diff options
Diffstat (limited to 'tests/coq/arrays')
| -rw-r--r-- | tests/coq/arrays/Arrays.v | 519 | ||||
| -rw-r--r-- | tests/coq/arrays/Makefile | 23 | ||||
| -rw-r--r-- | tests/coq/arrays/Primitives.v | 899 | ||||
| -rw-r--r-- | tests/coq/arrays/_CoqProject | 7 |
4 files changed, 1448 insertions, 0 deletions
diff --git a/tests/coq/arrays/Arrays.v b/tests/coq/arrays/Arrays.v new file mode 100644 index 00000000..3a6fb02f --- /dev/null +++ b/tests/coq/arrays/Arrays.v @@ -0,0 +1,519 @@ +(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *) +(** [arrays] *) +Require Import Primitives. +Import Primitives. +Require Import Coq.ZArith.ZArith. +Require Import List. +Import ListNotations. +Local Open Scope Primitives_scope. +Module Arrays. + +(** [arrays::AB] + Source: 'src/arrays.rs', lines 3:0-3:11 *) +Inductive AB_t := | AB_A : AB_t | AB_B : AB_t. + +(** [arrays::incr]: + Source: 'src/arrays.rs', lines 8:0-8:24 *) +Definition incr (x : u32) : result u32 := + u32_add x 1%u32. + +(** [arrays::array_to_shared_slice_]: + Source: 'src/arrays.rs', lines 16:0-16:53 *) +Definition array_to_shared_slice_ + (T : Type) (s : array T 32%usize) : result (slice T) := + array_to_slice T 32%usize s +. + +(** [arrays::array_to_mut_slice_]: + Source: 'src/arrays.rs', lines 21:0-21:58 *) +Definition array_to_mut_slice_ + (T : Type) (s : array T 32%usize) : + result ((slice T) * (slice T -> result (array T 32%usize))) + := + p <- array_to_slice_mut T 32%usize s; + let (s1, to_slice_mut_back) := p in + Return (s1, to_slice_mut_back) +. + +(** [arrays::array_len]: + Source: 'src/arrays.rs', lines 25:0-25:40 *) +Definition array_len (T : Type) (s : array T 32%usize) : result usize := + s1 <- array_to_slice T 32%usize s; let i := slice_len T s1 in Return i +. + +(** [arrays::shared_array_len]: + Source: 'src/arrays.rs', lines 29:0-29:48 *) +Definition shared_array_len (T : Type) (s : array T 32%usize) : result usize := + s1 <- array_to_slice T 32%usize s; let i := slice_len T s1 in Return i +. + +(** [arrays::shared_slice_len]: + Source: 'src/arrays.rs', lines 33:0-33:44 *) +Definition shared_slice_len (T : Type) (s : slice T) : result usize := + let i := slice_len T s in Return i +. + +(** [arrays::index_array_shared]: + Source: 'src/arrays.rs', lines 37:0-37:57 *) +Definition index_array_shared + (T : Type) (s : array T 32%usize) (i : usize) : result T := + array_index_usize T 32%usize s i +. + +(** [arrays::index_array_u32]: + Source: 'src/arrays.rs', lines 44:0-44:53 *) +Definition index_array_u32 (s : array u32 32%usize) (i : usize) : result u32 := + array_index_usize u32 32%usize s i +. + +(** [arrays::index_array_copy]: + Source: 'src/arrays.rs', lines 48:0-48:45 *) +Definition index_array_copy (x : array u32 32%usize) : result u32 := + array_index_usize u32 32%usize x 0%usize +. + +(** [arrays::index_mut_array]: + Source: 'src/arrays.rs', lines 52:0-52:62 *) +Definition index_mut_array + (T : Type) (s : array T 32%usize) (i : usize) : + result (T * (T -> result (array T 32%usize))) + := + p <- array_index_mut_usize T 32%usize s i; + let (t, index_mut_back) := p in + Return (t, index_mut_back) +. + +(** [arrays::index_slice]: + Source: 'src/arrays.rs', lines 56:0-56:46 *) +Definition index_slice (T : Type) (s : slice T) (i : usize) : result T := + slice_index_usize T s i +. + +(** [arrays::index_mut_slice]: + Source: 'src/arrays.rs', lines 60:0-60:58 *) +Definition index_mut_slice + (T : Type) (s : slice T) (i : usize) : + result (T * (T -> result (slice T))) + := + p <- slice_index_mut_usize T s i; + let (t, index_mut_back) := p in + Return (t, index_mut_back) +. + +(** [arrays::slice_subslice_shared_]: + Source: 'src/arrays.rs', lines 64:0-64:70 *) +Definition slice_subslice_shared_ + (x : slice u32) (y : usize) (z : usize) : result (slice u32) := + core_slice_index_Slice_index u32 (core_ops_range_Range usize) + (core_slice_index_SliceIndexRangeUsizeSliceTInst u32) x + {| core_ops_range_Range_start := y; core_ops_range_Range_end_ := z |} +. + +(** [arrays::slice_subslice_mut_]: + Source: 'src/arrays.rs', lines 68:0-68:75 *) +Definition slice_subslice_mut_ + (x : slice u32) (y : usize) (z : usize) : + result ((slice u32) * (slice u32 -> result (slice u32))) + := + p <- + core_slice_index_Slice_index_mut u32 (core_ops_range_Range usize) + (core_slice_index_SliceIndexRangeUsizeSliceTInst u32) x + {| core_ops_range_Range_start := y; core_ops_range_Range_end_ := z |}; + let (s, index_mut_back) := p in + Return (s, index_mut_back) +. + +(** [arrays::array_to_slice_shared_]: + Source: 'src/arrays.rs', lines 72:0-72:54 *) +Definition array_to_slice_shared_ + (x : array u32 32%usize) : result (slice u32) := + array_to_slice u32 32%usize x +. + +(** [arrays::array_to_slice_mut_]: + Source: 'src/arrays.rs', lines 76:0-76:59 *) +Definition array_to_slice_mut_ + (x : array u32 32%usize) : + result ((slice u32) * (slice u32 -> result (array u32 32%usize))) + := + p <- array_to_slice_mut u32 32%usize x; + let (s, to_slice_mut_back) := p in + Return (s, to_slice_mut_back) +. + +(** [arrays::array_subslice_shared_]: + Source: 'src/arrays.rs', lines 80:0-80:74 *) +Definition array_subslice_shared_ + (x : array u32 32%usize) (y : usize) (z : usize) : result (slice u32) := + core_array_Array_index u32 (core_ops_range_Range usize) 32%usize + (core_ops_index_IndexSliceTIInst u32 (core_ops_range_Range usize) + (core_slice_index_SliceIndexRangeUsizeSliceTInst u32)) x + {| core_ops_range_Range_start := y; core_ops_range_Range_end_ := z |} +. + +(** [arrays::array_subslice_mut_]: + Source: 'src/arrays.rs', lines 84:0-84:79 *) +Definition array_subslice_mut_ + (x : array u32 32%usize) (y : usize) (z : usize) : + result ((slice u32) * (slice u32 -> result (array u32 32%usize))) + := + p <- + core_array_Array_index_mut u32 (core_ops_range_Range usize) 32%usize + (core_ops_index_IndexMutSliceTIInst u32 (core_ops_range_Range usize) + (core_slice_index_SliceIndexRangeUsizeSliceTInst u32)) x + {| core_ops_range_Range_start := y; core_ops_range_Range_end_ := z |}; + let (s, index_mut_back) := p in + Return (s, index_mut_back) +. + +(** [arrays::index_slice_0]: + Source: 'src/arrays.rs', lines 88:0-88:38 *) +Definition index_slice_0 (T : Type) (s : slice T) : result T := + slice_index_usize T s 0%usize +. + +(** [arrays::index_array_0]: + Source: 'src/arrays.rs', lines 92:0-92:42 *) +Definition index_array_0 (T : Type) (s : array T 32%usize) : result T := + array_index_usize T 32%usize s 0%usize +. + +(** [arrays::index_index_array]: + Source: 'src/arrays.rs', lines 103:0-103:71 *) +Definition index_index_array + (s : array (array u32 32%usize) 32%usize) (i : usize) (j : usize) : + result u32 + := + a <- array_index_usize (array u32 32%usize) 32%usize s i; + array_index_usize u32 32%usize a j +. + +(** [arrays::update_update_array]: + Source: 'src/arrays.rs', lines 114:0-114:70 *) +Definition update_update_array + (s : array (array u32 32%usize) 32%usize) (i : usize) (j : usize) : + result unit + := + p <- array_index_mut_usize (array u32 32%usize) 32%usize s i; + let (a, index_mut_back) := p in + p1 <- array_index_mut_usize u32 32%usize a j; + let (_, index_mut_back1) := p1 in + a1 <- index_mut_back1 0%u32; + _ <- index_mut_back a1; + Return tt +. + +(** [arrays::array_local_deep_copy]: + Source: 'src/arrays.rs', lines 118:0-118:43 *) +Definition array_local_deep_copy (x : array u32 32%usize) : result unit := + Return tt +. + +(** [arrays::take_array]: + Source: 'src/arrays.rs', lines 122:0-122:30 *) +Definition take_array (a : array u32 2%usize) : result unit := + Return tt. + +(** [arrays::take_array_borrow]: + Source: 'src/arrays.rs', lines 123:0-123:38 *) +Definition take_array_borrow (a : array u32 2%usize) : result unit := + Return tt +. + +(** [arrays::take_slice]: + Source: 'src/arrays.rs', lines 124:0-124:28 *) +Definition take_slice (s : slice u32) : result unit := + Return tt. + +(** [arrays::take_mut_slice]: + Source: 'src/arrays.rs', lines 125:0-125:36 *) +Definition take_mut_slice (s : slice u32) : result (slice u32) := + Return s. + +(** [arrays::const_array]: + Source: 'src/arrays.rs', lines 127:0-127:32 *) +Definition const_array : result (array u32 2%usize) := + Return (mk_array u32 2%usize [ 0%u32; 0%u32 ]) +. + +(** [arrays::const_slice]: + Source: 'src/arrays.rs', lines 131:0-131:20 *) +Definition const_slice : result unit := + _ <- array_to_slice u32 2%usize (mk_array u32 2%usize [ 0%u32; 0%u32 ]); + Return tt +. + +(** [arrays::take_all]: + Source: 'src/arrays.rs', lines 141:0-141:17 *) +Definition take_all : result unit := + _ <- take_array (mk_array u32 2%usize [ 0%u32; 0%u32 ]); + _ <- take_array (mk_array u32 2%usize [ 0%u32; 0%u32 ]); + _ <- take_array_borrow (mk_array u32 2%usize [ 0%u32; 0%u32 ]); + s <- array_to_slice u32 2%usize (mk_array u32 2%usize [ 0%u32; 0%u32 ]); + _ <- take_slice s; + p <- array_to_slice_mut u32 2%usize (mk_array u32 2%usize [ 0%u32; 0%u32 ]); + let (s1, to_slice_mut_back) := p in + s2 <- take_mut_slice s1; + _ <- to_slice_mut_back s2; + Return tt +. + +(** [arrays::index_array]: + Source: 'src/arrays.rs', lines 155:0-155:38 *) +Definition index_array (x : array u32 2%usize) : result u32 := + array_index_usize u32 2%usize x 0%usize +. + +(** [arrays::index_array_borrow]: + Source: 'src/arrays.rs', lines 158:0-158:46 *) +Definition index_array_borrow (x : array u32 2%usize) : result u32 := + array_index_usize u32 2%usize x 0%usize +. + +(** [arrays::index_slice_u32_0]: + Source: 'src/arrays.rs', lines 162:0-162:42 *) +Definition index_slice_u32_0 (x : slice u32) : result u32 := + slice_index_usize u32 x 0%usize +. + +(** [arrays::index_mut_slice_u32_0]: + Source: 'src/arrays.rs', lines 166:0-166:50 *) +Definition index_mut_slice_u32_0 + (x : slice u32) : result (u32 * (slice u32)) := + i <- slice_index_usize u32 x 0%usize; Return (i, x) +. + +(** [arrays::index_all]: + Source: 'src/arrays.rs', lines 170:0-170:25 *) +Definition index_all : result u32 := + i <- index_array (mk_array u32 2%usize [ 0%u32; 0%u32 ]); + i1 <- index_array (mk_array u32 2%usize [ 0%u32; 0%u32 ]); + i2 <- u32_add i i1; + i3 <- index_array_borrow (mk_array u32 2%usize [ 0%u32; 0%u32 ]); + i4 <- u32_add i2 i3; + s <- array_to_slice u32 2%usize (mk_array u32 2%usize [ 0%u32; 0%u32 ]); + i5 <- index_slice_u32_0 s; + i6 <- u32_add i4 i5; + p <- array_to_slice_mut u32 2%usize (mk_array u32 2%usize [ 0%u32; 0%u32 ]); + let (s1, to_slice_mut_back) := p in + p1 <- index_mut_slice_u32_0 s1; + let (i7, s2) := p1 in + i8 <- u32_add i6 i7; + _ <- to_slice_mut_back s2; + Return i8 +. + +(** [arrays::update_array]: + Source: 'src/arrays.rs', lines 184:0-184:36 *) +Definition update_array (x : array u32 2%usize) : result unit := + p <- array_index_mut_usize u32 2%usize x 0%usize; + let (_, index_mut_back) := p in + _ <- index_mut_back 1%u32; + Return tt +. + +(** [arrays::update_array_mut_borrow]: + Source: 'src/arrays.rs', lines 187:0-187:48 *) +Definition update_array_mut_borrow + (x : array u32 2%usize) : result (array u32 2%usize) := + p <- array_index_mut_usize u32 2%usize x 0%usize; + let (_, index_mut_back) := p in + index_mut_back 1%u32 +. + +(** [arrays::update_mut_slice]: + Source: 'src/arrays.rs', lines 190:0-190:38 *) +Definition update_mut_slice (x : slice u32) : result (slice u32) := + p <- slice_index_mut_usize u32 x 0%usize; + let (_, index_mut_back) := p in + index_mut_back 1%u32 +. + +(** [arrays::update_all]: + Source: 'src/arrays.rs', lines 194:0-194:19 *) +Definition update_all : result unit := + _ <- update_array (mk_array u32 2%usize [ 0%u32; 0%u32 ]); + _ <- update_array (mk_array u32 2%usize [ 0%u32; 0%u32 ]); + a <- update_array_mut_borrow (mk_array u32 2%usize [ 0%u32; 0%u32 ]); + p <- array_to_slice_mut u32 2%usize a; + let (s, to_slice_mut_back) := p in + s1 <- update_mut_slice s; + _ <- to_slice_mut_back s1; + Return tt +. + +(** [arrays::range_all]: + Source: 'src/arrays.rs', lines 205:0-205:18 *) +Definition range_all : result unit := + p <- + core_array_Array_index_mut u32 (core_ops_range_Range usize) 4%usize + (core_ops_index_IndexMutSliceTIInst u32 (core_ops_range_Range usize) + (core_slice_index_SliceIndexRangeUsizeSliceTInst u32)) + (mk_array u32 4%usize [ 0%u32; 0%u32; 0%u32; 0%u32 ]) + {| + core_ops_range_Range_start := 1%usize; + core_ops_range_Range_end_ := 3%usize + |}; + let (s, index_mut_back) := p in + s1 <- update_mut_slice s; + _ <- index_mut_back s1; + Return tt +. + +(** [arrays::deref_array_borrow]: + Source: 'src/arrays.rs', lines 214:0-214:46 *) +Definition deref_array_borrow (x : array u32 2%usize) : result u32 := + array_index_usize u32 2%usize x 0%usize +. + +(** [arrays::deref_array_mut_borrow]: + Source: 'src/arrays.rs', lines 219:0-219:54 *) +Definition deref_array_mut_borrow + (x : array u32 2%usize) : result (u32 * (array u32 2%usize)) := + i <- array_index_usize u32 2%usize x 0%usize; Return (i, x) +. + +(** [arrays::take_array_t]: + Source: 'src/arrays.rs', lines 227:0-227:31 *) +Definition take_array_t (a : array AB_t 2%usize) : result unit := + Return tt. + +(** [arrays::non_copyable_array]: + Source: 'src/arrays.rs', lines 229:0-229:27 *) +Definition non_copyable_array : result unit := + _ <- take_array_t (mk_array AB_t 2%usize [ AB_A; AB_B ]); Return tt +. + +(** [arrays::sum]: loop 0: + Source: 'src/arrays.rs', lines 242:0-250:1 *) +Fixpoint sum_loop + (n : nat) (s : slice u32) (sum1 : u32) (i : usize) : result u32 := + match n with + | O => Fail_ OutOfFuel + | S n1 => + let i1 := slice_len u32 s in + if i s< i1 + then ( + i2 <- slice_index_usize u32 s i; + sum3 <- u32_add sum1 i2; + i3 <- usize_add i 1%usize; + sum_loop n1 s sum3 i3) + else Return sum1 + end +. + +(** [arrays::sum]: + Source: 'src/arrays.rs', lines 242:0-242:28 *) +Definition sum (n : nat) (s : slice u32) : result u32 := + sum_loop n s 0%u32 0%usize +. + +(** [arrays::sum2]: loop 0: + Source: 'src/arrays.rs', lines 252:0-261:1 *) +Fixpoint sum2_loop + (n : nat) (s : slice u32) (s2 : slice u32) (sum1 : u32) (i : usize) : + result u32 + := + match n with + | O => Fail_ OutOfFuel + | S n1 => + let i1 := slice_len u32 s in + if i s< i1 + then ( + i2 <- slice_index_usize u32 s i; + i3 <- slice_index_usize u32 s2 i; + i4 <- u32_add i2 i3; + sum3 <- u32_add sum1 i4; + i5 <- usize_add i 1%usize; + sum2_loop n1 s s2 sum3 i5) + else Return sum1 + end +. + +(** [arrays::sum2]: + Source: 'src/arrays.rs', lines 252:0-252:41 *) +Definition sum2 (n : nat) (s : slice u32) (s2 : slice u32) : result u32 := + let i := slice_len u32 s in + let i1 := slice_len u32 s2 in + if negb (i s= i1) then Fail_ Failure else sum2_loop n s s2 0%u32 0%usize +. + +(** [arrays::f0]: + Source: 'src/arrays.rs', lines 263:0-263:11 *) +Definition f0 : result unit := + p <- array_to_slice_mut u32 2%usize (mk_array u32 2%usize [ 1%u32; 2%u32 ]); + let (s, to_slice_mut_back) := p in + p1 <- slice_index_mut_usize u32 s 0%usize; + let (_, index_mut_back) := p1 in + s1 <- index_mut_back 1%u32; + _ <- to_slice_mut_back s1; + Return tt +. + +(** [arrays::f1]: + Source: 'src/arrays.rs', lines 268:0-268:11 *) +Definition f1 : result unit := + p <- + array_index_mut_usize u32 2%usize (mk_array u32 2%usize [ 1%u32; 2%u32 ]) + 0%usize; + let (_, index_mut_back) := p in + _ <- index_mut_back 1%u32; + Return tt +. + +(** [arrays::f2]: + Source: 'src/arrays.rs', lines 273:0-273:17 *) +Definition f2 (i : u32) : result unit := + Return tt. + +(** [arrays::f4]: + Source: 'src/arrays.rs', lines 282:0-282:54 *) +Definition f4 + (x : array u32 32%usize) (y : usize) (z : usize) : result (slice u32) := + core_array_Array_index u32 (core_ops_range_Range usize) 32%usize + (core_ops_index_IndexSliceTIInst u32 (core_ops_range_Range usize) + (core_slice_index_SliceIndexRangeUsizeSliceTInst u32)) x + {| core_ops_range_Range_start := y; core_ops_range_Range_end_ := z |} +. + +(** [arrays::f3]: + Source: 'src/arrays.rs', lines 275:0-275:18 *) +Definition f3 (n : nat) : result u32 := + i <- + array_index_usize u32 2%usize (mk_array u32 2%usize [ 1%u32; 2%u32 ]) + 0%usize; + _ <- f2 i; + let b := array_repeat u32 32%usize 0%u32 in + s <- array_to_slice u32 2%usize (mk_array u32 2%usize [ 1%u32; 2%u32 ]); + s1 <- f4 b 16%usize 18%usize; + sum2 n s s1 +. + +(** [arrays::SZ] + Source: 'src/arrays.rs', lines 286:0-286:19 *) +Definition sz_body : result usize := Return 32%usize. +Definition sz_c : usize := sz_body%global. + +(** [arrays::f5]: + Source: 'src/arrays.rs', lines 289:0-289:31 *) +Definition f5 (x : array u32 32%usize) : result u32 := + array_index_usize u32 32%usize x 0%usize +. + +(** [arrays::ite]: + Source: 'src/arrays.rs', lines 294:0-294:12 *) +Definition ite : result unit := + p <- array_to_slice_mut u32 2%usize (mk_array u32 2%usize [ 0%u32; 0%u32 ]); + let (s, to_slice_mut_back) := p in + p1 <- index_mut_slice_u32_0 s; + let (_, s1) := p1 in + p2 <- array_to_slice_mut u32 2%usize (mk_array u32 2%usize [ 0%u32; 0%u32 ]); + let (s2, to_slice_mut_back1) := p2 in + p3 <- index_mut_slice_u32_0 s2; + let (_, s3) := p3 in + _ <- to_slice_mut_back1 s3; + _ <- to_slice_mut_back s1; + Return tt +. + +End Arrays. diff --git a/tests/coq/arrays/Makefile b/tests/coq/arrays/Makefile new file mode 100644 index 00000000..1a5aee4a --- /dev/null +++ b/tests/coq/arrays/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/arrays/Primitives.v b/tests/coq/arrays/Primitives.v new file mode 100644 index 00000000..990e27e4 --- /dev/null +++ b/tests/coq/arrays/Primitives.v @@ -0,0 +1,899 @@ +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 * 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 => 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). + +(* 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::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 := Return x. +Definition alloc_boxed_Box_deref_mut (T : Type) (x : T) : result (T * (T -> result T)) := + Return (x, fun x => Return x). + +(* Trait instance *) +Definition alloc_boxed_Box_coreopsDerefInst (Self : Type) : core_ops_deref_Deref Self := {| + 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 + | Return x => Return (x, array_update_usize T n a i) + end. + +(*** Slice *) +Definition slice T := { l: list T | Z.of_nat (length l) <= usize_max}. + +Axiom slice_len : forall (T : Type) (s : slice T), usize. +Axiom slice_index_usize : forall (T : Type) (x : slice T) (i : usize), result T. +Axiom slice_update_usize : forall (T : Type) (x : slice T) (i : usize) (nx : T), result (slice T). + +Definition slice_index_mut_usize (T : Type) (s : slice T) (i : usize) : + result (T * (T -> result (slice T))) := + match slice_index_usize T s i with + | Fail_ e => Fail_ e + | Return x => Return (x, slice_update_usize T s i) + end. + +(*** Subslices *) + +Axiom array_to_slice : forall (T : Type) (n : usize) (x : array T n), result (slice T). +Axiom array_from_slice : forall (T : Type) (n : usize) (x : array T n) (s : slice T), result (array T n). + +Definition array_to_slice_mut (T : Type) (n : usize) (a : array T n) : + result (slice T * (slice T -> result (array T n))) := + match array_to_slice T n a with + | Fail_ e => Fail_ e + | Return x => Return (x, array_from_slice T n a) + end. + +Axiom array_subslice: forall (T : Type) (n : usize) (x : array T n) (r : core_ops_range_Range usize), result (slice T). +Axiom array_update_subslice: forall (T : Type) (n : usize) (x : array T n) (r : core_ops_range_Range usize) (ns : slice T), result (array T n). + +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. + +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])). + +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). + +Definition alloc_vec_Vec_index_mut_usize {T : Type} (v: alloc_vec_Vec T) (i: usize) : + result (T * (T -> result (alloc_vec_Vec T))) := + match alloc_vec_Vec_index_usize v i with + | Return x => + Return (x, alloc_vec_Vec_update_usize v i) + | Fail_ e => Fail_ e + end. + +(* Trait declaration: [core::slice::index::private_slice_index::Sealed] *) +Definition core_slice_index_private_slice_index_Sealed (self : Type) := unit. + +(* 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 => 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) * (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. diff --git a/tests/coq/arrays/_CoqProject b/tests/coq/arrays/_CoqProject new file mode 100644 index 00000000..a4e82408 --- /dev/null +++ b/tests/coq/arrays/_CoqProject @@ -0,0 +1,7 @@ +# This file was automatically generated - see ../Makefile +-R . Lib +-arg -w +-arg all + +Arrays.v +Primitives.v |