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-rw-r--r--tests/fstar-split/hashmap/Hashmap.Clauses.Template.fst71
-rw-r--r--tests/fstar-split/hashmap/Hashmap.Clauses.fst61
-rw-r--r--tests/fstar-split/hashmap/Hashmap.Funs.fst529
-rw-r--r--tests/fstar-split/hashmap/Hashmap.Properties.fst3186
-rw-r--r--tests/fstar-split/hashmap/Hashmap.Properties.fsti267
-rw-r--r--tests/fstar-split/hashmap/Hashmap.Types.fst23
-rw-r--r--tests/fstar-split/hashmap/Makefile49
-rw-r--r--tests/fstar-split/hashmap/Primitives.fst884
8 files changed, 0 insertions, 5070 deletions
diff --git a/tests/fstar-split/hashmap/Hashmap.Clauses.Template.fst b/tests/fstar-split/hashmap/Hashmap.Clauses.Template.fst
deleted file mode 100644
index 2733b371..00000000
--- a/tests/fstar-split/hashmap/Hashmap.Clauses.Template.fst
+++ /dev/null
@@ -1,71 +0,0 @@
-(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
-(** [hashmap]: templates for the decreases clauses *)
-module Hashmap.Clauses.Template
-open Primitives
-open Hashmap.Types
-
-#set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
-
-(** [hashmap::{hashmap::HashMap<T>}::allocate_slots]: decreases clause
- Source: 'src/hashmap.rs', lines 50:4-56:5 *)
-unfold
-let hashMap_allocate_slots_loop_decreases (t : Type0)
- (slots : alloc_vec_Vec (list_t t)) (n : usize) : nat =
- admit ()
-
-(** [hashmap::{hashmap::HashMap<T>}::clear]: decreases clause
- Source: 'src/hashmap.rs', lines 80:4-88:5 *)
-unfold
-let hashMap_clear_loop_decreases (t : Type0) (slots : alloc_vec_Vec (list_t t))
- (i : usize) : nat =
- admit ()
-
-(** [hashmap::{hashmap::HashMap<T>}::insert_in_list]: decreases clause
- Source: 'src/hashmap.rs', lines 97:4-114:5 *)
-unfold
-let hashMap_insert_in_list_loop_decreases (t : Type0) (key : usize) (value : t)
- (ls : list_t t) : nat =
- admit ()
-
-(** [hashmap::{hashmap::HashMap<T>}::move_elements_from_list]: decreases clause
- Source: 'src/hashmap.rs', lines 183:4-196:5 *)
-unfold
-let hashMap_move_elements_from_list_loop_decreases (t : Type0)
- (ntable : hashMap_t t) (ls : list_t t) : nat =
- admit ()
-
-(** [hashmap::{hashmap::HashMap<T>}::move_elements]: decreases clause
- Source: 'src/hashmap.rs', lines 171:4-180:5 *)
-unfold
-let hashMap_move_elements_loop_decreases (t : Type0) (ntable : hashMap_t t)
- (slots : alloc_vec_Vec (list_t t)) (i : usize) : nat =
- admit ()
-
-(** [hashmap::{hashmap::HashMap<T>}::contains_key_in_list]: decreases clause
- Source: 'src/hashmap.rs', lines 206:4-219:5 *)
-unfold
-let hashMap_contains_key_in_list_loop_decreases (t : Type0) (key : usize)
- (ls : list_t t) : nat =
- admit ()
-
-(** [hashmap::{hashmap::HashMap<T>}::get_in_list]: decreases clause
- Source: 'src/hashmap.rs', lines 224:4-237:5 *)
-unfold
-let hashMap_get_in_list_loop_decreases (t : Type0) (key : usize)
- (ls : list_t t) : nat =
- admit ()
-
-(** [hashmap::{hashmap::HashMap<T>}::get_mut_in_list]: decreases clause
- Source: 'src/hashmap.rs', lines 245:4-254:5 *)
-unfold
-let hashMap_get_mut_in_list_loop_decreases (t : Type0) (ls : list_t t)
- (key : usize) : nat =
- admit ()
-
-(** [hashmap::{hashmap::HashMap<T>}::remove_from_list]: decreases clause
- Source: 'src/hashmap.rs', lines 265:4-291:5 *)
-unfold
-let hashMap_remove_from_list_loop_decreases (t : Type0) (key : usize)
- (ls : list_t t) : nat =
- admit ()
-
diff --git a/tests/fstar-split/hashmap/Hashmap.Clauses.fst b/tests/fstar-split/hashmap/Hashmap.Clauses.fst
deleted file mode 100644
index 6c699d05..00000000
--- a/tests/fstar-split/hashmap/Hashmap.Clauses.fst
+++ /dev/null
@@ -1,61 +0,0 @@
-(** [hashmap]: the decreases clauses *)
-module Hashmap.Clauses
-open Primitives
-open FStar.List.Tot
-open Hashmap.Types
-
-#set-options "--z3rlimit 50 --fuel 0 --ifuel 1"
-
-(** [hashmap::HashMap::allocate_slots]: decreases clause *)
-unfold
-let hashMap_allocate_slots_loop_decreases (t : Type0)
- (slots : alloc_vec_Vec (list_t t)) (n : usize) : nat = n
-
-(** [hashmap::HashMap::clear]: decreases clause *)
-unfold
-let hashMap_clear_loop_decreases (t : Type0) (slots : alloc_vec_Vec (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_insert_in_list_loop_decreases (t : Type0) (key : usize) (value : t)
- (ls : list_t t) : list_t t =
- ls
-
-(** [hashmap::HashMap::move_elements_from_list]: decreases clause *)
-unfold
-let hashMap_move_elements_from_list_loop_decreases (t : Type0)
- (ntable : hashMap_t t) (ls : list_t t) : list_t t =
- ls
-
-(** [hashmap::HashMap::move_elements]: decreases clause *)
-unfold
-let hashMap_move_elements_loop_decreases (t : Type0) (ntable : hashMap_t t)
- (slots : alloc_vec_Vec (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_contains_key_in_list_loop_decreases (t : Type0) (key : usize)
- (ls : list_t t) : list_t t =
- ls
-
-(** [hashmap::HashMap::get_in_list]: decreases clause *)
-unfold
-let hashMap_get_in_list_loop_decreases (t : Type0) (key : usize) (ls : list_t t) :
- list_t t =
- ls
-
-(** [hashmap::HashMap::get_mut_in_list]: decreases clause *)
-unfold
-let hashMap_get_mut_in_list_loop_decreases (t : Type0) (ls : list_t t)
- (key : usize) : list_t t =
- ls
-
-(** [hashmap::HashMap::remove_from_list]: decreases clause *)
-unfold
-let hashMap_remove_from_list_loop_decreases (t : Type0) (key : usize)
- (ls : list_t t) : list_t t =
- ls
-
diff --git a/tests/fstar-split/hashmap/Hashmap.Funs.fst b/tests/fstar-split/hashmap/Hashmap.Funs.fst
deleted file mode 100644
index 290d49ee..00000000
--- a/tests/fstar-split/hashmap/Hashmap.Funs.fst
+++ /dev/null
@@ -1,529 +0,0 @@
-(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
-(** [hashmap]: function definitions *)
-module Hashmap.Funs
-open Primitives
-include Hashmap.Types
-include Hashmap.Clauses
-
-#set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
-
-(** [hashmap::hash_key]: forward function
- Source: 'src/hashmap.rs', lines 27:0-27:32 *)
-let hash_key (k : usize) : result usize =
- Return k
-
-(** [hashmap::{hashmap::HashMap<T>}::allocate_slots]: loop 0: forward function
- Source: 'src/hashmap.rs', lines 50:4-56:5 *)
-let rec hashMap_allocate_slots_loop
- (t : Type0) (slots : alloc_vec_Vec (list_t t)) (n : usize) :
- Tot (result (alloc_vec_Vec (list_t t)))
- (decreases (hashMap_allocate_slots_loop_decreases t slots n))
- =
- if n > 0
- then
- let* slots1 = alloc_vec_Vec_push (list_t t) slots List_Nil in
- let* n1 = usize_sub n 1 in
- hashMap_allocate_slots_loop t slots1 n1
- else Return slots
-
-(** [hashmap::{hashmap::HashMap<T>}::allocate_slots]: forward function
- Source: 'src/hashmap.rs', lines 50:4-50:76 *)
-let hashMap_allocate_slots
- (t : Type0) (slots : alloc_vec_Vec (list_t t)) (n : usize) :
- result (alloc_vec_Vec (list_t t))
- =
- hashMap_allocate_slots_loop t slots n
-
-(** [hashmap::{hashmap::HashMap<T>}::new_with_capacity]: forward function
- Source: 'src/hashmap.rs', lines 59:4-63:13 *)
-let hashMap_new_with_capacity
- (t : Type0) (capacity : usize) (max_load_dividend : usize)
- (max_load_divisor : usize) :
- result (hashMap_t t)
- =
- let* slots = hashMap_allocate_slots t (alloc_vec_Vec_new (list_t t)) capacity
- in
- let* i = usize_mul capacity max_load_dividend in
- let* i1 = usize_div i max_load_divisor in
- Return
- {
- num_entries = 0;
- max_load_factor = (max_load_dividend, max_load_divisor);
- max_load = i1;
- slots = slots
- }
-
-(** [hashmap::{hashmap::HashMap<T>}::new]: forward function
- Source: 'src/hashmap.rs', lines 75:4-75:24 *)
-let hashMap_new (t : Type0) : result (hashMap_t t) =
- hashMap_new_with_capacity t 32 4 5
-
-(** [hashmap::{hashmap::HashMap<T>}::clear]: loop 0: merged forward/backward function
- (there is a single backward function, and the forward function returns ())
- Source: 'src/hashmap.rs', lines 80:4-88:5 *)
-let rec hashMap_clear_loop
- (t : Type0) (slots : alloc_vec_Vec (list_t t)) (i : usize) :
- Tot (result (alloc_vec_Vec (list_t t)))
- (decreases (hashMap_clear_loop_decreases t slots i))
- =
- let i1 = alloc_vec_Vec_len (list_t t) slots in
- if i < i1
- then
- let* i2 = usize_add i 1 in
- let* slots1 =
- alloc_vec_Vec_index_mut_back (list_t t) usize
- (core_slice_index_SliceIndexUsizeSliceTInst (list_t t)) slots i
- List_Nil in
- hashMap_clear_loop t slots1 i2
- else Return slots
-
-(** [hashmap::{hashmap::HashMap<T>}::clear]: merged forward/backward function
- (there is a single backward function, and the forward function returns ())
- Source: 'src/hashmap.rs', lines 80:4-80:27 *)
-let hashMap_clear (t : Type0) (self : hashMap_t t) : result (hashMap_t t) =
- let* v = hashMap_clear_loop t self.slots 0 in
- Return { self with num_entries = 0; slots = v }
-
-(** [hashmap::{hashmap::HashMap<T>}::len]: forward function
- Source: 'src/hashmap.rs', lines 90:4-90:30 *)
-let hashMap_len (t : Type0) (self : hashMap_t t) : result usize =
- Return self.num_entries
-
-(** [hashmap::{hashmap::HashMap<T>}::insert_in_list]: loop 0: forward function
- Source: 'src/hashmap.rs', lines 97:4-114:5 *)
-let rec hashMap_insert_in_list_loop
- (t : Type0) (key : usize) (value : t) (ls : list_t t) :
- Tot (result bool)
- (decreases (hashMap_insert_in_list_loop_decreases t key value ls))
- =
- begin match ls with
- | List_Cons ckey _ tl ->
- if ckey = key
- then Return false
- else hashMap_insert_in_list_loop t key value tl
- | List_Nil -> Return true
- end
-
-(** [hashmap::{hashmap::HashMap<T>}::insert_in_list]: forward function
- Source: 'src/hashmap.rs', lines 97:4-97:71 *)
-let hashMap_insert_in_list
- (t : Type0) (key : usize) (value : t) (ls : list_t t) : result bool =
- hashMap_insert_in_list_loop t key value ls
-
-(** [hashmap::{hashmap::HashMap<T>}::insert_in_list]: loop 0: backward function 0
- Source: 'src/hashmap.rs', lines 97:4-114:5 *)
-let rec hashMap_insert_in_list_loop_back
- (t : Type0) (key : usize) (value : t) (ls : list_t t) :
- Tot (result (list_t t))
- (decreases (hashMap_insert_in_list_loop_decreases t key value ls))
- =
- begin match ls with
- | List_Cons ckey cvalue tl ->
- if ckey = key
- then Return (List_Cons ckey value tl)
- else
- let* tl1 = hashMap_insert_in_list_loop_back t key value tl in
- Return (List_Cons ckey cvalue tl1)
- | List_Nil -> Return (List_Cons key value List_Nil)
- end
-
-(** [hashmap::{hashmap::HashMap<T>}::insert_in_list]: backward function 0
- Source: 'src/hashmap.rs', lines 97:4-97:71 *)
-let hashMap_insert_in_list_back
- (t : Type0) (key : usize) (value : t) (ls : list_t t) : result (list_t t) =
- hashMap_insert_in_list_loop_back t key value ls
-
-(** [hashmap::{hashmap::HashMap<T>}::insert_no_resize]: merged forward/backward function
- (there is a single backward function, and the forward function returns ())
- Source: 'src/hashmap.rs', lines 117:4-117:54 *)
-let hashMap_insert_no_resize
- (t : Type0) (self : hashMap_t t) (key : usize) (value : t) :
- result (hashMap_t t)
- =
- let* hash = hash_key key in
- let i = alloc_vec_Vec_len (list_t t) self.slots in
- let* hash_mod = usize_rem hash i in
- let* l =
- alloc_vec_Vec_index_mut (list_t t) usize
- (core_slice_index_SliceIndexUsizeSliceTInst (list_t t)) self.slots
- hash_mod in
- let* inserted = hashMap_insert_in_list t key value l in
- if inserted
- then
- let* i1 = usize_add self.num_entries 1 in
- let* l1 = hashMap_insert_in_list_back t key value l in
- let* v =
- alloc_vec_Vec_index_mut_back (list_t t) usize
- (core_slice_index_SliceIndexUsizeSliceTInst (list_t t)) self.slots
- hash_mod l1 in
- Return { self with num_entries = i1; slots = v }
- else
- let* l1 = hashMap_insert_in_list_back t key value l in
- let* v =
- alloc_vec_Vec_index_mut_back (list_t t) usize
- (core_slice_index_SliceIndexUsizeSliceTInst (list_t t)) self.slots
- hash_mod l1 in
- Return { self with slots = v }
-
-(** [hashmap::{hashmap::HashMap<T>}::move_elements_from_list]: loop 0: merged forward/backward function
- (there is a single backward function, and the forward function returns ())
- Source: 'src/hashmap.rs', lines 183:4-196:5 *)
-let rec hashMap_move_elements_from_list_loop
- (t : Type0) (ntable : hashMap_t t) (ls : list_t t) :
- Tot (result (hashMap_t t))
- (decreases (hashMap_move_elements_from_list_loop_decreases t ntable ls))
- =
- begin match ls with
- | List_Cons k v tl ->
- let* ntable1 = hashMap_insert_no_resize t ntable k v in
- hashMap_move_elements_from_list_loop t ntable1 tl
- | List_Nil -> Return ntable
- end
-
-(** [hashmap::{hashmap::HashMap<T>}::move_elements_from_list]: merged forward/backward function
- (there is a single backward function, and the forward function returns ())
- Source: 'src/hashmap.rs', lines 183:4-183:72 *)
-let hashMap_move_elements_from_list
- (t : Type0) (ntable : hashMap_t t) (ls : list_t t) : result (hashMap_t t) =
- hashMap_move_elements_from_list_loop t ntable ls
-
-(** [hashmap::{hashmap::HashMap<T>}::move_elements]: loop 0: merged forward/backward function
- (there is a single backward function, and the forward function returns ())
- Source: 'src/hashmap.rs', lines 171:4-180:5 *)
-let rec hashMap_move_elements_loop
- (t : Type0) (ntable : hashMap_t t) (slots : alloc_vec_Vec (list_t t))
- (i : usize) :
- Tot (result ((hashMap_t t) & (alloc_vec_Vec (list_t t))))
- (decreases (hashMap_move_elements_loop_decreases t ntable slots i))
- =
- let i1 = alloc_vec_Vec_len (list_t t) slots in
- if i < i1
- then
- let* l =
- alloc_vec_Vec_index_mut (list_t t) usize
- (core_slice_index_SliceIndexUsizeSliceTInst (list_t t)) slots i in
- let ls = core_mem_replace (list_t t) l List_Nil in
- let* ntable1 = hashMap_move_elements_from_list t ntable ls in
- let* i2 = usize_add i 1 in
- let l1 = core_mem_replace_back (list_t t) l List_Nil in
- let* slots1 =
- alloc_vec_Vec_index_mut_back (list_t t) usize
- (core_slice_index_SliceIndexUsizeSliceTInst (list_t t)) slots i l1 in
- hashMap_move_elements_loop t ntable1 slots1 i2
- else Return (ntable, slots)
-
-(** [hashmap::{hashmap::HashMap<T>}::move_elements]: merged forward/backward function
- (there is a single backward function, and the forward function returns ())
- Source: 'src/hashmap.rs', lines 171:4-171:95 *)
-let hashMap_move_elements
- (t : Type0) (ntable : hashMap_t t) (slots : alloc_vec_Vec (list_t t))
- (i : usize) :
- result ((hashMap_t t) & (alloc_vec_Vec (list_t t)))
- =
- hashMap_move_elements_loop t ntable slots i
-
-(** [hashmap::{hashmap::HashMap<T>}::try_resize]: merged forward/backward function
- (there is a single backward function, and the forward function returns ())
- Source: 'src/hashmap.rs', lines 140:4-140:28 *)
-let hashMap_try_resize
- (t : Type0) (self : hashMap_t t) : result (hashMap_t t) =
- let* max_usize = scalar_cast U32 Usize core_u32_max in
- let capacity = alloc_vec_Vec_len (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_new_with_capacity t i3 i i1 in
- let* (ntable1, _) = hashMap_move_elements t ntable self.slots 0 in
- Return
- { ntable1 with num_entries = self.num_entries; max_load_factor = (i, i1)
- }
- else Return { self with max_load_factor = (i, i1) }
-
-(** [hashmap::{hashmap::HashMap<T>}::insert]: merged forward/backward function
- (there is a single backward function, and the forward function returns ())
- Source: 'src/hashmap.rs', lines 129:4-129:48 *)
-let hashMap_insert
- (t : Type0) (self : hashMap_t t) (key : usize) (value : t) :
- result (hashMap_t t)
- =
- let* self1 = hashMap_insert_no_resize t self key value in
- let* i = hashMap_len t self1 in
- if i > self1.max_load then hashMap_try_resize t self1 else Return self1
-
-(** [hashmap::{hashmap::HashMap<T>}::contains_key_in_list]: loop 0: forward function
- Source: 'src/hashmap.rs', lines 206:4-219:5 *)
-let rec hashMap_contains_key_in_list_loop
- (t : Type0) (key : usize) (ls : list_t t) :
- Tot (result bool)
- (decreases (hashMap_contains_key_in_list_loop_decreases t key ls))
- =
- begin match ls with
- | List_Cons ckey _ tl ->
- if ckey = key
- then Return true
- else hashMap_contains_key_in_list_loop t key tl
- | List_Nil -> Return false
- end
-
-(** [hashmap::{hashmap::HashMap<T>}::contains_key_in_list]: forward function
- Source: 'src/hashmap.rs', lines 206:4-206:68 *)
-let hashMap_contains_key_in_list
- (t : Type0) (key : usize) (ls : list_t t) : result bool =
- hashMap_contains_key_in_list_loop t key ls
-
-(** [hashmap::{hashmap::HashMap<T>}::contains_key]: forward function
- Source: 'src/hashmap.rs', lines 199:4-199:49 *)
-let hashMap_contains_key
- (t : Type0) (self : hashMap_t t) (key : usize) : result bool =
- let* hash = hash_key key in
- let i = alloc_vec_Vec_len (list_t t) self.slots in
- let* hash_mod = usize_rem hash i in
- let* l =
- alloc_vec_Vec_index (list_t t) usize
- (core_slice_index_SliceIndexUsizeSliceTInst (list_t t)) self.slots
- hash_mod in
- hashMap_contains_key_in_list t key l
-
-(** [hashmap::{hashmap::HashMap<T>}::get_in_list]: loop 0: forward function
- Source: 'src/hashmap.rs', lines 224:4-237:5 *)
-let rec hashMap_get_in_list_loop
- (t : Type0) (key : usize) (ls : list_t t) :
- Tot (result t) (decreases (hashMap_get_in_list_loop_decreases t key ls))
- =
- begin match ls with
- | List_Cons ckey cvalue tl ->
- if ckey = key then Return cvalue else hashMap_get_in_list_loop t key tl
- | List_Nil -> Fail Failure
- end
-
-(** [hashmap::{hashmap::HashMap<T>}::get_in_list]: forward function
- Source: 'src/hashmap.rs', lines 224:4-224:70 *)
-let hashMap_get_in_list (t : Type0) (key : usize) (ls : list_t t) : result t =
- hashMap_get_in_list_loop t key ls
-
-(** [hashmap::{hashmap::HashMap<T>}::get]: forward function
- Source: 'src/hashmap.rs', lines 239:4-239:55 *)
-let hashMap_get (t : Type0) (self : hashMap_t t) (key : usize) : result t =
- let* hash = hash_key key in
- let i = alloc_vec_Vec_len (list_t t) self.slots in
- let* hash_mod = usize_rem hash i in
- let* l =
- alloc_vec_Vec_index (list_t t) usize
- (core_slice_index_SliceIndexUsizeSliceTInst (list_t t)) self.slots
- hash_mod in
- hashMap_get_in_list t key l
-
-(** [hashmap::{hashmap::HashMap<T>}::get_mut_in_list]: loop 0: forward function
- Source: 'src/hashmap.rs', lines 245:4-254:5 *)
-let rec hashMap_get_mut_in_list_loop
- (t : Type0) (ls : list_t t) (key : usize) :
- Tot (result t) (decreases (hashMap_get_mut_in_list_loop_decreases t ls key))
- =
- begin match ls with
- | List_Cons ckey cvalue tl ->
- if ckey = key then Return cvalue else hashMap_get_mut_in_list_loop t tl key
- | List_Nil -> Fail Failure
- end
-
-(** [hashmap::{hashmap::HashMap<T>}::get_mut_in_list]: forward function
- Source: 'src/hashmap.rs', lines 245:4-245:86 *)
-let hashMap_get_mut_in_list
- (t : Type0) (ls : list_t t) (key : usize) : result t =
- hashMap_get_mut_in_list_loop t ls key
-
-(** [hashmap::{hashmap::HashMap<T>}::get_mut_in_list]: loop 0: backward function 0
- Source: 'src/hashmap.rs', lines 245:4-254:5 *)
-let rec hashMap_get_mut_in_list_loop_back
- (t : Type0) (ls : list_t t) (key : usize) (ret : t) :
- Tot (result (list_t t))
- (decreases (hashMap_get_mut_in_list_loop_decreases t ls key))
- =
- begin match ls with
- | List_Cons ckey cvalue tl ->
- if ckey = key
- then Return (List_Cons ckey ret tl)
- else
- let* tl1 = hashMap_get_mut_in_list_loop_back t tl key ret in
- Return (List_Cons ckey cvalue tl1)
- | List_Nil -> Fail Failure
- end
-
-(** [hashmap::{hashmap::HashMap<T>}::get_mut_in_list]: backward function 0
- Source: 'src/hashmap.rs', lines 245:4-245:86 *)
-let hashMap_get_mut_in_list_back
- (t : Type0) (ls : list_t t) (key : usize) (ret : t) : result (list_t t) =
- hashMap_get_mut_in_list_loop_back t ls key ret
-
-(** [hashmap::{hashmap::HashMap<T>}::get_mut]: forward function
- Source: 'src/hashmap.rs', lines 257:4-257:67 *)
-let hashMap_get_mut (t : Type0) (self : hashMap_t t) (key : usize) : result t =
- let* hash = hash_key key in
- let i = alloc_vec_Vec_len (list_t t) self.slots in
- let* hash_mod = usize_rem hash i in
- let* l =
- alloc_vec_Vec_index_mut (list_t t) usize
- (core_slice_index_SliceIndexUsizeSliceTInst (list_t t)) self.slots
- hash_mod in
- hashMap_get_mut_in_list t l key
-
-(** [hashmap::{hashmap::HashMap<T>}::get_mut]: backward function 0
- Source: 'src/hashmap.rs', lines 257:4-257:67 *)
-let hashMap_get_mut_back
- (t : Type0) (self : hashMap_t t) (key : usize) (ret : t) :
- result (hashMap_t t)
- =
- let* hash = hash_key key in
- let i = alloc_vec_Vec_len (list_t t) self.slots in
- let* hash_mod = usize_rem hash i in
- let* l =
- alloc_vec_Vec_index_mut (list_t t) usize
- (core_slice_index_SliceIndexUsizeSliceTInst (list_t t)) self.slots
- hash_mod in
- let* l1 = hashMap_get_mut_in_list_back t l key ret in
- let* v =
- alloc_vec_Vec_index_mut_back (list_t t) usize
- (core_slice_index_SliceIndexUsizeSliceTInst (list_t t)) self.slots
- hash_mod l1 in
- Return { self with slots = v }
-
-(** [hashmap::{hashmap::HashMap<T>}::remove_from_list]: loop 0: forward function
- Source: 'src/hashmap.rs', lines 265:4-291:5 *)
-let rec hashMap_remove_from_list_loop
- (t : Type0) (key : usize) (ls : list_t t) :
- Tot (result (option t))
- (decreases (hashMap_remove_from_list_loop_decreases t key ls))
- =
- begin match ls with
- | List_Cons ckey x tl ->
- if ckey = key
- then
- let mv_ls = core_mem_replace (list_t t) (List_Cons ckey x tl) List_Nil in
- begin match mv_ls with
- | List_Cons _ cvalue _ -> Return (Some cvalue)
- | List_Nil -> Fail Failure
- end
- else hashMap_remove_from_list_loop t key tl
- | List_Nil -> Return None
- end
-
-(** [hashmap::{hashmap::HashMap<T>}::remove_from_list]: forward function
- Source: 'src/hashmap.rs', lines 265:4-265:69 *)
-let hashMap_remove_from_list
- (t : Type0) (key : usize) (ls : list_t t) : result (option t) =
- hashMap_remove_from_list_loop t key ls
-
-(** [hashmap::{hashmap::HashMap<T>}::remove_from_list]: loop 0: backward function 1
- Source: 'src/hashmap.rs', lines 265:4-291:5 *)
-let rec hashMap_remove_from_list_loop_back
- (t : Type0) (key : usize) (ls : list_t t) :
- Tot (result (list_t t))
- (decreases (hashMap_remove_from_list_loop_decreases t key ls))
- =
- begin match ls with
- | List_Cons ckey x tl ->
- if ckey = key
- then
- let mv_ls = core_mem_replace (list_t t) (List_Cons ckey x tl) List_Nil in
- begin match mv_ls with
- | List_Cons _ _ tl1 -> Return tl1
- | List_Nil -> Fail Failure
- end
- else
- let* tl1 = hashMap_remove_from_list_loop_back t key tl in
- Return (List_Cons ckey x tl1)
- | List_Nil -> Return List_Nil
- end
-
-(** [hashmap::{hashmap::HashMap<T>}::remove_from_list]: backward function 1
- Source: 'src/hashmap.rs', lines 265:4-265:69 *)
-let hashMap_remove_from_list_back
- (t : Type0) (key : usize) (ls : list_t t) : result (list_t t) =
- hashMap_remove_from_list_loop_back t key ls
-
-(** [hashmap::{hashmap::HashMap<T>}::remove]: forward function
- Source: 'src/hashmap.rs', lines 294:4-294:52 *)
-let hashMap_remove
- (t : Type0) (self : hashMap_t t) (key : usize) : result (option t) =
- let* hash = hash_key key in
- let i = alloc_vec_Vec_len (list_t t) self.slots in
- let* hash_mod = usize_rem hash i in
- let* l =
- alloc_vec_Vec_index_mut (list_t t) usize
- (core_slice_index_SliceIndexUsizeSliceTInst (list_t t)) self.slots
- hash_mod in
- let* x = hashMap_remove_from_list t key l in
- begin match x with
- | None -> Return None
- | Some x1 -> let* _ = usize_sub self.num_entries 1 in Return (Some x1)
- end
-
-(** [hashmap::{hashmap::HashMap<T>}::remove]: backward function 0
- Source: 'src/hashmap.rs', lines 294:4-294:52 *)
-let hashMap_remove_back
- (t : Type0) (self : hashMap_t t) (key : usize) : result (hashMap_t t) =
- let* hash = hash_key key in
- let i = alloc_vec_Vec_len (list_t t) self.slots in
- let* hash_mod = usize_rem hash i in
- let* l =
- alloc_vec_Vec_index_mut (list_t t) usize
- (core_slice_index_SliceIndexUsizeSliceTInst (list_t t)) self.slots
- hash_mod in
- let* x = hashMap_remove_from_list t key l in
- begin match x with
- | None ->
- let* l1 = hashMap_remove_from_list_back t key l in
- let* v =
- alloc_vec_Vec_index_mut_back (list_t t) usize
- (core_slice_index_SliceIndexUsizeSliceTInst (list_t t)) self.slots
- hash_mod l1 in
- Return { self with slots = v }
- | Some _ ->
- let* i1 = usize_sub self.num_entries 1 in
- let* l1 = hashMap_remove_from_list_back t key l in
- let* v =
- alloc_vec_Vec_index_mut_back (list_t t) usize
- (core_slice_index_SliceIndexUsizeSliceTInst (list_t t)) self.slots
- hash_mod l1 in
- Return { self with num_entries = i1; slots = v }
- end
-
-(** [hashmap::test1]: forward function
- Source: 'src/hashmap.rs', lines 315:0-315:10 *)
-let test1 : result unit =
- let* hm = hashMap_new u64 in
- let* hm1 = hashMap_insert u64 hm 0 42 in
- let* hm2 = hashMap_insert u64 hm1 128 18 in
- let* hm3 = hashMap_insert u64 hm2 1024 138 in
- let* hm4 = hashMap_insert u64 hm3 1056 256 in
- let* i = hashMap_get u64 hm4 128 in
- if not (i = 18)
- then Fail Failure
- else
- let* hm5 = hashMap_get_mut_back u64 hm4 1024 56 in
- let* i1 = hashMap_get u64 hm5 1024 in
- if not (i1 = 56)
- then Fail Failure
- else
- let* x = hashMap_remove u64 hm5 1024 in
- begin match x with
- | None -> Fail Failure
- | Some x1 ->
- if not (x1 = 56)
- then Fail Failure
- else
- let* hm6 = hashMap_remove_back u64 hm5 1024 in
- let* i2 = hashMap_get u64 hm6 0 in
- if not (i2 = 42)
- then Fail Failure
- else
- let* i3 = hashMap_get u64 hm6 128 in
- if not (i3 = 18)
- then Fail Failure
- else
- let* i4 = hashMap_get u64 hm6 1056 in
- if not (i4 = 256) then Fail Failure else Return ()
- end
-
diff --git a/tests/fstar-split/hashmap/Hashmap.Properties.fst b/tests/fstar-split/hashmap/Hashmap.Properties.fst
deleted file mode 100644
index def520f0..00000000
--- a/tests/fstar-split/hashmap/Hashmap.Properties.fst
+++ /dev/null
@@ -1,3186 +0,0 @@
-(** Properties about the hashmap *)
-module Hashmap.Properties
-open Primitives
-open FStar.List.Tot
-open FStar.Mul
-open Hashmap.Types
-open Hashmap.Clauses
-open Hashmap.Funs
-
-#set-options "--z3rlimit 50 --fuel 0 --ifuel 1"
-
-let _align_fsti = ()
-
-/// The proofs:
-/// ===========
-///
-/// The proof strategy is to do exactly as with Low* proofs (we initially tried to
-/// prove more properties in one go, but it was a mistake):
-/// - prove that, under some preconditions, the low-level functions translated
-/// from Rust refine some higher-level functions
-/// - do functional proofs about those high-level functions to prove interesting
-/// properties about the hash map operations, and invariant preservation
-/// - combine everything
-///
-/// The fact that we work in a pure setting allows us to be more modular than when
-/// working with effects. For instance we can do a case disjunction (see the proofs
-/// for insert, which study the cases where the key is already/not in the hash map
-/// in separate proofs - we had initially tried to do them in one step: it is doable
-/// but requires some work, and the F* response time quickly becomes annoying while
-/// making progress, so we split them). We can also easily prove a refinement lemma,
-/// study the model, *then* combine those to also prove that the low-level function
-/// preserves the invariants, rather than do everything at once as is usually the
-/// case when doing intrinsic proofs with effects (I remember that having to prove
-/// invariants in one go *and* a refinement step, even small, can be extremely
-/// difficult in Low*).
-
-
-(*** Utilities *)
-
-/// We need many small helpers and lemmas, mostly about lists (and the ones we list
-/// here are not in the standard F* library).
-
-val index_append_lem (#a : Type0) (ls0 ls1 : list a) (i : nat{i < length ls0 + length ls1}) :
- Lemma (
- (i < length ls0 ==> index (ls0 @ ls1) i == index ls0 i) /\
- (i >= length ls0 ==> index (ls0 @ ls1) i == index ls1 (i - length ls0)))
- [SMTPat (index (ls0 @ ls1) i)]
-
-#push-options "--fuel 1"
-let rec index_append_lem #a ls0 ls1 i =
- match ls0 with
- | [] -> ()
- | x :: ls0' ->
- if i = 0 then ()
- else index_append_lem ls0' ls1 (i-1)
-#pop-options
-
-val index_map_lem (#a #b: Type0) (f : a -> Tot b) (ls : list a)
- (i : nat{i < length ls}) :
- Lemma (
- index (map f ls) i == f (index ls i))
- [SMTPat (index (map f ls) i)]
-
-#push-options "--fuel 1"
-let rec index_map_lem #a #b f ls i =
- match ls with
- | [] -> ()
- | x :: ls' ->
- if i = 0 then ()
- else index_map_lem f ls' (i-1)
-#pop-options
-
-val for_all_append (#a : Type0) (f : a -> Tot bool) (ls0 ls1 : list a) :
- Lemma (for_all f (ls0 @ ls1) = (for_all f ls0 && for_all f ls1))
-
-#push-options "--fuel 1"
-let rec for_all_append #a f ls0 ls1 =
- match ls0 with
- | [] -> ()
- | x :: ls0' ->
- for_all_append f ls0' ls1
-#pop-options
-
-/// Filter a list, stopping after we removed one element
-val filter_one (#a : Type) (f : a -> bool) (ls : list a) : list a
-
-let rec filter_one #a f ls =
- match ls with
- | [] -> []
- | x :: ls' -> if f x then x :: filter_one f ls' else ls'
-
-val find_append (#a : Type) (f : a -> bool) (ls0 ls1 : list a) :
- Lemma (
- find f (ls0 @ ls1) ==
- begin match find f ls0 with
- | Some x -> Some x
- | None -> find f ls1
- end)
-
-#push-options "--fuel 1"
-let rec find_append #a f ls0 ls1 =
- match ls0 with
- | [] -> ()
- | x :: ls0' ->
- if f x then
- begin
- assert(ls0 @ ls1 == x :: (ls0' @ ls1));
- assert(find f (ls0 @ ls1) == find f (x :: (ls0' @ ls1)));
- // Why do I have to do this?! Is it because of subtyping??
- assert(
- match find f (ls0 @ ls1) with
- | Some x' -> x' == x
- | None -> False)
- end
- else find_append f ls0' ls1
-#pop-options
-
-val length_flatten_update :
- #a:Type
- -> ls:list (list a)
- -> i:nat{i < length ls}
- -> x:list a ->
- Lemma (
- // We want this property:
- // ```
- // length (flatten (list_update ls i x)) =
- // length (flatten ls) - length (index ls i) + length x
- // ```
- length (flatten (list_update ls i x)) + length (index ls i) =
- length (flatten ls) + length x)
-
-#push-options "--fuel 1"
-let rec length_flatten_update #a ls i x =
- match ls with
- | x' :: ls' ->
- assert(flatten ls == x' @ flatten ls'); // Triggers patterns
- assert(length (flatten ls) == length x' + length (flatten ls'));
- if i = 0 then
- begin
- let ls1 = x :: ls' in
- assert(list_update ls i x == ls1);
- assert(flatten ls1 == x @ flatten ls'); // Triggers patterns
- assert(length (flatten ls1) == length x + length (flatten ls'));
- ()
- end
- else
- begin
- length_flatten_update ls' (i-1) x;
- let ls1 = x' :: list_update ls' (i-1) x in
- assert(flatten ls1 == x' @ flatten (list_update ls' (i-1) x)) // Triggers patterns
- end
-#pop-options
-
-val length_flatten_index :
- #a:Type
- -> ls:list (list a)
- -> i:nat{i < length ls} ->
- Lemma (
- length (flatten ls) >= length (index ls i))
-
-#push-options "--fuel 1"
-let rec length_flatten_index #a ls i =
- match ls with
- | x' :: ls' ->
- assert(flatten ls == x' @ flatten ls'); // Triggers patterns
- assert(length (flatten ls) == length x' + length (flatten ls'));
- if i = 0 then ()
- else length_flatten_index ls' (i-1)
-#pop-options
-
-val forall_index_equiv_list_for_all
- (#a : Type) (pred : a -> Tot bool) (ls : list a) :
- Lemma ((forall (i:nat{i < length ls}). pred (index ls i)) <==> for_all pred ls)
-
-#push-options "--fuel 1"
-let rec forall_index_equiv_list_for_all pred ls =
- match ls with
- | [] -> ()
- | x :: ls' ->
- assert(forall (i:nat{i < length ls'}). index ls' i == index ls (i+1));
- assert(forall (i:nat{0 < i /\ i < length ls}). index ls i == index ls' (i-1));
- assert(index ls 0 == x);
- forall_index_equiv_list_for_all pred ls'
-#pop-options
-
-val find_update:
- #a:Type
- -> f:(a -> Tot bool)
- -> ls:list a
- -> x:a
- -> ls':list a{length ls' == length ls}
-#push-options "--fuel 1"
-let rec find_update #a f ls x =
- match ls with
- | [] -> []
- | hd::tl ->
- if f hd then x :: tl else hd :: find_update f tl x
-#pop-options
-
-val pairwise_distinct : #a:eqtype -> ls:list a -> Tot bool
-let rec pairwise_distinct (#a : eqtype) (ls : list a) : Tot bool =
- match ls with
- | [] -> true
- | x :: ls' -> List.Tot.for_all (fun y -> x <> y) ls' && pairwise_distinct ls'
-
-val pairwise_rel : #a:Type -> pred:(a -> a -> Tot bool) -> ls:list a -> Tot bool
-let rec pairwise_rel #a pred ls =
- match ls with
- | [] -> true
- | x :: ls' ->
- for_all (pred x) ls' && pairwise_rel pred ls'
-
-#push-options "--fuel 1"
-let rec flatten_append (#a : Type) (l1 l2: list (list a)) :
- Lemma (flatten (l1 @ l2) == flatten l1 @ flatten l2) =
- match l1 with
- | [] -> ()
- | x :: l1' ->
- flatten_append l1' l2;
- append_assoc x (flatten l1') (flatten l2)
-#pop-options
-
-/// We don't use anonymous functions as parameters to other functions, but rather
-/// introduce auxiliary functions instead: otherwise we can't reason (because
-/// F*'s encoding to the SMT is imprecise for functions)
-let fst_is_disctinct (#a : eqtype) (#b : Type0) (p0 : a & b) (p1 : a & b) : Type0 =
- fst p0 <> fst p1
-
-(*** Lemmas about Primitives *)
-/// TODO: move those lemmas
-
-// TODO: rename to 'insert'?
-val list_update_index_dif_lem
- (#a : Type0) (ls : list a) (i : nat{i < length ls}) (x : a)
- (j : nat{j < length ls}) :
- Lemma (requires (j <> i))
- (ensures (index (list_update ls i x) j == index ls j))
- [SMTPat (index (list_update ls i x) j)]
-
-#push-options "--fuel 1"
-let rec list_update_index_dif_lem #a ls i x j =
- match ls with
- | x' :: ls ->
- if i = 0 then ()
- else if j = 0 then ()
- else
- list_update_index_dif_lem ls (i-1) x (j-1)
-#pop-options
-
-val map_list_update_lem
- (#a #b: Type0) (f : a -> Tot b)
- (ls : list a) (i : nat{i < length ls}) (x : a) :
- Lemma (list_update (map f ls) i (f x) == map f (list_update ls i x))
- [SMTPat (list_update (map f ls) i (f x))]
-
-#push-options "--fuel 1"
-let rec map_list_update_lem #a #b f ls i x =
- match ls with
- | x' :: ls' ->
- if i = 0 then ()
- else map_list_update_lem f ls' (i-1) x
-#pop-options
-
-(*** Invariants, models *)
-
-(**** Internals *)
-/// The following invariants, models, representation functions... are mostly
-/// for the purpose of the proofs.
-
-let is_pos_usize (n : nat) : Type0 = 0 < n /\ n <= usize_max
-type pos_usize = x:usize{x > 0}
-
-type binding (t : Type0) = key & t
-
-type slots_t (t : Type0) = alloc_vec_Vec (list_t t)
-
-/// We represent hash maps as associative lists
-type assoc_list (t : Type0) = list (binding t)
-
-/// Representation function for [list_t]
-let rec list_t_v (#t : Type0) (ls : list_t t) : assoc_list t =
- match ls with
- | List_Nil -> []
- | List_Cons k v tl -> (k,v) :: list_t_v tl
-
-let list_t_len (#t : Type0) (ls : list_t t) : nat = length (list_t_v ls)
-let list_t_index (#t : Type0) (ls : list_t t) (i : nat{i < list_t_len ls}) : binding t =
- index (list_t_v ls) i
-
-type slot_s (t : Type0) = list (binding t)
-type slots_s (t : Type0) = list (slot_s t)
-
-type slot_t (t : Type0) = list_t t
-let slot_t_v #t = list_t_v #t
-
-/// Representation function for the slots.
-let slots_t_v (#t : Type0) (slots : slots_t t) : slots_s t =
- map slot_t_v slots
-
-/// Representation function for the slots, seen as an associative list.
-let slots_t_al_v (#t : Type0) (slots : slots_t t) : assoc_list t =
- flatten (map list_t_v slots)
-
-/// High-level type for the hash-map, seen as a list of associative lists (one
-/// list per slot). This is the representation we use most, internally. Note that
-/// we later introduce a [map_s] representation, which is the one used in the
-/// lemmas shown to the user.
-type hashMap_s t = list (slot_s t)
-
-// TODO: why not always have the condition on the length?
-// 'nes': "non-empty slots"
-type hashMap_s_nes (t : Type0) : Type0 =
- hm:hashMap_s t{is_pos_usize (length hm)}
-
-/// Representation function for [hashMap_t] as a list of slots
-let hashMap_t_v (#t : Type0) (hm : hashMap_t t) : hashMap_s t =
- map list_t_v hm.slots
-
-/// Representation function for [hashMap_t] as an associative list
-let hashMap_t_al_v (#t : Type0) (hm : hashMap_t t) : assoc_list t =
- flatten (hashMap_t_v hm)
-
-// 'nes': "non-empty slots"
-type hashMap_t_nes (t : Type0) : Type0 =
- hm:hashMap_t t{is_pos_usize (length hm.slots)}
-
-let hash_key_s (k : key) : hash =
- Return?.v (hash_key k)
-
-let hash_mod_key (k : key) (len : usize{len > 0}) : hash =
- (hash_key_s k) % len
-
-let not_same_key (#t : Type0) (k : key) (b : binding t) : bool = fst b <> k
-let same_key (#t : Type0) (k : key) (b : binding t) : bool = fst b = k
-
-// We take a [nat] instead of a [hash] on purpose
-let same_hash_mod_key (#t : Type0) (len : usize{len > 0}) (h : nat) (b : binding t) : bool =
- hash_mod_key (fst b) len = h
-
-let binding_neq (#t : Type0) (b0 b1 : binding t) : bool = fst b0 <> fst b1
-
-let hashMap_t_len_s (#t : Type0) (hm : hashMap_t t) : nat =
- hm.num_entries
-
-let assoc_list_find (#t : Type0) (k : key) (slot : assoc_list t) : option t =
- match find (same_key k) slot with
- | None -> None
- | Some (_, v) -> Some v
-
-let slot_s_find (#t : Type0) (k : key) (slot : list (binding t)) : option t =
- assoc_list_find k slot
-
-let slot_t_find_s (#t : Type0) (k : key) (slot : list_t t) : option t =
- slot_s_find k (slot_t_v slot)
-
-// This is a simpler version of the "find" function, which captures the essence
-// of what happens and operates on [hashMap_s].
-let hashMap_s_find
- (#t : Type0) (hm : hashMap_s_nes t)
- (k : key) : option t =
- let i = hash_mod_key k (length hm) in
- let slot = index hm i in
- slot_s_find k slot
-
-let hashMap_s_len
- (#t : Type0) (hm : hashMap_s t) :
- nat =
- length (flatten hm)
-
-// Same as above, but operates on [hashMap_t]
-// Note that we don't reuse the above function on purpose: converting to a
-// [hashMap_s] then looking up an element is not the same as what we
-// wrote below.
-let hashMap_t_find_s
- (#t : Type0) (hm : hashMap_t t{length hm.slots > 0}) (k : key) : option t =
- let slots = hm.slots in
- let i = hash_mod_key k (length slots) in
- let slot = index slots i in
- slot_t_find_s k slot
-
-/// Invariants for the slots
-
-let slot_s_inv
- (#t : Type0) (len : usize{len > 0}) (i : usize) (slot : list (binding t)) : bool =
- // All the bindings are in the proper slot
- for_all (same_hash_mod_key len i) slot &&
- // All the keys are pairwise distinct
- pairwise_rel binding_neq slot
-
-let slot_t_inv (#t : Type0) (len : usize{len > 0}) (i : usize) (slot : list_t t) : bool =
- slot_s_inv len i (slot_t_v slot)
-
-let slots_s_inv (#t : Type0) (slots : slots_s t{length slots <= usize_max}) : Type0 =
- forall(i:nat{i < length slots}).
- {:pattern index slots i}
- slot_s_inv (length slots) i (index slots i)
-
-// At some point we tried to rewrite this in terms of [slots_s_inv]. However it
-// made a lot of proofs fail because those proofs relied on the [index_map_lem]
-// pattern. We tried writing others lemmas with patterns (like [slots_s_inv]
-// implies [slots_t_inv]) but it didn't succeed, so we keep things as they are.
-let slots_t_inv (#t : Type0) (slots : slots_t t{length slots <= usize_max}) : Type0 =
- forall(i:nat{i < length slots}).
- {:pattern index slots i}
- slot_t_inv (length slots) i (index slots i)
-
-let hashMap_s_inv (#t : Type0) (hm : hashMap_s t) : Type0 =
- length hm <= usize_max /\
- length hm > 0 /\
- slots_s_inv hm
-
-/// Base invariant for the hashmap (the complete invariant can be temporarily
-/// broken between the moment we inserted an element and the moment we resize)
-let hashMap_t_base_inv (#t : Type0) (hm : hashMap_t t) : Type0 =
- let al = hashMap_t_al_v hm in
- // [num_entries] correctly tracks the number of entries in the table
- // Note that it gives us that the length of the slots array is <= usize_max:
- // [> length <= usize_max
- // (because hashMap_num_entries has type `usize`)
- hm.num_entries = length al /\
- // Slots invariant
- slots_t_inv hm.slots /\
- // The capacity must be > 0 (otherwise we can't resize, because we
- // multiply the capacity by two!)
- length hm.slots > 0 /\
- // Load computation
- begin
- let capacity = length hm.slots in
- let (dividend, divisor) = hm.max_load_factor in
- 0 < dividend /\ dividend < divisor /\
- capacity * dividend >= divisor /\
- hm.max_load = (capacity * dividend) / divisor
- end
-
-/// We often need to frame some values
-let hashMap_t_same_params (#t : Type0) (hm0 hm1 : hashMap_t t) : Type0 =
- length hm0.slots = length hm1.slots /\
- hm0.max_load = hm1.max_load /\
- hm0.max_load_factor = hm1.max_load_factor
-
-/// The following invariants, etc. are meant to be revealed to the user through
-/// the .fsti.
-
-/// Invariant for the hashmap
-let hashMap_t_inv (#t : Type0) (hm : hashMap_t t) : Type0 =
- // Base invariant
- hashMap_t_base_inv hm /\
- // The hash map is either: not overloaded, or we can't resize it
- begin
- let (dividend, divisor) = hm.max_load_factor in
- hm.num_entries <= hm.max_load
- || length hm.slots * 2 * dividend > usize_max
- end
-
-(*** .fsti *)
-/// We reveal slightly different version of the above functions to the user
-
-let len_s (#t : Type0) (hm : hashMap_t t) : nat = hashMap_t_len_s hm
-
-/// This version doesn't take any precondition (contrary to [hashMap_t_find_s])
-let find_s (#t : Type0) (hm : hashMap_t t) (k : key) : option t =
- if length hm.slots = 0 then None
- else hashMap_t_find_s hm k
-
-(*** Overloading *)
-
-let hashMap_not_overloaded_lem #t hm = ()
-
-(*** allocate_slots *)
-
-/// Auxiliary lemma
-val slots_t_all_nil_inv_lem
- (#t : Type0) (slots : alloc_vec_Vec (list_t t){length slots <= usize_max}) :
- Lemma (requires (forall (i:nat{i < length slots}). index slots i == List_Nil))
- (ensures (slots_t_inv slots))
-
-#push-options "--fuel 1"
-let slots_t_all_nil_inv_lem #t slots = ()
-#pop-options
-
-val slots_t_al_v_all_nil_is_empty_lem
- (#t : Type0) (slots : alloc_vec_Vec (list_t t)) :
- Lemma (requires (forall (i:nat{i < length slots}). index slots i == List_Nil))
- (ensures (slots_t_al_v slots == []))
-
-#push-options "--fuel 1"
-let rec slots_t_al_v_all_nil_is_empty_lem #t slots =
- match slots with
- | [] -> ()
- | s :: slots' ->
- assert(forall (i:nat{i < length slots'}). index slots' i == index slots (i+1));
- slots_t_al_v_all_nil_is_empty_lem #t slots';
- assert(slots_t_al_v slots == list_t_v s @ slots_t_al_v slots');
- assert(slots_t_al_v slots == list_t_v s);
- assert(index slots 0 == List_Nil)
-#pop-options
-
-/// [allocate_slots]
-val hashMap_allocate_slots_lem
- (t : Type0) (slots : alloc_vec_Vec (list_t t)) (n : usize) :
- Lemma
- (requires (length slots + n <= usize_max))
- (ensures (
- match hashMap_allocate_slots t slots n with
- | Fail _ -> False
- | Return slots' ->
- length slots' = length slots + n /\
- // We leave the already allocated slots unchanged
- (forall (i:nat{i < length slots}). index slots' i == index slots i) /\
- // We allocate n additional empty slots
- (forall (i:nat{length slots <= i /\ i < length slots'}). index slots' i == List_Nil)))
- (decreases (hashMap_allocate_slots_loop_decreases t slots n))
-
-#push-options "--fuel 1"
-let rec hashMap_allocate_slots_lem t slots n =
- begin match n with
- | 0 -> ()
- | _ ->
- begin match alloc_vec_Vec_push (list_t t) slots List_Nil with
- | Fail _ -> ()
- | Return slots1 ->
- begin match usize_sub n 1 with
- | Fail _ -> ()
- | Return i ->
- hashMap_allocate_slots_lem t slots1 i;
- begin match hashMap_allocate_slots t slots1 i with
- | Fail _ -> ()
- | Return slots2 ->
- assert(length slots1 = length slots + 1);
- assert(slots1 == slots @ [List_Nil]); // Triggers patterns
- assert(index slots1 (length slots) == index [List_Nil] 0); // Triggers patterns
- assert(index slots1 (length slots) == List_Nil)
- end
- end
- end
- end
-#pop-options
-
-(*** new_with_capacity *)
-/// Under proper conditions, [new_with_capacity] doesn't fail and returns an empty hash map.
-val hashMap_new_with_capacity_lem
- (t : Type0) (capacity : usize)
- (max_load_dividend : usize) (max_load_divisor : usize) :
- Lemma
- (requires (
- 0 < max_load_dividend /\
- max_load_dividend < max_load_divisor /\
- 0 < capacity /\
- capacity * max_load_dividend >= max_load_divisor /\
- capacity * max_load_dividend <= usize_max))
- (ensures (
- match hashMap_new_with_capacity t capacity max_load_dividend max_load_divisor with
- | Fail _ -> False
- | Return hm ->
- // The hash map invariant is satisfied
- hashMap_t_inv hm /\
- // The parameters are correct
- hm.max_load_factor = (max_load_dividend, max_load_divisor) /\
- hm.max_load = (capacity * max_load_dividend) / max_load_divisor /\
- // The hash map has the specified capacity - we need to reveal this
- // otherwise the pre of [hashMap_t_find_s] is not satisfied.
- length hm.slots = capacity /\
- // The hash map has 0 values
- hashMap_t_len_s hm = 0 /\
- // It contains no bindings
- (forall k. hashMap_t_find_s hm k == None) /\
- // We need this low-level property for the invariant
- (forall(i:nat{i < length hm.slots}). index hm.slots i == List_Nil)))
-
-#push-options "--z3rlimit 50 --fuel 1"
-let hashMap_new_with_capacity_lem (t : Type0) (capacity : usize)
- (max_load_dividend : usize) (max_load_divisor : usize) =
- let v = alloc_vec_Vec_new (list_t t) in
- assert(length v = 0);
- hashMap_allocate_slots_lem t v capacity;
- begin match hashMap_allocate_slots t v capacity with
- | Fail _ -> assert(False)
- | Return v0 ->
- begin match usize_mul capacity max_load_dividend with
- | Fail _ -> assert(False)
- | Return i ->
- begin match usize_div i max_load_divisor with
- | Fail _ -> assert(False)
- | Return i0 ->
- let hm = MkhashMap_t 0 (max_load_dividend, max_load_divisor) i0 v0 in
- slots_t_all_nil_inv_lem v0;
- slots_t_al_v_all_nil_is_empty_lem hm.slots
- end
- end
- end
-#pop-options
-
-(*** new *)
-
-/// [new] doesn't fail and returns an empty hash map
-val hashMap_new_lem_aux (t : Type0) :
- Lemma
- (ensures (
- match hashMap_new t with
- | Fail _ -> False
- | Return hm ->
- // The hash map invariant is satisfied
- hashMap_t_inv hm /\
- // The hash map has 0 values
- hashMap_t_len_s hm = 0 /\
- // It contains no bindings
- (forall k. hashMap_t_find_s hm k == None)))
-
-#push-options "--fuel 1"
-let hashMap_new_lem_aux t =
- hashMap_new_with_capacity_lem t 32 4 5;
- match hashMap_new_with_capacity t 32 4 5 with
- | Fail _ -> ()
- | Return hm -> ()
-#pop-options
-
-/// The lemma we reveal in the .fsti
-let hashMap_new_lem t = hashMap_new_lem_aux t
-
-(*** clear *)
-/// [clear]: the loop doesn't fail and simply clears the slots starting at index i
-#push-options "--fuel 1"
-let rec hashMap_clear_loop_lem
- (t : Type0) (slots : alloc_vec_Vec (list_t t)) (i : usize) :
- Lemma
- (ensures (
- match hashMap_clear_loop t slots i with
- | Fail _ -> False
- | Return slots' ->
- // The length is preserved
- length slots' == length slots /\
- // The slots before i are left unchanged
- (forall (j:nat{j < i /\ j < length slots}). index slots' j == index slots j) /\
- // The slots after i are set to List_Nil
- (forall (j:nat{i <= j /\ j < length slots}). index slots' j == List_Nil)))
- (decreases (hashMap_clear_loop_decreases t slots i))
- =
- let i0 = alloc_vec_Vec_len (list_t t) slots in
- let b = i < i0 in
- if b
- then
- begin match alloc_vec_Vec_update_usize slots i List_Nil with
- | Fail _ -> ()
- | Return v ->
- begin match usize_add i 1 with
- | Fail _ -> ()
- | Return i1 ->
- hashMap_clear_loop_lem t v i1;
- begin match hashMap_clear_loop t v i1 with
- | Fail _ -> ()
- | Return slots1 ->
- assert(length slots1 == length slots);
- assert(forall (j:nat{i+1 <= j /\ j < length slots}). index slots1 j == List_Nil);
- assert(index slots1 i == List_Nil)
- end
- end
- end
- else ()
-#pop-options
-
-/// [clear] doesn't fail and turns the hash map into an empty map
-val hashMap_clear_lem_aux
- (#t : Type0) (self : hashMap_t t) :
- Lemma
- (requires (hashMap_t_base_inv self))
- (ensures (
- match hashMap_clear t self with
- | Fail _ -> False
- | Return hm ->
- // The hash map invariant is satisfied
- hashMap_t_base_inv hm /\
- // We preserved the parameters
- hashMap_t_same_params hm self /\
- // The hash map has 0 values
- hashMap_t_len_s hm = 0 /\
- // It contains no bindings
- (forall k. hashMap_t_find_s hm k == None)))
-
-// Being lazy: fuel 1 helps a lot...
-#push-options "--fuel 1"
-let hashMap_clear_lem_aux #t self =
- let p = self.max_load_factor in
- let i = self.max_load in
- let v = self.slots in
- hashMap_clear_loop_lem t v 0;
- begin match hashMap_clear_loop t v 0 with
- | Fail _ -> ()
- | Return slots1 ->
- slots_t_al_v_all_nil_is_empty_lem slots1;
- let hm1 = MkhashMap_t 0 p i slots1 in
- assert(hashMap_t_base_inv hm1);
- assert(hashMap_t_inv hm1)
- end
-#pop-options
-
-let hashMap_clear_lem #t self = hashMap_clear_lem_aux #t self
-
-(*** len *)
-
-/// [len]: we link it to a non-failing function.
-/// Rk.: we might want to make an analysis to not use an error monad to translate
-/// functions which statically can't fail.
-let hashMap_len_lem #t self = ()
-
-
-(*** insert_in_list *)
-
-(**** insert_in_list'fwd *)
-
-/// [insert_in_list]: returns true iff the key is not in the list (functional version)
-val hashMap_insert_in_list_lem
- (t : Type0) (key : usize) (value : t) (ls : list_t t) :
- Lemma
- (ensures (
- match hashMap_insert_in_list t key value ls with
- | Fail _ -> False
- | Return b ->
- b <==> (slot_t_find_s key ls == None)))
- (decreases (hashMap_insert_in_list_loop_decreases t key value ls))
-
-#push-options "--fuel 1"
-let rec hashMap_insert_in_list_lem t key value ls =
- begin match ls with
- | List_Cons ckey cvalue ls0 ->
- let b = ckey = key in
- if b
- then ()
- else
- begin
- hashMap_insert_in_list_lem t key value ls0;
- match hashMap_insert_in_list t key value ls0 with
- | Fail _ -> ()
- | Return b0 -> ()
- end
- | List_Nil ->
- assert(list_t_v ls == []);
- assert_norm(find (same_key #t key) [] == None)
- end
-#pop-options
-
-(**** insert_in_list'back *)
-
-/// The proofs about [insert_in_list] backward are easier to do in several steps:
-/// extrinsic proofs to the rescue!
-/// We first prove that [insert_in_list] refines the function we wrote above, then
-/// use this function to prove the invariants, etc.
-
-/// We write a helper which "captures" what [insert_in_list] does.
-/// We then reason about this helper to prove the high-level properties we want
-/// (functional properties, preservation of invariants, etc.).
-let hashMap_insert_in_list_s
- (#t : Type0) (key : usize) (value : t) (ls : list (binding t)) :
- list (binding t) =
- // Check if there is already a binding for the key
- match find (same_key key) ls with
- | None ->
- // No binding: append the binding to the end
- ls @ [(key,value)]
- | Some _ ->
- // There is already a binding: update it
- find_update (same_key key) ls (key,value)
-
-/// [insert_in_list]: if the key is not in the map, appends a new bindings (functional version)
-val hashMap_insert_in_list_back_lem_append_s
- (t : Type0) (key : usize) (value : t) (ls : list_t t) :
- Lemma
- (requires (
- slot_t_find_s key ls == None))
- (ensures (
- match hashMap_insert_in_list_back t key value ls with
- | Fail _ -> False
- | Return ls' ->
- list_t_v ls' == list_t_v ls @ [(key,value)]))
- (decreases (hashMap_insert_in_list_loop_decreases t key value ls))
-
-#push-options "--fuel 1"
-let rec hashMap_insert_in_list_back_lem_append_s t key value ls =
- begin match ls with
- | List_Cons ckey cvalue ls0 ->
- let b = ckey = key in
- if b
- then ()
- else
- begin
- hashMap_insert_in_list_back_lem_append_s t key value ls0;
- match hashMap_insert_in_list_back t key value ls0 with
- | Fail _ -> ()
- | Return l -> ()
- end
- | List_Nil -> ()
- end
-#pop-options
-
-/// [insert_in_list]: if the key is in the map, we update the binding (functional version)
-val hashMap_insert_in_list_back_lem_update_s
- (t : Type0) (key : usize) (value : t) (ls : list_t t) :
- Lemma
- (requires (
- Some? (find (same_key key) (list_t_v ls))))
- (ensures (
- match hashMap_insert_in_list_back t key value ls with
- | Fail _ -> False
- | Return ls' ->
- list_t_v ls' == find_update (same_key key) (list_t_v ls) (key,value)))
- (decreases (hashMap_insert_in_list_loop_decreases t key value ls))
-
-#push-options "--fuel 1"
-let rec hashMap_insert_in_list_back_lem_update_s t key value ls =
- begin match ls with
- | List_Cons ckey cvalue ls0 ->
- let b = ckey = key in
- if b
- then ()
- else
- begin
- hashMap_insert_in_list_back_lem_update_s t key value ls0;
- match hashMap_insert_in_list_back t key value ls0 with
- | Fail _ -> ()
- | Return l -> ()
- end
- | List_Nil -> ()
- end
-#pop-options
-
-/// Put everything together
-val hashMap_insert_in_list_back_lem_s
- (t : Type0) (key : usize) (value : t) (ls : list_t t) :
- Lemma
- (ensures (
- match hashMap_insert_in_list_back t key value ls with
- | Fail _ -> False
- | Return ls' ->
- list_t_v ls' == hashMap_insert_in_list_s key value (list_t_v ls)))
-
-let hashMap_insert_in_list_back_lem_s t key value ls =
- match find (same_key key) (list_t_v ls) with
- | None -> hashMap_insert_in_list_back_lem_append_s t key value ls
- | Some _ -> hashMap_insert_in_list_back_lem_update_s t key value ls
-
-(**** Invariants of insert_in_list_s *)
-
-/// Auxiliary lemmas
-/// We work on [hashMap_insert_in_list_s], the "high-level" version of [insert_in_list'back].
-///
-/// Note that in F* we can't have recursive proofs inside of other proofs, contrary
-/// to Coq, which makes it a bit cumbersome to prove auxiliary results like the
-/// following ones...
-
-(** Auxiliary lemmas: append case *)
-
-val slot_t_v_for_all_binding_neq_append_lem
- (t : Type0) (key : usize) (value : t) (ls : list (binding t)) (b : binding t) :
- Lemma
- (requires (
- fst b <> key /\
- for_all (binding_neq b) ls /\
- slot_s_find key ls == None))
- (ensures (
- for_all (binding_neq b) (ls @ [(key,value)])))
-
-#push-options "--fuel 1"
-let rec slot_t_v_for_all_binding_neq_append_lem t key value ls b =
- match ls with
- | [] -> ()
- | (ck, cv) :: cls ->
- slot_t_v_for_all_binding_neq_append_lem t key value cls b
-#pop-options
-
-val slot_s_inv_not_find_append_end_inv_lem
- (t : Type0) (len : usize{len > 0}) (key : usize) (value : t) (ls : list (binding t)) :
- Lemma
- (requires (
- slot_s_inv len (hash_mod_key key len) ls /\
- slot_s_find key ls == None))
- (ensures (
- let ls' = ls @ [(key,value)] in
- slot_s_inv len (hash_mod_key key len) ls' /\
- (slot_s_find key ls' == Some value) /\
- (forall k'. k' <> key ==> slot_s_find k' ls' == slot_s_find k' ls)))
-
-#push-options "--fuel 1"
-let rec slot_s_inv_not_find_append_end_inv_lem t len key value ls =
- match ls with
- | [] -> ()
- | (ck, cv) :: cls ->
- slot_s_inv_not_find_append_end_inv_lem t len key value cls;
- let h = hash_mod_key key len in
- let ls' = ls @ [(key,value)] in
- assert(for_all (same_hash_mod_key len h) ls');
- slot_t_v_for_all_binding_neq_append_lem t key value cls (ck, cv);
- assert(pairwise_rel binding_neq ls');
- assert(slot_s_inv len h ls')
-#pop-options
-
-/// [insert_in_list]: if the key is not in the map, appends a new bindings
-val hashMap_insert_in_list_s_lem_append
- (t : Type0) (len : usize{len > 0}) (key : usize) (value : t) (ls : list (binding t)) :
- Lemma
- (requires (
- slot_s_inv len (hash_mod_key key len) ls /\
- slot_s_find key ls == None))
- (ensures (
- let ls' = hashMap_insert_in_list_s key value ls in
- ls' == ls @ [(key,value)] /\
- // The invariant is preserved
- slot_s_inv len (hash_mod_key key len) ls' /\
- // [key] maps to [value]
- slot_s_find key ls' == Some value /\
- // The other bindings are preserved
- (forall k'. k' <> key ==> slot_s_find k' ls' == slot_s_find k' ls)))
-
-let hashMap_insert_in_list_s_lem_append t len key value ls =
- slot_s_inv_not_find_append_end_inv_lem t len key value ls
-
-/// [insert_in_list]: if the key is not in the map, appends a new bindings (quantifiers)
-/// Rk.: we don't use this lemma.
-/// TODO: remove?
-val hashMap_insert_in_list_back_lem_append
- (t : Type0) (len : usize{len > 0}) (key : usize) (value : t) (ls : list_t t) :
- Lemma
- (requires (
- slot_t_inv len (hash_mod_key key len) ls /\
- slot_t_find_s key ls == None))
- (ensures (
- match hashMap_insert_in_list_back t key value ls with
- | Fail _ -> False
- | Return ls' ->
- list_t_v ls' == list_t_v ls @ [(key,value)] /\
- // The invariant is preserved
- slot_t_inv len (hash_mod_key key len) ls' /\
- // [key] maps to [value]
- slot_t_find_s key ls' == Some value /\
- // The other bindings are preserved
- (forall k'. k' <> key ==> slot_t_find_s k' ls' == slot_t_find_s k' ls)))
-
-let hashMap_insert_in_list_back_lem_append t len key value ls =
- hashMap_insert_in_list_back_lem_s t key value ls;
- hashMap_insert_in_list_s_lem_append t len key value (list_t_v ls)
-
-(** Auxiliary lemmas: update case *)
-
-val slot_s_find_update_for_all_binding_neq_append_lem
- (t : Type0) (key : usize) (value : t) (ls : list (binding t)) (b : binding t) :
- Lemma
- (requires (
- fst b <> key /\
- for_all (binding_neq b) ls))
- (ensures (
- let ls' = find_update (same_key key) ls (key, value) in
- for_all (binding_neq b) ls'))
-
-#push-options "--fuel 1"
-let rec slot_s_find_update_for_all_binding_neq_append_lem t key value ls b =
- match ls with
- | [] -> ()
- | (ck, cv) :: cls ->
- slot_s_find_update_for_all_binding_neq_append_lem t key value cls b
-#pop-options
-
-/// Annoying auxiliary lemma we have to prove because there is no way to reason
-/// properly about closures.
-/// I'm really enjoying my time.
-val for_all_binding_neq_value_indep
- (#t : Type0) (key : key) (v0 v1 : t) (ls : list (binding t)) :
- Lemma (for_all (binding_neq (key,v0)) ls = for_all (binding_neq (key,v1)) ls)
-
-#push-options "--fuel 1"
-let rec for_all_binding_neq_value_indep #t key v0 v1 ls =
- match ls with
- | [] -> ()
- | _ :: ls' -> for_all_binding_neq_value_indep #t key v0 v1 ls'
-#pop-options
-
-val slot_s_inv_find_append_end_inv_lem
- (t : Type0) (len : usize{len > 0}) (key : usize) (value : t) (ls : list (binding t)) :
- Lemma
- (requires (
- slot_s_inv len (hash_mod_key key len) ls /\
- Some? (slot_s_find key ls)))
- (ensures (
- let ls' = find_update (same_key key) ls (key, value) in
- slot_s_inv len (hash_mod_key key len) ls' /\
- (slot_s_find key ls' == Some value) /\
- (forall k'. k' <> key ==> slot_s_find k' ls' == slot_s_find k' ls)))
-
-#push-options "--z3rlimit 50 --fuel 1"
-let rec slot_s_inv_find_append_end_inv_lem t len key value ls =
- match ls with
- | [] -> ()
- | (ck, cv) :: cls ->
- let h = hash_mod_key key len in
- let ls' = find_update (same_key key) ls (key, value) in
- if ck = key then
- begin
- assert(ls' == (ck,value) :: cls);
- assert(for_all (same_hash_mod_key len h) ls');
- // For pairwise_rel: binding_neq (ck, value) is actually independent
- // of `value`. Slightly annoying to prove in F*...
- assert(for_all (binding_neq (ck,cv)) cls);
- for_all_binding_neq_value_indep key cv value cls;
- assert(for_all (binding_neq (ck,value)) cls);
- assert(pairwise_rel binding_neq ls');
- assert(slot_s_inv len (hash_mod_key key len) ls')
- end
- else
- begin
- slot_s_inv_find_append_end_inv_lem t len key value cls;
- assert(for_all (same_hash_mod_key len h) ls');
- slot_s_find_update_for_all_binding_neq_append_lem t key value cls (ck, cv);
- assert(pairwise_rel binding_neq ls');
- assert(slot_s_inv len h ls')
- end
-#pop-options
-
-/// [insert_in_list]: if the key is in the map, update the bindings
-val hashMap_insert_in_list_s_lem_update
- (t : Type0) (len : usize{len > 0}) (key : usize) (value : t) (ls : list (binding t)) :
- Lemma
- (requires (
- slot_s_inv len (hash_mod_key key len) ls /\
- Some? (slot_s_find key ls)))
- (ensures (
- let ls' = hashMap_insert_in_list_s key value ls in
- ls' == find_update (same_key key) ls (key,value) /\
- // The invariant is preserved
- slot_s_inv len (hash_mod_key key len) ls' /\
- // [key] maps to [value]
- slot_s_find key ls' == Some value /\
- // The other bindings are preserved
- (forall k'. k' <> key ==> slot_s_find k' ls' == slot_s_find k' ls)))
-
-let hashMap_insert_in_list_s_lem_update t len key value ls =
- slot_s_inv_find_append_end_inv_lem t len key value ls
-
-
-/// [insert_in_list]: if the key is in the map, update the bindings
-/// TODO: not used: remove?
-val hashMap_insert_in_list_back_lem_update
- (t : Type0) (len : usize{len > 0}) (key : usize) (value : t) (ls : list_t t) :
- Lemma
- (requires (
- slot_t_inv len (hash_mod_key key len) ls /\
- Some? (slot_t_find_s key ls)))
- (ensures (
- match hashMap_insert_in_list_back t key value ls with
- | Fail _ -> False
- | Return ls' ->
- let als = list_t_v ls in
- list_t_v ls' == find_update (same_key key) als (key,value) /\
- // The invariant is preserved
- slot_t_inv len (hash_mod_key key len) ls' /\
- // [key] maps to [value]
- slot_t_find_s key ls' == Some value /\
- // The other bindings are preserved
- (forall k'. k' <> key ==> slot_t_find_s k' ls' == slot_t_find_s k' ls)))
-
-let hashMap_insert_in_list_back_lem_update t len key value ls =
- hashMap_insert_in_list_back_lem_s t key value ls;
- hashMap_insert_in_list_s_lem_update t len key value (list_t_v ls)
-
-(** Final lemmas about [insert_in_list] *)
-
-/// High-level version
-val hashMap_insert_in_list_s_lem
- (t : Type0) (len : usize{len > 0}) (key : usize) (value : t) (ls : list (binding t)) :
- Lemma
- (requires (
- slot_s_inv len (hash_mod_key key len) ls))
- (ensures (
- let ls' = hashMap_insert_in_list_s key value ls in
- // The invariant is preserved
- slot_s_inv len (hash_mod_key key len) ls' /\
- // [key] maps to [value]
- slot_s_find key ls' == Some value /\
- // The other bindings are preserved
- (forall k'. k' <> key ==> slot_s_find k' ls' == slot_s_find k' ls) /\
- // The length is incremented, iff we inserted a new key
- (match slot_s_find key ls with
- | None -> length ls' = length ls + 1
- | Some _ -> length ls' = length ls)))
-
-let hashMap_insert_in_list_s_lem t len key value ls =
- match slot_s_find key ls with
- | None ->
- assert_norm(length [(key,value)] = 1);
- hashMap_insert_in_list_s_lem_append t len key value ls
- | Some _ ->
- hashMap_insert_in_list_s_lem_update t len key value ls
-
-/// [insert_in_list]
-/// TODO: not used: remove?
-val hashMap_insert_in_list_back_lem
- (t : Type0) (len : usize{len > 0}) (key : usize) (value : t) (ls : list_t t) :
- Lemma
- (requires (slot_t_inv len (hash_mod_key key len) ls))
- (ensures (
- match hashMap_insert_in_list_back t key value ls with
- | Fail _ -> False
- | Return ls' ->
- // The invariant is preserved
- slot_t_inv len (hash_mod_key key len) ls' /\
- // [key] maps to [value]
- slot_t_find_s key ls' == Some value /\
- // The other bindings are preserved
- (forall k'. k' <> key ==> slot_t_find_s k' ls' == slot_t_find_s k' ls) /\
- // The length is incremented, iff we inserted a new key
- (match slot_t_find_s key ls with
- | None ->
- list_t_v ls' == list_t_v ls @ [(key,value)] /\
- list_t_len ls' = list_t_len ls + 1
- | Some _ ->
- list_t_v ls' == find_update (same_key key) (list_t_v ls) (key,value) /\
- list_t_len ls' = list_t_len ls)))
- (decreases (hashMap_insert_in_list_loop_decreases t key value ls))
-
-let hashMap_insert_in_list_back_lem t len key value ls =
- hashMap_insert_in_list_back_lem_s t key value ls;
- hashMap_insert_in_list_s_lem t len key value (list_t_v ls)
-
-(*** insert_no_resize *)
-
-(**** Refinement proof *)
-/// Same strategy as for [insert_in_list]: we introduce a high-level version of
-/// the function, and reason about it.
-/// We work on [hashMap_s] (we use a higher-level view of the hash-map, but
-/// not too high).
-
-/// A high-level version of insert, which doesn't check if the table is saturated
-let hashMap_insert_no_fail_s
- (#t : Type0) (hm : hashMap_s_nes t)
- (key : usize) (value : t) :
- hashMap_s t =
- let len = length hm in
- let i = hash_mod_key key len in
- let slot = index hm i in
- let slot' = hashMap_insert_in_list_s key value slot in
- let hm' = list_update hm i slot' in
- hm'
-
-// TODO: at some point I used hashMap_s_nes and it broke proofs...x
-let hashMap_insert_no_resize_s
- (#t : Type0) (hm : hashMap_s_nes t)
- (key : usize) (value : t) :
- result (hashMap_s t) =
- // Check if the table is saturated (too many entries, and we need to insert one)
- let num_entries = length (flatten hm) in
- if None? (hashMap_s_find hm key) && num_entries = usize_max then Fail Failure
- else Return (hashMap_insert_no_fail_s hm key value)
-
-/// Prove that [hashMap_insert_no_resize_s] is refined by
-/// [hashMap_insert_no_resize'fwd_back]
-val hashMap_insert_no_resize_lem_s
- (t : Type0) (self : hashMap_t t) (key : usize) (value : t) :
- Lemma
- (requires (
- hashMap_t_base_inv self /\
- hashMap_s_len (hashMap_t_v self) = hashMap_t_len_s self))
- (ensures (
- begin
- match hashMap_insert_no_resize t self key value,
- hashMap_insert_no_resize_s (hashMap_t_v self) key value
- with
- | Fail _, Fail _ -> True
- | Return hm, Return hm_v ->
- hashMap_t_base_inv hm /\
- hashMap_t_same_params hm self /\
- hashMap_t_v hm == hm_v /\
- hashMap_s_len hm_v == hashMap_t_len_s hm
- | _ -> False
- end))
-
-let hashMap_insert_no_resize_lem_s t self key value =
- begin match hash_key key with
- | Fail _ -> ()
- | Return i ->
- let i0 = self.num_entries in
- let p = self.max_load_factor in
- let i1 = self.max_load in
- let v = self.slots in
- let i2 = alloc_vec_Vec_len (list_t t) v in
- let len = length v in
- begin match usize_rem i i2 with
- | Fail _ -> ()
- | Return hash_mod ->
- begin match alloc_vec_Vec_index_usize v hash_mod with
- | Fail _ -> ()
- | Return l ->
- begin
- // Checking that: list_t_v (index ...) == index (hashMap_t_v ...) ...
- assert(list_t_v l == index (hashMap_t_v self) hash_mod);
- hashMap_insert_in_list_lem t key value l;
- match hashMap_insert_in_list t key value l with
- | Fail _ -> ()
- | Return b ->
- assert(b = None? (slot_s_find key (list_t_v l)));
- hashMap_insert_in_list_back_lem t len key value l;
- if b
- then
- begin match usize_add i0 1 with
- | Fail _ -> ()
- | Return i3 ->
- begin
- match hashMap_insert_in_list_back t key value l with
- | Fail _ -> ()
- | Return l0 ->
- begin match alloc_vec_Vec_update_usize v hash_mod l0 with
- | Fail _ -> ()
- | Return v0 ->
- let self_v = hashMap_t_v self in
- let hm = MkhashMap_t i3 p i1 v0 in
- let hm_v = hashMap_t_v hm in
- assert(hm_v == list_update self_v hash_mod (list_t_v l0));
- assert_norm(length [(key,value)] = 1);
- assert(length (list_t_v l0) = length (list_t_v l) + 1);
- length_flatten_update self_v hash_mod (list_t_v l0);
- assert(hashMap_s_len hm_v = hashMap_t_len_s hm)
- end
- end
- end
- else
- begin
- match hashMap_insert_in_list_back t key value l with
- | Fail _ -> ()
- | Return l0 ->
- begin match alloc_vec_Vec_update_usize v hash_mod l0 with
- | Fail _ -> ()
- | Return v0 ->
- let self_v = hashMap_t_v self in
- let hm = MkhashMap_t i0 p i1 v0 in
- let hm_v = hashMap_t_v hm in
- assert(hm_v == list_update self_v hash_mod (list_t_v l0));
- assert(length (list_t_v l0) = length (list_t_v l));
- length_flatten_update self_v hash_mod (list_t_v l0);
- assert(hashMap_s_len hm_v = hashMap_t_len_s hm)
- end
- end
- end
- end
- end
- end
-
-(**** insert_{no_fail,no_resize}: invariants *)
-
-let hashMap_s_updated_binding
- (#t : Type0) (hm : hashMap_s_nes t)
- (key : usize) (opt_value : option t) (hm' : hashMap_s_nes t) : Type0 =
- // [key] maps to [value]
- hashMap_s_find hm' key == opt_value /\
- // The other bindings are preserved
- (forall k'. k' <> key ==> hashMap_s_find hm' k' == hashMap_s_find hm k')
-
-let insert_post (#t : Type0) (hm : hashMap_s_nes t)
- (key : usize) (value : t) (hm' : hashMap_s_nes t) : Type0 =
- // The invariant is preserved
- hashMap_s_inv hm' /\
- // [key] maps to [value] and the other bindings are preserved
- hashMap_s_updated_binding hm key (Some value) hm' /\
- // The length is incremented, iff we inserted a new key
- (match hashMap_s_find hm key with
- | None -> hashMap_s_len hm' = hashMap_s_len hm + 1
- | Some _ -> hashMap_s_len hm' = hashMap_s_len hm)
-
-val hashMap_insert_no_fail_s_lem
- (#t : Type0) (hm : hashMap_s_nes t)
- (key : usize) (value : t) :
- Lemma
- (requires (hashMap_s_inv hm))
- (ensures (
- let hm' = hashMap_insert_no_fail_s hm key value in
- insert_post hm key value hm'))
-
-let hashMap_insert_no_fail_s_lem #t hm key value =
- let len = length hm in
- let i = hash_mod_key key len in
- let slot = index hm i in
- hashMap_insert_in_list_s_lem t len key value slot;
- let slot' = hashMap_insert_in_list_s key value slot in
- length_flatten_update hm i slot'
-
-val hashMap_insert_no_resize_s_lem
- (#t : Type0) (hm : hashMap_s_nes t)
- (key : usize) (value : t) :
- Lemma
- (requires (hashMap_s_inv hm))
- (ensures (
- match hashMap_insert_no_resize_s hm key value with
- | Fail _ ->
- // Can fail only if we need to create a new binding in
- // an already saturated map
- hashMap_s_len hm = usize_max /\
- None? (hashMap_s_find hm key)
- | Return hm' ->
- insert_post hm key value hm'))
-
-let hashMap_insert_no_resize_s_lem #t hm key value =
- let num_entries = length (flatten hm) in
- if None? (hashMap_s_find hm key) && num_entries = usize_max then ()
- else hashMap_insert_no_fail_s_lem hm key value
-
-
-(**** find after insert *)
-/// Lemmas about what happens if we call [find] after an insertion
-
-val hashMap_insert_no_resize_s_get_same_lem
- (#t : Type0) (hm : hashMap_s t)
- (key : usize) (value : t) :
- Lemma (requires (hashMap_s_inv hm))
- (ensures (
- match hashMap_insert_no_resize_s hm key value with
- | Fail _ -> True
- | Return hm' ->
- hashMap_s_find hm' key == Some value))
-
-let hashMap_insert_no_resize_s_get_same_lem #t hm key value =
- let num_entries = length (flatten hm) in
- if None? (hashMap_s_find hm key) && num_entries = usize_max then ()
- else
- begin
- let hm' = Return?.v (hashMap_insert_no_resize_s hm key value) in
- let len = length hm in
- let i = hash_mod_key key len in
- let slot = index hm i in
- hashMap_insert_in_list_s_lem t len key value slot
- end
-
-val hashMap_insert_no_resize_s_get_diff_lem
- (#t : Type0) (hm : hashMap_s t)
- (key : usize) (value : t) (key' : usize{key' <> key}) :
- Lemma (requires (hashMap_s_inv hm))
- (ensures (
- match hashMap_insert_no_resize_s hm key value with
- | Fail _ -> True
- | Return hm' ->
- hashMap_s_find hm' key' == hashMap_s_find hm key'))
-
-let hashMap_insert_no_resize_s_get_diff_lem #t hm key value key' =
- let num_entries = length (flatten hm) in
- if None? (hashMap_s_find hm key) && num_entries = usize_max then ()
- else
- begin
- let hm' = Return?.v (hashMap_insert_no_resize_s hm key value) in
- let len = length hm in
- let i = hash_mod_key key len in
- let slot = index hm i in
- hashMap_insert_in_list_s_lem t len key value slot;
- let i' = hash_mod_key key' len in
- if i <> i' then ()
- else
- begin
- ()
- end
- end
-
-
-(*** move_elements_from_list *)
-
-/// Having a great time here: if we use `result (hashMap_s_res t)` as the
-/// return type for [hashMap_move_elements_from_list_s] instead of having this
-/// awkward match, the proof of [hashMap_move_elements_lem_refin] fails.
-/// I guess it comes from F*'s poor subtyping.
-/// Followingly, I'm not taking any chance and using [result_hashMap_s]
-/// everywhere.
-type result_hashMap_s_nes (t : Type0) : Type0 =
- res:result (hashMap_s t) {
- match res with
- | Fail _ -> True
- | Return hm -> is_pos_usize (length hm)
- }
-
-let rec hashMap_move_elements_from_list_s
- (#t : Type0) (hm : hashMap_s_nes t)
- (ls : slot_s t) :
- // Do *NOT* use `result (hashMap_s t)`
- Tot (result_hashMap_s_nes t)
- (decreases ls) =
- match ls with
- | [] -> Return hm
- | (key, value) :: ls' ->
- match hashMap_insert_no_resize_s hm key value with
- | Fail e -> Fail e
- | Return hm' ->
- hashMap_move_elements_from_list_s hm' ls'
-
-/// Refinement lemma
-val hashMap_move_elements_from_list_lem
- (t : Type0) (ntable : hashMap_t_nes t) (ls : list_t t) :
- Lemma (requires (hashMap_t_base_inv ntable))
- (ensures (
- match hashMap_move_elements_from_list t ntable ls,
- hashMap_move_elements_from_list_s (hashMap_t_v ntable) (slot_t_v ls)
- with
- | Fail _, Fail _ -> True
- | Return hm', Return hm_v ->
- hashMap_t_base_inv hm' /\
- hashMap_t_v hm' == hm_v /\
- hashMap_t_same_params hm' ntable
- | _ -> False))
- (decreases (hashMap_move_elements_from_list_loop_decreases t ntable ls))
-
-#push-options "--fuel 1"
-let rec hashMap_move_elements_from_list_lem t ntable ls =
- begin match ls with
- | List_Cons k v tl ->
- assert(list_t_v ls == (k, v) :: list_t_v tl);
- let ls_v = list_t_v ls in
- let (_,_) :: tl_v = ls_v in
- hashMap_insert_no_resize_lem_s t ntable k v;
- begin match hashMap_insert_no_resize t ntable k v with
- | Fail _ -> ()
- | Return h ->
- let h_v = Return?.v (hashMap_insert_no_resize_s (hashMap_t_v ntable) k v) in
- assert(hashMap_t_v h == h_v);
- hashMap_move_elements_from_list_lem t h tl;
- begin match hashMap_move_elements_from_list t h tl with
- | Fail _ -> ()
- | Return h0 -> ()
- end
- end
- | List_Nil -> ()
- end
-#pop-options
-
-(*** move_elements *)
-
-(**** move_elements: refinement 0 *)
-/// The proof for [hashMap_move_elements_lem_refin] broke so many times
-/// (while it is supposed to be super simple!) that we decided to add one refinement
-/// level, to really do things step by step...
-/// Doing this refinement layer made me notice that maybe the problem came from
-/// the fact that at some point we have to prove `list_t_v List_Nil == []`: I
-/// added the corresponding assert to help Z3 and everything became stable.
-/// I finally didn't use this "simple" refinement lemma, but I still keep it here
-/// because it allows for easy comparisons with [hashMap_move_elements_s].
-
-/// [hashMap_move_elements] refines this function, which is actually almost
-/// the same (just a little bit shorter and cleaner, and has a pre).
-///
-/// The way I wrote the high-level model is the following:
-/// - I copy-pasted the definition of [hashMap_move_elements], wrote the
-/// signature which links this new definition to [hashMap_move_elements] and
-/// checked that the proof passed
-/// - I gradually simplified it, while making sure the proof still passes
-#push-options "--fuel 1"
-let rec hashMap_move_elements_s_simpl
- (t : Type0) (ntable : hashMap_t t)
- (slots : alloc_vec_Vec (list_t t))
- (i : usize{i <= length slots /\ length slots <= usize_max}) :
- Pure (result ((hashMap_t t) & (alloc_vec_Vec (list_t t))))
- (requires (True))
- (ensures (fun res ->
- match res, hashMap_move_elements t ntable slots i with
- | Fail _, Fail _ -> True
- | Return (ntable1, slots1), Return (ntable2, slots2) ->
- ntable1 == ntable2 /\
- slots1 == slots2
- | _ -> False))
- (decreases (hashMap_move_elements_loop_decreases t ntable slots i))
- =
- if i < length slots
- then
- let slot = index slots i in
- begin match hashMap_move_elements_from_list t ntable slot with
- | Fail e -> Fail e
- | Return hm' ->
- let slots' = list_update slots i List_Nil in
- hashMap_move_elements_s_simpl t hm' slots' (i+1)
- end
- else Return (ntable, slots)
-#pop-options
-
-(**** move_elements: refinement 1 *)
-/// We prove a second refinement lemma: calling [move_elements] refines a function
-/// which, for every slot, moves the element out of the slot. This first model is
-/// almost exactly the translated function, it just uses `list` instead of `list_t`.
-
-// Note that we ignore the returned slots (we thus don't return a pair:
-// only the new hash map in which we moved the elements from the slots):
-// this returned value is not used.
-let rec hashMap_move_elements_s
- (#t : Type0) (hm : hashMap_s_nes t)
- (slots : slots_s t) (i : usize{i <= length slots /\ length slots <= usize_max}) :
- Tot (result_hashMap_s_nes t)
- (decreases (length slots - i)) =
- let len = length slots in
- if i < len then
- begin
- let slot = index slots i in
- match hashMap_move_elements_from_list_s hm slot with
- | Fail e -> Fail e
- | Return hm' ->
- let slots' = list_update slots i [] in
- hashMap_move_elements_s hm' slots' (i+1)
- end
- else Return hm
-
-val hashMap_move_elements_lem_refin
- (t : Type0) (ntable : hashMap_t t)
- (slots : alloc_vec_Vec (list_t t)) (i : usize{i <= length slots}) :
- Lemma
- (requires (
- hashMap_t_base_inv ntable))
- (ensures (
- match hashMap_move_elements t ntable slots i,
- hashMap_move_elements_s (hashMap_t_v ntable) (slots_t_v slots) i
- with
- | Fail _, Fail _ -> True // We will prove later that this is not possible
- | Return (ntable', _), Return ntable'_v ->
- hashMap_t_base_inv ntable' /\
- hashMap_t_v ntable' == ntable'_v /\
- hashMap_t_same_params ntable' ntable
- | _ -> False))
- (decreases (length slots - i))
-
-#restart-solver
-#push-options "--fuel 1"
-let rec hashMap_move_elements_lem_refin t ntable slots i =
- assert(hashMap_t_base_inv ntable);
- let i0 = alloc_vec_Vec_len (list_t t) slots in
- let b = i < i0 in
- if b
- then
- begin match alloc_vec_Vec_index_usize slots i with
- | Fail _ -> ()
- | Return l ->
- let l0 = core_mem_replace (list_t t) l List_Nil in
- assert(l0 == l);
- hashMap_move_elements_from_list_lem t ntable l0;
- begin match hashMap_move_elements_from_list t ntable l0 with
- | Fail _ -> ()
- | Return h ->
- let l1 = core_mem_replace_back (list_t t) l List_Nil in
- assert(l1 == List_Nil);
- assert(slot_t_v #t List_Nil == []); // THIS IS IMPORTANT
- begin match alloc_vec_Vec_update_usize slots i l1 with
- | Fail _ -> ()
- | Return v ->
- begin match usize_add i 1 with
- | Fail _ -> ()
- | Return i1 ->
- hashMap_move_elements_lem_refin t h v i1;
- begin match hashMap_move_elements t h v i1 with
- | Fail _ ->
- assert(Fail? (hashMap_move_elements t ntable slots i));
- ()
- | Return (ntable', v0) -> ()
- end
- end
- end
- end
- end
- else ()
-#pop-options
-
-
-(**** move_elements: refinement 2 *)
-/// We prove a second refinement lemma: calling [move_elements] refines a function
-/// which moves every binding of the hash map seen as *one* associative list
-/// (and not a list of lists).
-
-/// [ntable] is the hash map to which we move the elements
-/// [slots] is the current hash map, from which we remove the elements, and seen
-/// as a "flat" associative list (and not a list of lists)
-/// This is actually exactly [hashMap_move_elements_from_list_s]...
-let rec hashMap_move_elements_s_flat
- (#t : Type0) (ntable : hashMap_s_nes t)
- (slots : assoc_list t) :
- Tot (result_hashMap_s_nes t)
- (decreases slots) =
- match slots with
- | [] -> Return ntable
- | (k,v) :: slots' ->
- match hashMap_insert_no_resize_s ntable k v with
- | Fail e -> Fail e
- | Return ntable' ->
- hashMap_move_elements_s_flat ntable' slots'
-
-/// The refinment lemmas
-/// First, auxiliary helpers.
-
-/// Flatten a list of lists, starting at index i
-val flatten_i :
- #a:Type
- -> l:list (list a)
- -> i:nat{i <= length l}
- -> Tot (list a) (decreases (length l - i))
-
-let rec flatten_i l i =
- if i < length l then
- index l i @ flatten_i l (i+1)
- else []
-
-let _ = assert(let l = [1;2] in l == hd l :: tl l)
-
-val flatten_i_incr :
- #a:Type
- -> l:list (list a)
- -> i:nat{Cons? l /\ i+1 <= length l} ->
- Lemma
- (ensures (
- (**) assert_norm(length (hd l :: tl l) == 1 + length (tl l));
- flatten_i l (i+1) == flatten_i (tl l) i))
- (decreases (length l - (i+1)))
-
-#push-options "--fuel 1"
-let rec flatten_i_incr l i =
- let x :: tl = l in
- if i + 1 < length l then
- begin
- assert(flatten_i l (i+1) == index l (i+1) @ flatten_i l (i+2));
- flatten_i_incr l (i+1);
- assert(flatten_i l (i+2) == flatten_i tl (i+1));
- assert(index l (i+1) == index tl i)
- end
- else ()
-#pop-options
-
-val flatten_0_is_flatten :
- #a:Type
- -> l:list (list a) ->
- Lemma
- (ensures (flatten_i l 0 == flatten l))
-
-#push-options "--fuel 1"
-let rec flatten_0_is_flatten #a l =
- match l with
- | [] -> ()
- | x :: l' ->
- flatten_i_incr l 0;
- flatten_0_is_flatten l'
-#pop-options
-
-/// Auxiliary lemma
-val flatten_nil_prefix_as_flatten_i :
- #a:Type
- -> l:list (list a)
- -> i:nat{i <= length l} ->
- Lemma (requires (forall (j:nat{j < i}). index l j == []))
- (ensures (flatten l == flatten_i l i))
-
-#push-options "--fuel 1"
-let rec flatten_nil_prefix_as_flatten_i #a l i =
- if i = 0 then flatten_0_is_flatten l
- else
- begin
- let x :: l' = l in
- assert(index l 0 == []);
- assert(x == []);
- assert(flatten l == flatten l');
- flatten_i_incr l (i-1);
- assert(flatten_i l i == flatten_i l' (i-1));
- assert(forall (j:nat{j < length l'}). index l' j == index l (j+1));
- flatten_nil_prefix_as_flatten_i l' (i-1);
- assert(flatten l' == flatten_i l' (i-1))
- end
-#pop-options
-
-/// The proof is trivial, the functions are the same.
-/// Just keeping two definitions to allow changes...
-val hashMap_move_elements_from_list_s_as_flat_lem
- (#t : Type0) (hm : hashMap_s_nes t)
- (ls : slot_s t) :
- Lemma
- (ensures (
- hashMap_move_elements_from_list_s hm ls ==
- hashMap_move_elements_s_flat hm ls))
- (decreases ls)
-
-#push-options "--fuel 1"
-let rec hashMap_move_elements_from_list_s_as_flat_lem #t hm ls =
- match ls with
- | [] -> ()
- | (key, value) :: ls' ->
- match hashMap_insert_no_resize_s hm key value with
- | Fail _ -> ()
- | Return hm' ->
- hashMap_move_elements_from_list_s_as_flat_lem hm' ls'
-#pop-options
-
-/// Composition of two calls to [hashMap_move_elements_s_flat]
-let hashMap_move_elements_s_flat_comp
- (#t : Type0) (hm : hashMap_s_nes t) (slot0 slot1 : slot_s t) :
- Tot (result_hashMap_s_nes t) =
- match hashMap_move_elements_s_flat hm slot0 with
- | Fail e -> Fail e
- | Return hm1 -> hashMap_move_elements_s_flat hm1 slot1
-
-/// High-level desc:
-/// move_elements (move_elements hm slot0) slo1 == move_elements hm (slot0 @ slot1)
-val hashMap_move_elements_s_flat_append_lem
- (#t : Type0) (hm : hashMap_s_nes t) (slot0 slot1 : slot_s t) :
- Lemma
- (ensures (
- match hashMap_move_elements_s_flat_comp hm slot0 slot1,
- hashMap_move_elements_s_flat hm (slot0 @ slot1)
- with
- | Fail _, Fail _ -> True
- | Return hm1, Return hm2 -> hm1 == hm2
- | _ -> False))
- (decreases (slot0))
-
-#push-options "--fuel 1"
-let rec hashMap_move_elements_s_flat_append_lem #t hm slot0 slot1 =
- match slot0 with
- | [] -> ()
- | (k,v) :: slot0' ->
- match hashMap_insert_no_resize_s hm k v with
- | Fail _ -> ()
- | Return hm' ->
- hashMap_move_elements_s_flat_append_lem hm' slot0' slot1
-#pop-options
-
-val flatten_i_same_suffix (#a : Type) (l0 l1 : list (list a)) (i : nat) :
- Lemma
- (requires (
- i <= length l0 /\
- length l0 = length l1 /\
- (forall (j:nat{i <= j /\ j < length l0}). index l0 j == index l1 j)))
- (ensures (flatten_i l0 i == flatten_i l1 i))
- (decreases (length l0 - i))
-
-#push-options "--fuel 1"
-let rec flatten_i_same_suffix #a l0 l1 i =
- if i < length l0 then
- flatten_i_same_suffix l0 l1 (i+1)
- else ()
-#pop-options
-
-/// Refinement lemma:
-/// [hashMap_move_elements_s] refines [hashMap_move_elements_s_flat]
-/// (actually the functions are equal on all inputs).
-val hashMap_move_elements_s_lem_refin_flat
- (#t : Type0) (hm : hashMap_s_nes t)
- (slots : slots_s t)
- (i : nat{i <= length slots /\ length slots <= usize_max}) :
- Lemma
- (ensures (
- match hashMap_move_elements_s hm slots i,
- hashMap_move_elements_s_flat hm (flatten_i slots i)
- with
- | Fail _, Fail _ -> True
- | Return hm, Return hm' -> hm == hm'
- | _ -> False))
- (decreases (length slots - i))
-
-#push-options "--fuel 1"
-let rec hashMap_move_elements_s_lem_refin_flat #t hm slots i =
- let len = length slots in
- if i < len then
- begin
- let slot = index slots i in
- hashMap_move_elements_from_list_s_as_flat_lem hm slot;
- match hashMap_move_elements_from_list_s hm slot with
- | Fail _ ->
- assert(flatten_i slots i == slot @ flatten_i slots (i+1));
- hashMap_move_elements_s_flat_append_lem hm slot (flatten_i slots (i+1));
- assert(Fail? (hashMap_move_elements_s_flat hm (flatten_i slots i)))
- | Return hm' ->
- let slots' = list_update slots i [] in
- flatten_i_same_suffix slots slots' (i+1);
- hashMap_move_elements_s_lem_refin_flat hm' slots' (i+1);
- hashMap_move_elements_s_flat_append_lem hm slot (flatten_i slots' (i+1));
- ()
- end
- else ()
-#pop-options
-
-let assoc_list_inv (#t : Type0) (al : assoc_list t) : Type0 =
- // All the keys are pairwise distinct
- pairwise_rel binding_neq al
-
-let disjoint_hm_al_on_key
- (#t : Type0) (hm : hashMap_s_nes t) (al : assoc_list t) (k : key) : Type0 =
- match hashMap_s_find hm k, assoc_list_find k al with
- | Some _, None
- | None, Some _
- | None, None -> True
- | Some _, Some _ -> False
-
-/// Playing a dangerous game here: using forall quantifiers
-let disjoint_hm_al (#t : Type0) (hm : hashMap_s_nes t) (al : assoc_list t) : Type0 =
- forall (k:key). disjoint_hm_al_on_key hm al k
-
-let find_in_union_hm_al
- (#t : Type0) (hm : hashMap_s_nes t) (al : assoc_list t) (k : key) :
- option t =
- match hashMap_s_find hm k with
- | Some b -> Some b
- | None -> assoc_list_find k al
-
-/// Auxiliary lemma
-val for_all_binding_neq_find_lem (#t : Type0) (k : key) (v : t) (al : assoc_list t) :
- Lemma (requires (for_all (binding_neq (k,v)) al))
- (ensures (assoc_list_find k al == None))
-
-#push-options "--fuel 1"
-let rec for_all_binding_neq_find_lem #t k v al =
- match al with
- | [] -> ()
- | b :: al' -> for_all_binding_neq_find_lem k v al'
-#pop-options
-
-val hashMap_move_elements_s_flat_lem
- (#t : Type0) (hm : hashMap_s_nes t) (al : assoc_list t) :
- Lemma
- (requires (
- // Invariants
- hashMap_s_inv hm /\
- assoc_list_inv al /\
- // The two are disjoint
- disjoint_hm_al hm al /\
- // We can add all the elements to the hashmap
- hashMap_s_len hm + length al <= usize_max))
- (ensures (
- match hashMap_move_elements_s_flat hm al with
- | Fail _ -> False // We can't fail
- | Return hm' ->
- // The invariant is preserved
- hashMap_s_inv hm' /\
- // The new hash map is the union of the two maps
- (forall (k:key). hashMap_s_find hm' k == find_in_union_hm_al hm al k) /\
- hashMap_s_len hm' = hashMap_s_len hm + length al))
- (decreases al)
-
-#restart-solver
-#push-options "--z3rlimit 200 --fuel 1"
-let rec hashMap_move_elements_s_flat_lem #t hm al =
- match al with
- | [] -> ()
- | (k,v) :: al' ->
- hashMap_insert_no_resize_s_lem hm k v;
- match hashMap_insert_no_resize_s hm k v with
- | Fail _ -> ()
- | Return hm' ->
- assert(hashMap_s_inv hm');
- assert(assoc_list_inv al');
- let disjoint_lem (k' : key) :
- Lemma (disjoint_hm_al_on_key hm' al' k')
- [SMTPat (disjoint_hm_al_on_key hm' al' k')] =
- if k' = k then
- begin
- assert(hashMap_s_find hm' k' == Some v);
- for_all_binding_neq_find_lem k v al';
- assert(assoc_list_find k' al' == None)
- end
- else
- begin
- assert(hashMap_s_find hm' k' == hashMap_s_find hm k');
- assert(assoc_list_find k' al' == assoc_list_find k' al)
- end
- in
- assert(disjoint_hm_al hm' al');
- assert(hashMap_s_len hm' + length al' <= usize_max);
- hashMap_move_elements_s_flat_lem hm' al'
-#pop-options
-
-/// We need to prove that the invariants on the "low-level" representations of
-/// the hash map imply the invariants on the "high-level" representations.
-
-val slots_t_inv_implies_slots_s_inv
- (#t : Type0) (slots : slots_t t{length slots <= usize_max}) :
- Lemma (requires (slots_t_inv slots))
- (ensures (slots_s_inv (slots_t_v slots)))
-
-let slots_t_inv_implies_slots_s_inv #t slots =
- // Ok, works fine: this lemma was useless.
- // Problem is: I can never really predict for sure with F*...
- ()
-
-val hashMap_t_base_inv_implies_hashMap_s_inv
- (#t : Type0) (hm : hashMap_t t) :
- Lemma (requires (hashMap_t_base_inv hm))
- (ensures (hashMap_s_inv (hashMap_t_v hm)))
-
-let hashMap_t_base_inv_implies_hashMap_s_inv #t hm = () // same as previous
-
-/// Introducing a "partial" version of the hash map invariant, which operates on
-/// a suffix of the hash map.
-let partial_hashMap_s_inv
- (#t : Type0) (len : usize{len > 0}) (offset : usize)
- (hm : hashMap_s t{offset + length hm <= usize_max}) : Type0 =
- forall(i:nat{i < length hm}). {:pattern index hm i} slot_s_inv len (offset + i) (index hm i)
-
-/// Auxiliary lemma.
-/// If a binding comes from a slot i, then its key is different from the keys
-/// of the bindings in the other slots (because the hashes of the keys are distinct).
-val binding_in_previous_slot_implies_neq
- (#t : Type0) (len : usize{len > 0})
- (i : usize) (b : binding t)
- (offset : usize{i < offset})
- (slots : hashMap_s t{offset + length slots <= usize_max}) :
- Lemma
- (requires (
- // The binding comes from a slot not in [slots]
- hash_mod_key (fst b) len = i /\
- // The slots are the well-formed suffix of a hash map
- partial_hashMap_s_inv len offset slots))
- (ensures (
- for_all (binding_neq b) (flatten slots)))
- (decreases slots)
-
-#push-options "--z3rlimit 100 --fuel 1"
-let rec binding_in_previous_slot_implies_neq #t len i b offset slots =
- match slots with
- | [] -> ()
- | s :: slots' ->
- assert(slot_s_inv len offset (index slots 0)); // Triggers patterns
- assert(slot_s_inv len offset s);
- // Proving TARGET. We use quantifiers.
- assert(for_all (same_hash_mod_key len offset) s);
- forall_index_equiv_list_for_all (same_hash_mod_key len offset) s;
- assert(forall (i:nat{i < length s}). same_hash_mod_key len offset (index s i));
- let aux (i:nat{i < length s}) :
- Lemma
- (requires (same_hash_mod_key len offset (index s i)))
- (ensures (binding_neq b (index s i)))
- [SMTPat (index s i)] = ()
- in
- assert(forall (i:nat{i < length s}). binding_neq b (index s i));
- forall_index_equiv_list_for_all (binding_neq b) s;
- assert(for_all (binding_neq b) s); // TARGET
- //
- assert(forall (i:nat{i < length slots'}). index slots' i == index slots (i+1)); // Triggers instantiations
- binding_in_previous_slot_implies_neq len i b (offset+1) slots';
- for_all_append (binding_neq b) s (flatten slots')
-#pop-options
-
-val partial_hashMap_s_inv_implies_assoc_list_lem
- (#t : Type0) (len : usize{len > 0}) (offset : usize)
- (hm : hashMap_s t{offset + length hm <= usize_max}) :
- Lemma
- (requires (
- partial_hashMap_s_inv len offset hm))
- (ensures (assoc_list_inv (flatten hm)))
- (decreases (length hm + length (flatten hm)))
-
-#push-options "--fuel 1"
-let rec partial_hashMap_s_inv_implies_assoc_list_lem #t len offset hm =
- match hm with
- | [] -> ()
- | slot :: hm' ->
- assert(flatten hm == slot @ flatten hm');
- assert(forall (i:nat{i < length hm'}). index hm' i == index hm (i+1)); // Triggers instantiations
- match slot with
- | [] ->
- assert(flatten hm == flatten hm');
- assert(partial_hashMap_s_inv len (offset+1) hm'); // Triggers instantiations
- partial_hashMap_s_inv_implies_assoc_list_lem len (offset+1) hm'
- | x :: slot' ->
- assert(flatten (slot' :: hm') == slot' @ flatten hm');
- let hm'' = slot' :: hm' in
- assert(forall (i:nat{0 < i /\ i < length hm''}). index hm'' i == index hm i); // Triggers instantiations
- assert(forall (i:nat{0 < i /\ i < length hm''}). slot_s_inv len (offset + i) (index hm'' i));
- assert(index hm 0 == slot); // Triggers instantiations
- assert(slot_s_inv len offset slot);
- assert(slot_s_inv len offset slot');
- assert(partial_hashMap_s_inv len offset hm'');
- partial_hashMap_s_inv_implies_assoc_list_lem len offset (slot' :: hm');
- // Proving that the key in `x` is different from all the other keys in
- // the flattened map
- assert(for_all (binding_neq x) slot');
- for_all_append (binding_neq x) slot' (flatten hm');
- assert(partial_hashMap_s_inv len (offset+1) hm');
- binding_in_previous_slot_implies_neq #t len offset x (offset+1) hm';
- assert(for_all (binding_neq x) (flatten hm'));
- assert(for_all (binding_neq x) (flatten (slot' :: hm')))
-#pop-options
-
-val hashMap_s_inv_implies_assoc_list_lem
- (#t : Type0) (hm : hashMap_s t) :
- Lemma (requires (hashMap_s_inv hm))
- (ensures (assoc_list_inv (flatten hm)))
-
-let hashMap_s_inv_implies_assoc_list_lem #t hm =
- partial_hashMap_s_inv_implies_assoc_list_lem (length hm) 0 hm
-
-val hashMap_t_base_inv_implies_assoc_list_lem
- (#t : Type0) (hm : hashMap_t t):
- Lemma (requires (hashMap_t_base_inv hm))
- (ensures (assoc_list_inv (hashMap_t_al_v hm)))
-
-let hashMap_t_base_inv_implies_assoc_list_lem #t hm =
- hashMap_s_inv_implies_assoc_list_lem (hashMap_t_v hm)
-
-/// For some reason, we can't write the below [forall] directly in the [ensures]
-/// clause of the next lemma: it makes Z3 fails even with a huge rlimit.
-/// I have no idea what's going on.
-let hashMap_is_assoc_list
- (#t : Type0) (ntable : hashMap_t t{length ntable.slots > 0})
- (al : assoc_list t) : Type0 =
- (forall (k:key). hashMap_t_find_s ntable k == assoc_list_find k al)
-
-let partial_hashMap_s_find
- (#t : Type0) (len : usize{len > 0}) (offset : usize)
- (hm : hashMap_s_nes t{offset + length hm = len})
- (k : key{hash_mod_key k len >= offset}) : option t =
- let i = hash_mod_key k len in
- let slot = index hm (i - offset) in
- slot_s_find k slot
-
-val not_same_hash_key_not_found_in_slot
- (#t : Type0) (len : usize{len > 0})
- (k : key)
- (i : usize)
- (slot : slot_s t) :
- Lemma
- (requires (
- hash_mod_key k len <> i /\
- slot_s_inv len i slot))
- (ensures (slot_s_find k slot == None))
-
-#push-options "--fuel 1"
-let rec not_same_hash_key_not_found_in_slot #t len k i slot =
- match slot with
- | [] -> ()
- | (k',v) :: slot' -> not_same_hash_key_not_found_in_slot len k i slot'
-#pop-options
-
-/// Small variation of [binding_in_previous_slot_implies_neq]: if the hash of
-/// a key links it to a previous slot, it can't be found in the slots after.
-val key_in_previous_slot_implies_not_found
- (#t : Type0) (len : usize{len > 0})
- (k : key)
- (offset : usize)
- (slots : hashMap_s t{offset + length slots = len}) :
- Lemma
- (requires (
- // The binding comes from a slot not in [slots]
- hash_mod_key k len < offset /\
- // The slots are the well-formed suffix of a hash map
- partial_hashMap_s_inv len offset slots))
- (ensures (
- assoc_list_find k (flatten slots) == None))
- (decreases slots)
-
-#push-options "--fuel 1"
-let rec key_in_previous_slot_implies_not_found #t len k offset slots =
- match slots with
- | [] -> ()
- | slot :: slots' ->
- find_append (same_key k) slot (flatten slots');
- assert(index slots 0 == slot); // Triggers instantiations
- not_same_hash_key_not_found_in_slot #t len k offset slot;
- assert(assoc_list_find k slot == None);
- assert(forall (i:nat{i < length slots'}). index slots' i == index slots (i+1)); // Triggers instantiations
- key_in_previous_slot_implies_not_found len k (offset+1) slots'
-#pop-options
-
-val partial_hashMap_s_is_assoc_list_lem
- (#t : Type0) (len : usize{len > 0}) (offset : usize)
- (hm : hashMap_s_nes t{offset + length hm = len})
- (k : key{hash_mod_key k len >= offset}) :
- Lemma
- (requires (
- partial_hashMap_s_inv len offset hm))
- (ensures (
- partial_hashMap_s_find len offset hm k == assoc_list_find k (flatten hm)))
- (decreases hm)
-
-#push-options "--fuel 1"
-let rec partial_hashMap_s_is_assoc_list_lem #t len offset hm k =
- match hm with
- | [] -> ()
- | slot :: hm' ->
- let h = hash_mod_key k len in
- let i = h - offset in
- if i = 0 then
- begin
- // We must look in the current slot
- assert(partial_hashMap_s_find len offset hm k == slot_s_find k slot);
- find_append (same_key k) slot (flatten hm');
- assert(forall (i:nat{i < length hm'}). index hm' i == index hm (i+1)); // Triggers instantiations
- key_in_previous_slot_implies_not_found #t len k (offset+1) hm';
- assert( // Of course, writing `== None` doesn't work...
- match find (same_key k) (flatten hm') with
- | None -> True
- | Some _ -> False);
- assert(
- find (same_key k) (flatten hm) ==
- begin match find (same_key k) slot with
- | Some x -> Some x
- | None -> find (same_key k) (flatten hm')
- end);
- ()
- end
- else
- begin
- // We must ignore the current slot
- assert(partial_hashMap_s_find len offset hm k ==
- partial_hashMap_s_find len (offset+1) hm' k);
- find_append (same_key k) slot (flatten hm');
- assert(index hm 0 == slot); // Triggers instantiations
- not_same_hash_key_not_found_in_slot #t len k offset slot;
- assert(forall (i:nat{i < length hm'}). index hm' i == index hm (i+1)); // Triggers instantiations
- partial_hashMap_s_is_assoc_list_lem #t len (offset+1) hm' k
- end
-#pop-options
-
-val hashMap_is_assoc_list_lem (#t : Type0) (hm : hashMap_t t) :
- Lemma (requires (hashMap_t_base_inv hm))
- (ensures (hashMap_is_assoc_list hm (hashMap_t_al_v hm)))
-
-let hashMap_is_assoc_list_lem #t hm =
- let aux (k:key) :
- Lemma (hashMap_t_find_s hm k == assoc_list_find k (hashMap_t_al_v hm))
- [SMTPat (hashMap_t_find_s hm k)] =
- let hm_v = hashMap_t_v hm in
- let len = length hm_v in
- partial_hashMap_s_is_assoc_list_lem #t len 0 hm_v k
- in
- ()
-
-/// The final lemma about [move_elements]: calling it on an empty hash table moves
-/// all the elements to this empty table.
-val hashMap_move_elements_lem
- (t : Type0) (ntable : hashMap_t t) (slots : alloc_vec_Vec (list_t t)) :
- Lemma
- (requires (
- let al = flatten (slots_t_v slots) in
- hashMap_t_base_inv ntable /\
- length al <= usize_max /\
- assoc_list_inv al /\
- // The table is empty
- hashMap_t_len_s ntable = 0 /\
- (forall (k:key). hashMap_t_find_s ntable k == None)))
- (ensures (
- let al = flatten (slots_t_v slots) in
- match hashMap_move_elements t ntable slots 0,
- hashMap_move_elements_s_flat (hashMap_t_v ntable) al
- with
- | Return (ntable', _), Return ntable'_v ->
- // The invariant is preserved
- hashMap_t_base_inv ntable' /\
- // We preserved the parameters
- hashMap_t_same_params ntable' ntable /\
- // The table has the same number of slots
- length ntable'.slots = length ntable.slots /\
- // The count is good
- hashMap_t_len_s ntable' = length al /\
- // The table can be linked to its model (we need this only to reveal
- // "pretty" functional lemmas to the user in the fsti - so that we
- // can write lemmas with SMT patterns - this is very F* specific)
- hashMap_t_v ntable' == ntable'_v /\
- // The new table contains exactly all the bindings from the slots
- // Rk.: see the comment for [hashMap_is_assoc_list]
- hashMap_is_assoc_list ntable' al
- | _ -> False // We can only succeed
- ))
-
-// Weird, dirty things happen below.
-// Manually unfolding some postconditions allowed to make the proof pass,
-// and also revealed the reason why some proofs failed with "Unknown assertion
-// failed" (resulting in the call to [flatten_0_is_flatten] for instance).
-// I think manually unfolding the postconditions allowed to account for the
-// lack of ifuel (this kind of proofs is annoying, really).
-#restart-solver
-#push-options "--z3rlimit 100"
-let hashMap_move_elements_lem t ntable slots =
- let ntable_v = hashMap_t_v ntable in
- let slots_v = slots_t_v slots in
- let al = flatten slots_v in
- hashMap_move_elements_lem_refin t ntable slots 0;
- begin
- match hashMap_move_elements t ntable slots 0,
- hashMap_move_elements_s ntable_v slots_v 0
- with
- | Fail _, Fail _ -> ()
- | Return (ntable', _), Return ntable'_v ->
- assert(hashMap_t_base_inv ntable');
- assert(hashMap_t_v ntable' == ntable'_v)
- | _ -> assert(False)
- end;
- hashMap_move_elements_s_lem_refin_flat ntable_v slots_v 0;
- begin
- match hashMap_move_elements_s ntable_v slots_v 0,
- hashMap_move_elements_s_flat ntable_v (flatten_i slots_v 0)
- with
- | Fail _, Fail _ -> ()
- | Return hm, Return hm' -> assert(hm == hm')
- | _ -> assert(False)
- end;
- flatten_0_is_flatten slots_v; // flatten_i slots_v 0 == flatten slots_v
- hashMap_move_elements_s_flat_lem ntable_v al;
- match hashMap_move_elements t ntable slots 0,
- hashMap_move_elements_s_flat ntable_v al
- with
- | Return (ntable', _), Return ntable'_v ->
- assert(hashMap_t_base_inv ntable');
- assert(length ntable'.slots = length ntable.slots);
- assert(hashMap_t_len_s ntable' = length al);
- assert(hashMap_t_v ntable' == ntable'_v);
- assert(hashMap_is_assoc_list ntable' al)
- | _ -> assert(False)
-#pop-options
-
-(*** try_resize *)
-
-/// High-level model 1.
-/// This is one is slightly "crude": we just simplify a bit the function.
-
-let hashMap_try_resize_s_simpl
- (#t : Type0)
- (hm : hashMap_t t) :
- Pure (result (hashMap_t t))
- (requires (
- let (divid, divis) = hm.max_load_factor in
- divid > 0 /\ divis > 0))
- (ensures (fun _ -> True)) =
- let capacity = length hm.slots in
- let (divid, divis) = hm.max_load_factor in
- if capacity <= (usize_max / 2) / divid then
- let ncapacity : usize = capacity * 2 in
- begin match hashMap_new_with_capacity t ncapacity divid divis with
- | Fail e -> Fail e
- | Return ntable ->
- match hashMap_move_elements t ntable hm.slots 0 with
- | Fail e -> Fail e
- | Return (ntable', _) ->
- let hm =
- { hm with slots = ntable'.slots;
- max_load = ntable'.max_load }
- in
- Return hm
- end
- else Return hm
-
-val hashMap_try_resize_lem_refin
- (t : Type0) (self : hashMap_t t) :
- Lemma
- (requires (
- let (divid, divis) = self.max_load_factor in
- divid > 0 /\ divis > 0))
- (ensures (
- match hashMap_try_resize t self,
- hashMap_try_resize_s_simpl self
- with
- | Fail _, Fail _ -> True
- | Return hm1, Return hm2 -> hm1 == hm2
- | _ -> False))
-
-let hashMap_try_resize_lem_refin t self = ()
-
-/// Isolating arithmetic proofs
-
-let gt_lem0 (n m q : nat) :
- Lemma (requires (m > 0 /\ n > q))
- (ensures (n * m > q * m)) = ()
-
-let ge_lem0 (n m q : nat) :
- Lemma (requires (m > 0 /\ n >= q))
- (ensures (n * m >= q * m)) = ()
-
-let gt_ge_trans (n m p : nat) :
- Lemma (requires (n > m /\ m >= p)) (ensures (n > p)) = ()
-
-let ge_trans (n m p : nat) :
- Lemma (requires (n >= m /\ m >= p)) (ensures (n >= p)) = ()
-
-#push-options "--z3rlimit 200"
-let gt_lem1 (n m q : nat) :
- Lemma (requires (m > 0 /\ n > q / m)) (ensures (n * m > q)) =
- assert(n >= q / m + 1);
- ge_lem0 n m (q / m + 1);
- assert(n * m >= (q / m) * m + m)
-#pop-options
-
-let gt_lem2 (n m p q : nat) :
- Lemma (requires (m > 0 /\ p > 0 /\ n > (q / m) / p)) (ensures (n * m * p > q)) =
- gt_lem1 n p (q / m);
- assert(n * p > q / m);
- gt_lem1 (n * p) m q
-
-let ge_lem1 (n m q : nat) :
- Lemma (requires (n >= m /\ q > 0))
- (ensures (n / q >= m / q)) =
- FStar.Math.Lemmas.lemma_div_le m n q
-
-#restart-solver
-#push-options "--z3rlimit 200"
-let times_divid_lem (n m p : pos) : Lemma ((n * m) / p >= n * (m / p))
- =
- FStar.Math.Lemmas.multiply_fractions m p;
- assert(m >= (m / p) * p);
- assert(n * m >= n * (m / p) * p); //
- ge_lem1 (n * m) (n * (m / p) * p) p;
- assert((n * m) / p >= (n * (m / p) * p) / p);
- assert(n * (m / p) * p = (n * (m / p)) * p);
- FStar.Math.Lemmas.cancel_mul_div (n * (m / p)) p;
- assert(((n * (m / p)) * p) / p = n * (m / p))
-#pop-options
-
-/// The good old arithmetic proofs and their unstability...
-/// At some point I thought it was stable because it worked with `--quake 100`.
-/// Of course, it broke the next time I checked the file...
-/// It seems things are ok when we check this proof on its own, but not when
-/// it is sent at the same time as the one above (though we put #restart-solver!).
-/// I also tried `--quake 1/100` to no avail: it seems that when Z3 decides to
-/// fail the first one, it fails them all. I inserted #restart-solver before
-/// the previous lemma to see if it had an effect (of course not).
-val new_max_load_lem
- (len : usize) (capacity : usize{capacity > 0})
- (divid : usize{divid > 0}) (divis : usize{divis > 0}) :
- Lemma
- (requires (
- let max_load = (capacity * divid) / divis in
- let ncapacity = 2 * capacity in
- let nmax_load = (ncapacity * divid) / divis in
- capacity > 0 /\ 0 < divid /\ divid < divis /\
- capacity * divid >= divis /\
- len = max_load + 1))
- (ensures (
- let max_load = (capacity * divid) / divis in
- let ncapacity = 2 * capacity in
- let nmax_load = (ncapacity * divid) / divis in
- len <= nmax_load))
-
-let mul_assoc (a b c : nat) : Lemma (a * b * c == a * (b * c)) = ()
-
-let ge_lem2 (a b c d : nat) : Lemma (requires (a >= b + c /\ c >= d)) (ensures (a >= b + d)) = ()
-let ge_div_lem1 (a b : nat) : Lemma (requires (a >= b /\ b > 0)) (ensures (a / b >= 1)) = ()
-
-#restart-solver
-#push-options "--z3rlimit 100 --z3cliopt smt.arith.nl=false"
-let new_max_load_lem len capacity divid divis =
- FStar.Math.Lemmas.paren_mul_left 2 capacity divid;
- mul_assoc 2 capacity divid;
- // The following assertion often breaks though it is given by the above
- // lemma. I really don't know what to do (I deactivated non-linear
- // arithmetic and added the previous lemma call, moved the assertion up,
- // boosted the rlimit...).
- assert(2 * capacity * divid == 2 * (capacity * divid));
- let max_load = (capacity * divid) / divis in
- let ncapacity = 2 * capacity in
- let nmax_load = (ncapacity * divid) / divis in
- assert(nmax_load = (2 * capacity * divid) / divis);
- times_divid_lem 2 (capacity * divid) divis;
- assert((2 * (capacity * divid)) / divis >= 2 * ((capacity * divid) / divis));
- assert(nmax_load >= 2 * ((capacity * divid) / divis));
- assert(nmax_load >= 2 * max_load);
- assert(nmax_load >= max_load + max_load);
- ge_div_lem1 (capacity * divid) divis;
- ge_lem2 nmax_load max_load max_load 1;
- assert(nmax_load >= max_load + 1)
-#pop-options
-
-val hashMap_try_resize_s_simpl_lem (#t : Type0) (hm : hashMap_t t) :
- Lemma
- (requires (
- // The base invariant is satisfied
- hashMap_t_base_inv hm /\
- // However, the "full" invariant is broken, as we call [try_resize]
- // only if the current number of entries is > the max load.
- //
- // There are two situations:
- // - either we just reached the max load
- // - or we were already saturated and can't resize
- (let (dividend, divisor) = hm.max_load_factor in
- hm.num_entries == hm.max_load + 1 \/
- length hm.slots * 2 * dividend > usize_max)
- ))
- (ensures (
- match hashMap_try_resize_s_simpl hm with
- | Fail _ -> False
- | Return hm' ->
- // The full invariant is now satisfied (the full invariant is "base
- // invariant" + the map is not overloaded (or can't be resized because
- // already too big)
- hashMap_t_inv hm' /\
- // It contains the same bindings as the initial map
- (forall (k:key). hashMap_t_find_s hm' k == hashMap_t_find_s hm k)))
-
-#restart-solver
-#push-options "--z3rlimit 400"
-let hashMap_try_resize_s_simpl_lem #t hm =
- let capacity = length hm.slots in
- let (divid, divis) = hm.max_load_factor in
- if capacity <= (usize_max / 2) / divid then
- begin
- let ncapacity : usize = capacity * 2 in
- assert(ncapacity * divid <= usize_max);
- assert(hashMap_t_len_s hm = hm.max_load + 1);
- new_max_load_lem (hashMap_t_len_s hm) capacity divid divis;
- hashMap_new_with_capacity_lem t ncapacity divid divis;
- match hashMap_new_with_capacity t ncapacity divid divis with
- | Fail _ -> ()
- | Return ntable ->
- let slots = hm.slots in
- let al = flatten (slots_t_v slots) in
- // Proving that: length al = hm.num_entries
- assert(al == flatten (map slot_t_v slots));
- assert(al == flatten (map list_t_v slots));
- assert(hashMap_t_al_v hm == flatten (hashMap_t_v hm));
- assert(hashMap_t_al_v hm == flatten (map list_t_v hm.slots));
- assert(al == hashMap_t_al_v hm);
- assert(hashMap_t_base_inv ntable);
- assert(length al = hm.num_entries);
- assert(length al <= usize_max);
- hashMap_t_base_inv_implies_assoc_list_lem hm;
- assert(assoc_list_inv al);
- assert(hashMap_t_len_s ntable = 0);
- assert(forall (k:key). hashMap_t_find_s ntable k == None);
- hashMap_move_elements_lem t ntable hm.slots;
- match hashMap_move_elements t ntable hm.slots 0 with
- | Fail _ -> ()
- | Return (ntable', _) ->
- hashMap_is_assoc_list_lem hm;
- assert(hashMap_is_assoc_list hm (hashMap_t_al_v hm));
- let hm' =
- { hm with slots = ntable'.slots;
- max_load = ntable'.max_load }
- in
- assert(hashMap_t_base_inv ntable');
- assert(hashMap_t_base_inv hm');
- assert(hashMap_t_len_s hm' = hashMap_t_len_s hm);
- new_max_load_lem (hashMap_t_len_s hm') capacity divid divis;
- assert(hashMap_t_len_s hm' <= hm'.max_load); // Requires a lemma
- assert(hashMap_t_inv hm')
- end
- else
- begin
- gt_lem2 capacity 2 divid usize_max;
- assert(capacity * 2 * divid > usize_max)
- end
-#pop-options
-
-let hashMap_t_same_bindings (#t : Type0) (hm hm' : hashMap_t_nes t) : Type0 =
- forall (k:key). hashMap_t_find_s hm k == hashMap_t_find_s hm' k
-
-/// The final lemma about [try_resize]
-val hashMap_try_resize_lem (#t : Type0) (hm : hashMap_t t) :
- Lemma
- (requires (
- hashMap_t_base_inv hm /\
- // However, the "full" invariant is broken, as we call [try_resize]
- // only if the current number of entries is > the max load.
- //
- // There are two situations:
- // - either we just reached the max load
- // - or we were already saturated and can't resize
- (let (dividend, divisor) = hm.max_load_factor in
- hm.num_entries == hm.max_load + 1 \/
- length hm.slots * 2 * dividend > usize_max)))
- (ensures (
- match hashMap_try_resize t hm with
- | Fail _ -> False
- | Return hm' ->
- // The full invariant is now satisfied (the full invariant is "base
- // invariant" + the map is not overloaded (or can't be resized because
- // already too big)
- hashMap_t_inv hm' /\
- // The length is the same
- hashMap_t_len_s hm' = hashMap_t_len_s hm /\
- // It contains the same bindings as the initial map
- hashMap_t_same_bindings hm' hm))
-
-let hashMap_try_resize_lem #t hm =
- hashMap_try_resize_lem_refin t hm;
- hashMap_try_resize_s_simpl_lem hm
-
-(*** insert *)
-
-/// The high-level model (very close to the original function: we don't need something
-/// very high level, just to clean it a bit)
-let hashMap_insert_s
- (#t : Type0) (self : hashMap_t t) (key : usize) (value : t) :
- result (hashMap_t t) =
- match hashMap_insert_no_resize t self key value with
- | Fail e -> Fail e
- | Return hm' ->
- if hashMap_t_len_s hm' > hm'.max_load then
- hashMap_try_resize t hm'
- else Return hm'
-
-val hashMap_insert_lem_refin
- (t : Type0) (self : hashMap_t t) (key : usize) (value : t) :
- Lemma (requires True)
- (ensures (
- match hashMap_insert t self key value,
- hashMap_insert_s self key value
- with
- | Fail _, Fail _ -> True
- | Return hm1, Return hm2 -> hm1 == hm2
- | _ -> False))
-
-let hashMap_insert_lem_refin t self key value = ()
-
-/// Helper
-let hashMap_insert_bindings_lem
- (t : Type0) (self : hashMap_t_nes t) (key : usize) (value : t)
- (hm' hm'' : hashMap_t_nes t) :
- Lemma
- (requires (
- hashMap_s_updated_binding (hashMap_t_v self) key
- (Some value) (hashMap_t_v hm') /\
- hashMap_t_same_bindings hm' hm''))
- (ensures (
- hashMap_s_updated_binding (hashMap_t_v self) key
- (Some value) (hashMap_t_v hm'')))
- = ()
-
-val hashMap_insert_lem_aux
- (#t : Type0) (self : hashMap_t t) (key : usize) (value : t) :
- Lemma (requires (hashMap_t_inv self))
- (ensures (
- match hashMap_insert t self key value with
- | Fail _ ->
- // We can fail only if:
- // - the key is not in the map and we need to add it
- // - we are already saturated
- hashMap_t_len_s self = usize_max /\
- None? (hashMap_t_find_s self key)
- | Return hm' ->
- // The invariant is preserved
- hashMap_t_inv hm' /\
- // [key] maps to [value] and the other bindings are preserved
- hashMap_s_updated_binding (hashMap_t_v self) key (Some value) (hashMap_t_v hm') /\
- // The length is incremented, iff we inserted a new key
- (match hashMap_t_find_s self key with
- | None -> hashMap_t_len_s hm' = hashMap_t_len_s self + 1
- | Some _ -> hashMap_t_len_s hm' = hashMap_t_len_s self)))
-
-#restart-solver
-#push-options "--z3rlimit 200"
-let hashMap_insert_lem_aux #t self key value =
- hashMap_insert_no_resize_lem_s t self key value;
- hashMap_insert_no_resize_s_lem (hashMap_t_v self) key value;
- match hashMap_insert_no_resize t self key value with
- | Fail _ -> ()
- | Return hm' ->
- // Expanding the post of [hashMap_insert_no_resize_lem_s]
- let self_v = hashMap_t_v self in
- let hm'_v = Return?.v (hashMap_insert_no_resize_s self_v key value) in
- assert(hashMap_t_base_inv hm');
- assert(hashMap_t_same_params hm' self);
- assert(hashMap_t_v hm' == hm'_v);
- assert(hashMap_s_len hm'_v == hashMap_t_len_s hm');
- // Expanding the post of [hashMap_insert_no_resize_s_lem]
- assert(insert_post self_v key value hm'_v);
- // Expanding [insert_post]
- assert(hashMap_s_inv hm'_v);
- assert(
- match hashMap_s_find self_v key with
- | None -> hashMap_s_len hm'_v = hashMap_s_len self_v + 1
- | Some _ -> hashMap_s_len hm'_v = hashMap_s_len self_v);
- if hashMap_t_len_s hm' > hm'.max_load then
- begin
- hashMap_try_resize_lem hm';
- // Expanding the post of [hashMap_try_resize_lem]
- let hm'' = Return?.v (hashMap_try_resize t hm') in
- assert(hashMap_t_inv hm'');
- let hm''_v = hashMap_t_v hm'' in
- assert(forall k. hashMap_t_find_s hm'' k == hashMap_t_find_s hm' k);
- assert(hashMap_t_len_s hm'' = hashMap_t_len_s hm'); // TODO
- // Proving the post
- assert(hashMap_t_inv hm'');
- hashMap_insert_bindings_lem t self key value hm' hm'';
- assert(
- match hashMap_t_find_s self key with
- | None -> hashMap_t_len_s hm'' = hashMap_t_len_s self + 1
- | Some _ -> hashMap_t_len_s hm'' = hashMap_t_len_s self)
- end
- else ()
-#pop-options
-
-let hashMap_insert_lem #t self key value =
- hashMap_insert_lem_aux #t self key value
-
-(*** contains_key *)
-
-(**** contains_key_in_list *)
-
-val hashMap_contains_key_in_list_lem
- (#t : Type0) (key : usize) (ls : list_t t) :
- Lemma
- (ensures (
- match hashMap_contains_key_in_list t key ls with
- | Fail _ -> False
- | Return b ->
- b = Some? (slot_t_find_s key ls)))
-
-
-#push-options "--fuel 1"
-let rec hashMap_contains_key_in_list_lem #t key ls =
- match ls with
- | List_Cons ckey x ls0 ->
- let b = ckey = key in
- if b
- then ()
- else
- begin
- hashMap_contains_key_in_list_lem key ls0;
- match hashMap_contains_key_in_list t key ls0 with
- | Fail _ -> ()
- | Return b0 -> ()
- end
- | List_Nil -> ()
-#pop-options
-
-(**** contains_key *)
-
-val hashMap_contains_key_lem_aux
- (#t : Type0) (self : hashMap_t_nes t) (key : usize) :
- Lemma
- (ensures (
- match hashMap_contains_key t self key with
- | Fail _ -> False
- | Return b -> b = Some? (hashMap_t_find_s self key)))
-
-let hashMap_contains_key_lem_aux #t self key =
- begin match hash_key key with
- | Fail _ -> ()
- | Return i ->
- let v = self.slots in
- let i0 = alloc_vec_Vec_len (list_t t) v in
- begin match usize_rem i i0 with
- | Fail _ -> ()
- | Return hash_mod ->
- begin match alloc_vec_Vec_index_usize v hash_mod with
- | Fail _ -> ()
- | Return l ->
- hashMap_contains_key_in_list_lem key l;
- begin match hashMap_contains_key_in_list t key l with
- | Fail _ -> ()
- | Return b -> ()
- end
- end
- end
- end
-
-/// The lemma in the .fsti
-let hashMap_contains_key_lem #t self key =
- hashMap_contains_key_lem_aux #t self key
-
-(*** get *)
-
-(**** get_in_list *)
-
-val hashMap_get_in_list_lem
- (#t : Type0) (key : usize) (ls : list_t t) :
- Lemma
- (ensures (
- match hashMap_get_in_list t key ls, slot_t_find_s key ls with
- | Fail _, None -> True
- | Return x, Some x' -> x == x'
- | _ -> False))
-
-#push-options "--fuel 1"
-let rec hashMap_get_in_list_lem #t key ls =
- begin match ls with
- | List_Cons ckey cvalue ls0 ->
- let b = ckey = key in
- if b
- then ()
- else
- begin
- hashMap_get_in_list_lem key ls0;
- match hashMap_get_in_list t key ls0 with
- | Fail _ -> ()
- | Return x -> ()
- end
- | List_Nil -> ()
- end
-#pop-options
-
-(**** get *)
-
-val hashMap_get_lem_aux
- (#t : Type0) (self : hashMap_t_nes t) (key : usize) :
- Lemma
- (ensures (
- match hashMap_get t self key, hashMap_t_find_s self key with
- | Fail _, None -> True
- | Return x, Some x' -> x == x'
- | _ -> False))
-
-let hashMap_get_lem_aux #t self key =
- begin match hash_key key with
- | Fail _ -> ()
- | Return i ->
- let v = self.slots in
- let i0 = alloc_vec_Vec_len (list_t t) v in
- begin match usize_rem i i0 with
- | Fail _ -> ()
- | Return hash_mod ->
- begin match alloc_vec_Vec_index_usize v hash_mod with
- | Fail _ -> ()
- | Return l ->
- begin
- hashMap_get_in_list_lem key l;
- match hashMap_get_in_list t key l with
- | Fail _ -> ()
- | Return x -> ()
- end
- end
- end
- end
-
-/// .fsti
-let hashMap_get_lem #t self key = hashMap_get_lem_aux #t self key
-
-(*** get_mut'fwd *)
-
-
-(**** get_mut_in_list'fwd *)
-
-val hashMap_get_mut_in_list_loop_lem
- (#t : Type0) (ls : list_t t) (key : usize) :
- Lemma
- (ensures (
- match hashMap_get_mut_in_list_loop t ls key, slot_t_find_s key ls with
- | Fail _, None -> True
- | Return x, Some x' -> x == x'
- | _ -> False))
-
-#push-options "--fuel 1"
-let rec hashMap_get_mut_in_list_loop_lem #t ls key =
- begin match ls with
- | List_Cons ckey cvalue ls0 ->
- let b = ckey = key in
- if b
- then ()
- else
- begin
- hashMap_get_mut_in_list_loop_lem ls0 key;
- match hashMap_get_mut_in_list_loop t ls0 key with
- | Fail _ -> ()
- | Return x -> ()
- end
- | List_Nil -> ()
- end
-#pop-options
-
-(**** get_mut'fwd *)
-
-val hashMap_get_mut_lem_aux
- (#t : Type0) (self : hashMap_t_nes t) (key : usize) :
- Lemma
- (ensures (
- match hashMap_get_mut t self key, hashMap_t_find_s self key with
- | Fail _, None -> True
- | Return x, Some x' -> x == x'
- | _ -> False))
-
-let hashMap_get_mut_lem_aux #t self key =
- begin match hash_key key with
- | Fail _ -> ()
- | Return i ->
- let v = self.slots in
- let i0 = alloc_vec_Vec_len (list_t t) v in
- begin match usize_rem i i0 with
- | Fail _ -> ()
- | Return hash_mod ->
- begin match alloc_vec_Vec_index_usize v hash_mod with
- | Fail _ -> ()
- | Return l ->
- begin
- hashMap_get_mut_in_list_loop_lem l key;
- match hashMap_get_mut_in_list_loop t l key with
- | Fail _ -> ()
- | Return x -> ()
- end
- end
- end
- end
-
-let hashMap_get_mut_lem #t self key =
- hashMap_get_mut_lem_aux #t self key
-
-(*** get_mut'back *)
-
-(**** get_mut_in_list'back *)
-
-val hashMap_get_mut_in_list_loop_back_lem
- (#t : Type0) (ls : list_t t) (key : usize) (ret : t) :
- Lemma
- (requires (Some? (slot_t_find_s key ls)))
- (ensures (
- match hashMap_get_mut_in_list_loop_back t ls key ret with
- | Fail _ -> False
- | Return ls' -> list_t_v ls' == find_update (same_key key) (list_t_v ls) (key,ret)
- | _ -> False))
-
-#push-options "--fuel 1"
-let rec hashMap_get_mut_in_list_loop_back_lem #t ls key ret =
- begin match ls with
- | List_Cons ckey cvalue ls0 ->
- let b = ckey = key in
- if b
- then let ls1 = List_Cons ckey ret ls0 in ()
- else
- begin
- hashMap_get_mut_in_list_loop_back_lem ls0 key ret;
- match hashMap_get_mut_in_list_loop_back t ls0 key ret with
- | Fail _ -> ()
- | Return l -> let ls1 = List_Cons ckey cvalue l in ()
- end
- | List_Nil -> ()
- end
-#pop-options
-
-(**** get_mut'back *)
-
-/// Refinement lemma
-val hashMap_get_mut_back_lem_refin
- (#t : Type0) (self : hashMap_t t{length self.slots > 0})
- (key : usize) (ret : t) :
- Lemma
- (requires (Some? (hashMap_t_find_s self key)))
- (ensures (
- match hashMap_get_mut_back t self key ret with
- | Fail _ -> False
- | Return hm' ->
- hashMap_t_v hm' == hashMap_insert_no_fail_s (hashMap_t_v self) key ret))
-
-let hashMap_get_mut_back_lem_refin #t self key ret =
- begin match hash_key key with
- | Fail _ -> ()
- | Return i ->
- let i0 = self.num_entries in
- let p = self.max_load_factor in
- let i1 = self.max_load in
- let v = self.slots in
- let i2 = alloc_vec_Vec_len (list_t t) v in
- begin match usize_rem i i2 with
- | Fail _ -> ()
- | Return hash_mod ->
- begin match alloc_vec_Vec_index_usize v hash_mod with
- | Fail _ -> ()
- | Return l ->
- begin
- hashMap_get_mut_in_list_loop_back_lem l key ret;
- match hashMap_get_mut_in_list_loop_back t l key ret with
- | Fail _ -> ()
- | Return l0 ->
- begin match alloc_vec_Vec_update_usize v hash_mod l0 with
- | Fail _ -> ()
- | Return v0 -> let self0 = MkhashMap_t i0 p i1 v0 in ()
- end
- end
- end
- end
- end
-
-/// Final lemma
-val hashMap_get_mut_back_lem_aux
- (#t : Type0) (hm : hashMap_t t)
- (key : usize) (ret : t) :
- Lemma
- (requires (
- hashMap_t_inv hm /\
- Some? (hashMap_t_find_s hm key)))
- (ensures (
- match hashMap_get_mut_back t hm key ret with
- | Fail _ -> False
- | Return hm' ->
- // Functional spec
- hashMap_t_v hm' == hashMap_insert_no_fail_s (hashMap_t_v hm) key ret /\
- // The invariant is preserved
- hashMap_t_inv hm' /\
- // The length is preserved
- hashMap_t_len_s hm' = hashMap_t_len_s hm /\
- // [key] maps to [value]
- hashMap_t_find_s hm' key == Some ret /\
- // The other bindings are preserved
- (forall k'. k' <> key ==> hashMap_t_find_s hm' k' == hashMap_t_find_s hm k')))
-
-let hashMap_get_mut_back_lem_aux #t hm key ret =
- let hm_v = hashMap_t_v hm in
- hashMap_get_mut_back_lem_refin hm key ret;
- match hashMap_get_mut_back t hm key ret with
- | Fail _ -> assert(False)
- | Return hm' ->
- hashMap_insert_no_fail_s_lem hm_v key ret
-
-/// .fsti
-let hashMap_get_mut_back_lem #t hm key ret = hashMap_get_mut_back_lem_aux hm key ret
-
-(*** remove'fwd *)
-
-val hashMap_remove_from_list_lem
- (#t : Type0) (key : usize) (ls : list_t t) :
- Lemma
- (ensures (
- match hashMap_remove_from_list t key ls with
- | Fail _ -> False
- | Return opt_x ->
- opt_x == slot_t_find_s key ls /\
- (Some? opt_x ==> length (slot_t_v ls) > 0)))
-
-#push-options "--fuel 1"
-let rec hashMap_remove_from_list_lem #t key ls =
- begin match ls with
- | List_Cons ckey x tl ->
- let b = ckey = key in
- if b
- then
- let mv_ls = core_mem_replace (list_t t) (List_Cons ckey x tl) List_Nil in
- begin match mv_ls with
- | List_Cons i cvalue tl0 -> ()
- | List_Nil -> ()
- end
- else
- begin
- hashMap_remove_from_list_lem key tl;
- match hashMap_remove_from_list t key tl with
- | Fail _ -> ()
- | Return opt -> ()
- end
- | List_Nil -> ()
- end
-#pop-options
-
-val hashMap_remove_lem_aux
- (#t : Type0) (self : hashMap_t t) (key : usize) :
- Lemma
- (requires (
- // We need the invariant to prove that upon decrementing the entries counter,
- // the counter doesn't become negative
- hashMap_t_inv self))
- (ensures (
- match hashMap_remove t self key with
- | Fail _ -> False
- | Return opt_x -> opt_x == hashMap_t_find_s self key))
-
-let hashMap_remove_lem_aux #t self key =
- begin match hash_key key with
- | Fail _ -> ()
- | Return i ->
- let i0 = self.num_entries in
- let v = self.slots in
- let i1 = alloc_vec_Vec_len (list_t t) v in
- begin match usize_rem i i1 with
- | Fail _ -> ()
- | Return hash_mod ->
- begin match alloc_vec_Vec_index_usize v hash_mod with
- | Fail _ -> ()
- | Return l ->
- begin
- hashMap_remove_from_list_lem key l;
- match hashMap_remove_from_list t key l with
- | Fail _ -> ()
- | Return x ->
- begin match x with
- | None -> ()
- | Some x0 ->
- begin
- assert(l == index v hash_mod);
- assert(length (list_t_v #t l) > 0);
- length_flatten_index (hashMap_t_v self) hash_mod;
- match usize_sub i0 1 with
- | Fail _ -> ()
- | Return _ -> ()
- end
- end
- end
- end
- end
- end
-
-/// .fsti
-let hashMap_remove_lem #t self key = hashMap_remove_lem_aux #t self key
-
-(*** remove'back *)
-
-(**** Refinement proofs *)
-
-/// High-level model for [remove_from_list'back]
-let hashMap_remove_from_list_s
- (#t : Type0) (key : usize) (ls : slot_s t) :
- slot_s t =
- filter_one (not_same_key key) ls
-
-/// Refinement lemma
-val hashMap_remove_from_list_back_lem_refin
- (#t : Type0) (key : usize) (ls : list_t t) :
- Lemma
- (ensures (
- match hashMap_remove_from_list_back t key ls with
- | Fail _ -> False
- | Return ls' ->
- list_t_v ls' == hashMap_remove_from_list_s key (list_t_v ls) /\
- // The length is decremented, iff the key was in the slot
- (let len = length (list_t_v ls) in
- let len' = length (list_t_v ls') in
- match slot_s_find key (list_t_v ls) with
- | None -> len = len'
- | Some _ -> len = len' + 1)))
-
-#push-options "--fuel 1"
-let rec hashMap_remove_from_list_back_lem_refin #t key ls =
- begin match ls with
- | List_Cons ckey x tl ->
- let b = ckey = key in
- if b
- then
- let mv_ls = core_mem_replace (list_t t) (List_Cons ckey x tl) List_Nil in
- begin match mv_ls with
- | List_Cons i cvalue tl0 -> ()
- | List_Nil -> ()
- end
- else
- begin
- hashMap_remove_from_list_back_lem_refin key tl;
- match hashMap_remove_from_list_back t key tl with
- | Fail _ -> ()
- | Return l -> let ls0 = List_Cons ckey x l in ()
- end
- | List_Nil -> ()
- end
-#pop-options
-
-/// High-level model for [remove_from_list'back]
-let hashMap_remove_s
- (#t : Type0) (self : hashMap_s_nes t) (key : usize) :
- hashMap_s t =
- let len = length self in
- let hash = hash_mod_key key len in
- let slot = index self hash in
- let slot' = hashMap_remove_from_list_s key slot in
- list_update self hash slot'
-
-/// Refinement lemma
-val hashMap_remove_back_lem_refin
- (#t : Type0) (self : hashMap_t_nes t) (key : usize) :
- Lemma
- (requires (
- // We need the invariant to prove that upon decrementing the entries counter,
- // the counter doesn't become negative
- hashMap_t_inv self))
- (ensures (
- match hashMap_remove_back t self key with
- | Fail _ -> False
- | Return hm' ->
- hashMap_t_same_params hm' self /\
- hashMap_t_v hm' == hashMap_remove_s (hashMap_t_v self) key /\
- // The length is decremented iff the key was in the map
- (let len = hashMap_t_len_s self in
- let len' = hashMap_t_len_s hm' in
- match hashMap_t_find_s self key with
- | None -> len = len'
- | Some _ -> len = len' + 1)))
-
-let hashMap_remove_back_lem_refin #t self key =
- begin match hash_key key with
- | Fail _ -> ()
- | Return i ->
- let i0 = self.num_entries in
- let p = self.max_load_factor in
- let i1 = self.max_load in
- let v = self.slots in
- let i2 = alloc_vec_Vec_len (list_t t) v in
- begin match usize_rem i i2 with
- | Fail _ -> ()
- | Return hash_mod ->
- begin match alloc_vec_Vec_index_usize v hash_mod with
- | Fail _ -> ()
- | Return l ->
- begin
- hashMap_remove_from_list_lem key l;
- match hashMap_remove_from_list t key l with
- | Fail _ -> ()
- | Return x ->
- begin match x with
- | None ->
- begin
- hashMap_remove_from_list_back_lem_refin key l;
- match hashMap_remove_from_list_back t key l with
- | Fail _ -> ()
- | Return l0 ->
- begin
- length_flatten_update (slots_t_v v) hash_mod (list_t_v l0);
- match alloc_vec_Vec_update_usize v hash_mod l0 with
- | Fail _ -> ()
- | Return v0 -> ()
- end
- end
- | Some x0 ->
- begin
- assert(l == index v hash_mod);
- assert(length (list_t_v #t l) > 0);
- length_flatten_index (hashMap_t_v self) hash_mod;
- match usize_sub i0 1 with
- | Fail _ -> ()
- | Return i3 ->
- begin
- hashMap_remove_from_list_back_lem_refin key l;
- match hashMap_remove_from_list_back t key l with
- | Fail _ -> ()
- | Return l0 ->
- begin
- length_flatten_update (slots_t_v v) hash_mod (list_t_v l0);
- match alloc_vec_Vec_update_usize v hash_mod l0 with
- | Fail _ -> ()
- | Return v0 -> ()
- end
- end
- end
- end
- end
- end
- end
- end
-
-(**** Invariants, high-level properties *)
-
-val hashMap_remove_from_list_s_lem
- (#t : Type0) (k : usize) (slot : slot_s t) (len : usize{len > 0}) (i : usize) :
- Lemma
- (requires (slot_s_inv len i slot))
- (ensures (
- let slot' = hashMap_remove_from_list_s k slot in
- slot_s_inv len i slot' /\
- slot_s_find k slot' == None /\
- (forall (k':key{k' <> k}). slot_s_find k' slot' == slot_s_find k' slot) /\
- // This postcondition is necessary to prove that the invariant is preserved
- // in the recursive calls. This allows us to do the proof in one go.
- (forall (b:binding t). for_all (binding_neq b) slot ==> for_all (binding_neq b) slot')
- ))
-
-#push-options "--fuel 1"
-let rec hashMap_remove_from_list_s_lem #t key slot len i =
- match slot with
- | [] -> ()
- | (k',v) :: slot' ->
- if k' <> key then
- begin
- hashMap_remove_from_list_s_lem key slot' len i;
- let slot'' = hashMap_remove_from_list_s key slot' in
- assert(for_all (same_hash_mod_key len i) ((k',v)::slot''));
- assert(for_all (binding_neq (k',v)) slot'); // Triggers instanciation
- assert(for_all (binding_neq (k',v)) slot'')
- end
- else
- begin
- assert(for_all (binding_neq (k',v)) slot');
- for_all_binding_neq_find_lem key v slot'
- end
-#pop-options
-
-val hashMap_remove_s_lem
- (#t : Type0) (self : hashMap_s_nes t) (key : usize) :
- Lemma
- (requires (hashMap_s_inv self))
- (ensures (
- let hm' = hashMap_remove_s self key in
- // The invariant is preserved
- hashMap_s_inv hm' /\
- // We updated the binding
- hashMap_s_updated_binding self key None hm'))
-
-let hashMap_remove_s_lem #t self key =
- let len = length self in
- let hash = hash_mod_key key len in
- let slot = index self hash in
- hashMap_remove_from_list_s_lem key slot len hash;
- let slot' = hashMap_remove_from_list_s key slot in
- let hm' = list_update self hash slot' in
- assert(hashMap_s_inv self)
-
-/// Final lemma about [remove'back]
-val hashMap_remove_back_lem_aux
- (#t : Type0) (self : hashMap_t t) (key : usize) :
- Lemma
- (requires (hashMap_t_inv self))
- (ensures (
- match hashMap_remove_back t self key with
- | Fail _ -> False
- | Return hm' ->
- hashMap_t_inv self /\
- hashMap_t_same_params hm' self /\
- // We updated the binding
- hashMap_s_updated_binding (hashMap_t_v self) key None (hashMap_t_v hm') /\
- hashMap_t_v hm' == hashMap_remove_s (hashMap_t_v self) key /\
- // The length is decremented iff the key was in the map
- (let len = hashMap_t_len_s self in
- let len' = hashMap_t_len_s hm' in
- match hashMap_t_find_s self key with
- | None -> len = len'
- | Some _ -> len = len' + 1)))
-
-let hashMap_remove_back_lem_aux #t self key =
- hashMap_remove_back_lem_refin self key;
- hashMap_remove_s_lem (hashMap_t_v self) key
-
-/// .fsti
-let hashMap_remove_back_lem #t self key =
- hashMap_remove_back_lem_aux #t self key
diff --git a/tests/fstar-split/hashmap/Hashmap.Properties.fsti b/tests/fstar-split/hashmap/Hashmap.Properties.fsti
deleted file mode 100644
index 26c0ec06..00000000
--- a/tests/fstar-split/hashmap/Hashmap.Properties.fsti
+++ /dev/null
@@ -1,267 +0,0 @@
-(** Properties about the hashmap *)
-module Hashmap.Properties
-open Primitives
-open FStar.List.Tot
-open FStar.Mul
-open Hashmap.Types
-open Hashmap.Clauses
-open Hashmap.Funs
-
-#set-options "--z3rlimit 50 --fuel 0 --ifuel 1"
-
-// Small trick to align the .fst and the .fsti
-val _align_fsti : unit
-
-(*** Utilities *)
-
-type key : eqtype = usize
-
-type hash : eqtype = usize
-
-val hashMap_t_inv (#t : Type0) (hm : hashMap_t t) : Type0
-
-val len_s (#t : Type0) (hm : hashMap_t t) : nat
-
-val find_s (#t : Type0) (hm : hashMap_t t) (k : key) : option t
-
-(*** Overloading *)
-
-/// Upon inserting *new* entries in the hash map, the slots vector is resized
-/// whenever we reach the max load, unless we can't resize anymore because
-/// there are already too many entries. This way, we maintain performance by
-/// limiting the hash collisions.
-/// This is expressed by the following property, which is maintained in the hash
-/// map invariant.
-val hashMap_not_overloaded_lem (#t : Type0) (hm : hashMap_t t) :
- Lemma
- (requires (hashMap_t_inv hm))
- (ensures (
- // The capacity is the number of slots
- let capacity = length hm.slots in
- // The max load factor defines a threshold on the number of entries:
- // if there are more entries than a given fraction of the number of slots,
- // we resize the slots vector to limit the hash collisions
- let (dividend, divisor) = hm.max_load_factor in
- // technicality: this postcondition won't typecheck if we don't reveal
- // that divisor > 0 (because of the division)
- divisor > 0 /\
- begin
- // The max load, computed as a fraction of the capacity
- let max_load = (capacity * dividend) / divisor in
- // The number of entries inserted in the map is given by [len_s] (see
- // the functional correctness lemmas, which state how this number evolves):
- let len = len_s hm in
- // We prove that:
- // - either the number of entries is <= than the max load threshold
- len <= max_load
- // - or we couldn't resize the map, because then the arithmetic computations
- // would overflow (note that we always multiply the number of slots by 2)
- || 2* capacity * dividend > usize_max
- end))
-
-(*** Functional correctness *)
-(**** [new'fwd] *)
-
-/// [new] doesn't fail and returns an empty hash map
-val hashMap_new_lem (t : Type0) :
- Lemma
- (ensures (
- match hashMap_new t with
- | Fail _ -> False
- | Return hm ->
- // The hash map invariant is satisfied
- hashMap_t_inv hm /\
- // The hash map has a length of 0
- len_s hm = 0 /\
- // It contains no bindings
- (forall k. find_s hm k == None)))
-
-(**** [clear] *)
-
-/// [clear] doesn't fail and turns the hash map into an empty map
-val hashMap_clear_lem
- (#t : Type0) (self : hashMap_t t) :
- Lemma
- (requires (hashMap_t_inv self))
- (ensures (
- match hashMap_clear t self with
- | Fail _ -> False
- | Return hm ->
- // The hash map invariant is satisfied
- hashMap_t_inv hm /\
- // The hash map has a length of 0
- len_s hm = 0 /\
- // It contains no bindings
- (forall k. find_s hm k == None)))
-
-(**** [len] *)
-
-/// [len] can't fail and returns the length (the number of elements) of the hash map
-val hashMap_len_lem (#t : Type0) (self : hashMap_t t) :
- Lemma
- (requires (hashMap_t_inv self))
- (ensures (
- match hashMap_len t self with
- | Fail _ -> False
- | Return l -> l = len_s self))
-
-
-(**** [insert'fwd_back] *)
-
-/// The backward function for [insert] (note it is named "...insert'fwd_back" because
-/// the forward function doesn't return anything, and was thus filtered - in a
-/// sense the effect of applying the forward function then the backward function is
-/// entirely encompassed by the effect of the backward function alone).
-///
-/// [insert'fwd_back] simply inserts a binding.
-val hashMap_insert_lem
- (#t : Type0) (self : hashMap_t t) (key : usize) (value : t) :
- Lemma
- (requires (hashMap_t_inv self))
- (ensures (
- match hashMap_insert t self key value with
- | Fail _ ->
- // We can fail only if:
- // - the key is not in the map and we thus need to add it
- None? (find_s self key) /\
- // - and we are already saturated (we can't increment the internal counter)
- len_s self = usize_max
- | Return hm' ->
- // The invariant is preserved
- hashMap_t_inv hm' /\
- // [key] maps to [value]
- find_s hm' key == Some value /\
- // The other bindings are preserved
- (forall k'. k' <> key ==> find_s hm' k' == find_s self k') /\
- begin
- // The length is incremented, iff we inserted a new key
- match find_s self key with
- | None -> len_s hm' = len_s self + 1
- | Some _ -> len_s hm' = len_s self
- end))
-
-
-(**** [contains_key] *)
-
-/// [contains_key'fwd] can't fail and returns `true` if and only if there is
-/// a binding for key [key]
-val hashMap_contains_key_lem
- (#t : Type0) (self : hashMap_t t) (key : usize) :
- Lemma
- (requires (hashMap_t_inv self))
- (ensures (
- match hashMap_contains_key t self key with
- | Fail _ -> False
- | Return b -> b = Some? (find_s self key)))
-
-(**** [get'fwd] *)
-
-/// [get] returns (a shared borrow to) the binding for key [key]
-val hashMap_get_lem
- (#t : Type0) (self : hashMap_t t) (key : usize) :
- Lemma
- (requires (hashMap_t_inv self))
- (ensures (
- match hashMap_get t self key, find_s self key with
- | Fail _, None -> True
- | Return x, Some x' -> x == x'
- | _ -> False))
-
-(**** [get_mut'fwd] *)
-
-/// [get_mut'fwd] returns (a mutable borrow to) the binding for key [key].
-///
-/// The *forward* function models the action of getting a borrow to an element
-/// in Rust, which gives the possibility of modifying this element in place. Then,
-/// upon ending the borrow, the effect of the modification is modelled in the
-/// translation through a call to the backward function.
-val hashMap_get_mut_lem
- (#t : Type0) (self : hashMap_t t) (key : usize) :
- Lemma
- (requires (hashMap_t_inv self))
- (ensures (
- match hashMap_get_mut t self key, find_s self key with
- | Fail _, None -> True
- | Return x, Some x' -> x == x'
- | _ -> False))
-
-
-(**** [get_mut'back] *)
-
-/// [get_mut'back] updates the binding for key [key], without failing.
-/// A call to [get_mut'back] must follow a call to [get_mut'fwd], which gives
-/// us that there must be a binding for key [key] in the map (otherwise we
-/// can't prove the absence of failure).
-val hashMap_get_mut_back_lem
- (#t : Type0) (hm : hashMap_t t) (key : usize) (ret : t) :
- Lemma
- (requires (
- hashMap_t_inv hm /\
- // A call to the backward function must follow a call to the forward
- // function, whose success gives us that there is a binding for the key.
- // In the case of *forward* functions, "success" has to be understood as
- // the absence of panics. When translating code from Rust to pure lambda
- // calculus, we have the property that the generated calls to the backward
- // functions can't fail (because their are preceded by calls to forward
- // functions, which must then have succeeded before): for a backward function,
- // "failure" is to be understood as the semantics getting stuck.
- // This is of course true unless we filtered the call to the forward function
- // because its effect is encompassed by the backward function, as with
- // [hashMap_clear]).
- Some? (find_s hm key)))
- (ensures (
- match hashMap_get_mut_back t hm key ret with
- | Fail _ -> False // Can't fail
- | Return hm' ->
- // The invariant is preserved
- hashMap_t_inv hm' /\
- // The length is preserved
- len_s hm' = len_s hm /\
- // [key] maps to the update value, [ret]
- find_s hm' key == Some ret /\
- // The other bindings are preserved
- (forall k'. k' <> key ==> find_s hm' k' == find_s hm k')))
-
-(**** [remove'fwd] *)
-
-/// [remove'fwd] returns the (optional) element which has been removed from the map
-/// (the rust function *moves* it out of the map). Note that the effect of the update
-/// on the map is modelles through the call to [remove'back] ([remove] takes a
-/// mutable borrow to the hash map as parameter).
-val hashMap_remove_lem
- (#t : Type0) (self : hashMap_t t) (key : usize) :
- Lemma
- (requires (hashMap_t_inv self))
- (ensures (
- match hashMap_remove t self key with
- | Fail _ -> False
- | Return opt_x -> opt_x == find_s self key))
-
-
-(**** [remove'back] *)
-
-/// The hash map given as parameter to [remove] is given through a mutable borrow:
-/// hence the backward function which gives back the updated map, without the
-/// binding.
-val hashMap_remove_back_lem
- (#t : Type0) (self : hashMap_t t) (key : usize) :
- Lemma
- (requires (hashMap_t_inv self))
- (ensures (
- match hashMap_remove_back t self key with
- | Fail _ -> False
- | Return hm' ->
- // The invariant is preserved
- hashMap_t_inv self /\
- // The binding for [key] is not there anymore
- find_s hm' key == None /\
- // The other bindings are preserved
- (forall k'. k' <> key ==> find_s hm' k' == find_s self k') /\
- begin
- // The length is decremented iff the key was in the map
- let len = len_s self in
- let len' = len_s hm' in
- match find_s self key with
- | None -> len = len'
- | Some _ -> len = len' + 1
- end))
diff --git a/tests/fstar-split/hashmap/Hashmap.Types.fst b/tests/fstar-split/hashmap/Hashmap.Types.fst
deleted file mode 100644
index ef96b1e9..00000000
--- a/tests/fstar-split/hashmap/Hashmap.Types.fst
+++ /dev/null
@@ -1,23 +0,0 @@
-(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
-(** [hashmap]: type definitions *)
-module Hashmap.Types
-open Primitives
-
-#set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
-
-(** [hashmap::List]
- Source: 'src/hashmap.rs', lines 19:0-19:16 *)
-type list_t (t : Type0) =
-| List_Cons : usize -> t -> list_t t -> list_t t
-| List_Nil : list_t t
-
-(** [hashmap::HashMap]
- Source: 'src/hashmap.rs', lines 35:0-35:21 *)
-type hashMap_t (t : Type0) =
-{
- num_entries : usize;
- max_load_factor : (usize & usize);
- max_load : usize;
- slots : alloc_vec_Vec (list_t t);
-}
-
diff --git a/tests/fstar-split/hashmap/Makefile b/tests/fstar-split/hashmap/Makefile
deleted file mode 100644
index fa7d1f36..00000000
--- a/tests/fstar-split/hashmap/Makefile
+++ /dev/null
@@ -1,49 +0,0 @@
-# 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/hashmap/Primitives.fst b/tests/fstar-split/hashmap/Primitives.fst
deleted file mode 100644
index a3ffbde4..00000000
--- a/tests/fstar-split/hashmap/Primitives.fst
+++ /dev/null
@@ -1,884 +0,0 @@
-/// 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()
generated by cgit v1.2.3 (git 2.25.1) at 2024-12-27 02:55:31 +0000