Regenerate the Coq test files

14 files changed, 1403 insertions, 80 deletions

diff --git a/tests/coq/array/Array_Funs.v b/tests/coq/array/Array.v
index 9980a6e8..825f73e0 100644
--- a/tests/coq/array/Array_Funs.v
+++ b/tests/coq/array/Array.v
@@ -1,14 +1,15 @@
 (** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
-(** [array]: function definitions *)
+(** [array] *)
 Require Import Primitives.
 Import Primitives.
 Require Import Coq.ZArith.ZArith.
 Require Import List.
 Import ListNotations.
 Local Open Scope Primitives_scope.
-Require Export Array_Types.
-Import Array_Types.
-Module Array_Funs.
+Module Array.
+
+(** [array::AB] *)
+Inductive AB_t := | AB_A : AB_t | AB_B : AB_t.
 
 (** [array::incr]: merged forward/backward function
     (there is a single backward function, and the forward function returns ()) *)
@@ -98,7 +99,7 @@ Definition index_mut_slice_back
 
 (** [array::slice_subslice_shared_]: forward function *)
 Definition slice_subslice_shared_
-  (n : nat) (x : slice u32) (y : usize) (z : usize) : result (slice u32) :=
+  (x : slice u32) (y : usize) (z : usize) : result (slice u32) :=
   core_slice_index_Slice_index u32 (core_ops_range_Range usize)
     (core_slice_index_Range_coresliceindexSliceIndexInst u32) x
     {| core_ops_range_Range_start := y; core_ops_range_Range_end_ := z |}
@@ -106,7 +107,7 @@ Definition slice_subslice_shared_
 
 (** [array::slice_subslice_mut_]: forward function *)
 Definition slice_subslice_mut_
-  (n : nat) (x : slice u32) (y : usize) (z : usize) : result (slice u32) :=
+  (x : slice u32) (y : usize) (z : usize) : result (slice u32) :=
   core_slice_index_Slice_index_mut u32 (core_ops_range_Range usize)
     (core_slice_index_Range_coresliceindexSliceIndexInst u32) x
     {| core_ops_range_Range_start := y; core_ops_range_Range_end_ := z |}
@@ -114,7 +115,7 @@ Definition slice_subslice_mut_
 
 (** [array::slice_subslice_mut_]: backward function 0 *)
 Definition slice_subslice_mut__back
-  (n : nat) (x : slice u32) (y : usize) (z : usize) (ret : slice u32) :
+  (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)
@@ -141,9 +142,7 @@ Definition array_to_slice_mut__back
 
 (** [array::array_subslice_shared_]: forward function *)
 Definition array_subslice_shared_
-  (n : nat) (x : array u32 32%usize) (y : usize) (z : usize) :
-  result (slice u32)
-  :=
+  (x : array u32 32%usize) (y : usize) (z : usize) : result (slice u32) :=
   core_array_Array_index u32 (core_ops_range_Range usize) 32%usize
     (core_slice_index_Slice_coreopsindexIndexInst u32 (core_ops_range_Range
     usize) (core_slice_index_Range_coresliceindexSliceIndexInst u32)) x
@@ -152,9 +151,7 @@ Definition array_subslice_shared_
 
 (** [array::array_subslice_mut_]: forward function *)
 Definition array_subslice_mut_
-  (n : nat) (x : array u32 32%usize) (y : usize) (z : usize) :
-  result (slice u32)
-  :=
+  (x : array u32 32%usize) (y : usize) (z : usize) : result (slice u32) :=
   core_array_Array_index_mut u32 (core_ops_range_Range usize) 32%usize
     (core_slice_index_Slice_coreopsindexIndexMutInst u32 (core_ops_range_Range
     usize) (core_slice_index_Range_coresliceindexSliceIndexInst u32)) x
@@ -163,8 +160,7 @@ Definition array_subslice_mut_
 
 (** [array::array_subslice_mut_]: backward function 0 *)
 Definition array_subslice_mut__back
-  (n : nat) (x : array u32 32%usize) (y : usize) (z : usize) (ret : slice u32)
-  :
+  (x : array u32 32%usize) (y : usize) (z : usize) (ret : slice u32) :
   result (array u32 32%usize)
   :=
   core_array_Array_index_mut_back u32 (core_ops_range_Range usize) 32%usize
@@ -310,7 +306,7 @@ Definition update_all : result unit :=
 .
 
 (** [array::range_all]: forward function *)
-Definition range_all (n : nat) : result unit :=
+Definition range_all : result unit :=
   s <-
     core_array_Array_index_mut u32 (core_ops_range_Range usize) 4%usize
       (core_slice_index_Slice_coreopsindexIndexMutInst u32
@@ -432,9 +428,7 @@ Definition f2 (i : u32) : result unit :=
 
 (** [array::f4]: forward function *)
 Definition f4
-  (n : nat) (x : array u32 32%usize) (y : usize) (z : usize) :
-  result (slice u32)
-  :=
+  (x : array u32 32%usize) (y : usize) (z : usize) : result (slice u32) :=
   core_array_Array_index u32 (core_ops_range_Range usize) 32%usize
     (core_slice_index_Slice_coreopsindexIndexInst u32 (core_ops_range_Range
     usize) (core_slice_index_Range_coresliceindexSliceIndexInst u32)) x
@@ -449,7 +443,7 @@ 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 n b 16%usize 18%usize;
+  s0 <- f4 b 16%usize 18%usize;
   sum2 n s s0
 .
 
@@ -473,4 +467,4 @@ Definition ite : result unit :=
   Return tt
 .
 
-End Array_Funs .
+End Array .
diff --git a/tests/coq/array/Array_Types.v b/tests/coq/array/Array_Types.v
deleted file mode 100644
index a13d64e6..00000000
--- a/tests/coq/array/Array_Types.v
+++ /dev/null
@@ -1,14 +0,0 @@
-(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
-(** [array]: type definitions *)
-Require Import Primitives.
-Import Primitives.
-Require Import Coq.ZArith.ZArith.
-Require Import List.
-Import ListNotations.
-Local Open Scope Primitives_scope.
-Module Array_Types.
-
-(** [array::AB] *)
-Inductive AB_t := | AB_A : AB_t | AB_B : AB_t.
-
-End Array_Types .
diff --git a/tests/coq/array/_CoqProject b/tests/coq/array/_CoqProject
index f33cefe6..87d8fc3d 100644
--- a/tests/coq/array/_CoqProject
+++ b/tests/coq/array/_CoqProject
@@ -3,6 +3,5 @@
 -arg -w
 -arg all
 
-Array_Funs.v
 Primitives.v
-Array_Types.v
+Array.v
diff --git a/tests/coq/betree/BetreeMain_Types.v b/tests/coq/betree/BetreeMain_Types.v
index ee26622e..933a670c 100644
--- a/tests/coq/betree/BetreeMain_Types.v
+++ b/tests/coq/betree/BetreeMain_Types.v
@@ -14,8 +14,8 @@ Inductive betree_List_t (T : Type) :=
 | Betree_List_Nil : betree_List_t T
 .
 
-Arguments Betree_List_Cons {T} _ _.
-Arguments Betree_List_Nil {T}.
+Arguments Betree_List_Cons { _ }.
+Arguments Betree_List_Nil { _ }.
 
 (** [betree_main::betree::UpsertFunState] *)
 Inductive betree_UpsertFunState_t :=
diff --git a/tests/coq/hashmap/Hashmap_Types.v b/tests/coq/hashmap/Hashmap_Types.v
index 63d30eeb..8529803d 100644
--- a/tests/coq/hashmap/Hashmap_Types.v
+++ b/tests/coq/hashmap/Hashmap_Types.v
@@ -14,8 +14,8 @@ Inductive List_t (T : Type) :=
 | List_Nil : List_t T
 .
 
-Arguments List_Cons {T} _ _ _.
-Arguments List_Nil {T}.
+Arguments List_Cons { _ }.
+Arguments List_Nil { _ }.
 
 (** [hashmap::HashMap] *)
 Record HashMap_t (T : Type) :=
@@ -27,10 +27,10 @@ mkHashMap_t {
 }
 .
 
-Arguments mkHashMap_t {T} _ _ _ _.
-Arguments hashMap_num_entries {T}.
-Arguments hashMap_max_load_factor {T}.
-Arguments hashMap_max_load {T}.
-Arguments hashMap_slots {T}.
+Arguments mkHashMap_t { _ }.
+Arguments hashMap_num_entries { _ }.
+Arguments hashMap_max_load_factor { _ }.
+Arguments hashMap_max_load { _ }.
+Arguments hashMap_slots { _ }.
 
 End Hashmap_Types .
diff --git a/tests/coq/hashmap_on_disk/HashmapMain_Types.v b/tests/coq/hashmap_on_disk/HashmapMain_Types.v
index 466119f8..95e5f35b 100644
--- a/tests/coq/hashmap_on_disk/HashmapMain_Types.v
+++ b/tests/coq/hashmap_on_disk/HashmapMain_Types.v
@@ -14,8 +14,8 @@ Inductive hashmap_List_t (T : Type) :=
 | Hashmap_List_Nil : hashmap_List_t T
 .
 
-Arguments Hashmap_List_Cons {T} _ _ _.
-Arguments Hashmap_List_Nil {T}.
+Arguments Hashmap_List_Cons { _ }.
+Arguments Hashmap_List_Nil { _ }.
 
 (** [hashmap_main::hashmap::HashMap] *)
 Record hashmap_HashMap_t (T : Type) :=
@@ -27,11 +27,11 @@ mkhashmap_HashMap_t {
 }
 .
 
-Arguments mkhashmap_HashMap_t {T} _ _ _ _.
-Arguments hashmap_HashMap_num_entries {T}.
-Arguments hashmap_HashMap_max_load_factor {T}.
-Arguments hashmap_HashMap_max_load {T}.
-Arguments hashmap_HashMap_slots {T}.
+Arguments mkhashmap_HashMap_t { _ }.
+Arguments hashmap_HashMap_num_entries { _ }.
+Arguments hashmap_HashMap_max_load_factor { _ }.
+Arguments hashmap_HashMap_max_load { _ }.
+Arguments hashmap_HashMap_slots { _ }.
 
 (** The state type used in the state-error monad *)
 Axiom state : Type.
diff --git a/tests/coq/misc/Constants.v b/tests/coq/misc/Constants.v
index 7cb1a642..03653f69 100644
--- a/tests/coq/misc/Constants.v
+++ b/tests/coq/misc/Constants.v
@@ -35,9 +35,9 @@ Definition mk_pair0 (x : u32) (y : u32) : result (u32 * u32) :=
 (** [constants::Pair] *)
 Record Pair_t (T1 T2 : Type) := mkPair_t { pair_x : T1; pair_y : T2; }.
 
-Arguments mkPair_t {T1} {T2} _ _.
-Arguments pair_x {T1} {T2}.
-Arguments pair_y {T1} {T2}.
+Arguments mkPair_t { _ _ }.
+Arguments pair_x { _ _ }.
+Arguments pair_y { _ _ }.
 
 (** [constants::mk_pair1]: forward function *)
 Definition mk_pair1 (x : u32) (y : u32) : result (Pair_t u32 u32) :=
@@ -65,8 +65,8 @@ Definition p3_c : Pair_t u32 u32 := p3_body%global.
 (** [constants::Wrap] *)
 Record Wrap_t (T : Type) := mkWrap_t { wrap_value : T; }.
 
-Arguments mkWrap_t {T} _.
-Arguments wrap_value {T}.
+Arguments mkWrap_t { _ }.
+Arguments wrap_value { _ }.
 
 (** [constants::Wrap::{0}::new]: forward function *)
 Definition wrap_new (T : Type) (value : T) : result (Wrap_t T) :=
diff --git a/tests/coq/misc/Loops.v b/tests/coq/misc/Loops.v
index 180a1d68..1c0eab17 100644
--- a/tests/coq/misc/Loops.v
+++ b/tests/coq/misc/Loops.v
@@ -96,8 +96,8 @@ Inductive List_t (T : Type) :=
 | List_Nil : List_t T
 .
 
-Arguments List_Cons {T} _ _.
-Arguments List_Nil {T}.
+Arguments List_Cons { _ }.
+Arguments List_Nil { _ }.
 
 (** [loops::list_mem]: loop 0: forward function *)
 Fixpoint list_mem_loop (n : nat) (x : u32) (ls : List_t u32) : result bool :=
diff --git a/tests/coq/misc/NoNestedBorrows.v b/tests/coq/misc/NoNestedBorrows.v
index e916ca4a..c7af496f 100644
--- a/tests/coq/misc/NoNestedBorrows.v
+++ b/tests/coq/misc/NoNestedBorrows.v
@@ -11,9 +11,9 @@ Module NoNestedBorrows.
 (** [no_nested_borrows::Pair] *)
 Record Pair_t (T1 T2 : Type) := mkPair_t { pair_x : T1; pair_y : T2; }.
 
-Arguments mkPair_t {T1} {T2} _ _.
-Arguments pair_x {T1} {T2}.
-Arguments pair_y {T1} {T2}.
+Arguments mkPair_t { _ _ }.
+Arguments pair_x { _ _ }.
+Arguments pair_y { _ _ }.
 
 (** [no_nested_borrows::List] *)
 Inductive List_t (T : Type) :=
@@ -21,13 +21,13 @@ Inductive List_t (T : Type) :=
 | List_Nil : List_t T
 .
 
-Arguments List_Cons {T} _ _.
-Arguments List_Nil {T}.
+Arguments List_Cons { _ }.
+Arguments List_Nil { _ }.
 
 (** [no_nested_borrows::One] *)
 Inductive One_t (T1 : Type) := | One_One : T1 -> One_t T1.
 
-Arguments One_One {T1} _.
+Arguments One_One { _ }.
 
 (** [no_nested_borrows::EmptyEnum] *)
 Inductive EmptyEnum_t := | EmptyEnum_Empty : EmptyEnum_t.
@@ -44,8 +44,8 @@ Inductive Sum_t (T1 T2 : Type) :=
 | Sum_Right : T2 -> Sum_t T1 T2
 .
 
-Arguments Sum_Left {T1} {T2} _.
-Arguments Sum_Right {T1} {T2} _.
+Arguments Sum_Left { _ _ }.
+Arguments Sum_Right { _ _ }.
 
 (** [no_nested_borrows::neg_test]: forward function *)
 Definition neg_test (x : i32) : result i32 :=
@@ -258,11 +258,11 @@ with NodeElem_t (T : Type) :=
 | NodeElem_Nil : NodeElem_t T
 .
 
-Arguments Tree_Leaf {T} _.
-Arguments Tree_Node {T} _ _ _.
+Arguments Tree_Leaf { _ }.
+Arguments Tree_Node { _ }.
 
-Arguments NodeElem_Cons {T} _ _.
-Arguments NodeElem_Nil {T}.
+Arguments NodeElem_Cons { _ }.
+Arguments NodeElem_Nil { _ }.
 
 (** [no_nested_borrows::list_length]: forward function *)
 Fixpoint list_length (T : Type) (l : List_t T) : result u32 :=
@@ -425,8 +425,8 @@ mkStructWithTuple_t {
 }
 .
 
-Arguments mkStructWithTuple_t {T1} {T2} _.
-Arguments structWithTuple_p {T1} {T2}.
+Arguments mkStructWithTuple_t { _ _ }.
+Arguments structWithTuple_p { _ _ }.
 
 (** [no_nested_borrows::new_tuple1]: forward function *)
 Definition new_tuple1 : result (StructWithTuple_t u32 u32) :=
@@ -450,8 +450,8 @@ mkStructWithPair_t {
 }
 .
 
-Arguments mkStructWithPair_t {T1} {T2} _.
-Arguments structWithPair_p {T1} {T2}.
+Arguments mkStructWithPair_t { _ _ }.
+Arguments structWithPair_p { _ _ }.
 
 (** [no_nested_borrows::new_pair1]: forward function *)
 Definition new_pair1 : result (StructWithPair_t u32 u32) :=
diff --git a/tests/coq/misc/Paper.v b/tests/coq/misc/Paper.v
index d397995b..d3852e6b 100644
--- a/tests/coq/misc/Paper.v
+++ b/tests/coq/misc/Paper.v
@@ -55,8 +55,8 @@ Inductive List_t (T : Type) :=
 | List_Nil : List_t T
 .
 
-Arguments List_Cons {T} _ _.
-Arguments List_Nil {T}.
+Arguments List_Cons { _ }.
+Arguments List_Nil { _ }.
 
 (** [paper::list_nth_mut]: forward function *)
 Fixpoint list_nth_mut (T : Type) (l : List_t T) (i : u32) : result T :=
diff --git a/tests/coq/misc/PoloniusList.v b/tests/coq/misc/PoloniusList.v
index 4f804b55..4848444f 100644
--- a/tests/coq/misc/PoloniusList.v
+++ b/tests/coq/misc/PoloniusList.v
@@ -14,8 +14,8 @@ Inductive List_t (T : Type) :=
 | List_Nil : List_t T
 .
 
-Arguments List_Cons {T} _ _.
-Arguments List_Nil {T}.
+Arguments List_Cons { _ }.
+Arguments List_Nil { _ }.
 
 (** [polonius_list::get_list_at_x]: forward function *)
 Fixpoint get_list_at_x (ls : List_t u32) (x : u32) : result (List_t u32) :=
diff --git a/tests/coq/traits/Primitives.v b/tests/coq/traits/Primitives.v
new file mode 100644
index 00000000..85e38f01
--- /dev/null
+++ b/tests/coq/traits/Primitives.v
@@ -0,0 +1,822 @@
+Require Import Lia.
+Require Coq.Strings.Ascii.
+Require Coq.Strings.String.
+Require Import Coq.Program.Equality.
+Require Import Coq.ZArith.ZArith.
+Require Import Coq.ZArith.Znat.
+Require Import List.
+Import ListNotations.
+
+Module Primitives.
+
+  (* TODO: use more *)
+Declare Scope Primitives_scope.
+
+(*** Result *)
+
+Inductive error :=
+  | Failure
+  | OutOfFuel.
+
+Inductive result A :=
+  | Return : A -> result A
+  | Fail_ : error -> result A.
+
+Arguments Return {_} a.
+Arguments Fail_ {_}.
+
+Definition bind {A B} (m: result A) (f: A -> result B) : result B :=
+  match m with
+  | Fail_ e => Fail_ e
+  | Return x => f x
+  end.
+
+Definition return_ {A: Type} (x: A) : result A := Return x.
+Definition fail_ {A: Type} (e: error) : result A := Fail_ e.
+
+Notation "x <- c1 ; c2" := (bind c1 (fun x => c2))
+  (at level 61, c1 at next level, right associativity).
+
+(** Monadic assert *)
+Definition massert (b: bool) : result unit :=
+  if b then Return tt else Fail_ Failure.
+
+(** Normalize and unwrap a successful result (used for globals) *)
+Definition eval_result_refl {A} {x} (a: result A) (p: a = Return x) : A :=
+  match a as r return (r = Return x -> A) with
+  | Return a' => fun _  => a'
+  | Fail_ e   => fun p' =>
+      False_rect _ (eq_ind (Fail_ e)
+          (fun e : result A =>
+          match e with
+          | Return _ => False
+          | Fail_ e => True
+          end)
+        I (Return x) p')
+  end p.
+
+Notation "x %global" := (eval_result_refl x eq_refl) (at level 40).
+Notation "x %return" := (eval_result_refl x eq_refl) (at level 40).
+
+(* Sanity check *)
+Check (if true then Return (1 + 2) else Fail_ Failure)%global = 3.
+
+(*** Misc *)
+
+Definition string := Coq.Strings.String.string.
+Definition char := Coq.Strings.Ascii.ascii.
+Definition char_of_byte := Coq.Strings.Ascii.ascii_of_byte.
+
+Definition core_mem_replace (a : Type) (x : a) (y : a) : a := x .
+Definition core_mem_replace_back (a : Type) (x : a) (y : a) : a := y .
+
+Record mut_raw_ptr (T : Type) := { mut_raw_ptr_v : T }.
+Record const_raw_ptr (T : Type) := { const_raw_ptr_v : T }.
+
+(*** Scalars *)
+
+Definition i8_min   : Z := -128%Z.
+Definition i8_max   : Z := 127%Z.
+Definition i16_min  : Z := -32768%Z.
+Definition i16_max  : Z := 32767%Z.
+Definition i32_min  : Z := -2147483648%Z.
+Definition i32_max  : Z := 2147483647%Z.
+Definition i64_min  : Z := -9223372036854775808%Z.
+Definition i64_max  : Z := 9223372036854775807%Z.
+Definition i128_min : Z := -170141183460469231731687303715884105728%Z.
+Definition i128_max : Z := 170141183460469231731687303715884105727%Z.
+Definition u8_min   : Z := 0%Z.
+Definition u8_max   : Z := 255%Z.
+Definition u16_min  : Z := 0%Z.
+Definition u16_max  : Z := 65535%Z.
+Definition u32_min  : Z := 0%Z.
+Definition u32_max  : Z := 4294967295%Z.
+Definition u64_min  : Z := 0%Z.
+Definition u64_max  : Z := 18446744073709551615%Z.
+Definition u128_min : Z := 0%Z.
+Definition u128_max : Z := 340282366920938463463374607431768211455%Z.
+
+(** The bounds of [isize] and [usize] vary with the architecture. *)
+Axiom isize_min : Z.
+Axiom isize_max : Z.
+Definition usize_min : Z := 0%Z.
+Axiom usize_max : Z.
+
+Open Scope Z_scope.
+
+(** We provide those lemmas to reason about the bounds of [isize] and [usize] *)
+Axiom isize_min_bound : isize_min <= i32_min.
+Axiom isize_max_bound : i32_max <= isize_max.
+Axiom usize_max_bound : u32_max <= usize_max.
+
+Inductive scalar_ty :=
+  | Isize
+  | I8
+  | I16
+  | I32
+  | I64
+  | I128
+  | Usize
+  | U8
+  | U16
+  | U32
+  | U64
+  | U128
+.
+
+Definition scalar_min (ty: scalar_ty) : Z :=
+  match ty with
+  | Isize => isize_min
+  | I8 => i8_min
+  | I16 => i16_min
+  | I32 => i32_min
+  | I64 => i64_min
+  | I128 => i128_min
+  | Usize => usize_min
+  | U8 => u8_min
+  | U16 => u16_min
+  | U32 => u32_min
+  | U64 => u64_min
+  | U128 => u128_min
+end.
+
+Definition scalar_max (ty: scalar_ty) : Z :=
+  match ty with
+  | Isize => isize_max
+  | I8 => i8_max
+  | I16 => i16_max
+  | I32 => i32_max
+  | I64 => i64_max
+  | I128 => i128_max
+  | Usize => usize_max
+  | U8 => u8_max
+  | U16 => u16_max
+  | U32 => u32_max
+  | U64 => u64_max
+  | U128 => u128_max
+end.
+
+(** We use the following conservative bounds to make sure we can compute bound
+    checks in most situations *)
+Definition scalar_min_cons (ty: scalar_ty) : Z :=
+  match ty with
+  | Isize => i32_min
+  | Usize => u32_min
+  | _ => scalar_min ty
+end.
+
+Definition scalar_max_cons (ty: scalar_ty) : Z :=
+  match ty with
+  | Isize => i32_max
+  | Usize => u32_max
+  | _ => scalar_max ty
+end.
+
+Lemma scalar_min_cons_valid : forall ty, scalar_min ty <= scalar_min_cons ty .
+Proof.
+  destruct ty; unfold scalar_min_cons, scalar_min; try lia.
+  - pose isize_min_bound; lia.
+  - apply Z.le_refl.
+Qed.
+
+Lemma scalar_max_cons_valid : forall ty, scalar_max ty >= scalar_max_cons ty .
+Proof.
+  destruct ty; unfold scalar_max_cons, scalar_max; try lia.
+  - pose isize_max_bound; lia.
+  - pose usize_max_bound. lia.
+Qed.
+
+Definition scalar (ty: scalar_ty) : Type :=
+ { x: Z | scalar_min ty <= x <= scalar_max ty }.
+
+Definition to_Z {ty} (x: scalar ty) : Z := proj1_sig x.
+
+(** Bounds checks: we start by using the conservative bounds, to make sure we
+    can compute in most situations, then we use the real bounds (for [isize]
+    and [usize]). *)
+Definition scalar_ge_min (ty: scalar_ty) (x: Z) : bool :=
+  Z.leb (scalar_min_cons ty) x || Z.leb (scalar_min ty) x.
+
+Definition scalar_le_max (ty: scalar_ty) (x: Z) : bool :=
+  Z.leb x (scalar_max_cons ty) || Z.leb x (scalar_max ty).
+
+Lemma scalar_ge_min_valid (ty: scalar_ty) (x: Z) :
+  scalar_ge_min ty x = true -> scalar_min ty <= x .
+Proof.
+  unfold scalar_ge_min.
+  pose (scalar_min_cons_valid ty).
+  lia.
+Qed.
+
+Lemma scalar_le_max_valid (ty: scalar_ty) (x: Z) :
+  scalar_le_max ty x = true -> x <= scalar_max ty .
+Proof.
+  unfold scalar_le_max.
+  pose (scalar_max_cons_valid ty).
+  lia.
+Qed.
+
+Definition scalar_in_bounds (ty: scalar_ty) (x: Z) : bool :=
+  scalar_ge_min ty x && scalar_le_max ty x .
+
+Lemma scalar_in_bounds_valid (ty: scalar_ty) (x: Z) :
+  scalar_in_bounds ty x = true -> scalar_min ty <= x <= scalar_max ty .
+Proof.
+  unfold scalar_in_bounds.
+  intros H.
+  destruct (scalar_ge_min ty x) eqn:Hmin.
+  - destruct (scalar_le_max ty x) eqn:Hmax.
+    + pose (scalar_ge_min_valid ty x Hmin).
+      pose (scalar_le_max_valid ty x Hmax).
+      lia.
+    + inversion H.
+  - inversion H.
+Qed.
+
+Import Sumbool.
+
+Definition mk_scalar (ty: scalar_ty) (x: Z) : result (scalar ty) :=
+  match sumbool_of_bool (scalar_in_bounds ty x) with
+  | left H => Return (exist _ x (scalar_in_bounds_valid _ _ H))
+  | right _ => Fail_ Failure
+  end.
+
+Definition scalar_add {ty} (x y: scalar ty) : result (scalar ty) := mk_scalar ty (to_Z x + to_Z y).
+
+Definition scalar_sub {ty} (x y: scalar ty) : result (scalar ty) := mk_scalar ty (to_Z x - to_Z y).
+
+Definition scalar_mul {ty} (x y: scalar ty) : result (scalar ty) := mk_scalar ty (to_Z x * to_Z y).
+
+Definition scalar_div {ty} (x y: scalar ty) : result (scalar ty) :=
+  if to_Z y =? 0 then Fail_ Failure else
+  mk_scalar ty (to_Z x / to_Z y).
+
+Definition scalar_rem {ty} (x y: scalar ty) : result (scalar ty) := mk_scalar ty (Z.rem (to_Z x) (to_Z y)).
+  
+Definition scalar_neg {ty} (x: scalar ty) : result (scalar ty) := mk_scalar ty (-(to_Z x)).
+
+(** Cast an integer from a [src_ty] to a [tgt_ty] *)
+(* TODO: check the semantics of casts in Rust *)
+Definition scalar_cast (src_ty tgt_ty : scalar_ty) (x : scalar src_ty) : result (scalar tgt_ty) :=
+  mk_scalar tgt_ty (to_Z x).
+
+(** Comparisons *)
+Definition scalar_leb {ty : scalar_ty} (x : scalar ty) (y : scalar ty) : bool :=
+  Z.leb (to_Z x) (to_Z y) .
+
+Definition scalar_ltb {ty : scalar_ty} (x : scalar ty) (y : scalar ty) : bool :=
+  Z.ltb (to_Z x) (to_Z y) .
+
+Definition scalar_geb {ty : scalar_ty} (x : scalar ty) (y : scalar ty) : bool :=
+  Z.geb (to_Z x) (to_Z y) .
+
+Definition scalar_gtb {ty : scalar_ty} (x : scalar ty) (y : scalar ty) : bool :=
+  Z.gtb (to_Z x) (to_Z y) .
+
+Definition scalar_eqb {ty : scalar_ty} (x : scalar ty) (y : scalar ty) : bool :=
+  Z.eqb (to_Z x) (to_Z y) .
+
+Definition scalar_neqb {ty : scalar_ty} (x : scalar ty) (y : scalar ty) : bool :=
+  negb (Z.eqb (to_Z x) (to_Z y)) .
+
+
+(** The scalar types *)
+Definition isize := scalar Isize.
+Definition i8    := scalar I8.
+Definition i16   := scalar I16.
+Definition i32   := scalar I32.
+Definition i64   := scalar I64.
+Definition i128  := scalar I128.
+Definition usize := scalar Usize.
+Definition u8    := scalar U8.
+Definition u16   := scalar U16.
+Definition u32   := scalar U32.
+Definition u64   := scalar U64.
+Definition u128  := scalar U128.
+
+(** Negaion *)
+Definition isize_neg := @scalar_neg Isize.
+Definition i8_neg    := @scalar_neg I8.
+Definition i16_neg   := @scalar_neg I16.
+Definition i32_neg   := @scalar_neg I32.
+Definition i64_neg   := @scalar_neg I64.
+Definition i128_neg  := @scalar_neg I128.
+
+(** Division *)
+Definition isize_div := @scalar_div Isize.
+Definition i8_div    := @scalar_div I8.
+Definition i16_div   := @scalar_div I16.
+Definition i32_div   := @scalar_div I32.
+Definition i64_div   := @scalar_div I64.
+Definition i128_div  := @scalar_div I128.
+Definition usize_div := @scalar_div Usize.
+Definition u8_div    := @scalar_div U8.
+Definition u16_div   := @scalar_div U16.
+Definition u32_div   := @scalar_div U32.
+Definition u64_div   := @scalar_div U64.
+Definition u128_div  := @scalar_div U128.
+
+(** Remainder *)
+Definition isize_rem := @scalar_rem Isize.
+Definition i8_rem    := @scalar_rem I8.
+Definition i16_rem   := @scalar_rem I16.
+Definition i32_rem   := @scalar_rem I32.
+Definition i64_rem   := @scalar_rem I64.
+Definition i128_rem  := @scalar_rem I128.
+Definition usize_rem := @scalar_rem Usize.
+Definition u8_rem    := @scalar_rem U8.
+Definition u16_rem   := @scalar_rem U16.
+Definition u32_rem   := @scalar_rem U32.
+Definition u64_rem   := @scalar_rem U64.
+Definition u128_rem  := @scalar_rem U128.
+
+(** Addition *)
+Definition isize_add := @scalar_add Isize.
+Definition i8_add    := @scalar_add I8.
+Definition i16_add   := @scalar_add I16.
+Definition i32_add   := @scalar_add I32.
+Definition i64_add   := @scalar_add I64.
+Definition i128_add  := @scalar_add I128.
+Definition usize_add := @scalar_add Usize.
+Definition u8_add    := @scalar_add U8.
+Definition u16_add   := @scalar_add U16.
+Definition u32_add   := @scalar_add U32.
+Definition u64_add   := @scalar_add U64.
+Definition u128_add  := @scalar_add U128.
+
+(** Substraction *)
+Definition isize_sub := @scalar_sub Isize.
+Definition i8_sub    := @scalar_sub I8.
+Definition i16_sub   := @scalar_sub I16.
+Definition i32_sub   := @scalar_sub I32.
+Definition i64_sub   := @scalar_sub I64.
+Definition i128_sub  := @scalar_sub I128.
+Definition usize_sub := @scalar_sub Usize.
+Definition u8_sub    := @scalar_sub U8.
+Definition u16_sub   := @scalar_sub U16.
+Definition u32_sub   := @scalar_sub U32.
+Definition u64_sub   := @scalar_sub U64.
+Definition u128_sub  := @scalar_sub U128.
+
+(** Multiplication *)
+Definition isize_mul := @scalar_mul Isize.
+Definition i8_mul    := @scalar_mul I8.
+Definition i16_mul   := @scalar_mul I16.
+Definition i32_mul   := @scalar_mul I32.
+Definition i64_mul   := @scalar_mul I64.
+Definition i128_mul  := @scalar_mul I128.
+Definition usize_mul := @scalar_mul Usize.
+Definition u8_mul    := @scalar_mul U8.
+Definition u16_mul   := @scalar_mul U16.
+Definition u32_mul   := @scalar_mul U32.
+Definition u64_mul   := @scalar_mul U64.
+Definition u128_mul  := @scalar_mul U128.
+
+(** Small utility *)
+Definition usize_to_nat (x: usize) : nat := Z.to_nat (to_Z x).
+
+(** Notations *)
+Notation "x %isize" := ((mk_scalar Isize x)%return) (at level 9).
+Notation "x %i8"    := ((mk_scalar I8    x)%return) (at level 9).
+Notation "x %i16"   := ((mk_scalar I16   x)%return) (at level 9).
+Notation "x %i32"   := ((mk_scalar I32   x)%return) (at level 9).
+Notation "x %i64"   := ((mk_scalar I64   x)%return) (at level 9).
+Notation "x %i128"  := ((mk_scalar I128  x)%return) (at level 9).
+Notation "x %usize" := ((mk_scalar Usize x)%return) (at level 9).
+Notation "x %u8"    := ((mk_scalar U8    x)%return) (at level 9).
+Notation "x %u16"   := ((mk_scalar U16   x)%return) (at level 9).
+Notation "x %u32"   := ((mk_scalar U32   x)%return) (at level 9).
+Notation "x %u64"   := ((mk_scalar U64   x)%return) (at level 9).
+Notation "x %u128"  := ((mk_scalar U128  x)%return) (at level 9).
+
+Notation "x s= y" := (scalar_eqb x y)  (at level 80) : Primitives_scope.
+Notation "x s<> y" := (scalar_neqb x y) (at level 80) : Primitives_scope.
+Notation "x s<= y" := (scalar_leb x y)  (at level 80) : Primitives_scope.
+Notation "x s< y" := (scalar_ltb x y)  (at level 80) : Primitives_scope.
+Notation "x s>= y" := (scalar_geb x y)  (at level 80) : Primitives_scope.
+Notation "x s> y" := (scalar_gtb x y)  (at level 80) : Primitives_scope.
+
+(** Constants *)
+Definition core_u8_max    := u8_max %u32.
+Definition core_u16_max   := u16_max %u32.
+Definition core_u32_max   := u32_max %u32.
+Definition core_u64_max   := u64_max %u64.
+Definition core_u128_max  := u64_max %u128.
+Axiom core_usize_max : usize. (** TODO *)
+Definition core_i8_max    := i8_max %i32.
+Definition core_i16_max   := i16_max %i32.
+Definition core_i32_max   := i32_max %i32.
+Definition core_i64_max   := i64_max %i64.
+Definition core_i128_max  := i64_max %i128.
+Axiom core_isize_max : isize. (** TODO *)
+
+(*** core::ops *)
+
+(* Trait declaration: [core::ops::index::Index] *)
+Record core_ops_index_Index (Self Idx : Type) := mk_core_ops_index_Index {
+  core_ops_index_Index_Output : Type;
+  core_ops_index_Index_index : Self -> Idx -> result core_ops_index_Index_Output;
+}.
+Arguments mk_core_ops_index_Index {_ _}.
+Arguments core_ops_index_Index_Output {_ _}.
+Arguments core_ops_index_Index_index {_ _}.
+
+(* Trait declaration: [core::ops::index::IndexMut] *)
+Record core_ops_index_IndexMut (Self Idx : Type) := mk_core_ops_index_IndexMut {
+  core_ops_index_IndexMut_indexInst : core_ops_index_Index Self Idx;
+  core_ops_index_IndexMut_index_mut : Self -> Idx -> result core_ops_index_IndexMut_indexInst.(core_ops_index_Index_Output);
+  core_ops_index_IndexMut_index_mut_back : Self -> Idx -> core_ops_index_IndexMut_indexInst.(core_ops_index_Index_Output) -> result Self;
+}.
+Arguments mk_core_ops_index_IndexMut {_ _}.
+Arguments core_ops_index_IndexMut_indexInst {_ _}.
+Arguments core_ops_index_IndexMut_index_mut {_ _}.
+Arguments core_ops_index_IndexMut_index_mut_back {_ _}.
+
+(* Trait declaration [core::ops::deref::Deref] *)
+Record core_ops_deref_Deref (Self : Type) := mk_core_ops_deref_Deref {
+  core_ops_deref_Deref_target : Type;
+  core_ops_deref_Deref_deref : Self -> result core_ops_deref_Deref_target;
+}.
+Arguments mk_core_ops_deref_Deref {_}.
+Arguments core_ops_deref_Deref_target {_}.
+Arguments core_ops_deref_Deref_deref {_}.
+
+(* Trait declaration [core::ops::deref::DerefMut] *)
+Record core_ops_deref_DerefMut (Self : Type) := mk_core_ops_deref_DerefMut {
+  core_ops_deref_DerefMut_derefInst : core_ops_deref_Deref Self;
+  core_ops_deref_DerefMut_deref_mut : Self -> result core_ops_deref_DerefMut_derefInst.(core_ops_deref_Deref_target);
+  core_ops_deref_DerefMut_deref_mut_back : Self -> core_ops_deref_DerefMut_derefInst.(core_ops_deref_Deref_target) -> result Self;
+}.
+Arguments mk_core_ops_deref_DerefMut {_}.
+Arguments core_ops_deref_DerefMut_derefInst {_}.
+Arguments core_ops_deref_DerefMut_deref_mut {_}.
+Arguments core_ops_deref_DerefMut_deref_mut_back {_}.
+
+Record core_ops_range_Range (T : Type) := mk_core_ops_range_Range {
+  core_ops_range_Range_start : T;
+  core_ops_range_Range_end_ : T;
+}.
+Arguments mk_core_ops_range_Range {_}.
+Arguments core_ops_range_Range_start {_}.
+Arguments core_ops_range_Range_end_ {_}.
+
+(*** [alloc] *)
+
+Definition alloc_boxed_Box_deref (T : Type) (x : T) : result T := Return x.
+Definition alloc_boxed_Box_deref_mut (T : Type) (x : T) : result T := Return x.
+Definition alloc_boxed_Box_deref_mut_back (T : Type) (_ : T) (x : T) : result T := Return x.
+
+(* Trait instance *)
+Definition alloc_boxed_Box_coreOpsDerefInst (Self : Type) : core_ops_deref_Deref Self := {|
+  core_ops_deref_Deref_target := Self;
+  core_ops_deref_Deref_deref := alloc_boxed_Box_deref Self;
+|}.
+
+(* Trait instance *)
+Definition alloc_boxed_Box_coreOpsDerefMutInst (Self : Type) : core_ops_deref_DerefMut Self := {|
+  core_ops_deref_DerefMut_derefInst := alloc_boxed_Box_coreOpsDerefInst Self;
+  core_ops_deref_DerefMut_deref_mut := alloc_boxed_Box_deref_mut Self;
+  core_ops_deref_DerefMut_deref_mut_back := alloc_boxed_Box_deref_mut_back Self;
+|}.
+
+
+(*** Arrays *)
+Definition array T (n : usize) := { l: list T | Z.of_nat (length l) = to_Z n}.
+
+Lemma le_0_usize_max : 0 <= usize_max.
+Proof.
+  pose (H := usize_max_bound).
+  unfold u32_max in H.
+  lia.
+Qed.
+
+Lemma eqb_imp_eq (x y : Z) : Z.eqb x y = true -> x = y.
+Proof.
+  lia.
+Qed.
+
+(* TODO: finish the definitions *)
+Axiom mk_array : forall (T : Type) (n : usize) (l : list T), array T n.
+
+(* For initialization *)
+Axiom array_repeat : forall (T : Type) (n : usize) (x : T), array T n.
+
+Axiom array_index_usize : forall (T : Type) (n : usize) (x : array T n) (i : usize), result T.
+Axiom array_update_usize : forall (T : Type) (n : usize) (x : array T n) (i : usize) (nx : T), result (array T n).
+
+(*** Slice *)
+Definition slice T := { l: list T | Z.of_nat (length l) <= usize_max}.
+
+Axiom slice_len : forall (T : Type) (s : slice T), usize.
+Axiom slice_index_usize : forall (T : Type) (x : slice T) (i : usize), result T.
+Axiom slice_update_usize : forall (T : Type) (x : slice T) (i : usize) (nx : T), result (slice T).
+
+(*** Subslices *)
+
+Axiom array_to_slice : forall (T : Type) (n : usize) (x : array T n), result (slice T).
+Axiom array_from_slice : forall (T : Type) (n : usize) (x : array T n) (s : slice T), result (array T n).
+
+Axiom array_subslice: forall (T : Type) (n : usize) (x : array T n) (r : core_ops_range_Range usize), result (slice T).
+Axiom array_update_subslice: forall (T : Type) (n : usize) (x : array T n) (r : core_ops_range_Range usize) (ns : slice T), result (array T n).
+
+Axiom slice_subslice: forall (T : Type) (x : slice T) (r : core_ops_range_Range usize), result (slice T).
+Axiom slice_update_subslice: forall (T : Type) (x : slice T) (r : core_ops_range_Range usize) (ns : slice T), result (slice T).
+
+(*** Vectors *)
+
+Definition alloc_vec_Vec T := { l: list T | Z.of_nat (length l) <= usize_max }.
+
+Definition alloc_vec_Vec_to_list {T: Type} (v: alloc_vec_Vec T) : list T := proj1_sig v.
+
+Definition alloc_vec_Vec_length {T: Type} (v: alloc_vec_Vec T) : Z := Z.of_nat (length (alloc_vec_Vec_to_list v)).
+
+Definition alloc_vec_Vec_new (T: Type) : alloc_vec_Vec T := (exist _ [] le_0_usize_max).
+
+Lemma alloc_vec_Vec_len_in_usize {T} (v: alloc_vec_Vec T) : usize_min <= alloc_vec_Vec_length v <= usize_max.
+Proof.
+  unfold alloc_vec_Vec_length, usize_min.
+  split.
+  - lia.
+  - apply (proj2_sig v).
+Qed.
+
+Definition alloc_vec_Vec_len (T: Type) (v: alloc_vec_Vec T) : usize :=
+  exist _ (alloc_vec_Vec_length v) (alloc_vec_Vec_len_in_usize v).
+
+Fixpoint list_update {A} (l: list A) (n: nat) (a: A)
+  : list A :=
+  match l with
+  | []     => []
+  | x :: t => match n with
+    | 0%nat => a :: t
+    | S m => x :: (list_update t m a)
+end end.
+
+Definition alloc_vec_Vec_bind {A B} (v: alloc_vec_Vec A) (f: list A -> result (list B)) : result (alloc_vec_Vec B) :=
+  l <- f (alloc_vec_Vec_to_list v) ;
+  match sumbool_of_bool (scalar_le_max Usize (Z.of_nat (length l))) with
+  | left H => Return (exist _ l (scalar_le_max_valid _ _ H))
+  | right _ => Fail_ Failure
+  end.
+
+(* The **forward** function shouldn't be used *)
+Definition alloc_vec_Vec_push_fwd (T: Type) (v: alloc_vec_Vec T) (x: T) : unit := tt.
+
+Definition alloc_vec_Vec_push (T: Type) (v: alloc_vec_Vec T) (x: T) : result (alloc_vec_Vec T) :=
+  alloc_vec_Vec_bind v (fun l => Return (l ++ [x])).
+
+(* The **forward** function shouldn't be used *)
+Definition alloc_vec_Vec_insert_fwd (T: Type) (v: alloc_vec_Vec T) (i: usize) (x: T) : result unit :=
+  if to_Z i <? alloc_vec_Vec_length v then Return tt else Fail_ Failure.
+
+Definition alloc_vec_Vec_insert (T: Type) (v: alloc_vec_Vec T) (i: usize) (x: T) : result (alloc_vec_Vec T) :=
+  alloc_vec_Vec_bind v (fun l =>
+    if to_Z i <? Z.of_nat (length l)
+    then Return (list_update l (usize_to_nat i) x)
+    else Fail_ Failure).
+
+(* Helper *)
+Axiom alloc_vec_Vec_index_usize : forall {T : Type} (v : alloc_vec_Vec T) (i : usize) (x : T), result T.
+
+(* Helper *)
+Axiom alloc_vec_Vec_update_usize : forall {T : Type} (v : alloc_vec_Vec T) (i : usize) (x : T), result (alloc_vec_Vec T).
+
+(* Trait declaration: [core::slice::index::private_slice_index::Sealed] *)
+Definition core_slice_index_private_slice_index_Sealed (self : Type) := unit.
+
+(* Trait declaration: [core::slice::index::SliceIndex] *)
+Record core_slice_index_SliceIndex (Self T : Type) := mk_core_slice_index_SliceIndex {
+  core_slice_index_SliceIndex_sealedInst : core_slice_index_private_slice_index_Sealed Self;
+  core_slice_index_SliceIndex_Output : Type;
+  core_slice_index_SliceIndex_get : Self -> T -> result (option core_slice_index_SliceIndex_Output);
+  core_slice_index_SliceIndex_get_mut : Self -> T -> result (option core_slice_index_SliceIndex_Output);
+  core_slice_index_SliceIndex_get_mut_back : Self -> T -> option core_slice_index_SliceIndex_Output -> result T;
+  core_slice_index_SliceIndex_get_unchecked : Self -> const_raw_ptr T -> result (const_raw_ptr core_slice_index_SliceIndex_Output);
+  core_slice_index_SliceIndex_get_unchecked_mut : Self -> mut_raw_ptr T -> result (mut_raw_ptr core_slice_index_SliceIndex_Output);
+  core_slice_index_SliceIndex_index : Self -> T -> result core_slice_index_SliceIndex_Output;
+  core_slice_index_SliceIndex_index_mut : Self -> T -> result core_slice_index_SliceIndex_Output;
+  core_slice_index_SliceIndex_index_mut_back : Self -> T -> core_slice_index_SliceIndex_Output -> result T;
+}.
+Arguments mk_core_slice_index_SliceIndex {_ _}.
+Arguments core_slice_index_SliceIndex_sealedInst {_ _}.
+Arguments core_slice_index_SliceIndex_Output {_ _}.
+Arguments core_slice_index_SliceIndex_get {_ _}.
+Arguments core_slice_index_SliceIndex_get_mut {_ _}.
+Arguments core_slice_index_SliceIndex_get_mut_back {_ _}.
+Arguments core_slice_index_SliceIndex_get_unchecked {_ _}.
+Arguments core_slice_index_SliceIndex_get_unchecked_mut {_ _}.
+Arguments core_slice_index_SliceIndex_index {_ _}.
+Arguments core_slice_index_SliceIndex_index_mut {_ _}.
+Arguments core_slice_index_SliceIndex_index_mut_back {_ _}.
+
+(* [core::slice::index::[T]::index]: forward function *)
+Definition core_slice_index_Slice_index
+  (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T))
+  (s : slice T) (i : Idx) : result inst.(core_slice_index_SliceIndex_Output) :=
+  x <- inst.(core_slice_index_SliceIndex_get) i s;
+  match x with
+  | None => Fail_ Failure
+  | Some x => Return x
+  end.
+
+(* [core::slice::index::Range:::get]: forward function *)
+Axiom core_slice_index_Range_get : forall (T : Type) (i : core_ops_range_Range usize) (s : slice T), result (option (slice T)).
+
+(* [core::slice::index::Range::get_mut]: forward function *)
+Axiom core_slice_index_Range_get_mut :
+  forall (T : Type), core_ops_range_Range usize -> slice T -> result (option (slice T)).
+
+(* [core::slice::index::Range::get_mut]: backward function 0 *)
+Axiom core_slice_index_Range_get_mut_back :
+  forall (T : Type), core_ops_range_Range usize -> slice T -> option (slice T) -> result (slice T).
+
+(* [core::slice::index::Range::get_unchecked]: forward function *)
+Definition core_slice_index_Range_get_unchecked
+  (T : Type) :
+  core_ops_range_Range usize -> const_raw_ptr (slice T) -> result (const_raw_ptr (slice T)) :=
+  (* Don't know what the model should be - for now we always fail to make
+     sure code which uses it fails *)
+  fun _ _ => Fail_ Failure.
+
+(* [core::slice::index::Range::get_unchecked_mut]: forward function *)
+Definition core_slice_index_Range_get_unchecked_mut
+  (T : Type) :
+  core_ops_range_Range usize -> mut_raw_ptr (slice T) -> result (mut_raw_ptr (slice T)) :=
+  (* Don't know what the model should be - for now we always fail to make
+    sure code which uses it fails *)
+  fun _ _ => Fail_ Failure.
+
+(* [core::slice::index::Range::index]: forward function *)
+Axiom core_slice_index_Range_index :
+  forall (T : Type), core_ops_range_Range usize -> slice T -> result (slice T).
+
+(* [core::slice::index::Range::index_mut]: forward function *)
+Axiom core_slice_index_Range_index_mut :
+  forall (T : Type), core_ops_range_Range usize -> slice T -> result (slice T).
+
+(* [core::slice::index::Range::index_mut]: backward function 0 *)
+Axiom core_slice_index_Range_index_mut_back :
+  forall (T : Type), core_ops_range_Range usize -> slice T -> slice T -> result (slice T).
+
+(* [core::slice::index::[T]::index_mut]: forward function *)
+Axiom core_slice_index_Slice_index_mut :
+  forall (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T)),
+  slice T -> Idx -> result inst.(core_slice_index_SliceIndex_Output).
+
+(* [core::slice::index::[T]::index_mut]: backward function 0 *)
+Axiom core_slice_index_Slice_index_mut_back :
+  forall (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T)),
+  slice T -> Idx -> inst.(core_slice_index_SliceIndex_Output) -> result (slice T).
+
+(* [core::array::[T; N]::index]: forward function *)
+Axiom core_array_Array_index :
+  forall (T Idx : Type) (N : usize) (inst : core_ops_index_Index (slice T) Idx)
+  (a : array T N) (i : Idx), result inst.(core_ops_index_Index_Output).
+
+(* [core::array::[T; N]::index_mut]: forward function *)
+Axiom core_array_Array_index_mut :
+  forall (T Idx : Type) (N : usize) (inst : core_ops_index_IndexMut (slice T) Idx)
+  (a : array T N) (i : Idx), result inst.(core_ops_index_IndexMut_indexInst).(core_ops_index_Index_Output).
+
+(* [core::array::[T; N]::index_mut]: backward function 0 *)
+Axiom core_array_Array_index_mut_back :
+  forall (T Idx : Type) (N : usize) (inst : core_ops_index_IndexMut (slice T) Idx)
+  (a : array T N) (i : Idx) (x : inst.(core_ops_index_IndexMut_indexInst).(core_ops_index_Index_Output)), result (array T N).
+
+(* Trait implementation: [core::slice::index::[T]] *)
+Definition core_slice_index_Slice_coreopsindexIndexInst (T Idx : Type)
+  (inst : core_slice_index_SliceIndex Idx (slice T)) :
+  core_ops_index_Index (slice T) Idx := {|
+  core_ops_index_Index_Output := inst.(core_slice_index_SliceIndex_Output);
+  core_ops_index_Index_index := core_slice_index_Slice_index T Idx inst;
+|}.
+
+(* Trait implementation: [core::slice::index::private_slice_index::Range] *)
+Definition core_slice_index_private_slice_index_Range_coresliceindexprivate_slice_indexSealedInst
+  : core_slice_index_private_slice_index_Sealed (core_ops_range_Range usize) := tt.
+
+(* Trait implementation: [core::slice::index::Range] *)
+Definition core_slice_index_Range_coresliceindexSliceIndexInst (T : Type) :
+  core_slice_index_SliceIndex (core_ops_range_Range usize) (slice T) := {|
+  core_slice_index_SliceIndex_sealedInst := core_slice_index_private_slice_index_Range_coresliceindexprivate_slice_indexSealedInst;
+  core_slice_index_SliceIndex_Output := slice T;
+  core_slice_index_SliceIndex_get := core_slice_index_Range_get T;
+  core_slice_index_SliceIndex_get_mut := core_slice_index_Range_get_mut T;
+  core_slice_index_SliceIndex_get_mut_back := core_slice_index_Range_get_mut_back T;
+  core_slice_index_SliceIndex_get_unchecked := core_slice_index_Range_get_unchecked T;
+  core_slice_index_SliceIndex_get_unchecked_mut := core_slice_index_Range_get_unchecked_mut T;
+  core_slice_index_SliceIndex_index := core_slice_index_Range_index T;
+  core_slice_index_SliceIndex_index_mut := core_slice_index_Range_index_mut T;
+  core_slice_index_SliceIndex_index_mut_back := core_slice_index_Range_index_mut_back T;
+|}.
+
+(* Trait implementation: [core::slice::index::[T]] *)
+Definition core_slice_index_Slice_coreopsindexIndexMutInst (T Idx : Type)
+  (inst : core_slice_index_SliceIndex Idx (slice T)) :
+  core_ops_index_IndexMut (slice T) Idx := {|
+  core_ops_index_IndexMut_indexInst := core_slice_index_Slice_coreopsindexIndexInst T Idx inst;
+  core_ops_index_IndexMut_index_mut := core_slice_index_Slice_index_mut T Idx inst;
+  core_ops_index_IndexMut_index_mut_back := core_slice_index_Slice_index_mut_back T Idx inst;
+|}.
+
+(* Trait implementation: [core::array::[T; N]] *)
+Definition core_array_Array_coreopsindexIndexInst (T Idx : Type) (N : usize)
+  (inst : core_ops_index_Index (slice T) Idx) :
+  core_ops_index_Index (array T N) Idx := {|
+  core_ops_index_Index_Output := inst.(core_ops_index_Index_Output);
+  core_ops_index_Index_index := core_array_Array_index T Idx N inst;
+|}.
+
+(* Trait implementation: [core::array::[T; N]] *)
+Definition core_array_Array_coreopsindexIndexMutInst (T Idx : Type) (N : usize)
+  (inst : core_ops_index_IndexMut (slice T) Idx) :
+  core_ops_index_IndexMut (array T N) Idx := {|
+  core_ops_index_IndexMut_indexInst := core_array_Array_coreopsindexIndexInst T Idx N inst.(core_ops_index_IndexMut_indexInst);
+  core_ops_index_IndexMut_index_mut := core_array_Array_index_mut T Idx N inst;
+  core_ops_index_IndexMut_index_mut_back := core_array_Array_index_mut_back T Idx N inst;
+|}.
+
+(* [core::slice::index::usize::get]: forward function *)
+Axiom core_slice_index_usize_get : forall (T : Type), usize -> slice T -> result (option T).
+
+(* [core::slice::index::usize::get_mut]: forward function *)
+Axiom core_slice_index_usize_get_mut : forall (T : Type), usize -> slice T -> result (option T).
+
+(* [core::slice::index::usize::get_mut]: backward function 0 *)
+Axiom core_slice_index_usize_get_mut_back :
+  forall (T : Type), usize -> slice T -> option T -> result (slice T).
+
+(* [core::slice::index::usize::get_unchecked]: forward function *)
+Axiom core_slice_index_usize_get_unchecked :
+  forall (T : Type), usize -> const_raw_ptr (slice T) -> result (const_raw_ptr T).
+
+(* [core::slice::index::usize::get_unchecked_mut]: forward function *)
+Axiom core_slice_index_usize_get_unchecked_mut :
+  forall (T : Type), usize -> mut_raw_ptr (slice T) -> result (mut_raw_ptr T).
+
+(* [core::slice::index::usize::index]: forward function *)
+Axiom core_slice_index_usize_index : forall (T : Type), usize -> slice T -> result T.
+
+(* [core::slice::index::usize::index_mut]: forward function *)
+Axiom core_slice_index_usize_index_mut : forall (T : Type), usize -> slice T -> result T.
+
+(* [core::slice::index::usize::index_mut]: backward function 0 *)
+Axiom core_slice_index_usize_index_mut_back :
+  forall (T : Type), usize -> slice T -> T -> result (slice T).
+
+(* Trait implementation: [core::slice::index::private_slice_index::usize] *)
+Definition core_slice_index_private_slice_index_usize_coresliceindexprivate_slice_indexSealedInst
+  : core_slice_index_private_slice_index_Sealed usize := tt.
+
+(* Trait implementation: [core::slice::index::usize] *)
+Definition core_slice_index_usize_coresliceindexSliceIndexInst (T : Type) :
+  core_slice_index_SliceIndex usize (slice T) := {|
+  core_slice_index_SliceIndex_sealedInst := core_slice_index_private_slice_index_usize_coresliceindexprivate_slice_indexSealedInst;
+  core_slice_index_SliceIndex_Output := T;
+  core_slice_index_SliceIndex_get := core_slice_index_usize_get T;
+  core_slice_index_SliceIndex_get_mut := core_slice_index_usize_get_mut T;
+  core_slice_index_SliceIndex_get_mut_back := core_slice_index_usize_get_mut_back T;
+  core_slice_index_SliceIndex_get_unchecked := core_slice_index_usize_get_unchecked T;
+  core_slice_index_SliceIndex_get_unchecked_mut := core_slice_index_usize_get_unchecked_mut T;
+  core_slice_index_SliceIndex_index := core_slice_index_usize_index T;
+  core_slice_index_SliceIndex_index_mut := core_slice_index_usize_index_mut T;
+  core_slice_index_SliceIndex_index_mut_back := core_slice_index_usize_index_mut_back T;
+|}.
+
+(* [alloc::vec::Vec::index]: forward function *)
+Axiom alloc_vec_Vec_index : forall (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T))
+  (Self : alloc_vec_Vec T) (i : Idx), result inst.(core_slice_index_SliceIndex_Output).
+
+(* [alloc::vec::Vec::index_mut]: forward function *)
+Axiom alloc_vec_Vec_index_mut : forall (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T))
+  (Self : alloc_vec_Vec T) (i : Idx), result inst.(core_slice_index_SliceIndex_Output).
+
+(* [alloc::vec::Vec::index_mut]: backward function 0 *)
+Axiom alloc_vec_Vec_index_mut_back :
+  forall (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T))
+  (Self : alloc_vec_Vec T) (i : Idx) (x : inst.(core_slice_index_SliceIndex_Output)), result (alloc_vec_Vec T).
+
+(* Trait implementation: [alloc::vec::Vec] *)
+Definition alloc_vec_Vec_coreopsindexIndexInst (T Idx : Type)
+  (inst : core_slice_index_SliceIndex Idx (slice T)) :
+  core_ops_index_Index (alloc_vec_Vec T) Idx := {|
+  core_ops_index_Index_Output := inst.(core_slice_index_SliceIndex_Output);
+  core_ops_index_Index_index := alloc_vec_Vec_index T Idx inst;
+|}.
+
+(* Trait implementation: [alloc::vec::Vec] *)
+Definition alloc_vec_Vec_coreopsindexIndexMutInst (T Idx : Type)
+  (inst : core_slice_index_SliceIndex Idx (slice T)) :
+  core_ops_index_IndexMut (alloc_vec_Vec T) Idx := {|
+  core_ops_index_IndexMut_indexInst := alloc_vec_Vec_coreopsindexIndexInst T Idx inst;
+  core_ops_index_IndexMut_index_mut := alloc_vec_Vec_index_mut T Idx inst;
+  core_ops_index_IndexMut_index_mut_back := alloc_vec_Vec_index_mut_back T Idx inst;
+|}.
+
+(*** Theorems *)
+
+Axiom alloc_vec_Vec_index_mut_back_eq : forall {a : Type} (v : alloc_vec_Vec a) (i : usize) (x : a),
+  alloc_vec_Vec_index_mut_back a usize (core_slice_index_usize_coresliceindexSliceIndexInst a) v i x =
+    alloc_vec_Vec_update_usize v i x.
+
+End Primitives.
diff --git a/tests/coq/traits/Traits.v b/tests/coq/traits/Traits.v
new file mode 100644
index 00000000..e104fb66
--- /dev/null
+++ b/tests/coq/traits/Traits.v
@@ -0,0 +1,520 @@
+(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
+(** [traits] *)
+Require Import Primitives.
+Import Primitives.
+Require Import Coq.ZArith.ZArith.
+Require Import List.
+Import ListNotations.
+Local Open Scope Primitives_scope.
+Module Traits.
+
+(** Trait declaration: [traits::BoolTrait] *)
+Record BoolTrait_t (Self : Type) := mkBoolTrait_t {
+  BoolTrait_t_get_bool : Self -> result bool;
+}.
+
+Arguments mkBoolTrait_t { _ }.
+Arguments BoolTrait_t_get_bool { _ }.
+
+(** [traits::Bool::{0}::get_bool]: forward function *)
+Definition bool_get_bool (self : bool) : result bool :=
+  Return self.
+
+(** Trait implementation: [traits::Bool::{0}] *)
+Definition Bool_BoolTraitInst : BoolTrait_t bool := {|
+  BoolTrait_t_get_bool := bool_get_bool;
+|}.
+
+(** [traits::BoolTrait::ret_true]: forward function *)
+Definition boolTrait_ret_true
+  {Self : Type} (self_clause : BoolTrait_t Self) (self : Self) : result bool :=
+  Return true
+.
+
+(** [traits::test_bool_trait_bool]: forward function *)
+Definition test_bool_trait_bool (x : bool) : result bool :=
+  b <- bool_get_bool x;
+  if b then boolTrait_ret_true Bool_BoolTraitInst x else Return false
+.
+
+(** [traits::Option::{1}::get_bool]: forward function *)
+Definition option_get_bool (T : Type) (self : option T) : result bool :=
+  match self with | None => Return false | Some t => Return true end
+.
+
+(** Trait implementation: [traits::Option::{1}] *)
+Definition Option_BoolTraitInst (T : Type) : BoolTrait_t (option T) := {|
+  BoolTrait_t_get_bool := option_get_bool T;
+|}.
+
+(** [traits::test_bool_trait_option]: forward function *)
+Definition test_bool_trait_option (T : Type) (x : option T) : result bool :=
+  b <- option_get_bool T x;
+  if b then boolTrait_ret_true (Option_BoolTraitInst T) x else Return false
+.
+
+(** [traits::test_bool_trait]: forward function *)
+Definition test_bool_trait
+  (T : Type) (inst : BoolTrait_t T) (x : T) : result bool :=
+  inst.(BoolTrait_t_get_bool) x
+.
+
+(** Trait declaration: [traits::ToU64] *)
+Record ToU64_t (Self : Type) := mkToU64_t {
+  ToU64_t_to_u64 : Self -> result u64;
+}.
+
+Arguments mkToU64_t { _ }.
+Arguments ToU64_t_to_u64 { _ }.
+
+(** [traits::u64::{2}::to_u64]: forward function *)
+Definition u64_to_u64 (self : u64) : result u64 :=
+  Return self.
+
+(** Trait implementation: [traits::u64::{2}] *)
+Definition u64_ToU64Inst : ToU64_t u64 := {| ToU64_t_to_u64 := u64_to_u64; |}.
+
+(** [traits::Tuple2::{3}::to_u64]: forward function *)
+Definition tuple2_to_u64
+  (A : Type) (inst : ToU64_t A) (self : (A * A)) : result u64 :=
+  let (t, t0) := self in
+  i <- inst.(ToU64_t_to_u64) t;
+  i0 <- inst.(ToU64_t_to_u64) t0;
+  u64_add i i0
+.
+
+(** Trait implementation: [traits::Tuple2::{3}] *)
+Definition Tuple2_ToU64Inst (A : Type) (inst : ToU64_t A) : ToU64_t (A * A)
+  := {|
+  ToU64_t_to_u64 := tuple2_to_u64 A inst;
+|}.
+
+(** [traits::f]: forward function *)
+Definition f (T : Type) (inst : ToU64_t T) (x : (T * T)) : result u64 :=
+  tuple2_to_u64 T inst x
+.
+
+(** [traits::g]: forward function *)
+Definition g (T : Type) (inst : ToU64_t (T * T)) (x : (T * T)) : result u64 :=
+  inst.(ToU64_t_to_u64) x
+.
+
+(** [traits::h0]: forward function *)
+Definition h0 (x : u64) : result u64 :=
+  u64_to_u64 x.
+
+(** [traits::Wrapper] *)
+Record Wrapper_t (T : Type) := mkWrapper_t { wrapper_x : T; }.
+
+Arguments mkWrapper_t { _ }.
+Arguments wrapper_x { _ }.
+
+(** [traits::Wrapper::{4}::to_u64]: forward function *)
+Definition wrapper_to_u64
+  (T : Type) (inst : ToU64_t T) (self : Wrapper_t T) : result u64 :=
+  inst.(ToU64_t_to_u64) self.(wrapper_x)
+.
+
+(** Trait implementation: [traits::Wrapper::{4}] *)
+Definition Wrapper_ToU64Inst (T : Type) (inst : ToU64_t T) : ToU64_t (Wrapper_t
+  T) := {|
+  ToU64_t_to_u64 := wrapper_to_u64 T inst;
+|}.
+
+(** [traits::h1]: forward function *)
+Definition h1 (x : Wrapper_t u64) : result u64 :=
+  wrapper_to_u64 u64 u64_ToU64Inst x
+.
+
+(** [traits::h2]: forward function *)
+Definition h2 (T : Type) (inst : ToU64_t T) (x : Wrapper_t T) : result u64 :=
+  wrapper_to_u64 T inst x
+.
+
+(** Trait declaration: [traits::ToType] *)
+Record ToType_t (Self T : Type) := mkToType_t {
+  ToType_t_to_type : Self -> result T;
+}.
+
+Arguments mkToType_t { _ _ }.
+Arguments ToType_t_to_type { _ _ }.
+
+(** [traits::u64::{5}::to_type]: forward function *)
+Definition u64_to_type (self : u64) : result bool :=
+  Return (self s> 0%u64).
+
+(** Trait implementation: [traits::u64::{5}] *)
+Definition u64_ToTypeInst : ToType_t u64 bool := {|
+  ToType_t_to_type := u64_to_type;
+|}.
+
+(** Trait declaration: [traits::OfType] *)
+Record OfType_t (Self : Type) := mkOfType_t {
+  OfType_t_of_type : forall (T : Type) (inst : ToType_t T Self), T -> result
+    Self;
+}.
+
+Arguments mkOfType_t { _ }.
+Arguments OfType_t_of_type { _ }.
+
+(** [traits::h3]: forward function *)
+Definition h3
+  (T1 T2 : Type) (inst : OfType_t T1) (inst0 : ToType_t T2 T1) (y : T2) :
+  result T1
+  :=
+  inst.(OfType_t_of_type) T2 inst0 y
+.
+
+(** Trait declaration: [traits::OfTypeBis] *)
+Record OfTypeBis_t (Self T : Type) := mkOfTypeBis_t {
+  OfTypeBis_tOfTypeBis_t_parent_clause_0 : ToType_t T Self;
+  OfTypeBis_t_of_type : T -> result Self;
+}.
+
+Arguments mkOfTypeBis_t { _ _ }.
+Arguments OfTypeBis_tOfTypeBis_t_parent_clause_0 { _ _ }.
+Arguments OfTypeBis_t_of_type { _ _ }.
+
+(** [traits::h4]: forward function *)
+Definition h4
+  (T1 T2 : Type) (inst : OfTypeBis_t T1 T2) (inst0 : ToType_t T2 T1) (y : T2) :
+  result T1
+  :=
+  inst.(OfTypeBis_t_of_type) y
+.
+
+(** [traits::TestType] *)
+Record TestType_t (T : Type) := mkTestType_t { testType_0 : T; }.
+
+Arguments mkTestType_t { _ }.
+Arguments testType_0 { _ }.
+
+(** [traits::TestType::{6}::test::TestType1] *)
+Record TestType_test_TestType1_t :=
+mkTestType_test_TestType1_t {
+  testType_test_TestType1_0 : u64;
+}
+.
+
+(** Trait declaration: [traits::TestType::{6}::test::TestTrait] *)
+Record TestType_test_TestTrait_t (Self : Type) := mkTestType_test_TestTrait_t {
+  TestType_test_TestTrait_t_test : Self -> result bool;
+}.
+
+Arguments mkTestType_test_TestTrait_t { _ }.
+Arguments TestType_test_TestTrait_t_test { _ }.
+
+(** [traits::TestType::{6}::test::TestType1::{0}::test]: forward function *)
+Definition testType_test_TestType1_test
+  (self : TestType_test_TestType1_t) : result bool :=
+  Return (self.(testType_test_TestType1_0) s> 1%u64)
+.
+
+(** Trait implementation: [traits::TestType::{6}::test::TestType1::{0}] *)
+Definition TestType_test_TestType1_TestType_test_TestTraitInst :
+  TestType_test_TestTrait_t TestType_test_TestType1_t := {|
+  TestType_test_TestTrait_t_test := testType_test_TestType1_test;
+|}.
+
+(** [traits::TestType::{6}::test]: forward function *)
+Definition testType_test
+  (T : Type) (inst : ToU64_t T) (self : TestType_t T) (x : T) : result bool :=
+  x0 <- inst.(ToU64_t_to_u64) x;
+  if x0 s> 0%u64
+  then testType_test_TestType1_test {| testType_test_TestType1_0 := 0%u64 |}
+  else Return false
+.
+
+(** [traits::BoolWrapper] *)
+Record BoolWrapper_t := mkBoolWrapper_t { boolWrapper_0 : bool; }.
+
+(** [traits::BoolWrapper::{7}::to_type]: forward function *)
+Definition boolWrapper_to_type
+  (T : Type) (inst : ToType_t bool T) (self : BoolWrapper_t) : result T :=
+  inst.(ToType_t_to_type) self.(boolWrapper_0)
+.
+
+(** Trait implementation: [traits::BoolWrapper::{7}] *)
+Definition BoolWrapper_ToTypeInst (T : Type) (inst : ToType_t bool T) :
+  ToType_t BoolWrapper_t T := {|
+  ToType_t_to_type := boolWrapper_to_type T inst;
+|}.
+
+(** [traits::WithConstTy::LEN2] *)
+Definition with_const_ty_len2_body : result usize := Return 32%usize.
+Definition with_const_ty_len2_c : usize := with_const_ty_len2_body%global.
+
+(** Trait declaration: [traits::WithConstTy] *)
+Record WithConstTy_t (Self : Type) (LEN : usize) := mkWithConstTy_t {
+  WithConstTy_tWithConstTy_t_LEN1 : usize;
+  WithConstTy_tWithConstTy_t_LEN2 : usize;
+  WithConstTy_tWithConstTy_t_V : Type;
+  WithConstTy_tWithConstTy_t_W : Type;
+  WithConstTy_tWithConstTy_t_W_clause_0 : ToU64_t WithConstTy_tWithConstTy_t_W;
+  WithConstTy_t_f : WithConstTy_tWithConstTy_t_W -> array u8 LEN -> result
+    WithConstTy_tWithConstTy_t_W;
+}.
+
+Arguments mkWithConstTy_t { _ _ }.
+Arguments WithConstTy_tWithConstTy_t_LEN1 { _ _ }.
+Arguments WithConstTy_tWithConstTy_t_LEN2 { _ _ }.
+Arguments WithConstTy_tWithConstTy_t_V { _ _ }.
+Arguments WithConstTy_tWithConstTy_t_W { _ _ }.
+Arguments WithConstTy_tWithConstTy_t_W_clause_0 { _ _ }.
+Arguments WithConstTy_t_f { _ _ }.
+
+(** [traits::Bool::{8}::LEN1] *)
+Definition bool_len1_body : result usize := Return 12%usize.
+Definition bool_len1_c : usize := bool_len1_body%global.
+
+(** [traits::Bool::{8}::f]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ()) *)
+Definition bool_f (i : u64) (a : array u8 32%usize) : result u64 :=
+  Return i.
+
+(** Trait implementation: [traits::Bool::{8}] *)
+Definition Bool_WithConstTyInst : WithConstTy_t bool 32%usize := {|
+  WithConstTy_tWithConstTy_t_LEN1 := bool_len1_c;
+  WithConstTy_tWithConstTy_t_LEN2 := with_const_ty_len2_c;
+  WithConstTy_tWithConstTy_t_V := u8;
+  WithConstTy_tWithConstTy_t_W := u64;
+  WithConstTy_tWithConstTy_t_W_clause_0 := u64_ToU64Inst;
+  WithConstTy_t_f := bool_f;
+|}.
+
+(** [traits::use_with_const_ty1]: forward function *)
+Definition use_with_const_ty1
+  (H : Type) (LEN : usize) (inst : WithConstTy_t H LEN) : result usize :=
+  let i := inst.(WithConstTy_tWithConstTy_t_LEN1) in Return i
+.
+
+(** [traits::use_with_const_ty2]: forward function *)
+Definition use_with_const_ty2
+  (H : Type) (LEN : usize) (inst : WithConstTy_t H LEN)
+  (w : inst.(WithConstTy_tWithConstTy_t_W)) :
+  result unit
+  :=
+  Return tt
+.
+
+(** [traits::use_with_const_ty3]: forward function *)
+Definition use_with_const_ty3
+  (H : Type) (LEN : usize) (inst : WithConstTy_t H LEN)
+  (x : inst.(WithConstTy_tWithConstTy_t_W)) :
+  result u64
+  :=
+  inst.(WithConstTy_tWithConstTy_t_W_clause_0).(ToU64_t_to_u64) x
+.
+
+(** [traits::test_where1]: forward function *)
+Definition test_where1 (T : Type) (_x : T) : result unit :=
+  Return tt.
+
+(** [traits::test_where2]: forward function *)
+Definition test_where2
+  (T : Type) (inst : WithConstTy_t T 32%usize) (_x : u32) : result unit :=
+  Return tt
+.
+
+(** [alloc::string::String] *)
+Axiom alloc_string_String_t : Type.
+
+(** Trait declaration: [traits::ParentTrait0] *)
+Record ParentTrait0_t (Self : Type) := mkParentTrait0_t {
+  ParentTrait0_tParentTrait0_t_W : Type;
+  ParentTrait0_t_get_name : Self -> result alloc_string_String_t;
+  ParentTrait0_t_get_w : Self -> result ParentTrait0_tParentTrait0_t_W;
+}.
+
+Arguments mkParentTrait0_t { _ }.
+Arguments ParentTrait0_tParentTrait0_t_W { _ }.
+Arguments ParentTrait0_t_get_name { _ }.
+Arguments ParentTrait0_t_get_w { _ }.
+
+(** Trait declaration: [traits::ParentTrait1] *)
+Record ParentTrait1_t (Self : Type) := mkParentTrait1_t{}.
+
+Arguments mkParentTrait1_t { _ }.
+
+(** Trait declaration: [traits::ChildTrait] *)
+Record ChildTrait_t (Self : Type) := mkChildTrait_t {
+  ChildTrait_tChildTrait_t_parent_clause_0 : ParentTrait0_t Self;
+  ChildTrait_tChildTrait_t_parent_clause_1 : ParentTrait1_t Self;
+}.
+
+Arguments mkChildTrait_t { _ }.
+Arguments ChildTrait_tChildTrait_t_parent_clause_0 { _ }.
+Arguments ChildTrait_tChildTrait_t_parent_clause_1 { _ }.
+
+(** [traits::test_child_trait1]: forward function *)
+Definition test_child_trait1
+  (T : Type) (inst : ChildTrait_t T) (x : T) : result alloc_string_String_t :=
+  inst.(ChildTrait_tChildTrait_t_parent_clause_0).(ParentTrait0_t_get_name) x
+.
+
+(** [traits::test_child_trait2]: forward function *)
+Definition test_child_trait2
+  (T : Type) (inst : ChildTrait_t T) (x : T) :
+  result
+    inst.(ChildTrait_tChildTrait_t_parent_clause_0).(ParentTrait0_tParentTrait0_t_W)
+  :=
+  inst.(ChildTrait_tChildTrait_t_parent_clause_0).(ParentTrait0_t_get_w) x
+.
+
+(** [traits::order1]: forward function *)
+Definition order1
+  (T U : Type) (inst : ParentTrait0_t T) (inst0 : ParentTrait0_t U) :
+  result unit
+  :=
+  Return tt
+.
+
+(** Trait declaration: [traits::ChildTrait1] *)
+Record ChildTrait1_t (Self : Type) := mkChildTrait1_t {
+  ChildTrait1_tChildTrait1_t_parent_clause_0 : ParentTrait1_t Self;
+}.
+
+Arguments mkChildTrait1_t { _ }.
+Arguments ChildTrait1_tChildTrait1_t_parent_clause_0 { _ }.
+
+(** Trait implementation: [traits::usize::{9}] *)
+Definition usize_ParentTrait1Inst : ParentTrait1_t usize := mkParentTrait1_t.
+
+(** Trait implementation: [traits::usize::{10}] *)
+Definition usize_ChildTrait1Inst : ChildTrait1_t usize := {|
+  ChildTrait1_tChildTrait1_t_parent_clause_0 := usize_ParentTrait1Inst;
+|}.
+
+(** Trait declaration: [traits::Iterator] *)
+Record Iterator_t (Self : Type) := mkIterator_t {
+  Iterator_tIterator_t_Item : Type;
+}.
+
+Arguments mkIterator_t { _ }.
+Arguments Iterator_tIterator_t_Item { _ }.
+
+(** Trait declaration: [traits::IntoIterator] *)
+Record IntoIterator_t (Self : Type) := mkIntoIterator_t {
+  IntoIterator_tIntoIterator_t_Item : Type;
+  IntoIterator_tIntoIterator_t_IntoIter : Type;
+  IntoIterator_tIntoIterator_t_IntoIter_clause_0 : Iterator_t
+    IntoIterator_tIntoIterator_t_IntoIter;
+  IntoIterator_t_into_iter : Self -> result
+    IntoIterator_tIntoIterator_t_IntoIter;
+}.
+
+Arguments mkIntoIterator_t { _ }.
+Arguments IntoIterator_tIntoIterator_t_Item { _ }.
+Arguments IntoIterator_tIntoIterator_t_IntoIter { _ }.
+Arguments IntoIterator_tIntoIterator_t_IntoIter_clause_0 { _ }.
+Arguments IntoIterator_t_into_iter { _ }.
+
+(** Trait declaration: [traits::FromResidual] *)
+Record FromResidual_t (Self T : Type) := mkFromResidual_t{}.
+
+Arguments mkFromResidual_t { _ _ }.
+
+(** Trait declaration: [traits::Try] *)
+Record Try_t (Self : Type) := mkTry_t {
+  Try_tTry_t_Residual : Type;
+  Try_tTry_t_parent_clause_0 : FromResidual_t Self Try_tTry_t_Residual;
+}.
+
+Arguments mkTry_t { _ }.
+Arguments Try_tTry_t_Residual { _ }.
+Arguments Try_tTry_t_parent_clause_0 { _ }.
+
+(** Trait declaration: [traits::WithTarget] *)
+Record WithTarget_t (Self : Type) := mkWithTarget_t {
+  WithTarget_tWithTarget_t_Target : Type;
+}.
+
+Arguments mkWithTarget_t { _ }.
+Arguments WithTarget_tWithTarget_t_Target { _ }.
+
+(** Trait declaration: [traits::ParentTrait2] *)
+Record ParentTrait2_t (Self : Type) := mkParentTrait2_t {
+  ParentTrait2_tParentTrait2_t_U : Type;
+  ParentTrait2_tParentTrait2_t_U_clause_0 : WithTarget_t
+    ParentTrait2_tParentTrait2_t_U;
+}.
+
+Arguments mkParentTrait2_t { _ }.
+Arguments ParentTrait2_tParentTrait2_t_U { _ }.
+Arguments ParentTrait2_tParentTrait2_t_U_clause_0 { _ }.
+
+(** Trait declaration: [traits::ChildTrait2] *)
+Record ChildTrait2_t (Self : Type) := mkChildTrait2_t {
+  ChildTrait2_tChildTrait2_t_parent_clause_0 : ParentTrait2_t Self;
+  ChildTrait2_t_convert :
+    (ChildTrait2_tChildTrait2_t_parent_clause_0).(ParentTrait2_tParentTrait2_t_U)
+    -> result
+    (ChildTrait2_tChildTrait2_t_parent_clause_0).(ParentTrait2_tParentTrait2_t_U_clause_0).(WithTarget_tWithTarget_t_Target);
+}.
+
+Arguments mkChildTrait2_t { _ }.
+Arguments ChildTrait2_tChildTrait2_t_parent_clause_0 { _ }.
+Arguments ChildTrait2_t_convert { _ }.
+
+(** Trait implementation: [traits::u32::{11}] *)
+Definition u32_WithTargetInst : WithTarget_t u32 := {|
+  WithTarget_tWithTarget_t_Target := u32;
+|}.
+
+(** Trait implementation: [traits::u32::{12}] *)
+Definition u32_ParentTrait2Inst : ParentTrait2_t u32 := {|
+  ParentTrait2_tParentTrait2_t_U := u32;
+  ParentTrait2_tParentTrait2_t_U_clause_0 := u32_WithTargetInst;
+|}.
+
+(** [traits::u32::{13}::convert]: forward function *)
+Definition u32_convert (x : u32) : result u32 :=
+  Return x.
+
+(** Trait implementation: [traits::u32::{13}] *)
+Definition u32_ChildTrait2Inst : ChildTrait2_t u32 := {|
+  ChildTrait2_tChildTrait2_t_parent_clause_0 := u32_ParentTrait2Inst;
+  ChildTrait2_t_convert := u32_convert;
+|}.
+
+(** [traits::incr_u32]: forward function *)
+Definition incr_u32 (x : u32) : result u32 :=
+  u32_add x 1%u32.
+
+(** Trait declaration: [traits::CFnOnce] *)
+Record CFnOnce_t (Self Args : Type) := mkCFnOnce_t {
+  CFnOnce_tCFnOnce_t_Output : Type;
+  CFnOnce_t_call_once : Self -> Args -> result CFnOnce_tCFnOnce_t_Output;
+}.
+
+Arguments mkCFnOnce_t { _ _ }.
+Arguments CFnOnce_tCFnOnce_t_Output { _ _ }.
+Arguments CFnOnce_t_call_once { _ _ }.
+
+(** Trait declaration: [traits::CFnMut] *)
+Record CFnMut_t (Self Args : Type) := mkCFnMut_t {
+  CFnMut_tCFnMut_t_parent_clause_0 : CFnOnce_t Self Args;
+  CFnMut_t_call_mut : Self -> Args -> result
+    (CFnMut_tCFnMut_t_parent_clause_0).(CFnOnce_tCFnOnce_t_Output);
+  CFnMut_t_call_mut_back : Self -> Args ->
+    (CFnMut_tCFnMut_t_parent_clause_0).(CFnOnce_tCFnOnce_t_Output) -> result
+    Self;
+}.
+
+Arguments mkCFnMut_t { _ _ }.
+Arguments CFnMut_tCFnMut_t_parent_clause_0 { _ _ }.
+Arguments CFnMut_t_call_mut { _ _ }.
+Arguments CFnMut_t_call_mut_back { _ _ }.
+
+(** Trait declaration: [traits::CFn] *)
+Record CFn_t (Self Args : Type) := mkCFn_t {
+  CFn_tCFn_t_parent_clause_0 : CFnMut_t Self Args;
+  CFn_t_call_mut : Self -> Args -> result
+    (CFn_tCFn_t_parent_clause_0).(CFnMut_tCFnMut_t_parent_clause_0).(CFnOnce_tCFnOnce_t_Output);
+}.
+
+Arguments mkCFn_t { _ _ }.
+Arguments CFn_tCFn_t_parent_clause_0 { _ _ }.
+Arguments CFn_t_call_mut { _ _ }.
+
+End Traits .
diff --git a/tests/coq/traits/_CoqProject b/tests/coq/traits/_CoqProject
index d573657e..5b6199fc 100644
--- a/tests/coq/traits/_CoqProject
+++ b/tests/coq/traits/_CoqProject
@@ -3,3 +3,5 @@
 -arg -w
 -arg all
 
+Traits.v
+Primitives.v