
 
-/- [hashmap::{hashmap::HashMap<T>}::contains_key_in_list]: loop 0: forward function
+/- [hashmap::{hashmap::HashMap<T>}::contains_key_in_list]: loop 0:
    Source: 'src/hashmap.rs', lines 206:4-219:5 -/
 divergent def HashMap.contains_key_in_list_loop
   (T : Type) (key : Usize) (ls : List T) : Result Bool :=
   match ls with
-  | List.Cons ckey t tl =>
+  | List.Cons ckey _ tl =>
     if ckey = key
     then Result.ret true
     else HashMap.contains_key_in_list_loop T key tl
   | List.Nil => Result.ret false
 
-/- [hashmap::{hashmap::HashMap<T>}::contains_key_in_list]: forward function
+/- [hashmap::{hashmap::HashMap<T>}::contains_key_in_list]:
    Source: 'src/hashmap.rs', lines 206:4-206:68 -/
 def HashMap.contains_key_in_list
   (T : Type) (key : Usize) (ls : List T) : Result Bool :=
   HashMap.contains_key_in_list_loop T key ls
 
-/- [hashmap::{hashmap::HashMap<T>}::contains_key]: forward function
+/- [hashmap::{hashmap::HashMap<T>}::contains_key]:
    Source: 'src/hashmap.rs', lines 199:4-199:49 -/
 def HashMap.contains_key
   (T : Type) (self : HashMap T) (key : Usize) : Result Bool :=
   do
-    let hash ← hash_key key
-    let i := alloc.vec.Vec.len (List T) self.slots
-    let hash_mod ← hash % i
-    let l ←
-      alloc.vec.Vec.index (List T) Usize
-        (core.slice.index.SliceIndexUsizeSliceTInst (List T)) self.slots
-        hash_mod
-    HashMap.contains_key_in_list T key l
-
-/- [hashmap::{hashmap::HashMap<T>}::get_in_list]: loop 0: forward function
+  let hash ← hash_key key
+  let i := alloc.vec.Vec.len (List T) self.slots
+  let hash_mod ← hash % i
+  let l ←
+    alloc.vec.Vec.index (List T) Usize
+      (core.slice.index.SliceIndexUsizeSliceTInst (List T)) self.slots hash_mod
+  HashMap.contains_key_in_list T key l
+
+/- [hashmap::{hashmap::HashMap<T>}::get_in_list]: loop 0:
    Source: 'src/hashmap.rs', lines 224:4-237:5 -/
 divergent def HashMap.get_in_list_loop
   (T : Type) (key : Usize) (ls : List T) : Result T :=
@@ -297,231 +265,170 @@ divergent def HashMap.get_in_list_loop
     else HashMap.get_in_list_loop T key tl
   | List.Nil => Result.fail .panic
 
-/- [hashmap::{hashmap::HashMap<T>}::get_in_list]: forward function
+/- [hashmap::{hashmap::HashMap<T>}::get_in_list]:
    Source: 'src/hashmap.rs', lines 224:4-224:70 -/
 def HashMap.get_in_list (T : Type) (key : Usize) (ls : List T) : Result T :=
   HashMap.get_in_list_loop T key ls
 
-/- [hashmap::{hashmap::HashMap<T>}::get]: forward function
+/- [hashmap::{hashmap::HashMap<T>}::get]:
    Source: 'src/hashmap.rs', lines 239:4-239:55 -/
 def HashMap.get (T : Type) (self : HashMap T) (key : Usize) : Result T :=
   do
-    let hash ← hash_key key
-    let i := alloc.vec.Vec.len (List T) self.slots
-    let hash_mod ← hash % i
-    let l ←
-      alloc.vec.Vec.index (List T) Usize
-        (core.slice.index.SliceIndexUsizeSliceTInst (List T)) self.slots
-        hash_mod
-    HashMap.get_in_list T key l
-
-/- [hashmap::{hashmap::HashMap<T>}::get_mut_in_list]: loop 0: forward function
+  let hash ← hash_key key
+  let i := alloc.vec.Vec.len (List T) self.slots
+  let hash_mod ← hash % i
+  let l ←
+    alloc.vec.Vec.index (List T) Usize
+      (core.slice.index.SliceIndexUsizeSliceTInst (List T)) self.slots hash_mod
+  HashMap.get_in_list T key l
+
+/- [hashmap::{hashmap::HashMap<T>}::get_mut_in_list]: loop 0:
    Source: 'src/hashmap.rs', lines 245:4-254:5 -/
 divergent def HashMap.get_mut_in_list_loop
-  (T : Type) (ls : List T) (key : Usize) : Result T :=
-  match ls with
-  | List.Cons ckey cvalue tl =>
-    if ckey = key
-    then Result.ret cvalue
-    else HashMap.get_mut_in_list_loop T tl key
-  | List.Nil => Result.fail .panic
-
-/- [hashmap::{hashmap::HashMap<T>}::get_mut_in_list]: forward function
-   Source: 'src/hashmap.rs', lines 245:4-245:86 -/
-def HashMap.get_mut_in_list
-  (T : Type) (ls : List T) (key : Usize) : Result T :=
-  HashMap.get_mut_in_list_loop T ls key
-
-/- [hashmap::{hashmap::HashMap<T>}::get_mut_in_list]: loop 0: backward function 0
-   Source: 'src/hashmap.rs', lines 245:4-254:5 -/
-divergent def HashMap.get_mut_in_list_loop_back
-  (T : Type) (ls : List T) (key : Usize) (ret : T) : Result (List T) :=
+  (T : Type) (ls : List T) (key : Usize) :
+  Result (T × (T → Result (List T)))
+  :=
   match ls with
   | List.Cons ckey cvalue tl =>
     if ckey = key
-    then Result.ret (List.Cons ckey ret tl)
+    then
+      let back_'a := fun ret => Result.ret (List.Cons ckey ret tl)
+      Result.ret (cvalue, back_'a)
     else
       do
-        let tl0 ← HashMap.get_mut_in_list_loop_back T tl key ret
-        Result.ret (List.Cons ckey cvalue tl0)
+      let (t, back_'a) ← HashMap.get_mut_in_list_loop T tl key
+      let back_'a1 :=
+        fun ret =>
+          do
+          let tl1 ← back_'a ret
+          Result.ret (List.Cons ckey cvalue tl1)
+      Result.ret (t, back_'a1)
   | List.Nil => Result.fail .panic
 
-/- [hashmap::{hashmap::HashMap<T>}::get_mut_in_list]: backward function 0
+/- [hashmap::{hashmap::HashMap<T>}::get_mut_in_list]:
    Source: 'src/hashmap.rs', lines 245:4-245:86 -/
-def HashMap.get_mut_in_list_back
-  (T : Type) (ls : List T) (key : Usize) (ret : T) : Result (List T) :=
-  HashMap.get_mut_in_list_loop_back T ls key ret
-
-/- [hashmap::{hashmap::HashMap<T>}::get_mut]: forward function
-   Source: 'src/hashmap.rs', lines 257:4-257:67 -/
-def HashMap.get_mut (T : Type) (self : HashMap T) (key : Usize) : Result T :=
+def HashMap.get_mut_in_list
+  (T : Type) (ls : List T) (key : Usize) :
+  Result (T × (T → Result (List T)))
+  :=
   do
-    let hash ← hash_key key
-    let i := alloc.vec.Vec.len (List T) self.slots
-    let hash_mod ← hash % i
-    let l ←
-      alloc.vec.Vec.index_mut (List T) Usize
-        (core.slice.index.SliceIndexUsizeSliceTInst (List T)) self.slots
-        hash_mod
-    HashMap.get_mut_in_list T l key
+  let (t, back_'a) ← HashMap.get_mut_in_list_loop T ls key
+  Result.ret (t, back_'a)
 
-/- [hashmap::{hashmap::HashMap<T>}::get_mut]: backward function 0
+/- [hashmap::{hashmap::HashMap<T>}::get_mut]:
    Source: 'src/hashmap.rs', lines 257:4-257:67 -/
-def HashMap.get_mut_back
-  (T : Type) (self : HashMap T) (key : Usize) (ret : T) : Result (HashMap T) :=
+def HashMap.get_mut
+  (T : Type) (self : HashMap T) (key : Usize) :
+  Result (T × (T → Result (HashMap T)))
+  :=
   do
-    let hash ← hash_key key
-    let i := alloc.vec.Vec.len (List T) self.slots
-    let hash_mod ← hash % i
-    let l ←
-      alloc.vec.Vec.index_mut (List T) Usize
-        (core.slice.index.SliceIndexUsizeSliceTInst (List T)) self.slots
-        hash_mod
-    let l0 ← HashMap.get_mut_in_list_back T l key ret
-    let v ←
-      alloc.vec.Vec.index_mut_back (List T) Usize
-        (core.slice.index.SliceIndexUsizeSliceTInst (List T)) self.slots
-        hash_mod l0
-    Result.ret { self with slots := v }
-
-/- [hashmap::{hashmap::HashMap<T>}::remove_from_list]: loop 0: forward function
-   Source: 'src/hashmap.rs', lines 265:4-291:5 -/
-divergent def HashMap.remove_from_list_loop
-  (T : Type) (key : Usize) (ls : List T) : Result (Option T) :=
-  match ls with
-  | List.Cons ckey t tl =>
-    if ckey = key
-    then
-      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 (some cvalue)
-      | List.Nil => Result.fail .panic
-    else HashMap.remove_from_list_loop T key tl
-  | List.Nil => Result.ret none
-
-/- [hashmap::{hashmap::HashMap<T>}::remove_from_list]: forward function
-   Source: 'src/hashmap.rs', lines 265:4-265:69 -/
-def HashMap.remove_from_list
-  (T : Type) (key : Usize) (ls : List T) : Result (Option T) :=
-  HashMap.remove_from_list_loop T key ls
+  let hash ← hash_key key
+  let i := alloc.vec.Vec.len (List T) self.slots
+  let hash_mod ← hash % i
+  let (l, index_mut_back) ←
+    alloc.vec.Vec.index_mut (List T) Usize
+      (core.slice.index.SliceIndexUsizeSliceTInst (List T)) self.slots hash_mod
+  let (t, get_mut_in_list_back) ← HashMap.get_mut_in_list T l key
+  let back_'a :=
+    fun ret =>
+      do
+      let l1 ← get_mut_in_list_back ret
+      let v ← index_mut_back l1
+      Result.ret { self with slots := v }
+  Result.ret (t, back_'a)
 
-/- [hashmap::{hashmap::HashMap<T>}::remove_from_list]: loop 0: backward function 1
+/- [hashmap::{hashmap::HashMap<T>}::remove_from_list]: loop 0:
    Source: 'src/hashmap.rs', lines 265:4-291:5 -/
-divergent def HashMap.remove_from_list_loop_back
-  (T : Type) (key : Usize) (ls : List T) : Result (List T) :=
+divergent def HashMap.remove_from_list_loop
+  (T : Type) (key : Usize) (ls : List T) : Result ((Option T) × (List T)) :=
   match ls with
   | List.Cons ckey t tl =>
     if ckey = key
     then
-      let mv_ls := core.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.Cons _ cvalue tl1 => Result.ret (some cvalue, tl1)
       | List.Nil => Result.fail .panic
     else
       do
-        let tl0 ← HashMap.remove_from_list_loop_back T key tl
-        Result.ret (List.Cons ckey t tl0)
-  | List.Nil => Result.ret List.Nil
+      let (o, back) ← HashMap.remove_from_list_loop T key tl
+      Result.ret (o, List.Cons ckey t back)
+  | List.Nil => Result.ret (none, List.Nil)
 
-/- [hashmap::{hashmap::HashMap<T>}::remove_from_list]: backward function 1
+/- [hashmap::{hashmap::HashMap<T>}::remove_from_list]:
    Source: 'src/hashmap.rs', lines 265:4-265:69 -/
-def HashMap.remove_from_list_back
-  (T : Type) (key : Usize) (ls : List T) : Result (List T) :=
-  HashMap.remove_from_list_loop_back T key ls
+def HashMap.remove_from_list
+  (T : Type) (key : Usize) (ls : List T) : Result ((Option T) × (List T)) :=
+  HashMap.remove_from_list_loop T key ls
 
-/- [hashmap::{hashmap::HashMap<T>}::remove]: forward function
+/- [hashmap::{hashmap::HashMap<T>}::remove]:
    Source: 'src/hashmap.rs', lines 294:4-294:52 -/
 def HashMap.remove
-  (T : Type) (self : HashMap T) (key : Usize) : Result (Option T) :=
-  do
-    let hash ← hash_key key
-    let i := alloc.vec.Vec.len (List T) self.slots
-    let hash_mod ← hash % i
-    let l ←
-      alloc.vec.Vec.index_mut (List T) Usize
-        (core.slice.index.SliceIndexUsizeSliceTInst (List T)) self.slots
-        hash_mod
-    let x ← HashMap.remove_from_list T key l
-    match x with
-    | none => Result.ret none
-    | some x0 => do
-                   let _ ← self.num_entries - 1#usize
-                   Result.ret (some x0)
-
-/- [hashmap::{hashmap::HashMap<T>}::remove]: backward function 0
-   Source: 'src/hashmap.rs', lines 294:4-294:52 -/
-def HashMap.remove_back
-  (T : Type) (self : HashMap T) (key : Usize) : Result (HashMap T) :=
+  (T : Type) (self : HashMap T) (key : Usize) :
+  Result ((Option T) × (HashMap T))
+  :=
   do
-    let hash ← hash_key key
-    let i := alloc.vec.Vec.len (List T) self.slots
-    let hash_mod ← hash % i
-    let l ←
-      alloc.vec.Vec.index_mut (List T) Usize
-        (core.slice.index.SliceIndexUsizeSliceTInst (List T)) self.slots
-        hash_mod
-    let x ← HashMap.remove_from_list T key l
-    match x with
-    | none =>
-      do
-        let l0 ← HashMap.remove_from_list_back T key l
-        let v ←
-          alloc.vec.Vec.index_mut_back (List T) Usize
-            (core.slice.index.SliceIndexUsizeSliceTInst (List T)) self.slots
-            hash_mod l0
-        Result.ret { self with slots := v }
-    | some x0 =>
-      do
-        let i0 ← self.num_entries - 1#usize
-        let l0 ← HashMap.remove_from_list_back T key l
-        let v ←
-          alloc.vec.Vec.index_mut_back (List T) Usize
-            (core.slice.index.SliceIndexUsizeSliceTInst (List T)) self.slots
-            hash_mod l0
-        Result.ret { self with num_entries := i0, slots := v }
-
-/- [hashmap::test1]: forward function
+  let hash ← hash_key key
+  let i := alloc.vec.Vec.len (List T) self.slots
+  let hash_mod ← hash % i
+  let (l, index_mut_back) ←
+    alloc.vec.Vec.index_mut (List T) Usize
+      (core.slice.index.SliceIndexUsizeSliceTInst (List T)) self.slots hash_mod
+  let (x, l1) ← HashMap.remove_from_list T key l
+  match x with
+  | none =>
+    do
+    let v ← index_mut_back l1
+    Result.ret (none, { self with slots := v })
+  | some x1 =>
+    do
+    let i1 ← self.num_entries - 1#usize
+    let v ← index_mut_back l1
+    Result.ret (some x1, { self with num_entries := i1, slots := v })
+
+/- [hashmap::test1]:
    Source: 'src/hashmap.rs', lines 315:0-315:10 -/
 def test1 : Result Unit :=
   do
-    let hm ← HashMap.new U64
-    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)
+  let hm ← HashMap.new U64
+  let hm1 ← HashMap.insert U64 hm 0#usize 42#u64
+  let hm2 ← HashMap.insert U64 hm1 128#usize 18#u64
+  let hm3 ← HashMap.insert U64 hm2 1024#usize 138#u64
+  let hm4 ← HashMap.insert U64 hm3 1056#usize 256#u64
+  let i ← HashMap.get U64 hm4 128#usize
+  if not (i = 18#u64)
+  then Result.fail .panic
+  else
+    do
+    let (_, get_mut_back) ← HashMap.get_mut U64 hm4 1024#usize
+    let hm5 ← get_mut_back 56#u64
+    let i1 ← HashMap.get U64 hm5 1024#usize
+    if not (i1 = 56#u64)
     then Result.fail .panic
     else
       do
-        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)
+      let (x, hm6) ← HashMap.remove U64 hm5 1024#usize
+      match x with
+      | none => Result.fail .panic
+      | some x1 =>
+        if not (x1 = 56#u64)
         then Result.fail .panic
         else
           do
-            let x ← HashMap.remove U64 hm4 1024#usize
-            match x with
-            | none => Result.fail .panic
-            | some x0 =>
-              if not (x0 = 56#u64)
+          let i2 ← HashMap.get U64 hm6 0#usize
+          if not (i2 = 42#u64)
+          then Result.fail .panic
+          else
+            do
+            let i3 ← HashMap.get U64 hm6 128#usize
+            if not (i3 = 18#u64)
+            then Result.fail .panic
+            else
+              do
+              let i4 ← HashMap.get U64 hm6 1056#usize
+              if not (i4 = 256#u64)
               then Result.fail .panic
-              else
-                do
-                  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 .panic
-                  else
-                    do
-                      let i2 ← HashMap.get U64 hm5 128#usize
-                      if not (i2 = 18#u64)
-                      then Result.fail .panic
-                      else
-                        do
-                          let i3 ← HashMap.get U64 hm5 1056#usize
-                          if not (i3 = 256#u64)
-                          then Result.fail .panic
-                          else Result.ret ()
+              else Result.ret ()
 
 end hashmap
diff --git a/tests/lean/Hashmap/Properties.lean b/tests/lean/Hashmap/Properties.lean
index e79c422d..7215e286 100644
--- a/tests/lean/Hashmap/Properties.lean
+++ b/tests/lean/Hashmap/Properties.lean
@@ -55,71 +55,6 @@ theorem match_lawful_beq [BEq α] [LawfulBEq α] [DecidableEq α] (x y : α) :
   (x == y) = (if x = y then true else false) := by
   split <;> simp_all
 
-@[pspec]
-theorem insert_in_list_spec0 {α : Type} (key: Usize) (value: α) (ls: List α) :
-  ∃ b,
-    insert_in_list α key value ls = ret b ∧
-    (b ↔ ls.lookup key = none)
-  := match ls with
-  | .Nil => by simp [insert_in_list, insert_in_list_loop]
-  | .Cons k v tl =>
-    if h: k = key then -- TODO: The order of k/key matters
-      by
-        simp [insert_in_list]
-        rw [insert_in_list_loop]
-        simp [h]
-    else
-      have ⟨ b, hi ⟩ := insert_in_list_spec0 key value tl
-      by
-        exists b
-        simp [insert_in_list]
-        rw [insert_in_list_loop] -- TODO: Using simp leads to infinite recursion
-        simp only [insert_in_list] at hi
-        simp [*]
-
--- Variation: use progress
-theorem insert_in_list_spec1 {α : Type} (key: Usize) (value: α) (ls: List α) :
-  ∃ b,
-    insert_in_list α key value ls = ret b ∧
-    (b ↔ ls.lookup key = none)
-  := match ls with
-  | .Nil => by simp [insert_in_list, insert_in_list_loop]
-  | .Cons k v tl =>
-    if h: k = key then -- TODO: The order of k/key matters
-      by
-        simp [insert_in_list]
-        rw [insert_in_list_loop]
-        simp [h]
-    else
-      by
-        simp only [insert_in_list]
-        rw [insert_in_list_loop]
-        conv => rhs; ext; simp [*]
-        progress keep heq as ⟨ b, hi ⟩
-        simp only [insert_in_list] at heq
-        exists b
-
--- Variation: use tactics from the beginning
-theorem insert_in_list_spec2 {α : Type} (key: Usize) (value: α) (ls: List α) :
-  ∃ b,
-    insert_in_list α key value ls = ret b ∧
-    (b ↔ (ls.lookup key = none))
-  := by
-  induction ls
-  case Nil => simp [insert_in_list, insert_in_list_loop]
-  case Cons k v tl ih =>
-    simp only [insert_in_list]
-    rw [insert_in_list_loop]
-    simp only
-    if h: k = key then
-     simp [h]
-    else
-     conv => rhs; ext; left; simp [h] -- TODO: Simplify
-     simp only [insert_in_list] at ih;
-     -- TODO: give the possibility of using underscores
-     progress as ⟨ b, h ⟩
-     simp [*]
-
 def distinct_keys (ls : Core.List (Usize × α)) := ls.pairwise_rel (λ x y => x.fst ≠ y.fst)
 
 def hash_mod_key (k : Usize) (l : Int) : Int :=
@@ -175,11 +110,16 @@ def inv (hm : HashMap α) : Prop :=
   base_inv hm
   -- TODO: either the hashmap is not overloaded, or we can't resize it
 
-theorem insert_in_list_back_spec_aux {α : Type} (l : Int) (key: Usize) (value: α) (l0: List α)
+-- This rewriting lemma is problematic below
+attribute [-simp] Bool.exists_bool
+
+theorem insert_in_list_spec_aux {α : Type} (l : Int) (key: Usize) (value: α) (l0: List α)
   (hinv : slot_s_inv_hash l (hash_mod_key key l) l0.v)
   (hdk : distinct_keys l0.v) :
-  ∃ l1,
-    insert_in_list_back α key value l0 = ret l1 ∧
+  ∃ b l1,
+    insert_in_list α key value l0 = ret (b, l1) ∧
+    -- The boolean is true ↔ we inserted a new binding
+    (b ↔ (l0.lookup key = none)) ∧
     -- We update the binding
     l1.lookup key = value ∧
     (∀ k, k ≠ key → l1.lookup k = l0.lookup k) ∧
@@ -193,16 +133,19 @@ theorem insert_in_list_back_spec_aux {α : Type} (l : Int) (key: Usize) (value:
     distinct_keys l1.v ∧
     -- We need this auxiliary property to prove that the keys distinct properties is preserved
     (∀ k, k ≠ key → l0.v.allP (λ (k1, _) => k ≠ k1) → l1.v.allP (λ (k1, _) => k ≠ k1))
-  := match l0 with
-  | .Nil => by checkpoint
+  :=
+  match l0 with
+  | .Nil => by
+    exists true -- TODO: why do we need to do this?
     simp (config := {contextual := true})
-      [insert_in_list_back, insert_in_list_loop_back,
+      [insert_in_list, insert_in_list_loop,
        List.v, slot_s_inv_hash, distinct_keys, List.pairwise_rel]
   | .Cons k v tl0 =>
-     if h: k = key then by checkpoint
-       simp [insert_in_list_back]
-       rw [insert_in_list_loop_back]
+     if h: k = key then by
+       rw [insert_in_list]
+       rw [insert_in_list_loop]
        simp [h]
+       exists false; simp -- TODO: why do we need to do this?
        split_conjs
        . intros; simp [*]
        . simp [List.v, slot_s_inv_hash] at *
@@ -210,17 +153,17 @@ theorem insert_in_list_back_spec_aux {α : Type} (l : Int) (key: Usize) (value:
        . simp [*, distinct_keys] at *
          apply hdk
        . tauto
-     else by checkpoint
-       simp [insert_in_list_back]
-       rw [insert_in_list_loop_back]
+     else by
+       rw [insert_in_list]
+       rw [insert_in_list_loop]
        simp [h]
        have : slot_s_inv_hash l (hash_mod_key key l) (List.v tl0) := by checkpoint
          simp_all [List.v, slot_s_inv_hash]
        have : distinct_keys (List.v tl0) := by checkpoint
          simp [distinct_keys] at hdk
          simp [hdk, distinct_keys]
-       progress keep heq as ⟨ tl1 .. ⟩
-       simp only [insert_in_list_back] at heq
+       progress keep heq as ⟨ b, tl1 .. ⟩
+       simp only [insert_in_list] at heq
        have : slot_s_inv_hash l (hash_mod_key key l) (List.v (List.Cons k v tl1)) := by checkpoint
          simp [List.v, slot_s_inv_hash] at *
          simp [*]
@@ -228,14 +171,16 @@ theorem insert_in_list_back_spec_aux {α : Type} (l : Int) (key: Usize) (value:
          simp [distinct_keys] at *
          simp [*]
        -- TODO: canonize addition by default?
+       exists b
        simp_all [Int.add_assoc, Int.add_comm, Int.add_left_comm]
 
 @[pspec]
-theorem insert_in_list_back_spec {α : Type} (l : Int) (key: Usize) (value: α) (l0: List α)
+theorem insert_in_list_spec {α : Type} (l : Int) (key: Usize) (value: α) (l0: List α)
   (hinv : slot_s_inv_hash l (hash_mod_key key l) l0.v)
   (hdk : distinct_keys l0.v) :
-  ∃ l1,
-    insert_in_list_back α key value l0 = ret l1 ∧
+  ∃ b l1,
+    insert_in_list α key value l0 = ret (b, l1) ∧
+    (b ↔ (l0.lookup key = none)) ∧
     -- We update the binding
     l1.lookup key = value ∧
     (∀ k, k ≠ key → l1.lookup k = l0.lookup k) ∧
@@ -248,7 +193,8 @@ theorem insert_in_list_back_spec {α : Type} (l : Int) (key: Usize) (value: α)
     -- The keys are distinct
     distinct_keys l1.v
   := by
-  progress with insert_in_list_back_spec_aux as ⟨ l1 .. ⟩
+  progress with insert_in_list_spec_aux as ⟨ b, l1 .. ⟩
+  exists b
   exists l1
 
 @[simp]
@@ -286,7 +232,7 @@ set_option pp.coercions false -- do not print coercions with ↑ (this doesn't p
 
 -- The proof below is a bit expensive, so we need to increase the maximum number
 -- of heart beats
-set_option maxHeartbeats 400000
+set_option maxHeartbeats 1000000
 
 theorem insert_no_resize_spec {α : Type} (hm : HashMap α) (key : Usize) (value : α)
   (hinv : hm.inv) (hnsat : hm.lookup key = none → hm.len_s < Usize.max) :
@@ -315,9 +261,19 @@ theorem insert_no_resize_spec {α : Type} (hm : HashMap α) (key : Usize) (value
       simp [hinv]
     -- TODO: we want to automate that
     simp [*, Int.emod_lt_of_pos]
-  progress as ⟨ l, h_leq ⟩
-  -- TODO: make progress use the names written in the goal
-  progress as ⟨ inserted ⟩
+  progress as ⟨ l, index_mut_back, h_leq, h_index_mut_back ⟩
+  simp [h_index_mut_back] at *; clear h_index_mut_back index_mut_back
+  have h_slot :
+    slot_s_inv_hash hm.slots.length (hash_mod_key key hm.slots.length) l.v := by
+    simp [inv] at hinv
+    have h := (hinv.right.left hash_mod.val (by assumption) (by assumption)).right
+    simp [slot_t_inv, hhm] at h
+    simp [h, hhm, h_leq]
+  have hd : distinct_keys l.v := by
+    simp [inv, slots_t_inv, slot_t_inv] at hinv
+    have h := hinv.right.left hash_mod.val (by assumption) (by assumption)
+    simp [h, h_leq]
+  progress as ⟨ inserted, l0, _, _, _, _, hlen .. ⟩
   rw [if_update_eq] -- TODO: necessary because we don't have a join
   -- TODO: progress to ...
   have hipost :
@@ -336,20 +292,9 @@ theorem insert_no_resize_spec {α : Type} (hm : HashMap α) (key : Usize) (value
     else
       simp [*, Pure.pure]
   progress as ⟨ i0 ⟩
-  have h_slot : slot_s_inv_hash hm.slots.length (hash_mod_key key hm.slots.length) l.v
-    := by
-    simp [inv] at hinv
-    have h := (hinv.right.left hash_mod.val (by assumption) (by assumption)).right
-    simp [slot_t_inv, hhm] at h
-    simp [h, hhm, h_leq]
-  have hd : distinct_keys l.v := by checkpoint
-    simp [inv, slots_t_inv, slot_t_inv] at hinv
-    have h := hinv.right.left hash_mod.val (by assumption) (by assumption)
-    simp [h, h_leq]
   -- TODO: hide the variables and only keep the props
   -- TODO: allow providing terms to progress to instantiate the meta variables
   -- which are not propositions
-  progress as ⟨ l0, _, _, _, hlen .. ⟩
   progress keep hv as ⟨ v, h_veq ⟩
   -- TODO: update progress to automate that
   -- TODO: later I don't want to inline nhm - we need to control simp: deactivate
@@ -428,8 +373,7 @@ theorem insert_no_resize_spec {α : Type} (hm : HashMap α) (key : Usize) (value
         simp [*]
       else
         simp [*]
-    . -- TODO: simp[*] fails: "(deterministic) timeout at 'whnf'"
-      simp [hinv, h_veq, nhm_eq]
+    . simp [hinv, h_veq, nhm_eq]
   simp_all
 
 end HashMap
diff --git a/tests/lean/HashmapMain/Funs.lean b/tests/lean/HashmapMain/Funs.lean
index f87ad355..ebed2570 100644
--- a/tests/lean/HashmapMain/Funs.lean
+++ b/tests/lean/HashmapMain/Funs.lean
@@ -7,12 +7,12 @@ open Primitives
 
 namespace hashmap_main
 
-/- [hashmap_main::hashmap::hash_key]: forward function
+/- [hashmap_main::hashmap::hash_key]:
    Source: 'src/hashmap.rs', lines 27:0-27:32 -/
 def hashmap.hash_key (k : Usize) : Result Usize :=
   Result.ret k
 
-/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::allocate_slots]: loop 0: forward function
+/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::allocate_slots]: loop 0:
    Source: 'src/hashmap.rs', lines 50:4-56:5 -/
 divergent def hashmap.HashMap.allocate_slots_loop
   (T : Type) (slots : alloc.vec.Vec (hashmap.List T)) (n : Usize) :
@@ -21,12 +21,12 @@ divergent def hashmap.HashMap.allocate_slots_loop
   if n > 0#usize
   then
     do
-      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
+    let v ← alloc.vec.Vec.push (hashmap.List T) slots hashmap.List.Nil
+    let n1 ← n - 1#usize
+    hashmap.HashMap.allocate_slots_loop T v n1
   else Result.ret slots
 
-/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::allocate_slots]: forward function
+/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::allocate_slots]:
    Source: 'src/hashmap.rs', lines 50:4-50:76 -/
 def hashmap.HashMap.allocate_slots
   (T : Type) (slots : alloc.vec.Vec (hashmap.List T)) (n : Usize) :
@@ -34,7 +34,7 @@ def hashmap.HashMap.allocate_slots
   :=
   hashmap.HashMap.allocate_slots_loop T slots n
 
-/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::new_with_capacity]: forward function
+/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::new_with_capacity]:
    Source: 'src/hashmap.rs', lines 59:4-63:13 -/
 def hashmap.HashMap.new_with_capacity
   (T : Type) (capacity : Usize) (max_load_dividend : Usize)
@@ -42,136 +42,106 @@ def hashmap.HashMap.new_with_capacity
   Result (hashmap.HashMap T)
   :=
   do
-    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 := 0#usize,
-        max_load_factor := (max_load_dividend, max_load_divisor),
-        max_load := i0,
-        slots := slots
-      }
-
-/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::new]: forward function
+  let slots ←
+    hashmap.HashMap.allocate_slots T (alloc.vec.Vec.new (hashmap.List T))
+      capacity
+  let i ← capacity * max_load_dividend
+  let i1 ← i / max_load_divisor
+  Result.ret
+    {
+      num_entries := 0#usize,
+      max_load_factor := (max_load_dividend, max_load_divisor),
+      max_load := i1,
+      slots := slots
+    }
+
+/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::new]:
    Source: 'src/hashmap.rs', lines 75:4-75:24 -/
 def hashmap.HashMap.new (T : Type) : Result (hashmap.HashMap T) :=
   hashmap.HashMap.new_with_capacity T 32#usize 4#usize 5#usize
 
-/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::clear]: loop 0: merged forward/backward function
-   (there is a single backward function, and the forward function returns ())
+/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::clear]: loop 0:
    Source: 'src/hashmap.rs', lines 80:4-88:5 -/
 divergent def hashmap.HashMap.clear_loop
   (T : Type) (slots : alloc.vec.Vec (hashmap.List T)) (i : Usize) :
   Result (alloc.vec.Vec (hashmap.List T))
   :=
-  let i0 := alloc.vec.Vec.len (hashmap.List T) slots
-  if i < i0
+  let i1 := alloc.vec.Vec.len (hashmap.List T) slots
+  if i < i1
   then
     do
-      let i1 ← i + 1#usize
-      let slots0 ←
-        alloc.vec.Vec.index_mut_back (hashmap.List T) Usize
-          (core.slice.index.SliceIndexUsizeSliceTInst (hashmap.List T)) slots i
-          hashmap.List.Nil
-      hashmap.HashMap.clear_loop T slots0 i1
+    let (_, index_mut_back) ←
+      alloc.vec.Vec.index_mut (hashmap.List T) Usize
+        (core.slice.index.SliceIndexUsizeSliceTInst (hashmap.List T)) slots i
+    let i2 ← i + 1#usize
+    let slots1 ← index_mut_back hashmap.List.Nil
+    hashmap.HashMap.clear_loop T slots1 i2
   else Result.ret slots
 
-/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::clear]: merged forward/backward function
-   (there is a single backward function, and the forward function returns ())
+/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::clear]:
    Source: 'src/hashmap.rs', lines 80:4-80:27 -/
 def hashmap.HashMap.clear
   (T : Type) (self : hashmap.HashMap T) : Result (hashmap.HashMap T) :=
   do
-    let v ← hashmap.HashMap.clear_loop T self.slots 0#usize
-    Result.ret { self with num_entries := 0#usize, slots := v }
+  let back ← hashmap.HashMap.clear_loop T self.slots 0#usize
+  Result.ret { self with num_entries := 0#usize, slots := back }
 
-/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::len]: forward function
+/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::len]:
    Source: 'src/hashmap.rs', lines 90:4-90:30 -/
 def hashmap.HashMap.len (T : Type) (self : hashmap.HashMap T) : Result Usize :=
   Result.ret self.num_entries
 
-/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::insert_in_list]: loop 0: forward function
+/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::insert_in_list]: loop 0:
    Source: 'src/hashmap.rs', lines 97:4-114:5 -/
 divergent def hashmap.HashMap.insert_in_list_loop
-  (T : Type) (key : Usize) (value : T) (ls : hashmap.List T) : Result Bool :=
-  match ls with
-  | hashmap.List.Cons ckey cvalue tl =>
-    if ckey = key
-    then Result.ret false
-    else hashmap.HashMap.insert_in_list_loop T key value tl
-  | hashmap.List.Nil => Result.ret true
-
-/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::insert_in_list]: forward function
-   Source: 'src/hashmap.rs', lines 97:4-97:71 -/
-def hashmap.HashMap.insert_in_list
-  (T : Type) (key : Usize) (value : T) (ls : hashmap.List T) : Result Bool :=
-  hashmap.HashMap.insert_in_list_loop T key value ls
-
-/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::insert_in_list]: loop 0: backward function 0
-   Source: 'src/hashmap.rs', lines 97:4-114:5 -/
-divergent def hashmap.HashMap.insert_in_list_loop_back
   (T : Type) (key : Usize) (value : T) (ls : hashmap.List T) :
-  Result (hashmap.List T)
+  Result (Bool × (hashmap.List T))
   :=
   match ls with
   | hashmap.List.Cons ckey cvalue tl =>
     if ckey = key
-    then Result.ret (hashmap.List.Cons ckey value tl)
+    then Result.ret (false, hashmap.List.Cons ckey value tl)
     else
       do
-        let tl0 ← hashmap.HashMap.insert_in_list_loop_back T key value tl
-        Result.ret (hashmap.List.Cons ckey cvalue tl0)
+      let (b, back) ← hashmap.HashMap.insert_in_list_loop T key value tl
+      Result.ret (b, hashmap.List.Cons ckey cvalue back)
   | hashmap.List.Nil =>
-    let l := hashmap.List.Nil
-    Result.ret (hashmap.List.Cons key value l)
+    Result.ret (true, hashmap.List.Cons key value hashmap.List.Nil)
 
-/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::insert_in_list]: backward function 0
+/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::insert_in_list]:
    Source: 'src/hashmap.rs', lines 97:4-97:71 -/
-def hashmap.HashMap.insert_in_list_back
+def hashmap.HashMap.insert_in_list
   (T : Type) (key : Usize) (value : T) (ls : hashmap.List T) :
-  Result (hashmap.List T)
+  Result (Bool × (hashmap.List T))
   :=
-  hashmap.HashMap.insert_in_list_loop_back T key value ls
+  hashmap.HashMap.insert_in_list_loop T key value ls
 
-/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::insert_no_resize]: merged forward/backward function
-   (there is a single backward function, and the forward function returns ())
+/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::insert_no_resize]:
    Source: 'src/hashmap.rs', lines 117:4-117:54 -/
 def hashmap.HashMap.insert_no_resize
   (T : Type) (self : hashmap.HashMap T) (key : Usize) (value : T) :
   Result (hashmap.HashMap T)
   :=
   do
-    let hash ← hashmap.hash_key key
-    let i := alloc.vec.Vec.len (hashmap.List T) self.slots
-    let hash_mod ← hash % i
-    let l ←
-      alloc.vec.Vec.index_mut (hashmap.List T) Usize
-        (core.slice.index.SliceIndexUsizeSliceTInst (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 + 1#usize
-        let l0 ← hashmap.HashMap.insert_in_list_back T key value l
-        let v ←
-          alloc.vec.Vec.index_mut_back (hashmap.List T) Usize
-            (core.slice.index.SliceIndexUsizeSliceTInst (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 ←
-          alloc.vec.Vec.index_mut_back (hashmap.List T) Usize
-            (core.slice.index.SliceIndexUsizeSliceTInst (hashmap.List T))
-            self.slots hash_mod l0
-        Result.ret { self with slots := v }
-
-/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::move_elements_from_list]: loop 0: merged forward/backward function
-   (there is a single backward function, and the forward function returns ())
+  let hash ← hashmap.hash_key key
+  let i := alloc.vec.Vec.len (hashmap.List T) self.slots
+  let hash_mod ← hash % i
+  let (l, index_mut_back) ←
+    alloc.vec.Vec.index_mut (hashmap.List T) Usize
+      (core.slice.index.SliceIndexUsizeSliceTInst (hashmap.List T)) self.slots
+      hash_mod
+  let (inserted, l1) ← hashmap.HashMap.insert_in_list T key value l
+  if inserted
+  then
+    do
+    let i1 ← self.num_entries + 1#usize
+    let v ← index_mut_back l1
+    Result.ret { self with num_entries := i1, slots := v }
+  else do
+       let v ← index_mut_back l1
+       Result.ret { self with slots := v }
+
+/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::move_elements_from_list]: loop 0:
    Source: 'src/hashmap.rs', lines 183:4-196:5 -/
 divergent def hashmap.HashMap.move_elements_from_list_loop
   (T : Type) (ntable : hashmap.HashMap T) (ls : hashmap.List T) :
@@ -180,12 +150,11 @@ divergent def hashmap.HashMap.move_elements_from_list_loop
   match ls with
   | hashmap.List.Cons k v tl =>
     do
-      let ntable0 ← hashmap.HashMap.insert_no_resize T ntable k v
-      hashmap.HashMap.move_elements_from_list_loop T ntable0 tl
+    let hm ← hashmap.HashMap.insert_no_resize T ntable k v
+    hashmap.HashMap.move_elements_from_list_loop T hm tl
   | hashmap.List.Nil => Result.ret ntable
 
-/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::move_elements_from_list]: merged forward/backward function
-   (there is a single backward function, and the forward function returns ())
+/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::move_elements_from_list]:
    Source: 'src/hashmap.rs', lines 183:4-183:72 -/
 def hashmap.HashMap.move_elements_from_list
   (T : Type) (ntable : hashmap.HashMap T) (ls : hashmap.List T) :
@@ -193,114 +162,111 @@ def hashmap.HashMap.move_elements_from_list
   :=
   hashmap.HashMap.move_elements_from_list_loop T ntable ls
 
-/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::move_elements]: loop 0: merged forward/backward function
-   (there is a single backward function, and the forward function returns ())
+/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::move_elements]: loop 0:
    Source: 'src/hashmap.rs', lines 171:4-180:5 -/
 divergent def hashmap.HashMap.move_elements_loop
   (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 := alloc.vec.Vec.len (hashmap.List T) slots
-  if i < i0
+  let i1 := alloc.vec.Vec.len (hashmap.List T) slots
+  if i < i1
   then
     do
-      let l ←
-        alloc.vec.Vec.index_mut (hashmap.List T) Usize
-          (core.slice.index.SliceIndexUsizeSliceTInst (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 + 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.SliceIndexUsizeSliceTInst (hashmap.List T)) slots i
-          l0
-      hashmap.HashMap.move_elements_loop T ntable0 slots0 i1
+    let (l, index_mut_back) ←
+      alloc.vec.Vec.index_mut (hashmap.List T) Usize
+        (core.slice.index.SliceIndexUsizeSliceTInst (hashmap.List T)) slots i
+    let (ls, l1) := core.mem.replace (hashmap.List T) l hashmap.List.Nil
+    let hm ← hashmap.HashMap.move_elements_from_list T ntable ls
+    let i2 ← i + 1#usize
+    let slots1 ← index_mut_back l1
+    let back_'a ← hashmap.HashMap.move_elements_loop T hm slots1 i2
+    let (hm1, v) := back_'a
+    Result.ret (hm1, v)
   else Result.ret (ntable, slots)
 
-/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::move_elements]: merged forward/backward function
-   (there is a single backward function, and the forward function returns ())
+/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::move_elements]:
    Source: 'src/hashmap.rs', lines 171:4-171:95 -/
 def hashmap.HashMap.move_elements
   (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
+  do
+  let back_'a ← hashmap.HashMap.move_elements_loop T ntable slots i
+  let (hm, v) := back_'a
+  Result.ret (hm, v)
 
-/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::try_resize]: merged forward/backward function
-   (there is a single backward function, and the forward function returns ())
+/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::try_resize]:
    Source: 'src/hashmap.rs', lines 140:4-140:28 -/
 def hashmap.HashMap.try_resize
   (T : Type) (self : hashmap.HashMap T) : Result (hashmap.HashMap T) :=
   do
-    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 * 2#usize
-        let ntable ← hashmap.HashMap.new_with_capacity T i2 i i0
-        let (ntable0, _) ←
-          hashmap.HashMap.move_elements T ntable self.slots 0#usize
-        Result.ret
-          {
-            ntable0
-              with
-              num_entries := self.num_entries, max_load_factor := (i, i0)
-          }
-    else Result.ret { self with max_load_factor := (i, i0) }
-
-/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::insert]: merged forward/backward function
-   (there is a single backward function, and the forward function returns ())
+  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, i1) := self.max_load_factor
+  let i2 ← n1 / i
+  if capacity <= i2
+  then
+    do
+    let i3 ← capacity * 2#usize
+    let ntable ← hashmap.HashMap.new_with_capacity T i3 i i1
+    let p ← hashmap.HashMap.move_elements T ntable self.slots 0#usize
+    let (ntable1, _) := p
+    Result.ret
+      {
+        ntable1
+          with
+          num_entries := self.num_entries, max_load_factor := (i, i1)
+      }
+  else Result.ret { self with max_load_factor := (i, i1) }
+
+/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::insert]:
    Source: 'src/hashmap.rs', lines 129:4-129:48 -/
 def hashmap.HashMap.insert
   (T : Type) (self : hashmap.HashMap T) (key : Usize) (value : T) :
   Result (hashmap.HashMap T)
   :=
   do
-    let self0 ← hashmap.HashMap.insert_no_resize T self key value
-    let i ← hashmap.HashMap.len T self0
-    if i > self0.max_load
-    then hashmap.HashMap.try_resize T self0
-    else Result.ret self0
+  let hm ← hashmap.HashMap.insert_no_resize T self key value
+  let i ← hashmap.HashMap.len T hm
+  if i > hm.max_load
+  then hashmap.HashMap.try_resize T hm
+  else Result.ret hm
 
-/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::contains_key_in_list]: loop 0: forward function
+/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::contains_key_in_list]: loop 0:
    Source: 'src/hashmap.rs', lines 206:4-219:5 -/
 divergent def hashmap.HashMap.contains_key_in_list_loop
   (T : Type) (key : Usize) (ls : hashmap.List T) : Result Bool :=
   match ls with
-  | hashmap.List.Cons ckey t tl =>
+  | hashmap.List.Cons ckey _ tl =>
     if ckey = key
     then Result.ret true
     else hashmap.HashMap.contains_key_in_list_loop T key tl
   | hashmap.List.Nil => Result.ret false
 
-/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::contains_key_in_list]: forward function
+/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::contains_key_in_list]:
    Source: 'src/hashmap.rs', lines 206:4-206:68 -/
 def hashmap.HashMap.contains_key_in_list
   (T : Type) (key : Usize) (ls : hashmap.List T) : Result Bool :=
   hashmap.HashMap.contains_key_in_list_loop T key ls
 
-/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::contains_key]: forward function
+/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::contains_key]:
    Source: 'src/hashmap.rs', lines 199:4-199:49 -/
 def hashmap.HashMap.contains_key
   (T : Type) (self : hashmap.HashMap T) (key : Usize) : Result Bool :=
   do
-    let hash ← hashmap.hash_key key
-    let i := alloc.vec.Vec.len (hashmap.List T) self.slots
-    let hash_mod ← hash % i
-    let l ←
-      alloc.vec.Vec.index (hashmap.List T) Usize
-        (core.slice.index.SliceIndexUsizeSliceTInst (hashmap.List T))
-        self.slots hash_mod
-    hashmap.HashMap.contains_key_in_list T key l
-
-/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_in_list]: loop 0: forward function
+  let hash ← hashmap.hash_key key
+  let i := alloc.vec.Vec.len (hashmap.List T) self.slots
+  let hash_mod ← hash % i
+  let l ←
+    alloc.vec.Vec.index (hashmap.List T) Usize
+      (core.slice.index.SliceIndexUsizeSliceTInst (hashmap.List T)) self.slots
+      hash_mod
+  hashmap.HashMap.contains_key_in_list T key l
+
+/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_in_list]: loop 0:
    Source: 'src/hashmap.rs', lines 224:4-237:5 -/
 divergent def hashmap.HashMap.get_in_list_loop
   (T : Type) (key : Usize) (ls : hashmap.List T) : Result T :=
@@ -311,259 +277,193 @@ divergent def hashmap.HashMap.get_in_list_loop
     else hashmap.HashMap.get_in_list_loop T key tl
   | hashmap.List.Nil => Result.fail .panic
 
-/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_in_list]: forward function
+/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_in_list]:
    Source: 'src/hashmap.rs', lines 224:4-224:70 -/
 def hashmap.HashMap.get_in_list
   (T : Type) (key : Usize) (ls : hashmap.List T) : Result T :=
   hashmap.HashMap.get_in_list_loop T key ls
 
-/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get]: forward function
+/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get]:
    Source: 'src/hashmap.rs', lines 239:4-239:55 -/
 def hashmap.HashMap.get
   (T : Type) (self : hashmap.HashMap T) (key : Usize) : Result T :=
   do
-    let hash ← hashmap.hash_key key
-    let i := alloc.vec.Vec.len (hashmap.List T) self.slots
-    let hash_mod ← hash % i
-    let l ←
-      alloc.vec.Vec.index (hashmap.List T) Usize
-        (core.slice.index.SliceIndexUsizeSliceTInst (hashmap.List T))
-        self.slots hash_mod
-    hashmap.HashMap.get_in_list T key l
-
-/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_mut_in_list]: loop 0: forward function
+  let hash ← hashmap.hash_key key
+  let i := alloc.vec.Vec.len (hashmap.List T) self.slots
+  let hash_mod ← hash % i
+  let l ←
+    alloc.vec.Vec.index (hashmap.List T) Usize
+      (core.slice.index.SliceIndexUsizeSliceTInst (hashmap.List T)) self.slots
+      hash_mod
+  hashmap.HashMap.get_in_list T key l
+
+/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_mut_in_list]: loop 0:
    Source: 'src/hashmap.rs', lines 245:4-254:5 -/
 divergent def hashmap.HashMap.get_mut_in_list_loop
-  (T : Type) (ls : hashmap.List T) (key : Usize) : Result T :=
-  match ls with
-  | hashmap.List.Cons ckey cvalue tl =>
-    if ckey = key
-    then Result.ret cvalue
-    else hashmap.HashMap.get_mut_in_list_loop T tl key
-  | hashmap.List.Nil => Result.fail .panic
-
-/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_mut_in_list]: forward function
-   Source: 'src/hashmap.rs', lines 245:4-245:86 -/
-def hashmap.HashMap.get_mut_in_list
-  (T : Type) (ls : hashmap.List T) (key : Usize) : Result T :=
-  hashmap.HashMap.get_mut_in_list_loop T ls key
-
-/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_mut_in_list]: loop 0: backward function 0
-   Source: 'src/hashmap.rs', lines 245:4-254:5 -/
-divergent def hashmap.HashMap.get_mut_in_list_loop_back
-  (T : Type) (ls : hashmap.List T) (key : Usize) (ret : T) :
-  Result (hashmap.List T)
+  (T : Type) (ls : hashmap.List T) (key : Usize) :
+  Result (T × (T → Result (hashmap.List T)))
   :=
   match ls with
   | hashmap.List.Cons ckey cvalue tl =>
     if ckey = key
-    then Result.ret (hashmap.List.Cons ckey ret tl)
+    then
+      let back_'a := fun ret => Result.ret (hashmap.List.Cons ckey ret tl)
+      Result.ret (cvalue, back_'a)
     else
       do
-        let tl0 ← hashmap.HashMap.get_mut_in_list_loop_back T tl key ret
-        Result.ret (hashmap.List.Cons ckey cvalue tl0)
+      let (t, back_'a) ← hashmap.HashMap.get_mut_in_list_loop T tl key
+      let back_'a1 :=
+        fun ret =>
+          do
+          let tl1 ← back_'a ret
+          Result.ret (hashmap.List.Cons ckey cvalue tl1)
+      Result.ret (t, back_'a1)
   | hashmap.List.Nil => Result.fail .panic
 
-/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_mut_in_list]: backward function 0
+/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_mut_in_list]:
    Source: 'src/hashmap.rs', lines 245:4-245:86 -/
-def hashmap.HashMap.get_mut_in_list_back
-  (T : Type) (ls : hashmap.List T) (key : Usize) (ret : T) :
-  Result (hashmap.List T)
+def hashmap.HashMap.get_mut_in_list
+  (T : Type) (ls : hashmap.List T) (key : Usize) :
+  Result (T × (T → Result (hashmap.List T)))
   :=
-  hashmap.HashMap.get_mut_in_list_loop_back T ls key ret
-
-/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_mut]: forward function
-   Source: 'src/hashmap.rs', lines 257:4-257:67 -/
-def hashmap.HashMap.get_mut
-  (T : Type) (self : hashmap.HashMap T) (key : Usize) : Result T :=
   do
-    let hash ← hashmap.hash_key key
-    let i := alloc.vec.Vec.len (hashmap.List T) self.slots
-    let hash_mod ← hash % i
-    let l ←
-      alloc.vec.Vec.index_mut (hashmap.List T) Usize
-        (core.slice.index.SliceIndexUsizeSliceTInst (hashmap.List T))
-        self.slots hash_mod
-    hashmap.HashMap.get_mut_in_list T l key
+  let (t, back_'a) ← hashmap.HashMap.get_mut_in_list_loop T ls key
+  Result.ret (t, back_'a)
 
-/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_mut]: backward function 0
+/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_mut]:
    Source: 'src/hashmap.rs', lines 257:4-257:67 -/
-def hashmap.HashMap.get_mut_back
-  (T : Type) (self : hashmap.HashMap T) (key : Usize) (ret : T) :
-  Result (hashmap.HashMap T)
+def hashmap.HashMap.get_mut
+  (T : Type) (self : hashmap.HashMap T) (key : Usize) :
+  Result (T × (T → Result (hashmap.HashMap T)))
   :=
   do
-    let hash ← hashmap.hash_key key
-    let i := alloc.vec.Vec.len (hashmap.List T) self.slots
-    let hash_mod ← hash % i
-    let l ←
-      alloc.vec.Vec.index_mut (hashmap.List T) Usize
-        (core.slice.index.SliceIndexUsizeSliceTInst (hashmap.List T))
-        self.slots hash_mod
-    let l0 ← hashmap.HashMap.get_mut_in_list_back T l key ret
-    let v ←
-      alloc.vec.Vec.index_mut_back (hashmap.List T) Usize
-        (core.slice.index.SliceIndexUsizeSliceTInst (hashmap.List T))
-        self.slots hash_mod l0
-    Result.ret { self with slots := v }
-
-/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::remove_from_list]: loop 0: forward function
-   Source: 'src/hashmap.rs', lines 265:4-291:5 -/
-divergent def hashmap.HashMap.remove_from_list_loop
-  (T : Type) (key : Usize) (ls : hashmap.List T) : Result (Option T) :=
-  match ls with
-  | hashmap.List.Cons ckey t tl =>
-    if ckey = key
-    then
-      let mv_ls :=
-        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 (some cvalue)
-      | hashmap.List.Nil => Result.fail .panic
-    else hashmap.HashMap.remove_from_list_loop T key tl
-  | hashmap.List.Nil => Result.ret none
-
-/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::remove_from_list]: forward function
-   Source: 'src/hashmap.rs', lines 265:4-265:69 -/
-def hashmap.HashMap.remove_from_list
-  (T : Type) (key : Usize) (ls : hashmap.List T) : Result (Option T) :=
-  hashmap.HashMap.remove_from_list_loop T key ls
+  let hash ← hashmap.hash_key key
+  let i := alloc.vec.Vec.len (hashmap.List T) self.slots
+  let hash_mod ← hash % i
+  let (l, index_mut_back) ←
+    alloc.vec.Vec.index_mut (hashmap.List T) Usize
+      (core.slice.index.SliceIndexUsizeSliceTInst (hashmap.List T)) self.slots
+      hash_mod
+  let (t, get_mut_in_list_back) ← hashmap.HashMap.get_mut_in_list T l key
+  let back_'a :=
+    fun ret =>
+      do
+      let l1 ← get_mut_in_list_back ret
+      let v ← index_mut_back l1
+      Result.ret { self with slots := v }
+  Result.ret (t, back_'a)
 
-/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::remove_from_list]: loop 0: backward function 1
+/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::remove_from_list]: loop 0:
    Source: 'src/hashmap.rs', lines 265:4-291:5 -/
-divergent def hashmap.HashMap.remove_from_list_loop_back
-  (T : Type) (key : Usize) (ls : hashmap.List T) : Result (hashmap.List T) :=
+divergent def hashmap.HashMap.remove_from_list_loop
+  (T : Type) (key : Usize) (ls : hashmap.List T) :
+  Result ((Option T) × (hashmap.List T))
+  :=
   match ls with
   | hashmap.List.Cons ckey t tl =>
     if ckey = key
     then
-      let mv_ls :=
+      let (mv_ls, _) :=
         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
+      | hashmap.List.Cons _ cvalue tl1 => Result.ret (some cvalue, tl1)
       | hashmap.List.Nil => Result.fail .panic
     else
       do
-        let tl0 ← hashmap.HashMap.remove_from_list_loop_back T key tl
-        Result.ret (hashmap.List.Cons ckey t tl0)
-  | hashmap.List.Nil => Result.ret hashmap.List.Nil
+      let (o, back) ← hashmap.HashMap.remove_from_list_loop T key tl
+      Result.ret (o, hashmap.List.Cons ckey t back)
+  | hashmap.List.Nil => Result.ret (none, hashmap.List.Nil)
 
-/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::remove_from_list]: backward function 1
+/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::remove_from_list]:
    Source: 'src/hashmap.rs', lines 265:4-265:69 -/
-def hashmap.HashMap.remove_from_list_back
-  (T : Type) (key : Usize) (ls : hashmap.List T) : Result (hashmap.List T) :=
-  hashmap.HashMap.remove_from_list_loop_back T key ls
+def hashmap.HashMap.remove_from_list
+  (T : Type) (key : Usize) (ls : hashmap.List T) :
+  Result ((Option T) × (hashmap.List T))
+  :=
+  hashmap.HashMap.remove_from_list_loop T key ls
 
-/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::remove]: forward function
+/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::remove]:
    Source: 'src/hashmap.rs', lines 294:4-294:52 -/
 def hashmap.HashMap.remove
-  (T : Type) (self : hashmap.HashMap T) (key : Usize) : Result (Option T) :=
-  do
-    let hash ← hashmap.hash_key key
-    let i := alloc.vec.Vec.len (hashmap.List T) self.slots
-    let hash_mod ← hash % i
-    let l ←
-      alloc.vec.Vec.index_mut (hashmap.List T) Usize
-        (core.slice.index.SliceIndexUsizeSliceTInst (hashmap.List T))
-        self.slots hash_mod
-    let x ← hashmap.HashMap.remove_from_list T key l
-    match x with
-    | none => Result.ret none
-    | some x0 => do
-                   let _ ← self.num_entries - 1#usize
-                   Result.ret (some x0)
-
-/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::remove]: backward function 0
-   Source: 'src/hashmap.rs', lines 294:4-294:52 -/
-def hashmap.HashMap.remove_back
   (T : Type) (self : hashmap.HashMap T) (key : Usize) :
-  Result (hashmap.HashMap T)
+  Result ((Option T) × (hashmap.HashMap T))
   :=
   do
-    let hash ← hashmap.hash_key key
-    let i := alloc.vec.Vec.len (hashmap.List T) self.slots
-    let hash_mod ← hash % i
-    let l ←
-      alloc.vec.Vec.index_mut (hashmap.List T) Usize
-        (core.slice.index.SliceIndexUsizeSliceTInst (hashmap.List T))
-        self.slots hash_mod
-    let x ← hashmap.HashMap.remove_from_list T key l
-    match x with
-    | none =>
-      do
-        let l0 ← hashmap.HashMap.remove_from_list_back T key l
-        let v ←
-          alloc.vec.Vec.index_mut_back (hashmap.List T) Usize
-            (core.slice.index.SliceIndexUsizeSliceTInst (hashmap.List T))
-            self.slots hash_mod l0
-        Result.ret { self with slots := v }
-    | some x0 =>
-      do
-        let i0 ← self.num_entries - 1#usize
-        let l0 ← hashmap.HashMap.remove_from_list_back T key l
-        let v ←
-          alloc.vec.Vec.index_mut_back (hashmap.List T) Usize
-            (core.slice.index.SliceIndexUsizeSliceTInst (hashmap.List T))
-            self.slots hash_mod l0
-        Result.ret { self with num_entries := i0, slots := v }
-
-/- [hashmap_main::hashmap::test1]: forward function
+  let hash ← hashmap.hash_key key
+  let i := alloc.vec.Vec.len (hashmap.List T) self.slots
+  let hash_mod ← hash % i
+  let (l, index_mut_back) ←
+    alloc.vec.Vec.index_mut (hashmap.List T) Usize
+      (core.slice.index.SliceIndexUsizeSliceTInst (hashmap.List T)) self.slots
+      hash_mod
+  let (x, l1) ← hashmap.HashMap.remove_from_list T key l
+  match x with
+  | none =>
+    do
+    let v ← index_mut_back l1
+    Result.ret (none, { self with slots := v })
+  | some x1 =>
+    do
+    let i1 ← self.num_entries - 1#usize
+    let v ← index_mut_back l1
+    Result.ret (some x1, { self with num_entries := i1, slots := v })
+
+/- [hashmap_main::hashmap::test1]:
    Source: 'src/hashmap.rs', lines 315:0-315:10 -/
 def hashmap.test1 : Result Unit :=
   do
-    let hm ← hashmap.HashMap.new U64
-    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)
+  let hm ← hashmap.HashMap.new U64
+  let hm1 ← hashmap.HashMap.insert U64 hm 0#usize 42#u64
+  let hm2 ← hashmap.HashMap.insert U64 hm1 128#usize 18#u64
+  let hm3 ← hashmap.HashMap.insert U64 hm2 1024#usize 138#u64
+  let hm4 ← hashmap.HashMap.insert U64 hm3 1056#usize 256#u64
+  let i ← hashmap.HashMap.get U64 hm4 128#usize
+  if not (i = 18#u64)
+  then Result.fail .panic
+  else
+    do
+    let (_, get_mut_back) ← hashmap.HashMap.get_mut U64 hm4 1024#usize
+    let hm5 ← get_mut_back 56#u64
+    let i1 ← hashmap.HashMap.get U64 hm5 1024#usize
+    if not (i1 = 56#u64)
     then Result.fail .panic
     else
       do
-        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)
+      let (x, hm6) ← hashmap.HashMap.remove U64 hm5 1024#usize
+      match x with
+      | none => Result.fail .panic
+      | some x1 =>
+        if not (x1 = 56#u64)
         then Result.fail .panic
         else
           do
-            let x ← hashmap.HashMap.remove U64 hm4 1024#usize
-            match x with
-            | none => Result.fail .panic
-            | some x0 =>
-              if not (x0 = 56#u64)
+          let i2 ← hashmap.HashMap.get U64 hm6 0#usize
+          if not (i2 = 42#u64)
+          then Result.fail .panic
+          else
+            do
+            let i3 ← hashmap.HashMap.get U64 hm6 128#usize
+            if not (i3 = 18#u64)
+            then Result.fail .panic
+            else
+              do
+              let i4 ← hashmap.HashMap.get U64 hm6 1056#usize
+              if not (i4 = 256#u64)
               then Result.fail .panic
-              else
-                do
-                  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 .panic
-                  else
-                    do
-                      let i2 ← hashmap.HashMap.get U64 hm5 128#usize
-                      if not (i2 = 18#u64)
-                      then Result.fail .panic
-                      else
-                        do
-                          let i3 ← hashmap.HashMap.get U64 hm5 1056#usize
-                          if not (i3 = 256#u64)
-                          then Result.fail .panic
-                          else Result.ret ()
-
-/- [hashmap_main::insert_on_disk]: forward function
+              else Result.ret ()
+
+/- [hashmap_main::insert_on_disk]:
    Source: 'src/hashmap_main.rs', lines 7:0-7:43 -/
 def insert_on_disk
   (key : Usize) (value : U64) (st : State) : Result (State × Unit) :=
   do
-    let (st0, hm) ← hashmap_utils.deserialize st
-    let hm0 ← hashmap.HashMap.insert U64 hm key value
-    let (st1, _) ← hashmap_utils.serialize hm0 st0
-    Result.ret (st1, ())
+  let (st1, hm) ← hashmap_utils.deserialize st
+  let hm1 ← hashmap.HashMap.insert U64 hm key value
+  let (st2, _) ← hashmap_utils.serialize hm1 st1
+  Result.ret (st2, ())
 
-/- [hashmap_main::main]: forward function
+/- [hashmap_main::main]:
    Source: 'src/hashmap_main.rs', lines 16:0-16:13 -/
 def main : Result Unit :=
   Result.ret ()
diff --git a/tests/lean/HashmapMain/FunsExternal_Template.lean b/tests/lean/HashmapMain/FunsExternal_Template.lean
index 02ca5b0e..c09edbd2 100644
--- a/tests/lean/HashmapMain/FunsExternal_Template.lean
+++ b/tests/lean/HashmapMain/FunsExternal_Template.lean
@@ -6,12 +6,12 @@ import HashmapMain.Types
 open Primitives
 open hashmap_main
 
-/- [hashmap_main::hashmap_utils::deserialize]: forward function
+/- [hashmap_main::hashmap_utils::deserialize]:
    Source: 'src/hashmap_utils.rs', lines 10:0-10:43 -/
 axiom hashmap_utils.deserialize
   : State → Result (State × (hashmap.HashMap U64))
 
-/- [hashmap_main::hashmap_utils::serialize]: forward function
+/- [hashmap_main::hashmap_utils::serialize]:
    Source: 'src/hashmap_utils.rs', lines 5:0-5:42 -/
 axiom hashmap_utils.serialize
   : hashmap.HashMap U64 → State → Result (State × Unit)
diff --git a/tests/lean/Loops.lean b/tests/lean/Loops.lean
index 08aa08a5..fbb4616f 100644
--- a/tests/lean/Loops.lean
+++ b/tests/lean/Loops.lean
@@ -5,73 +5,72 @@ open Primitives
 
 namespace loops
 
-/- [loops::sum]: loop 0: forward function
+/- [loops::sum]: loop 0:
    Source: 'src/loops.rs', lines 4:0-14:1 -/
 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
+       let s1 ← s + i
+       let i1 ← i + 1#u32
+       sum_loop max i1 s1
   else s * 2#u32
 
-/- [loops::sum]: forward function
+/- [loops::sum]:
    Source: 'src/loops.rs', lines 4:0-4:27 -/
 def sum (max : U32) : Result U32 :=
   sum_loop max 0#u32 0#u32
 
-/- [loops::sum_with_mut_borrows]: loop 0: forward function
+/- [loops::sum_with_mut_borrows]: loop 0:
    Source: 'src/loops.rs', lines 19:0-31:1 -/
 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
+    let ms1 ← ms + mi
+    let mi1 ← mi + 1#u32
+    sum_with_mut_borrows_loop max mi1 ms1
   else ms * 2#u32
 
-/- [loops::sum_with_mut_borrows]: forward function
+/- [loops::sum_with_mut_borrows]:
    Source: 'src/loops.rs', lines 19:0-19:44 -/
 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
+/- [loops::sum_with_shared_borrows]: loop 0:
    Source: 'src/loops.rs', lines 34:0-48:1 -/
 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
+    let i1 ← i + 1#u32
+    let s1 ← s + i1
+    sum_with_shared_borrows_loop max i1 s1
   else s * 2#u32
 
-/- [loops::sum_with_shared_borrows]: forward function
+/- [loops::sum_with_shared_borrows]:
    Source: 'src/loops.rs', lines 34:0-34:47 -/
 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 ())
+/- [loops::clear]: loop 0:
    Source: 'src/loops.rs', lines 52:0-58:1 -/
 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
+  let i1 := alloc.vec.Vec.len U32 v
+  if i < i1
   then
     do
-      let i1 ← i + 1#usize
-      let v0 ←
-        alloc.vec.Vec.index_mut_back U32 Usize
-          (core.slice.index.SliceIndexUsizeSliceTInst U32) v i 0#u32
-      clear_loop v0 i1
+    let (_, index_mut_back) ←
+      alloc.vec.Vec.index_mut U32 Usize
+        (core.slice.index.SliceIndexUsizeSliceTInst U32) v i
+    let i2 ← i + 1#usize
+    let v1 ← index_mut_back 0#u32
+    clear_loop v1 i2
   else Result.ret v
 
-/- [loops::clear]: merged forward/backward function
-   (there is a single backward function, and the forward function returns ())
+/- [loops::clear]:
    Source: 'src/loops.rs', lines 52:0-52:30 -/
 def clear (v : alloc.vec.Vec U32) : Result (alloc.vec.Vec U32) :=
   clear_loop v 0#usize
@@ -82,7 +81,7 @@ inductive List (T : Type) :=
 | Cons : T → List T → List T
 | Nil : List T
 
-/- [loops::list_mem]: loop 0: forward function
+/- [loops::list_mem]: loop 0:
    Source: 'src/loops.rs', lines 66:0-75:1 -/
 divergent def list_mem_loop (x : U32) (ls : List U32) : Result Bool :=
   match ls with
@@ -91,51 +90,41 @@ divergent def list_mem_loop (x : U32) (ls : List U32) : Result Bool :=
                       else list_mem_loop x tl
   | List.Nil => Result.ret false
 
-/- [loops::list_mem]: forward function
+/- [loops::list_mem]:
    Source: 'src/loops.rs', lines 66:0-66:52 -/
 def list_mem (x : U32) (ls : List U32) : Result Bool :=
   list_mem_loop x ls
 
-/- [loops::list_nth_mut_loop]: loop 0: forward function
+/- [loops::list_nth_mut_loop]: loop 0:
    Source: 'src/loops.rs', lines 78:0-88:1 -/
 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 .panic
-
-/- [loops::list_nth_mut_loop]: forward function
-   Source: 'src/loops.rs', lines 78:0-78:71 -/
-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
-   Source: 'src/loops.rs', lines 78:0-88:1 -/
-divergent def list_nth_mut_loop_loop_back
-  (T : Type) (ls : List T) (i : U32) (ret : T) : Result (List T) :=
+  (T : Type) (ls : List T) (i : U32) : Result (T × (T → Result (List T))) :=
   match ls with
   | List.Cons x tl =>
     if i = 0#u32
-    then Result.ret (List.Cons ret tl)
+    then
+      let back := fun ret => Result.ret (List.Cons ret tl)
+      Result.ret (x, back)
     else
       do
-        let i0 ← i - 1#u32
-        let tl0 ← list_nth_mut_loop_loop_back T tl i0 ret
-        Result.ret (List.Cons x tl0)
+      let i1 ← i - 1#u32
+      let (t, back) ← list_nth_mut_loop_loop T tl i1
+      let back1 :=
+        fun ret => do
+                   let tl1 ← back ret
+                   Result.ret (List.Cons x tl1)
+      Result.ret (t, back1)
   | List.Nil => Result.fail .panic
 
-/- [loops::list_nth_mut_loop]: backward function 0
+/- [loops::list_nth_mut_loop]:
    Source: 'src/loops.rs', lines 78:0-78:71 -/
-def list_nth_mut_loop_back
-  (T : Type) (ls : List T) (i : U32) (ret : T) : Result (List T) :=
-  list_nth_mut_loop_loop_back T ls i ret
+def list_nth_mut_loop
+  (T : Type) (ls : List T) (i : U32) : Result (T × (T → Result (List T))) :=
+  do
+  let (t, back) ← list_nth_mut_loop_loop T ls i
+  Result.ret (t, back)
 
-/- [loops::list_nth_shared_loop]: loop 0: forward function
+/- [loops::list_nth_shared_loop]: loop 0:
    Source: 'src/loops.rs', lines 91:0-101:1 -/
 divergent def list_nth_shared_loop_loop
   (T : Type) (ls : List T) (i : U32) : Result T :=
@@ -144,64 +133,54 @@ divergent def list_nth_shared_loop_loop
     if i = 0#u32
     then Result.ret x
     else do
-           let i0 ← i - 1#u32
-           list_nth_shared_loop_loop T tl i0
+         let i1 ← i - 1#u32
+         list_nth_shared_loop_loop T tl i1
   | List.Nil => Result.fail .panic
 
-/- [loops::list_nth_shared_loop]: forward function
+/- [loops::list_nth_shared_loop]:
    Source: 'src/loops.rs', lines 91:0-91:66 -/
 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
+/- [loops::get_elem_mut]: loop 0:
    Source: 'src/loops.rs', lines 103:0-117:1 -/
-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 .panic
-
-/- [loops::get_elem_mut]: forward function
-   Source: 'src/loops.rs', lines 103:0-103:73 -/
-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.SliceIndexUsizeSliceTInst (List Usize)) slots 0#usize
-    get_elem_mut_loop x l
-
-/- [loops::get_elem_mut]: loop 0: backward function 0
-   Source: 'src/loops.rs', lines 103:0-117:1 -/
-divergent def get_elem_mut_loop_back
-  (x : Usize) (ls : List Usize) (ret : Usize) : Result (List Usize) :=
+divergent def get_elem_mut_loop
+  (x : Usize) (ls : List Usize) :
+  Result (Usize × (Usize → Result (List Usize)))
+  :=
   match ls with
   | List.Cons y tl =>
     if y = x
-    then Result.ret (List.Cons ret tl)
+    then
+      let back := fun ret => Result.ret (List.Cons ret tl)
+      Result.ret (y, back)
     else
       do
-        let tl0 ← get_elem_mut_loop_back x tl ret
-        Result.ret (List.Cons y tl0)
+      let (i, back) ← get_elem_mut_loop x tl
+      let back1 :=
+        fun ret => do
+                   let tl1 ← back ret
+                   Result.ret (List.Cons y tl1)
+      Result.ret (i, back1)
   | List.Nil => Result.fail .panic
 
-/- [loops::get_elem_mut]: backward function 0
+/- [loops::get_elem_mut]:
    Source: 'src/loops.rs', lines 103:0-103:73 -/
-def get_elem_mut_back
-  (slots : alloc.vec.Vec (List Usize)) (x : Usize) (ret : Usize) :
-  Result (alloc.vec.Vec (List Usize))
+def get_elem_mut
+  (slots : alloc.vec.Vec (List Usize)) (x : Usize) :
+  Result (Usize × (Usize → Result (alloc.vec.Vec (List Usize))))
   :=
   do
-    let l ←
-      alloc.vec.Vec.index_mut (List Usize) Usize
-        (core.slice.index.SliceIndexUsizeSliceTInst (List Usize)) slots 0#usize
-    let l0 ← get_elem_mut_loop_back x l ret
-    alloc.vec.Vec.index_mut_back (List Usize) Usize
+  let (l, index_mut_back) ←
+    alloc.vec.Vec.index_mut (List Usize) Usize
       (core.slice.index.SliceIndexUsizeSliceTInst (List Usize)) slots 0#usize
-      l0
+  let (i, back) ← get_elem_mut_loop x l
+  let back1 := fun ret => do
+                          let l1 ← back ret
+                          index_mut_back l1
+  Result.ret (i, back1)
 
-/- [loops::get_elem_shared]: loop 0: forward function
+/- [loops::get_elem_shared]: loop 0:
    Source: 'src/loops.rs', lines 119:0-133:1 -/
 divergent def get_elem_shared_loop
   (x : Usize) (ls : List Usize) : Result Usize :=
@@ -211,76 +190,63 @@ divergent def get_elem_shared_loop
                       else get_elem_shared_loop x tl
   | List.Nil => Result.fail .panic
 
-/- [loops::get_elem_shared]: forward function
+/- [loops::get_elem_shared]:
    Source: 'src/loops.rs', lines 119:0-119:68 -/
 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.SliceIndexUsizeSliceTInst (List Usize)) slots 0#usize
-    get_elem_shared_loop x l
-
-/- [loops::id_mut]: forward function
-   Source: 'src/loops.rs', lines 135:0-135:50 -/
-def id_mut (T : Type) (ls : List T) : Result (List T) :=
-  Result.ret ls
+  let l ←
+    alloc.vec.Vec.index (List Usize) Usize
+      (core.slice.index.SliceIndexUsizeSliceTInst (List Usize)) slots 0#usize
+  get_elem_shared_loop x l
 
-/- [loops::id_mut]: backward function 0
+/- [loops::id_mut]:
    Source: 'src/loops.rs', lines 135:0-135:50 -/
-def id_mut_back (T : Type) (ls : List T) (ret : List T) : Result (List T) :=
-  Result.ret ret
+def id_mut
+  (T : Type) (ls : List T) :
+  Result ((List T) × (List T → Result (List T)))
+  :=
+  Result.ret (ls, Result.ret)
 
-/- [loops::id_shared]: forward function
+/- [loops::id_shared]:
    Source: 'src/loops.rs', lines 139:0-139:45 -/
 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
+/- [loops::list_nth_mut_loop_with_id]: loop 0:
    Source: 'src/loops.rs', lines 144:0-155:1 -/
 divergent def list_nth_mut_loop_with_id_loop
-  (T : Type) (i : U32) (ls : List T) : Result T :=
+  (T : Type) (i : U32) (ls : List T) : Result (T × (T → Result (List 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 .panic
-
-/- [loops::list_nth_mut_loop_with_id]: forward function
-   Source: 'src/loops.rs', lines 144:0-144:75 -/
-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
-   Source: 'src/loops.rs', lines 144:0-155:1 -/
-divergent def list_nth_mut_loop_with_id_loop_back
-  (T : Type) (i : U32) (ls : List T) (ret : T) : Result (List T) :=
-  match ls with
-  | List.Cons x tl =>
-    if i = 0#u32
-    then Result.ret (List.Cons ret tl)
+    then
+      let back := fun ret => Result.ret (List.Cons ret tl)
+      Result.ret (x, back)
     else
       do
-        let i0 ← i - 1#u32
-        let tl0 ← list_nth_mut_loop_with_id_loop_back T i0 tl ret
-        Result.ret (List.Cons x tl0)
+      let i1 ← i - 1#u32
+      let (t, back) ← list_nth_mut_loop_with_id_loop T i1 tl
+      let back1 :=
+        fun ret => do
+                   let tl1 ← back ret
+                   Result.ret (List.Cons x tl1)
+      Result.ret (t, back1)
   | List.Nil => Result.fail .panic
 
-/- [loops::list_nth_mut_loop_with_id]: backward function 0
+/- [loops::list_nth_mut_loop_with_id]:
    Source: 'src/loops.rs', lines 144:0-144:75 -/
-def list_nth_mut_loop_with_id_back
-  (T : Type) (ls : List T) (i : U32) (ret : T) : Result (List T) :=
+def list_nth_mut_loop_with_id
+  (T : Type) (ls : List T) (i : U32) : Result (T × (T → Result (List T))) :=
   do
-    let ls0 ← id_mut T ls
-    let l ← list_nth_mut_loop_with_id_loop_back T i ls0 ret
-    id_mut_back T ls l
-
-/- [loops::list_nth_shared_loop_with_id]: loop 0: forward function
+  let (ls1, id_mut_back) ← id_mut T ls
+  let (t, back) ← list_nth_mut_loop_with_id_loop T i ls1
+  let back1 := fun ret => do
+                          let l ← back ret
+                          id_mut_back l
+  Result.ret (t, back1)
+
+/- [loops::list_nth_shared_loop_with_id]: loop 0:
    Source: 'src/loops.rs', lines 158:0-169:1 -/
 divergent def list_nth_shared_loop_with_id_loop
   (T : Type) (i : U32) (ls : List T) : Result T :=
@@ -289,97 +255,60 @@ divergent def list_nth_shared_loop_with_id_loop
     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
+         let i1 ← i - 1#u32
+         list_nth_shared_loop_with_id_loop T i1 tl
   | List.Nil => Result.fail .panic
 
-/- [loops::list_nth_shared_loop_with_id]: forward function
+/- [loops::list_nth_shared_loop_with_id]:
    Source: 'src/loops.rs', lines 158:0-158:70 -/
 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
+  let ls1 ← id_shared T ls
+  list_nth_shared_loop_with_id_loop T i ls1
 
-/- [loops::list_nth_mut_loop_pair]: loop 0: forward function
+/- [loops::list_nth_mut_loop_pair]: loop 0:
    Source: 'src/loops.rs', lines 174:0-195:1 -/
 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 .panic
-  | List.Nil => Result.fail .panic
-
-/- [loops::list_nth_mut_loop_pair]: forward function
-   Source: 'src/loops.rs', lines 174:0-178:27 -/
-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
-   Source: 'src/loops.rs', lines 174:0-195:1 -/
-divergent def list_nth_mut_loop_pair_loop_back'a
-  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret : T) :
-  Result (List T)
+  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) :
+  Result ((T × T) × (T → Result (List T)) × (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 ret tl0)
+      then
+        let back_'a := fun ret => Result.ret (List.Cons ret tl0)
+        let back_'b := fun ret => Result.ret (List.Cons ret tl1)
+        Result.ret ((x0, x1), back_'a, back_'b)
       else
         do
-          let i0 ← i - 1#u32
-          let tl00 ← list_nth_mut_loop_pair_loop_back'a T tl0 tl1 i0 ret
-          Result.ret (List.Cons x0 tl00)
+        let i1 ← i - 1#u32
+        let (p, back_'a, back_'b) ← list_nth_mut_loop_pair_loop T tl0 tl1 i1
+        let back_'a1 :=
+          fun ret => do
+                     let tl01 ← back_'a ret
+                     Result.ret (List.Cons x0 tl01)
+        let back_'b1 :=
+          fun ret => do
+                     let tl11 ← back_'b ret
+                     Result.ret (List.Cons x1 tl11)
+        Result.ret (p, back_'a1, back_'b1)
     | List.Nil => Result.fail .panic
   | List.Nil => Result.fail .panic
 
-/- [loops::list_nth_mut_loop_pair]: backward function 0
+/- [loops::list_nth_mut_loop_pair]:
    Source: 'src/loops.rs', lines 174:0-178:27 -/
-def list_nth_mut_loop_pair_back'a
-  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret : T) :
-  Result (List T)
-  :=
-  list_nth_mut_loop_pair_loop_back'a T ls0 ls1 i ret
-
-/- [loops::list_nth_mut_loop_pair]: loop 0: backward function 1
-   Source: 'src/loops.rs', lines 174:0-195:1 -/
-divergent def list_nth_mut_loop_pair_loop_back'b
-  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret : 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 ret tl1)
-      else
-        do
-          let i0 ← i - 1#u32
-          let tl10 ← list_nth_mut_loop_pair_loop_back'b T tl0 tl1 i0 ret
-          Result.ret (List.Cons x1 tl10)
-    | List.Nil => Result.fail .panic
-  | List.Nil => Result.fail .panic
-
-/- [loops::list_nth_mut_loop_pair]: backward function 1
-   Source: 'src/loops.rs', lines 174:0-178:27 -/
-def list_nth_mut_loop_pair_back'b
-  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret : T) :
-  Result (List T)
+def list_nth_mut_loop_pair
+  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) :
+  Result ((T × T) × (T → Result (List T)) × (T → Result (List T)))
   :=
-  list_nth_mut_loop_pair_loop_back'b T ls0 ls1 i ret
+  do
+  let (p, back_'a, back_'b) ← list_nth_mut_loop_pair_loop T ls0 ls1 i
+  Result.ret (p, back_'a, back_'b)
 
-/- [loops::list_nth_shared_loop_pair]: loop 0: forward function
+/- [loops::list_nth_shared_loop_pair]: loop 0:
    Source: 'src/loops.rs', lines 198:0-219:1 -/
 divergent def list_nth_shared_loop_pair_loop
   (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
@@ -390,71 +319,58 @@ divergent def list_nth_shared_loop_pair_loop
       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
+           let i1 ← i - 1#u32
+           list_nth_shared_loop_pair_loop T tl0 tl1 i1
     | List.Nil => Result.fail .panic
   | List.Nil => Result.fail .panic
 
-/- [loops::list_nth_shared_loop_pair]: forward function
+/- [loops::list_nth_shared_loop_pair]:
    Source: 'src/loops.rs', lines 198:0-202:19 -/
 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
+/- [loops::list_nth_mut_loop_pair_merge]: loop 0:
    Source: 'src/loops.rs', lines 223:0-238:1 -/
 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 .panic
-  | List.Nil => Result.fail .panic
-
-/- [loops::list_nth_mut_loop_pair_merge]: forward function
-   Source: 'src/loops.rs', lines 223:0-227:27 -/
-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
-   Source: 'src/loops.rs', lines 223:0-238:1 -/
-divergent def list_nth_mut_loop_pair_merge_loop_back
-  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret : (T × T)) :
-  Result ((List T) × (List T))
+  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) :
+  Result ((T × T) × ((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) := ret
-           Result.ret (List.Cons t tl0, List.Cons t0 tl1)
+      then
+        let back_'a :=
+          fun ret =>
+            let (t, t1) := ret
+            Result.ret (List.Cons t tl0, List.Cons t1 tl1)
+        Result.ret ((x0, x1), back_'a)
       else
         do
-          let i0 ← i - 1#u32
-          let (tl00, tl10) ←
-            list_nth_mut_loop_pair_merge_loop_back T tl0 tl1 i0 ret
-          Result.ret (List.Cons x0 tl00, List.Cons x1 tl10)
+        let i1 ← i - 1#u32
+        let (p, back_'a) ← list_nth_mut_loop_pair_merge_loop T tl0 tl1 i1
+        let back_'a1 :=
+          fun ret =>
+            do
+            let (tl01, tl11) ← back_'a ret
+            Result.ret (List.Cons x0 tl01, List.Cons x1 tl11)
+        Result.ret (p, back_'a1)
     | List.Nil => Result.fail .panic
   | List.Nil => Result.fail .panic
 
-/- [loops::list_nth_mut_loop_pair_merge]: backward function 0
+/- [loops::list_nth_mut_loop_pair_merge]:
    Source: 'src/loops.rs', lines 223:0-227:27 -/
-def list_nth_mut_loop_pair_merge_back
-  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret : (T × T)) :
-  Result ((List T) × (List T))
+def list_nth_mut_loop_pair_merge
+  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) :
+  Result ((T × T) × ((T × T) → Result ((List T) × (List T))))
   :=
-  list_nth_mut_loop_pair_merge_loop_back T ls0 ls1 i ret
+  do
+  let (p, back_'a) ← list_nth_mut_loop_pair_merge_loop T ls0 ls1 i
+  Result.ret (p, back_'a)
 
-/- [loops::list_nth_shared_loop_pair_merge]: loop 0: forward function
+/- [loops::list_nth_shared_loop_pair_merge]: loop 0:
    Source: 'src/loops.rs', lines 241:0-256:1 -/
 divergent def list_nth_shared_loop_pair_merge_loop
   (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
@@ -466,221 +382,161 @@ divergent def list_nth_shared_loop_pair_merge_loop
       then Result.ret (x0, x1)
       else
         do
-          let i0 ← i - 1#u32
-          list_nth_shared_loop_pair_merge_loop T tl0 tl1 i0
+        let i1 ← i - 1#u32
+        list_nth_shared_loop_pair_merge_loop T tl0 tl1 i1
     | List.Nil => Result.fail .panic
   | List.Nil => Result.fail .panic
 
-/- [loops::list_nth_shared_loop_pair_merge]: forward function
+/- [loops::list_nth_shared_loop_pair_merge]:
    Source: 'src/loops.rs', lines 241:0-245:19 -/
 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
+/- [loops::list_nth_mut_shared_loop_pair]: loop 0:
    Source: 'src/loops.rs', lines 259:0-274:1 -/
 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 .panic
-  | List.Nil => Result.fail .panic
-
-/- [loops::list_nth_mut_shared_loop_pair]: forward function
-   Source: 'src/loops.rs', lines 259:0-263:23 -/
-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
-   Source: 'src/loops.rs', lines 259:0-274:1 -/
-divergent def list_nth_mut_shared_loop_pair_loop_back
-  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret : T) :
-  Result (List T)
+  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) :
+  Result ((T × T) × (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 ret tl0)
+      then
+        let back_'a := fun ret => Result.ret (List.Cons ret tl0)
+        Result.ret ((x0, x1), back_'a)
       else
         do
-          let i0 ← i - 1#u32
-          let tl00 ← list_nth_mut_shared_loop_pair_loop_back T tl0 tl1 i0 ret
-          Result.ret (List.Cons x0 tl00)
+        let i1 ← i - 1#u32
+        let (p, back_'a) ← list_nth_mut_shared_loop_pair_loop T tl0 tl1 i1
+        let back_'a1 :=
+          fun ret => do
+                     let tl01 ← back_'a ret
+                     Result.ret (List.Cons x0 tl01)
+        Result.ret (p, back_'a1)
     | List.Nil => Result.fail .panic
   | List.Nil => Result.fail .panic
 
-/- [loops::list_nth_mut_shared_loop_pair]: backward function 0
+/- [loops::list_nth_mut_shared_loop_pair]:
    Source: 'src/loops.rs', lines 259:0-263:23 -/
-def list_nth_mut_shared_loop_pair_back
-  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret : T) :
-  Result (List T)
+def list_nth_mut_shared_loop_pair
+  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) :
+  Result ((T × T) × (T → Result (List T)))
   :=
-  list_nth_mut_shared_loop_pair_loop_back T ls0 ls1 i ret
+  do
+  let (p, back_'a) ← list_nth_mut_shared_loop_pair_loop T ls0 ls1 i
+  Result.ret (p, back_'a)
 
-/- [loops::list_nth_mut_shared_loop_pair_merge]: loop 0: forward function
+/- [loops::list_nth_mut_shared_loop_pair_merge]: loop 0:
    Source: 'src/loops.rs', lines 278:0-293:1 -/
 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 .panic
-  | List.Nil => Result.fail .panic
-
-/- [loops::list_nth_mut_shared_loop_pair_merge]: forward function
-   Source: 'src/loops.rs', lines 278:0-282:23 -/
-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
-   Source: 'src/loops.rs', lines 278:0-293:1 -/
-divergent def list_nth_mut_shared_loop_pair_merge_loop_back
-  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret : T) :
-  Result (List T)
+  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) :
+  Result ((T × T) × (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 ret tl0)
+      then
+        let back_'a := fun ret => Result.ret (List.Cons ret tl0)
+        Result.ret ((x0, x1), back_'a)
       else
         do
-          let i0 ← i - 1#u32
-          let tl00 ←
-            list_nth_mut_shared_loop_pair_merge_loop_back T tl0 tl1 i0 ret
-          Result.ret (List.Cons x0 tl00)
+        let i1 ← i - 1#u32
+        let (p, back_'a) ←
+          list_nth_mut_shared_loop_pair_merge_loop T tl0 tl1 i1
+        let back_'a1 :=
+          fun ret => do
+                     let tl01 ← back_'a ret
+                     Result.ret (List.Cons x0 tl01)
+        Result.ret (p, back_'a1)
     | List.Nil => Result.fail .panic
   | List.Nil => Result.fail .panic
 
-/- [loops::list_nth_mut_shared_loop_pair_merge]: backward function 0
+/- [loops::list_nth_mut_shared_loop_pair_merge]:
    Source: 'src/loops.rs', lines 278:0-282:23 -/
-def list_nth_mut_shared_loop_pair_merge_back
-  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret : T) :
-  Result (List T)
+def list_nth_mut_shared_loop_pair_merge
+  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) :
+  Result ((T × T) × (T → Result (List T)))
   :=
-  list_nth_mut_shared_loop_pair_merge_loop_back T ls0 ls1 i ret
+  do
+  let (p, back_'a) ← list_nth_mut_shared_loop_pair_merge_loop T ls0 ls1 i
+  Result.ret (p, back_'a)
 
-/- [loops::list_nth_shared_mut_loop_pair]: loop 0: forward function
+/- [loops::list_nth_shared_mut_loop_pair]: loop 0:
    Source: 'src/loops.rs', lines 297:0-312:1 -/
 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 .panic
-  | List.Nil => Result.fail .panic
-
-/- [loops::list_nth_shared_mut_loop_pair]: forward function
-   Source: 'src/loops.rs', lines 297:0-301:23 -/
-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
-   Source: 'src/loops.rs', lines 297:0-312:1 -/
-divergent def list_nth_shared_mut_loop_pair_loop_back
-  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret : T) :
-  Result (List T)
+  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) :
+  Result ((T × T) × (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 ret tl1)
+      then
+        let back_'b := fun ret => Result.ret (List.Cons ret tl1)
+        Result.ret ((x0, x1), back_'b)
       else
         do
-          let i0 ← i - 1#u32
-          let tl10 ← list_nth_shared_mut_loop_pair_loop_back T tl0 tl1 i0 ret
-          Result.ret (List.Cons x1 tl10)
+        let i1 ← i - 1#u32
+        let (p, back_'b) ← list_nth_shared_mut_loop_pair_loop T tl0 tl1 i1
+        let back_'b1 :=
+          fun ret => do
+                     let tl11 ← back_'b ret
+                     Result.ret (List.Cons x1 tl11)
+        Result.ret (p, back_'b1)
     | List.Nil => Result.fail .panic
   | List.Nil => Result.fail .panic
 
-/- [loops::list_nth_shared_mut_loop_pair]: backward function 1
+/- [loops::list_nth_shared_mut_loop_pair]:
    Source: 'src/loops.rs', lines 297:0-301:23 -/
-def list_nth_shared_mut_loop_pair_back
-  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret : T) :
-  Result (List T)
+def list_nth_shared_mut_loop_pair
+  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) :
+  Result ((T × T) × (T → Result (List T)))
   :=
-  list_nth_shared_mut_loop_pair_loop_back T ls0 ls1 i ret
+  do
+  let (p, back_'b) ← list_nth_shared_mut_loop_pair_loop T ls0 ls1 i
+  Result.ret (p, back_'b)
 
-/- [loops::list_nth_shared_mut_loop_pair_merge]: loop 0: forward function
+/- [loops::list_nth_shared_mut_loop_pair_merge]: loop 0:
    Source: 'src/loops.rs', lines 316:0-331:1 -/
 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 .panic
-  | List.Nil => Result.fail .panic
-
-/- [loops::list_nth_shared_mut_loop_pair_merge]: forward function
-   Source: 'src/loops.rs', lines 316:0-320:23 -/
-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
-   Source: 'src/loops.rs', lines 316:0-331:1 -/
-divergent def list_nth_shared_mut_loop_pair_merge_loop_back
-  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret : T) :
-  Result (List T)
+  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) :
+  Result ((T × T) × (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 ret tl1)
+      then
+        let back_'a := fun ret => Result.ret (List.Cons ret tl1)
+        Result.ret ((x0, x1), back_'a)
       else
         do
-          let i0 ← i - 1#u32
-          let tl10 ←
-            list_nth_shared_mut_loop_pair_merge_loop_back T tl0 tl1 i0 ret
-          Result.ret (List.Cons x1 tl10)
+        let i1 ← i - 1#u32
+        let (p, back_'a) ←
+          list_nth_shared_mut_loop_pair_merge_loop T tl0 tl1 i1
+        let back_'a1 :=
+          fun ret => do
+                     let tl11 ← back_'a ret
+                     Result.ret (List.Cons x1 tl11)
+        Result.ret (p, back_'a1)
     | List.Nil => Result.fail .panic
   | List.Nil => Result.fail .panic
 
-/- [loops::list_nth_shared_mut_loop_pair_merge]: backward function 0
+/- [loops::list_nth_shared_mut_loop_pair_merge]:
    Source: 'src/loops.rs', lines 316:0-320:23 -/
-def list_nth_shared_mut_loop_pair_merge_back
-  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret : T) :
-  Result (List T)
+def list_nth_shared_mut_loop_pair_merge
+  (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) :
+  Result ((T × T) × (T → Result (List T)))
   :=
-  list_nth_shared_mut_loop_pair_merge_loop_back T ls0 ls1 i ret
+  do
+  let (p, back_'a) ← list_nth_shared_mut_loop_pair_merge_loop T ls0 ls1 i
+  Result.ret (p, back_'a)
 
 end loops
diff --git a/tests/lean/NoNestedBorrows.lean b/tests/lean/NoNestedBorrows.lean
index 0bce3a64..0dd29429 100644
--- a/tests/lean/NoNestedBorrows.lean
+++ b/tests/lean/NoNestedBorrows.lean
@@ -43,98 +43,98 @@ inductive Sum (T1 T2 : Type) :=
 | Left : T1 → Sum T1 T2
 | Right : T2 → Sum T1 T2
 
-/- [no_nested_borrows::neg_test]: forward function
+/- [no_nested_borrows::neg_test]:
    Source: 'src/no_nested_borrows.rs', lines 48:0-48:30 -/
 def neg_test (x : I32) : Result I32 :=
   - x
 
-/- [no_nested_borrows::add_u32]: forward function
+/- [no_nested_borrows::add_u32]:
    Source: 'src/no_nested_borrows.rs', lines 54:0-54:37 -/
 def add_u32 (x : U32) (y : U32) : Result U32 :=
   x + y
 
-/- [no_nested_borrows::subs_u32]: forward function
+/- [no_nested_borrows::subs_u32]:
    Source: 'src/no_nested_borrows.rs', lines 60:0-60:38 -/
 def subs_u32 (x : U32) (y : U32) : Result U32 :=
   x - y
 
-/- [no_nested_borrows::div_u32]: forward function
+/- [no_nested_borrows::div_u32]:
    Source: 'src/no_nested_borrows.rs', lines 66:0-66:37 -/
 def div_u32 (x : U32) (y : U32) : Result U32 :=
   x / y
 
-/- [no_nested_borrows::div_u32_const]: forward function
+/- [no_nested_borrows::div_u32_const]:
    Source: 'src/no_nested_borrows.rs', lines 73:0-73:35 -/
 def div_u32_const (x : U32) : Result U32 :=
   x / 2#u32
 
-/- [no_nested_borrows::rem_u32]: forward function
+/- [no_nested_borrows::rem_u32]:
    Source: 'src/no_nested_borrows.rs', lines 78:0-78:37 -/
 def rem_u32 (x : U32) (y : U32) : Result U32 :=
   x % y
 
-/- [no_nested_borrows::mul_u32]: forward function
+/- [no_nested_borrows::mul_u32]:
    Source: 'src/no_nested_borrows.rs', lines 82:0-82:37 -/
 def mul_u32 (x : U32) (y : U32) : Result U32 :=
   x * y
 
-/- [no_nested_borrows::add_i32]: forward function
+/- [no_nested_borrows::add_i32]:
    Source: 'src/no_nested_borrows.rs', lines 88:0-88:37 -/
 def add_i32 (x : I32) (y : I32) : Result I32 :=
   x + y
 
-/- [no_nested_borrows::subs_i32]: forward function
+/- [no_nested_borrows::subs_i32]:
    Source: 'src/no_nested_borrows.rs', lines 92:0-92:38 -/
 def subs_i32 (x : I32) (y : I32) : Result I32 :=
   x - y
 
-/- [no_nested_borrows::div_i32]: forward function
+/- [no_nested_borrows::div_i32]:
    Source: 'src/no_nested_borrows.rs', lines 96:0-96:37 -/
 def div_i32 (x : I32) (y : I32) : Result I32 :=
   x / y
 
-/- [no_nested_borrows::div_i32_const]: forward function
+/- [no_nested_borrows::div_i32_const]:
    Source: 'src/no_nested_borrows.rs', lines 100:0-100:35 -/
 def div_i32_const (x : I32) : Result I32 :=
   x / 2#i32
 
-/- [no_nested_borrows::rem_i32]: forward function
+/- [no_nested_borrows::rem_i32]:
    Source: 'src/no_nested_borrows.rs', lines 104:0-104:37 -/
 def rem_i32 (x : I32) (y : I32) : Result I32 :=
   x % y
 
-/- [no_nested_borrows::mul_i32]: forward function
+/- [no_nested_borrows::mul_i32]:
    Source: 'src/no_nested_borrows.rs', lines 108:0-108:37 -/
 def mul_i32 (x : I32) (y : I32) : Result I32 :=
   x * y
 
-/- [no_nested_borrows::mix_arith_u32]: forward function
+/- [no_nested_borrows::mix_arith_u32]:
    Source: 'src/no_nested_borrows.rs', lines 112:0-112:51 -/
 def mix_arith_u32 (x : U32) (y : U32) (z : U32) : Result U32 :=
   do
-    let i ← x + y
-    let i0 ← x / y
-    let i1 ← i * i0
-    let i2 ← z % y
-    let i3 ← x - i2
-    let i4 ← i1 + i3
-    let i5 ← x + y
-    let i6 ← i5 + z
-    i4 % i6
-
-/- [no_nested_borrows::mix_arith_i32]: forward function
+  let i ← x + y
+  let i1 ← x / y
+  let i2 ← i * i1
+  let i3 ← z % y
+  let i4 ← x - i3
+  let i5 ← i2 + i4
+  let i6 ← x + y
+  let i7 ← i6 + z
+  i5 % i7
+
+/- [no_nested_borrows::mix_arith_i32]:
    Source: 'src/no_nested_borrows.rs', lines 116:0-116:51 -/
 def mix_arith_i32 (x : I32) (y : I32) (z : I32) : Result I32 :=
   do
-    let i ← x + y
-    let i0 ← x / y
-    let i1 ← i * i0
-    let i2 ← z % y
-    let i3 ← x - i2
-    let i4 ← i1 + i3
-    let i5 ← x + y
-    let i6 ← i5 + z
-    i4 % i6
+  let i ← x + y
+  let i1 ← x / y
+  let i2 ← i * i1
+  let i3 ← z % y
+  let i4 ← x - i3
+  let i5 ← i2 + i4
+  let i6 ← x + y
+  let i7 ← i6 + z
+  i5 % i7
 
 /- [no_nested_borrows::CONST0]
    Source: 'src/no_nested_borrows.rs', lines 125:0-125:23 -/
@@ -146,65 +146,65 @@ def const0_c : Usize := eval_global const0_body (by simp)
 def const1_body : Result Usize := 2#usize * 2#usize
 def const1_c : Usize := eval_global const1_body (by simp)
 
-/- [no_nested_borrows::cast_u32_to_i32]: forward function
+/- [no_nested_borrows::cast_u32_to_i32]:
    Source: 'src/no_nested_borrows.rs', lines 128:0-128:37 -/
 def cast_u32_to_i32 (x : U32) : Result I32 :=
   Scalar.cast .I32 x
 
-/- [no_nested_borrows::cast_bool_to_i32]: forward function
+/- [no_nested_borrows::cast_bool_to_i32]:
    Source: 'src/no_nested_borrows.rs', lines 132:0-132:39 -/
 def cast_bool_to_i32 (x : Bool) : Result I32 :=
   Scalar.cast_bool .I32 x
 
-/- [no_nested_borrows::cast_bool_to_bool]: forward function
+/- [no_nested_borrows::cast_bool_to_bool]:
    Source: 'src/no_nested_borrows.rs', lines 137:0-137:41 -/
 def cast_bool_to_bool (x : Bool) : Result Bool :=
   Result.ret x
 
-/- [no_nested_borrows::test2]: forward function
+/- [no_nested_borrows::test2]:
    Source: 'src/no_nested_borrows.rs', lines 142:0-142:14 -/
 def test2 : Result Unit :=
   do
-    let _ ← 23#u32 + 44#u32
-    Result.ret ()
+  let _ ← 23#u32 + 44#u32
+  Result.ret ()
 
 /- Unit test for [no_nested_borrows::test2] -/
 #assert (test2 == Result.ret ())
 
-/- [no_nested_borrows::get_max]: forward function
+/- [no_nested_borrows::get_max]:
    Source: 'src/no_nested_borrows.rs', lines 154:0-154:37 -/
 def get_max (x : U32) (y : U32) : Result U32 :=
   if x >= y
   then Result.ret x
   else Result.ret y
 
-/- [no_nested_borrows::test3]: forward function
+/- [no_nested_borrows::test3]:
    Source: 'src/no_nested_borrows.rs', lines 162:0-162:14 -/
 def test3 : Result Unit :=
   do
-    let x ← get_max 4#u32 3#u32
-    let y ← get_max 10#u32 11#u32
-    let z ← x + y
-    if not (z = 15#u32)
-    then Result.fail .panic
-    else Result.ret ()
+  let x ← get_max 4#u32 3#u32
+  let y ← get_max 10#u32 11#u32
+  let z ← x + y
+  if not (z = 15#u32)
+  then Result.fail .panic
+  else Result.ret ()
 
 /- Unit test for [no_nested_borrows::test3] -/
 #assert (test3 == Result.ret ())
 
-/- [no_nested_borrows::test_neg1]: forward function
+/- [no_nested_borrows::test_neg1]:
    Source: 'src/no_nested_borrows.rs', lines 169:0-169:18 -/
 def test_neg1 : Result Unit :=
   do
-    let y ← - 3#i32
-    if not (y = (-(3:Int))#i32)
-    then Result.fail .panic
-    else Result.ret ()
+  let y ← - 3#i32
+  if not (y = (-(3:Int))#i32)
+  then Result.fail .panic
+  else Result.ret ()
 
 /- Unit test for [no_nested_borrows::test_neg1] -/
 #assert (test_neg1 == Result.ret ())
 
-/- [no_nested_borrows::refs_test1]: forward function
+/- [no_nested_borrows::refs_test1]:
    Source: 'src/no_nested_borrows.rs', lines 176:0-176:19 -/
 def refs_test1 : Result Unit :=
   if not (1#i32 = 1#i32)
@@ -214,7 +214,7 @@ def refs_test1 : Result Unit :=
 /- Unit test for [no_nested_borrows::refs_test1] -/
 #assert (refs_test1 == Result.ret ())
 
-/- [no_nested_borrows::refs_test2]: forward function
+/- [no_nested_borrows::refs_test2]:
    Source: 'src/no_nested_borrows.rs', lines 187:0-187:19 -/
 def refs_test2 : Result Unit :=
   if not (2#i32 = 2#i32)
@@ -232,7 +232,7 @@ def refs_test2 : Result Unit :=
 /- Unit test for [no_nested_borrows::refs_test2] -/
 #assert (refs_test2 == Result.ret ())
 
-/- [no_nested_borrows::test_list1]: forward function
+/- [no_nested_borrows::test_list1]:
    Source: 'src/no_nested_borrows.rs', lines 203:0-203:19 -/
 def test_list1 : Result Unit :=
   Result.ret ()
@@ -240,128 +240,123 @@ def test_list1 : Result Unit :=
 /- Unit test for [no_nested_borrows::test_list1] -/
 #assert (test_list1 == Result.ret ())
 
-/- [no_nested_borrows::test_box1]: forward function
+/- [no_nested_borrows::test_box1]:
    Source: 'src/no_nested_borrows.rs', lines 208:0-208:18 -/
 def test_box1 : Result Unit :=
   do
-    let b := 0#i32
-    let b0 ← alloc.boxed.Box.deref_mut_back I32 b 1#i32
-    let x ← alloc.boxed.Box.deref I32 b0
-    if not (x = 1#i32)
-    then Result.fail .panic
-    else Result.ret ()
+  let (_, deref_mut_back) ← alloc.boxed.Box.deref_mut I32 0#i32
+  let b ← deref_mut_back 1#i32
+  let x ← alloc.boxed.Box.deref I32 b
+  if not (x = 1#i32)
+  then Result.fail .panic
+  else Result.ret ()
 
 /- Unit test for [no_nested_borrows::test_box1] -/
 #assert (test_box1 == Result.ret ())
 
-/- [no_nested_borrows::copy_int]: forward function
+/- [no_nested_borrows::copy_int]:
    Source: 'src/no_nested_borrows.rs', lines 218:0-218:30 -/
 def copy_int (x : I32) : Result I32 :=
   Result.ret x
 
-/- [no_nested_borrows::test_unreachable]: forward function
+/- [no_nested_borrows::test_unreachable]:
    Source: 'src/no_nested_borrows.rs', lines 224:0-224:32 -/
 def test_unreachable (b : Bool) : Result Unit :=
   if b
   then Result.fail .panic
   else Result.ret ()
 
-/- [no_nested_borrows::test_panic]: forward function
+/- [no_nested_borrows::test_panic]:
    Source: 'src/no_nested_borrows.rs', lines 232:0-232:26 -/
 def test_panic (b : Bool) : Result Unit :=
   if b
   then Result.fail .panic
   else Result.ret ()
 
-/- [no_nested_borrows::test_copy_int]: forward function
+/- [no_nested_borrows::test_copy_int]:
    Source: 'src/no_nested_borrows.rs', lines 239:0-239:22 -/
 def test_copy_int : Result Unit :=
   do
-    let y ← copy_int 0#i32
-    if not (0#i32 = y)
-    then Result.fail .panic
-    else Result.ret ()
+  let y ← copy_int 0#i32
+  if not (0#i32 = y)
+  then Result.fail .panic
+  else Result.ret ()
 
 /- Unit test for [no_nested_borrows::test_copy_int] -/
 #assert (test_copy_int == Result.ret ())
 
-/- [no_nested_borrows::is_cons]: forward function
+/- [no_nested_borrows::is_cons]:
    Source: 'src/no_nested_borrows.rs', lines 246:0-246:38 -/
 def is_cons (T : Type) (l : List T) : Result Bool :=
   match l with
-  | List.Cons t l0 => Result.ret true
+  | List.Cons _ _ => Result.ret true
   | List.Nil => Result.ret false
 
-/- [no_nested_borrows::test_is_cons]: forward function
+/- [no_nested_borrows::test_is_cons]:
    Source: 'src/no_nested_borrows.rs', lines 253:0-253:21 -/
 def test_is_cons : Result Unit :=
   do
-    let l := List.Nil
-    let b ← is_cons I32 (List.Cons 0#i32 l)
-    if not b
-    then Result.fail .panic
-    else Result.ret ()
+  let b ← is_cons I32 (List.Cons 0#i32 List.Nil)
+  if not b
+  then Result.fail .panic
+  else Result.ret ()
 
 /- Unit test for [no_nested_borrows::test_is_cons] -/
 #assert (test_is_cons == Result.ret ())
 
-/- [no_nested_borrows::split_list]: forward function
+/- [no_nested_borrows::split_list]:
    Source: 'src/no_nested_borrows.rs', lines 259:0-259:48 -/
 def split_list (T : Type) (l : List T) : Result (T × (List T)) :=
   match l with
   | List.Cons hd tl => Result.ret (hd, tl)
   | List.Nil => Result.fail .panic
 
-/- [no_nested_borrows::test_split_list]: forward function
+/- [no_nested_borrows::test_split_list]:
    Source: 'src/no_nested_borrows.rs', lines 267:0-267:24 -/
 def test_split_list : Result Unit :=
   do
-    let l := List.Nil
-    let p ← split_list I32 (List.Cons 0#i32 l)
-    let (hd, _) := p
-    if not (hd = 0#i32)
-    then Result.fail .panic
-    else Result.ret ()
+  let p ← split_list I32 (List.Cons 0#i32 List.Nil)
+  let (hd, _) := p
+  if not (hd = 0#i32)
+  then Result.fail .panic
+  else Result.ret ()
 
 /- Unit test for [no_nested_borrows::test_split_list] -/
 #assert (test_split_list == Result.ret ())
 
-/- [no_nested_borrows::choose]: forward function
+/- [no_nested_borrows::choose]:
    Source: 'src/no_nested_borrows.rs', lines 274:0-274:70 -/
-def choose (T : Type) (b : Bool) (x : T) (y : T) : Result T :=
+def choose
+  (T : Type) (b : Bool) (x : T) (y : T) :
+  Result (T × (T → Result (T × T)))
+  :=
   if b
-  then Result.ret x
-  else Result.ret y
+  then let back_'a := fun ret => Result.ret (ret, y)
+       Result.ret (x, back_'a)
+  else let back_'a := fun ret => Result.ret (x, ret)
+       Result.ret (y, back_'a)
 
-/- [no_nested_borrows::choose]: backward function 0
-   Source: 'src/no_nested_borrows.rs', lines 274:0-274:70 -/
-def choose_back
-  (T : Type) (b : Bool) (x : T) (y : T) (ret : T) : Result (T × T) :=
-  if b
-  then Result.ret (ret, y)
-  else Result.ret (x, ret)
-
-/- [no_nested_borrows::choose_test]: forward function
+/- [no_nested_borrows::choose_test]:
    Source: 'src/no_nested_borrows.rs', lines 282:0-282:20 -/
 def choose_test : Result Unit :=
   do
-    let z ← choose I32 true 0#i32 0#i32
-    let z0 ← z + 1#i32
-    if not (z0 = 1#i32)
+  let (z, choose_back) ← choose I32 true 0#i32 0#i32
+  let z1 ← z + 1#i32
+  if not (z1 = 1#i32)
+  then Result.fail .panic
+  else
+    do
+    let (x, y) ← choose_back z1
+    if not (x = 1#i32)
     then Result.fail .panic
-    else
-      do
-        let (x, y) ← choose_back I32 true 0#i32 0#i32 z0
-        if not (x = 1#i32)
-        then Result.fail .panic
-        else if not (y = 0#i32)
-             then Result.fail .panic
-             else Result.ret ()
+    else if not (y = 0#i32)
+         then Result.fail .panic
+         else Result.ret ()
 
 /- Unit test for [no_nested_borrows::choose_test] -/
 #assert (choose_test == Result.ret ())
 
-/- [no_nested_borrows::test_char]: forward function
+/- [no_nested_borrows::test_char]:
    Source: 'src/no_nested_borrows.rs', lines 294:0-294:26 -/
 def test_char : Result Char :=
   Result.ret 'a'
@@ -382,16 +377,16 @@ inductive NodeElem (T : Type) :=
 
 end
 
-/- [no_nested_borrows::list_length]: forward function
+/- [no_nested_borrows::list_length]:
    Source: 'src/no_nested_borrows.rs', lines 339:0-339:48 -/
 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
-                        1#u32 + i
+  | List.Cons _ l1 => do
+                      let i ← list_length T l1
+                      1#u32 + i
   | List.Nil => Result.ret 0#u32
 
-/- [no_nested_borrows::list_nth_shared]: forward function
+/- [no_nested_borrows::list_nth_shared]:
    Source: 'src/no_nested_borrows.rs', lines 347:0-347:62 -/
 divergent def list_nth_shared (T : Type) (l : List T) (i : U32) : Result T :=
   match l with
@@ -399,38 +394,33 @@ divergent def list_nth_shared (T : Type) (l : List T) (i : U32) : Result T :=
     if i = 0#u32
     then Result.ret x
     else do
-           let i0 ← i - 1#u32
-           list_nth_shared T tl i0
+         let i1 ← i - 1#u32
+         list_nth_shared T tl i1
   | List.Nil => Result.fail .panic
 
-/- [no_nested_borrows::list_nth_mut]: forward function
+/- [no_nested_borrows::list_nth_mut]:
    Source: 'src/no_nested_borrows.rs', lines 363:0-363:67 -/
-divergent def list_nth_mut (T : Type) (l : List T) (i : U32) : Result T :=
+divergent def list_nth_mut
+  (T : Type) (l : List T) (i : U32) : Result (T × (T → Result (List T))) :=
   match l with
   | List.Cons x tl =>
     if i = 0#u32
-    then Result.ret x
-    else do
-           let i0 ← i - 1#u32
-           list_nth_mut T tl i0
-  | List.Nil => Result.fail .panic
-
-/- [no_nested_borrows::list_nth_mut]: backward function 0
-   Source: 'src/no_nested_borrows.rs', lines 363:0-363:67 -/
-divergent def list_nth_mut_back
-  (T : Type) (l : List T) (i : U32) (ret : T) : Result (List T) :=
-  match l with
-  | List.Cons x tl =>
-    if i = 0#u32
-    then Result.ret (List.Cons ret tl)
+    then
+      let back_'a := fun ret => Result.ret (List.Cons ret tl)
+      Result.ret (x, back_'a)
     else
       do
-        let i0 ← i - 1#u32
-        let tl0 ← list_nth_mut_back T tl i0 ret
-        Result.ret (List.Cons x tl0)
+      let i1 ← i - 1#u32
+      let (t, list_nth_mut_back) ← list_nth_mut T tl i1
+      let back_'a :=
+        fun ret =>
+          do
+          let tl1 ← list_nth_mut_back ret
+          Result.ret (List.Cons x tl1)
+      Result.ret (t, back_'a)
   | List.Nil => Result.fail .panic
 
-/- [no_nested_borrows::list_rev_aux]: forward function
+/- [no_nested_borrows::list_rev_aux]:
    Source: 'src/no_nested_borrows.rs', lines 379:0-379:63 -/
 divergent def list_rev_aux
   (T : Type) (li : List T) (lo : List T) : Result (List T) :=
@@ -438,136 +428,113 @@ divergent def list_rev_aux
   | List.Cons hd tl => list_rev_aux T tl (List.Cons hd lo)
   | List.Nil => Result.ret lo
 
-/- [no_nested_borrows::list_rev]: merged forward/backward function
-   (there is a single backward function, and the forward function returns ())
+/- [no_nested_borrows::list_rev]:
    Source: 'src/no_nested_borrows.rs', lines 393:0-393:42 -/
 def list_rev (T : Type) (l : List T) : Result (List T) :=
-  let li := core.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
+/- [no_nested_borrows::test_list_functions]:
    Source: 'src/no_nested_borrows.rs', lines 398:0-398:28 -/
 def test_list_functions : Result Unit :=
   do
-    let l := List.Nil
-    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)
+  let l := List.Cons 2#i32 List.Nil
+  let l1 := List.Cons 1#i32 l
+  let i ← list_length I32 (List.Cons 0#i32 l1)
+  if not (i = 3#u32)
+  then Result.fail .panic
+  else
+    do
+    let i1 ← list_nth_shared I32 (List.Cons 0#i32 l1) 0#u32
+    if not (i1 = 0#i32)
     then Result.fail .panic
     else
       do
-        let i0 ← list_nth_shared I32 (List.Cons 0#i32 l1) 0#u32
-        if not (i0 = 0#i32)
+      let i2 ← list_nth_shared I32 (List.Cons 0#i32 l1) 1#u32
+      if not (i2 = 1#i32)
+      then Result.fail .panic
+      else
+        do
+        let i3 ← list_nth_shared I32 (List.Cons 0#i32 l1) 2#u32
+        if not (i3 = 2#i32)
         then Result.fail .panic
         else
           do
-            let i1 ← list_nth_shared I32 (List.Cons 0#i32 l1) 1#u32
-            if not (i1 = 1#i32)
+          let (_, list_nth_mut_back) ←
+            list_nth_mut I32 (List.Cons 0#i32 l1) 1#u32
+          let ls ← list_nth_mut_back 3#i32
+          let i4 ← list_nth_shared I32 ls 0#u32
+          if not (i4 = 0#i32)
+          then Result.fail .panic
+          else
+            do
+            let i5 ← list_nth_shared I32 ls 1#u32
+            if not (i5 = 3#i32)
             then Result.fail .panic
             else
               do
-                let i2 ← list_nth_shared I32 (List.Cons 0#i32 l1) 2#u32
-                if not (i2 = 2#i32)
-                then Result.fail .panic
-                else
-                  do
-                    let ls ←
-                      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 .panic
-                    else
-                      do
-                        let i4 ← list_nth_shared I32 ls 1#u32
-                        if not (i4 = 3#i32)
-                        then Result.fail .panic
-                        else
-                          do
-                            let i5 ← list_nth_shared I32 ls 2#u32
-                            if not (i5 = 2#i32)
-                            then Result.fail .panic
-                            else Result.ret ()
+              let i6 ← list_nth_shared I32 ls 2#u32
+              if not (i6 = 2#i32)
+              then Result.fail .panic
+              else Result.ret ()
 
 /- Unit test for [no_nested_borrows::test_list_functions] -/
 #assert (test_list_functions == Result.ret ())
 
-/- [no_nested_borrows::id_mut_pair1]: forward function
-   Source: 'src/no_nested_borrows.rs', lines 414:0-414:89 -/
-def id_mut_pair1 (T1 T2 : Type) (x : T1) (y : T2) : Result (T1 × T2) :=
-  Result.ret (x, y)
-
-/- [no_nested_borrows::id_mut_pair1]: backward function 0
+/- [no_nested_borrows::id_mut_pair1]:
    Source: 'src/no_nested_borrows.rs', lines 414:0-414:89 -/
-def id_mut_pair1_back
-  (T1 T2 : Type) (x : T1) (y : T2) (ret : (T1 × T2)) : Result (T1 × T2) :=
-  let (t, t0) := ret
-  Result.ret (t, t0)
-
-/- [no_nested_borrows::id_mut_pair2]: forward function
-   Source: 'src/no_nested_borrows.rs', lines 418:0-418:88 -/
-def id_mut_pair2 (T1 T2 : Type) (p : (T1 × T2)) : Result (T1 × T2) :=
-  let (t, t0) := p
-  Result.ret (t, t0)
-
-/- [no_nested_borrows::id_mut_pair2]: backward function 0
+def id_mut_pair1
+  (T1 T2 : Type) (x : T1) (y : T2) :
+  Result ((T1 × T2) × ((T1 × T2) → Result (T1 × T2)))
+  :=
+  let back_'a := fun ret => let (t, t1) := ret
+                            Result.ret (t, t1)
+  Result.ret ((x, y), back_'a)
+
+/- [no_nested_borrows::id_mut_pair2]:
    Source: 'src/no_nested_borrows.rs', lines 418:0-418:88 -/
-def id_mut_pair2_back
-  (T1 T2 : Type) (p : (T1 × T2)) (ret : (T1 × T2)) : Result (T1 × T2) :=
-  let (t, t0) := ret
-  Result.ret (t, t0)
-
-/- [no_nested_borrows::id_mut_pair3]: forward function
-   Source: 'src/no_nested_borrows.rs', lines 422:0-422:93 -/
-def id_mut_pair3 (T1 T2 : Type) (x : T1) (y : T2) : Result (T1 × T2) :=
-  Result.ret (x, y)
-
-/- [no_nested_borrows::id_mut_pair3]: backward function 0
-   Source: 'src/no_nested_borrows.rs', lines 422:0-422:93 -/
-def id_mut_pair3_back'a
-  (T1 T2 : Type) (x : T1) (y : T2) (ret : T1) : Result T1 :=
-  Result.ret ret
-
-/- [no_nested_borrows::id_mut_pair3]: backward function 1
+def id_mut_pair2
+  (T1 T2 : Type) (p : (T1 × T2)) :
+  Result ((T1 × T2) × ((T1 × T2) → Result (T1 × T2)))
+  :=
+  let (t, t1) := p
+  let back_'a := fun ret => let (t2, t3) := ret
+                            Result.ret (t2, t3)
+  Result.ret ((t, t1), back_'a)
+
+/- [no_nested_borrows::id_mut_pair3]:
    Source: 'src/no_nested_borrows.rs', lines 422:0-422:93 -/
-def id_mut_pair3_back'b
-  (T1 T2 : Type) (x : T1) (y : T2) (ret : T2) : Result T2 :=
-  Result.ret ret
+def id_mut_pair3
+  (T1 T2 : Type) (x : T1) (y : T2) :
+  Result ((T1 × T2) × (T1 → Result T1) × (T2 → Result T2))
+  :=
+  Result.ret ((x, y), Result.ret, Result.ret)
 
-/- [no_nested_borrows::id_mut_pair4]: forward function
+/- [no_nested_borrows::id_mut_pair4]:
    Source: 'src/no_nested_borrows.rs', lines 426:0-426:92 -/
-def id_mut_pair4 (T1 T2 : Type) (p : (T1 × T2)) : Result (T1 × T2) :=
-  let (t, t0) := p
-  Result.ret (t, t0)
-
-/- [no_nested_borrows::id_mut_pair4]: backward function 0
-   Source: 'src/no_nested_borrows.rs', lines 426:0-426:92 -/
-def id_mut_pair4_back'a
-  (T1 T2 : Type) (p : (T1 × T2)) (ret : T1) : Result T1 :=
-  Result.ret ret
-
-/- [no_nested_borrows::id_mut_pair4]: backward function 1
-   Source: 'src/no_nested_borrows.rs', lines 426:0-426:92 -/
-def id_mut_pair4_back'b
-  (T1 T2 : Type) (p : (T1 × T2)) (ret : T2) : Result T2 :=
-  Result.ret ret
+def id_mut_pair4
+  (T1 T2 : Type) (p : (T1 × T2)) :
+  Result ((T1 × T2) × (T1 → Result T1) × (T2 → Result T2))
+  :=
+  let (t, t1) := p
+  Result.ret ((t, t1), Result.ret, Result.ret)
 
 /- [no_nested_borrows::StructWithTuple]
    Source: 'src/no_nested_borrows.rs', lines 433:0-433:34 -/
 structure StructWithTuple (T1 T2 : Type) where
   p : (T1 × T2)
 
-/- [no_nested_borrows::new_tuple1]: forward function
+/- [no_nested_borrows::new_tuple1]:
    Source: 'src/no_nested_borrows.rs', lines 437:0-437:48 -/
 def new_tuple1 : Result (StructWithTuple U32 U32) :=
   Result.ret { p := (1#u32, 2#u32) }
 
-/- [no_nested_borrows::new_tuple2]: forward function
+/- [no_nested_borrows::new_tuple2]:
    Source: 'src/no_nested_borrows.rs', lines 441:0-441:48 -/
 def new_tuple2 : Result (StructWithTuple I16 I16) :=
   Result.ret { p := (1#i16, 2#i16) }
 
-/- [no_nested_borrows::new_tuple3]: forward function
+/- [no_nested_borrows::new_tuple3]:
    Source: 'src/no_nested_borrows.rs', lines 445:0-445:48 -/
 def new_tuple3 : Result (StructWithTuple U64 I64) :=
   Result.ret { p := (1#u64, 2#i64) }
@@ -577,42 +544,42 @@ def new_tuple3 : Result (StructWithTuple U64 I64) :=
 structure StructWithPair (T1 T2 : Type) where
   p : Pair T1 T2
 
-/- [no_nested_borrows::new_pair1]: forward function
+/- [no_nested_borrows::new_pair1]:
    Source: 'src/no_nested_borrows.rs', lines 454:0-454:46 -/
 def new_pair1 : Result (StructWithPair U32 U32) :=
   Result.ret { p := { x := 1#u32, y := 2#u32 } }
 
-/- [no_nested_borrows::test_constants]: forward function
+/- [no_nested_borrows::test_constants]:
    Source: 'src/no_nested_borrows.rs', lines 462:0-462:23 -/
 def test_constants : Result Unit :=
   do
-    let swt ← new_tuple1
-    let (i, _) := swt.p
-    if not (i = 1#u32)
+  let swt ← new_tuple1
+  let (i, _) := swt.p
+  if not (i = 1#u32)
+  then Result.fail .panic
+  else
+    do
+    let swt1 ← new_tuple2
+    let (i1, _) := swt1.p
+    if not (i1 = 1#i16)
     then Result.fail .panic
     else
       do
-        let swt0 ← new_tuple2
-        let (i0, _) := swt0.p
-        if not (i0 = 1#i16)
+      let swt2 ← new_tuple3
+      let (i2, _) := swt2.p
+      if not (i2 = 1#u64)
+      then Result.fail .panic
+      else
+        do
+        let swp ← new_pair1
+        if not (swp.p.x = 1#u32)
         then Result.fail .panic
-        else
-          do
-            let swt1 ← new_tuple3
-            let (i1, _) := swt1.p
-            if not (i1 = 1#u64)
-            then Result.fail .panic
-            else
-              do
-                let swp ← new_pair1
-                if not (swp.p.x = 1#u32)
-                then Result.fail .panic
-                else Result.ret ()
+        else Result.ret ()
 
 /- Unit test for [no_nested_borrows::test_constants] -/
 #assert (test_constants == Result.ret ())
 
-/- [no_nested_borrows::test_weird_borrows1]: forward function
+/- [no_nested_borrows::test_weird_borrows1]:
    Source: 'src/no_nested_borrows.rs', lines 471:0-471:28 -/
 def test_weird_borrows1 : Result Unit :=
   Result.ret ()
@@ -620,65 +587,80 @@ def test_weird_borrows1 : Result Unit :=
 /- Unit test for [no_nested_borrows::test_weird_borrows1] -/
 #assert (test_weird_borrows1 == Result.ret ())
 
-/- [no_nested_borrows::test_mem_replace]: merged forward/backward function
-   (there is a single backward function, and the forward function returns ())
+/- [no_nested_borrows::test_mem_replace]:
    Source: 'src/no_nested_borrows.rs', lines 481:0-481:37 -/
 def test_mem_replace (px : U32) : Result U32 :=
-  let y := core.mem.replace U32 px 1#u32
+  let (y, _) := core.mem.replace U32 px 1#u32
   if not (y = 0#u32)
   then Result.fail .panic
   else Result.ret 2#u32
 
-/- [no_nested_borrows::test_shared_borrow_bool1]: forward function
+/- [no_nested_borrows::test_shared_borrow_bool1]:
    Source: 'src/no_nested_borrows.rs', lines 488:0-488:47 -/
 def test_shared_borrow_bool1 (b : Bool) : Result U32 :=
   if b
   then Result.ret 0#u32
   else Result.ret 1#u32
 
-/- [no_nested_borrows::test_shared_borrow_bool2]: forward function
+/- [no_nested_borrows::test_shared_borrow_bool2]:
    Source: 'src/no_nested_borrows.rs', lines 501:0-501:40 -/
 def test_shared_borrow_bool2 : Result U32 :=
   Result.ret 0#u32
 
-/- [no_nested_borrows::test_shared_borrow_enum1]: forward function
+/- [no_nested_borrows::test_shared_borrow_enum1]:
    Source: 'src/no_nested_borrows.rs', lines 516:0-516:52 -/
 def test_shared_borrow_enum1 (l : List U32) : Result U32 :=
   match l with
-  | List.Cons i l0 => Result.ret 1#u32
+  | List.Cons _ _ => Result.ret 1#u32
   | List.Nil => Result.ret 0#u32
 
-/- [no_nested_borrows::test_shared_borrow_enum2]: forward function
+/- [no_nested_borrows::test_shared_borrow_enum2]:
    Source: 'src/no_nested_borrows.rs', lines 528:0-528:40 -/
 def test_shared_borrow_enum2 : Result U32 :=
   Result.ret 0#u32
 
-/- [no_nested_borrows::Tuple]
+/- [no_nested_borrows::incr]:
    Source: 'src/no_nested_borrows.rs', lines 539:0-539:24 -/
+def incr (x : U32) : Result U32 :=
+  x + 1#u32
+
+/- [no_nested_borrows::call_incr]:
+   Source: 'src/no_nested_borrows.rs', lines 543:0-543:35 -/
+def call_incr (x : U32) : Result U32 :=
+  incr x
+
+/- [no_nested_borrows::read_then_incr]:
+   Source: 'src/no_nested_borrows.rs', lines 548:0-548:41 -/
+def read_then_incr (x : U32) : Result (U32 × U32) :=
+  do
+  let x1 ← x + 1#u32
+  Result.ret (x, x1)
+
+/- [no_nested_borrows::Tuple]
+   Source: 'src/no_nested_borrows.rs', lines 554:0-554:24 -/
 def Tuple (T1 T2 : Type) := T1 × T2
 
-/- [no_nested_borrows::use_tuple_struct]: merged forward/backward function
-   (there is a single backward function, and the forward function returns ())
-   Source: 'src/no_nested_borrows.rs', lines 541:0-541:48 -/
+/- [no_nested_borrows::use_tuple_struct]:
+   Source: 'src/no_nested_borrows.rs', lines 556:0-556:48 -/
 def use_tuple_struct (x : Tuple U32 U32) : Result (Tuple U32 U32) :=
   Result.ret (1#u32, x.1)
 
-/- [no_nested_borrows::create_tuple_struct]: forward function
-   Source: 'src/no_nested_borrows.rs', lines 545:0-545:61 -/
+/- [no_nested_borrows::create_tuple_struct]:
+   Source: 'src/no_nested_borrows.rs', lines 560:0-560:61 -/
 def create_tuple_struct (x : U32) (y : U64) : Result (Tuple U32 U64) :=
   Result.ret (x, y)
 
 /- [no_nested_borrows::IdType]
-   Source: 'src/no_nested_borrows.rs', lines 550:0-550:20 -/
+   Source: 'src/no_nested_borrows.rs', lines 565:0-565:20 -/
 @[reducible] def IdType (T : Type) := T
 
-/- [no_nested_borrows::use_id_type]: forward function
-   Source: 'src/no_nested_borrows.rs', lines 552:0-552:40 -/
+/- [no_nested_borrows::use_id_type]:
+   Source: 'src/no_nested_borrows.rs', lines 567:0-567:40 -/
 def use_id_type (T : Type) (x : IdType T) : Result T :=
   Result.ret x
 
-/- [no_nested_borrows::create_id_type]: forward function
-   Source: 'src/no_nested_borrows.rs', lines 556:0-556:43 -/
+/- [no_nested_borrows::create_id_type]:
+   Source: 'src/no_nested_borrows.rs', lines 571:0-571:43 -/
 def create_id_type (T : Type) (x : T) : Result (IdType T) :=
   Result.ret x
 
diff --git a/tests/lean/Paper.lean b/tests/lean/Paper.lean
index 08386bb7..a35c8db0 100644
--- a/tests/lean/Paper.lean
+++ b/tests/lean/Paper.lean
@@ -5,55 +5,51 @@ open Primitives
 
 namespace paper
 
-/- [paper::ref_incr]: merged forward/backward function
-   (there is a single backward function, and the forward function returns ())
+/- [paper::ref_incr]:
    Source: 'src/paper.rs', lines 4:0-4:28 -/
 def ref_incr (x : I32) : Result I32 :=
   x + 1#i32
 
-/- [paper::test_incr]: forward function
+/- [paper::test_incr]:
    Source: 'src/paper.rs', lines 8:0-8:18 -/
 def test_incr : Result Unit :=
   do
-    let x ← ref_incr 0#i32
-    if not (x = 1#i32)
-    then Result.fail .panic
-    else Result.ret ()
+  let i ← ref_incr 0#i32
+  if not (i = 1#i32)
+  then Result.fail .panic
+  else Result.ret ()
 
 /- Unit test for [paper::test_incr] -/
 #assert (test_incr == Result.ret ())
 
-/- [paper::choose]: forward function
-   Source: 'src/paper.rs', lines 15:0-15:70 -/
-def choose (T : Type) (b : Bool) (x : T) (y : T) : Result T :=
-  if b
-  then Result.ret x
-  else Result.ret y
-
-/- [paper::choose]: backward function 0
+/- [paper::choose]:
    Source: 'src/paper.rs', lines 15:0-15:70 -/
-def choose_back
-  (T : Type) (b : Bool) (x : T) (y : T) (ret : T) : Result (T × T) :=
+def choose
+  (T : Type) (b : Bool) (x : T) (y : T) :
+  Result (T × (T → Result (T × T)))
+  :=
   if b
-  then Result.ret (ret, y)
-  else Result.ret (x, ret)
+  then let back_'a := fun ret => Result.ret (ret, y)
+       Result.ret (x, back_'a)
+  else let back_'a := fun ret => Result.ret (x, ret)
+       Result.ret (y, back_'a)
 
-/- [paper::test_choose]: forward function
+/- [paper::test_choose]:
    Source: 'src/paper.rs', lines 23:0-23:20 -/
 def test_choose : Result Unit :=
   do
-    let z ← choose I32 true 0#i32 0#i32
-    let z0 ← z + 1#i32
-    if not (z0 = 1#i32)
+  let (z, choose_back) ← choose I32 true 0#i32 0#i32
+  let z1 ← z + 1#i32
+  if not (z1 = 1#i32)
+  then Result.fail .panic
+  else
+    do
+    let (x, y) ← choose_back z1
+    if not (x = 1#i32)
     then Result.fail .panic
-    else
-      do
-        let (x, y) ← choose_back I32 true 0#i32 0#i32 z0
-        if not (x = 1#i32)
-        then Result.fail .panic
-        else if not (y = 0#i32)
-             then Result.fail .panic
-             else Result.ret ()
+    else if not (y = 0#i32)
+         then Result.fail .panic
+         else Result.ret ()
 
 /- Unit test for [paper::test_choose] -/
 #assert (test_choose == Result.ret ())
@@ -64,68 +60,62 @@ inductive List (T : Type) :=
 | Cons : T → List T → List T
 | Nil : List T
 
-/- [paper::list_nth_mut]: forward function
+/- [paper::list_nth_mut]:
    Source: 'src/paper.rs', lines 42:0-42:67 -/
-divergent def list_nth_mut (T : Type) (l : List T) (i : U32) : Result T :=
+divergent def list_nth_mut
+  (T : Type) (l : List T) (i : U32) : Result (T × (T → Result (List T))) :=
   match l with
   | List.Cons x tl =>
     if i = 0#u32
-    then Result.ret x
-    else do
-           let i0 ← i - 1#u32
-           list_nth_mut T tl i0
-  | List.Nil => Result.fail .panic
-
-/- [paper::list_nth_mut]: backward function 0
-   Source: 'src/paper.rs', lines 42:0-42:67 -/
-divergent def list_nth_mut_back
-  (T : Type) (l : List T) (i : U32) (ret : T) : Result (List T) :=
-  match l with
-  | List.Cons x tl =>
-    if i = 0#u32
-    then Result.ret (List.Cons ret tl)
+    then
+      let back_'a := fun ret => Result.ret (List.Cons ret tl)
+      Result.ret (x, back_'a)
     else
       do
-        let i0 ← i - 1#u32
-        let tl0 ← list_nth_mut_back T tl i0 ret
-        Result.ret (List.Cons x tl0)
+      let i1 ← i - 1#u32
+      let (t, list_nth_mut_back) ← list_nth_mut T tl i1
+      let back_'a :=
+        fun ret =>
+          do
+          let tl1 ← list_nth_mut_back ret
+          Result.ret (List.Cons x tl1)
+      Result.ret (t, back_'a)
   | List.Nil => Result.fail .panic
 
-/- [paper::sum]: forward function
+/- [paper::sum]:
    Source: 'src/paper.rs', lines 57:0-57:32 -/
 divergent def sum (l : List I32) : Result I32 :=
   match l with
   | List.Cons x tl => do
-                        let i ← sum tl
-                        x + i
+                      let i ← sum tl
+                      x + i
   | List.Nil => Result.ret 0#i32
 
-/- [paper::test_nth]: forward function
+/- [paper::test_nth]:
    Source: 'src/paper.rs', lines 68:0-68:17 -/
 def test_nth : Result Unit :=
   do
-    let l := List.Nil
-    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 = 7#i32)
-    then Result.fail .panic
-    else Result.ret ()
+  let l := List.Cons 3#i32 List.Nil
+  let l1 := List.Cons 2#i32 l
+  let (x, list_nth_mut_back) ← list_nth_mut I32 (List.Cons 1#i32 l1) 2#u32
+  let x1 ← x + 1#i32
+  let l2 ← list_nth_mut_back x1
+  let i ← sum l2
+  if not (i = 7#i32)
+  then Result.fail .panic
+  else Result.ret ()
 
 /- Unit test for [paper::test_nth] -/
 #assert (test_nth == Result.ret ())
 
-/- [paper::call_choose]: forward function
+/- [paper::call_choose]:
    Source: 'src/paper.rs', lines 76:0-76:44 -/
 def call_choose (p : (U32 × U32)) : Result U32 :=
   do
-    let (px, py) := p
-    let pz ← choose U32 true px py
-    let pz0 ← pz + 1#u32
-    let (px0, _) ← choose_back U32 true px py pz0
-    Result.ret px0
+  let (px, py) := p
+  let (pz, choose_back) ← choose U32 true px py
+  let pz1 ← pz + 1#u32
+  let (px1, _) ← choose_back pz1
+  Result.ret px1
 
 end paper
diff --git a/tests/lean/PoloniusList.lean b/tests/lean/PoloniusList.lean
index 37f0dffb..59c557a0 100644
--- a/tests/lean/PoloniusList.lean
+++ b/tests/lean/PoloniusList.lean
@@ -11,28 +11,25 @@ inductive List (T : Type) :=
 | Cons : T → List T → List T
 | Nil : List T
 
-/- [polonius_list::get_list_at_x]: forward function
+/- [polonius_list::get_list_at_x]:
    Source: 'src/polonius_list.rs', lines 13:0-13:76 -/
-divergent def get_list_at_x (ls : List U32) (x : U32) : Result (List U32) :=
+divergent def get_list_at_x
+  (ls : List U32) (x : U32) :
+  Result ((List U32) × (List U32 → Result (List U32)))
+  :=
   match ls with
   | List.Cons hd tl =>
     if hd = x
-    then Result.ret (List.Cons hd tl)
-    else get_list_at_x tl x
-  | List.Nil => Result.ret List.Nil
-
-/- [polonius_list::get_list_at_x]: backward function 0
-   Source: 'src/polonius_list.rs', lines 13:0-13:76 -/
-divergent def get_list_at_x_back
-  (ls : List U32) (x : U32) (ret : List U32) : Result (List U32) :=
-  match ls with
-  | List.Cons hd tl =>
-    if hd = x
-    then Result.ret ret
+    then Result.ret (List.Cons hd tl, Result.ret)
     else
       do
-        let tl0 ← get_list_at_x_back tl x ret
-        Result.ret (List.Cons hd tl0)
-  | List.Nil => Result.ret ret
+      let (l, get_list_at_x_back) ← get_list_at_x tl x
+      let back_'a :=
+        fun ret =>
+          do
+          let tl1 ← get_list_at_x_back ret
+          Result.ret (List.Cons hd tl1)
+      Result.ret (l, back_'a)
+  | List.Nil => Result.ret (List.Nil, Result.ret)
 
 end polonius_list
diff --git a/tests/lean/Traits.lean b/tests/lean/Traits.lean
index 17118203..35f9e5bf 100644
--- a/tests/lean/Traits.lean
+++ b/tests/lean/Traits.lean
@@ -10,7 +10,7 @@ namespace traits
 structure BoolTrait (Self : Type) where
   get_bool : Self → Result Bool
 
-/- [traits::{bool}::get_bool]: forward function
+/- [traits::{bool}::get_bool]:
    Source: 'src/traits.rs', lines 12:4-12:30 -/
 def Bool.get_bool (self : Bool) : Result Bool :=
   Result.ret self
@@ -21,27 +21,27 @@ def traits.BoolTraitBoolInst : BoolTrait Bool := {
   get_bool := Bool.get_bool
 }
 
-/- [traits::BoolTrait::ret_true]: forward function
+/- [traits::BoolTrait::ret_true]:
    Source: 'src/traits.rs', lines 6:4-6:30 -/
 def BoolTrait.ret_true
   {Self : Type} (self_clause : BoolTrait Self) (self : Self) : Result Bool :=
   Result.ret true
 
-/- [traits::test_bool_trait_bool]: forward function
+/- [traits::test_bool_trait_bool]:
    Source: 'src/traits.rs', lines 17:0-17:44 -/
 def test_bool_trait_bool (x : Bool) : Result Bool :=
   do
-    let b ← Bool.get_bool x
-    if b
-    then BoolTrait.ret_true traits.BoolTraitBoolInst x
-    else Result.ret false
+  let b ← Bool.get_bool x
+  if b
+  then BoolTrait.ret_true traits.BoolTraitBoolInst x
+  else Result.ret false
 
-/- [traits::{core::option::Option<T>#1}::get_bool]: forward function
+/- [traits::{core::option::Option<T>#1}::get_bool]:
    Source: 'src/traits.rs', lines 23:4-23:30 -/
 def Option.get_bool (T : Type) (self : Option T) : Result Bool :=
   match self with
   | none => Result.ret false
-  | some t => Result.ret true
+  | some _ => Result.ret true
 
 /- Trait implementation: [traits::{core::option::Option<T>#1}]
    Source: 'src/traits.rs', lines 22:0-22:31 -/
@@ -50,16 +50,16 @@ def traits.BoolTraitcoreoptionOptionTInst (T : Type) : BoolTrait (Option T)
   get_bool := Option.get_bool T
 }
 
-/- [traits::test_bool_trait_option]: forward function
+/- [traits::test_bool_trait_option]:
    Source: 'src/traits.rs', lines 31:0-31:54 -/
 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 (traits.BoolTraitcoreoptionOptionTInst T) x
-    else Result.ret false
+  let b ← Option.get_bool T x
+  if b
+  then BoolTrait.ret_true (traits.BoolTraitcoreoptionOptionTInst T) x
+  else Result.ret false
 
-/- [traits::test_bool_trait]: forward function
+/- [traits::test_bool_trait]:
    Source: 'src/traits.rs', lines 35:0-35:50 -/
 def test_bool_trait
   (T : Type) (BoolTraitTInst : BoolTrait T) (x : T) : Result Bool :=
@@ -70,7 +70,7 @@ def test_bool_trait
 structure ToU64 (Self : Type) where
   to_u64 : Self → Result U64
 
-/- [traits::{u64#2}::to_u64]: forward function
+/- [traits::{u64#2}::to_u64]:
    Source: 'src/traits.rs', lines 44:4-44:26 -/
 def U64.to_u64 (self : U64) : Result U64 :=
   Result.ret self
@@ -81,15 +81,15 @@ def traits.ToU64U64Inst : ToU64 U64 := {
   to_u64 := U64.to_u64
 }
 
-/- [traits::{(A, A)#3}::to_u64]: forward function
+/- [traits::{(A, A)#3}::to_u64]:
    Source: 'src/traits.rs', lines 50:4-50:26 -/
 def Pair.to_u64
   (A : Type) (ToU64AInst : ToU64 A) (self : (A × A)) : Result U64 :=
   do
-    let (t, t0) := self
-    let i ← ToU64AInst.to_u64 t
-    let i0 ← ToU64AInst.to_u64 t0
-    i + i0
+  let (t, t1) := self
+  let i ← ToU64AInst.to_u64 t
+  let i1 ← ToU64AInst.to_u64 t1
+  i + i1
 
 /- Trait implementation: [traits::{(A, A)#3}]
    Source: 'src/traits.rs', lines 49:0-49:31 -/
@@ -98,18 +98,18 @@ def traits.ToU64TupleAAInst (A : Type) (ToU64AInst : ToU64 A) : ToU64 (A × A)
   to_u64 := Pair.to_u64 A ToU64AInst
 }
 
-/- [traits::f]: forward function
+/- [traits::f]:
    Source: 'src/traits.rs', lines 55:0-55:36 -/
 def f (T : Type) (ToU64TInst : ToU64 T) (x : (T × T)) : Result U64 :=
   Pair.to_u64 T ToU64TInst x
 
-/- [traits::g]: forward function
+/- [traits::g]:
    Source: 'src/traits.rs', lines 59:0-61:18 -/
 def g
   (T : Type) (ToU64TupleTTInst : ToU64 (T × T)) (x : (T × T)) : Result U64 :=
   ToU64TupleTTInst.to_u64 x
 
-/- [traits::h0]: forward function
+/- [traits::h0]:
    Source: 'src/traits.rs', lines 66:0-66:24 -/
 def h0 (x : U64) : Result U64 :=
   U64.to_u64 x
@@ -119,7 +119,7 @@ def h0 (x : U64) : Result U64 :=
 structure Wrapper (T : Type) where
   x : T
 
-/- [traits::{traits::Wrapper<T>#4}::to_u64]: forward function
+/- [traits::{traits::Wrapper<T>#4}::to_u64]:
    Source: 'src/traits.rs', lines 75:4-75:26 -/
 def Wrapper.to_u64
   (T : Type) (ToU64TInst : ToU64 T) (self : Wrapper T) : Result U64 :=
@@ -132,12 +132,12 @@ def traits.ToU64traitsWrapperTInst (T : Type) (ToU64TInst : ToU64 T) : ToU64
   to_u64 := Wrapper.to_u64 T ToU64TInst
 }
 
-/- [traits::h1]: forward function
+/- [traits::h1]:
    Source: 'src/traits.rs', lines 80:0-80:33 -/
 def h1 (x : Wrapper U64) : Result U64 :=
   Wrapper.to_u64 U64 traits.ToU64U64Inst x
 
-/- [traits::h2]: forward function
+/- [traits::h2]:
    Source: 'src/traits.rs', lines 84:0-84:41 -/
 def h2 (T : Type) (ToU64TInst : ToU64 T) (x : Wrapper T) : Result U64 :=
   Wrapper.to_u64 T ToU64TInst x
@@ -147,7 +147,7 @@ def h2 (T : Type) (ToU64TInst : ToU64 T) (x : Wrapper T) : Result U64 :=
 structure ToType (Self T : Type) where
   to_type : Self → Result T
 
-/- [traits::{u64#5}::to_type]: forward function
+/- [traits::{u64#5}::to_type]:
    Source: 'src/traits.rs', lines 93:4-93:28 -/
 def U64.to_type (self : U64) : Result Bool :=
   Result.ret (self > 0#u64)
@@ -164,7 +164,7 @@ structure OfType (Self : Type) where
   of_type : forall (T : Type) (ToTypeTSelfInst : ToType T Self), T → Result
     Self
 
-/- [traits::h3]: forward function
+/- [traits::h3]:
    Source: 'src/traits.rs', lines 104:0-104:50 -/
 def h3
   (T1 T2 : Type) (OfTypeT1Inst : OfType T1) (ToTypeT2T1Inst : ToType T2 T1)
@@ -179,7 +179,7 @@ structure OfTypeBis (Self T : Type) where
   ToTypeTSelfInst : ToType T Self
   of_type : T → Result Self
 
-/- [traits::h4]: forward function
+/- [traits::h4]:
    Source: 'src/traits.rs', lines 118:0-118:57 -/
 def h4
   (T1 T2 : Type) (OfTypeBisT1T2Inst : OfTypeBis T1 T2) (ToTypeT2T1Inst : ToType
@@ -201,7 +201,7 @@ def h4
 structure TestType.test.TestTrait (Self : Type) where
   test : Self → Result Bool
 
-/- [traits::{traits::TestType<T>#6}::test::{traits::{traits::TestType<T>#6}::test::TestType1}::test]: forward function
+/- [traits::{traits::TestType<T>#6}::test::{traits::{traits::TestType<T>#6}::test::TestType1}::test]:
    Source: 'src/traits.rs', lines 139:12-139:34 -/
 def TestType.test.TestType1.test
   (self : TestType.test.TestType1) : Result Bool :=
@@ -214,23 +214,23 @@ def traits.TestType.test.TestTraittraitstraitsTestTypeTtestTestType1Inst :
   test := TestType.test.TestType1.test
 }
 
-/- [traits::{traits::TestType<T>#6}::test]: forward function
+/- [traits::{traits::TestType<T>#6}::test]:
    Source: 'src/traits.rs', lines 126:4-126:36 -/
 def TestType.test
   (T : Type) (ToU64TInst : ToU64 T) (self : TestType T) (x : T) :
   Result Bool
   :=
   do
-    let x0 ← ToU64TInst.to_u64 x
-    if x0 > 0#u64
-    then TestType.test.TestType1.test 0#u64
-    else Result.ret false
+  let x1 ← ToU64TInst.to_u64 x
+  if x1 > 0#u64
+  then TestType.test.TestType1.test 0#u64
+  else Result.ret false
 
 /- [traits::BoolWrapper]
    Source: 'src/traits.rs', lines 150:0-150:22 -/
 @[reducible] def BoolWrapper := Bool
 
-/- [traits::{traits::BoolWrapper#7}::to_type]: forward function
+/- [traits::{traits::BoolWrapper#7}::to_type]:
    Source: 'src/traits.rs', lines 156:4-156:25 -/
 def BoolWrapper.to_type
   (T : Type) (ToTypeBoolTInst : ToType Bool T) (self : BoolWrapper) :
@@ -266,8 +266,7 @@ structure WithConstTy (Self : Type) (LEN : Usize) where
 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 ())
+/- [traits::{bool#8}::f]:
    Source: 'src/traits.rs', lines 180:4-180:39 -/
 def Bool.f (i : U64) (a : Array U8 32#usize) : Result U64 :=
   Result.ret i
@@ -283,16 +282,15 @@ def traits.WithConstTyBool32Inst : WithConstTy Bool 32#usize := {
   f := Bool.f
 }
 
-/- [traits::use_with_const_ty1]: forward function
+/- [traits::use_with_const_ty1]:
    Source: 'src/traits.rs', lines 183:0-183:75 -/
 def use_with_const_ty1
   (H : Type) (LEN : Usize) (WithConstTyHLENInst : WithConstTy H LEN) :
   Result Usize
   :=
-  let i := WithConstTyHLENInst.LEN1
-  Result.ret i
+  Result.ret WithConstTyHLENInst.LEN1
 
-/- [traits::use_with_const_ty2]: forward function
+/- [traits::use_with_const_ty2]:
    Source: 'src/traits.rs', lines 187:0-187:73 -/
 def use_with_const_ty2
   (H : Type) (LEN : Usize) (WithConstTyHLENInst : WithConstTy H LEN)
@@ -301,7 +299,7 @@ def use_with_const_ty2
   :=
   Result.ret ()
 
-/- [traits::use_with_const_ty3]: forward function
+/- [traits::use_with_const_ty3]:
    Source: 'src/traits.rs', lines 189:0-189:80 -/
 def use_with_const_ty3
   (H : Type) (LEN : Usize) (WithConstTyHLENInst : WithConstTy H LEN)
@@ -310,12 +308,12 @@ def use_with_const_ty3
   :=
   WithConstTyHLENInst.W_clause_0.to_u64 x
 
-/- [traits::test_where1]: forward function
+/- [traits::test_where1]:
    Source: 'src/traits.rs', lines 193:0-193:40 -/
 def test_where1 (T : Type) (_x : T) : Result Unit :=
   Result.ret ()
 
-/- [traits::test_where2]: forward function
+/- [traits::test_where2]:
    Source: 'src/traits.rs', lines 194:0-194:57 -/
 def test_where2
   (T : Type) (WithConstTyT32Inst : WithConstTy T 32#usize) (_x : U32) :
@@ -340,22 +338,30 @@ structure ChildTrait (Self : Type) where
   ParentTrait0SelfInst : ParentTrait0 Self
   ParentTrait1SelfInst : ParentTrait1 Self
 
-/- [traits::test_child_trait1]: forward function
-   Source: 'src/traits.rs', lines 209:0-209:56 -/
+/- [traits::test_parent_trait0]:
+   Source: 'src/traits.rs', lines 208:0-208:57 -/
+def test_parent_trait0
+  (T : Type) (ParentTrait0TInst : ParentTrait0 T) (x : T) :
+  Result ParentTrait0TInst.W
+  :=
+  ParentTrait0TInst.get_w x
+
+/- [traits::test_child_trait1]:
+   Source: 'src/traits.rs', lines 213:0-213:56 -/
 def test_child_trait1
   (T : Type) (ChildTraitTInst : ChildTrait T) (x : T) : Result String :=
   ChildTraitTInst.ParentTrait0SelfInst.get_name x
 
-/- [traits::test_child_trait2]: forward function
-   Source: 'src/traits.rs', lines 213:0-213:54 -/
+/- [traits::test_child_trait2]:
+   Source: 'src/traits.rs', lines 217:0-217:54 -/
 def test_child_trait2
   (T : Type) (ChildTraitTInst : ChildTrait T) (x : T) :
   Result ChildTraitTInst.ParentTrait0SelfInst.W
   :=
   ChildTraitTInst.ParentTrait0SelfInst.get_w x
 
-/- [traits::order1]: forward function
-   Source: 'src/traits.rs', lines 219:0-219:59 -/
+/- [traits::order1]:
+   Source: 'src/traits.rs', lines 223:0-223:59 -/
 def order1
   (T U : Type) (ParentTrait0TInst : ParentTrait0 T) (ParentTrait0UInst :
   ParentTrait0 U) :
@@ -364,28 +370,28 @@ def order1
   Result.ret ()
 
 /- Trait declaration: [traits::ChildTrait1]
-   Source: 'src/traits.rs', lines 222:0-222:35 -/
+   Source: 'src/traits.rs', lines 226:0-226:35 -/
 structure ChildTrait1 (Self : Type) where
   ParentTrait1SelfInst : ParentTrait1 Self
 
 /- Trait implementation: [traits::{usize#9}]
-   Source: 'src/traits.rs', lines 224:0-224:27 -/
+   Source: 'src/traits.rs', lines 228:0-228:27 -/
 def traits.ParentTrait1UsizeInst : ParentTrait1 Usize := {
 }
 
 /- Trait implementation: [traits::{usize#10}]
-   Source: 'src/traits.rs', lines 225:0-225:26 -/
+   Source: 'src/traits.rs', lines 229:0-229:26 -/
 def traits.ChildTrait1UsizeInst : ChildTrait1 Usize := {
   ParentTrait1SelfInst := traits.ParentTrait1UsizeInst
 }
 
 /- Trait declaration: [traits::Iterator]
-   Source: 'src/traits.rs', lines 229:0-229:18 -/
+   Source: 'src/traits.rs', lines 233:0-233:18 -/
 structure Iterator (Self : Type) where
   Item : Type
 
 /- Trait declaration: [traits::IntoIterator]
-   Source: 'src/traits.rs', lines 233:0-233:22 -/
+   Source: 'src/traits.rs', lines 237:0-237:22 -/
 structure IntoIterator (Self : Type) where
   Item : Type
   IntoIter : Type
@@ -393,76 +399,86 @@ structure IntoIterator (Self : Type) where
   into_iter : Self → Result IntoIter
 
 /- Trait declaration: [traits::FromResidual]
-   Source: 'src/traits.rs', lines 250:0-250:21 -/
+   Source: 'src/traits.rs', lines 254:0-254:21 -/
 structure FromResidual (Self T : Type) where
 
 /- Trait declaration: [traits::Try]
-   Source: 'src/traits.rs', lines 246:0-246:48 -/
+   Source: 'src/traits.rs', lines 250:0-250:48 -/
 structure Try (Self : Type) where
   Residual : Type
   FromResidualSelftraitsTrySelfResidualInst : FromResidual Self Residual
 
 /- Trait declaration: [traits::WithTarget]
-   Source: 'src/traits.rs', lines 252:0-252:20 -/
+   Source: 'src/traits.rs', lines 256:0-256:20 -/
 structure WithTarget (Self : Type) where
   Target : Type
 
 /- Trait declaration: [traits::ParentTrait2]
-   Source: 'src/traits.rs', lines 256:0-256:22 -/
+   Source: 'src/traits.rs', lines 260:0-260:22 -/
 structure ParentTrait2 (Self : Type) where
   U : Type
   U_clause_0 : WithTarget U
 
 /- Trait declaration: [traits::ChildTrait2]
-   Source: 'src/traits.rs', lines 260:0-260:35 -/
+   Source: 'src/traits.rs', lines 264:0-264:35 -/
 structure ChildTrait2 (Self : Type) where
   ParentTrait2SelfInst : ParentTrait2 Self
   convert : ParentTrait2SelfInst.U → Result
     ParentTrait2SelfInst.U_clause_0.Target
 
 /- Trait implementation: [traits::{u32#11}]
-   Source: 'src/traits.rs', lines 264:0-264:23 -/
+   Source: 'src/traits.rs', lines 268:0-268:23 -/
 def traits.WithTargetU32Inst : WithTarget U32 := {
   Target := U32
 }
 
 /- Trait implementation: [traits::{u32#12}]
-   Source: 'src/traits.rs', lines 268:0-268:25 -/
+   Source: 'src/traits.rs', lines 272:0-272:25 -/
 def traits.ParentTrait2U32Inst : ParentTrait2 U32 := {
   U := U32
   U_clause_0 := traits.WithTargetU32Inst
 }
 
-/- [traits::{u32#13}::convert]: forward function
-   Source: 'src/traits.rs', lines 273:4-273:29 -/
+/- [traits::{u32#13}::convert]:
+   Source: 'src/traits.rs', lines 277:4-277:29 -/
 def U32.convert (x : U32) : Result U32 :=
   Result.ret x
 
 /- Trait implementation: [traits::{u32#13}]
-   Source: 'src/traits.rs', lines 272:0-272:24 -/
+   Source: 'src/traits.rs', lines 276:0-276:24 -/
 def traits.ChildTrait2U32Inst : ChildTrait2 U32 := {
   ParentTrait2SelfInst := traits.ParentTrait2U32Inst
   convert := U32.convert
 }
 
 /- Trait declaration: [traits::CFnOnce]
-   Source: 'src/traits.rs', lines 286:0-286:23 -/
+   Source: 'src/traits.rs', lines 290:0-290:23 -/
 structure CFnOnce (Self Args : Type) where
   Output : Type
   call_once : Self → Args → Result Output
 
 /- Trait declaration: [traits::CFnMut]
-   Source: 'src/traits.rs', lines 292:0-292:37 -/
+   Source: 'src/traits.rs', lines 296:0-296:37 -/
 structure CFnMut (Self Args : Type) where
   CFnOnceSelfArgsInst : CFnOnce Self Args
-  call_mut : Self → Args → Result CFnOnceSelfArgsInst.Output
-  call_mut_back : Self → Args → CFnOnceSelfArgsInst.Output → Result Self
+  call_mut : Self → Args → Result (CFnOnceSelfArgsInst.Output × Self)
 
 /- Trait declaration: [traits::CFn]
-   Source: 'src/traits.rs', lines 296:0-296:33 -/
+   Source: 'src/traits.rs', lines 300:0-300:33 -/
 structure CFn (Self Args : Type) where
   CFnMutSelfArgsInst : CFnMut Self Args
-  call_mut : Self → Args → Result
-    CFnMutSelfArgsInst.CFnOnceSelfArgsInst.Output
+  call : Self → Args → Result CFnMutSelfArgsInst.CFnOnceSelfArgsInst.Output
+
+/- Trait declaration: [traits::GetTrait]
+   Source: 'src/traits.rs', lines 304:0-304:18 -/
+structure GetTrait (Self : Type) where
+  W : Type
+  get_w : Self → Result W
+
+/- [traits::test_get_trait]:
+   Source: 'src/traits.rs', lines 309:0-309:49 -/
+def test_get_trait
+  (T : Type) (GetTraitTInst : GetTrait T) (x : T) : Result GetTraitTInst.W :=
+  GetTraitTInst.get_w x
 
 end traits