Merge pull request #213 from AeneasVerif/cleanup-tests

1 files changed, 0 insertions, 981 deletions

diff --git a/tests/coq/hashmap_main/Primitives.v b/tests/coq/hashmap_main/Primitives.v
deleted file mode 100644
index b29fce43..00000000
--- a/tests/coq/hashmap_main/Primitives.v
+++ /dev/null
@@ -1,981 +0,0 @@
-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 :=
-  | Ok : A -> result A
-  | Fail_ : error -> result A.
-
-Arguments Ok {_} a.
-Arguments Fail_ {_}.
-
-Definition bind {A B} (m: result A) (f: A -> result B) : result B :=
-  match m with
-  | Fail_ e => Fail_ e
-  | Ok x => f x
-  end.
-
-Definition return_ {A: Type} (x: A) : result A := Ok 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 Ok tt else Fail_ Failure.
-
-(** Normalize and unwrap a successful result (used for globals) *)
-Definition eval_result_refl {A} {x} (a: result A) (p: a = Ok x) : A :=
-  match a as r return (r = Ok x -> A) with
-  | Ok a' => fun _  => a'
-  | Fail_ e   => fun p' =>
-      False_rect _ (eq_ind (Fail_ e)
-          (fun e : result A =>
-          match e with
-          | Ok _ => False
-          | Fail_ e => True
-          end)
-        I (Ok 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 Ok (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 * a := (x, x) .
-
-Record mut_raw_ptr (T : Type) := { mut_raw_ptr_v : T }.
-Record const_raw_ptr (T : Type) := { const_raw_ptr_v : T }.
-
-(*** 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 => Ok (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)).
-
-Axiom scalar_xor : forall ty, scalar ty -> scalar ty -> scalar ty. (* TODO *)
-Axiom scalar_or : forall ty, scalar ty -> scalar ty -> scalar ty. (* TODO *)
-Axiom scalar_and : forall ty, scalar ty -> scalar ty -> scalar ty. (* TODO *)
-Axiom scalar_shl : forall ty0 ty1, scalar ty0 -> scalar ty1 -> result (scalar ty0). (* TODO *)
-Axiom scalar_shr : forall ty0 ty1, scalar ty0 -> scalar ty1 -> result (scalar ty0). (* TODO *)
-
-(** 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).
-
-(* This can't fail, but for now we make all casts faillible (easier for the translation) *)
-Definition scalar_cast_bool (tgt_ty : scalar_ty) (x : bool) : result (scalar tgt_ty) :=
-  mk_scalar tgt_ty (if x then 1 else 0).
-
-(** 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.
-
-(** Xor *)
-Definition u8_xor := @scalar_xor U8.
-Definition u16_xor := @scalar_xor U16.
-Definition u32_xor := @scalar_xor U32.
-Definition u64_xor := @scalar_xor U64.
-Definition u128_xor := @scalar_xor U128.
-Definition usize_xor := @scalar_xor Usize.
-Definition i8_xor := @scalar_xor I8.
-Definition i16_xor := @scalar_xor I16.
-Definition i32_xor := @scalar_xor I32.
-Definition i64_xor := @scalar_xor I64.
-Definition i128_xor := @scalar_xor I128.
-Definition isize_xor := @scalar_xor Isize.
-
-(** Or *)
-Definition u8_or := @scalar_or U8.
-Definition u16_or := @scalar_or U16.
-Definition u32_or := @scalar_or U32.
-Definition u64_or := @scalar_or U64.
-Definition u128_or := @scalar_or U128.
-Definition usize_or := @scalar_or Usize.
-Definition i8_or := @scalar_or I8.
-Definition i16_or := @scalar_or I16.
-Definition i32_or := @scalar_or I32.
-Definition i64_or := @scalar_or I64.
-Definition i128_or := @scalar_or I128.
-Definition isize_or := @scalar_or Isize.
-
-(** And *)
-Definition u8_and := @scalar_and U8.
-Definition u16_and := @scalar_and U16.
-Definition u32_and := @scalar_and U32.
-Definition u64_and := @scalar_and U64.
-Definition u128_and := @scalar_and U128.
-Definition usize_and := @scalar_and Usize.
-Definition i8_and := @scalar_and I8.
-Definition i16_and := @scalar_and I16.
-Definition i32_and := @scalar_and I32.
-Definition i64_and := @scalar_and I64.
-Definition i128_and := @scalar_and I128.
-Definition isize_and := @scalar_and Isize.
-
-(** Shift left *)
-Definition u8_shl {ty} := @scalar_shl U8 ty.
-Definition u16_shl {ty} := @scalar_shl U16 ty.
-Definition u32_shl {ty} := @scalar_shl U32 ty.
-Definition u64_shl {ty} := @scalar_shl U64 ty.
-Definition u128_shl {ty} := @scalar_shl U128 ty.
-Definition usize_shl {ty} := @scalar_shl Usize ty.
-Definition i8_shl {ty} := @scalar_shl I8 ty.
-Definition i16_shl {ty} := @scalar_shl I16 ty.
-Definition i32_shl {ty} := @scalar_shl I32 ty.
-Definition i64_shl {ty} := @scalar_shl I64 ty.
-Definition i128_shl {ty} := @scalar_shl I128 ty.
-Definition isize_shl {ty} := @scalar_shl Isize ty.
-
-(** Shift right *)
-Definition u8_shr {ty} := @scalar_shr U8 ty.
-Definition u16_shr {ty} := @scalar_shr U16 ty.
-Definition u32_shr {ty} := @scalar_shr U32 ty.
-Definition u64_shr {ty} := @scalar_shr U64 ty.
-Definition u128_shr {ty} := @scalar_shr U128 ty.
-Definition usize_shr {ty} := @scalar_shr Usize ty.
-Definition i8_shr {ty} := @scalar_shr I8 ty.
-Definition i16_shr {ty} := @scalar_shr I16 ty.
-Definition i32_shr {ty} := @scalar_shr I32 ty.
-Definition i64_shr {ty} := @scalar_shr I64 ty.
-Definition i128_shr {ty} := @scalar_shr I128 ty.
-Definition isize_shr {ty} := @scalar_shr Isize ty.
-
-(** 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 *)
-
-(** Trait declaration: [core::clone::Clone] *)
-Record core_clone_Clone (self : Type) := {
-  clone : self -> result self
-}.
-
-Definition core_clone_impls_CloneBool_clone (b : bool) : bool := b.
-
-Definition core_clone_CloneBool : core_clone_Clone bool := {|
-  clone := fun b => Ok (core_clone_impls_CloneBool_clone b)
-|}.
-
-Definition core_clone_impls_CloneUsize_clone (x : usize) : usize := x.
-Definition core_clone_impls_CloneU8_clone (x : u8) : u8 := x.
-Definition core_clone_impls_CloneU16_clone (x : u16) : u16 := x.
-Definition core_clone_impls_CloneU32_clone (x : u32) : u32 := x.
-Definition core_clone_impls_CloneU64_clone (x : u64) : u64 := x.
-Definition core_clone_impls_CloneU128_clone (x : u128) : u128 := x.
-
-Definition core_clone_impls_CloneIsize_clone (x : isize) : isize := x.
-Definition core_clone_impls_CloneI8_clone (x : i8) : i8 := x.
-Definition core_clone_impls_CloneI16_clone (x : i16) : i16 := x.
-Definition core_clone_impls_CloneI32_clone (x : i32) : i32 := x.
-Definition core_clone_impls_CloneI64_clone (x : i64) : i64 := x.
-Definition core_clone_impls_CloneI128_clone (x : i128) : i128 := x.
-
-Definition core_clone_CloneUsize : core_clone_Clone usize := {|
-  clone := fun x => Ok (core_clone_impls_CloneUsize_clone x)
-|}.
-
-Definition core_clone_CloneU8 : core_clone_Clone u8 := {|
-  clone := fun x => Ok (core_clone_impls_CloneU8_clone x)
-|}.
-
-Definition core_clone_CloneU16 : core_clone_Clone u16 := {|
-  clone := fun x => Ok (core_clone_impls_CloneU16_clone x)
-|}.
-
-Definition core_clone_CloneU32 : core_clone_Clone u32 := {|
-  clone := fun x => Ok (core_clone_impls_CloneU32_clone x)
-|}.
-
-Definition core_clone_CloneU64 : core_clone_Clone u64 := {|
-  clone := fun x => Ok (core_clone_impls_CloneU64_clone x)
-|}.
-
-Definition core_clone_CloneU128 : core_clone_Clone u128 := {|
-  clone := fun x => Ok (core_clone_impls_CloneU128_clone x)
-|}.
-
-Definition core_clone_CloneIsize : core_clone_Clone isize := {|
-  clone := fun x => Ok (core_clone_impls_CloneIsize_clone x)
-|}.
-
-Definition core_clone_CloneI8 : core_clone_Clone i8 := {|
-  clone := fun x => Ok (core_clone_impls_CloneI8_clone x)
-|}.
-
-Definition core_clone_CloneI16 : core_clone_Clone i16 := {|
-  clone := fun x => Ok (core_clone_impls_CloneI16_clone x)
-|}.
-
-Definition core_clone_CloneI32 : core_clone_Clone i32 := {|
-  clone := fun x => Ok (core_clone_impls_CloneI32_clone x)
-|}.
-
-Definition core_clone_CloneI64 : core_clone_Clone i64 := {|
-  clone := fun x => Ok (core_clone_impls_CloneI64_clone x)
-|}.
-
-Definition core_clone_CloneI128 : core_clone_Clone i128 := {|
-  clone := fun x => Ok (core_clone_impls_CloneI128_clone x)
-|}.
-
-(** [core::option::{core::option::Option<T>}::unwrap] *)
-Definition core_option_Option_unwrap (T : Type) (x : option T) : result T :=
-  match x with
-  | None => Fail_ Failure
-  | Some x => Ok x
-  end.
-
-(*** 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_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 {_ _}.
-
-(* 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_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 {_}.
-
-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 := Ok x.
-Definition alloc_boxed_Box_deref_mut (T : Type) (x : T) : result (T * (T -> result T)) :=
-  Ok (x, fun x => Ok 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;
-|}.
-
-
-(*** 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).
-
-Definition array_index_mut_usize (T : Type) (n : usize) (a : array T n) (i : usize) :
-  result (T * (T -> result (array T n))) :=
-  match array_index_usize T n a i with
-  | Fail_ e => Fail_ e
-  | Ok x => Ok (x, array_update_usize T n a i)
-  end.
-
-(*** 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).
-
-Definition slice_index_mut_usize (T : Type) (s : slice T) (i : usize) :
-  result (T * (T -> result (slice T))) :=
-  match slice_index_usize T s i with
-  | Fail_ e => Fail_ e
-  | Ok x => Ok (x, slice_update_usize T s i)
-  end.
-
-(*** Subslices *)
-
-Axiom array_to_slice : forall (T : Type) (n : usize) (x : array T n), result (slice T).
-Axiom array_from_slice : forall (T : Type) (n : usize) (x : array T n) (s : slice T), result (array T n).
-
-Definition array_to_slice_mut (T : Type) (n : usize) (a : array T n) :
-  result (slice T * (slice T -> result (array T n))) :=
-  match array_to_slice T n a with
-  | Fail_ e => Fail_ e
-  | Ok x => Ok (x, array_from_slice T n a)
-  end.
-
-Axiom array_subslice: forall (T : Type) (n : usize) (x : array T n) (r : core_ops_range_Range usize), result (slice T).
-Axiom array_update_subslice: forall (T : Type) (n : usize) (x : array T n) (r : core_ops_range_Range usize) (ns : slice T), result (array T n).
-
-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 => Ok (exist _ l (scalar_le_max_valid _ _ H))
-  | right _ => Fail_ Failure
-  end.
-
-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 => Ok (l ++ [x])).
-
-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 Ok (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), 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).
-
-Definition alloc_vec_Vec_index_mut_usize {T : Type} (v: alloc_vec_Vec T) (i: usize) :
-  result (T * (T -> result (alloc_vec_Vec T))) :=
-  match alloc_vec_Vec_index_usize v i with
-  | Ok x =>
-    Ok (x, alloc_vec_Vec_update_usize v i)
-  | Fail_ e => Fail_ e
-  end.
-
-(* Trait declaration: [core::slice::index::private_slice_index::Sealed] *)
-Definition core_slice_index_private_slice_index_Sealed (self : Type) := unit.
-
-(* 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 * (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_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_unchecked {_ _}.
-Arguments core_slice_index_SliceIndex_get_unchecked_mut {_ _}.
-Arguments core_slice_index_SliceIndex_index {_ _}.
-Arguments core_slice_index_SliceIndex_index_mut {_ _}.
-
-(* [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 => Ok x
-  end.
-
-(* [core::slice::index::Range:::get]: forward function *)
-Axiom core_slice_index_RangeUsize_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_RangeUsize_get_mut :
-  forall (T : Type),
-    core_ops_range_Range usize -> slice T ->
-    result (option (slice T) * (option (slice T) -> result (slice T))).
-
-(* [core::slice::index::Range::get_unchecked]: forward function *)
-Definition core_slice_index_RangeUsize_get_unchecked
-  (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_RangeUsize_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_RangeUsize_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_RangeUsize_index_mut :
-  forall (T : Type), core_ops_range_Range usize -> slice T -> result (slice T * (slice T -> result (slice T))).
-
-(* [core::slice::index::[T]::index_mut]: forward function *)
-Axiom core_slice_index_Slice_index_mut :
-  forall (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T)),
-  slice T -> Idx ->
-  result (inst.(core_slice_index_SliceIndex_Output) *
-          (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) *
-          (inst.(core_ops_index_IndexMut_indexInst).(core_ops_index_Index_Output) -> result (array T N))).
-
-(* Trait implementation: [core::slice::index::private_slice_index::Range] *)
-Definition core_slice_index_private_slice_index_SealedRangeUsizeInst
-  : core_slice_index_private_slice_index_Sealed (core_ops_range_Range usize) := tt.
-
-(* Trait implementation: [core::slice::index::Range] *)
-Definition core_slice_index_SliceIndexRangeUsizeSliceTInst (T : Type) :
-  core_slice_index_SliceIndex (core_ops_range_Range usize) (slice T) := {|
-  core_slice_index_SliceIndex_sealedInst := core_slice_index_private_slice_index_SealedRangeUsizeInst;
-  core_slice_index_SliceIndex_Output := slice T;
-  core_slice_index_SliceIndex_get := core_slice_index_RangeUsize_get T;
-  core_slice_index_SliceIndex_get_mut := core_slice_index_RangeUsize_get_mut T;
-  core_slice_index_SliceIndex_get_unchecked := core_slice_index_RangeUsize_get_unchecked T;
-  core_slice_index_SliceIndex_get_unchecked_mut := core_slice_index_RangeUsize_get_unchecked_mut T;
-  core_slice_index_SliceIndex_index := core_slice_index_RangeUsize_index T;
-  core_slice_index_SliceIndex_index_mut := core_slice_index_RangeUsize_index_mut T;
-|}.
-
-(* Trait implementation: [core::slice::index::[T]] *)
-Definition core_ops_index_IndexSliceTIInst (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::[T]] *)
-Definition core_ops_index_IndexMutSliceTIInst (T Idx : Type)
-  (inst : core_slice_index_SliceIndex Idx (slice T)) :
-  core_ops_index_IndexMut (slice T) Idx := {|
-  core_ops_index_IndexMut_indexInst := core_ops_index_IndexSliceTIInst T Idx inst;
-  core_ops_index_IndexMut_index_mut := core_slice_index_Slice_index_mut T Idx inst;
-|}.
-
-(* Trait implementation: [core::array::[T; N]] *)
-Definition core_ops_index_IndexArrayInst (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_ops_index_IndexMutArrayInst (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_ops_index_IndexArrayInst T Idx N inst.(core_ops_index_IndexMut_indexInst);
-  core_ops_index_IndexMut_index_mut := core_array_Array_index_mut T Idx N inst;
-|}.
-
-(* [core::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 * (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 * (T -> result (slice T))).
-
-(* Trait implementation: [core::slice::index::private_slice_index::usize] *)
-Definition core_slice_index_private_slice_index_SealedUsizeInst
-  : core_slice_index_private_slice_index_Sealed usize := tt.
-
-(* Trait implementation: [core::slice::index::usize] *)
-Definition core_slice_index_SliceIndexUsizeSliceTInst (T : Type) :
-  core_slice_index_SliceIndex usize (slice T) := {|
-  core_slice_index_SliceIndex_sealedInst := core_slice_index_private_slice_index_SealedUsizeInst;
-  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_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;
-|}.
-
-(* [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) *
-          (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;
-|}.
-
-(*** Theorems *)
-
-Axiom alloc_vec_Vec_index_eq : forall {a : Type} (v : alloc_vec_Vec a) (i : usize) (x : a),
-  alloc_vec_Vec_index a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i =
-    alloc_vec_Vec_index_usize v i.
-
-Axiom alloc_vec_Vec_index_mut_eq : forall {a : Type} (v : alloc_vec_Vec a) (i : usize) (x : a),
-  alloc_vec_Vec_index_mut a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i =
-    alloc_vec_Vec_index_mut_usize v i.
-
-End Primitives.