diff options
Diffstat (limited to '')
| -rw-r--r-- | tests/fstar-split/array/Array.Clauses.Template.fst | 21 | ||||
| -rw-r--r-- | tests/fstar-split/array/Array.Clauses.fst | 19 | ||||
| -rw-r--r-- | tests/fstar-split/array/Array.Funs.fst | 445 | ||||
| -rw-r--r-- | tests/fstar-split/array/Array.Types.fst | 11 | ||||
| -rw-r--r-- | tests/fstar-split/array/Makefile | 49 | ||||
| -rw-r--r-- | tests/fstar-split/array/Primitives.fst | 884 |
6 files changed, 1429 insertions, 0 deletions
diff --git a/tests/fstar-split/array/Array.Clauses.Template.fst b/tests/fstar-split/array/Array.Clauses.Template.fst new file mode 100644 index 00000000..b2f2649c --- /dev/null +++ b/tests/fstar-split/array/Array.Clauses.Template.fst @@ -0,0 +1,21 @@ +(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *) +(** [array]: templates for the decreases clauses *) +module Array.Clauses.Template +open Primitives +open Array.Types + +#set-options "--z3rlimit 50 --fuel 1 --ifuel 1" + +(** [array::sum]: decreases clause + Source: 'src/array.rs', lines 242:0-250:1 *) +unfold +let sum_loop_decreases (s : slice u32) (sum1 : u32) (i : usize) : nat = + admit () + +(** [array::sum2]: decreases clause + Source: 'src/array.rs', lines 252:0-261:1 *) +unfold +let sum2_loop_decreases (s : slice u32) (s2 : slice u32) (sum1 : u32) + (i : usize) : nat = + admit () + diff --git a/tests/fstar-split/array/Array.Clauses.fst b/tests/fstar-split/array/Array.Clauses.fst new file mode 100644 index 00000000..68cbf216 --- /dev/null +++ b/tests/fstar-split/array/Array.Clauses.fst @@ -0,0 +1,19 @@ +(** [array]: decreases clauses *) +module Array.Clauses +open Primitives +open Array.Types +open FStar.List.Tot + +#set-options "--z3rlimit 50 --fuel 1 --ifuel 1" + +(** [array::sum]: decreases clause *) +unfold +let sum_loop_decreases (s : slice u32) (sum : u32) (i : usize) : nat = + if i < length s then length s - i else 0 + +(** [array::sum2]: decreases clause *) +unfold +let sum2_loop_decreases (s : slice u32) (s2 : slice u32) (sum : u32) + (i : usize) : nat = + if i < length s then length s - i else 0 + diff --git a/tests/fstar-split/array/Array.Funs.fst b/tests/fstar-split/array/Array.Funs.fst new file mode 100644 index 00000000..30b19702 --- /dev/null +++ b/tests/fstar-split/array/Array.Funs.fst @@ -0,0 +1,445 @@ +(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *) +(** [array]: function definitions *) +module Array.Funs +open Primitives +include Array.Types +include Array.Clauses + +#set-options "--z3rlimit 50 --fuel 1 --ifuel 1" + +(** [array::incr]: merged forward/backward function + (there is a single backward function, and the forward function returns ()) + Source: 'src/array.rs', lines 8:0-8:24 *) +let incr (x : u32) : result u32 = + u32_add x 1 + +(** [array::array_to_shared_slice_]: forward function + Source: 'src/array.rs', lines 16:0-16:53 *) +let array_to_shared_slice_ (t : Type0) (s : array t 32) : result (slice t) = + array_to_slice t 32 s + +(** [array::array_to_mut_slice_]: forward function + Source: 'src/array.rs', lines 21:0-21:58 *) +let array_to_mut_slice_ (t : Type0) (s : array t 32) : result (slice t) = + array_to_slice t 32 s + +(** [array::array_to_mut_slice_]: backward function 0 + Source: 'src/array.rs', lines 21:0-21:58 *) +let array_to_mut_slice__back + (t : Type0) (s : array t 32) (ret : slice t) : result (array t 32) = + array_from_slice t 32 s ret + +(** [array::array_len]: forward function + Source: 'src/array.rs', lines 25:0-25:40 *) +let array_len (t : Type0) (s : array t 32) : result usize = + let* s1 = array_to_slice t 32 s in let i = slice_len t s1 in Return i + +(** [array::shared_array_len]: forward function + Source: 'src/array.rs', lines 29:0-29:48 *) +let shared_array_len (t : Type0) (s : array t 32) : result usize = + let* s1 = array_to_slice t 32 s in let i = slice_len t s1 in Return i + +(** [array::shared_slice_len]: forward function + Source: 'src/array.rs', lines 33:0-33:44 *) +let shared_slice_len (t : Type0) (s : slice t) : result usize = + let i = slice_len t s in Return i + +(** [array::index_array_shared]: forward function + Source: 'src/array.rs', lines 37:0-37:57 *) +let index_array_shared (t : Type0) (s : array t 32) (i : usize) : result t = + array_index_usize t 32 s i + +(** [array::index_array_u32]: forward function + Source: 'src/array.rs', lines 44:0-44:53 *) +let index_array_u32 (s : array u32 32) (i : usize) : result u32 = + array_index_usize u32 32 s i + +(** [array::index_array_copy]: forward function + Source: 'src/array.rs', lines 48:0-48:45 *) +let index_array_copy (x : array u32 32) : result u32 = + array_index_usize u32 32 x 0 + +(** [array::index_mut_array]: forward function + Source: 'src/array.rs', lines 52:0-52:62 *) +let index_mut_array (t : Type0) (s : array t 32) (i : usize) : result t = + array_index_usize t 32 s i + +(** [array::index_mut_array]: backward function 0 + Source: 'src/array.rs', lines 52:0-52:62 *) +let index_mut_array_back + (t : Type0) (s : array t 32) (i : usize) (ret : t) : result (array t 32) = + array_update_usize t 32 s i ret + +(** [array::index_slice]: forward function + Source: 'src/array.rs', lines 56:0-56:46 *) +let index_slice (t : Type0) (s : slice t) (i : usize) : result t = + slice_index_usize t s i + +(** [array::index_mut_slice]: forward function + Source: 'src/array.rs', lines 60:0-60:58 *) +let index_mut_slice (t : Type0) (s : slice t) (i : usize) : result t = + slice_index_usize t s i + +(** [array::index_mut_slice]: backward function 0 + Source: 'src/array.rs', lines 60:0-60:58 *) +let index_mut_slice_back + (t : Type0) (s : slice t) (i : usize) (ret : t) : result (slice t) = + slice_update_usize t s i ret + +(** [array::slice_subslice_shared_]: forward function + Source: 'src/array.rs', lines 64:0-64:70 *) +let 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 + { start = y; end_ = z } + +(** [array::slice_subslice_mut_]: forward function + Source: 'src/array.rs', lines 68:0-68:75 *) +let slice_subslice_mut_ + (x : slice u32) (y : usize) (z : usize) : result (slice u32) = + core_slice_index_Slice_index_mut u32 (core_ops_range_Range usize) + (core_slice_index_SliceIndexRangeUsizeSliceTInst u32) x + { start = y; end_ = z } + +(** [array::slice_subslice_mut_]: backward function 0 + Source: 'src/array.rs', lines 68:0-68:75 *) +let slice_subslice_mut__back + (x : slice u32) (y : usize) (z : usize) (ret : slice u32) : + result (slice u32) + = + core_slice_index_Slice_index_mut_back u32 (core_ops_range_Range usize) + (core_slice_index_SliceIndexRangeUsizeSliceTInst u32) x + { start = y; end_ = z } ret + +(** [array::array_to_slice_shared_]: forward function + Source: 'src/array.rs', lines 72:0-72:54 *) +let array_to_slice_shared_ (x : array u32 32) : result (slice u32) = + array_to_slice u32 32 x + +(** [array::array_to_slice_mut_]: forward function + Source: 'src/array.rs', lines 76:0-76:59 *) +let array_to_slice_mut_ (x : array u32 32) : result (slice u32) = + array_to_slice u32 32 x + +(** [array::array_to_slice_mut_]: backward function 0 + Source: 'src/array.rs', lines 76:0-76:59 *) +let array_to_slice_mut__back + (x : array u32 32) (ret : slice u32) : result (array u32 32) = + array_from_slice u32 32 x ret + +(** [array::array_subslice_shared_]: forward function + Source: 'src/array.rs', lines 80:0-80:74 *) +let array_subslice_shared_ + (x : array u32 32) (y : usize) (z : usize) : result (slice u32) = + core_array_Array_index u32 (core_ops_range_Range usize) 32 + (core_ops_index_IndexSliceTIInst u32 (core_ops_range_Range usize) + (core_slice_index_SliceIndexRangeUsizeSliceTInst u32)) x + { start = y; end_ = z } + +(** [array::array_subslice_mut_]: forward function + Source: 'src/array.rs', lines 84:0-84:79 *) +let array_subslice_mut_ + (x : array u32 32) (y : usize) (z : usize) : result (slice u32) = + core_array_Array_index_mut u32 (core_ops_range_Range usize) 32 + (core_ops_index_IndexMutSliceTIInst u32 (core_ops_range_Range usize) + (core_slice_index_SliceIndexRangeUsizeSliceTInst u32)) x + { start = y; end_ = z } + +(** [array::array_subslice_mut_]: backward function 0 + Source: 'src/array.rs', lines 84:0-84:79 *) +let array_subslice_mut__back + (x : array u32 32) (y : usize) (z : usize) (ret : slice u32) : + result (array u32 32) + = + core_array_Array_index_mut_back u32 (core_ops_range_Range usize) 32 + (core_ops_index_IndexMutSliceTIInst u32 (core_ops_range_Range usize) + (core_slice_index_SliceIndexRangeUsizeSliceTInst u32)) x + { start = y; end_ = z } ret + +(** [array::index_slice_0]: forward function + Source: 'src/array.rs', lines 88:0-88:38 *) +let index_slice_0 (t : Type0) (s : slice t) : result t = + slice_index_usize t s 0 + +(** [array::index_array_0]: forward function + Source: 'src/array.rs', lines 92:0-92:42 *) +let index_array_0 (t : Type0) (s : array t 32) : result t = + array_index_usize t 32 s 0 + +(** [array::index_index_array]: forward function + Source: 'src/array.rs', lines 103:0-103:71 *) +let index_index_array + (s : array (array u32 32) 32) (i : usize) (j : usize) : result u32 = + let* a = array_index_usize (array u32 32) 32 s i in + array_index_usize u32 32 a j + +(** [array::update_update_array]: forward function + Source: 'src/array.rs', lines 114:0-114:70 *) +let update_update_array + (s : array (array u32 32) 32) (i : usize) (j : usize) : result unit = + let* a = array_index_usize (array u32 32) 32 s i in + let* a1 = array_update_usize u32 32 a j 0 in + let* _ = array_update_usize (array u32 32) 32 s i a1 in + Return () + +(** [array::array_local_deep_copy]: forward function + Source: 'src/array.rs', lines 118:0-118:43 *) +let array_local_deep_copy (x : array u32 32) : result unit = + Return () + +(** [array::take_array]: forward function + Source: 'src/array.rs', lines 122:0-122:30 *) +let take_array (a : array u32 2) : result unit = + Return () + +(** [array::take_array_borrow]: forward function + Source: 'src/array.rs', lines 123:0-123:38 *) +let take_array_borrow (a : array u32 2) : result unit = + Return () + +(** [array::take_slice]: forward function + Source: 'src/array.rs', lines 124:0-124:28 *) +let take_slice (s : slice u32) : result unit = + Return () + +(** [array::take_mut_slice]: merged forward/backward function + (there is a single backward function, and the forward function returns ()) + Source: 'src/array.rs', lines 125:0-125:36 *) +let take_mut_slice (s : slice u32) : result (slice u32) = + Return s + +(** [array::const_array]: forward function + Source: 'src/array.rs', lines 127:0-127:32 *) +let const_array : result (array u32 2) = + Return (mk_array u32 2 [ 0; 0 ]) + +(** [array::const_slice]: forward function + Source: 'src/array.rs', lines 131:0-131:20 *) +let const_slice : result unit = + let* _ = array_to_slice u32 2 (mk_array u32 2 [ 0; 0 ]) in Return () + +(** [array::take_all]: forward function + Source: 'src/array.rs', lines 141:0-141:17 *) +let take_all : result unit = + let* _ = take_array (mk_array u32 2 [ 0; 0 ]) in + let* _ = take_array_borrow (mk_array u32 2 [ 0; 0 ]) in + let* s = array_to_slice u32 2 (mk_array u32 2 [ 0; 0 ]) in + let* _ = take_slice s in + let* s1 = array_to_slice u32 2 (mk_array u32 2 [ 0; 0 ]) in + let* s2 = take_mut_slice s1 in + let* _ = array_from_slice u32 2 (mk_array u32 2 [ 0; 0 ]) s2 in + Return () + +(** [array::index_array]: forward function + Source: 'src/array.rs', lines 155:0-155:38 *) +let index_array (x : array u32 2) : result u32 = + array_index_usize u32 2 x 0 + +(** [array::index_array_borrow]: forward function + Source: 'src/array.rs', lines 158:0-158:46 *) +let index_array_borrow (x : array u32 2) : result u32 = + array_index_usize u32 2 x 0 + +(** [array::index_slice_u32_0]: forward function + Source: 'src/array.rs', lines 162:0-162:42 *) +let index_slice_u32_0 (x : slice u32) : result u32 = + slice_index_usize u32 x 0 + +(** [array::index_mut_slice_u32_0]: forward function + Source: 'src/array.rs', lines 166:0-166:50 *) +let index_mut_slice_u32_0 (x : slice u32) : result u32 = + slice_index_usize u32 x 0 + +(** [array::index_mut_slice_u32_0]: backward function 0 + Source: 'src/array.rs', lines 166:0-166:50 *) +let index_mut_slice_u32_0_back (x : slice u32) : result (slice u32) = + let* _ = slice_index_usize u32 x 0 in Return x + +(** [array::index_all]: forward function + Source: 'src/array.rs', lines 170:0-170:25 *) +let index_all : result u32 = + let* i = index_array (mk_array u32 2 [ 0; 0 ]) in + let* i1 = index_array (mk_array u32 2 [ 0; 0 ]) in + let* i2 = u32_add i i1 in + let* i3 = index_array_borrow (mk_array u32 2 [ 0; 0 ]) in + let* i4 = u32_add i2 i3 in + let* s = array_to_slice u32 2 (mk_array u32 2 [ 0; 0 ]) in + let* i5 = index_slice_u32_0 s in + let* i6 = u32_add i4 i5 in + let* s1 = array_to_slice u32 2 (mk_array u32 2 [ 0; 0 ]) in + let* i7 = index_mut_slice_u32_0 s1 in + let* i8 = u32_add i6 i7 in + let* s2 = index_mut_slice_u32_0_back s1 in + let* _ = array_from_slice u32 2 (mk_array u32 2 [ 0; 0 ]) s2 in + Return i8 + +(** [array::update_array]: forward function + Source: 'src/array.rs', lines 184:0-184:36 *) +let update_array (x : array u32 2) : result unit = + let* _ = array_update_usize u32 2 x 0 1 in Return () + +(** [array::update_array_mut_borrow]: merged forward/backward function + (there is a single backward function, and the forward function returns ()) + Source: 'src/array.rs', lines 187:0-187:48 *) +let update_array_mut_borrow (x : array u32 2) : result (array u32 2) = + array_update_usize u32 2 x 0 1 + +(** [array::update_mut_slice]: merged forward/backward function + (there is a single backward function, and the forward function returns ()) + Source: 'src/array.rs', lines 190:0-190:38 *) +let update_mut_slice (x : slice u32) : result (slice u32) = + slice_update_usize u32 x 0 1 + +(** [array::update_all]: forward function + Source: 'src/array.rs', lines 194:0-194:19 *) +let update_all : result unit = + let* _ = update_array (mk_array u32 2 [ 0; 0 ]) in + let* x = update_array_mut_borrow (mk_array u32 2 [ 0; 0 ]) in + let* s = array_to_slice u32 2 x in + let* s1 = update_mut_slice s in + let* _ = array_from_slice u32 2 x s1 in + Return () + +(** [array::range_all]: forward function + Source: 'src/array.rs', lines 205:0-205:18 *) +let range_all : result unit = + let* s = + core_array_Array_index_mut u32 (core_ops_range_Range usize) 4 + (core_ops_index_IndexMutSliceTIInst u32 (core_ops_range_Range usize) + (core_slice_index_SliceIndexRangeUsizeSliceTInst u32)) + (mk_array u32 4 [ 0; 0; 0; 0 ]) { start = 1; end_ = 3 } in + let* s1 = update_mut_slice s in + let* _ = + core_array_Array_index_mut_back u32 (core_ops_range_Range usize) 4 + (core_ops_index_IndexMutSliceTIInst u32 (core_ops_range_Range usize) + (core_slice_index_SliceIndexRangeUsizeSliceTInst u32)) + (mk_array u32 4 [ 0; 0; 0; 0 ]) { start = 1; end_ = 3 } s1 in + Return () + +(** [array::deref_array_borrow]: forward function + Source: 'src/array.rs', lines 214:0-214:46 *) +let deref_array_borrow (x : array u32 2) : result u32 = + array_index_usize u32 2 x 0 + +(** [array::deref_array_mut_borrow]: forward function + Source: 'src/array.rs', lines 219:0-219:54 *) +let deref_array_mut_borrow (x : array u32 2) : result u32 = + array_index_usize u32 2 x 0 + +(** [array::deref_array_mut_borrow]: backward function 0 + Source: 'src/array.rs', lines 219:0-219:54 *) +let deref_array_mut_borrow_back (x : array u32 2) : result (array u32 2) = + let* _ = array_index_usize u32 2 x 0 in Return x + +(** [array::take_array_t]: forward function + Source: 'src/array.rs', lines 227:0-227:31 *) +let take_array_t (a : array aB_t 2) : result unit = + Return () + +(** [array::non_copyable_array]: forward function + Source: 'src/array.rs', lines 229:0-229:27 *) +let non_copyable_array : result unit = + let* _ = take_array_t (mk_array aB_t 2 [ AB_A; AB_B ]) in Return () + +(** [array::sum]: loop 0: forward function + Source: 'src/array.rs', lines 242:0-250:1 *) +let rec sum_loop + (s : slice u32) (sum1 : u32) (i : usize) : + Tot (result u32) (decreases (sum_loop_decreases s sum1 i)) + = + let i1 = slice_len u32 s in + if i < i1 + then + let* i2 = slice_index_usize u32 s i in + let* sum3 = u32_add sum1 i2 in + let* i3 = usize_add i 1 in + sum_loop s sum3 i3 + else Return sum1 + +(** [array::sum]: forward function + Source: 'src/array.rs', lines 242:0-242:28 *) +let sum (s : slice u32) : result u32 = + sum_loop s 0 0 + +(** [array::sum2]: loop 0: forward function + Source: 'src/array.rs', lines 252:0-261:1 *) +let rec sum2_loop + (s : slice u32) (s2 : slice u32) (sum1 : u32) (i : usize) : + Tot (result u32) (decreases (sum2_loop_decreases s s2 sum1 i)) + = + let i1 = slice_len u32 s in + if i < i1 + then + let* i2 = slice_index_usize u32 s i in + let* i3 = slice_index_usize u32 s2 i in + let* i4 = u32_add i2 i3 in + let* sum3 = u32_add sum1 i4 in + let* i5 = usize_add i 1 in + sum2_loop s s2 sum3 i5 + else Return sum1 + +(** [array::sum2]: forward function + Source: 'src/array.rs', lines 252:0-252:41 *) +let sum2 (s : slice u32) (s2 : slice u32) : result u32 = + let i = slice_len u32 s in + let i1 = slice_len u32 s2 in + if not (i = i1) then Fail Failure else sum2_loop s s2 0 0 + +(** [array::f0]: forward function + Source: 'src/array.rs', lines 263:0-263:11 *) +let f0 : result unit = + let* s = array_to_slice u32 2 (mk_array u32 2 [ 1; 2 ]) in + let* s1 = slice_update_usize u32 s 0 1 in + let* _ = array_from_slice u32 2 (mk_array u32 2 [ 1; 2 ]) s1 in + Return () + +(** [array::f1]: forward function + Source: 'src/array.rs', lines 268:0-268:11 *) +let f1 : result unit = + let* _ = array_update_usize u32 2 (mk_array u32 2 [ 1; 2 ]) 0 1 in Return () + +(** [array::f2]: forward function + Source: 'src/array.rs', lines 273:0-273:17 *) +let f2 (i : u32) : result unit = + Return () + +(** [array::f4]: forward function + Source: 'src/array.rs', lines 282:0-282:54 *) +let f4 (x : array u32 32) (y : usize) (z : usize) : result (slice u32) = + core_array_Array_index u32 (core_ops_range_Range usize) 32 + (core_ops_index_IndexSliceTIInst u32 (core_ops_range_Range usize) + (core_slice_index_SliceIndexRangeUsizeSliceTInst u32)) x + { start = y; end_ = z } + +(** [array::f3]: forward function + Source: 'src/array.rs', lines 275:0-275:18 *) +let f3 : result u32 = + let* i = array_index_usize u32 2 (mk_array u32 2 [ 1; 2 ]) 0 in + let* _ = f2 i in + let b = array_repeat u32 32 0 in + let* s = array_to_slice u32 2 (mk_array u32 2 [ 1; 2 ]) in + let* s1 = f4 b 16 18 in + sum2 s s1 + +(** [array::SZ] + Source: 'src/array.rs', lines 286:0-286:19 *) +let sz_body : result usize = Return 32 +let sz_c : usize = eval_global sz_body + +(** [array::f5]: forward function + Source: 'src/array.rs', lines 289:0-289:31 *) +let f5 (x : array u32 32) : result u32 = + array_index_usize u32 32 x 0 + +(** [array::ite]: forward function + Source: 'src/array.rs', lines 294:0-294:12 *) +let ite : result unit = + let* s = array_to_slice u32 2 (mk_array u32 2 [ 0; 0 ]) in + let* s1 = array_to_slice u32 2 (mk_array u32 2 [ 0; 0 ]) in + let* s2 = index_mut_slice_u32_0_back s1 in + let* _ = array_from_slice u32 2 (mk_array u32 2 [ 0; 0 ]) s2 in + let* s3 = index_mut_slice_u32_0_back s in + let* _ = array_from_slice u32 2 (mk_array u32 2 [ 0; 0 ]) s3 in + Return () + diff --git a/tests/fstar-split/array/Array.Types.fst b/tests/fstar-split/array/Array.Types.fst new file mode 100644 index 00000000..312f6018 --- /dev/null +++ b/tests/fstar-split/array/Array.Types.fst @@ -0,0 +1,11 @@ +(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *) +(** [array]: type definitions *) +module Array.Types +open Primitives + +#set-options "--z3rlimit 50 --fuel 1 --ifuel 1" + +(** [array::AB] + Source: 'src/array.rs', lines 3:0-3:11 *) +type aB_t = | AB_A : aB_t | AB_B : aB_t + diff --git a/tests/fstar-split/array/Makefile b/tests/fstar-split/array/Makefile new file mode 100644 index 00000000..fa7d1f36 --- /dev/null +++ b/tests/fstar-split/array/Makefile @@ -0,0 +1,49 @@ +# This file was automatically generated - modify ../Makefile.template instead +INCLUDE_DIRS = . + +FSTAR_INCLUDES = $(addprefix --include ,$(INCLUDE_DIRS)) + +FSTAR_HINTS ?= --use_hints --use_hint_hashes --record_hints + +FSTAR_OPTIONS = $(FSTAR_HINTS) \ + --cache_checked_modules $(FSTAR_INCLUDES) --cmi \ + --warn_error '+241@247+285-274' \ + +FSTAR_EXE ?= fstar.exe +FSTAR_NO_FLAGS = $(FSTAR_EXE) --already_cached 'Prims FStar LowStar Steel' --odir obj --cache_dir obj + +FSTAR = $(FSTAR_NO_FLAGS) $(FSTAR_OPTIONS) + +# The F* roots are used to compute the dependency graph, and generate the .depend file +FSTAR_ROOTS ?= $(wildcard *.fst *.fsti) + +# Build all the files +all: $(addprefix obj/,$(addsuffix .checked,$(FSTAR_ROOTS))) + +# This is the right way to ensure the .depend file always gets re-built. +ifeq (,$(filter %-in,$(MAKECMDGOALS))) +ifndef NODEPEND +ifndef MAKE_RESTARTS +.depend: .FORCE + $(FSTAR_NO_FLAGS) --dep full $(notdir $(FSTAR_ROOTS)) > $@ + +.PHONY: .FORCE +.FORCE: +endif +endif + +include .depend +endif + +# For the interactive mode +%.fst-in %.fsti-in: + @echo $(FSTAR_OPTIONS) + +# Generete the .checked files in batch mode +%.checked: + $(FSTAR) $(FSTAR_OPTIONS) $< && \ + touch -c $@ + +.PHONY: clean +clean: + rm -f obj/* diff --git a/tests/fstar-split/array/Primitives.fst b/tests/fstar-split/array/Primitives.fst new file mode 100644 index 00000000..a3ffbde4 --- /dev/null +++ b/tests/fstar-split/array/Primitives.fst @@ -0,0 +1,884 @@ +/// This file lists primitive and assumed functions and types +module Primitives +open FStar.Mul +open FStar.List.Tot + +#set-options "--z3rlimit 15 --fuel 0 --ifuel 1" + +(*** Utilities *) +val list_update (#a : Type0) (ls : list a) (i : nat{i < length ls}) (x : a) : + ls':list a{ + length ls' = length ls /\ + index ls' i == x + } +#push-options "--fuel 1" +let rec list_update #a ls i x = + match ls with + | x' :: ls -> if i = 0 then x :: ls else x' :: list_update ls (i-1) x +#pop-options + +(*** Result *) +type error : Type0 = +| Failure +| OutOfFuel + +type result (a : Type0) : Type0 = +| Return : v:a -> result a +| Fail : e:error -> result a + +// Monadic return operator +unfold let return (#a : Type0) (x : a) : result a = Return x + +// Monadic bind operator. +// Allows to use the notation: +// ``` +// let* x = y in +// ... +// ``` +unfold let (let*) (#a #b : Type0) (m: result a) + (f: (x:a) -> Pure (result b) (requires (m == Return x)) (ensures fun _ -> True)) : + result b = + match m with + | Return x -> f x + | Fail e -> Fail e + +// Monadic assert(...) +let massert (b:bool) : result unit = if b then Return () else Fail Failure + +// Normalize and unwrap a successful result (used for globals). +let eval_global (#a : Type0) (x : result a{Return? (normalize_term x)}) : a = Return?.v x + +(*** Misc *) +type char = FStar.Char.char +type string = string + +let is_zero (n: nat) : bool = n = 0 +let decrease (n: nat{n > 0}) : nat = n - 1 + +let core_mem_replace (a : Type0) (x : a) (y : a) : a = x +let core_mem_replace_back (a : Type0) (x : a) (y : a) : a = y + +// We don't really use raw pointers for now +type mut_raw_ptr (t : Type0) = { v : t } +type const_raw_ptr (t : Type0) = { v : t } + +(*** Scalars *) +/// Rem.: most of the following code was partially generated + +assume val size_numbits : pos + +// TODO: we could use FStar.Int.int_t and FStar.UInt.int_t + +let isize_min : int = -9223372036854775808 // TODO: should be opaque +let isize_max : int = 9223372036854775807 // TODO: should be opaque +let i8_min : int = -128 +let i8_max : int = 127 +let i16_min : int = -32768 +let i16_max : int = 32767 +let i32_min : int = -2147483648 +let i32_max : int = 2147483647 +let i64_min : int = -9223372036854775808 +let i64_max : int = 9223372036854775807 +let i128_min : int = -170141183460469231731687303715884105728 +let i128_max : int = 170141183460469231731687303715884105727 +let usize_min : int = 0 +let usize_max : int = 4294967295 // TODO: should be opaque +let u8_min : int = 0 +let u8_max : int = 255 +let u16_min : int = 0 +let u16_max : int = 65535 +let u32_min : int = 0 +let u32_max : int = 4294967295 +let u64_min : int = 0 +let u64_max : int = 18446744073709551615 +let u128_min : int = 0 +let u128_max : int = 340282366920938463463374607431768211455 + +type scalar_ty = +| Isize +| I8 +| I16 +| I32 +| I64 +| I128 +| Usize +| U8 +| U16 +| U32 +| U64 +| U128 + +let is_unsigned = function + | Isize | I8 | I16 | I32 | I64 | I128 -> false + | Usize | U8 | U16 | U32 | U64 | U128 -> true + +let scalar_min (ty : scalar_ty) : int = + 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 + +let scalar_max (ty : scalar_ty) : int = + 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 + +type scalar (ty : scalar_ty) : eqtype = x:int{scalar_min ty <= x && x <= scalar_max ty} + +let mk_scalar (ty : scalar_ty) (x : int) : result (scalar ty) = + if scalar_min ty <= x && scalar_max ty >= x then Return x else Fail Failure + +let scalar_neg (#ty : scalar_ty) (x : scalar ty) : result (scalar ty) = mk_scalar ty (-x) + +let scalar_div (#ty : scalar_ty) (x : scalar ty) (y : scalar ty) : result (scalar ty) = + if y <> 0 then mk_scalar ty (x / y) else Fail Failure + +/// The remainder operation +let int_rem (x : int) (y : int{y <> 0}) : int = + if x >= 0 then (x % y) else -(x % y) + +(* Checking consistency with Rust *) +let _ = assert_norm(int_rem 1 2 = 1) +let _ = assert_norm(int_rem (-1) 2 = -1) +let _ = assert_norm(int_rem 1 (-2) = 1) +let _ = assert_norm(int_rem (-1) (-2) = -1) + +let scalar_rem (#ty : scalar_ty) (x : scalar ty) (y : scalar ty) : result (scalar ty) = + if y <> 0 then mk_scalar ty (int_rem x y) else Fail Failure + +let scalar_add (#ty : scalar_ty) (x : scalar ty) (y : scalar ty) : result (scalar ty) = + mk_scalar ty (x + y) + +let scalar_sub (#ty : scalar_ty) (x : scalar ty) (y : scalar ty) : result (scalar ty) = + mk_scalar ty (x - y) + +let scalar_mul (#ty : scalar_ty) (x : scalar ty) (y : scalar ty) : result (scalar ty) = + mk_scalar ty (x * y) + +let scalar_xor (#ty : scalar_ty) + (x : scalar ty) (y : scalar ty) : scalar ty = + match ty with + | U8 -> FStar.UInt.logxor #8 x y + | U16 -> FStar.UInt.logxor #16 x y + | U32 -> FStar.UInt.logxor #32 x y + | U64 -> FStar.UInt.logxor #64 x y + | U128 -> FStar.UInt.logxor #128 x y + | Usize -> admit() // TODO + | I8 -> + // Encoding issues... + normalize_spec (FStar.Int.int_t 8); + normalize_spec (scalar I8); + FStar.Int.logxor #8 x y + | I16 -> + // Encoding issues... + normalize_spec (FStar.Int.int_t 16); + normalize_spec (scalar I16); + FStar.Int.logxor #16 x y + | I32 -> FStar.Int.logxor #32 x y + | I64 -> FStar.Int.logxor #64 x y + | I128 -> + // Encoding issues... + normalize_spec (FStar.Int.int_t 128); + normalize_spec (scalar I128); + FStar.Int.logxor #128 x y + | Isize -> admit() // TODO + +let scalar_or (#ty : scalar_ty) + (x : scalar ty) (y : scalar ty) : scalar ty = + match ty with + | U8 -> FStar.UInt.logor #8 x y + | U16 -> FStar.UInt.logor #16 x y + | U32 -> FStar.UInt.logor #32 x y + | U64 -> FStar.UInt.logor #64 x y + | U128 -> FStar.UInt.logor #128 x y + | Usize -> admit() // TODO + | I8 -> + // Encoding issues... + normalize_spec (FStar.Int.int_t 8); + normalize_spec (scalar I8); + FStar.Int.logor #8 x y + | I16 -> + // Encoding issues... + normalize_spec (FStar.Int.int_t 16); + normalize_spec (scalar I16); + FStar.Int.logor #16 x y + | I32 -> FStar.Int.logor #32 x y + | I64 -> FStar.Int.logor #64 x y + | I128 -> + // Encoding issues... + normalize_spec (FStar.Int.int_t 128); + normalize_spec (scalar I128); + FStar.Int.logor #128 x y + | Isize -> admit() // TODO + +let scalar_and (#ty : scalar_ty) + (x : scalar ty) (y : scalar ty) : scalar ty = + match ty with + | U8 -> FStar.UInt.logand #8 x y + | U16 -> FStar.UInt.logand #16 x y + | U32 -> FStar.UInt.logand #32 x y + | U64 -> FStar.UInt.logand #64 x y + | U128 -> FStar.UInt.logand #128 x y + | Usize -> admit() // TODO + | I8 -> + // Encoding issues... + normalize_spec (FStar.Int.int_t 8); + normalize_spec (scalar I8); + FStar.Int.logand #8 x y + | I16 -> + // Encoding issues... + normalize_spec (FStar.Int.int_t 16); + normalize_spec (scalar I16); + FStar.Int.logand #16 x y + | I32 -> FStar.Int.logand #32 x y + | I64 -> FStar.Int.logand #64 x y + | I128 -> + // Encoding issues... + normalize_spec (FStar.Int.int_t 128); + normalize_spec (scalar I128); + FStar.Int.logand #128 x y + | Isize -> admit() // TODO + +// Shift left +let scalar_shl (#ty0 #ty1 : scalar_ty) + (x : scalar ty0) (y : scalar ty1) : result (scalar ty0) = + admit() + +// Shift right +let scalar_shr (#ty0 #ty1 : scalar_ty) + (x : scalar ty0) (y : scalar ty1) : result (scalar ty0) = + admit() + +(** Cast an integer from a [src_ty] to a [tgt_ty] *) +// TODO: check the semantics of casts in Rust +let scalar_cast (src_ty : scalar_ty) (tgt_ty : scalar_ty) (x : scalar src_ty) : result (scalar tgt_ty) = + mk_scalar tgt_ty x + +// This can't fail, but for now we make all casts faillible (easier for the translation) +let scalar_cast_bool (tgt_ty : scalar_ty) (x : bool) : result (scalar tgt_ty) = + mk_scalar tgt_ty (if x then 1 else 0) + +/// The scalar types +type isize : eqtype = scalar Isize +type i8 : eqtype = scalar I8 +type i16 : eqtype = scalar I16 +type i32 : eqtype = scalar I32 +type i64 : eqtype = scalar I64 +type i128 : eqtype = scalar I128 +type usize : eqtype = scalar Usize +type u8 : eqtype = scalar U8 +type u16 : eqtype = scalar U16 +type u32 : eqtype = scalar U32 +type u64 : eqtype = scalar U64 +type u128 : eqtype = scalar U128 + + +let core_isize_min : isize = isize_min +let core_isize_max : isize = isize_max +let core_i8_min : i8 = i8_min +let core_i8_max : i8 = i8_max +let core_i16_min : i16 = i16_min +let core_i16_max : i16 = i16_max +let core_i32_min : i32 = i32_min +let core_i32_max : i32 = i32_max +let core_i64_min : i64 = i64_min +let core_i64_max : i64 = i64_max +let core_i128_min : i128 = i128_min +let core_i128_max : i128 = i128_max + +let core_usize_min : usize = usize_min +let core_usize_max : usize = usize_max +let core_u8_min : u8 = u8_min +let core_u8_max : u8 = u8_max +let core_u16_min : u16 = u16_min +let core_u16_max : u16 = u16_max +let core_u32_min : u32 = u32_min +let core_u32_max : u32 = u32_max +let core_u64_min : u64 = u64_min +let core_u64_max : u64 = u64_max +let core_u128_min : u128 = u128_min +let core_u128_max : u128 = u128_max + +/// Negation +let isize_neg = scalar_neg #Isize +let i8_neg = scalar_neg #I8 +let i16_neg = scalar_neg #I16 +let i32_neg = scalar_neg #I32 +let i64_neg = scalar_neg #I64 +let i128_neg = scalar_neg #I128 + +/// Division +let isize_div = scalar_div #Isize +let i8_div = scalar_div #I8 +let i16_div = scalar_div #I16 +let i32_div = scalar_div #I32 +let i64_div = scalar_div #I64 +let i128_div = scalar_div #I128 +let usize_div = scalar_div #Usize +let u8_div = scalar_div #U8 +let u16_div = scalar_div #U16 +let u32_div = scalar_div #U32 +let u64_div = scalar_div #U64 +let u128_div = scalar_div #U128 + +/// Remainder +let isize_rem = scalar_rem #Isize +let i8_rem = scalar_rem #I8 +let i16_rem = scalar_rem #I16 +let i32_rem = scalar_rem #I32 +let i64_rem = scalar_rem #I64 +let i128_rem = scalar_rem #I128 +let usize_rem = scalar_rem #Usize +let u8_rem = scalar_rem #U8 +let u16_rem = scalar_rem #U16 +let u32_rem = scalar_rem #U32 +let u64_rem = scalar_rem #U64 +let u128_rem = scalar_rem #U128 + +/// Addition +let isize_add = scalar_add #Isize +let i8_add = scalar_add #I8 +let i16_add = scalar_add #I16 +let i32_add = scalar_add #I32 +let i64_add = scalar_add #I64 +let i128_add = scalar_add #I128 +let usize_add = scalar_add #Usize +let u8_add = scalar_add #U8 +let u16_add = scalar_add #U16 +let u32_add = scalar_add #U32 +let u64_add = scalar_add #U64 +let u128_add = scalar_add #U128 + +/// Subtraction +let isize_sub = scalar_sub #Isize +let i8_sub = scalar_sub #I8 +let i16_sub = scalar_sub #I16 +let i32_sub = scalar_sub #I32 +let i64_sub = scalar_sub #I64 +let i128_sub = scalar_sub #I128 +let usize_sub = scalar_sub #Usize +let u8_sub = scalar_sub #U8 +let u16_sub = scalar_sub #U16 +let u32_sub = scalar_sub #U32 +let u64_sub = scalar_sub #U64 +let u128_sub = scalar_sub #U128 + +/// Multiplication +let isize_mul = scalar_mul #Isize +let i8_mul = scalar_mul #I8 +let i16_mul = scalar_mul #I16 +let i32_mul = scalar_mul #I32 +let i64_mul = scalar_mul #I64 +let i128_mul = scalar_mul #I128 +let usize_mul = scalar_mul #Usize +let u8_mul = scalar_mul #U8 +let u16_mul = scalar_mul #U16 +let u32_mul = scalar_mul #U32 +let u64_mul = scalar_mul #U64 +let u128_mul = scalar_mul #U128 + +/// Xor +let u8_xor = scalar_xor #U8 +let u16_xor = scalar_xor #U16 +let u32_xor = scalar_xor #U32 +let u64_xor = scalar_xor #U64 +let u128_xor = scalar_xor #U128 +let usize_xor = scalar_xor #Usize +let i8_xor = scalar_xor #I8 +let i16_xor = scalar_xor #I16 +let i32_xor = scalar_xor #I32 +let i64_xor = scalar_xor #I64 +let i128_xor = scalar_xor #I128 +let isize_xor = scalar_xor #Isize + +/// Or +let u8_or = scalar_or #U8 +let u16_or = scalar_or #U16 +let u32_or = scalar_or #U32 +let u64_or = scalar_or #U64 +let u128_or = scalar_or #U128 +let usize_or = scalar_or #Usize +let i8_or = scalar_or #I8 +let i16_or = scalar_or #I16 +let i32_or = scalar_or #I32 +let i64_or = scalar_or #I64 +let i128_or = scalar_or #I128 +let isize_or = scalar_or #Isize + +/// And +let u8_and = scalar_and #U8 +let u16_and = scalar_and #U16 +let u32_and = scalar_and #U32 +let u64_and = scalar_and #U64 +let u128_and = scalar_and #U128 +let usize_and = scalar_and #Usize +let i8_and = scalar_and #I8 +let i16_and = scalar_and #I16 +let i32_and = scalar_and #I32 +let i64_and = scalar_and #I64 +let i128_and = scalar_and #I128 +let isize_and = scalar_and #Isize + +/// Shift left +let u8_shl #ty = scalar_shl #U8 #ty +let u16_shl #ty = scalar_shl #U16 #ty +let u32_shl #ty = scalar_shl #U32 #ty +let u64_shl #ty = scalar_shl #U64 #ty +let u128_shl #ty = scalar_shl #U128 #ty +let usize_shl #ty = scalar_shl #Usize #ty +let i8_shl #ty = scalar_shl #I8 #ty +let i16_shl #ty = scalar_shl #I16 #ty +let i32_shl #ty = scalar_shl #I32 #ty +let i64_shl #ty = scalar_shl #I64 #ty +let i128_shl #ty = scalar_shl #I128 #ty +let isize_shl #ty = scalar_shl #Isize #ty + +/// Shift right +let u8_shr #ty = scalar_shr #U8 #ty +let u16_shr #ty = scalar_shr #U16 #ty +let u32_shr #ty = scalar_shr #U32 #ty +let u64_shr #ty = scalar_shr #U64 #ty +let u128_shr #ty = scalar_shr #U128 #ty +let usize_shr #ty = scalar_shr #Usize #ty +let i8_shr #ty = scalar_shr #I8 #ty +let i16_shr #ty = scalar_shr #I16 #ty +let i32_shr #ty = scalar_shr #I32 #ty +let i64_shr #ty = scalar_shr #I64 #ty +let i128_shr #ty = scalar_shr #I128 #ty +let isize_shr #ty = scalar_shr #Isize #ty + +(*** core::ops *) + +// Trait declaration: [core::ops::index::Index] +noeq type core_ops_index_Index (self idx : Type0) = { + output : Type0; + index : self → idx → result output +} + +// Trait declaration: [core::ops::index::IndexMut] +noeq type core_ops_index_IndexMut (self idx : Type0) = { + indexInst : core_ops_index_Index self idx; + index_mut : self → idx → result indexInst.output; + index_mut_back : self → idx → indexInst.output → result self; +} + +// Trait declaration [core::ops::deref::Deref] +noeq type core_ops_deref_Deref (self : Type0) = { + target : Type0; + deref : self → result target; +} + +// Trait declaration [core::ops::deref::DerefMut] +noeq type core_ops_deref_DerefMut (self : Type0) = { + derefInst : core_ops_deref_Deref self; + deref_mut : self → result derefInst.target; + deref_mut_back : self → derefInst.target → result self; +} + +type core_ops_range_Range (a : Type0) = { + start : a; + end_ : a; +} + +(*** [alloc] *) + +let alloc_boxed_Box_deref (t : Type0) (x : t) : result t = Return x +let alloc_boxed_Box_deref_mut (t : Type0) (x : t) : result t = Return x +let alloc_boxed_Box_deref_mut_back (t : Type) (_ : t) (x : t) : result t = Return x + +// Trait instance +let alloc_boxed_Box_coreopsDerefInst (self : Type0) : core_ops_deref_Deref self = { + target = self; + deref = alloc_boxed_Box_deref self; +} + +// Trait instance +let alloc_boxed_Box_coreopsDerefMutInst (self : Type0) : core_ops_deref_DerefMut self = { + derefInst = alloc_boxed_Box_coreopsDerefInst self; + deref_mut = alloc_boxed_Box_deref_mut self; + deref_mut_back = alloc_boxed_Box_deref_mut_back self; +} + +(*** Array *) +type array (a : Type0) (n : usize) = s:list a{length s = n} + +// We tried putting the normalize_term condition as a refinement on the list +// but it didn't work. It works with the requires clause. +let mk_array (a : Type0) (n : usize) + (l : list a) : + Pure (array a n) + (requires (normalize_term(FStar.List.Tot.length l) = n)) + (ensures (fun _ -> True)) = + normalize_term_spec (FStar.List.Tot.length l); + l + +let array_index_usize (a : Type0) (n : usize) (x : array a n) (i : usize) : result a = + if i < length x then Return (index x i) + else Fail Failure + +let array_update_usize (a : Type0) (n : usize) (x : array a n) (i : usize) (nx : a) : result (array a n) = + if i < length x then Return (list_update x i nx) + else Fail Failure + +(*** Slice *) +type slice (a : Type0) = s:list a{length s <= usize_max} + +let slice_len (a : Type0) (s : slice a) : usize = length s + +let slice_index_usize (a : Type0) (x : slice a) (i : usize) : result a = + if i < length x then Return (index x i) + else Fail Failure + +let slice_update_usize (a : Type0) (x : slice a) (i : usize) (nx : a) : result (slice a) = + if i < length x then Return (list_update x i nx) + else Fail Failure + +(*** Subslices *) + +let array_to_slice (a : Type0) (n : usize) (x : array a n) : result (slice a) = Return x +let array_from_slice (a : Type0) (n : usize) (x : array a n) (s : slice a) : result (array a n) = + if length s = n then Return s + else Fail Failure + +// TODO: finish the definitions below (there lacks [List.drop] and [List.take] in the standard library *) +let array_subslice (a : Type0) (n : usize) (x : array a n) (r : core_ops_range_Range usize) : result (slice a) = + admit() + +let array_update_subslice (a : Type0) (n : usize) (x : array a n) (r : core_ops_range_Range usize) (ns : slice a) : result (array a n) = + admit() + +let array_repeat (a : Type0) (n : usize) (x : a) : array a n = + admit() + +let slice_subslice (a : Type0) (x : slice a) (r : core_ops_range_Range usize) : result (slice a) = + admit() + +let slice_update_subslice (a : Type0) (x : slice a) (r : core_ops_range_Range usize) (ns : slice a) : result (slice a) = + admit() + +(*** Vector *) +type alloc_vec_Vec (a : Type0) = v:list a{length v <= usize_max} + +let alloc_vec_Vec_new (a : Type0) : alloc_vec_Vec a = assert_norm(length #a [] == 0); [] +let alloc_vec_Vec_len (a : Type0) (v : alloc_vec_Vec a) : usize = length v + +// Helper +let alloc_vec_Vec_index_usize (#a : Type0) (v : alloc_vec_Vec a) (i : usize) : result a = + if i < length v then Return (index v i) else Fail Failure +// Helper +let alloc_vec_Vec_update_usize (#a : Type0) (v : alloc_vec_Vec a) (i : usize) (x : a) : result (alloc_vec_Vec a) = + if i < length v then Return (list_update v i x) else Fail Failure + +// The **forward** function shouldn't be used +let alloc_vec_Vec_push_fwd (a : Type0) (v : alloc_vec_Vec a) (x : a) : unit = () +let alloc_vec_Vec_push (a : Type0) (v : alloc_vec_Vec a) (x : a) : + Pure (result (alloc_vec_Vec a)) + (requires True) + (ensures (fun res -> + match res with + | Fail e -> e == Failure + | Return v' -> length v' = length v + 1)) = + if length v < usize_max then begin + (**) assert_norm(length [x] == 1); + (**) append_length v [x]; + (**) assert(length (append v [x]) = length v + 1); + Return (append v [x]) + end + else Fail Failure + +// The **forward** function shouldn't be used +let alloc_vec_Vec_insert_fwd (a : Type0) (v : alloc_vec_Vec a) (i : usize) (x : a) : result unit = + if i < length v then Return () else Fail Failure +let alloc_vec_Vec_insert (a : Type0) (v : alloc_vec_Vec a) (i : usize) (x : a) : result (alloc_vec_Vec a) = + if i < length v then Return (list_update v i x) else Fail Failure + +// Trait declaration: [core::slice::index::private_slice_index::Sealed] +type core_slice_index_private_slice_index_Sealed (self : Type0) = unit + +// Trait declaration: [core::slice::index::SliceIndex] +noeq type core_slice_index_SliceIndex (self t : Type0) = { + sealedInst : core_slice_index_private_slice_index_Sealed self; + output : Type0; + get : self → t → result (option output); + get_mut : self → t → result (option output); + get_mut_back : self → t → option output → result t; + get_unchecked : self → const_raw_ptr t → result (const_raw_ptr output); + get_unchecked_mut : self → mut_raw_ptr t → result (mut_raw_ptr output); + index : self → t → result output; + index_mut : self → t → result output; + index_mut_back : self → t → output → result t; +} + +// [core::slice::index::[T]::index]: forward function +let core_slice_index_Slice_index + (t idx : Type0) (inst : core_slice_index_SliceIndex idx (slice t)) + (s : slice t) (i : idx) : result inst.output = + let* x = inst.get i s in + match x with + | None -> Fail Failure + | Some x -> Return x + +// [core::slice::index::Range:::get]: forward function +let core_slice_index_RangeUsize_get (t : Type0) (i : core_ops_range_Range usize) (s : slice t) : + result (option (slice t)) = + admit () // TODO + +// [core::slice::index::Range::get_mut]: forward function +let core_slice_index_RangeUsize_get_mut + (t : Type0) : core_ops_range_Range usize → slice t → result (option (slice t)) = + admit () // TODO + +// [core::slice::index::Range::get_mut]: backward function 0 +let core_slice_index_RangeUsize_get_mut_back + (t : Type0) : + core_ops_range_Range usize → slice t → option (slice t) → result (slice t) = + admit () // TODO + +// [core::slice::index::Range::get_unchecked]: forward function +let core_slice_index_RangeUsize_get_unchecked + (t : Type0) : + 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 +let core_slice_index_RangeUsize_get_unchecked_mut + (t : Type0) : + 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 +let core_slice_index_RangeUsize_index + (t : Type0) : core_ops_range_Range usize → slice t → result (slice t) = + admit () // TODO + +// [core::slice::index::Range::index_mut]: forward function +let core_slice_index_RangeUsize_index_mut + (t : Type0) : core_ops_range_Range usize → slice t → result (slice t) = + admit () // TODO + +// [core::slice::index::Range::index_mut]: backward function 0 +let core_slice_index_RangeUsize_index_mut_back + (t : Type0) : core_ops_range_Range usize → slice t → slice t → result (slice t) = + admit () // TODO + +// [core::slice::index::[T]::index_mut]: forward function +let core_slice_index_Slice_index_mut + (t idx : Type0) (inst : core_slice_index_SliceIndex idx (slice t)) : + slice t → idx → result inst.output = + admit () // + +// [core::slice::index::[T]::index_mut]: backward function 0 +let core_slice_index_Slice_index_mut_back + (t idx : Type0) (inst : core_slice_index_SliceIndex idx (slice t)) : + slice t → idx → inst.output → result (slice t) = + admit () // TODO + +// [core::array::[T; N]::index]: forward function +let core_array_Array_index + (t idx : Type0) (n : usize) (inst : core_ops_index_Index (slice t) idx) + (a : array t n) (i : idx) : result inst.output = + admit () // TODO + +// [core::array::[T; N]::index_mut]: forward function +let core_array_Array_index_mut + (t idx : Type0) (n : usize) (inst : core_ops_index_IndexMut (slice t) idx) + (a : array t n) (i : idx) : result inst.indexInst.output = + admit () // TODO + +// [core::array::[T; N]::index_mut]: backward function 0 +let core_array_Array_index_mut_back + (t idx : Type0) (n : usize) (inst : core_ops_index_IndexMut (slice t) idx) + (a : array t n) (i : idx) (x : inst.indexInst.output) : result (array t n) = + admit () // TODO + +// Trait implementation: [core::slice::index::private_slice_index::Range] +let core_slice_index_private_slice_index_SealedRangeUsizeInst + : core_slice_index_private_slice_index_Sealed (core_ops_range_Range usize) = () + +// Trait implementation: [core::slice::index::Range] +let core_slice_index_SliceIndexRangeUsizeSliceTInst (t : Type0) : + core_slice_index_SliceIndex (core_ops_range_Range usize) (slice t) = { + sealedInst = core_slice_index_private_slice_index_SealedRangeUsizeInst; + output = slice t; + get = core_slice_index_RangeUsize_get t; + get_mut = core_slice_index_RangeUsize_get_mut t; + get_mut_back = core_slice_index_RangeUsize_get_mut_back t; + get_unchecked = core_slice_index_RangeUsize_get_unchecked t; + get_unchecked_mut = core_slice_index_RangeUsize_get_unchecked_mut t; + index = core_slice_index_RangeUsize_index t; + index_mut = core_slice_index_RangeUsize_index_mut t; + index_mut_back = core_slice_index_RangeUsize_index_mut_back t; +} + +// Trait implementation: [core::slice::index::[T]] +let core_ops_index_IndexSliceTIInst (t idx : Type0) + (inst : core_slice_index_SliceIndex idx (slice t)) : + core_ops_index_Index (slice t) idx = { + output = inst.output; + index = core_slice_index_Slice_index t idx inst; +} + +// Trait implementation: [core::slice::index::[T]] +let core_ops_index_IndexMutSliceTIInst (t idx : Type0) + (inst : core_slice_index_SliceIndex idx (slice t)) : + core_ops_index_IndexMut (slice t) idx = { + indexInst = core_ops_index_IndexSliceTIInst t idx inst; + index_mut = core_slice_index_Slice_index_mut t idx inst; + index_mut_back = core_slice_index_Slice_index_mut_back t idx inst; +} + +// Trait implementation: [core::array::[T; N]] +let core_ops_index_IndexArrayInst (t idx : Type0) (n : usize) + (inst : core_ops_index_Index (slice t) idx) : + core_ops_index_Index (array t n) idx = { + output = inst.output; + index = core_array_Array_index t idx n inst; +} + +// Trait implementation: [core::array::[T; N]] +let core_ops_index_IndexMutArrayIInst (t idx : Type0) (n : usize) + (inst : core_ops_index_IndexMut (slice t) idx) : + core_ops_index_IndexMut (array t n) idx = { + indexInst = core_ops_index_IndexArrayInst t idx n inst.indexInst; + index_mut = core_array_Array_index_mut t idx n inst; + index_mut_back = core_array_Array_index_mut_back t idx n inst; +} + +// [core::slice::index::usize::get]: forward function +let core_slice_index_usize_get + (t : Type0) : usize → slice t → result (option t) = + admit () // TODO + +// [core::slice::index::usize::get_mut]: forward function +let core_slice_index_usize_get_mut + (t : Type0) : usize → slice t → result (option t) = + admit () // TODO + +// [core::slice::index::usize::get_mut]: backward function 0 +let core_slice_index_usize_get_mut_back + (t : Type0) : usize → slice t → option t → result (slice t) = + admit () // TODO + +// [core::slice::index::usize::get_unchecked]: forward function +let core_slice_index_usize_get_unchecked + (t : Type0) : usize → const_raw_ptr (slice t) → result (const_raw_ptr t) = + admit () // TODO + +// [core::slice::index::usize::get_unchecked_mut]: forward function +let core_slice_index_usize_get_unchecked_mut + (t : Type0) : usize → mut_raw_ptr (slice t) → result (mut_raw_ptr t) = + admit () // TODO + +// [core::slice::index::usize::index]: forward function +let core_slice_index_usize_index (t : Type0) : usize → slice t → result t = + admit () // TODO + +// [core::slice::index::usize::index_mut]: forward function +let core_slice_index_usize_index_mut (t : Type0) : usize → slice t → result t = + admit () // TODO + +// [core::slice::index::usize::index_mut]: backward function 0 +let core_slice_index_usize_index_mut_back + (t : Type0) : usize → slice t → t → result (slice t) = + admit () // TODO + +// Trait implementation: [core::slice::index::private_slice_index::usize] +let core_slice_index_private_slice_index_SealedUsizeInst + : core_slice_index_private_slice_index_Sealed usize = () + +// Trait implementation: [core::slice::index::usize] +let core_slice_index_SliceIndexUsizeSliceTInst (t : Type0) : + core_slice_index_SliceIndex usize (slice t) = { + sealedInst = core_slice_index_private_slice_index_SealedUsizeInst; + output = t; + get = core_slice_index_usize_get t; + get_mut = core_slice_index_usize_get_mut t; + get_mut_back = core_slice_index_usize_get_mut_back t; + get_unchecked = core_slice_index_usize_get_unchecked t; + get_unchecked_mut = core_slice_index_usize_get_unchecked_mut t; + index = core_slice_index_usize_index t; + index_mut = core_slice_index_usize_index_mut t; + index_mut_back = core_slice_index_usize_index_mut_back t; +} + +// [alloc::vec::Vec::index]: forward function +let alloc_vec_Vec_index (t idx : Type0) (inst : core_slice_index_SliceIndex idx (slice t)) + (self : alloc_vec_Vec t) (i : idx) : result inst.output = + admit () // TODO + +// [alloc::vec::Vec::index_mut]: forward function +let alloc_vec_Vec_index_mut (t idx : Type0) (inst : core_slice_index_SliceIndex idx (slice t)) + (self : alloc_vec_Vec t) (i : idx) : result inst.output = + admit () // TODO + +// [alloc::vec::Vec::index_mut]: backward function 0 +let alloc_vec_Vec_index_mut_back + (t idx : Type0) (inst : core_slice_index_SliceIndex idx (slice t)) + (self : alloc_vec_Vec t) (i : idx) (x : inst.output) : result (alloc_vec_Vec t) = + admit () // TODO + +// Trait implementation: [alloc::vec::Vec] +let alloc_vec_Vec_coreopsindexIndexInst (t idx : Type0) + (inst : core_slice_index_SliceIndex idx (slice t)) : + core_ops_index_Index (alloc_vec_Vec t) idx = { + output = inst.output; + index = alloc_vec_Vec_index t idx inst; +} + +// Trait implementation: [alloc::vec::Vec] +let alloc_vec_Vec_coreopsindexIndexMutInst (t idx : Type0) + (inst : core_slice_index_SliceIndex idx (slice t)) : + core_ops_index_IndexMut (alloc_vec_Vec t) idx = { + indexInst = alloc_vec_Vec_coreopsindexIndexInst t idx inst; + index_mut = alloc_vec_Vec_index_mut t idx inst; + index_mut_back = alloc_vec_Vec_index_mut_back t idx inst; +} + +(*** Theorems *) + +let alloc_vec_Vec_index_eq (#a : Type0) (v : alloc_vec_Vec a) (i : usize) : + Lemma ( + alloc_vec_Vec_index a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i == + alloc_vec_Vec_index_usize v i) + [SMTPat (alloc_vec_Vec_index a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i)] + = + admit() + +let alloc_vec_Vec_index_mut_eq (#a : Type0) (v : alloc_vec_Vec a) (i : usize) : + Lemma ( + alloc_vec_Vec_index_mut a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i == + alloc_vec_Vec_index_usize v i) + [SMTPat (alloc_vec_Vec_index_mut a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i)] + = + admit() + +let alloc_vec_Vec_index_mut_back_eq (#a : Type0) (v : alloc_vec_Vec a) (i : usize) (x : a) : + Lemma ( + alloc_vec_Vec_index_mut_back a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i x == + alloc_vec_Vec_update_usize v i x) + [SMTPat (alloc_vec_Vec_index_mut_back a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i x)] + = + admit() |