diff options
Diffstat (limited to 'tests/coq/traits')
| -rw-r--r-- | tests/coq/traits/Makefile | 23 | ||||
| -rw-r--r-- | tests/coq/traits/Primitives.v | 906 | ||||
| -rw-r--r-- | tests/coq/traits/Traits.v | 609 | ||||
| -rw-r--r-- | tests/coq/traits/_CoqProject | 7 |
4 files changed, 1545 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..99ffe070 --- /dev/null +++ b/tests/coq/traits/Primitives.v @@ -0,0 +1,906 @@ +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)). + +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). + +(** 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::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), 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_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)). + +(* [core::slice::index::Range::get_mut]: backward function 0 *) +Axiom core_slice_index_RangeUsize_get_mut_back : + forall (T : Type), core_ops_range_Range usize -> slice T -> option (slice T) -> result (slice T). + +(* [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). + +(* [core::slice::index::Range::index_mut]: backward function 0 *) +Axiom core_slice_index_RangeUsize_index_mut_back : + forall (T : Type), core_ops_range_Range usize -> slice T -> slice T -> result (slice T). + +(* [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::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_mut_back := core_slice_index_RangeUsize_get_mut_back T; + core_slice_index_SliceIndex_get_unchecked := core_slice_index_RangeUsize_get_unchecked T; + core_slice_index_SliceIndex_get_unchecked_mut := core_slice_index_RangeUsize_get_unchecked_mut T; + core_slice_index_SliceIndex_index := core_slice_index_RangeUsize_index T; + core_slice_index_SliceIndex_index_mut := core_slice_index_RangeUsize_index_mut T; + core_slice_index_SliceIndex_index_mut_back := core_slice_index_RangeUsize_index_mut_back T; +|}. + +(* Trait implementation: [core::slice::index::[T]] *) +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; + 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_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_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_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_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_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_usize v i. + +Axiom alloc_vec_Vec_index_mut_back_eq : forall {a : Type} (v : alloc_vec_Vec a) (i : usize) (x : a), + alloc_vec_Vec_index_mut_back a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i x = + alloc_vec_Vec_update_usize v i x. + +End Primitives. diff --git a/tests/coq/traits/Traits.v b/tests/coq/traits/Traits.v new file mode 100644 index 00000000..549a7116 --- /dev/null +++ b/tests/coq/traits/Traits.v @@ -0,0 +1,609 @@ +(** 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] + Source: 'src/traits.rs', lines 1:0-1:19 *) +Record BoolTrait_t (Self : Type) := mkBoolTrait_t { + BoolTrait_t_get_bool : Self -> result bool; +}. + +Arguments mkBoolTrait_t { _ }. +Arguments BoolTrait_t_get_bool { _ }. + +(** [traits::{bool}::get_bool]: forward function + Source: 'src/traits.rs', lines 12:4-12:30 *) +Definition bool_get_bool (self : bool) : result bool := + Return self. + +(** Trait implementation: [traits::{bool}] + Source: 'src/traits.rs', lines 11:0-11:23 *) +Definition traits_BoolTraitBoolInst : BoolTrait_t bool := {| + BoolTrait_t_get_bool := bool_get_bool; +|}. + +(** [traits::BoolTrait::ret_true]: forward function + Source: 'src/traits.rs', lines 6:4-6:30 *) +Definition boolTrait_ret_true + {Self : Type} (self_clause : BoolTrait_t Self) (self : Self) : result bool := + Return true +. + +(** [traits::test_bool_trait_bool]: forward function + Source: 'src/traits.rs', lines 17:0-17:44 *) +Definition test_bool_trait_bool (x : bool) : result bool := + b <- bool_get_bool x; + if b then boolTrait_ret_true traits_BoolTraitBoolInst x else Return false +. + +(** [traits::{core::option::Option<T>#1}::get_bool]: forward function + Source: 'src/traits.rs', lines 23:4-23:30 *) +Definition option_get_bool (T : Type) (self : option T) : result bool := + match self with | None => Return false | Some t => Return true end +. + +(** Trait implementation: [traits::{core::option::Option<T>#1}] + Source: 'src/traits.rs', lines 22:0-22:31 *) +Definition traits_BoolTraitcoreoptionOptionTInst (T : Type) : BoolTrait_t + (option T) := {| + BoolTrait_t_get_bool := option_get_bool T; +|}. + +(** [traits::test_bool_trait_option]: forward function + Source: 'src/traits.rs', lines 31:0-31:54 *) +Definition test_bool_trait_option (T : Type) (x : option T) : result bool := + b <- option_get_bool T x; + if b + then boolTrait_ret_true (traits_BoolTraitcoreoptionOptionTInst T) x + else Return false +. + +(** [traits::test_bool_trait]: forward function + Source: 'src/traits.rs', lines 35:0-35:50 *) +Definition test_bool_trait + (T : Type) (boolTraitTInst : BoolTrait_t T) (x : T) : result bool := + boolTraitTInst.(BoolTrait_t_get_bool) x +. + +(** Trait declaration: [traits::ToU64] + Source: 'src/traits.rs', lines 39:0-39:15 *) +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 + Source: 'src/traits.rs', lines 44:4-44:26 *) +Definition u64_to_u64 (self : u64) : result u64 := + Return self. + +(** Trait implementation: [traits::{u64#2}] + Source: 'src/traits.rs', lines 43:0-43:18 *) +Definition traits_ToU64U64Inst : ToU64_t u64 := {| + ToU64_t_to_u64 := u64_to_u64; +|}. + +(** [traits::{(A, A)#3}::to_u64]: forward function + Source: 'src/traits.rs', lines 50:4-50:26 *) +Definition pair_to_u64 + (A : Type) (toU64AInst : ToU64_t A) (self : (A * A)) : result u64 := + let (t, t0) := self in + i <- toU64AInst.(ToU64_t_to_u64) t; + i0 <- toU64AInst.(ToU64_t_to_u64) t0; + u64_add i i0 +. + +(** Trait implementation: [traits::{(A, A)#3}] + Source: 'src/traits.rs', lines 49:0-49:31 *) +Definition traits_ToU64TupleAAInst (A : Type) (toU64AInst : ToU64_t A) : + ToU64_t (A * A) := {| + ToU64_t_to_u64 := pair_to_u64 A toU64AInst; +|}. + +(** [traits::f]: forward function + Source: 'src/traits.rs', lines 55:0-55:36 *) +Definition f (T : Type) (toU64TInst : ToU64_t T) (x : (T * T)) : result u64 := + pair_to_u64 T toU64TInst x +. + +(** [traits::g]: forward function + Source: 'src/traits.rs', lines 59:0-61:18 *) +Definition g + (T : Type) (toU64TupleTTInst : ToU64_t (T * T)) (x : (T * T)) : result u64 := + toU64TupleTTInst.(ToU64_t_to_u64) x +. + +(** [traits::h0]: forward function + Source: 'src/traits.rs', lines 66:0-66:24 *) +Definition h0 (x : u64) : result u64 := + u64_to_u64 x. + +(** [traits::Wrapper] + Source: 'src/traits.rs', lines 70:0-70:21 *) +Record Wrapper_t (T : Type) := mkWrapper_t { wrapper_x : T; }. + +Arguments mkWrapper_t { _ }. +Arguments wrapper_x { _ }. + +(** [traits::{traits::Wrapper<T>#4}::to_u64]: forward function + Source: 'src/traits.rs', lines 75:4-75:26 *) +Definition wrapper_to_u64 + (T : Type) (toU64TInst : ToU64_t T) (self : Wrapper_t T) : result u64 := + toU64TInst.(ToU64_t_to_u64) self.(wrapper_x) +. + +(** Trait implementation: [traits::{traits::Wrapper<T>#4}] + Source: 'src/traits.rs', lines 74:0-74:35 *) +Definition traits_ToU64traitsWrapperTInst (T : Type) (toU64TInst : ToU64_t T) : + ToU64_t (Wrapper_t T) := {| + ToU64_t_to_u64 := wrapper_to_u64 T toU64TInst; +|}. + +(** [traits::h1]: forward function + Source: 'src/traits.rs', lines 80:0-80:33 *) +Definition h1 (x : Wrapper_t u64) : result u64 := + wrapper_to_u64 u64 traits_ToU64U64Inst x +. + +(** [traits::h2]: forward function + Source: 'src/traits.rs', lines 84:0-84:41 *) +Definition h2 + (T : Type) (toU64TInst : ToU64_t T) (x : Wrapper_t T) : result u64 := + wrapper_to_u64 T toU64TInst x +. + +(** Trait declaration: [traits::ToType] + Source: 'src/traits.rs', lines 88:0-88:19 *) +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 + Source: 'src/traits.rs', lines 93:4-93:28 *) +Definition u64_to_type (self : u64) : result bool := + Return (self s> 0%u64). + +(** Trait implementation: [traits::{u64#5}] + Source: 'src/traits.rs', lines 92:0-92:25 *) +Definition traits_ToTypeU64BoolInst : ToType_t u64 bool := {| + ToType_t_to_type := u64_to_type; +|}. + +(** Trait declaration: [traits::OfType] + Source: 'src/traits.rs', lines 98:0-98:16 *) +Record OfType_t (Self : Type) := mkOfType_t { + OfType_t_of_type : forall (T : Type) (toTypeTSelfInst : ToType_t T Self), T + -> result Self; +}. + +Arguments mkOfType_t { _ }. +Arguments OfType_t_of_type { _ }. + +(** [traits::h3]: forward function + Source: 'src/traits.rs', lines 104:0-104:50 *) +Definition h3 + (T1 T2 : Type) (ofTypeT1Inst : OfType_t T1) (toTypeT2T1Inst : ToType_t T2 T1) + (y : T2) : + result T1 + := + ofTypeT1Inst.(OfType_t_of_type) T2 toTypeT2T1Inst y +. + +(** Trait declaration: [traits::OfTypeBis] + Source: 'src/traits.rs', lines 109:0-109:36 *) +Record OfTypeBis_t (Self T : Type) := mkOfTypeBis_t { + OfTypeBis_tOfTypeBis_t_ToTypeTSelfInst : ToType_t T Self; + OfTypeBis_t_of_type : T -> result Self; +}. + +Arguments mkOfTypeBis_t { _ _ }. +Arguments OfTypeBis_tOfTypeBis_t_ToTypeTSelfInst { _ _ }. +Arguments OfTypeBis_t_of_type { _ _ }. + +(** [traits::h4]: forward function + Source: 'src/traits.rs', lines 118:0-118:57 *) +Definition h4 + (T1 T2 : Type) (ofTypeBisT1T2Inst : OfTypeBis_t T1 T2) (toTypeT2T1Inst : + ToType_t T2 T1) (y : T2) : + result T1 + := + ofTypeBisT1T2Inst.(OfTypeBis_t_of_type) y +. + +(** [traits::TestType] + Source: 'src/traits.rs', lines 122:0-122:22 *) +Record TestType_t (T : Type) := mkTestType_t { testType_0 : T; }. + +Arguments mkTestType_t { _ }. +Arguments testType_0 { _ }. + +(** [traits::{traits::TestType<T>#6}::test::TestType1] + Source: 'src/traits.rs', lines 127:8-127:24 *) +Record TestType_test_TestType1_t := +mkTestType_test_TestType1_t { + testType_test_TestType1_0 : u64; +} +. + +(** Trait declaration: [traits::{traits::TestType<T>#6}::test::TestTrait] + Source: 'src/traits.rs', lines 128:8-128:23 *) +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::{traits::TestType<T>#6}::test::{traits::{traits::TestType<T>#6}::test::TestType1}::test]: forward function + Source: 'src/traits.rs', lines 139:12-139:34 *) +Definition testType_test_TestType1_test + (self : TestType_test_TestType1_t) : result bool := + Return (self.(testType_test_TestType1_0) s> 1%u64) +. + +(** Trait implementation: [traits::{traits::TestType<T>#6}::test::{traits::{traits::TestType<T>#6}::test::TestType1}] + Source: 'src/traits.rs', lines 138:8-138:36 *) +Definition traits_TestType_test_TestTraittraitstraitsTestTypeTtestTestType1Inst + : TestType_test_TestTrait_t TestType_test_TestType1_t := {| + TestType_test_TestTrait_t_test := testType_test_TestType1_test; +|}. + +(** [traits::{traits::TestType<T>#6}::test]: forward function + Source: 'src/traits.rs', lines 126:4-126:36 *) +Definition testType_test + (T : Type) (toU64TInst : ToU64_t T) (self : TestType_t T) (x : T) : + result bool + := + x0 <- toU64TInst.(ToU64_t_to_u64) x; + if x0 s> 0%u64 + then testType_test_TestType1_test {| testType_test_TestType1_0 := 0%u64 |} + else Return false +. + +(** [traits::BoolWrapper] + Source: 'src/traits.rs', lines 150:0-150:22 *) +Record BoolWrapper_t := mkBoolWrapper_t { boolWrapper_0 : bool; }. + +(** [traits::{traits::BoolWrapper#7}::to_type]: forward function + Source: 'src/traits.rs', lines 156:4-156:25 *) +Definition boolWrapper_to_type + (T : Type) (toTypeBoolTInst : ToType_t bool T) (self : BoolWrapper_t) : + result T + := + toTypeBoolTInst.(ToType_t_to_type) self.(boolWrapper_0) +. + +(** Trait implementation: [traits::{traits::BoolWrapper#7}] + Source: 'src/traits.rs', lines 152:0-152:33 *) +Definition traits_ToTypetraitsBoolWrapperTInst (T : Type) (toTypeBoolTInst : + ToType_t bool T) : ToType_t BoolWrapper_t T := {| + ToType_t_to_type := boolWrapper_to_type T toTypeBoolTInst; +|}. + +(** [traits::WithConstTy::LEN2] + Source: 'src/traits.rs', lines 164:4-164:21 *) +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] + Source: 'src/traits.rs', lines 161:0-161:39 *) +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] + Source: 'src/traits.rs', lines 175:4-175:21 *) +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 ()) + Source: 'src/traits.rs', lines 180:4-180:39 *) +Definition bool_f (i : u64) (a : array u8 32%usize) : result u64 := + Return i. + +(** Trait implementation: [traits::{bool#8}] + Source: 'src/traits.rs', lines 174:0-174:29 *) +Definition traits_WithConstTyBool32Inst : 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 := traits_ToU64U64Inst; + WithConstTy_t_f := bool_f; +|}. + +(** [traits::use_with_const_ty1]: forward function + Source: 'src/traits.rs', lines 183:0-183:75 *) +Definition use_with_const_ty1 + (H : Type) (LEN : usize) (withConstTyHLENInst : WithConstTy_t H LEN) : + result usize + := + let i := withConstTyHLENInst.(WithConstTy_tWithConstTy_t_LEN1) in Return i +. + +(** [traits::use_with_const_ty2]: forward function + Source: 'src/traits.rs', lines 187:0-187:73 *) +Definition use_with_const_ty2 + (H : Type) (LEN : usize) (withConstTyHLENInst : WithConstTy_t H LEN) + (w : withConstTyHLENInst.(WithConstTy_tWithConstTy_t_W)) : + result unit + := + Return tt +. + +(** [traits::use_with_const_ty3]: forward function + Source: 'src/traits.rs', lines 189:0-189:80 *) +Definition use_with_const_ty3 + (H : Type) (LEN : usize) (withConstTyHLENInst : WithConstTy_t H LEN) + (x : withConstTyHLENInst.(WithConstTy_tWithConstTy_t_W)) : + result u64 + := + withConstTyHLENInst.(WithConstTy_tWithConstTy_t_W_clause_0).(ToU64_t_to_u64) + x +. + +(** [traits::test_where1]: forward function + Source: 'src/traits.rs', lines 193:0-193:40 *) +Definition test_where1 (T : Type) (_x : T) : result unit := + Return tt. + +(** [traits::test_where2]: forward function + Source: 'src/traits.rs', lines 194:0-194:57 *) +Definition test_where2 + (T : Type) (withConstTyT32Inst : WithConstTy_t T 32%usize) (_x : u32) : + result unit + := + Return tt +. + +(** Trait declaration: [traits::ParentTrait0] + Source: 'src/traits.rs', lines 200:0-200:22 *) +Record ParentTrait0_t (Self : Type) := mkParentTrait0_t { + ParentTrait0_tParentTrait0_t_W : Type; + ParentTrait0_t_get_name : Self -> result string; + 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] + Source: 'src/traits.rs', lines 205:0-205:22 *) +Record ParentTrait1_t (Self : Type) := mkParentTrait1_t{}. + +Arguments mkParentTrait1_t { _ }. + +(** Trait declaration: [traits::ChildTrait] + Source: 'src/traits.rs', lines 206:0-206:49 *) +Record ChildTrait_t (Self : Type) := mkChildTrait_t { + ChildTrait_tChildTrait_t_ParentTrait0SelfInst : ParentTrait0_t Self; + ChildTrait_tChildTrait_t_ParentTrait1SelfInst : ParentTrait1_t Self; +}. + +Arguments mkChildTrait_t { _ }. +Arguments ChildTrait_tChildTrait_t_ParentTrait0SelfInst { _ }. +Arguments ChildTrait_tChildTrait_t_ParentTrait1SelfInst { _ }. + +(** [traits::test_child_trait1]: forward function + Source: 'src/traits.rs', lines 209:0-209:56 *) +Definition test_child_trait1 + (T : Type) (childTraitTInst : ChildTrait_t T) (x : T) : result string := + childTraitTInst.(ChildTrait_tChildTrait_t_ParentTrait0SelfInst).(ParentTrait0_t_get_name) + x +. + +(** [traits::test_child_trait2]: forward function + Source: 'src/traits.rs', lines 213:0-213:54 *) +Definition test_child_trait2 + (T : Type) (childTraitTInst : ChildTrait_t T) (x : T) : + result + childTraitTInst.(ChildTrait_tChildTrait_t_ParentTrait0SelfInst).(ParentTrait0_tParentTrait0_t_W) + := + childTraitTInst.(ChildTrait_tChildTrait_t_ParentTrait0SelfInst).(ParentTrait0_t_get_w) + x +. + +(** [traits::order1]: forward function + Source: 'src/traits.rs', lines 219:0-219:59 *) +Definition order1 + (T U : Type) (parentTrait0TInst : ParentTrait0_t T) (parentTrait0UInst : + ParentTrait0_t U) : + result unit + := + Return tt +. + +(** Trait declaration: [traits::ChildTrait1] + Source: 'src/traits.rs', lines 222:0-222:35 *) +Record ChildTrait1_t (Self : Type) := mkChildTrait1_t { + ChildTrait1_tChildTrait1_t_ParentTrait1SelfInst : ParentTrait1_t Self; +}. + +Arguments mkChildTrait1_t { _ }. +Arguments ChildTrait1_tChildTrait1_t_ParentTrait1SelfInst { _ }. + +(** Trait implementation: [traits::{usize#9}] + Source: 'src/traits.rs', lines 224:0-224:27 *) +Definition traits_ParentTrait1UsizeInst : ParentTrait1_t usize + := mkParentTrait1_t. + +(** Trait implementation: [traits::{usize#10}] + Source: 'src/traits.rs', lines 225:0-225:26 *) +Definition traits_ChildTrait1UsizeInst : ChildTrait1_t usize := {| + ChildTrait1_tChildTrait1_t_ParentTrait1SelfInst := + traits_ParentTrait1UsizeInst; +|}. + +(** Trait declaration: [traits::Iterator] + Source: 'src/traits.rs', lines 229:0-229:18 *) +Record Iterator_t (Self : Type) := mkIterator_t { + Iterator_tIterator_t_Item : Type; +}. + +Arguments mkIterator_t { _ }. +Arguments Iterator_tIterator_t_Item { _ }. + +(** Trait declaration: [traits::IntoIterator] + Source: 'src/traits.rs', lines 233:0-233:22 *) +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] + Source: 'src/traits.rs', lines 250:0-250:21 *) +Record FromResidual_t (Self T : Type) := mkFromResidual_t{}. + +Arguments mkFromResidual_t { _ _ }. + +(** Trait declaration: [traits::Try] + Source: 'src/traits.rs', lines 246:0-246:48 *) +Record Try_t (Self : Type) := mkTry_t { + Try_tTry_t_Residual : Type; + Try_tTry_t_FromResidualSelftraitsTrySelfResidualInst : FromResidual_t Self + Try_tTry_t_Residual; +}. + +Arguments mkTry_t { _ }. +Arguments Try_tTry_t_Residual { _ }. +Arguments Try_tTry_t_FromResidualSelftraitsTrySelfResidualInst { _ }. + +(** Trait declaration: [traits::WithTarget] + Source: 'src/traits.rs', lines 252:0-252:20 *) +Record WithTarget_t (Self : Type) := mkWithTarget_t { + WithTarget_tWithTarget_t_Target : Type; +}. + +Arguments mkWithTarget_t { _ }. +Arguments WithTarget_tWithTarget_t_Target { _ }. + +(** Trait declaration: [traits::ParentTrait2] + Source: 'src/traits.rs', lines 256:0-256:22 *) +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] + Source: 'src/traits.rs', lines 260:0-260:35 *) +Record ChildTrait2_t (Self : Type) := mkChildTrait2_t { + ChildTrait2_tChildTrait2_t_ParentTrait2SelfInst : ParentTrait2_t Self; + ChildTrait2_t_convert : + (ChildTrait2_tChildTrait2_t_ParentTrait2SelfInst).(ParentTrait2_tParentTrait2_t_U) + -> result + (ChildTrait2_tChildTrait2_t_ParentTrait2SelfInst).(ParentTrait2_tParentTrait2_t_U_clause_0).(WithTarget_tWithTarget_t_Target); +}. + +Arguments mkChildTrait2_t { _ }. +Arguments ChildTrait2_tChildTrait2_t_ParentTrait2SelfInst { _ }. +Arguments ChildTrait2_t_convert { _ }. + +(** Trait implementation: [traits::{u32#11}] + Source: 'src/traits.rs', lines 264:0-264:23 *) +Definition traits_WithTargetU32Inst : WithTarget_t u32 := {| + WithTarget_tWithTarget_t_Target := u32; +|}. + +(** Trait implementation: [traits::{u32#12}] + Source: 'src/traits.rs', lines 268:0-268:25 *) +Definition traits_ParentTrait2U32Inst : ParentTrait2_t u32 := {| + ParentTrait2_tParentTrait2_t_U := u32; + ParentTrait2_tParentTrait2_t_U_clause_0 := traits_WithTargetU32Inst; +|}. + +(** [traits::{u32#13}::convert]: forward function + Source: 'src/traits.rs', lines 273:4-273:29 *) +Definition u32_convert (x : u32) : result u32 := + Return x. + +(** Trait implementation: [traits::{u32#13}] + Source: 'src/traits.rs', lines 272:0-272:24 *) +Definition traits_ChildTrait2U32Inst : ChildTrait2_t u32 := {| + ChildTrait2_tChildTrait2_t_ParentTrait2SelfInst := + traits_ParentTrait2U32Inst; + ChildTrait2_t_convert := u32_convert; +|}. + +(** Trait declaration: [traits::CFnOnce] + Source: 'src/traits.rs', lines 286:0-286:23 *) +Record CFnOnce_t (Self Args : Type) := mkCFnOnce_t { + CFnOnce_tCFnOnce_t_Output : Type; + CFnOnce_t_call_once : Self -> Args -> result CFnOnce_tCFnOnce_t_Output; +}. + +Arguments mkCFnOnce_t { _ _ }. +Arguments CFnOnce_tCFnOnce_t_Output { _ _ }. +Arguments CFnOnce_t_call_once { _ _ }. + +(** Trait declaration: [traits::CFnMut] + Source: 'src/traits.rs', lines 292:0-292:37 *) +Record CFnMut_t (Self Args : Type) := mkCFnMut_t { + CFnMut_tCFnMut_t_CFnOnceSelfArgsInst : CFnOnce_t Self Args; + CFnMut_t_call_mut : Self -> Args -> result + (CFnMut_tCFnMut_t_CFnOnceSelfArgsInst).(CFnOnce_tCFnOnce_t_Output); + CFnMut_t_call_mut_back : Self -> Args -> + (CFnMut_tCFnMut_t_CFnOnceSelfArgsInst).(CFnOnce_tCFnOnce_t_Output) -> + result Self; +}. + +Arguments mkCFnMut_t { _ _ }. +Arguments CFnMut_tCFnMut_t_CFnOnceSelfArgsInst { _ _ }. +Arguments CFnMut_t_call_mut { _ _ }. +Arguments CFnMut_t_call_mut_back { _ _ }. + +(** Trait declaration: [traits::CFn] + Source: 'src/traits.rs', lines 296:0-296:33 *) +Record CFn_t (Self Args : Type) := mkCFn_t { + CFn_tCFn_t_CFnMutSelfArgsInst : CFnMut_t Self Args; + CFn_t_call_mut : Self -> Args -> result + (CFn_tCFn_t_CFnMutSelfArgsInst).(CFnMut_tCFnMut_t_CFnOnceSelfArgsInst).(CFnOnce_tCFnOnce_t_Output); +}. + +Arguments mkCFn_t { _ _ }. +Arguments CFn_tCFn_t_CFnMutSelfArgsInst { _ _ }. +Arguments CFn_t_call_mut { _ _ }. + +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 |