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-rw-r--r--tests/coq/traits/Makefile23
-rw-r--r--tests/coq/traits/Primitives.v822
-rw-r--r--tests/coq/traits/Traits.v520
-rw-r--r--tests/coq/traits/_CoqProject7
4 files changed, 1372 insertions, 0 deletions
diff --git a/tests/coq/traits/Makefile b/tests/coq/traits/Makefile
new file mode 100644
index 00000000..1a5aee4a
--- /dev/null
+++ b/tests/coq/traits/Makefile
@@ -0,0 +1,23 @@
+# This file was automatically generated - modify ../Makefile.template instead
+# Makefile originally taken from coq-club
+
+%: Makefile.coq phony
+ +make -f Makefile.coq $@
+
+all: Makefile.coq
+ +make -f Makefile.coq all
+
+clean: Makefile.coq
+ +make -f Makefile.coq clean
+ rm -f Makefile.coq
+
+Makefile.coq: _CoqProject Makefile
+ coq_makefile -f _CoqProject | sed 's/$$(COQCHK) $$(COQCHKFLAGS) $$(COQLIBS)/$$(COQCHK) $$(COQCHKFLAGS) $$(subst -Q,-R,$$(COQLIBS))/' > Makefile.coq
+
+_CoqProject: ;
+
+Makefile: ;
+
+phony: ;
+
+.PHONY: all clean phony
diff --git a/tests/coq/traits/Primitives.v b/tests/coq/traits/Primitives.v
new file mode 100644
index 00000000..85e38f01
--- /dev/null
+++ b/tests/coq/traits/Primitives.v
@@ -0,0 +1,822 @@
+Require Import Lia.
+Require Coq.Strings.Ascii.
+Require Coq.Strings.String.
+Require Import Coq.Program.Equality.
+Require Import Coq.ZArith.ZArith.
+Require Import Coq.ZArith.Znat.
+Require Import List.
+Import ListNotations.
+
+Module Primitives.
+
+ (* TODO: use more *)
+Declare Scope Primitives_scope.
+
+(*** Result *)
+
+Inductive error :=
+ | Failure
+ | OutOfFuel.
+
+Inductive result A :=
+ | Return : A -> result A
+ | Fail_ : error -> result A.
+
+Arguments Return {_} a.
+Arguments Fail_ {_}.
+
+Definition bind {A B} (m: result A) (f: A -> result B) : result B :=
+ match m with
+ | Fail_ e => Fail_ e
+ | Return x => f x
+ end.
+
+Definition return_ {A: Type} (x: A) : result A := Return x.
+Definition fail_ {A: Type} (e: error) : result A := Fail_ e.
+
+Notation "x <- c1 ; c2" := (bind c1 (fun x => c2))
+ (at level 61, c1 at next level, right associativity).
+
+(** Monadic assert *)
+Definition massert (b: bool) : result unit :=
+ if b then Return tt else Fail_ Failure.
+
+(** Normalize and unwrap a successful result (used for globals) *)
+Definition eval_result_refl {A} {x} (a: result A) (p: a = Return x) : A :=
+ match a as r return (r = Return x -> A) with
+ | Return a' => fun _ => a'
+ | Fail_ e => fun p' =>
+ False_rect _ (eq_ind (Fail_ e)
+ (fun e : result A =>
+ match e with
+ | Return _ => False
+ | Fail_ e => True
+ end)
+ I (Return x) p')
+ end p.
+
+Notation "x %global" := (eval_result_refl x eq_refl) (at level 40).
+Notation "x %return" := (eval_result_refl x eq_refl) (at level 40).
+
+(* Sanity check *)
+Check (if true then Return (1 + 2) else Fail_ Failure)%global = 3.
+
+(*** Misc *)
+
+Definition string := Coq.Strings.String.string.
+Definition char := Coq.Strings.Ascii.ascii.
+Definition char_of_byte := Coq.Strings.Ascii.ascii_of_byte.
+
+Definition core_mem_replace (a : Type) (x : a) (y : a) : a := x .
+Definition core_mem_replace_back (a : Type) (x : a) (y : a) : a := y .
+
+Record mut_raw_ptr (T : Type) := { mut_raw_ptr_v : T }.
+Record const_raw_ptr (T : Type) := { const_raw_ptr_v : T }.
+
+(*** Scalars *)
+
+Definition i8_min : Z := -128%Z.
+Definition i8_max : Z := 127%Z.
+Definition i16_min : Z := -32768%Z.
+Definition i16_max : Z := 32767%Z.
+Definition i32_min : Z := -2147483648%Z.
+Definition i32_max : Z := 2147483647%Z.
+Definition i64_min : Z := -9223372036854775808%Z.
+Definition i64_max : Z := 9223372036854775807%Z.
+Definition i128_min : Z := -170141183460469231731687303715884105728%Z.
+Definition i128_max : Z := 170141183460469231731687303715884105727%Z.
+Definition u8_min : Z := 0%Z.
+Definition u8_max : Z := 255%Z.
+Definition u16_min : Z := 0%Z.
+Definition u16_max : Z := 65535%Z.
+Definition u32_min : Z := 0%Z.
+Definition u32_max : Z := 4294967295%Z.
+Definition u64_min : Z := 0%Z.
+Definition u64_max : Z := 18446744073709551615%Z.
+Definition u128_min : Z := 0%Z.
+Definition u128_max : Z := 340282366920938463463374607431768211455%Z.
+
+(** The bounds of [isize] and [usize] vary with the architecture. *)
+Axiom isize_min : Z.
+Axiom isize_max : Z.
+Definition usize_min : Z := 0%Z.
+Axiom usize_max : Z.
+
+Open Scope Z_scope.
+
+(** We provide those lemmas to reason about the bounds of [isize] and [usize] *)
+Axiom isize_min_bound : isize_min <= i32_min.
+Axiom isize_max_bound : i32_max <= isize_max.
+Axiom usize_max_bound : u32_max <= usize_max.
+
+Inductive scalar_ty :=
+ | Isize
+ | I8
+ | I16
+ | I32
+ | I64
+ | I128
+ | Usize
+ | U8
+ | U16
+ | U32
+ | U64
+ | U128
+.
+
+Definition scalar_min (ty: scalar_ty) : Z :=
+ match ty with
+ | Isize => isize_min
+ | I8 => i8_min
+ | I16 => i16_min
+ | I32 => i32_min
+ | I64 => i64_min
+ | I128 => i128_min
+ | Usize => usize_min
+ | U8 => u8_min
+ | U16 => u16_min
+ | U32 => u32_min
+ | U64 => u64_min
+ | U128 => u128_min
+end.
+
+Definition scalar_max (ty: scalar_ty) : Z :=
+ match ty with
+ | Isize => isize_max
+ | I8 => i8_max
+ | I16 => i16_max
+ | I32 => i32_max
+ | I64 => i64_max
+ | I128 => i128_max
+ | Usize => usize_max
+ | U8 => u8_max
+ | U16 => u16_max
+ | U32 => u32_max
+ | U64 => u64_max
+ | U128 => u128_max
+end.
+
+(** We use the following conservative bounds to make sure we can compute bound
+ checks in most situations *)
+Definition scalar_min_cons (ty: scalar_ty) : Z :=
+ match ty with
+ | Isize => i32_min
+ | Usize => u32_min
+ | _ => scalar_min ty
+end.
+
+Definition scalar_max_cons (ty: scalar_ty) : Z :=
+ match ty with
+ | Isize => i32_max
+ | Usize => u32_max
+ | _ => scalar_max ty
+end.
+
+Lemma scalar_min_cons_valid : forall ty, scalar_min ty <= scalar_min_cons ty .
+Proof.
+ destruct ty; unfold scalar_min_cons, scalar_min; try lia.
+ - pose isize_min_bound; lia.
+ - apply Z.le_refl.
+Qed.
+
+Lemma scalar_max_cons_valid : forall ty, scalar_max ty >= scalar_max_cons ty .
+Proof.
+ destruct ty; unfold scalar_max_cons, scalar_max; try lia.
+ - pose isize_max_bound; lia.
+ - pose usize_max_bound. lia.
+Qed.
+
+Definition scalar (ty: scalar_ty) : Type :=
+ { x: Z | scalar_min ty <= x <= scalar_max ty }.
+
+Definition to_Z {ty} (x: scalar ty) : Z := proj1_sig x.
+
+(** Bounds checks: we start by using the conservative bounds, to make sure we
+ can compute in most situations, then we use the real bounds (for [isize]
+ and [usize]). *)
+Definition scalar_ge_min (ty: scalar_ty) (x: Z) : bool :=
+ Z.leb (scalar_min_cons ty) x || Z.leb (scalar_min ty) x.
+
+Definition scalar_le_max (ty: scalar_ty) (x: Z) : bool :=
+ Z.leb x (scalar_max_cons ty) || Z.leb x (scalar_max ty).
+
+Lemma scalar_ge_min_valid (ty: scalar_ty) (x: Z) :
+ scalar_ge_min ty x = true -> scalar_min ty <= x .
+Proof.
+ unfold scalar_ge_min.
+ pose (scalar_min_cons_valid ty).
+ lia.
+Qed.
+
+Lemma scalar_le_max_valid (ty: scalar_ty) (x: Z) :
+ scalar_le_max ty x = true -> x <= scalar_max ty .
+Proof.
+ unfold scalar_le_max.
+ pose (scalar_max_cons_valid ty).
+ lia.
+Qed.
+
+Definition scalar_in_bounds (ty: scalar_ty) (x: Z) : bool :=
+ scalar_ge_min ty x && scalar_le_max ty x .
+
+Lemma scalar_in_bounds_valid (ty: scalar_ty) (x: Z) :
+ scalar_in_bounds ty x = true -> scalar_min ty <= x <= scalar_max ty .
+Proof.
+ unfold scalar_in_bounds.
+ intros H.
+ destruct (scalar_ge_min ty x) eqn:Hmin.
+ - destruct (scalar_le_max ty x) eqn:Hmax.
+ + pose (scalar_ge_min_valid ty x Hmin).
+ pose (scalar_le_max_valid ty x Hmax).
+ lia.
+ + inversion H.
+ - inversion H.
+Qed.
+
+Import Sumbool.
+
+Definition mk_scalar (ty: scalar_ty) (x: Z) : result (scalar ty) :=
+ match sumbool_of_bool (scalar_in_bounds ty x) with
+ | left H => Return (exist _ x (scalar_in_bounds_valid _ _ H))
+ | right _ => Fail_ Failure
+ end.
+
+Definition scalar_add {ty} (x y: scalar ty) : result (scalar ty) := mk_scalar ty (to_Z x + to_Z y).
+
+Definition scalar_sub {ty} (x y: scalar ty) : result (scalar ty) := mk_scalar ty (to_Z x - to_Z y).
+
+Definition scalar_mul {ty} (x y: scalar ty) : result (scalar ty) := mk_scalar ty (to_Z x * to_Z y).
+
+Definition scalar_div {ty} (x y: scalar ty) : result (scalar ty) :=
+ if to_Z y =? 0 then Fail_ Failure else
+ mk_scalar ty (to_Z x / to_Z y).
+
+Definition scalar_rem {ty} (x y: scalar ty) : result (scalar ty) := mk_scalar ty (Z.rem (to_Z x) (to_Z y)).
+
+Definition scalar_neg {ty} (x: scalar ty) : result (scalar ty) := mk_scalar ty (-(to_Z x)).
+
+(** Cast an integer from a [src_ty] to a [tgt_ty] *)
+(* TODO: check the semantics of casts in Rust *)
+Definition scalar_cast (src_ty tgt_ty : scalar_ty) (x : scalar src_ty) : result (scalar tgt_ty) :=
+ mk_scalar tgt_ty (to_Z x).
+
+(** Comparisons *)
+Definition scalar_leb {ty : scalar_ty} (x : scalar ty) (y : scalar ty) : bool :=
+ Z.leb (to_Z x) (to_Z y) .
+
+Definition scalar_ltb {ty : scalar_ty} (x : scalar ty) (y : scalar ty) : bool :=
+ Z.ltb (to_Z x) (to_Z y) .
+
+Definition scalar_geb {ty : scalar_ty} (x : scalar ty) (y : scalar ty) : bool :=
+ Z.geb (to_Z x) (to_Z y) .
+
+Definition scalar_gtb {ty : scalar_ty} (x : scalar ty) (y : scalar ty) : bool :=
+ Z.gtb (to_Z x) (to_Z y) .
+
+Definition scalar_eqb {ty : scalar_ty} (x : scalar ty) (y : scalar ty) : bool :=
+ Z.eqb (to_Z x) (to_Z y) .
+
+Definition scalar_neqb {ty : scalar_ty} (x : scalar ty) (y : scalar ty) : bool :=
+ negb (Z.eqb (to_Z x) (to_Z y)) .
+
+
+(** The scalar types *)
+Definition isize := scalar Isize.
+Definition i8 := scalar I8.
+Definition i16 := scalar I16.
+Definition i32 := scalar I32.
+Definition i64 := scalar I64.
+Definition i128 := scalar I128.
+Definition usize := scalar Usize.
+Definition u8 := scalar U8.
+Definition u16 := scalar U16.
+Definition u32 := scalar U32.
+Definition u64 := scalar U64.
+Definition u128 := scalar U128.
+
+(** Negaion *)
+Definition isize_neg := @scalar_neg Isize.
+Definition i8_neg := @scalar_neg I8.
+Definition i16_neg := @scalar_neg I16.
+Definition i32_neg := @scalar_neg I32.
+Definition i64_neg := @scalar_neg I64.
+Definition i128_neg := @scalar_neg I128.
+
+(** Division *)
+Definition isize_div := @scalar_div Isize.
+Definition i8_div := @scalar_div I8.
+Definition i16_div := @scalar_div I16.
+Definition i32_div := @scalar_div I32.
+Definition i64_div := @scalar_div I64.
+Definition i128_div := @scalar_div I128.
+Definition usize_div := @scalar_div Usize.
+Definition u8_div := @scalar_div U8.
+Definition u16_div := @scalar_div U16.
+Definition u32_div := @scalar_div U32.
+Definition u64_div := @scalar_div U64.
+Definition u128_div := @scalar_div U128.
+
+(** Remainder *)
+Definition isize_rem := @scalar_rem Isize.
+Definition i8_rem := @scalar_rem I8.
+Definition i16_rem := @scalar_rem I16.
+Definition i32_rem := @scalar_rem I32.
+Definition i64_rem := @scalar_rem I64.
+Definition i128_rem := @scalar_rem I128.
+Definition usize_rem := @scalar_rem Usize.
+Definition u8_rem := @scalar_rem U8.
+Definition u16_rem := @scalar_rem U16.
+Definition u32_rem := @scalar_rem U32.
+Definition u64_rem := @scalar_rem U64.
+Definition u128_rem := @scalar_rem U128.
+
+(** Addition *)
+Definition isize_add := @scalar_add Isize.
+Definition i8_add := @scalar_add I8.
+Definition i16_add := @scalar_add I16.
+Definition i32_add := @scalar_add I32.
+Definition i64_add := @scalar_add I64.
+Definition i128_add := @scalar_add I128.
+Definition usize_add := @scalar_add Usize.
+Definition u8_add := @scalar_add U8.
+Definition u16_add := @scalar_add U16.
+Definition u32_add := @scalar_add U32.
+Definition u64_add := @scalar_add U64.
+Definition u128_add := @scalar_add U128.
+
+(** Substraction *)
+Definition isize_sub := @scalar_sub Isize.
+Definition i8_sub := @scalar_sub I8.
+Definition i16_sub := @scalar_sub I16.
+Definition i32_sub := @scalar_sub I32.
+Definition i64_sub := @scalar_sub I64.
+Definition i128_sub := @scalar_sub I128.
+Definition usize_sub := @scalar_sub Usize.
+Definition u8_sub := @scalar_sub U8.
+Definition u16_sub := @scalar_sub U16.
+Definition u32_sub := @scalar_sub U32.
+Definition u64_sub := @scalar_sub U64.
+Definition u128_sub := @scalar_sub U128.
+
+(** Multiplication *)
+Definition isize_mul := @scalar_mul Isize.
+Definition i8_mul := @scalar_mul I8.
+Definition i16_mul := @scalar_mul I16.
+Definition i32_mul := @scalar_mul I32.
+Definition i64_mul := @scalar_mul I64.
+Definition i128_mul := @scalar_mul I128.
+Definition usize_mul := @scalar_mul Usize.
+Definition u8_mul := @scalar_mul U8.
+Definition u16_mul := @scalar_mul U16.
+Definition u32_mul := @scalar_mul U32.
+Definition u64_mul := @scalar_mul U64.
+Definition u128_mul := @scalar_mul U128.
+
+(** Small utility *)
+Definition usize_to_nat (x: usize) : nat := Z.to_nat (to_Z x).
+
+(** Notations *)
+Notation "x %isize" := ((mk_scalar Isize x)%return) (at level 9).
+Notation "x %i8" := ((mk_scalar I8 x)%return) (at level 9).
+Notation "x %i16" := ((mk_scalar I16 x)%return) (at level 9).
+Notation "x %i32" := ((mk_scalar I32 x)%return) (at level 9).
+Notation "x %i64" := ((mk_scalar I64 x)%return) (at level 9).
+Notation "x %i128" := ((mk_scalar I128 x)%return) (at level 9).
+Notation "x %usize" := ((mk_scalar Usize x)%return) (at level 9).
+Notation "x %u8" := ((mk_scalar U8 x)%return) (at level 9).
+Notation "x %u16" := ((mk_scalar U16 x)%return) (at level 9).
+Notation "x %u32" := ((mk_scalar U32 x)%return) (at level 9).
+Notation "x %u64" := ((mk_scalar U64 x)%return) (at level 9).
+Notation "x %u128" := ((mk_scalar U128 x)%return) (at level 9).
+
+Notation "x s= y" := (scalar_eqb x y) (at level 80) : Primitives_scope.
+Notation "x s<> y" := (scalar_neqb x y) (at level 80) : Primitives_scope.
+Notation "x s<= y" := (scalar_leb x y) (at level 80) : Primitives_scope.
+Notation "x s< y" := (scalar_ltb x y) (at level 80) : Primitives_scope.
+Notation "x s>= y" := (scalar_geb x y) (at level 80) : Primitives_scope.
+Notation "x s> y" := (scalar_gtb x y) (at level 80) : Primitives_scope.
+
+(** Constants *)
+Definition core_u8_max := u8_max %u32.
+Definition core_u16_max := u16_max %u32.
+Definition core_u32_max := u32_max %u32.
+Definition core_u64_max := u64_max %u64.
+Definition core_u128_max := u64_max %u128.
+Axiom core_usize_max : usize. (** TODO *)
+Definition core_i8_max := i8_max %i32.
+Definition core_i16_max := i16_max %i32.
+Definition core_i32_max := i32_max %i32.
+Definition core_i64_max := i64_max %i64.
+Definition core_i128_max := i64_max %i128.
+Axiom core_isize_max : isize. (** TODO *)
+
+(*** core::ops *)
+
+(* Trait declaration: [core::ops::index::Index] *)
+Record core_ops_index_Index (Self Idx : Type) := mk_core_ops_index_Index {
+ core_ops_index_Index_Output : Type;
+ core_ops_index_Index_index : Self -> Idx -> result core_ops_index_Index_Output;
+}.
+Arguments mk_core_ops_index_Index {_ _}.
+Arguments core_ops_index_Index_Output {_ _}.
+Arguments core_ops_index_Index_index {_ _}.
+
+(* Trait declaration: [core::ops::index::IndexMut] *)
+Record core_ops_index_IndexMut (Self Idx : Type) := mk_core_ops_index_IndexMut {
+ core_ops_index_IndexMut_indexInst : core_ops_index_Index Self Idx;
+ core_ops_index_IndexMut_index_mut : Self -> Idx -> result core_ops_index_IndexMut_indexInst.(core_ops_index_Index_Output);
+ core_ops_index_IndexMut_index_mut_back : Self -> Idx -> core_ops_index_IndexMut_indexInst.(core_ops_index_Index_Output) -> result Self;
+}.
+Arguments mk_core_ops_index_IndexMut {_ _}.
+Arguments core_ops_index_IndexMut_indexInst {_ _}.
+Arguments core_ops_index_IndexMut_index_mut {_ _}.
+Arguments core_ops_index_IndexMut_index_mut_back {_ _}.
+
+(* Trait declaration [core::ops::deref::Deref] *)
+Record core_ops_deref_Deref (Self : Type) := mk_core_ops_deref_Deref {
+ core_ops_deref_Deref_target : Type;
+ core_ops_deref_Deref_deref : Self -> result core_ops_deref_Deref_target;
+}.
+Arguments mk_core_ops_deref_Deref {_}.
+Arguments core_ops_deref_Deref_target {_}.
+Arguments core_ops_deref_Deref_deref {_}.
+
+(* Trait declaration [core::ops::deref::DerefMut] *)
+Record core_ops_deref_DerefMut (Self : Type) := mk_core_ops_deref_DerefMut {
+ core_ops_deref_DerefMut_derefInst : core_ops_deref_Deref Self;
+ core_ops_deref_DerefMut_deref_mut : Self -> result core_ops_deref_DerefMut_derefInst.(core_ops_deref_Deref_target);
+ core_ops_deref_DerefMut_deref_mut_back : Self -> core_ops_deref_DerefMut_derefInst.(core_ops_deref_Deref_target) -> result Self;
+}.
+Arguments mk_core_ops_deref_DerefMut {_}.
+Arguments core_ops_deref_DerefMut_derefInst {_}.
+Arguments core_ops_deref_DerefMut_deref_mut {_}.
+Arguments core_ops_deref_DerefMut_deref_mut_back {_}.
+
+Record core_ops_range_Range (T : Type) := mk_core_ops_range_Range {
+ core_ops_range_Range_start : T;
+ core_ops_range_Range_end_ : T;
+}.
+Arguments mk_core_ops_range_Range {_}.
+Arguments core_ops_range_Range_start {_}.
+Arguments core_ops_range_Range_end_ {_}.
+
+(*** [alloc] *)
+
+Definition alloc_boxed_Box_deref (T : Type) (x : T) : result T := Return x.
+Definition alloc_boxed_Box_deref_mut (T : Type) (x : T) : result T := Return x.
+Definition alloc_boxed_Box_deref_mut_back (T : Type) (_ : T) (x : T) : result T := Return x.
+
+(* Trait instance *)
+Definition alloc_boxed_Box_coreOpsDerefInst (Self : Type) : core_ops_deref_Deref Self := {|
+ core_ops_deref_Deref_target := Self;
+ core_ops_deref_Deref_deref := alloc_boxed_Box_deref Self;
+|}.
+
+(* Trait instance *)
+Definition alloc_boxed_Box_coreOpsDerefMutInst (Self : Type) : core_ops_deref_DerefMut Self := {|
+ core_ops_deref_DerefMut_derefInst := alloc_boxed_Box_coreOpsDerefInst Self;
+ core_ops_deref_DerefMut_deref_mut := alloc_boxed_Box_deref_mut Self;
+ core_ops_deref_DerefMut_deref_mut_back := alloc_boxed_Box_deref_mut_back Self;
+|}.
+
+
+(*** Arrays *)
+Definition array T (n : usize) := { l: list T | Z.of_nat (length l) = to_Z n}.
+
+Lemma le_0_usize_max : 0 <= usize_max.
+Proof.
+ pose (H := usize_max_bound).
+ unfold u32_max in H.
+ lia.
+Qed.
+
+Lemma eqb_imp_eq (x y : Z) : Z.eqb x y = true -> x = y.
+Proof.
+ lia.
+Qed.
+
+(* TODO: finish the definitions *)
+Axiom mk_array : forall (T : Type) (n : usize) (l : list T), array T n.
+
+(* For initialization *)
+Axiom array_repeat : forall (T : Type) (n : usize) (x : T), array T n.
+
+Axiom array_index_usize : forall (T : Type) (n : usize) (x : array T n) (i : usize), result T.
+Axiom array_update_usize : forall (T : Type) (n : usize) (x : array T n) (i : usize) (nx : T), result (array T n).
+
+(*** Slice *)
+Definition slice T := { l: list T | Z.of_nat (length l) <= usize_max}.
+
+Axiom slice_len : forall (T : Type) (s : slice T), usize.
+Axiom slice_index_usize : forall (T : Type) (x : slice T) (i : usize), result T.
+Axiom slice_update_usize : forall (T : Type) (x : slice T) (i : usize) (nx : T), result (slice T).
+
+(*** Subslices *)
+
+Axiom array_to_slice : forall (T : Type) (n : usize) (x : array T n), result (slice T).
+Axiom array_from_slice : forall (T : Type) (n : usize) (x : array T n) (s : slice T), result (array T n).
+
+Axiom array_subslice: forall (T : Type) (n : usize) (x : array T n) (r : core_ops_range_Range usize), result (slice T).
+Axiom array_update_subslice: forall (T : Type) (n : usize) (x : array T n) (r : core_ops_range_Range usize) (ns : slice T), result (array T n).
+
+Axiom slice_subslice: forall (T : Type) (x : slice T) (r : core_ops_range_Range usize), result (slice T).
+Axiom slice_update_subslice: forall (T : Type) (x : slice T) (r : core_ops_range_Range usize) (ns : slice T), result (slice T).
+
+(*** Vectors *)
+
+Definition alloc_vec_Vec T := { l: list T | Z.of_nat (length l) <= usize_max }.
+
+Definition alloc_vec_Vec_to_list {T: Type} (v: alloc_vec_Vec T) : list T := proj1_sig v.
+
+Definition alloc_vec_Vec_length {T: Type} (v: alloc_vec_Vec T) : Z := Z.of_nat (length (alloc_vec_Vec_to_list v)).
+
+Definition alloc_vec_Vec_new (T: Type) : alloc_vec_Vec T := (exist _ [] le_0_usize_max).
+
+Lemma alloc_vec_Vec_len_in_usize {T} (v: alloc_vec_Vec T) : usize_min <= alloc_vec_Vec_length v <= usize_max.
+Proof.
+ unfold alloc_vec_Vec_length, usize_min.
+ split.
+ - lia.
+ - apply (proj2_sig v).
+Qed.
+
+Definition alloc_vec_Vec_len (T: Type) (v: alloc_vec_Vec T) : usize :=
+ exist _ (alloc_vec_Vec_length v) (alloc_vec_Vec_len_in_usize v).
+
+Fixpoint list_update {A} (l: list A) (n: nat) (a: A)
+ : list A :=
+ match l with
+ | [] => []
+ | x :: t => match n with
+ | 0%nat => a :: t
+ | S m => x :: (list_update t m a)
+end end.
+
+Definition alloc_vec_Vec_bind {A B} (v: alloc_vec_Vec A) (f: list A -> result (list B)) : result (alloc_vec_Vec B) :=
+ l <- f (alloc_vec_Vec_to_list v) ;
+ match sumbool_of_bool (scalar_le_max Usize (Z.of_nat (length l))) with
+ | left H => Return (exist _ l (scalar_le_max_valid _ _ H))
+ | right _ => Fail_ Failure
+ end.
+
+(* The **forward** function shouldn't be used *)
+Definition alloc_vec_Vec_push_fwd (T: Type) (v: alloc_vec_Vec T) (x: T) : unit := tt.
+
+Definition alloc_vec_Vec_push (T: Type) (v: alloc_vec_Vec T) (x: T) : result (alloc_vec_Vec T) :=
+ alloc_vec_Vec_bind v (fun l => Return (l ++ [x])).
+
+(* The **forward** function shouldn't be used *)
+Definition alloc_vec_Vec_insert_fwd (T: Type) (v: alloc_vec_Vec T) (i: usize) (x: T) : result unit :=
+ if to_Z i <? alloc_vec_Vec_length v then Return tt else Fail_ Failure.
+
+Definition alloc_vec_Vec_insert (T: Type) (v: alloc_vec_Vec T) (i: usize) (x: T) : result (alloc_vec_Vec T) :=
+ alloc_vec_Vec_bind v (fun l =>
+ if to_Z i <? Z.of_nat (length l)
+ then Return (list_update l (usize_to_nat i) x)
+ else Fail_ Failure).
+
+(* Helper *)
+Axiom alloc_vec_Vec_index_usize : forall {T : Type} (v : alloc_vec_Vec T) (i : usize) (x : T), result T.
+
+(* Helper *)
+Axiom alloc_vec_Vec_update_usize : forall {T : Type} (v : alloc_vec_Vec T) (i : usize) (x : T), result (alloc_vec_Vec T).
+
+(* Trait declaration: [core::slice::index::private_slice_index::Sealed] *)
+Definition core_slice_index_private_slice_index_Sealed (self : Type) := unit.
+
+(* Trait declaration: [core::slice::index::SliceIndex] *)
+Record core_slice_index_SliceIndex (Self T : Type) := mk_core_slice_index_SliceIndex {
+ core_slice_index_SliceIndex_sealedInst : core_slice_index_private_slice_index_Sealed Self;
+ core_slice_index_SliceIndex_Output : Type;
+ core_slice_index_SliceIndex_get : Self -> T -> result (option core_slice_index_SliceIndex_Output);
+ core_slice_index_SliceIndex_get_mut : Self -> T -> result (option core_slice_index_SliceIndex_Output);
+ core_slice_index_SliceIndex_get_mut_back : Self -> T -> option core_slice_index_SliceIndex_Output -> result T;
+ core_slice_index_SliceIndex_get_unchecked : Self -> const_raw_ptr T -> result (const_raw_ptr core_slice_index_SliceIndex_Output);
+ core_slice_index_SliceIndex_get_unchecked_mut : Self -> mut_raw_ptr T -> result (mut_raw_ptr core_slice_index_SliceIndex_Output);
+ core_slice_index_SliceIndex_index : Self -> T -> result core_slice_index_SliceIndex_Output;
+ core_slice_index_SliceIndex_index_mut : Self -> T -> result core_slice_index_SliceIndex_Output;
+ core_slice_index_SliceIndex_index_mut_back : Self -> T -> core_slice_index_SliceIndex_Output -> result T;
+}.
+Arguments mk_core_slice_index_SliceIndex {_ _}.
+Arguments core_slice_index_SliceIndex_sealedInst {_ _}.
+Arguments core_slice_index_SliceIndex_Output {_ _}.
+Arguments core_slice_index_SliceIndex_get {_ _}.
+Arguments core_slice_index_SliceIndex_get_mut {_ _}.
+Arguments core_slice_index_SliceIndex_get_mut_back {_ _}.
+Arguments core_slice_index_SliceIndex_get_unchecked {_ _}.
+Arguments core_slice_index_SliceIndex_get_unchecked_mut {_ _}.
+Arguments core_slice_index_SliceIndex_index {_ _}.
+Arguments core_slice_index_SliceIndex_index_mut {_ _}.
+Arguments core_slice_index_SliceIndex_index_mut_back {_ _}.
+
+(* [core::slice::index::[T]::index]: forward function *)
+Definition core_slice_index_Slice_index
+ (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T))
+ (s : slice T) (i : Idx) : result inst.(core_slice_index_SliceIndex_Output) :=
+ x <- inst.(core_slice_index_SliceIndex_get) i s;
+ match x with
+ | None => Fail_ Failure
+ | Some x => Return x
+ end.
+
+(* [core::slice::index::Range:::get]: forward function *)
+Axiom core_slice_index_Range_get : forall (T : Type) (i : core_ops_range_Range usize) (s : slice T), result (option (slice T)).
+
+(* [core::slice::index::Range::get_mut]: forward function *)
+Axiom core_slice_index_Range_get_mut :
+ forall (T : Type), core_ops_range_Range usize -> slice T -> result (option (slice T)).
+
+(* [core::slice::index::Range::get_mut]: backward function 0 *)
+Axiom core_slice_index_Range_get_mut_back :
+ forall (T : Type), core_ops_range_Range usize -> slice T -> option (slice T) -> result (slice T).
+
+(* [core::slice::index::Range::get_unchecked]: forward function *)
+Definition core_slice_index_Range_get_unchecked
+ (T : Type) :
+ core_ops_range_Range usize -> const_raw_ptr (slice T) -> result (const_raw_ptr (slice T)) :=
+ (* Don't know what the model should be - for now we always fail to make
+ sure code which uses it fails *)
+ fun _ _ => Fail_ Failure.
+
+(* [core::slice::index::Range::get_unchecked_mut]: forward function *)
+Definition core_slice_index_Range_get_unchecked_mut
+ (T : Type) :
+ core_ops_range_Range usize -> mut_raw_ptr (slice T) -> result (mut_raw_ptr (slice T)) :=
+ (* Don't know what the model should be - for now we always fail to make
+ sure code which uses it fails *)
+ fun _ _ => Fail_ Failure.
+
+(* [core::slice::index::Range::index]: forward function *)
+Axiom core_slice_index_Range_index :
+ forall (T : Type), core_ops_range_Range usize -> slice T -> result (slice T).
+
+(* [core::slice::index::Range::index_mut]: forward function *)
+Axiom core_slice_index_Range_index_mut :
+ forall (T : Type), core_ops_range_Range usize -> slice T -> result (slice T).
+
+(* [core::slice::index::Range::index_mut]: backward function 0 *)
+Axiom core_slice_index_Range_index_mut_back :
+ forall (T : Type), core_ops_range_Range usize -> slice T -> slice T -> result (slice T).
+
+(* [core::slice::index::[T]::index_mut]: forward function *)
+Axiom core_slice_index_Slice_index_mut :
+ forall (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T)),
+ slice T -> Idx -> result inst.(core_slice_index_SliceIndex_Output).
+
+(* [core::slice::index::[T]::index_mut]: backward function 0 *)
+Axiom core_slice_index_Slice_index_mut_back :
+ forall (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T)),
+ slice T -> Idx -> inst.(core_slice_index_SliceIndex_Output) -> result (slice T).
+
+(* [core::array::[T; N]::index]: forward function *)
+Axiom core_array_Array_index :
+ forall (T Idx : Type) (N : usize) (inst : core_ops_index_Index (slice T) Idx)
+ (a : array T N) (i : Idx), result inst.(core_ops_index_Index_Output).
+
+(* [core::array::[T; N]::index_mut]: forward function *)
+Axiom core_array_Array_index_mut :
+ forall (T Idx : Type) (N : usize) (inst : core_ops_index_IndexMut (slice T) Idx)
+ (a : array T N) (i : Idx), result inst.(core_ops_index_IndexMut_indexInst).(core_ops_index_Index_Output).
+
+(* [core::array::[T; N]::index_mut]: backward function 0 *)
+Axiom core_array_Array_index_mut_back :
+ forall (T Idx : Type) (N : usize) (inst : core_ops_index_IndexMut (slice T) Idx)
+ (a : array T N) (i : Idx) (x : inst.(core_ops_index_IndexMut_indexInst).(core_ops_index_Index_Output)), result (array T N).
+
+(* Trait implementation: [core::slice::index::[T]] *)
+Definition core_slice_index_Slice_coreopsindexIndexInst (T Idx : Type)
+ (inst : core_slice_index_SliceIndex Idx (slice T)) :
+ core_ops_index_Index (slice T) Idx := {|
+ core_ops_index_Index_Output := inst.(core_slice_index_SliceIndex_Output);
+ core_ops_index_Index_index := core_slice_index_Slice_index T Idx inst;
+|}.
+
+(* Trait implementation: [core::slice::index::private_slice_index::Range] *)
+Definition core_slice_index_private_slice_index_Range_coresliceindexprivate_slice_indexSealedInst
+ : core_slice_index_private_slice_index_Sealed (core_ops_range_Range usize) := tt.
+
+(* Trait implementation: [core::slice::index::Range] *)
+Definition core_slice_index_Range_coresliceindexSliceIndexInst (T : Type) :
+ core_slice_index_SliceIndex (core_ops_range_Range usize) (slice T) := {|
+ core_slice_index_SliceIndex_sealedInst := core_slice_index_private_slice_index_Range_coresliceindexprivate_slice_indexSealedInst;
+ core_slice_index_SliceIndex_Output := slice T;
+ core_slice_index_SliceIndex_get := core_slice_index_Range_get T;
+ core_slice_index_SliceIndex_get_mut := core_slice_index_Range_get_mut T;
+ core_slice_index_SliceIndex_get_mut_back := core_slice_index_Range_get_mut_back T;
+ core_slice_index_SliceIndex_get_unchecked := core_slice_index_Range_get_unchecked T;
+ core_slice_index_SliceIndex_get_unchecked_mut := core_slice_index_Range_get_unchecked_mut T;
+ core_slice_index_SliceIndex_index := core_slice_index_Range_index T;
+ core_slice_index_SliceIndex_index_mut := core_slice_index_Range_index_mut T;
+ core_slice_index_SliceIndex_index_mut_back := core_slice_index_Range_index_mut_back T;
+|}.
+
+(* Trait implementation: [core::slice::index::[T]] *)
+Definition core_slice_index_Slice_coreopsindexIndexMutInst (T Idx : Type)
+ (inst : core_slice_index_SliceIndex Idx (slice T)) :
+ core_ops_index_IndexMut (slice T) Idx := {|
+ core_ops_index_IndexMut_indexInst := core_slice_index_Slice_coreopsindexIndexInst T Idx inst;
+ core_ops_index_IndexMut_index_mut := core_slice_index_Slice_index_mut T Idx inst;
+ core_ops_index_IndexMut_index_mut_back := core_slice_index_Slice_index_mut_back T Idx inst;
+|}.
+
+(* Trait implementation: [core::array::[T; N]] *)
+Definition core_array_Array_coreopsindexIndexInst (T Idx : Type) (N : usize)
+ (inst : core_ops_index_Index (slice T) Idx) :
+ core_ops_index_Index (array T N) Idx := {|
+ core_ops_index_Index_Output := inst.(core_ops_index_Index_Output);
+ core_ops_index_Index_index := core_array_Array_index T Idx N inst;
+|}.
+
+(* Trait implementation: [core::array::[T; N]] *)
+Definition core_array_Array_coreopsindexIndexMutInst (T Idx : Type) (N : usize)
+ (inst : core_ops_index_IndexMut (slice T) Idx) :
+ core_ops_index_IndexMut (array T N) Idx := {|
+ core_ops_index_IndexMut_indexInst := core_array_Array_coreopsindexIndexInst T Idx N inst.(core_ops_index_IndexMut_indexInst);
+ core_ops_index_IndexMut_index_mut := core_array_Array_index_mut T Idx N inst;
+ core_ops_index_IndexMut_index_mut_back := core_array_Array_index_mut_back T Idx N inst;
+|}.
+
+(* [core::slice::index::usize::get]: forward function *)
+Axiom core_slice_index_usize_get : forall (T : Type), usize -> slice T -> result (option T).
+
+(* [core::slice::index::usize::get_mut]: forward function *)
+Axiom core_slice_index_usize_get_mut : forall (T : Type), usize -> slice T -> result (option T).
+
+(* [core::slice::index::usize::get_mut]: backward function 0 *)
+Axiom core_slice_index_usize_get_mut_back :
+ forall (T : Type), usize -> slice T -> option T -> result (slice T).
+
+(* [core::slice::index::usize::get_unchecked]: forward function *)
+Axiom core_slice_index_usize_get_unchecked :
+ forall (T : Type), usize -> const_raw_ptr (slice T) -> result (const_raw_ptr T).
+
+(* [core::slice::index::usize::get_unchecked_mut]: forward function *)
+Axiom core_slice_index_usize_get_unchecked_mut :
+ forall (T : Type), usize -> mut_raw_ptr (slice T) -> result (mut_raw_ptr T).
+
+(* [core::slice::index::usize::index]: forward function *)
+Axiom core_slice_index_usize_index : forall (T : Type), usize -> slice T -> result T.
+
+(* [core::slice::index::usize::index_mut]: forward function *)
+Axiom core_slice_index_usize_index_mut : forall (T : Type), usize -> slice T -> result T.
+
+(* [core::slice::index::usize::index_mut]: backward function 0 *)
+Axiom core_slice_index_usize_index_mut_back :
+ forall (T : Type), usize -> slice T -> T -> result (slice T).
+
+(* Trait implementation: [core::slice::index::private_slice_index::usize] *)
+Definition core_slice_index_private_slice_index_usize_coresliceindexprivate_slice_indexSealedInst
+ : core_slice_index_private_slice_index_Sealed usize := tt.
+
+(* Trait implementation: [core::slice::index::usize] *)
+Definition core_slice_index_usize_coresliceindexSliceIndexInst (T : Type) :
+ core_slice_index_SliceIndex usize (slice T) := {|
+ core_slice_index_SliceIndex_sealedInst := core_slice_index_private_slice_index_usize_coresliceindexprivate_slice_indexSealedInst;
+ core_slice_index_SliceIndex_Output := T;
+ core_slice_index_SliceIndex_get := core_slice_index_usize_get T;
+ core_slice_index_SliceIndex_get_mut := core_slice_index_usize_get_mut T;
+ core_slice_index_SliceIndex_get_mut_back := core_slice_index_usize_get_mut_back T;
+ core_slice_index_SliceIndex_get_unchecked := core_slice_index_usize_get_unchecked T;
+ core_slice_index_SliceIndex_get_unchecked_mut := core_slice_index_usize_get_unchecked_mut T;
+ core_slice_index_SliceIndex_index := core_slice_index_usize_index T;
+ core_slice_index_SliceIndex_index_mut := core_slice_index_usize_index_mut T;
+ core_slice_index_SliceIndex_index_mut_back := core_slice_index_usize_index_mut_back T;
+|}.
+
+(* [alloc::vec::Vec::index]: forward function *)
+Axiom alloc_vec_Vec_index : forall (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T))
+ (Self : alloc_vec_Vec T) (i : Idx), result inst.(core_slice_index_SliceIndex_Output).
+
+(* [alloc::vec::Vec::index_mut]: forward function *)
+Axiom alloc_vec_Vec_index_mut : forall (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T))
+ (Self : alloc_vec_Vec T) (i : Idx), result inst.(core_slice_index_SliceIndex_Output).
+
+(* [alloc::vec::Vec::index_mut]: backward function 0 *)
+Axiom alloc_vec_Vec_index_mut_back :
+ forall (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T))
+ (Self : alloc_vec_Vec T) (i : Idx) (x : inst.(core_slice_index_SliceIndex_Output)), result (alloc_vec_Vec T).
+
+(* Trait implementation: [alloc::vec::Vec] *)
+Definition alloc_vec_Vec_coreopsindexIndexInst (T Idx : Type)
+ (inst : core_slice_index_SliceIndex Idx (slice T)) :
+ core_ops_index_Index (alloc_vec_Vec T) Idx := {|
+ core_ops_index_Index_Output := inst.(core_slice_index_SliceIndex_Output);
+ core_ops_index_Index_index := alloc_vec_Vec_index T Idx inst;
+|}.
+
+(* Trait implementation: [alloc::vec::Vec] *)
+Definition alloc_vec_Vec_coreopsindexIndexMutInst (T Idx : Type)
+ (inst : core_slice_index_SliceIndex Idx (slice T)) :
+ core_ops_index_IndexMut (alloc_vec_Vec T) Idx := {|
+ core_ops_index_IndexMut_indexInst := alloc_vec_Vec_coreopsindexIndexInst T Idx inst;
+ core_ops_index_IndexMut_index_mut := alloc_vec_Vec_index_mut T Idx inst;
+ core_ops_index_IndexMut_index_mut_back := alloc_vec_Vec_index_mut_back T Idx inst;
+|}.
+
+(*** Theorems *)
+
+Axiom alloc_vec_Vec_index_mut_back_eq : forall {a : Type} (v : alloc_vec_Vec a) (i : usize) (x : a),
+ alloc_vec_Vec_index_mut_back a usize (core_slice_index_usize_coresliceindexSliceIndexInst a) v i x =
+ alloc_vec_Vec_update_usize v i x.
+
+End Primitives.
diff --git a/tests/coq/traits/Traits.v b/tests/coq/traits/Traits.v
new file mode 100644
index 00000000..e104fb66
--- /dev/null
+++ b/tests/coq/traits/Traits.v
@@ -0,0 +1,520 @@
+(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
+(** [traits] *)
+Require Import Primitives.
+Import Primitives.
+Require Import Coq.ZArith.ZArith.
+Require Import List.
+Import ListNotations.
+Local Open Scope Primitives_scope.
+Module Traits.
+
+(** Trait declaration: [traits::BoolTrait] *)
+Record BoolTrait_t (Self : Type) := mkBoolTrait_t {
+ BoolTrait_t_get_bool : Self -> result bool;
+}.
+
+Arguments mkBoolTrait_t { _ }.
+Arguments BoolTrait_t_get_bool { _ }.
+
+(** [traits::Bool::{0}::get_bool]: forward function *)
+Definition bool_get_bool (self : bool) : result bool :=
+ Return self.
+
+(** Trait implementation: [traits::Bool::{0}] *)
+Definition Bool_BoolTraitInst : BoolTrait_t bool := {|
+ BoolTrait_t_get_bool := bool_get_bool;
+|}.
+
+(** [traits::BoolTrait::ret_true]: forward function *)
+Definition boolTrait_ret_true
+ {Self : Type} (self_clause : BoolTrait_t Self) (self : Self) : result bool :=
+ Return true
+.
+
+(** [traits::test_bool_trait_bool]: forward function *)
+Definition test_bool_trait_bool (x : bool) : result bool :=
+ b <- bool_get_bool x;
+ if b then boolTrait_ret_true Bool_BoolTraitInst x else Return false
+.
+
+(** [traits::Option::{1}::get_bool]: forward function *)
+Definition option_get_bool (T : Type) (self : option T) : result bool :=
+ match self with | None => Return false | Some t => Return true end
+.
+
+(** Trait implementation: [traits::Option::{1}] *)
+Definition Option_BoolTraitInst (T : Type) : BoolTrait_t (option T) := {|
+ BoolTrait_t_get_bool := option_get_bool T;
+|}.
+
+(** [traits::test_bool_trait_option]: forward function *)
+Definition test_bool_trait_option (T : Type) (x : option T) : result bool :=
+ b <- option_get_bool T x;
+ if b then boolTrait_ret_true (Option_BoolTraitInst T) x else Return false
+.
+
+(** [traits::test_bool_trait]: forward function *)
+Definition test_bool_trait
+ (T : Type) (inst : BoolTrait_t T) (x : T) : result bool :=
+ inst.(BoolTrait_t_get_bool) x
+.
+
+(** Trait declaration: [traits::ToU64] *)
+Record ToU64_t (Self : Type) := mkToU64_t {
+ ToU64_t_to_u64 : Self -> result u64;
+}.
+
+Arguments mkToU64_t { _ }.
+Arguments ToU64_t_to_u64 { _ }.
+
+(** [traits::u64::{2}::to_u64]: forward function *)
+Definition u64_to_u64 (self : u64) : result u64 :=
+ Return self.
+
+(** Trait implementation: [traits::u64::{2}] *)
+Definition u64_ToU64Inst : ToU64_t u64 := {| ToU64_t_to_u64 := u64_to_u64; |}.
+
+(** [traits::Tuple2::{3}::to_u64]: forward function *)
+Definition tuple2_to_u64
+ (A : Type) (inst : ToU64_t A) (self : (A * A)) : result u64 :=
+ let (t, t0) := self in
+ i <- inst.(ToU64_t_to_u64) t;
+ i0 <- inst.(ToU64_t_to_u64) t0;
+ u64_add i i0
+.
+
+(** Trait implementation: [traits::Tuple2::{3}] *)
+Definition Tuple2_ToU64Inst (A : Type) (inst : ToU64_t A) : ToU64_t (A * A)
+ := {|
+ ToU64_t_to_u64 := tuple2_to_u64 A inst;
+|}.
+
+(** [traits::f]: forward function *)
+Definition f (T : Type) (inst : ToU64_t T) (x : (T * T)) : result u64 :=
+ tuple2_to_u64 T inst x
+.
+
+(** [traits::g]: forward function *)
+Definition g (T : Type) (inst : ToU64_t (T * T)) (x : (T * T)) : result u64 :=
+ inst.(ToU64_t_to_u64) x
+.
+
+(** [traits::h0]: forward function *)
+Definition h0 (x : u64) : result u64 :=
+ u64_to_u64 x.
+
+(** [traits::Wrapper] *)
+Record Wrapper_t (T : Type) := mkWrapper_t { wrapper_x : T; }.
+
+Arguments mkWrapper_t { _ }.
+Arguments wrapper_x { _ }.
+
+(** [traits::Wrapper::{4}::to_u64]: forward function *)
+Definition wrapper_to_u64
+ (T : Type) (inst : ToU64_t T) (self : Wrapper_t T) : result u64 :=
+ inst.(ToU64_t_to_u64) self.(wrapper_x)
+.
+
+(** Trait implementation: [traits::Wrapper::{4}] *)
+Definition Wrapper_ToU64Inst (T : Type) (inst : ToU64_t T) : ToU64_t (Wrapper_t
+ T) := {|
+ ToU64_t_to_u64 := wrapper_to_u64 T inst;
+|}.
+
+(** [traits::h1]: forward function *)
+Definition h1 (x : Wrapper_t u64) : result u64 :=
+ wrapper_to_u64 u64 u64_ToU64Inst x
+.
+
+(** [traits::h2]: forward function *)
+Definition h2 (T : Type) (inst : ToU64_t T) (x : Wrapper_t T) : result u64 :=
+ wrapper_to_u64 T inst x
+.
+
+(** Trait declaration: [traits::ToType] *)
+Record ToType_t (Self T : Type) := mkToType_t {
+ ToType_t_to_type : Self -> result T;
+}.
+
+Arguments mkToType_t { _ _ }.
+Arguments ToType_t_to_type { _ _ }.
+
+(** [traits::u64::{5}::to_type]: forward function *)
+Definition u64_to_type (self : u64) : result bool :=
+ Return (self s> 0%u64).
+
+(** Trait implementation: [traits::u64::{5}] *)
+Definition u64_ToTypeInst : ToType_t u64 bool := {|
+ ToType_t_to_type := u64_to_type;
+|}.
+
+(** Trait declaration: [traits::OfType] *)
+Record OfType_t (Self : Type) := mkOfType_t {
+ OfType_t_of_type : forall (T : Type) (inst : ToType_t T Self), T -> result
+ Self;
+}.
+
+Arguments mkOfType_t { _ }.
+Arguments OfType_t_of_type { _ }.
+
+(** [traits::h3]: forward function *)
+Definition h3
+ (T1 T2 : Type) (inst : OfType_t T1) (inst0 : ToType_t T2 T1) (y : T2) :
+ result T1
+ :=
+ inst.(OfType_t_of_type) T2 inst0 y
+.
+
+(** Trait declaration: [traits::OfTypeBis] *)
+Record OfTypeBis_t (Self T : Type) := mkOfTypeBis_t {
+ OfTypeBis_tOfTypeBis_t_parent_clause_0 : ToType_t T Self;
+ OfTypeBis_t_of_type : T -> result Self;
+}.
+
+Arguments mkOfTypeBis_t { _ _ }.
+Arguments OfTypeBis_tOfTypeBis_t_parent_clause_0 { _ _ }.
+Arguments OfTypeBis_t_of_type { _ _ }.
+
+(** [traits::h4]: forward function *)
+Definition h4
+ (T1 T2 : Type) (inst : OfTypeBis_t T1 T2) (inst0 : ToType_t T2 T1) (y : T2) :
+ result T1
+ :=
+ inst.(OfTypeBis_t_of_type) y
+.
+
+(** [traits::TestType] *)
+Record TestType_t (T : Type) := mkTestType_t { testType_0 : T; }.
+
+Arguments mkTestType_t { _ }.
+Arguments testType_0 { _ }.
+
+(** [traits::TestType::{6}::test::TestType1] *)
+Record TestType_test_TestType1_t :=
+mkTestType_test_TestType1_t {
+ testType_test_TestType1_0 : u64;
+}
+.
+
+(** Trait declaration: [traits::TestType::{6}::test::TestTrait] *)
+Record TestType_test_TestTrait_t (Self : Type) := mkTestType_test_TestTrait_t {
+ TestType_test_TestTrait_t_test : Self -> result bool;
+}.
+
+Arguments mkTestType_test_TestTrait_t { _ }.
+Arguments TestType_test_TestTrait_t_test { _ }.
+
+(** [traits::TestType::{6}::test::TestType1::{0}::test]: forward function *)
+Definition testType_test_TestType1_test
+ (self : TestType_test_TestType1_t) : result bool :=
+ Return (self.(testType_test_TestType1_0) s> 1%u64)
+.
+
+(** Trait implementation: [traits::TestType::{6}::test::TestType1::{0}] *)
+Definition TestType_test_TestType1_TestType_test_TestTraitInst :
+ TestType_test_TestTrait_t TestType_test_TestType1_t := {|
+ TestType_test_TestTrait_t_test := testType_test_TestType1_test;
+|}.
+
+(** [traits::TestType::{6}::test]: forward function *)
+Definition testType_test
+ (T : Type) (inst : ToU64_t T) (self : TestType_t T) (x : T) : result bool :=
+ x0 <- inst.(ToU64_t_to_u64) x;
+ if x0 s> 0%u64
+ then testType_test_TestType1_test {| testType_test_TestType1_0 := 0%u64 |}
+ else Return false
+.
+
+(** [traits::BoolWrapper] *)
+Record BoolWrapper_t := mkBoolWrapper_t { boolWrapper_0 : bool; }.
+
+(** [traits::BoolWrapper::{7}::to_type]: forward function *)
+Definition boolWrapper_to_type
+ (T : Type) (inst : ToType_t bool T) (self : BoolWrapper_t) : result T :=
+ inst.(ToType_t_to_type) self.(boolWrapper_0)
+.
+
+(** Trait implementation: [traits::BoolWrapper::{7}] *)
+Definition BoolWrapper_ToTypeInst (T : Type) (inst : ToType_t bool T) :
+ ToType_t BoolWrapper_t T := {|
+ ToType_t_to_type := boolWrapper_to_type T inst;
+|}.
+
+(** [traits::WithConstTy::LEN2] *)
+Definition with_const_ty_len2_body : result usize := Return 32%usize.
+Definition with_const_ty_len2_c : usize := with_const_ty_len2_body%global.
+
+(** Trait declaration: [traits::WithConstTy] *)
+Record WithConstTy_t (Self : Type) (LEN : usize) := mkWithConstTy_t {
+ WithConstTy_tWithConstTy_t_LEN1 : usize;
+ WithConstTy_tWithConstTy_t_LEN2 : usize;
+ WithConstTy_tWithConstTy_t_V : Type;
+ WithConstTy_tWithConstTy_t_W : Type;
+ WithConstTy_tWithConstTy_t_W_clause_0 : ToU64_t WithConstTy_tWithConstTy_t_W;
+ WithConstTy_t_f : WithConstTy_tWithConstTy_t_W -> array u8 LEN -> result
+ WithConstTy_tWithConstTy_t_W;
+}.
+
+Arguments mkWithConstTy_t { _ _ }.
+Arguments WithConstTy_tWithConstTy_t_LEN1 { _ _ }.
+Arguments WithConstTy_tWithConstTy_t_LEN2 { _ _ }.
+Arguments WithConstTy_tWithConstTy_t_V { _ _ }.
+Arguments WithConstTy_tWithConstTy_t_W { _ _ }.
+Arguments WithConstTy_tWithConstTy_t_W_clause_0 { _ _ }.
+Arguments WithConstTy_t_f { _ _ }.
+
+(** [traits::Bool::{8}::LEN1] *)
+Definition bool_len1_body : result usize := Return 12%usize.
+Definition bool_len1_c : usize := bool_len1_body%global.
+
+(** [traits::Bool::{8}::f]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ()) *)
+Definition bool_f (i : u64) (a : array u8 32%usize) : result u64 :=
+ Return i.
+
+(** Trait implementation: [traits::Bool::{8}] *)
+Definition Bool_WithConstTyInst : WithConstTy_t bool 32%usize := {|
+ WithConstTy_tWithConstTy_t_LEN1 := bool_len1_c;
+ WithConstTy_tWithConstTy_t_LEN2 := with_const_ty_len2_c;
+ WithConstTy_tWithConstTy_t_V := u8;
+ WithConstTy_tWithConstTy_t_W := u64;
+ WithConstTy_tWithConstTy_t_W_clause_0 := u64_ToU64Inst;
+ WithConstTy_t_f := bool_f;
+|}.
+
+(** [traits::use_with_const_ty1]: forward function *)
+Definition use_with_const_ty1
+ (H : Type) (LEN : usize) (inst : WithConstTy_t H LEN) : result usize :=
+ let i := inst.(WithConstTy_tWithConstTy_t_LEN1) in Return i
+.
+
+(** [traits::use_with_const_ty2]: forward function *)
+Definition use_with_const_ty2
+ (H : Type) (LEN : usize) (inst : WithConstTy_t H LEN)
+ (w : inst.(WithConstTy_tWithConstTy_t_W)) :
+ result unit
+ :=
+ Return tt
+.
+
+(** [traits::use_with_const_ty3]: forward function *)
+Definition use_with_const_ty3
+ (H : Type) (LEN : usize) (inst : WithConstTy_t H LEN)
+ (x : inst.(WithConstTy_tWithConstTy_t_W)) :
+ result u64
+ :=
+ inst.(WithConstTy_tWithConstTy_t_W_clause_0).(ToU64_t_to_u64) x
+.
+
+(** [traits::test_where1]: forward function *)
+Definition test_where1 (T : Type) (_x : T) : result unit :=
+ Return tt.
+
+(** [traits::test_where2]: forward function *)
+Definition test_where2
+ (T : Type) (inst : WithConstTy_t T 32%usize) (_x : u32) : result unit :=
+ Return tt
+.
+
+(** [alloc::string::String] *)
+Axiom alloc_string_String_t : Type.
+
+(** Trait declaration: [traits::ParentTrait0] *)
+Record ParentTrait0_t (Self : Type) := mkParentTrait0_t {
+ ParentTrait0_tParentTrait0_t_W : Type;
+ ParentTrait0_t_get_name : Self -> result alloc_string_String_t;
+ ParentTrait0_t_get_w : Self -> result ParentTrait0_tParentTrait0_t_W;
+}.
+
+Arguments mkParentTrait0_t { _ }.
+Arguments ParentTrait0_tParentTrait0_t_W { _ }.
+Arguments ParentTrait0_t_get_name { _ }.
+Arguments ParentTrait0_t_get_w { _ }.
+
+(** Trait declaration: [traits::ParentTrait1] *)
+Record ParentTrait1_t (Self : Type) := mkParentTrait1_t{}.
+
+Arguments mkParentTrait1_t { _ }.
+
+(** Trait declaration: [traits::ChildTrait] *)
+Record ChildTrait_t (Self : Type) := mkChildTrait_t {
+ ChildTrait_tChildTrait_t_parent_clause_0 : ParentTrait0_t Self;
+ ChildTrait_tChildTrait_t_parent_clause_1 : ParentTrait1_t Self;
+}.
+
+Arguments mkChildTrait_t { _ }.
+Arguments ChildTrait_tChildTrait_t_parent_clause_0 { _ }.
+Arguments ChildTrait_tChildTrait_t_parent_clause_1 { _ }.
+
+(** [traits::test_child_trait1]: forward function *)
+Definition test_child_trait1
+ (T : Type) (inst : ChildTrait_t T) (x : T) : result alloc_string_String_t :=
+ inst.(ChildTrait_tChildTrait_t_parent_clause_0).(ParentTrait0_t_get_name) x
+.
+
+(** [traits::test_child_trait2]: forward function *)
+Definition test_child_trait2
+ (T : Type) (inst : ChildTrait_t T) (x : T) :
+ result
+ inst.(ChildTrait_tChildTrait_t_parent_clause_0).(ParentTrait0_tParentTrait0_t_W)
+ :=
+ inst.(ChildTrait_tChildTrait_t_parent_clause_0).(ParentTrait0_t_get_w) x
+.
+
+(** [traits::order1]: forward function *)
+Definition order1
+ (T U : Type) (inst : ParentTrait0_t T) (inst0 : ParentTrait0_t U) :
+ result unit
+ :=
+ Return tt
+.
+
+(** Trait declaration: [traits::ChildTrait1] *)
+Record ChildTrait1_t (Self : Type) := mkChildTrait1_t {
+ ChildTrait1_tChildTrait1_t_parent_clause_0 : ParentTrait1_t Self;
+}.
+
+Arguments mkChildTrait1_t { _ }.
+Arguments ChildTrait1_tChildTrait1_t_parent_clause_0 { _ }.
+
+(** Trait implementation: [traits::usize::{9}] *)
+Definition usize_ParentTrait1Inst : ParentTrait1_t usize := mkParentTrait1_t.
+
+(** Trait implementation: [traits::usize::{10}] *)
+Definition usize_ChildTrait1Inst : ChildTrait1_t usize := {|
+ ChildTrait1_tChildTrait1_t_parent_clause_0 := usize_ParentTrait1Inst;
+|}.
+
+(** Trait declaration: [traits::Iterator] *)
+Record Iterator_t (Self : Type) := mkIterator_t {
+ Iterator_tIterator_t_Item : Type;
+}.
+
+Arguments mkIterator_t { _ }.
+Arguments Iterator_tIterator_t_Item { _ }.
+
+(** Trait declaration: [traits::IntoIterator] *)
+Record IntoIterator_t (Self : Type) := mkIntoIterator_t {
+ IntoIterator_tIntoIterator_t_Item : Type;
+ IntoIterator_tIntoIterator_t_IntoIter : Type;
+ IntoIterator_tIntoIterator_t_IntoIter_clause_0 : Iterator_t
+ IntoIterator_tIntoIterator_t_IntoIter;
+ IntoIterator_t_into_iter : Self -> result
+ IntoIterator_tIntoIterator_t_IntoIter;
+}.
+
+Arguments mkIntoIterator_t { _ }.
+Arguments IntoIterator_tIntoIterator_t_Item { _ }.
+Arguments IntoIterator_tIntoIterator_t_IntoIter { _ }.
+Arguments IntoIterator_tIntoIterator_t_IntoIter_clause_0 { _ }.
+Arguments IntoIterator_t_into_iter { _ }.
+
+(** Trait declaration: [traits::FromResidual] *)
+Record FromResidual_t (Self T : Type) := mkFromResidual_t{}.
+
+Arguments mkFromResidual_t { _ _ }.
+
+(** Trait declaration: [traits::Try] *)
+Record Try_t (Self : Type) := mkTry_t {
+ Try_tTry_t_Residual : Type;
+ Try_tTry_t_parent_clause_0 : FromResidual_t Self Try_tTry_t_Residual;
+}.
+
+Arguments mkTry_t { _ }.
+Arguments Try_tTry_t_Residual { _ }.
+Arguments Try_tTry_t_parent_clause_0 { _ }.
+
+(** Trait declaration: [traits::WithTarget] *)
+Record WithTarget_t (Self : Type) := mkWithTarget_t {
+ WithTarget_tWithTarget_t_Target : Type;
+}.
+
+Arguments mkWithTarget_t { _ }.
+Arguments WithTarget_tWithTarget_t_Target { _ }.
+
+(** Trait declaration: [traits::ParentTrait2] *)
+Record ParentTrait2_t (Self : Type) := mkParentTrait2_t {
+ ParentTrait2_tParentTrait2_t_U : Type;
+ ParentTrait2_tParentTrait2_t_U_clause_0 : WithTarget_t
+ ParentTrait2_tParentTrait2_t_U;
+}.
+
+Arguments mkParentTrait2_t { _ }.
+Arguments ParentTrait2_tParentTrait2_t_U { _ }.
+Arguments ParentTrait2_tParentTrait2_t_U_clause_0 { _ }.
+
+(** Trait declaration: [traits::ChildTrait2] *)
+Record ChildTrait2_t (Self : Type) := mkChildTrait2_t {
+ ChildTrait2_tChildTrait2_t_parent_clause_0 : ParentTrait2_t Self;
+ ChildTrait2_t_convert :
+ (ChildTrait2_tChildTrait2_t_parent_clause_0).(ParentTrait2_tParentTrait2_t_U)
+ -> result
+ (ChildTrait2_tChildTrait2_t_parent_clause_0).(ParentTrait2_tParentTrait2_t_U_clause_0).(WithTarget_tWithTarget_t_Target);
+}.
+
+Arguments mkChildTrait2_t { _ }.
+Arguments ChildTrait2_tChildTrait2_t_parent_clause_0 { _ }.
+Arguments ChildTrait2_t_convert { _ }.
+
+(** Trait implementation: [traits::u32::{11}] *)
+Definition u32_WithTargetInst : WithTarget_t u32 := {|
+ WithTarget_tWithTarget_t_Target := u32;
+|}.
+
+(** Trait implementation: [traits::u32::{12}] *)
+Definition u32_ParentTrait2Inst : ParentTrait2_t u32 := {|
+ ParentTrait2_tParentTrait2_t_U := u32;
+ ParentTrait2_tParentTrait2_t_U_clause_0 := u32_WithTargetInst;
+|}.
+
+(** [traits::u32::{13}::convert]: forward function *)
+Definition u32_convert (x : u32) : result u32 :=
+ Return x.
+
+(** Trait implementation: [traits::u32::{13}] *)
+Definition u32_ChildTrait2Inst : ChildTrait2_t u32 := {|
+ ChildTrait2_tChildTrait2_t_parent_clause_0 := u32_ParentTrait2Inst;
+ ChildTrait2_t_convert := u32_convert;
+|}.
+
+(** [traits::incr_u32]: forward function *)
+Definition incr_u32 (x : u32) : result u32 :=
+ u32_add x 1%u32.
+
+(** Trait declaration: [traits::CFnOnce] *)
+Record CFnOnce_t (Self Args : Type) := mkCFnOnce_t {
+ CFnOnce_tCFnOnce_t_Output : Type;
+ CFnOnce_t_call_once : Self -> Args -> result CFnOnce_tCFnOnce_t_Output;
+}.
+
+Arguments mkCFnOnce_t { _ _ }.
+Arguments CFnOnce_tCFnOnce_t_Output { _ _ }.
+Arguments CFnOnce_t_call_once { _ _ }.
+
+(** Trait declaration: [traits::CFnMut] *)
+Record CFnMut_t (Self Args : Type) := mkCFnMut_t {
+ CFnMut_tCFnMut_t_parent_clause_0 : CFnOnce_t Self Args;
+ CFnMut_t_call_mut : Self -> Args -> result
+ (CFnMut_tCFnMut_t_parent_clause_0).(CFnOnce_tCFnOnce_t_Output);
+ CFnMut_t_call_mut_back : Self -> Args ->
+ (CFnMut_tCFnMut_t_parent_clause_0).(CFnOnce_tCFnOnce_t_Output) -> result
+ Self;
+}.
+
+Arguments mkCFnMut_t { _ _ }.
+Arguments CFnMut_tCFnMut_t_parent_clause_0 { _ _ }.
+Arguments CFnMut_t_call_mut { _ _ }.
+Arguments CFnMut_t_call_mut_back { _ _ }.
+
+(** Trait declaration: [traits::CFn] *)
+Record CFn_t (Self Args : Type) := mkCFn_t {
+ CFn_tCFn_t_parent_clause_0 : CFnMut_t Self Args;
+ CFn_t_call_mut : Self -> Args -> result
+ (CFn_tCFn_t_parent_clause_0).(CFnMut_tCFnMut_t_parent_clause_0).(CFnOnce_tCFnOnce_t_Output);
+}.
+
+Arguments mkCFn_t { _ _ }.
+Arguments CFn_tCFn_t_parent_clause_0 { _ _ }.
+Arguments CFn_t_call_mut { _ _ }.
+
+End Traits .
diff --git a/tests/coq/traits/_CoqProject b/tests/coq/traits/_CoqProject
new file mode 100644
index 00000000..5b6199fc
--- /dev/null
+++ b/tests/coq/traits/_CoqProject
@@ -0,0 +1,7 @@
+# This file was automatically generated - see ../Makefile
+-R . Lib
+-arg -w
+-arg all
+
+Traits.v
+Primitives.v