diff options
Diffstat (limited to 'tests/fstar/hashmap_main')
| -rw-r--r-- | tests/fstar/hashmap_main/HashmapMain.Clauses.Template.fst | 72 | ||||
| -rw-r--r-- | tests/fstar/hashmap_main/HashmapMain.Clauses.fst | 61 | ||||
| -rw-r--r-- | tests/fstar/hashmap_main/HashmapMain.Funs.fst | 446 | ||||
| -rw-r--r-- | tests/fstar/hashmap_main/HashmapMain.FunsExternal.fsti | 18 | ||||
| -rw-r--r-- | tests/fstar/hashmap_main/HashmapMain.Properties.fst | 48 | ||||
| -rw-r--r-- | tests/fstar/hashmap_main/HashmapMain.Types.fst | 24 | ||||
| -rw-r--r-- | tests/fstar/hashmap_main/HashmapMain.TypesExternal.fsti | 10 | ||||
| -rw-r--r-- | tests/fstar/hashmap_main/Makefile | 49 | ||||
| -rw-r--r-- | tests/fstar/hashmap_main/Primitives.fst | 929 |
9 files changed, 1657 insertions, 0 deletions
diff --git a/tests/fstar/hashmap_main/HashmapMain.Clauses.Template.fst b/tests/fstar/hashmap_main/HashmapMain.Clauses.Template.fst new file mode 100644 index 00000000..cdd73210 --- /dev/null +++ b/tests/fstar/hashmap_main/HashmapMain.Clauses.Template.fst @@ -0,0 +1,72 @@ +(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *) +(** [hashmap_main]: templates for the decreases clauses *) +module HashmapMain.Clauses.Template +open Primitives +open HashmapMain.Types + +#set-options "--z3rlimit 50 --fuel 1 --ifuel 1" + +(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::allocate_slots]: decreases clause + Source: 'tests/src/hashmap.rs', lines 58:4-64:5 *) +unfold +let hashmap_HashMap_allocate_slots_loop_decreases (t : Type0) + (slots : alloc_vec_Vec (hashmap_List_t t)) (n : usize) : nat = + admit () + +(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::clear]: decreases clause + Source: 'tests/src/hashmap.rs', lines 88:4-96:5 *) +unfold +let hashmap_HashMap_clear_loop_decreases (t : Type0) + (slots : alloc_vec_Vec (hashmap_List_t t)) (i : usize) : nat = + admit () + +(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::insert_in_list]: decreases clause + Source: 'tests/src/hashmap.rs', lines 105:4-122:5 *) +unfold +let hashmap_HashMap_insert_in_list_loop_decreases (t : Type0) (key : usize) + (value : t) (ls : hashmap_List_t t) : nat = + admit () + +(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::move_elements_from_list]: decreases clause + Source: 'tests/src/hashmap.rs', lines 191:4-204:5 *) +unfold +let hashmap_HashMap_move_elements_from_list_loop_decreases (t : Type0) + (ntable : hashmap_HashMap_t t) (ls : hashmap_List_t t) : nat = + admit () + +(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::move_elements]: decreases clause + Source: 'tests/src/hashmap.rs', lines 179:4-188:5 *) +unfold +let hashmap_HashMap_move_elements_loop_decreases (t : Type0) + (ntable : hashmap_HashMap_t t) (slots : alloc_vec_Vec (hashmap_List_t t)) + (i : usize) : nat = + admit () + +(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::contains_key_in_list]: decreases clause + Source: 'tests/src/hashmap.rs', lines 214:4-227:5 *) +unfold +let hashmap_HashMap_contains_key_in_list_loop_decreases (t : Type0) + (key : usize) (ls : hashmap_List_t t) : nat = + admit () + +(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_in_list]: decreases clause + Source: 'tests/src/hashmap.rs', lines 232:4-245:5 *) +unfold +let hashmap_HashMap_get_in_list_loop_decreases (t : Type0) (key : usize) + (ls : hashmap_List_t t) : nat = + admit () + +(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_mut_in_list]: decreases clause + Source: 'tests/src/hashmap.rs', lines 253:4-262:5 *) +unfold +let hashmap_HashMap_get_mut_in_list_loop_decreases (t : Type0) + (ls : hashmap_List_t t) (key : usize) : nat = + admit () + +(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::remove_from_list]: decreases clause + Source: 'tests/src/hashmap.rs', lines 273:4-299:5 *) +unfold +let hashmap_HashMap_remove_from_list_loop_decreases (t : Type0) (key : usize) + (ls : hashmap_List_t t) : nat = + admit () + diff --git a/tests/fstar/hashmap_main/HashmapMain.Clauses.fst b/tests/fstar/hashmap_main/HashmapMain.Clauses.fst new file mode 100644 index 00000000..be5a4ab1 --- /dev/null +++ b/tests/fstar/hashmap_main/HashmapMain.Clauses.fst @@ -0,0 +1,61 @@ +(** [hashmap]: the decreases clauses *) +module HashmapMain.Clauses +open Primitives +open FStar.List.Tot +open HashmapMain.Types + +#set-options "--z3rlimit 50 --fuel 0 --ifuel 1" + +(** [hashmap::HashMap::allocate_slots]: decreases clause *) +unfold +let hashmap_HashMap_allocate_slots_loop_decreases (t : Type0) (slots : alloc_vec_Vec (hashmap_List_t t)) + (n : usize) : nat = n + +(** [hashmap::HashMap::clear]: decreases clause *) +unfold +let hashmap_HashMap_clear_loop_decreases (t : Type0) (slots : alloc_vec_Vec (hashmap_List_t t)) + (i : usize) : nat = + if i < length slots then length slots - i else 0 + +(** [hashmap::HashMap::insert_in_list]: decreases clause *) +unfold +let hashmap_HashMap_insert_in_list_loop_decreases (t : Type0) (key : usize) (value : t) + (ls : hashmap_List_t t) : hashmap_List_t t = + ls + +(** [hashmap::HashMap::move_elements_from_list]: decreases clause *) +unfold +let hashmap_HashMap_move_elements_from_list_loop_decreases (t : Type0) + (ntable : hashmap_HashMap_t t) (ls : hashmap_List_t t) : hashmap_List_t t = + ls + +(** [hashmap::HashMap::move_elements]: decreases clause *) +unfold +let hashmap_HashMap_move_elements_loop_decreases (t : Type0) (ntable : hashmap_HashMap_t t) + (slots : alloc_vec_Vec (hashmap_List_t t)) (i : usize) : nat = + if i < length slots then length slots - i else 0 + +(** [hashmap::HashMap::contains_key_in_list]: decreases clause *) +unfold +let hashmap_HashMap_contains_key_in_list_loop_decreases (t : Type0) (key : usize) + (ls : hashmap_List_t t) : hashmap_List_t t = + ls + +(** [hashmap::HashMap::get_in_list]: decreases clause *) +unfold +let hashmap_HashMap_get_in_list_loop_decreases (t : Type0) (key : usize) (ls : hashmap_List_t t) : + hashmap_List_t t = + ls + +(** [hashmap::HashMap::get_mut_in_list]: decreases clause *) +unfold +let hashmap_HashMap_get_mut_in_list_loop_decreases (t : Type0) + (ls : hashmap_List_t t) (key : usize) : hashmap_List_t t = + ls + +(** [hashmap::HashMap::remove_from_list]: decreases clause *) +unfold +let hashmap_HashMap_remove_from_list_loop_decreases (t : Type0) (key : usize) + (ls : hashmap_List_t t) : hashmap_List_t t = + ls + diff --git a/tests/fstar/hashmap_main/HashmapMain.Funs.fst b/tests/fstar/hashmap_main/HashmapMain.Funs.fst new file mode 100644 index 00000000..c88a746e --- /dev/null +++ b/tests/fstar/hashmap_main/HashmapMain.Funs.fst @@ -0,0 +1,446 @@ +(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *) +(** [hashmap_main]: function definitions *) +module HashmapMain.Funs +open Primitives +include HashmapMain.Types +include HashmapMain.FunsExternal +include HashmapMain.Clauses + +#set-options "--z3rlimit 50 --fuel 1 --ifuel 1" + +(** [hashmap_main::hashmap::hash_key]: + Source: 'tests/src/hashmap.rs', lines 35:0-35:32 *) +let hashmap_hash_key (k : usize) : result usize = + Ok k + +(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::allocate_slots]: loop 0: + Source: 'tests/src/hashmap.rs', lines 58:4-64:5 *) +let rec hashmap_HashMap_allocate_slots_loop + (t : Type0) (slots : alloc_vec_Vec (hashmap_List_t t)) (n : usize) : + Tot (result (alloc_vec_Vec (hashmap_List_t t))) + (decreases (hashmap_HashMap_allocate_slots_loop_decreases t slots n)) + = + if n > 0 + then + let* slots1 = alloc_vec_Vec_push (hashmap_List_t t) slots Hashmap_List_Nil + in + let* n1 = usize_sub n 1 in + hashmap_HashMap_allocate_slots_loop t slots1 n1 + else Ok slots + +(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::allocate_slots]: + Source: 'tests/src/hashmap.rs', lines 58:4-58:76 *) +let hashmap_HashMap_allocate_slots + (t : Type0) (slots : alloc_vec_Vec (hashmap_List_t t)) (n : usize) : + result (alloc_vec_Vec (hashmap_List_t t)) + = + hashmap_HashMap_allocate_slots_loop t slots n + +(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::new_with_capacity]: + Source: 'tests/src/hashmap.rs', lines 67:4-71:13 *) +let hashmap_HashMap_new_with_capacity + (t : Type0) (capacity : usize) (max_load_dividend : usize) + (max_load_divisor : usize) : + result (hashmap_HashMap_t t) + = + let* slots = + hashmap_HashMap_allocate_slots t (alloc_vec_Vec_new (hashmap_List_t t)) + capacity in + let* i = usize_mul capacity max_load_dividend in + let* i1 = usize_div i max_load_divisor in + Ok + { + num_entries = 0; + max_load_factor = (max_load_dividend, max_load_divisor); + max_load = i1; + slots = slots + } + +(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::new]: + Source: 'tests/src/hashmap.rs', lines 83:4-83:24 *) +let hashmap_HashMap_new (t : Type0) : result (hashmap_HashMap_t t) = + hashmap_HashMap_new_with_capacity t 32 4 5 + +(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::clear]: loop 0: + Source: 'tests/src/hashmap.rs', lines 88:4-96:5 *) +let rec hashmap_HashMap_clear_loop + (t : Type0) (slots : alloc_vec_Vec (hashmap_List_t t)) (i : usize) : + Tot (result (alloc_vec_Vec (hashmap_List_t t))) + (decreases (hashmap_HashMap_clear_loop_decreases t slots i)) + = + let i1 = alloc_vec_Vec_len (hashmap_List_t t) slots in + if i < i1 + then + let* (_, index_mut_back) = + alloc_vec_Vec_index_mut (hashmap_List_t t) usize + (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t t)) slots i + in + let* i2 = usize_add i 1 in + let* slots1 = index_mut_back Hashmap_List_Nil in + hashmap_HashMap_clear_loop t slots1 i2 + else Ok slots + +(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::clear]: + Source: 'tests/src/hashmap.rs', lines 88:4-88:27 *) +let hashmap_HashMap_clear + (t : Type0) (self : hashmap_HashMap_t t) : result (hashmap_HashMap_t t) = + let* hm = hashmap_HashMap_clear_loop t self.slots 0 in + Ok { self with num_entries = 0; slots = hm } + +(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::len]: + Source: 'tests/src/hashmap.rs', lines 98:4-98:30 *) +let hashmap_HashMap_len + (t : Type0) (self : hashmap_HashMap_t t) : result usize = + Ok self.num_entries + +(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::insert_in_list]: loop 0: + Source: 'tests/src/hashmap.rs', lines 105:4-122:5 *) +let rec hashmap_HashMap_insert_in_list_loop + (t : Type0) (key : usize) (value : t) (ls : hashmap_List_t t) : + Tot (result (bool & (hashmap_List_t t))) + (decreases (hashmap_HashMap_insert_in_list_loop_decreases t key value ls)) + = + begin match ls with + | Hashmap_List_Cons ckey cvalue tl -> + if ckey = key + then Ok (false, Hashmap_List_Cons ckey value tl) + else + let* (b, tl1) = hashmap_HashMap_insert_in_list_loop t key value tl in + Ok (b, Hashmap_List_Cons ckey cvalue tl1) + | Hashmap_List_Nil -> Ok (true, Hashmap_List_Cons key value Hashmap_List_Nil) + end + +(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::insert_in_list]: + Source: 'tests/src/hashmap.rs', lines 105:4-105:71 *) +let hashmap_HashMap_insert_in_list + (t : Type0) (key : usize) (value : t) (ls : hashmap_List_t t) : + result (bool & (hashmap_List_t t)) + = + hashmap_HashMap_insert_in_list_loop t key value ls + +(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::insert_no_resize]: + Source: 'tests/src/hashmap.rs', lines 125:4-125:54 *) +let hashmap_HashMap_insert_no_resize + (t : Type0) (self : hashmap_HashMap_t t) (key : usize) (value : t) : + result (hashmap_HashMap_t t) + = + let* hash = hashmap_hash_key key in + let i = alloc_vec_Vec_len (hashmap_List_t t) self.slots in + let* hash_mod = usize_rem hash i in + let* (l, index_mut_back) = + alloc_vec_Vec_index_mut (hashmap_List_t t) usize + (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t t)) + self.slots hash_mod in + let* (inserted, l1) = hashmap_HashMap_insert_in_list t key value l in + if inserted + then + let* i1 = usize_add self.num_entries 1 in + let* v = index_mut_back l1 in + Ok { self with num_entries = i1; slots = v } + else let* v = index_mut_back l1 in Ok { self with slots = v } + +(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::move_elements_from_list]: loop 0: + Source: 'tests/src/hashmap.rs', lines 191:4-204:5 *) +let rec hashmap_HashMap_move_elements_from_list_loop + (t : Type0) (ntable : hashmap_HashMap_t t) (ls : hashmap_List_t t) : + Tot (result (hashmap_HashMap_t t)) + (decreases ( + hashmap_HashMap_move_elements_from_list_loop_decreases t ntable ls)) + = + begin match ls with + | Hashmap_List_Cons k v tl -> + let* ntable1 = hashmap_HashMap_insert_no_resize t ntable k v in + hashmap_HashMap_move_elements_from_list_loop t ntable1 tl + | Hashmap_List_Nil -> Ok ntable + end + +(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::move_elements_from_list]: + Source: 'tests/src/hashmap.rs', lines 191:4-191:72 *) +let hashmap_HashMap_move_elements_from_list + (t : Type0) (ntable : hashmap_HashMap_t t) (ls : hashmap_List_t t) : + result (hashmap_HashMap_t t) + = + hashmap_HashMap_move_elements_from_list_loop t ntable ls + +(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::move_elements]: loop 0: + Source: 'tests/src/hashmap.rs', lines 179:4-188:5 *) +let rec hashmap_HashMap_move_elements_loop + (t : Type0) (ntable : hashmap_HashMap_t t) + (slots : alloc_vec_Vec (hashmap_List_t t)) (i : usize) : + Tot (result ((hashmap_HashMap_t t) & (alloc_vec_Vec (hashmap_List_t t)))) + (decreases (hashmap_HashMap_move_elements_loop_decreases t ntable slots i)) + = + let i1 = alloc_vec_Vec_len (hashmap_List_t t) slots in + if i < i1 + then + let* (l, index_mut_back) = + alloc_vec_Vec_index_mut (hashmap_List_t t) usize + (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t t)) slots i + in + let (ls, l1) = core_mem_replace (hashmap_List_t t) l Hashmap_List_Nil in + let* ntable1 = hashmap_HashMap_move_elements_from_list t ntable ls in + let* i2 = usize_add i 1 in + let* slots1 = index_mut_back l1 in + hashmap_HashMap_move_elements_loop t ntable1 slots1 i2 + else Ok (ntable, slots) + +(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::move_elements]: + Source: 'tests/src/hashmap.rs', lines 179:4-179:95 *) +let hashmap_HashMap_move_elements + (t : Type0) (ntable : hashmap_HashMap_t t) + (slots : alloc_vec_Vec (hashmap_List_t t)) (i : usize) : + result ((hashmap_HashMap_t t) & (alloc_vec_Vec (hashmap_List_t t))) + = + hashmap_HashMap_move_elements_loop t ntable slots i + +(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::try_resize]: + Source: 'tests/src/hashmap.rs', lines 148:4-148:28 *) +let hashmap_HashMap_try_resize + (t : Type0) (self : hashmap_HashMap_t t) : result (hashmap_HashMap_t t) = + let* max_usize = scalar_cast U32 Usize core_u32_max in + let capacity = alloc_vec_Vec_len (hashmap_List_t t) self.slots in + let* n1 = usize_div max_usize 2 in + let (i, i1) = self.max_load_factor in + let* i2 = usize_div n1 i in + if capacity <= i2 + then + let* i3 = usize_mul capacity 2 in + let* ntable = hashmap_HashMap_new_with_capacity t i3 i i1 in + let* p = hashmap_HashMap_move_elements t ntable self.slots 0 in + let (ntable1, _) = p in + Ok + { ntable1 with num_entries = self.num_entries; max_load_factor = (i, i1) + } + else Ok { self with max_load_factor = (i, i1) } + +(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::insert]: + Source: 'tests/src/hashmap.rs', lines 137:4-137:48 *) +let hashmap_HashMap_insert + (t : Type0) (self : hashmap_HashMap_t t) (key : usize) (value : t) : + result (hashmap_HashMap_t t) + = + let* self1 = hashmap_HashMap_insert_no_resize t self key value in + let* i = hashmap_HashMap_len t self1 in + if i > self1.max_load then hashmap_HashMap_try_resize t self1 else Ok self1 + +(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::contains_key_in_list]: loop 0: + Source: 'tests/src/hashmap.rs', lines 214:4-227:5 *) +let rec hashmap_HashMap_contains_key_in_list_loop + (t : Type0) (key : usize) (ls : hashmap_List_t t) : + Tot (result bool) + (decreases (hashmap_HashMap_contains_key_in_list_loop_decreases t key ls)) + = + begin match ls with + | Hashmap_List_Cons ckey _ tl -> + if ckey = key + then Ok true + else hashmap_HashMap_contains_key_in_list_loop t key tl + | Hashmap_List_Nil -> Ok false + end + +(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::contains_key_in_list]: + Source: 'tests/src/hashmap.rs', lines 214:4-214:68 *) +let hashmap_HashMap_contains_key_in_list + (t : Type0) (key : usize) (ls : hashmap_List_t t) : result bool = + hashmap_HashMap_contains_key_in_list_loop t key ls + +(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::contains_key]: + Source: 'tests/src/hashmap.rs', lines 207:4-207:49 *) +let hashmap_HashMap_contains_key + (t : Type0) (self : hashmap_HashMap_t t) (key : usize) : result bool = + let* hash = hashmap_hash_key key in + let i = alloc_vec_Vec_len (hashmap_List_t t) self.slots in + let* hash_mod = usize_rem hash i in + let* l = + alloc_vec_Vec_index (hashmap_List_t t) usize + (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t t)) + self.slots hash_mod in + hashmap_HashMap_contains_key_in_list t key l + +(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_in_list]: loop 0: + Source: 'tests/src/hashmap.rs', lines 232:4-245:5 *) +let rec hashmap_HashMap_get_in_list_loop + (t : Type0) (key : usize) (ls : hashmap_List_t t) : + Tot (result t) + (decreases (hashmap_HashMap_get_in_list_loop_decreases t key ls)) + = + begin match ls with + | Hashmap_List_Cons ckey cvalue tl -> + if ckey = key then Ok cvalue else hashmap_HashMap_get_in_list_loop t key tl + | Hashmap_List_Nil -> Fail Failure + end + +(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_in_list]: + Source: 'tests/src/hashmap.rs', lines 232:4-232:70 *) +let hashmap_HashMap_get_in_list + (t : Type0) (key : usize) (ls : hashmap_List_t t) : result t = + hashmap_HashMap_get_in_list_loop t key ls + +(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get]: + Source: 'tests/src/hashmap.rs', lines 247:4-247:55 *) +let hashmap_HashMap_get + (t : Type0) (self : hashmap_HashMap_t t) (key : usize) : result t = + let* hash = hashmap_hash_key key in + let i = alloc_vec_Vec_len (hashmap_List_t t) self.slots in + let* hash_mod = usize_rem hash i in + let* l = + alloc_vec_Vec_index (hashmap_List_t t) usize + (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t t)) + self.slots hash_mod in + hashmap_HashMap_get_in_list t key l + +(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_mut_in_list]: loop 0: + Source: 'tests/src/hashmap.rs', lines 253:4-262:5 *) +let rec hashmap_HashMap_get_mut_in_list_loop + (t : Type0) (ls : hashmap_List_t t) (key : usize) : + Tot (result (t & (t -> result (hashmap_List_t t)))) + (decreases (hashmap_HashMap_get_mut_in_list_loop_decreases t ls key)) + = + begin match ls with + | Hashmap_List_Cons ckey cvalue tl -> + if ckey = key + then + let back = fun ret -> Ok (Hashmap_List_Cons ckey ret tl) in + Ok (cvalue, back) + else + let* (x, back) = hashmap_HashMap_get_mut_in_list_loop t tl key in + let back1 = + fun ret -> + let* tl1 = back ret in Ok (Hashmap_List_Cons ckey cvalue tl1) in + Ok (x, back1) + | Hashmap_List_Nil -> Fail Failure + end + +(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_mut_in_list]: + Source: 'tests/src/hashmap.rs', lines 253:4-253:86 *) +let hashmap_HashMap_get_mut_in_list + (t : Type0) (ls : hashmap_List_t t) (key : usize) : + result (t & (t -> result (hashmap_List_t t))) + = + hashmap_HashMap_get_mut_in_list_loop t ls key + +(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_mut]: + Source: 'tests/src/hashmap.rs', lines 265:4-265:67 *) +let hashmap_HashMap_get_mut + (t : Type0) (self : hashmap_HashMap_t t) (key : usize) : + result (t & (t -> result (hashmap_HashMap_t t))) + = + let* hash = hashmap_hash_key key in + let i = alloc_vec_Vec_len (hashmap_List_t t) self.slots in + let* hash_mod = usize_rem hash i in + let* (l, index_mut_back) = + alloc_vec_Vec_index_mut (hashmap_List_t t) usize + (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t t)) + self.slots hash_mod in + let* (x, get_mut_in_list_back) = hashmap_HashMap_get_mut_in_list t l key in + let back = + fun ret -> + let* l1 = get_mut_in_list_back ret in + let* v = index_mut_back l1 in + Ok { self with slots = v } in + Ok (x, back) + +(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::remove_from_list]: loop 0: + Source: 'tests/src/hashmap.rs', lines 273:4-299:5 *) +let rec hashmap_HashMap_remove_from_list_loop + (t : Type0) (key : usize) (ls : hashmap_List_t t) : + Tot (result ((option t) & (hashmap_List_t t))) + (decreases (hashmap_HashMap_remove_from_list_loop_decreases t key ls)) + = + begin match ls with + | Hashmap_List_Cons ckey x tl -> + if ckey = key + then + let (mv_ls, _) = + core_mem_replace (hashmap_List_t t) (Hashmap_List_Cons ckey x tl) + Hashmap_List_Nil in + begin match mv_ls with + | Hashmap_List_Cons _ cvalue tl1 -> Ok (Some cvalue, tl1) + | Hashmap_List_Nil -> Fail Failure + end + else + let* (o, tl1) = hashmap_HashMap_remove_from_list_loop t key tl in + Ok (o, Hashmap_List_Cons ckey x tl1) + | Hashmap_List_Nil -> Ok (None, Hashmap_List_Nil) + end + +(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::remove_from_list]: + Source: 'tests/src/hashmap.rs', lines 273:4-273:69 *) +let hashmap_HashMap_remove_from_list + (t : Type0) (key : usize) (ls : hashmap_List_t t) : + result ((option t) & (hashmap_List_t t)) + = + hashmap_HashMap_remove_from_list_loop t key ls + +(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::remove]: + Source: 'tests/src/hashmap.rs', lines 302:4-302:52 *) +let hashmap_HashMap_remove + (t : Type0) (self : hashmap_HashMap_t t) (key : usize) : + result ((option t) & (hashmap_HashMap_t t)) + = + let* hash = hashmap_hash_key key in + let i = alloc_vec_Vec_len (hashmap_List_t t) self.slots in + let* hash_mod = usize_rem hash i in + let* (l, index_mut_back) = + alloc_vec_Vec_index_mut (hashmap_List_t t) usize + (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t t)) + self.slots hash_mod in + let* (x, l1) = hashmap_HashMap_remove_from_list t key l in + begin match x with + | None -> let* v = index_mut_back l1 in Ok (None, { self with slots = v }) + | Some x1 -> + let* i1 = usize_sub self.num_entries 1 in + let* v = index_mut_back l1 in + Ok (Some x1, { self with num_entries = i1; slots = v }) + end + +(** [hashmap_main::hashmap::test1]: + Source: 'tests/src/hashmap.rs', lines 323:0-323:10 *) +let hashmap_test1 : result unit = + let* hm = hashmap_HashMap_new u64 in + let* hm1 = hashmap_HashMap_insert u64 hm 0 42 in + let* hm2 = hashmap_HashMap_insert u64 hm1 128 18 in + let* hm3 = hashmap_HashMap_insert u64 hm2 1024 138 in + let* hm4 = hashmap_HashMap_insert u64 hm3 1056 256 in + let* i = hashmap_HashMap_get u64 hm4 128 in + if not (i = 18) + then Fail Failure + else + let* (_, get_mut_back) = hashmap_HashMap_get_mut u64 hm4 1024 in + let* hm5 = get_mut_back 56 in + let* i1 = hashmap_HashMap_get u64 hm5 1024 in + if not (i1 = 56) + then Fail Failure + else + let* (x, hm6) = hashmap_HashMap_remove u64 hm5 1024 in + begin match x with + | None -> Fail Failure + | Some x1 -> + if not (x1 = 56) + then Fail Failure + else + let* i2 = hashmap_HashMap_get u64 hm6 0 in + if not (i2 = 42) + then Fail Failure + else + let* i3 = hashmap_HashMap_get u64 hm6 128 in + if not (i3 = 18) + then Fail Failure + else + let* i4 = hashmap_HashMap_get u64 hm6 1056 in + if not (i4 = 256) then Fail Failure else Ok () + end + +(** [hashmap_main::insert_on_disk]: + Source: 'tests/src/hashmap_main.rs', lines 13:0-13:43 *) +let insert_on_disk + (key : usize) (value : u64) (st : state) : result (state & unit) = + let* (st1, hm) = hashmap_utils_deserialize st in + let* hm1 = hashmap_HashMap_insert u64 hm key value in + hashmap_utils_serialize hm1 st1 + +(** [hashmap_main::main]: + Source: 'tests/src/hashmap_main.rs', lines 22:0-22:13 *) +let main : result unit = + Ok () + diff --git a/tests/fstar/hashmap_main/HashmapMain.FunsExternal.fsti b/tests/fstar/hashmap_main/HashmapMain.FunsExternal.fsti new file mode 100644 index 00000000..cc20d988 --- /dev/null +++ b/tests/fstar/hashmap_main/HashmapMain.FunsExternal.fsti @@ -0,0 +1,18 @@ +(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *) +(** [hashmap_main]: external function declarations *) +module HashmapMain.FunsExternal +open Primitives +include HashmapMain.Types + +#set-options "--z3rlimit 50 --fuel 1 --ifuel 1" + +(** [hashmap_main::hashmap_utils::deserialize]: + Source: 'tests/src/hashmap_utils.rs', lines 11:0-11:43 *) +val hashmap_utils_deserialize + : state -> result (state & (hashmap_HashMap_t u64)) + +(** [hashmap_main::hashmap_utils::serialize]: + Source: 'tests/src/hashmap_utils.rs', lines 6:0-6:42 *) +val hashmap_utils_serialize + : hashmap_HashMap_t u64 -> state -> result (state & unit) + diff --git a/tests/fstar/hashmap_main/HashmapMain.Properties.fst b/tests/fstar/hashmap_main/HashmapMain.Properties.fst new file mode 100644 index 00000000..beb3dc2c --- /dev/null +++ b/tests/fstar/hashmap_main/HashmapMain.Properties.fst @@ -0,0 +1,48 @@ +(** Properties about the hashmap written on disk *) +module HashmapMain.Properties +open Primitives +open HashmapMain.Funs + +#set-options "--z3rlimit 50 --fuel 0 --ifuel 1" + +/// Below, we focus on the functions to read from disk/write to disk to showcase +/// how such reasoning which mixes opaque functions together with a state-error +/// monad can be performed. + +(*** Hypotheses *) + +/// [state_v] gives us the hash map currently stored on disk +assume +val state_v : state -> hashmap_HashMap_t u64 + +/// [serialize] updates the hash map stored on disk +assume +val serialize_lem (hm : hashmap_HashMap_t u64) (st : state) : Lemma ( + match hashmap_utils_serialize hm st with + | Fail _ -> True + | Ok (st', ()) -> state_v st' == hm) + [SMTPat (hashmap_utils_serialize hm st)] + +/// [deserialize] gives us the hash map stored on disk, without updating it +assume +val deserialize_lem (st : state) : Lemma ( + match hashmap_utils_deserialize st with + | Fail _ -> True + | Ok (st', hm) -> hm == state_v st /\ st' == st) + [SMTPat (hashmap_utils_deserialize st)] + +(*** Lemmas *) + +/// The obvious lemma about [insert_on_disk]: the updated hash map stored on disk +/// is exactly the hash map produced from inserting the binding ([key], [value]) +/// in the hash map previously stored on disk. +val insert_on_disk_lem (key : usize) (value : u64) (st : state) : Lemma ( + match insert_on_disk key value st with + | Fail _ -> True + | Ok (st', ()) -> + let hm = state_v st in + match hashmap_HashMap_insert u64 hm key value with + | Fail _ -> False + | Ok hm' -> hm' == state_v st') + +let insert_on_disk_lem key value st = () diff --git a/tests/fstar/hashmap_main/HashmapMain.Types.fst b/tests/fstar/hashmap_main/HashmapMain.Types.fst new file mode 100644 index 00000000..85bcaeea --- /dev/null +++ b/tests/fstar/hashmap_main/HashmapMain.Types.fst @@ -0,0 +1,24 @@ +(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *) +(** [hashmap_main]: type definitions *) +module HashmapMain.Types +open Primitives +include HashmapMain.TypesExternal + +#set-options "--z3rlimit 50 --fuel 1 --ifuel 1" + +(** [hashmap_main::hashmap::List] + Source: 'tests/src/hashmap.rs', lines 27:0-27:16 *) +type hashmap_List_t (t : Type0) = +| Hashmap_List_Cons : usize -> t -> hashmap_List_t t -> hashmap_List_t t +| Hashmap_List_Nil : hashmap_List_t t + +(** [hashmap_main::hashmap::HashMap] + Source: 'tests/src/hashmap.rs', lines 43:0-43:21 *) +type hashmap_HashMap_t (t : Type0) = +{ + num_entries : usize; + max_load_factor : (usize & usize); + max_load : usize; + slots : alloc_vec_Vec (hashmap_List_t t); +} + diff --git a/tests/fstar/hashmap_main/HashmapMain.TypesExternal.fsti b/tests/fstar/hashmap_main/HashmapMain.TypesExternal.fsti new file mode 100644 index 00000000..75747408 --- /dev/null +++ b/tests/fstar/hashmap_main/HashmapMain.TypesExternal.fsti @@ -0,0 +1,10 @@ +(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *) +(** [hashmap_main]: external type declarations *) +module HashmapMain.TypesExternal +open Primitives + +#set-options "--z3rlimit 50 --fuel 1 --ifuel 1" + +(** The state type used in the state-error monad *) +val state : Type0 + diff --git a/tests/fstar/hashmap_main/Makefile b/tests/fstar/hashmap_main/Makefile new file mode 100644 index 00000000..fa7d1f36 --- /dev/null +++ b/tests/fstar/hashmap_main/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/hashmap_main/Primitives.fst b/tests/fstar/hashmap_main/Primitives.fst new file mode 100644 index 00000000..9951ccc3 --- /dev/null +++ b/tests/fstar/hashmap_main/Primitives.fst @@ -0,0 +1,929 @@ +/// 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 = +| Ok : v:a -> result a +| Fail : e:error -> result a + +// Monadic return operator +unfold let return (#a : Type0) (x : a) : result a = Ok 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 == Ok x)) (ensures fun _ -> True)) : + result b = + match m with + | Ok x -> f x + | Fail e -> Fail e + +// Monadic assert(...) +let massert (b:bool) : result unit = if b then Ok () else Fail Failure + +// Normalize and unwrap a successful result (used for globals). +let eval_global (#a : Type0) (x : result a{Ok? (normalize_term x)}) : a = Ok?.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 & a = (x, x) + +// 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 Ok 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 *) + +/// Trait declaration: [core::clone::Clone] +noeq type core_clone_Clone (self : Type0) = { + clone : self → result self +} + +let core_clone_impls_CloneBool_clone (b : bool) : bool = b + +let core_clone_CloneBool : core_clone_Clone bool = { + clone = fun b -> Ok (core_clone_impls_CloneBool_clone b) +} + +let core_clone_impls_CloneUsize_clone (x : usize) : usize = x +let core_clone_impls_CloneU8_clone (x : u8) : u8 = x +let core_clone_impls_CloneU16_clone (x : u16) : u16 = x +let core_clone_impls_CloneU32_clone (x : u32) : u32 = x +let core_clone_impls_CloneU64_clone (x : u64) : u64 = x +let core_clone_impls_CloneU128_clone (x : u128) : u128 = x + +let core_clone_impls_CloneIsize_clone (x : isize) : isize = x +let core_clone_impls_CloneI8_clone (x : i8) : i8 = x +let core_clone_impls_CloneI16_clone (x : i16) : i16 = x +let core_clone_impls_CloneI32_clone (x : i32) : i32 = x +let core_clone_impls_CloneI64_clone (x : i64) : i64 = x +let core_clone_impls_CloneI128_clone (x : i128) : i128 = x + +let core_clone_CloneUsize : core_clone_Clone usize = { + clone = fun x -> Ok (core_clone_impls_CloneUsize_clone x) +} + +let core_clone_CloneU8 : core_clone_Clone u8 = { + clone = fun x -> Ok (core_clone_impls_CloneU8_clone x) +} + +let core_clone_CloneU16 : core_clone_Clone u16 = { + clone = fun x -> Ok (core_clone_impls_CloneU16_clone x) +} + +let core_clone_CloneU32 : core_clone_Clone u32 = { + clone = fun x -> Ok (core_clone_impls_CloneU32_clone x) +} + +let core_clone_CloneU64 : core_clone_Clone u64 = { + clone = fun x -> Ok (core_clone_impls_CloneU64_clone x) +} + +let core_clone_CloneU128 : core_clone_Clone u128 = { + clone = fun x -> Ok (core_clone_impls_CloneU128_clone x) +} + +let core_clone_CloneIsize : core_clone_Clone isize = { + clone = fun x -> Ok (core_clone_impls_CloneIsize_clone x) +} + +let core_clone_CloneI8 : core_clone_Clone i8 = { + clone = fun x -> Ok (core_clone_impls_CloneI8_clone x) +} + +let core_clone_CloneI16 : core_clone_Clone i16 = { + clone = fun x -> Ok (core_clone_impls_CloneI16_clone x) +} + +let core_clone_CloneI32 : core_clone_Clone i32 = { + clone = fun x -> Ok (core_clone_impls_CloneI32_clone x) +} + +let core_clone_CloneI64 : core_clone_Clone i64 = { + clone = fun x -> Ok (core_clone_impls_CloneI64_clone x) +} + +let core_clone_CloneI128 : core_clone_Clone i128 = { + clone = fun x -> Ok (core_clone_impls_CloneI128_clone x) +} + +(** [core::option::{core::option::Option<T>}::unwrap] *) +let core_option_Option_unwrap (t : Type0) (x : option t) : result t = + match x with + | None -> Fail Failure + | Some x -> Ok x + +(*** 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 & (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 & (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 = Ok x +let alloc_boxed_Box_deref_mut (t : Type0) (x : t) : result (t & (t -> result t)) = + Ok (x, (fun x -> Ok 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; +} + +(*** 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 Ok (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 Ok (list_update x i nx) + else Fail Failure + +let array_index_mut_usize (a : Type0) (n : usize) (x : array a n) (i : usize) : + result (a & (a -> result (array a n))) = + match array_index_usize a n x i with + | Fail e -> Fail e + | Ok v -> + Ok (v, array_update_usize a n x i) + +(*** 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 Ok (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 Ok (list_update x i nx) + else Fail Failure + +let slice_index_mut_usize (a : Type0) (s : slice a) (i : usize) : + result (a & (a -> result (slice a))) = + match slice_index_usize a s i with + | Fail e -> Fail e + | Ok x -> + Ok (x, slice_update_usize a s i) + +(*** Subslices *) + +let array_to_slice (a : Type0) (n : usize) (x : array a n) : result (slice a) = Ok 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 Ok s + else Fail Failure + +let array_to_slice_mut (a : Type0) (n : usize) (x : array a n) : + result (slice a & (slice a -> result (array a n))) = + Ok (x, array_from_slice a n x) + +// 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 Ok (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 Ok (list_update v i x) else Fail Failure + +let alloc_vec_Vec_index_mut_usize (#a : Type0) (v: alloc_vec_Vec a) (i: usize) : + result (a & (a → result (alloc_vec_Vec a))) = + match alloc_vec_Vec_index_usize v i with + | Ok x -> + Ok (x, alloc_vec_Vec_update_usize v i) + | Fail e -> Fail e + +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 + | Ok 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); + Ok (append v [x]) + end + 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 Ok (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 & (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 & (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 -> Ok 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) & (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 & (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 & (inst.output -> result (slice t))) = + admit () // + +// [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 & (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_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; +} + +// 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; +} + +// 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; +} + +// [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 & (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 & (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_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; +} + +// [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 & (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; +} + +(*** 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_mut_usize v i) + [SMTPat (alloc_vec_Vec_index_mut a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i)] + = + admit() |