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-rw-r--r--tests/fstar/hashmap/Hashmap.Properties.fst1648
-rw-r--r--tests/fstar/hashmap/Hashmap.Properties.fsti100
-rw-r--r--tests/fstar/hashmap/Primitives.fst18
3 files changed, 891 insertions, 875 deletions
diff --git a/tests/fstar/hashmap/Hashmap.Properties.fst b/tests/fstar/hashmap/Hashmap.Properties.fst
index 49d96cd5..def520f0 100644
--- a/tests/fstar/hashmap/Hashmap.Properties.fst
+++ b/tests/fstar/hashmap/Hashmap.Properties.fst
@@ -272,7 +272,7 @@ type pos_usize = x:usize{x > 0}
type binding (t : Type0) = key & t
-type slots_t (t : Type0) = vec (list_t 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)
@@ -280,8 +280,8 @@ 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
- | ListNil -> []
- | ListCons k v tl -> (k,v) :: list_t_v tl
+ | 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 =
@@ -305,30 +305,30 @@ let slots_t_al_v (#t : Type0) (slots : slots_t t) : assoc_list t =
/// 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 hash_map_s t = list (slot_s t)
+type hashMap_s t = list (slot_s t)
// TODO: why not always have the condition on the length?
// 'nes': "non-empty slots"
-type hash_map_s_nes (t : Type0) : Type0 =
- hm:hash_map_s t{is_pos_usize (length hm)}
+type hashMap_s_nes (t : Type0) : Type0 =
+ hm:hashMap_s t{is_pos_usize (length hm)}
-/// Representation function for [hash_map_t] as a list of slots
-let hash_map_t_v (#t : Type0) (hm : hash_map_t t) : hash_map_s t =
- map list_t_v hm.hash_map_slots
+/// 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 [hash_map_t] as an associative list
-let hash_map_t_al_v (#t : Type0) (hm : hash_map_t t) : assoc_list t =
- flatten (hash_map_t_v hm)
+/// 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 hash_map_t_nes (t : Type0) : Type0 =
- hm:hash_map_t t{is_pos_usize (length hm.hash_map_slots)}
+type hashMap_t_nes (t : Type0) : Type0 =
+ hm:hashMap_t t{is_pos_usize (length hm.slots)}
-let hash_key (k : key) : hash =
- Return?.v (hash_key_fwd k)
+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 k) % len
+ (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
@@ -339,8 +339,8 @@ let same_hash_mod_key (#t : Type0) (len : usize{len > 0}) (h : nat) (b : binding
let binding_neq (#t : Type0) (b0 b1 : binding t) : bool = fst b0 <> fst b1
-let hash_map_t_len_s (#t : Type0) (hm : hash_map_t t) : nat =
- hm.hash_map_num_entries
+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
@@ -354,26 +354,26 @@ 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 [hash_map_s].
-let hash_map_s_find
- (#t : Type0) (hm : hash_map_s_nes t)
+// 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 hash_map_s_len
- (#t : Type0) (hm : hash_map_s t) :
+let hashMap_s_len
+ (#t : Type0) (hm : hashMap_s t) :
nat =
length (flatten hm)
-// Same as above, but operates on [hash_map_t]
+// Same as above, but operates on [hashMap_t]
// Note that we don't reuse the above function on purpose: converting to a
-// [hash_map_s] then looking up an element is not the same as what we
+// [hashMap_s] then looking up an element is not the same as what we
// wrote below.
-let hash_map_t_find_s
- (#t : Type0) (hm : hash_map_t t{length hm.hash_map_slots > 0}) (k : key) : option t =
- let slots = hm.hash_map_slots in
+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
@@ -404,74 +404,74 @@ let slots_t_inv (#t : Type0) (slots : slots_t t{length slots <= usize_max}) : Ty
{:pattern index slots i}
slot_t_inv (length slots) i (index slots i)
-let hash_map_s_inv (#t : Type0) (hm : hash_map_s t) : Type0 =
+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 hash_map_t_base_inv (#t : Type0) (hm : hash_map_t t) : Type0 =
- let al = hash_map_t_al_v hm in
+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 hash_map_num_entries has type `usize`)
- hm.hash_map_num_entries = length al /\
+ // (because hashMap_num_entries has type `usize`)
+ hm.num_entries = length al /\
// Slots invariant
- slots_t_inv hm.hash_map_slots /\
+ slots_t_inv hm.slots /\
// The capacity must be > 0 (otherwise we can't resize, because we
// multiply the capacity by two!)
- length hm.hash_map_slots > 0 /\
+ length hm.slots > 0 /\
// Load computation
begin
- let capacity = length hm.hash_map_slots in
- let (dividend, divisor) = hm.hash_map_max_load_factor in
+ let capacity = length hm.slots in
+ let (dividend, divisor) = hm.max_load_factor in
0 < dividend /\ dividend < divisor /\
capacity * dividend >= divisor /\
- hm.hash_map_max_load = (capacity * dividend) / divisor
+ hm.max_load = (capacity * dividend) / divisor
end
/// We often need to frame some values
-let hash_map_t_same_params (#t : Type0) (hm0 hm1 : hash_map_t t) : Type0 =
- length hm0.hash_map_slots = length hm1.hash_map_slots /\
- hm0.hash_map_max_load = hm1.hash_map_max_load /\
- hm0.hash_map_max_load_factor = hm1.hash_map_max_load_factor
+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 hash_map_t_inv (#t : Type0) (hm : hash_map_t t) : Type0 =
+let hashMap_t_inv (#t : Type0) (hm : hashMap_t t) : Type0 =
// Base invariant
- hash_map_t_base_inv hm /\
+ hashMap_t_base_inv hm /\
// The hash map is either: not overloaded, or we can't resize it
begin
- let (dividend, divisor) = hm.hash_map_max_load_factor in
- hm.hash_map_num_entries <= hm.hash_map_max_load
- || length hm.hash_map_slots * 2 * dividend > usize_max
+ 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 : hash_map_t t) : nat = hash_map_t_len_s hm
+let len_s (#t : Type0) (hm : hashMap_t t) : nat = hashMap_t_len_s hm
-/// This version doesn't take any precondition (contrary to [hash_map_t_find_s])
-let find_s (#t : Type0) (hm : hash_map_t t) (k : key) : option t =
- if length hm.hash_map_slots = 0 then None
- else hash_map_t_find_s hm k
+/// 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 hash_map_not_overloaded_lem #t hm = ()
+let hashMap_not_overloaded_lem #t hm = ()
(*** allocate_slots *)
/// Auxiliary lemma
val slots_t_all_nil_inv_lem
- (#t : Type0) (slots : vec (list_t t){length slots <= usize_max}) :
- Lemma (requires (forall (i:nat{i < length slots}). index slots i == ListNil))
+ (#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"
@@ -479,8 +479,8 @@ let slots_t_all_nil_inv_lem #t slots = ()
#pop-options
val slots_t_al_v_all_nil_is_empty_lem
- (#t : Type0) (slots : vec (list_t t)) :
- Lemma (requires (forall (i:nat{i < length slots}). index slots i == ListNil))
+ (#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"
@@ -492,44 +492,44 @@ let rec slots_t_al_v_all_nil_is_empty_lem #t slots =
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 == ListNil)
+ assert(index slots 0 == List_Nil)
#pop-options
/// [allocate_slots]
-val hash_map_allocate_slots_fwd_lem
- (t : Type0) (slots : vec (list_t t)) (n : usize) :
+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 hash_map_allocate_slots_fwd t slots n with
+ 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 == ListNil)))
- (decreases (hash_map_allocate_slots_loop_decreases t slots n))
+ (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 hash_map_allocate_slots_fwd_lem t slots n =
+let rec hashMap_allocate_slots_lem t slots n =
begin match n with
| 0 -> ()
| _ ->
- begin match vec_push_back (list_t t) slots ListNil with
+ 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 ->
- hash_map_allocate_slots_fwd_lem t slots1 i;
- begin match hash_map_allocate_slots_fwd t slots1 i with
+ 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 @ [ListNil]); // Triggers patterns
- assert(index slots1 (length slots) == index [ListNil] 0); // Triggers patterns
- assert(index slots1 (length slots) == ListNil)
+ 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
@@ -538,7 +538,7 @@ let rec hash_map_allocate_slots_fwd_lem t slots n =
(*** new_with_capacity *)
/// Under proper conditions, [new_with_capacity] doesn't fail and returns an empty hash map.
-val hash_map_new_with_capacity_fwd_lem
+val hashMap_new_with_capacity_lem
(t : Type0) (capacity : usize)
(max_load_dividend : usize) (max_load_divisor : usize) :
Lemma
@@ -549,31 +549,31 @@ val hash_map_new_with_capacity_fwd_lem
capacity * max_load_dividend >= max_load_divisor /\
capacity * max_load_dividend <= usize_max))
(ensures (
- match hash_map_new_with_capacity_fwd t capacity max_load_dividend max_load_divisor with
+ match hashMap_new_with_capacity t capacity max_load_dividend max_load_divisor with
| Fail _ -> False
| Return hm ->
// The hash map invariant is satisfied
- hash_map_t_inv hm /\
+ hashMap_t_inv hm /\
// The parameters are correct
- hm.hash_map_max_load_factor = (max_load_dividend, max_load_divisor) /\
- hm.hash_map_max_load = (capacity * max_load_dividend) / max_load_divisor /\
+ 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 [hash_map_t_find_s] is not satisfied.
- length hm.hash_map_slots = capacity /\
+ // otherwise the pre of [hashMap_t_find_s] is not satisfied.
+ length hm.slots = capacity /\
// The hash map has 0 values
- hash_map_t_len_s hm = 0 /\
+ hashMap_t_len_s hm = 0 /\
// It contains no bindings
- (forall k. hash_map_t_find_s hm k == None) /\
+ (forall k. hashMap_t_find_s hm k == None) /\
// We need this low-level property for the invariant
- (forall(i:nat{i < length hm.hash_map_slots}). index hm.hash_map_slots i == ListNil)))
+ (forall(i:nat{i < length hm.slots}). index hm.slots i == List_Nil)))
#push-options "--z3rlimit 50 --fuel 1"
-let hash_map_new_with_capacity_fwd_lem (t : Type0) (capacity : usize)
+let hashMap_new_with_capacity_lem (t : Type0) (capacity : usize)
(max_load_dividend : usize) (max_load_divisor : usize) =
- let v = vec_new (list_t t) in
+ let v = alloc_vec_Vec_new (list_t t) in
assert(length v = 0);
- hash_map_allocate_slots_fwd_lem t v capacity;
- begin match hash_map_allocate_slots_fwd t v capacity with
+ 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
@@ -582,9 +582,9 @@ let hash_map_new_with_capacity_fwd_lem (t : Type0) (capacity : usize)
begin match usize_div i max_load_divisor with
| Fail _ -> assert(False)
| Return i0 ->
- let hm = Mkhash_map_t 0 (max_load_dividend, max_load_divisor) i0 v0 in
+ 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.hash_map_slots
+ slots_t_al_v_all_nil_is_empty_lem hm.slots
end
end
end
@@ -593,65 +593,65 @@ let hash_map_new_with_capacity_fwd_lem (t : Type0) (capacity : usize)
(*** new *)
/// [new] doesn't fail and returns an empty hash map
-val hash_map_new_fwd_lem_aux (t : Type0) :
+val hashMap_new_lem_aux (t : Type0) :
Lemma
(ensures (
- match hash_map_new_fwd t with
+ match hashMap_new t with
| Fail _ -> False
| Return hm ->
// The hash map invariant is satisfied
- hash_map_t_inv hm /\
+ hashMap_t_inv hm /\
// The hash map has 0 values
- hash_map_t_len_s hm = 0 /\
+ hashMap_t_len_s hm = 0 /\
// It contains no bindings
- (forall k. hash_map_t_find_s hm k == None)))
+ (forall k. hashMap_t_find_s hm k == None)))
#push-options "--fuel 1"
-let hash_map_new_fwd_lem_aux t =
- hash_map_new_with_capacity_fwd_lem t 32 4 5;
- match hash_map_new_with_capacity_fwd t 32 4 5 with
+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 hash_map_new_fwd_lem t = hash_map_new_fwd_lem_aux t
+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 hash_map_clear_loop_fwd_back_lem
- (t : Type0) (slots : vec (list_t t)) (i : usize) :
+let rec hashMap_clear_loop_lem
+ (t : Type0) (slots : alloc_vec_Vec (list_t t)) (i : usize) :
Lemma
(ensures (
- match hash_map_clear_loop_fwd_back t slots i with
+ 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 ListNil
- (forall (j:nat{i <= j /\ j < length slots}). index slots' j == ListNil)))
- (decreases (hash_map_clear_loop_decreases t slots i))
+ // 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 = vec_len (list_t t) slots in
+ let i0 = alloc_vec_Vec_len (list_t t) slots in
let b = i < i0 in
if b
then
- begin match vec_index_mut_back (list_t t) slots i ListNil with
+ 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 ->
- hash_map_clear_loop_fwd_back_lem t v i1;
- begin match hash_map_clear_loop_fwd_back t v i1 with
+ 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 == ListNil);
- assert(index slots1 i == ListNil)
+ assert(forall (j:nat{i+1 <= j /\ j < length slots}). index slots1 j == List_Nil);
+ assert(index slots1 i == List_Nil)
end
end
end
@@ -659,80 +659,80 @@ let rec hash_map_clear_loop_fwd_back_lem
#pop-options
/// [clear] doesn't fail and turns the hash map into an empty map
-val hash_map_clear_fwd_back_lem_aux
- (#t : Type0) (self : hash_map_t t) :
+val hashMap_clear_lem_aux
+ (#t : Type0) (self : hashMap_t t) :
Lemma
- (requires (hash_map_t_base_inv self))
+ (requires (hashMap_t_base_inv self))
(ensures (
- match hash_map_clear_fwd_back t self with
+ match hashMap_clear t self with
| Fail _ -> False
| Return hm ->
// The hash map invariant is satisfied
- hash_map_t_base_inv hm /\
+ hashMap_t_base_inv hm /\
// We preserved the parameters
- hash_map_t_same_params hm self /\
+ hashMap_t_same_params hm self /\
// The hash map has 0 values
- hash_map_t_len_s hm = 0 /\
+ hashMap_t_len_s hm = 0 /\
// It contains no bindings
- (forall k. hash_map_t_find_s hm k == None)))
+ (forall k. hashMap_t_find_s hm k == None)))
// Being lazy: fuel 1 helps a lot...
#push-options "--fuel 1"
-let hash_map_clear_fwd_back_lem_aux #t self =
- let p = self.hash_map_max_load_factor in
- let i = self.hash_map_max_load in
- let v = self.hash_map_slots in
- hash_map_clear_loop_fwd_back_lem t v 0;
- begin match hash_map_clear_loop_fwd_back t v 0 with
+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 = Mkhash_map_t 0 p i slots1 in
- assert(hash_map_t_base_inv hm1);
- assert(hash_map_t_inv hm1)
+ let hm1 = MkhashMap_t 0 p i slots1 in
+ assert(hashMap_t_base_inv hm1);
+ assert(hashMap_t_inv hm1)
end
#pop-options
-let hash_map_clear_fwd_back_lem #t self = hash_map_clear_fwd_back_lem_aux #t self
+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 hash_map_len_fwd_lem #t self = ()
+let hashMap_len_lem #t self = ()
(*** insert_in_list *)
(**** insert_in_list'fwd *)
-/// [insert_in_list_fwd]: returns true iff the key is not in the list (functional version)
-val hash_map_insert_in_list_fwd_lem
+/// [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 hash_map_insert_in_list_fwd t key value ls with
+ match hashMap_insert_in_list t key value ls with
| Fail _ -> False
| Return b ->
b <==> (slot_t_find_s key ls == None)))
- (decreases (hash_map_insert_in_list_loop_decreases t key value ls))
+ (decreases (hashMap_insert_in_list_loop_decreases t key value ls))
#push-options "--fuel 1"
-let rec hash_map_insert_in_list_fwd_lem t key value ls =
+let rec hashMap_insert_in_list_lem t key value ls =
begin match ls with
- | ListCons ckey cvalue ls0 ->
+ | List_Cons ckey cvalue ls0 ->
let b = ckey = key in
if b
then ()
else
begin
- hash_map_insert_in_list_fwd_lem t key value ls0;
- match hash_map_insert_in_list_fwd t key value ls0 with
+ hashMap_insert_in_list_lem t key value ls0;
+ match hashMap_insert_in_list t key value ls0 with
| Fail _ -> ()
| Return b0 -> ()
end
- | ListNil ->
+ | List_Nil ->
assert(list_t_v ls == []);
assert_norm(find (same_key #t key) [] == None)
end
@@ -748,7 +748,7 @@ let rec hash_map_insert_in_list_fwd_lem t key value ls =
/// 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 hash_map_insert_in_list_s
+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
@@ -761,86 +761,86 @@ let hash_map_insert_in_list_s
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 hash_map_insert_in_list_back_lem_append_s
+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 hash_map_insert_in_list_back t key value ls with
+ 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 (hash_map_insert_in_list_loop_decreases t key value ls))
+ (decreases (hashMap_insert_in_list_loop_decreases t key value ls))
#push-options "--fuel 1"
-let rec hash_map_insert_in_list_back_lem_append_s t key value ls =
+let rec hashMap_insert_in_list_back_lem_append_s t key value ls =
begin match ls with
- | ListCons ckey cvalue ls0 ->
+ | List_Cons ckey cvalue ls0 ->
let b = ckey = key in
if b
then ()
else
begin
- hash_map_insert_in_list_back_lem_append_s t key value ls0;
- match hash_map_insert_in_list_back t key value ls0 with
+ 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
- | ListNil -> ()
+ | List_Nil -> ()
end
#pop-options
/// [insert_in_list]: if the key is in the map, we update the binding (functional version)
-val hash_map_insert_in_list_back_lem_update_s
+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 hash_map_insert_in_list_back t key value ls with
+ 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 (hash_map_insert_in_list_loop_decreases t key value ls))
+ (decreases (hashMap_insert_in_list_loop_decreases t key value ls))
#push-options "--fuel 1"
-let rec hash_map_insert_in_list_back_lem_update_s t key value ls =
+let rec hashMap_insert_in_list_back_lem_update_s t key value ls =
begin match ls with
- | ListCons ckey cvalue ls0 ->
+ | List_Cons ckey cvalue ls0 ->
let b = ckey = key in
if b
then ()
else
begin
- hash_map_insert_in_list_back_lem_update_s t key value ls0;
- match hash_map_insert_in_list_back t key value ls0 with
+ 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
- | ListNil -> ()
+ | List_Nil -> ()
end
#pop-options
/// Put everything together
-val hash_map_insert_in_list_back_lem_s
+val hashMap_insert_in_list_back_lem_s
(t : Type0) (key : usize) (value : t) (ls : list_t t) :
Lemma
(ensures (
- match hash_map_insert_in_list_back t key value ls with
+ match hashMap_insert_in_list_back t key value ls with
| Fail _ -> False
| Return ls' ->
- list_t_v ls' == hash_map_insert_in_list_s key value (list_t_v ls)))
+ list_t_v ls' == hashMap_insert_in_list_s key value (list_t_v ls)))
-let hash_map_insert_in_list_back_lem_s t key value ls =
+let hashMap_insert_in_list_back_lem_s t key value ls =
match find (same_key key) (list_t_v ls) with
- | None -> hash_map_insert_in_list_back_lem_append_s t key value ls
- | Some _ -> hash_map_insert_in_list_back_lem_update_s t key value ls
+ | 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 [hash_map_insert_in_list_s], the "high-level" version of [insert_in_list'back].
+/// 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
@@ -893,14 +893,14 @@ let rec slot_s_inv_not_find_append_end_inv_lem t len key value ls =
#pop-options
/// [insert_in_list]: if the key is not in the map, appends a new bindings
-val hash_map_insert_in_list_s_lem_append
+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' = hash_map_insert_in_list_s key value ls in
+ 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' /\
@@ -909,20 +909,20 @@ val hash_map_insert_in_list_s_lem_append
// The other bindings are preserved
(forall k'. k' <> key ==> slot_s_find k' ls' == slot_s_find k' ls)))
-let hash_map_insert_in_list_s_lem_append t len key value 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 hash_map_insert_in_list_back_lem_append
+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 hash_map_insert_in_list_back t key value ls with
+ 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)] /\
@@ -933,9 +933,9 @@ val hash_map_insert_in_list_back_lem_append
// The other bindings are preserved
(forall k'. k' <> key ==> slot_t_find_s k' ls' == slot_t_find_s k' ls)))
-let hash_map_insert_in_list_back_lem_append t len key value ls =
- hash_map_insert_in_list_back_lem_s t key value ls;
- hash_map_insert_in_list_s_lem_append t len key value (list_t_v 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 *)
@@ -1013,14 +1013,14 @@ let rec slot_s_inv_find_append_end_inv_lem t len key value ls =
#pop-options
/// [insert_in_list]: if the key is in the map, update the bindings
-val hash_map_insert_in_list_s_lem_update
+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' = hash_map_insert_in_list_s key value ls in
+ 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' /\
@@ -1029,20 +1029,20 @@ val hash_map_insert_in_list_s_lem_update
// The other bindings are preserved
(forall k'. k' <> key ==> slot_s_find k' ls' == slot_s_find k' ls)))
-let hash_map_insert_in_list_s_lem_update t len key value 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 hash_map_insert_in_list_back_lem_update
+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 hash_map_insert_in_list_back t key value ls with
+ match hashMap_insert_in_list_back t key value ls with
| Fail _ -> False
| Return ls' ->
let als = list_t_v ls in
@@ -1054,20 +1054,20 @@ val hash_map_insert_in_list_back_lem_update
// The other bindings are preserved
(forall k'. k' <> key ==> slot_t_find_s k' ls' == slot_t_find_s k' ls)))
-let hash_map_insert_in_list_back_lem_update t len key value ls =
- hash_map_insert_in_list_back_lem_s t key value ls;
- hash_map_insert_in_list_s_lem_update t len key value (list_t_v 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 hash_map_insert_in_list_s_lem
+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' = hash_map_insert_in_list_s key value ls in
+ 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]
@@ -1079,22 +1079,22 @@ val hash_map_insert_in_list_s_lem
| None -> length ls' = length ls + 1
| Some _ -> length ls' = length ls)))
-let hash_map_insert_in_list_s_lem t len key value 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);
- hash_map_insert_in_list_s_lem_append t len key value ls
+ hashMap_insert_in_list_s_lem_append t len key value ls
| Some _ ->
- hash_map_insert_in_list_s_lem_update t len key value ls
+ hashMap_insert_in_list_s_lem_update t len key value ls
/// [insert_in_list]
/// TODO: not used: remove?
-val hash_map_insert_in_list_back_lem
+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 hash_map_insert_in_list_back t key value ls with
+ match hashMap_insert_in_list_back t key value ls with
| Fail _ -> False
| Return ls' ->
// The invariant is preserved
@@ -1111,127 +1111,127 @@ val hash_map_insert_in_list_back_lem
| 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 (hash_map_insert_in_list_loop_decreases t key value ls))
+ (decreases (hashMap_insert_in_list_loop_decreases t key value ls))
-let hash_map_insert_in_list_back_lem t len key value ls =
- hash_map_insert_in_list_back_lem_s t key value ls;
- hash_map_insert_in_list_s_lem t len key value (list_t_v 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 [hash_map_s] (we use a higher-level view of the hash-map, but
+/// 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 hash_map_insert_no_fail_s
- (#t : Type0) (hm : hash_map_s_nes t)
+let hashMap_insert_no_fail_s
+ (#t : Type0) (hm : hashMap_s_nes t)
(key : usize) (value : t) :
- hash_map_s 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' = hash_map_insert_in_list_s key value slot 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 hash_map_s_nes and it broke proofs...x
-let hash_map_insert_no_resize_s
- (#t : Type0) (hm : hash_map_s_nes t)
+// 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 (hash_map_s 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? (hash_map_s_find hm key) && num_entries = usize_max then Fail Failure
- else Return (hash_map_insert_no_fail_s hm key value)
+ 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 [hash_map_insert_no_resize_s] is refined by
-/// [hash_map_insert_no_resize'fwd_back]
-val hash_map_insert_no_resize_fwd_back_lem_s
- (t : Type0) (self : hash_map_t t) (key : usize) (value : t) :
+/// 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 (
- hash_map_t_base_inv self /\
- hash_map_s_len (hash_map_t_v self) = hash_map_t_len_s self))
+ hashMap_t_base_inv self /\
+ hashMap_s_len (hashMap_t_v self) = hashMap_t_len_s self))
(ensures (
begin
- match hash_map_insert_no_resize_fwd_back t self key value,
- hash_map_insert_no_resize_s (hash_map_t_v self) key value
+ 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 ->
- hash_map_t_base_inv hm /\
- hash_map_t_same_params hm self /\
- hash_map_t_v hm == hm_v /\
- hash_map_s_len hm_v == hash_map_t_len_s hm
+ 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 hash_map_insert_no_resize_fwd_back_lem_s t self key value =
- begin match hash_key_fwd key with
+let hashMap_insert_no_resize_lem_s t self key value =
+ begin match hash_key key with
| Fail _ -> ()
| Return i ->
- let i0 = self.hash_map_num_entries in
- let p = self.hash_map_max_load_factor in
- let i1 = self.hash_map_max_load in
- let v = self.hash_map_slots in
- let i2 = vec_len (list_t t) v in
+ 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 vec_index_mut_fwd (list_t t) v hash_mod with
+ begin match alloc_vec_Vec_index_usize v hash_mod with
| Fail _ -> ()
| Return l ->
begin
- // Checking that: list_t_v (index ...) == index (hash_map_t_v ...) ...
- assert(list_t_v l == index (hash_map_t_v self) hash_mod);
- hash_map_insert_in_list_fwd_lem t key value l;
- match hash_map_insert_in_list_fwd t key value l with
+ // 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)));
- hash_map_insert_in_list_back_lem t len key value 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 hash_map_insert_in_list_back t key value l with
+ match hashMap_insert_in_list_back t key value l with
| Fail _ -> ()
| Return l0 ->
- begin match vec_index_mut_back (list_t t) v hash_mod l0 with
+ begin match alloc_vec_Vec_update_usize v hash_mod l0 with
| Fail _ -> ()
| Return v0 ->
- let self_v = hash_map_t_v self in
- let hm = Mkhash_map_t i3 p i1 v0 in
- let hm_v = hash_map_t_v hm in
+ 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(hash_map_s_len hm_v = hash_map_t_len_s hm)
+ assert(hashMap_s_len hm_v = hashMap_t_len_s hm)
end
end
end
else
begin
- match hash_map_insert_in_list_back t key value l with
+ match hashMap_insert_in_list_back t key value l with
| Fail _ -> ()
| Return l0 ->
- begin match vec_index_mut_back (list_t t) v hash_mod l0 with
+ begin match alloc_vec_Vec_update_usize v hash_mod l0 with
| Fail _ -> ()
| Return v0 ->
- let self_v = hash_map_t_v self in
- let hm = Mkhash_map_t i0 p i1 v0 in
- let hm_v = hash_map_t_v hm in
+ 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(hash_map_s_len hm_v = hash_map_t_len_s hm)
+ assert(hashMap_s_len hm_v = hashMap_t_len_s hm)
end
end
end
@@ -1241,108 +1241,108 @@ let hash_map_insert_no_resize_fwd_back_lem_s t self key value =
(**** insert_{no_fail,no_resize}: invariants *)
-let hash_map_s_updated_binding
- (#t : Type0) (hm : hash_map_s_nes t)
- (key : usize) (opt_value : option t) (hm' : hash_map_s_nes t) : Type0 =
+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]
- hash_map_s_find hm' key == opt_value /\
+ hashMap_s_find hm' key == opt_value /\
// The other bindings are preserved
- (forall k'. k' <> key ==> hash_map_s_find hm' k' == hash_map_s_find hm k')
+ (forall k'. k' <> key ==> hashMap_s_find hm' k' == hashMap_s_find hm k')
-let insert_post (#t : Type0) (hm : hash_map_s_nes t)
- (key : usize) (value : t) (hm' : hash_map_s_nes t) : Type0 =
+let insert_post (#t : Type0) (hm : hashMap_s_nes t)
+ (key : usize) (value : t) (hm' : hashMap_s_nes t) : Type0 =
// The invariant is preserved
- hash_map_s_inv hm' /\
+ hashMap_s_inv hm' /\
// [key] maps to [value] and the other bindings are preserved
- hash_map_s_updated_binding hm key (Some value) hm' /\
+ hashMap_s_updated_binding hm key (Some value) hm' /\
// The length is incremented, iff we inserted a new key
- (match hash_map_s_find hm key with
- | None -> hash_map_s_len hm' = hash_map_s_len hm + 1
- | Some _ -> hash_map_s_len hm' = hash_map_s_len hm)
+ (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 hash_map_insert_no_fail_s_lem
- (#t : Type0) (hm : hash_map_s_nes t)
+val hashMap_insert_no_fail_s_lem
+ (#t : Type0) (hm : hashMap_s_nes t)
(key : usize) (value : t) :
Lemma
- (requires (hash_map_s_inv hm))
+ (requires (hashMap_s_inv hm))
(ensures (
- let hm' = hash_map_insert_no_fail_s hm key value in
+ let hm' = hashMap_insert_no_fail_s hm key value in
insert_post hm key value hm'))
-let hash_map_insert_no_fail_s_lem #t hm key value =
+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
- hash_map_insert_in_list_s_lem t len key value slot;
- let slot' = hash_map_insert_in_list_s key value slot 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 hash_map_insert_no_resize_s_lem
- (#t : Type0) (hm : hash_map_s_nes t)
+val hashMap_insert_no_resize_s_lem
+ (#t : Type0) (hm : hashMap_s_nes t)
(key : usize) (value : t) :
Lemma
- (requires (hash_map_s_inv hm))
+ (requires (hashMap_s_inv hm))
(ensures (
- match hash_map_insert_no_resize_s hm key value with
+ 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
- hash_map_s_len hm = usize_max /\
- None? (hash_map_s_find hm key)
+ hashMap_s_len hm = usize_max /\
+ None? (hashMap_s_find hm key)
| Return hm' ->
insert_post hm key value hm'))
-let hash_map_insert_no_resize_s_lem #t hm key value =
+let hashMap_insert_no_resize_s_lem #t hm key value =
let num_entries = length (flatten hm) in
- if None? (hash_map_s_find hm key) && num_entries = usize_max then ()
- else hash_map_insert_no_fail_s_lem hm key value
+ 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 hash_map_insert_no_resize_s_get_same_lem
- (#t : Type0) (hm : hash_map_s t)
+val hashMap_insert_no_resize_s_get_same_lem
+ (#t : Type0) (hm : hashMap_s t)
(key : usize) (value : t) :
- Lemma (requires (hash_map_s_inv hm))
+ Lemma (requires (hashMap_s_inv hm))
(ensures (
- match hash_map_insert_no_resize_s hm key value with
+ match hashMap_insert_no_resize_s hm key value with
| Fail _ -> True
| Return hm' ->
- hash_map_s_find hm' key == Some value))
+ hashMap_s_find hm' key == Some value))
-let hash_map_insert_no_resize_s_get_same_lem #t hm key value =
+let hashMap_insert_no_resize_s_get_same_lem #t hm key value =
let num_entries = length (flatten hm) in
- if None? (hash_map_s_find hm key) && num_entries = usize_max then ()
+ if None? (hashMap_s_find hm key) && num_entries = usize_max then ()
else
begin
- let hm' = Return?.v (hash_map_insert_no_resize_s hm key value) in
+ 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
- hash_map_insert_in_list_s_lem t len key value slot
+ hashMap_insert_in_list_s_lem t len key value slot
end
-val hash_map_insert_no_resize_s_get_diff_lem
- (#t : Type0) (hm : hash_map_s t)
+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 (hash_map_s_inv hm))
+ Lemma (requires (hashMap_s_inv hm))
(ensures (
- match hash_map_insert_no_resize_s hm key value with
+ match hashMap_insert_no_resize_s hm key value with
| Fail _ -> True
| Return hm' ->
- hash_map_s_find hm' key' == hash_map_s_find hm key'))
+ hashMap_s_find hm' key' == hashMap_s_find hm key'))
-let hash_map_insert_no_resize_s_get_diff_lem #t hm key value key' =
+let hashMap_insert_no_resize_s_get_diff_lem #t hm key value key' =
let num_entries = length (flatten hm) in
- if None? (hash_map_s_find hm key) && num_entries = usize_max then ()
+ if None? (hashMap_s_find hm key) && num_entries = usize_max then ()
else
begin
- let hm' = Return?.v (hash_map_insert_no_resize_s hm key value) in
+ 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
- hash_map_insert_in_list_s_lem t len key value slot;
+ hashMap_insert_in_list_s_lem t len key value slot;
let i' = hash_mod_key key' len in
if i <> i' then ()
else
@@ -1354,116 +1354,116 @@ let hash_map_insert_no_resize_s_get_diff_lem #t hm key value key' =
(*** move_elements_from_list *)
-/// Having a great time here: if we use `result (hash_map_s_res t)` as the
-/// return type for [hash_map_move_elements_from_list_s] instead of having this
-/// awkward match, the proof of [hash_map_move_elements_fwd_back_lem_refin] fails.
+/// 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_hash_map_s]
+/// Followingly, I'm not taking any chance and using [result_hashMap_s]
/// everywhere.
-type result_hash_map_s_nes (t : Type0) : Type0 =
- res:result (hash_map_s t) {
+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 hash_map_move_elements_from_list_s
- (#t : Type0) (hm : hash_map_s_nes t)
+let rec hashMap_move_elements_from_list_s
+ (#t : Type0) (hm : hashMap_s_nes t)
(ls : slot_s t) :
- // Do *NOT* use `result (hash_map_s t)`
- Tot (result_hash_map_s_nes 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 hash_map_insert_no_resize_s hm key value with
+ match hashMap_insert_no_resize_s hm key value with
| Fail e -> Fail e
| Return hm' ->
- hash_map_move_elements_from_list_s hm' ls'
+ hashMap_move_elements_from_list_s hm' ls'
/// Refinement lemma
-val hash_map_move_elements_from_list_fwd_back_lem
- (t : Type0) (ntable : hash_map_t_nes t) (ls : list_t t) :
- Lemma (requires (hash_map_t_base_inv ntable))
+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 hash_map_move_elements_from_list_fwd_back t ntable ls,
- hash_map_move_elements_from_list_s (hash_map_t_v ntable) (slot_t_v ls)
+ 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 ->
- hash_map_t_base_inv hm' /\
- hash_map_t_v hm' == hm_v /\
- hash_map_t_same_params hm' ntable
+ hashMap_t_base_inv hm' /\
+ hashMap_t_v hm' == hm_v /\
+ hashMap_t_same_params hm' ntable
| _ -> False))
- (decreases (hash_map_move_elements_from_list_loop_decreases t ntable ls))
+ (decreases (hashMap_move_elements_from_list_loop_decreases t ntable ls))
#push-options "--fuel 1"
-let rec hash_map_move_elements_from_list_fwd_back_lem t ntable ls =
+let rec hashMap_move_elements_from_list_lem t ntable ls =
begin match ls with
- | ListCons k v tl ->
+ | 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
- hash_map_insert_no_resize_fwd_back_lem_s t ntable k v;
- begin match hash_map_insert_no_resize_fwd_back t ntable k v with
+ 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 (hash_map_insert_no_resize_s (hash_map_t_v ntable) k v) in
- assert(hash_map_t_v h == h_v);
- hash_map_move_elements_from_list_fwd_back_lem t h tl;
- begin match hash_map_move_elements_from_list_fwd_back t h tl with
+ 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
- | ListNil -> ()
+ | List_Nil -> ()
end
#pop-options
(*** move_elements *)
(**** move_elements: refinement 0 *)
-/// The proof for [hash_map_move_elements_fwd_back_lem_refin] broke so many times
+/// 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 ListNil == []`: I
+/// 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 [hash_map_move_elements_s].
+/// because it allows for easy comparisons with [hashMap_move_elements_s].
-/// [hash_map_move_elements_fwd] refines this function, which is actually almost
+/// [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 [hash_map_move_elements_fwd], wrote the
-/// signature which links this new definition to [hash_map_move_elements_fwd] and
+/// - 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 hash_map_move_elements_s_simpl
- (t : Type0) (ntable : hash_map_t t)
- (slots : vec (list_t t))
+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 ((hash_map_t t) & (vec (list_t t))))
+ Pure (result ((hashMap_t t) & (alloc_vec_Vec (list_t t))))
(requires (True))
(ensures (fun res ->
- match res, hash_map_move_elements_fwd_back t ntable slots i with
+ 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 (hash_map_move_elements_loop_decreases t ntable slots i))
+ (decreases (hashMap_move_elements_loop_decreases t ntable slots i))
=
if i < length slots
then
let slot = index slots i in
- begin match hash_map_move_elements_from_list_fwd_back t ntable slot with
+ begin match hashMap_move_elements_from_list t ntable slot with
| Fail e -> Fail e
| Return hm' ->
- let slots' = list_update slots i ListNil in
- hash_map_move_elements_s_simpl t hm' slots' (i+1)
+ 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
@@ -1476,71 +1476,71 @@ let rec hash_map_move_elements_s_simpl
// 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 hash_map_move_elements_s
- (#t : Type0) (hm : hash_map_s_nes t)
+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_hash_map_s_nes t)
+ 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 hash_map_move_elements_from_list_s hm slot with
+ match hashMap_move_elements_from_list_s hm slot with
| Fail e -> Fail e
| Return hm' ->
let slots' = list_update slots i [] in
- hash_map_move_elements_s hm' slots' (i+1)
+ hashMap_move_elements_s hm' slots' (i+1)
end
else Return hm
-val hash_map_move_elements_fwd_back_lem_refin
- (t : Type0) (ntable : hash_map_t t)
- (slots : vec (list_t t)) (i : usize{i <= length slots}) :
+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 (
- hash_map_t_base_inv ntable))
+ hashMap_t_base_inv ntable))
(ensures (
- match hash_map_move_elements_fwd_back t ntable slots i,
- hash_map_move_elements_s (hash_map_t_v ntable) (slots_t_v slots) i
+ 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 ->
- hash_map_t_base_inv ntable' /\
- hash_map_t_v ntable' == ntable'_v /\
- hash_map_t_same_params ntable' ntable
+ 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 hash_map_move_elements_fwd_back_lem_refin t ntable slots i =
- assert(hash_map_t_base_inv ntable);
- let i0 = vec_len (list_t t) slots in
+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 vec_index_mut_fwd (list_t t) slots i with
+ begin match alloc_vec_Vec_index_usize slots i with
| Fail _ -> ()
| Return l ->
- let l0 = mem_replace_fwd (list_t t) l ListNil in
+ let l0 = core_mem_replace (list_t t) l List_Nil in
assert(l0 == l);
- hash_map_move_elements_from_list_fwd_back_lem t ntable l0;
- begin match hash_map_move_elements_from_list_fwd_back t ntable l0 with
+ 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 = mem_replace_back (list_t t) l ListNil in
- assert(l1 == ListNil);
- assert(slot_t_v #t ListNil == []); // THIS IS IMPORTANT
- begin match vec_index_mut_back (list_t t) slots i l1 with
+ 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 ->
- hash_map_move_elements_fwd_back_lem_refin t h v i1;
- begin match hash_map_move_elements_fwd_back t h v i1 with
+ hashMap_move_elements_lem_refin t h v i1;
+ begin match hashMap_move_elements t h v i1 with
| Fail _ ->
- assert(Fail? (hash_map_move_elements_fwd_back t ntable slots i));
+ assert(Fail? (hashMap_move_elements t ntable slots i));
()
| Return (ntable', v0) -> ()
end
@@ -1560,19 +1560,19 @@ let rec hash_map_move_elements_fwd_back_lem_refin t ntable slots i =
/// [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 [hash_map_move_elements_from_list_s]...
-let rec hash_map_move_elements_s_flat
- (#t : Type0) (ntable : hash_map_s_nes t)
+/// 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_hash_map_s_nes t)
+ Tot (result_hashMap_s_nes t)
(decreases slots) =
match slots with
| [] -> Return ntable
| (k,v) :: slots' ->
- match hash_map_insert_no_resize_s ntable k v with
+ match hashMap_insert_no_resize_s ntable k v with
| Fail e -> Fail e
| Return ntable' ->
- hash_map_move_elements_s_flat ntable' slots'
+ hashMap_move_elements_s_flat ntable' slots'
/// The refinment lemmas
/// First, auxiliary helpers.
@@ -1656,42 +1656,42 @@ let rec flatten_nil_prefix_as_flatten_i #a l i =
/// The proof is trivial, the functions are the same.
/// Just keeping two definitions to allow changes...
-val hash_map_move_elements_from_list_s_as_flat_lem
- (#t : Type0) (hm : hash_map_s_nes t)
+val hashMap_move_elements_from_list_s_as_flat_lem
+ (#t : Type0) (hm : hashMap_s_nes t)
(ls : slot_s t) :
Lemma
(ensures (
- hash_map_move_elements_from_list_s hm ls ==
- hash_map_move_elements_s_flat hm ls))
+ hashMap_move_elements_from_list_s hm ls ==
+ hashMap_move_elements_s_flat hm ls))
(decreases ls)
#push-options "--fuel 1"
-let rec hash_map_move_elements_from_list_s_as_flat_lem #t hm ls =
+let rec hashMap_move_elements_from_list_s_as_flat_lem #t hm ls =
match ls with
| [] -> ()
| (key, value) :: ls' ->
- match hash_map_insert_no_resize_s hm key value with
+ match hashMap_insert_no_resize_s hm key value with
| Fail _ -> ()
| Return hm' ->
- hash_map_move_elements_from_list_s_as_flat_lem hm' ls'
+ hashMap_move_elements_from_list_s_as_flat_lem hm' ls'
#pop-options
-/// Composition of two calls to [hash_map_move_elements_s_flat]
-let hash_map_move_elements_s_flat_comp
- (#t : Type0) (hm : hash_map_s_nes t) (slot0 slot1 : slot_s t) :
- Tot (result_hash_map_s_nes t) =
- match hash_map_move_elements_s_flat hm slot0 with
+/// 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 -> hash_map_move_elements_s_flat hm1 slot1
+ | 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 hash_map_move_elements_s_flat_append_lem
- (#t : Type0) (hm : hash_map_s_nes t) (slot0 slot1 : slot_s t) :
+val hashMap_move_elements_s_flat_append_lem
+ (#t : Type0) (hm : hashMap_s_nes t) (slot0 slot1 : slot_s t) :
Lemma
(ensures (
- match hash_map_move_elements_s_flat_comp hm slot0 slot1,
- hash_map_move_elements_s_flat hm (slot0 @ slot1)
+ 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
@@ -1699,14 +1699,14 @@ val hash_map_move_elements_s_flat_append_lem
(decreases (slot0))
#push-options "--fuel 1"
-let rec hash_map_move_elements_s_flat_append_lem #t hm slot0 slot1 =
+let rec hashMap_move_elements_s_flat_append_lem #t hm slot0 slot1 =
match slot0 with
| [] -> ()
| (k,v) :: slot0' ->
- match hash_map_insert_no_resize_s hm k v with
+ match hashMap_insert_no_resize_s hm k v with
| Fail _ -> ()
| Return hm' ->
- hash_map_move_elements_s_flat_append_lem hm' slot0' slot1
+ 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) :
@@ -1726,16 +1726,16 @@ let rec flatten_i_same_suffix #a l0 l1 i =
#pop-options
/// Refinement lemma:
-/// [hash_map_move_elements_s] refines [hash_map_move_elements_s_flat]
+/// [hashMap_move_elements_s] refines [hashMap_move_elements_s_flat]
/// (actually the functions are equal on all inputs).
-val hash_map_move_elements_s_lem_refin_flat
- (#t : Type0) (hm : hash_map_s_nes t)
+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 hash_map_move_elements_s hm slots i,
- hash_map_move_elements_s_flat hm (flatten_i slots i)
+ 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'
@@ -1743,22 +1743,22 @@ val hash_map_move_elements_s_lem_refin_flat
(decreases (length slots - i))
#push-options "--fuel 1"
-let rec hash_map_move_elements_s_lem_refin_flat #t hm slots i =
+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
- hash_map_move_elements_from_list_s_as_flat_lem hm slot;
- match hash_map_move_elements_from_list_s hm slot with
+ 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));
- hash_map_move_elements_s_flat_append_lem hm slot (flatten_i slots (i+1));
- assert(Fail? (hash_map_move_elements_s_flat hm (flatten_i slots i)))
+ 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);
- hash_map_move_elements_s_lem_refin_flat hm' slots' (i+1);
- hash_map_move_elements_s_flat_append_lem hm slot (flatten_i 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 ()
@@ -1769,21 +1769,21 @@ let assoc_list_inv (#t : Type0) (al : assoc_list t) : Type0 =
pairwise_rel binding_neq al
let disjoint_hm_al_on_key
- (#t : Type0) (hm : hash_map_s_nes t) (al : assoc_list t) (k : key) : Type0 =
- match hash_map_s_find hm k, assoc_list_find k al with
+ (#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 : hash_map_s_nes t) (al : assoc_list t) : Type0 =
+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 : hash_map_s_nes t) (al : assoc_list t) (k : key) :
+ (#t : Type0) (hm : hashMap_s_nes t) (al : assoc_list t) (k : key) :
option t =
- match hash_map_s_find hm k with
+ match hashMap_s_find hm k with
| Some b -> Some b
| None -> assoc_list_find k al
@@ -1799,58 +1799,58 @@ let rec for_all_binding_neq_find_lem #t k v al =
| b :: al' -> for_all_binding_neq_find_lem k v al'
#pop-options
-val hash_map_move_elements_s_flat_lem
- (#t : Type0) (hm : hash_map_s_nes t) (al : assoc_list t) :
+val hashMap_move_elements_s_flat_lem
+ (#t : Type0) (hm : hashMap_s_nes t) (al : assoc_list t) :
Lemma
(requires (
// Invariants
- hash_map_s_inv hm /\
+ 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
- hash_map_s_len hm + length al <= usize_max))
+ hashMap_s_len hm + length al <= usize_max))
(ensures (
- match hash_map_move_elements_s_flat hm al with
+ match hashMap_move_elements_s_flat hm al with
| Fail _ -> False // We can't fail
| Return hm' ->
// The invariant is preserved
- hash_map_s_inv hm' /\
+ hashMap_s_inv hm' /\
// The new hash map is the union of the two maps
- (forall (k:key). hash_map_s_find hm' k == find_in_union_hm_al hm al k) /\
- hash_map_s_len hm' = hash_map_s_len hm + length al))
+ (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 hash_map_move_elements_s_flat_lem #t hm al =
+let rec hashMap_move_elements_s_flat_lem #t hm al =
match al with
| [] -> ()
| (k,v) :: al' ->
- hash_map_insert_no_resize_s_lem hm k v;
- match hash_map_insert_no_resize_s hm k v with
+ hashMap_insert_no_resize_s_lem hm k v;
+ match hashMap_insert_no_resize_s hm k v with
| Fail _ -> ()
| Return hm' ->
- assert(hash_map_s_inv 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(hash_map_s_find hm' k' == Some v);
+ 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(hash_map_s_find hm' k' == hash_map_s_find hm k');
+ 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(hash_map_s_len hm' + length al' <= usize_max);
- hash_map_move_elements_s_flat_lem 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
@@ -1866,18 +1866,18 @@ let slots_t_inv_implies_slots_s_inv #t slots =
// Problem is: I can never really predict for sure with F*...
()
-val hash_map_t_base_inv_implies_hash_map_s_inv
- (#t : Type0) (hm : hash_map_t t) :
- Lemma (requires (hash_map_t_base_inv hm))
- (ensures (hash_map_s_inv (hash_map_t_v hm)))
+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 hash_map_t_base_inv_implies_hash_map_s_inv #t hm = () // same as previous
+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_hash_map_s_inv
+let partial_hashMap_s_inv
(#t : Type0) (len : usize{len > 0}) (offset : usize)
- (hm : hash_map_s t{offset + length hm <= usize_max}) : Type0 =
+ (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.
@@ -1887,13 +1887,13 @@ val binding_in_previous_slot_implies_neq
(#t : Type0) (len : usize{len > 0})
(i : usize) (b : binding t)
(offset : usize{i < offset})
- (slots : hash_map_s t{offset + length slots <= usize_max}) :
+ (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_hash_map_s_inv len offset slots))
+ partial_hashMap_s_inv len offset slots))
(ensures (
for_all (binding_neq b) (flatten slots)))
(decreases slots)
@@ -1924,17 +1924,17 @@ let rec binding_in_previous_slot_implies_neq #t len i b offset slots =
for_all_append (binding_neq b) s (flatten slots')
#pop-options
-val partial_hash_map_s_inv_implies_assoc_list_lem
+val partial_hashMap_s_inv_implies_assoc_list_lem
(#t : Type0) (len : usize{len > 0}) (offset : usize)
- (hm : hash_map_s t{offset + length hm <= usize_max}) :
+ (hm : hashMap_s t{offset + length hm <= usize_max}) :
Lemma
(requires (
- partial_hash_map_s_inv len offset hm))
+ 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_hash_map_s_inv_implies_assoc_list_lem #t len offset hm =
+let rec partial_hashMap_s_inv_implies_assoc_list_lem #t len offset hm =
match hm with
| [] -> ()
| slot :: hm' ->
@@ -1943,8 +1943,8 @@ let rec partial_hash_map_s_inv_implies_assoc_list_lem #t len offset hm =
match slot with
| [] ->
assert(flatten hm == flatten hm');
- assert(partial_hash_map_s_inv len (offset+1) hm'); // Triggers instantiations
- partial_hash_map_s_inv_implies_assoc_list_lem len (offset+1) 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
@@ -1953,45 +1953,45 @@ let rec partial_hash_map_s_inv_implies_assoc_list_lem #t len offset hm =
assert(index hm 0 == slot); // Triggers instantiations
assert(slot_s_inv len offset slot);
assert(slot_s_inv len offset slot');
- assert(partial_hash_map_s_inv len offset hm'');
- partial_hash_map_s_inv_implies_assoc_list_lem len offset (slot' :: hm');
+ 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_hash_map_s_inv len (offset+1) 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 hash_map_s_inv_implies_assoc_list_lem
- (#t : Type0) (hm : hash_map_s t) :
- Lemma (requires (hash_map_s_inv hm))
+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 hash_map_s_inv_implies_assoc_list_lem #t hm =
- partial_hash_map_s_inv_implies_assoc_list_lem (length hm) 0 hm
+let hashMap_s_inv_implies_assoc_list_lem #t hm =
+ partial_hashMap_s_inv_implies_assoc_list_lem (length hm) 0 hm
-val hash_map_t_base_inv_implies_assoc_list_lem
- (#t : Type0) (hm : hash_map_t t):
- Lemma (requires (hash_map_t_base_inv hm))
- (ensures (assoc_list_inv (hash_map_t_al_v 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 hash_map_t_base_inv_implies_assoc_list_lem #t hm =
- hash_map_s_inv_implies_assoc_list_lem (hash_map_t_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 hash_map_is_assoc_list
- (#t : Type0) (ntable : hash_map_t t{length ntable.hash_map_slots > 0})
+let hashMap_is_assoc_list
+ (#t : Type0) (ntable : hashMap_t t{length ntable.slots > 0})
(al : assoc_list t) : Type0 =
- (forall (k:key). hash_map_t_find_s ntable k == assoc_list_find k al)
+ (forall (k:key). hashMap_t_find_s ntable k == assoc_list_find k al)
-let partial_hash_map_s_find
+let partial_hashMap_s_find
(#t : Type0) (len : usize{len > 0}) (offset : usize)
- (hm : hash_map_s_nes t{offset + length hm = len})
+ (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
@@ -2021,13 +2021,13 @@ val key_in_previous_slot_implies_not_found
(#t : Type0) (len : usize{len > 0})
(k : key)
(offset : usize)
- (slots : hash_map_s t{offset + length slots = len}) :
+ (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_hash_map_s_inv len offset slots))
+ partial_hashMap_s_inv len offset slots))
(ensures (
assoc_list_find k (flatten slots) == None))
(decreases slots)
@@ -2045,19 +2045,19 @@ let rec key_in_previous_slot_implies_not_found #t len k offset slots =
key_in_previous_slot_implies_not_found len k (offset+1) slots'
#pop-options
-val partial_hash_map_s_is_assoc_list_lem
+val partial_hashMap_s_is_assoc_list_lem
(#t : Type0) (len : usize{len > 0}) (offset : usize)
- (hm : hash_map_s_nes t{offset + length hm = len})
+ (hm : hashMap_s_nes t{offset + length hm = len})
(k : key{hash_mod_key k len >= offset}) :
Lemma
(requires (
- partial_hash_map_s_inv len offset hm))
+ partial_hashMap_s_inv len offset hm))
(ensures (
- partial_hash_map_s_find len offset hm k == assoc_list_find k (flatten hm)))
+ partial_hashMap_s_find len offset hm k == assoc_list_find k (flatten hm)))
(decreases hm)
#push-options "--fuel 1"
-let rec partial_hash_map_s_is_assoc_list_lem #t len offset hm k =
+let rec partial_hashMap_s_is_assoc_list_lem #t len offset hm k =
match hm with
| [] -> ()
| slot :: hm' ->
@@ -2066,7 +2066,7 @@ let rec partial_hash_map_s_is_assoc_list_lem #t len offset hm k =
if i = 0 then
begin
// We must look in the current slot
- assert(partial_hash_map_s_find len offset hm k == slot_s_find k 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';
@@ -2085,64 +2085,64 @@ let rec partial_hash_map_s_is_assoc_list_lem #t len offset hm k =
else
begin
// We must ignore the current slot
- assert(partial_hash_map_s_find len offset hm k ==
- partial_hash_map_s_find len (offset+1) hm' k);
+ 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_hash_map_s_is_assoc_list_lem #t len (offset+1) hm' k
+ partial_hashMap_s_is_assoc_list_lem #t len (offset+1) hm' k
end
#pop-options
-val hash_map_is_assoc_list_lem (#t : Type0) (hm : hash_map_t t) :
- Lemma (requires (hash_map_t_base_inv hm))
- (ensures (hash_map_is_assoc_list hm (hash_map_t_al_v hm)))
+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 hash_map_is_assoc_list_lem #t hm =
+let hashMap_is_assoc_list_lem #t hm =
let aux (k:key) :
- Lemma (hash_map_t_find_s hm k == assoc_list_find k (hash_map_t_al_v hm))
- [SMTPat (hash_map_t_find_s hm k)] =
- let hm_v = hash_map_t_v hm in
+ 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_hash_map_s_is_assoc_list_lem #t len 0 hm_v k
+ 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 hash_map_move_elements_fwd_back_lem
- (t : Type0) (ntable : hash_map_t t) (slots : vec (list_t t)) :
+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
- hash_map_t_base_inv ntable /\
+ hashMap_t_base_inv ntable /\
length al <= usize_max /\
assoc_list_inv al /\
// The table is empty
- hash_map_t_len_s ntable = 0 /\
- (forall (k:key). hash_map_t_find_s ntable k == None)))
+ 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 hash_map_move_elements_fwd_back t ntable slots 0,
- hash_map_move_elements_s_flat (hash_map_t_v ntable) al
+ 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
- hash_map_t_base_inv ntable' /\
+ hashMap_t_base_inv ntable' /\
// We preserved the parameters
- hash_map_t_same_params ntable' ntable /\
+ hashMap_t_same_params ntable' ntable /\
// The table has the same number of slots
- length ntable'.hash_map_slots = length ntable.hash_map_slots /\
+ length ntable'.slots = length ntable.slots /\
// The count is good
- hash_map_t_len_s ntable' = length al /\
+ 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)
- hash_map_t_v ntable' == ntable'_v /\
+ hashMap_t_v ntable' == ntable'_v /\
// The new table contains exactly all the bindings from the slots
- // Rk.: see the comment for [hash_map_is_assoc_list]
- hash_map_is_assoc_list ntable' al
+ // Rk.: see the comment for [hashMap_is_assoc_list]
+ hashMap_is_assoc_list ntable' al
| _ -> False // We can only succeed
))
@@ -2154,41 +2154,41 @@ val hash_map_move_elements_fwd_back_lem
// lack of ifuel (this kind of proofs is annoying, really).
#restart-solver
#push-options "--z3rlimit 100"
-let hash_map_move_elements_fwd_back_lem t ntable slots =
- let ntable_v = hash_map_t_v ntable in
+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
- hash_map_move_elements_fwd_back_lem_refin t ntable slots 0;
+ hashMap_move_elements_lem_refin t ntable slots 0;
begin
- match hash_map_move_elements_fwd_back t ntable slots 0,
- hash_map_move_elements_s ntable_v slots_v 0
+ 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(hash_map_t_base_inv ntable');
- assert(hash_map_t_v ntable' == ntable'_v)
+ assert(hashMap_t_base_inv ntable');
+ assert(hashMap_t_v ntable' == ntable'_v)
| _ -> assert(False)
end;
- hash_map_move_elements_s_lem_refin_flat ntable_v slots_v 0;
+ hashMap_move_elements_s_lem_refin_flat ntable_v slots_v 0;
begin
- match hash_map_move_elements_s ntable_v slots_v 0,
- hash_map_move_elements_s_flat ntable_v (flatten_i slots_v 0)
+ 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
- hash_map_move_elements_s_flat_lem ntable_v al;
- match hash_map_move_elements_fwd_back t ntable slots 0,
- hash_map_move_elements_s_flat ntable_v al
+ 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(hash_map_t_base_inv ntable');
- assert(length ntable'.hash_map_slots = length ntable.hash_map_slots);
- assert(hash_map_t_len_s ntable' = length al);
- assert(hash_map_t_v ntable' == ntable'_v);
- assert(hash_map_is_assoc_list ntable' al)
+ 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
@@ -2197,47 +2197,47 @@ let hash_map_move_elements_fwd_back_lem t ntable slots =
/// High-level model 1.
/// This is one is slightly "crude": we just simplify a bit the function.
-let hash_map_try_resize_s_simpl
+let hashMap_try_resize_s_simpl
(#t : Type0)
- (hm : hash_map_t t) :
- Pure (result (hash_map_t t))
+ (hm : hashMap_t t) :
+ Pure (result (hashMap_t t))
(requires (
- let (divid, divis) = hm.hash_map_max_load_factor in
+ let (divid, divis) = hm.max_load_factor in
divid > 0 /\ divis > 0))
(ensures (fun _ -> True)) =
- let capacity = length hm.hash_map_slots in
- let (divid, divis) = hm.hash_map_max_load_factor in
+ 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 hash_map_new_with_capacity_fwd t ncapacity divid divis with
+ begin match hashMap_new_with_capacity t ncapacity divid divis with
| Fail e -> Fail e
| Return ntable ->
- match hash_map_move_elements_fwd_back t ntable hm.hash_map_slots 0 with
+ match hashMap_move_elements t ntable hm.slots 0 with
| Fail e -> Fail e
| Return (ntable', _) ->
let hm =
- { hm with hash_map_slots = ntable'.hash_map_slots;
- hash_map_max_load = ntable'.hash_map_max_load }
+ { hm with slots = ntable'.slots;
+ max_load = ntable'.max_load }
in
Return hm
end
else Return hm
-val hash_map_try_resize_fwd_back_lem_refin
- (t : Type0) (self : hash_map_t t) :
+val hashMap_try_resize_lem_refin
+ (t : Type0) (self : hashMap_t t) :
Lemma
(requires (
- let (divid, divis) = self.hash_map_max_load_factor in
+ let (divid, divis) = self.max_load_factor in
divid > 0 /\ divis > 0))
(ensures (
- match hash_map_try_resize_fwd_back t self,
- hash_map_try_resize_s_simpl self
+ match hashMap_try_resize t self,
+ hashMap_try_resize_s_simpl self
with
| Fail _, Fail _ -> True
| Return hm1, Return hm2 -> hm1 == hm2
| _ -> False))
-let hash_map_try_resize_fwd_back_lem_refin t self = ()
+let hashMap_try_resize_lem_refin t self = ()
/// Isolating arithmetic proofs
@@ -2342,78 +2342,78 @@ let new_max_load_lem len capacity divid divis =
assert(nmax_load >= max_load + 1)
#pop-options
-val hash_map_try_resize_s_simpl_lem (#t : Type0) (hm : hash_map_t t) :
+val hashMap_try_resize_s_simpl_lem (#t : Type0) (hm : hashMap_t t) :
Lemma
(requires (
// The base invariant is satisfied
- hash_map_t_base_inv hm /\
+ 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.hash_map_max_load_factor in
- hm.hash_map_num_entries == hm.hash_map_max_load + 1 \/
- length hm.hash_map_slots * 2 * dividend > usize_max)
+ (let (dividend, divisor) = hm.max_load_factor in
+ hm.num_entries == hm.max_load + 1 \/
+ length hm.slots * 2 * dividend > usize_max)
))
(ensures (
- match hash_map_try_resize_s_simpl hm with
+ 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)
- hash_map_t_inv hm' /\
+ hashMap_t_inv hm' /\
// It contains the same bindings as the initial map
- (forall (k:key). hash_map_t_find_s hm' k == hash_map_t_find_s hm k)))
+ (forall (k:key). hashMap_t_find_s hm' k == hashMap_t_find_s hm k)))
#restart-solver
#push-options "--z3rlimit 400"
-let hash_map_try_resize_s_simpl_lem #t hm =
- let capacity = length hm.hash_map_slots in
- let (divid, divis) = hm.hash_map_max_load_factor in
+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(hash_map_t_len_s hm = hm.hash_map_max_load + 1);
- new_max_load_lem (hash_map_t_len_s hm) capacity divid divis;
- hash_map_new_with_capacity_fwd_lem t ncapacity divid divis;
- match hash_map_new_with_capacity_fwd t ncapacity divid divis with
+ 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.hash_map_slots in
+ let slots = hm.slots in
let al = flatten (slots_t_v slots) in
- // Proving that: length al = hm.hash_map_num_entries
+ // Proving that: length al = hm.num_entries
assert(al == flatten (map slot_t_v slots));
assert(al == flatten (map list_t_v slots));
- assert(hash_map_t_al_v hm == flatten (hash_map_t_v hm));
- assert(hash_map_t_al_v hm == flatten (map list_t_v hm.hash_map_slots));
- assert(al == hash_map_t_al_v hm);
- assert(hash_map_t_base_inv ntable);
- assert(length al = hm.hash_map_num_entries);
+ 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);
- hash_map_t_base_inv_implies_assoc_list_lem hm;
+ hashMap_t_base_inv_implies_assoc_list_lem hm;
assert(assoc_list_inv al);
- assert(hash_map_t_len_s ntable = 0);
- assert(forall (k:key). hash_map_t_find_s ntable k == None);
- hash_map_move_elements_fwd_back_lem t ntable hm.hash_map_slots;
- match hash_map_move_elements_fwd_back t ntable hm.hash_map_slots 0 with
+ 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', _) ->
- hash_map_is_assoc_list_lem hm;
- assert(hash_map_is_assoc_list hm (hash_map_t_al_v hm));
+ hashMap_is_assoc_list_lem hm;
+ assert(hashMap_is_assoc_list hm (hashMap_t_al_v hm));
let hm' =
- { hm with hash_map_slots = ntable'.hash_map_slots;
- hash_map_max_load = ntable'.hash_map_max_load }
+ { hm with slots = ntable'.slots;
+ max_load = ntable'.max_load }
in
- assert(hash_map_t_base_inv ntable');
- assert(hash_map_t_base_inv hm');
- assert(hash_map_t_len_s hm' = hash_map_t_len_s hm);
- new_max_load_lem (hash_map_t_len_s hm') capacity divid divis;
- assert(hash_map_t_len_s hm' <= hm'.hash_map_max_load); // Requires a lemma
- assert(hash_map_t_inv hm')
+ 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
@@ -2422,203 +2422,203 @@ let hash_map_try_resize_s_simpl_lem #t hm =
end
#pop-options
-let hash_map_t_same_bindings (#t : Type0) (hm hm' : hash_map_t_nes t) : Type0 =
- forall (k:key). hash_map_t_find_s hm k == hash_map_t_find_s hm' k
+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 hash_map_try_resize_fwd_back_lem (#t : Type0) (hm : hash_map_t t) :
+val hashMap_try_resize_lem (#t : Type0) (hm : hashMap_t t) :
Lemma
(requires (
- hash_map_t_base_inv hm /\
+ 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.hash_map_max_load_factor in
- hm.hash_map_num_entries == hm.hash_map_max_load + 1 \/
- length hm.hash_map_slots * 2 * dividend > usize_max)))
+ (let (dividend, divisor) = hm.max_load_factor in
+ hm.num_entries == hm.max_load + 1 \/
+ length hm.slots * 2 * dividend > usize_max)))
(ensures (
- match hash_map_try_resize_fwd_back t hm with
+ 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)
- hash_map_t_inv hm' /\
+ hashMap_t_inv hm' /\
// The length is the same
- hash_map_t_len_s hm' = hash_map_t_len_s hm /\
+ hashMap_t_len_s hm' = hashMap_t_len_s hm /\
// It contains the same bindings as the initial map
- hash_map_t_same_bindings hm' hm))
+ hashMap_t_same_bindings hm' hm))
-let hash_map_try_resize_fwd_back_lem #t hm =
- hash_map_try_resize_fwd_back_lem_refin t hm;
- hash_map_try_resize_s_simpl_lem 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 hash_map_insert_s
- (#t : Type0) (self : hash_map_t t) (key : usize) (value : t) :
- result (hash_map_t t) =
- match hash_map_insert_no_resize_fwd_back t self key value with
+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 hash_map_t_len_s hm' > hm'.hash_map_max_load then
- hash_map_try_resize_fwd_back t hm'
+ if hashMap_t_len_s hm' > hm'.max_load then
+ hashMap_try_resize t hm'
else Return hm'
-val hash_map_insert_fwd_back_lem_refin
- (t : Type0) (self : hash_map_t t) (key : usize) (value : t) :
+val hashMap_insert_lem_refin
+ (t : Type0) (self : hashMap_t t) (key : usize) (value : t) :
Lemma (requires True)
(ensures (
- match hash_map_insert_fwd_back t self key value,
- hash_map_insert_s self key value
+ 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 hash_map_insert_fwd_back_lem_refin t self key value = ()
+let hashMap_insert_lem_refin t self key value = ()
/// Helper
-let hash_map_insert_fwd_back_bindings_lem
- (t : Type0) (self : hash_map_t_nes t) (key : usize) (value : t)
- (hm' hm'' : hash_map_t_nes t) :
+let hashMap_insert_bindings_lem
+ (t : Type0) (self : hashMap_t_nes t) (key : usize) (value : t)
+ (hm' hm'' : hashMap_t_nes t) :
Lemma
(requires (
- hash_map_s_updated_binding (hash_map_t_v self) key
- (Some value) (hash_map_t_v hm') /\
- hash_map_t_same_bindings hm' hm''))
+ hashMap_s_updated_binding (hashMap_t_v self) key
+ (Some value) (hashMap_t_v hm') /\
+ hashMap_t_same_bindings hm' hm''))
(ensures (
- hash_map_s_updated_binding (hash_map_t_v self) key
- (Some value) (hash_map_t_v hm'')))
+ hashMap_s_updated_binding (hashMap_t_v self) key
+ (Some value) (hashMap_t_v hm'')))
= ()
-val hash_map_insert_fwd_back_lem_aux
- (#t : Type0) (self : hash_map_t t) (key : usize) (value : t) :
- Lemma (requires (hash_map_t_inv self))
+val hashMap_insert_lem_aux
+ (#t : Type0) (self : hashMap_t t) (key : usize) (value : t) :
+ Lemma (requires (hashMap_t_inv self))
(ensures (
- match hash_map_insert_fwd_back t self key value with
+ 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
- hash_map_t_len_s self = usize_max /\
- None? (hash_map_t_find_s self key)
+ hashMap_t_len_s self = usize_max /\
+ None? (hashMap_t_find_s self key)
| Return hm' ->
// The invariant is preserved
- hash_map_t_inv hm' /\
+ hashMap_t_inv hm' /\
// [key] maps to [value] and the other bindings are preserved
- hash_map_s_updated_binding (hash_map_t_v self) key (Some value) (hash_map_t_v hm') /\
+ 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 hash_map_t_find_s self key with
- | None -> hash_map_t_len_s hm' = hash_map_t_len_s self + 1
- | Some _ -> hash_map_t_len_s hm' = hash_map_t_len_s self)))
+ (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 hash_map_insert_fwd_back_lem_aux #t self key value =
- hash_map_insert_no_resize_fwd_back_lem_s t self key value;
- hash_map_insert_no_resize_s_lem (hash_map_t_v self) key value;
- match hash_map_insert_no_resize_fwd_back t self key value with
+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 [hash_map_insert_no_resize_fwd_back_lem_s]
- let self_v = hash_map_t_v self in
- let hm'_v = Return?.v (hash_map_insert_no_resize_s self_v key value) in
- assert(hash_map_t_base_inv hm');
- assert(hash_map_t_same_params hm' self);
- assert(hash_map_t_v hm' == hm'_v);
- assert(hash_map_s_len hm'_v == hash_map_t_len_s hm');
- // Expanding the post of [hash_map_insert_no_resize_s_lem]
+ // 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(hash_map_s_inv hm'_v);
+ assert(hashMap_s_inv hm'_v);
assert(
- match hash_map_s_find self_v key with
- | None -> hash_map_s_len hm'_v = hash_map_s_len self_v + 1
- | Some _ -> hash_map_s_len hm'_v = hash_map_s_len self_v);
- if hash_map_t_len_s hm' > hm'.hash_map_max_load then
+ 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
- hash_map_try_resize_fwd_back_lem hm';
- // Expanding the post of [hash_map_try_resize_fwd_back_lem]
- let hm'' = Return?.v (hash_map_try_resize_fwd_back t hm') in
- assert(hash_map_t_inv hm'');
- let hm''_v = hash_map_t_v hm'' in
- assert(forall k. hash_map_t_find_s hm'' k == hash_map_t_find_s hm' k);
- assert(hash_map_t_len_s hm'' = hash_map_t_len_s hm'); // TODO
+ 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(hash_map_t_inv hm'');
- hash_map_insert_fwd_back_bindings_lem t self key value hm' hm'';
+ assert(hashMap_t_inv hm'');
+ hashMap_insert_bindings_lem t self key value hm' hm'';
assert(
- match hash_map_t_find_s self key with
- | None -> hash_map_t_len_s hm'' = hash_map_t_len_s self + 1
- | Some _ -> hash_map_t_len_s hm'' = hash_map_t_len_s self)
+ 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 hash_map_insert_fwd_back_lem #t self key value =
- hash_map_insert_fwd_back_lem_aux #t self key value
+let hashMap_insert_lem #t self key value =
+ hashMap_insert_lem_aux #t self key value
(*** contains_key *)
(**** contains_key_in_list *)
-val hash_map_contains_key_in_list_fwd_lem
+val hashMap_contains_key_in_list_lem
(#t : Type0) (key : usize) (ls : list_t t) :
Lemma
(ensures (
- match hash_map_contains_key_in_list_fwd t key ls with
+ 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 hash_map_contains_key_in_list_fwd_lem #t key ls =
+let rec hashMap_contains_key_in_list_lem #t key ls =
match ls with
- | ListCons ckey x ls0 ->
+ | List_Cons ckey x ls0 ->
let b = ckey = key in
if b
then ()
else
begin
- hash_map_contains_key_in_list_fwd_lem key ls0;
- match hash_map_contains_key_in_list_fwd t key ls0 with
+ hashMap_contains_key_in_list_lem key ls0;
+ match hashMap_contains_key_in_list t key ls0 with
| Fail _ -> ()
| Return b0 -> ()
end
- | ListNil -> ()
+ | List_Nil -> ()
#pop-options
(**** contains_key *)
-val hash_map_contains_key_fwd_lem_aux
- (#t : Type0) (self : hash_map_t_nes t) (key : usize) :
+val hashMap_contains_key_lem_aux
+ (#t : Type0) (self : hashMap_t_nes t) (key : usize) :
Lemma
(ensures (
- match hash_map_contains_key_fwd t self key with
+ match hashMap_contains_key t self key with
| Fail _ -> False
- | Return b -> b = Some? (hash_map_t_find_s self key)))
+ | Return b -> b = Some? (hashMap_t_find_s self key)))
-let hash_map_contains_key_fwd_lem_aux #t self key =
- begin match hash_key_fwd key with
+let hashMap_contains_key_lem_aux #t self key =
+ begin match hash_key key with
| Fail _ -> ()
| Return i ->
- let v = self.hash_map_slots in
- let i0 = vec_len (list_t t) v in
+ 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 vec_index_fwd (list_t t) v hash_mod with
+ begin match alloc_vec_Vec_index_usize v hash_mod with
| Fail _ -> ()
| Return l ->
- hash_map_contains_key_in_list_fwd_lem key l;
- begin match hash_map_contains_key_in_list_fwd t key l with
+ hashMap_contains_key_in_list_lem key l;
+ begin match hashMap_contains_key_in_list t key l with
| Fail _ -> ()
| Return b -> ()
end
@@ -2627,66 +2627,66 @@ let hash_map_contains_key_fwd_lem_aux #t self key =
end
/// The lemma in the .fsti
-let hash_map_contains_key_fwd_lem #t self key =
- hash_map_contains_key_fwd_lem_aux #t self key
+let hashMap_contains_key_lem #t self key =
+ hashMap_contains_key_lem_aux #t self key
(*** get *)
(**** get_in_list *)
-val hash_map_get_in_list_fwd_lem
+val hashMap_get_in_list_lem
(#t : Type0) (key : usize) (ls : list_t t) :
Lemma
(ensures (
- match hash_map_get_in_list_fwd t key ls, slot_t_find_s key ls with
+ 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 hash_map_get_in_list_fwd_lem #t key ls =
+let rec hashMap_get_in_list_lem #t key ls =
begin match ls with
- | ListCons ckey cvalue ls0 ->
+ | List_Cons ckey cvalue ls0 ->
let b = ckey = key in
if b
then ()
else
begin
- hash_map_get_in_list_fwd_lem key ls0;
- match hash_map_get_in_list_fwd t key ls0 with
+ hashMap_get_in_list_lem key ls0;
+ match hashMap_get_in_list t key ls0 with
| Fail _ -> ()
| Return x -> ()
end
- | ListNil -> ()
+ | List_Nil -> ()
end
#pop-options
(**** get *)
-val hash_map_get_fwd_lem_aux
- (#t : Type0) (self : hash_map_t_nes t) (key : usize) :
+val hashMap_get_lem_aux
+ (#t : Type0) (self : hashMap_t_nes t) (key : usize) :
Lemma
(ensures (
- match hash_map_get_fwd t self key, hash_map_t_find_s self key with
+ match hashMap_get t self key, hashMap_t_find_s self key with
| Fail _, None -> True
| Return x, Some x' -> x == x'
| _ -> False))
-let hash_map_get_fwd_lem_aux #t self key =
- begin match hash_key_fwd key with
+let hashMap_get_lem_aux #t self key =
+ begin match hash_key key with
| Fail _ -> ()
| Return i ->
- let v = self.hash_map_slots in
- let i0 = vec_len (list_t t) v in
+ 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 vec_index_fwd (list_t t) v hash_mod with
+ begin match alloc_vec_Vec_index_usize v hash_mod with
| Fail _ -> ()
| Return l ->
begin
- hash_map_get_in_list_fwd_lem key l;
- match hash_map_get_in_list_fwd t key l with
+ hashMap_get_in_list_lem key l;
+ match hashMap_get_in_list t key l with
| Fail _ -> ()
| Return x -> ()
end
@@ -2695,66 +2695,66 @@ let hash_map_get_fwd_lem_aux #t self key =
end
/// .fsti
-let hash_map_get_fwd_lem #t self key = hash_map_get_fwd_lem_aux #t self key
+let hashMap_get_lem #t self key = hashMap_get_lem_aux #t self key
(*** get_mut'fwd *)
(**** get_mut_in_list'fwd *)
-val hash_map_get_mut_in_list_loop_fwd_lem
+val hashMap_get_mut_in_list_loop_lem
(#t : Type0) (ls : list_t t) (key : usize) :
Lemma
(ensures (
- match hash_map_get_mut_in_list_loop_fwd t ls key, slot_t_find_s key ls with
+ 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 hash_map_get_mut_in_list_loop_fwd_lem #t ls key =
+let rec hashMap_get_mut_in_list_loop_lem #t ls key =
begin match ls with
- | ListCons ckey cvalue ls0 ->
+ | List_Cons ckey cvalue ls0 ->
let b = ckey = key in
if b
then ()
else
begin
- hash_map_get_mut_in_list_loop_fwd_lem ls0 key;
- match hash_map_get_mut_in_list_loop_fwd t ls0 key with
+ hashMap_get_mut_in_list_loop_lem ls0 key;
+ match hashMap_get_mut_in_list_loop t ls0 key with
| Fail _ -> ()
| Return x -> ()
end
- | ListNil -> ()
+ | List_Nil -> ()
end
#pop-options
(**** get_mut'fwd *)
-val hash_map_get_mut_fwd_lem_aux
- (#t : Type0) (self : hash_map_t_nes t) (key : usize) :
+val hashMap_get_mut_lem_aux
+ (#t : Type0) (self : hashMap_t_nes t) (key : usize) :
Lemma
(ensures (
- match hash_map_get_mut_fwd t self key, hash_map_t_find_s self key with
+ 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 hash_map_get_mut_fwd_lem_aux #t self key =
- begin match hash_key_fwd key with
+let hashMap_get_mut_lem_aux #t self key =
+ begin match hash_key key with
| Fail _ -> ()
| Return i ->
- let v = self.hash_map_slots in
- let i0 = vec_len (list_t t) v in
+ 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 vec_index_fwd (list_t t) v hash_mod with
+ begin match alloc_vec_Vec_index_usize v hash_mod with
| Fail _ -> ()
| Return l ->
begin
- hash_map_get_mut_in_list_loop_fwd_lem l key;
- match hash_map_get_mut_in_list_loop_fwd t l key with
+ hashMap_get_mut_in_list_loop_lem l key;
+ match hashMap_get_mut_in_list_loop t l key with
| Fail _ -> ()
| Return x -> ()
end
@@ -2762,78 +2762,78 @@ let hash_map_get_mut_fwd_lem_aux #t self key =
end
end
-let hash_map_get_mut_fwd_lem #t self key =
- hash_map_get_mut_fwd_lem_aux #t self key
+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 hash_map_get_mut_in_list_loop_back_lem
+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 hash_map_get_mut_in_list_loop_back t ls key ret with
+ 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 hash_map_get_mut_in_list_loop_back_lem #t ls key ret =
+let rec hashMap_get_mut_in_list_loop_back_lem #t ls key ret =
begin match ls with
- | ListCons ckey cvalue ls0 ->
+ | List_Cons ckey cvalue ls0 ->
let b = ckey = key in
if b
- then let ls1 = ListCons ckey ret ls0 in ()
+ then let ls1 = List_Cons ckey ret ls0 in ()
else
begin
- hash_map_get_mut_in_list_loop_back_lem ls0 key ret;
- match hash_map_get_mut_in_list_loop_back t ls0 key ret with
+ 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 = ListCons ckey cvalue l in ()
+ | Return l -> let ls1 = List_Cons ckey cvalue l in ()
end
- | ListNil -> ()
+ | List_Nil -> ()
end
#pop-options
(**** get_mut'back *)
/// Refinement lemma
-val hash_map_get_mut_back_lem_refin
- (#t : Type0) (self : hash_map_t t{length self.hash_map_slots > 0})
+val hashMap_get_mut_back_lem_refin
+ (#t : Type0) (self : hashMap_t t{length self.slots > 0})
(key : usize) (ret : t) :
Lemma
- (requires (Some? (hash_map_t_find_s self key)))
+ (requires (Some? (hashMap_t_find_s self key)))
(ensures (
- match hash_map_get_mut_back t self key ret with
+ match hashMap_get_mut_back t self key ret with
| Fail _ -> False
| Return hm' ->
- hash_map_t_v hm' == hash_map_insert_no_fail_s (hash_map_t_v self) key ret))
+ hashMap_t_v hm' == hashMap_insert_no_fail_s (hashMap_t_v self) key ret))
-let hash_map_get_mut_back_lem_refin #t self key ret =
- begin match hash_key_fwd key with
+let hashMap_get_mut_back_lem_refin #t self key ret =
+ begin match hash_key key with
| Fail _ -> ()
| Return i ->
- let i0 = self.hash_map_num_entries in
- let p = self.hash_map_max_load_factor in
- let i1 = self.hash_map_max_load in
- let v = self.hash_map_slots in
- let i2 = vec_len (list_t t) v in
+ 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 vec_index_mut_fwd (list_t t) v hash_mod with
+ begin match alloc_vec_Vec_index_usize v hash_mod with
| Fail _ -> ()
| Return l ->
begin
- hash_map_get_mut_in_list_loop_back_lem l key ret;
- match hash_map_get_mut_in_list_loop_back t l key ret with
+ 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 vec_index_mut_back (list_t t) v hash_mod l0 with
+ begin match alloc_vec_Vec_update_usize v hash_mod l0 with
| Fail _ -> ()
- | Return v0 -> let self0 = Mkhash_map_t i0 p i1 v0 in ()
+ | Return v0 -> let self0 = MkhashMap_t i0 p i1 v0 in ()
end
end
end
@@ -2841,102 +2841,102 @@ let hash_map_get_mut_back_lem_refin #t self key ret =
end
/// Final lemma
-val hash_map_get_mut_back_lem_aux
- (#t : Type0) (hm : hash_map_t t)
+val hashMap_get_mut_back_lem_aux
+ (#t : Type0) (hm : hashMap_t t)
(key : usize) (ret : t) :
Lemma
(requires (
- hash_map_t_inv hm /\
- Some? (hash_map_t_find_s hm key)))
+ hashMap_t_inv hm /\
+ Some? (hashMap_t_find_s hm key)))
(ensures (
- match hash_map_get_mut_back t hm key ret with
+ match hashMap_get_mut_back t hm key ret with
| Fail _ -> False
| Return hm' ->
// Functional spec
- hash_map_t_v hm' == hash_map_insert_no_fail_s (hash_map_t_v hm) key ret /\
+ hashMap_t_v hm' == hashMap_insert_no_fail_s (hashMap_t_v hm) key ret /\
// The invariant is preserved
- hash_map_t_inv hm' /\
+ hashMap_t_inv hm' /\
// The length is preserved
- hash_map_t_len_s hm' = hash_map_t_len_s hm /\
+ hashMap_t_len_s hm' = hashMap_t_len_s hm /\
// [key] maps to [value]
- hash_map_t_find_s hm' key == Some ret /\
+ hashMap_t_find_s hm' key == Some ret /\
// The other bindings are preserved
- (forall k'. k' <> key ==> hash_map_t_find_s hm' k' == hash_map_t_find_s hm k')))
+ (forall k'. k' <> key ==> hashMap_t_find_s hm' k' == hashMap_t_find_s hm k')))
-let hash_map_get_mut_back_lem_aux #t hm key ret =
- let hm_v = hash_map_t_v hm in
- hash_map_get_mut_back_lem_refin hm key ret;
- match hash_map_get_mut_back t hm key ret with
+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' ->
- hash_map_insert_no_fail_s_lem hm_v key ret
+ hashMap_insert_no_fail_s_lem hm_v key ret
/// .fsti
-let hash_map_get_mut_back_lem #t hm key ret = hash_map_get_mut_back_lem_aux hm key ret
+let hashMap_get_mut_back_lem #t hm key ret = hashMap_get_mut_back_lem_aux hm key ret
(*** remove'fwd *)
-val hash_map_remove_from_list_fwd_lem
+val hashMap_remove_from_list_lem
(#t : Type0) (key : usize) (ls : list_t t) :
Lemma
(ensures (
- match hash_map_remove_from_list_fwd t key ls with
+ 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 hash_map_remove_from_list_fwd_lem #t key ls =
+let rec hashMap_remove_from_list_lem #t key ls =
begin match ls with
- | ListCons ckey x tl ->
+ | List_Cons ckey x tl ->
let b = ckey = key in
if b
then
- let mv_ls = mem_replace_fwd (list_t t) (ListCons ckey x tl) ListNil in
+ let mv_ls = core_mem_replace (list_t t) (List_Cons ckey x tl) List_Nil in
begin match mv_ls with
- | ListCons i cvalue tl0 -> ()
- | ListNil -> ()
+ | List_Cons i cvalue tl0 -> ()
+ | List_Nil -> ()
end
else
begin
- hash_map_remove_from_list_fwd_lem key tl;
- match hash_map_remove_from_list_fwd t key tl with
+ hashMap_remove_from_list_lem key tl;
+ match hashMap_remove_from_list t key tl with
| Fail _ -> ()
| Return opt -> ()
end
- | ListNil -> ()
+ | List_Nil -> ()
end
#pop-options
-val hash_map_remove_fwd_lem_aux
- (#t : Type0) (self : hash_map_t t) (key : usize) :
+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
- hash_map_t_inv self))
+ hashMap_t_inv self))
(ensures (
- match hash_map_remove_fwd t self key with
+ match hashMap_remove t self key with
| Fail _ -> False
- | Return opt_x -> opt_x == hash_map_t_find_s self key))
+ | Return opt_x -> opt_x == hashMap_t_find_s self key))
-let hash_map_remove_fwd_lem_aux #t self key =
- begin match hash_key_fwd key with
+let hashMap_remove_lem_aux #t self key =
+ begin match hash_key key with
| Fail _ -> ()
| Return i ->
- let i0 = self.hash_map_num_entries in
- let v = self.hash_map_slots in
- let i1 = vec_len (list_t t) v in
+ 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 vec_index_mut_fwd (list_t t) v hash_mod with
+ begin match alloc_vec_Vec_index_usize v hash_mod with
| Fail _ -> ()
| Return l ->
begin
- hash_map_remove_from_list_fwd_lem key l;
- match hash_map_remove_from_list_fwd t key l with
+ hashMap_remove_from_list_lem key l;
+ match hashMap_remove_from_list t key l with
| Fail _ -> ()
| Return x ->
begin match x with
@@ -2945,7 +2945,7 @@ let hash_map_remove_fwd_lem_aux #t self key =
begin
assert(l == index v hash_mod);
assert(length (list_t_v #t l) > 0);
- length_flatten_index (hash_map_t_v self) hash_mod;
+ length_flatten_index (hashMap_t_v self) hash_mod;
match usize_sub i0 1 with
| Fail _ -> ()
| Return _ -> ()
@@ -2957,27 +2957,27 @@ let hash_map_remove_fwd_lem_aux #t self key =
end
/// .fsti
-let hash_map_remove_fwd_lem #t self key = hash_map_remove_fwd_lem_aux #t self key
+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 hash_map_remove_from_list_s
+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 hash_map_remove_from_list_back_lem_refin
+val hashMap_remove_from_list_back_lem_refin
(#t : Type0) (key : usize) (ls : list_t t) :
Lemma
(ensures (
- match hash_map_remove_from_list_back t key ls with
+ match hashMap_remove_from_list_back t key ls with
| Fail _ -> False
| Return ls' ->
- list_t_v ls' == hash_map_remove_from_list_s key (list_t_v 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
@@ -2986,89 +2986,89 @@ val hash_map_remove_from_list_back_lem_refin
| Some _ -> len = len' + 1)))
#push-options "--fuel 1"
-let rec hash_map_remove_from_list_back_lem_refin #t key ls =
+let rec hashMap_remove_from_list_back_lem_refin #t key ls =
begin match ls with
- | ListCons ckey x tl ->
+ | List_Cons ckey x tl ->
let b = ckey = key in
if b
then
- let mv_ls = mem_replace_fwd (list_t t) (ListCons ckey x tl) ListNil in
+ let mv_ls = core_mem_replace (list_t t) (List_Cons ckey x tl) List_Nil in
begin match mv_ls with
- | ListCons i cvalue tl0 -> ()
- | ListNil -> ()
+ | List_Cons i cvalue tl0 -> ()
+ | List_Nil -> ()
end
else
begin
- hash_map_remove_from_list_back_lem_refin key tl;
- match hash_map_remove_from_list_back t key tl with
+ hashMap_remove_from_list_back_lem_refin key tl;
+ match hashMap_remove_from_list_back t key tl with
| Fail _ -> ()
- | Return l -> let ls0 = ListCons ckey x l in ()
+ | Return l -> let ls0 = List_Cons ckey x l in ()
end
- | ListNil -> ()
+ | List_Nil -> ()
end
#pop-options
/// High-level model for [remove_from_list'back]
-let hash_map_remove_s
- (#t : Type0) (self : hash_map_s_nes t) (key : usize) :
- hash_map_s t =
+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' = hash_map_remove_from_list_s key slot in
+ let slot' = hashMap_remove_from_list_s key slot in
list_update self hash slot'
/// Refinement lemma
-val hash_map_remove_back_lem_refin
- (#t : Type0) (self : hash_map_t_nes t) (key : usize) :
+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
- hash_map_t_inv self))
+ hashMap_t_inv self))
(ensures (
- match hash_map_remove_back t self key with
+ match hashMap_remove_back t self key with
| Fail _ -> False
| Return hm' ->
- hash_map_t_same_params hm' self /\
- hash_map_t_v hm' == hash_map_remove_s (hash_map_t_v self) key /\
+ 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 = hash_map_t_len_s self in
- let len' = hash_map_t_len_s hm' in
- match hash_map_t_find_s self key with
+ (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 hash_map_remove_back_lem_refin #t self key =
- begin match hash_key_fwd key with
+let hashMap_remove_back_lem_refin #t self key =
+ begin match hash_key key with
| Fail _ -> ()
| Return i ->
- let i0 = self.hash_map_num_entries in
- let p = self.hash_map_max_load_factor in
- let i1 = self.hash_map_max_load in
- let v = self.hash_map_slots in
- let i2 = vec_len (list_t t) v in
+ 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 vec_index_mut_fwd (list_t t) v hash_mod with
+ begin match alloc_vec_Vec_index_usize v hash_mod with
| Fail _ -> ()
| Return l ->
begin
- hash_map_remove_from_list_fwd_lem key l;
- match hash_map_remove_from_list_fwd t key l with
+ 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
- hash_map_remove_from_list_back_lem_refin key l;
- match hash_map_remove_from_list_back t key l with
+ 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 vec_index_mut_back (list_t t) v hash_mod l0 with
+ match alloc_vec_Vec_update_usize v hash_mod l0 with
| Fail _ -> ()
| Return v0 -> ()
end
@@ -3077,18 +3077,18 @@ let hash_map_remove_back_lem_refin #t self key =
begin
assert(l == index v hash_mod);
assert(length (list_t_v #t l) > 0);
- length_flatten_index (hash_map_t_v self) hash_mod;
+ length_flatten_index (hashMap_t_v self) hash_mod;
match usize_sub i0 1 with
| Fail _ -> ()
| Return i3 ->
begin
- hash_map_remove_from_list_back_lem_refin key l;
- match hash_map_remove_from_list_back t key l with
+ 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 vec_index_mut_back (list_t t) v hash_mod l0 with
+ match alloc_vec_Vec_update_usize v hash_mod l0 with
| Fail _ -> ()
| Return v0 -> ()
end
@@ -3102,12 +3102,12 @@ let hash_map_remove_back_lem_refin #t self key =
(**** Invariants, high-level properties *)
-val hash_map_remove_from_list_s_lem
+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' = hash_map_remove_from_list_s k slot in
+ 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) /\
@@ -3117,14 +3117,14 @@ val hash_map_remove_from_list_s_lem
))
#push-options "--fuel 1"
-let rec hash_map_remove_from_list_s_lem #t key slot len i =
+let rec hashMap_remove_from_list_s_lem #t key slot len i =
match slot with
| [] -> ()
| (k',v) :: slot' ->
if k' <> key then
begin
- hash_map_remove_from_list_s_lem key slot' len i;
- let slot'' = hash_map_remove_from_list_s key slot' in
+ 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'')
@@ -3136,51 +3136,51 @@ let rec hash_map_remove_from_list_s_lem #t key slot len i =
end
#pop-options
-val hash_map_remove_s_lem
- (#t : Type0) (self : hash_map_s_nes t) (key : usize) :
+val hashMap_remove_s_lem
+ (#t : Type0) (self : hashMap_s_nes t) (key : usize) :
Lemma
- (requires (hash_map_s_inv self))
+ (requires (hashMap_s_inv self))
(ensures (
- let hm' = hash_map_remove_s self key in
+ let hm' = hashMap_remove_s self key in
// The invariant is preserved
- hash_map_s_inv hm' /\
+ hashMap_s_inv hm' /\
// We updated the binding
- hash_map_s_updated_binding self key None hm'))
+ hashMap_s_updated_binding self key None hm'))
-let hash_map_remove_s_lem #t self key =
+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
- hash_map_remove_from_list_s_lem key slot len hash;
- let slot' = hash_map_remove_from_list_s key slot 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(hash_map_s_inv self)
+ assert(hashMap_s_inv self)
/// Final lemma about [remove'back]
-val hash_map_remove_back_lem_aux
- (#t : Type0) (self : hash_map_t t) (key : usize) :
+val hashMap_remove_back_lem_aux
+ (#t : Type0) (self : hashMap_t t) (key : usize) :
Lemma
- (requires (hash_map_t_inv self))
+ (requires (hashMap_t_inv self))
(ensures (
- match hash_map_remove_back t self key with
+ match hashMap_remove_back t self key with
| Fail _ -> False
| Return hm' ->
- hash_map_t_inv self /\
- hash_map_t_same_params hm' self /\
+ hashMap_t_inv self /\
+ hashMap_t_same_params hm' self /\
// We updated the binding
- hash_map_s_updated_binding (hash_map_t_v self) key None (hash_map_t_v hm') /\
- hash_map_t_v hm' == hash_map_remove_s (hash_map_t_v self) key /\
+ 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 = hash_map_t_len_s self in
- let len' = hash_map_t_len_s hm' in
- match hash_map_t_find_s self key with
+ (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 hash_map_remove_back_lem_aux #t self key =
- hash_map_remove_back_lem_refin self key;
- hash_map_remove_s_lem (hash_map_t_v self) key
+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 hash_map_remove_back_lem #t self key =
- hash_map_remove_back_lem_aux #t self key
+let hashMap_remove_back_lem #t self key =
+ hashMap_remove_back_lem_aux #t self key
diff --git a/tests/fstar/hashmap/Hashmap.Properties.fsti b/tests/fstar/hashmap/Hashmap.Properties.fsti
index 0a4f0134..26c0ec06 100644
--- a/tests/fstar/hashmap/Hashmap.Properties.fsti
+++ b/tests/fstar/hashmap/Hashmap.Properties.fsti
@@ -18,11 +18,11 @@ type key : eqtype = usize
type hash : eqtype = usize
-val hash_map_t_inv (#t : Type0) (hm : hash_map_t t) : Type0
+val hashMap_t_inv (#t : Type0) (hm : hashMap_t t) : Type0
-val len_s (#t : Type0) (hm : hash_map_t t) : nat
+val len_s (#t : Type0) (hm : hashMap_t t) : nat
-val find_s (#t : Type0) (hm : hash_map_t t) (k : key) : option t
+val find_s (#t : Type0) (hm : hashMap_t t) (k : key) : option t
(*** Overloading *)
@@ -32,16 +32,16 @@ val find_s (#t : Type0) (hm : hash_map_t t) (k : key) : option t
/// limiting the hash collisions.
/// This is expressed by the following property, which is maintained in the hash
/// map invariant.
-val hash_map_not_overloaded_lem (#t : Type0) (hm : hash_map_t t) :
+val hashMap_not_overloaded_lem (#t : Type0) (hm : hashMap_t t) :
Lemma
- (requires (hash_map_t_inv hm))
+ (requires (hashMap_t_inv hm))
(ensures (
// The capacity is the number of slots
- let capacity = length hm.hash_map_slots in
+ 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.hash_map_max_load_factor in
+ 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 /\
@@ -63,14 +63,14 @@ val hash_map_not_overloaded_lem (#t : Type0) (hm : hash_map_t t) :
(**** [new'fwd] *)
/// [new] doesn't fail and returns an empty hash map
-val hash_map_new_fwd_lem (t : Type0) :
+val hashMap_new_lem (t : Type0) :
Lemma
(ensures (
- match hash_map_new_fwd t with
+ match hashMap_new t with
| Fail _ -> False
| Return hm ->
// The hash map invariant is satisfied
- hash_map_t_inv hm /\
+ hashMap_t_inv hm /\
// The hash map has a length of 0
len_s hm = 0 /\
// It contains no bindings
@@ -79,16 +79,16 @@ val hash_map_new_fwd_lem (t : Type0) :
(**** [clear] *)
/// [clear] doesn't fail and turns the hash map into an empty map
-val hash_map_clear_fwd_back_lem
- (#t : Type0) (self : hash_map_t t) :
+val hashMap_clear_lem
+ (#t : Type0) (self : hashMap_t t) :
Lemma
- (requires (hash_map_t_inv self))
+ (requires (hashMap_t_inv self))
(ensures (
- match hash_map_clear_fwd_back t self with
+ match hashMap_clear t self with
| Fail _ -> False
| Return hm ->
// The hash map invariant is satisfied
- hash_map_t_inv hm /\
+ hashMap_t_inv hm /\
// The hash map has a length of 0
len_s hm = 0 /\
// It contains no bindings
@@ -97,11 +97,11 @@ val hash_map_clear_fwd_back_lem
(**** [len] *)
/// [len] can't fail and returns the length (the number of elements) of the hash map
-val hash_map_len_fwd_lem (#t : Type0) (self : hash_map_t t) :
+val hashMap_len_lem (#t : Type0) (self : hashMap_t t) :
Lemma
- (requires (hash_map_t_inv self))
+ (requires (hashMap_t_inv self))
(ensures (
- match hash_map_len_fwd t self with
+ match hashMap_len t self with
| Fail _ -> False
| Return l -> l = len_s self))
@@ -114,12 +114,12 @@ val hash_map_len_fwd_lem (#t : Type0) (self : hash_map_t t) :
/// entirely encompassed by the effect of the backward function alone).
///
/// [insert'fwd_back] simply inserts a binding.
-val hash_map_insert_fwd_back_lem
- (#t : Type0) (self : hash_map_t t) (key : usize) (value : t) :
+val hashMap_insert_lem
+ (#t : Type0) (self : hashMap_t t) (key : usize) (value : t) :
Lemma
- (requires (hash_map_t_inv self))
+ (requires (hashMap_t_inv self))
(ensures (
- match hash_map_insert_fwd_back t self key value with
+ 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
@@ -128,7 +128,7 @@ val hash_map_insert_fwd_back_lem
len_s self = usize_max
| Return hm' ->
// The invariant is preserved
- hash_map_t_inv hm' /\
+ hashMap_t_inv hm' /\
// [key] maps to [value]
find_s hm' key == Some value /\
// The other bindings are preserved
@@ -145,24 +145,24 @@ val hash_map_insert_fwd_back_lem
/// [contains_key'fwd] can't fail and returns `true` if and only if there is
/// a binding for key [key]
-val hash_map_contains_key_fwd_lem
- (#t : Type0) (self : hash_map_t t) (key : usize) :
+val hashMap_contains_key_lem
+ (#t : Type0) (self : hashMap_t t) (key : usize) :
Lemma
- (requires (hash_map_t_inv self))
+ (requires (hashMap_t_inv self))
(ensures (
- match hash_map_contains_key_fwd t self key with
+ 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 hash_map_get_fwd_lem
- (#t : Type0) (self : hash_map_t t) (key : usize) :
+val hashMap_get_lem
+ (#t : Type0) (self : hashMap_t t) (key : usize) :
Lemma
- (requires (hash_map_t_inv self))
+ (requires (hashMap_t_inv self))
(ensures (
- match hash_map_get_fwd t self key, find_s self key with
+ match hashMap_get t self key, find_s self key with
| Fail _, None -> True
| Return x, Some x' -> x == x'
| _ -> False))
@@ -175,12 +175,12 @@ val hash_map_get_fwd_lem
/// 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 hash_map_get_mut_fwd_lem
- (#t : Type0) (self : hash_map_t t) (key : usize) :
+val hashMap_get_mut_lem
+ (#t : Type0) (self : hashMap_t t) (key : usize) :
Lemma
- (requires (hash_map_t_inv self))
+ (requires (hashMap_t_inv self))
(ensures (
- match hash_map_get_mut_fwd t self key, find_s self key with
+ match hashMap_get_mut t self key, find_s self key with
| Fail _, None -> True
| Return x, Some x' -> x == x'
| _ -> False))
@@ -192,11 +192,11 @@ val hash_map_get_mut_fwd_lem
/// 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 hash_map_get_mut_back_lem
- (#t : Type0) (hm : hash_map_t t) (key : usize) (ret : t) :
+val hashMap_get_mut_back_lem
+ (#t : Type0) (hm : hashMap_t t) (key : usize) (ret : t) :
Lemma
(requires (
- hash_map_t_inv hm /\
+ 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
@@ -207,14 +207,14 @@ val hash_map_get_mut_back_lem
// "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
- // [hash_map_clear_fwd_back]).
+ // [hashMap_clear]).
Some? (find_s hm key)))
(ensures (
- match hash_map_get_mut_back t hm key ret with
+ match hashMap_get_mut_back t hm key ret with
| Fail _ -> False // Can't fail
| Return hm' ->
// The invariant is preserved
- hash_map_t_inv hm' /\
+ hashMap_t_inv hm' /\
// The length is preserved
len_s hm' = len_s hm /\
// [key] maps to the update value, [ret]
@@ -228,12 +228,12 @@ val hash_map_get_mut_back_lem
/// (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 hash_map_remove_fwd_lem
- (#t : Type0) (self : hash_map_t t) (key : usize) :
+val hashMap_remove_lem
+ (#t : Type0) (self : hashMap_t t) (key : usize) :
Lemma
- (requires (hash_map_t_inv self))
+ (requires (hashMap_t_inv self))
(ensures (
- match hash_map_remove_fwd t self key with
+ match hashMap_remove t self key with
| Fail _ -> False
| Return opt_x -> opt_x == find_s self key))
@@ -243,16 +243,16 @@ val hash_map_remove_fwd_lem
/// 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 hash_map_remove_back_lem
- (#t : Type0) (self : hash_map_t t) (key : usize) :
+val hashMap_remove_back_lem
+ (#t : Type0) (self : hashMap_t t) (key : usize) :
Lemma
- (requires (hash_map_t_inv self))
+ (requires (hashMap_t_inv self))
(ensures (
- match hash_map_remove_back t self key with
+ match hashMap_remove_back t self key with
| Fail _ -> False
| Return hm' ->
// The invariant is preserved
- hash_map_t_inv self /\
+ hashMap_t_inv self /\
// The binding for [key] is not there anymore
find_s hm' key == None /\
// The other bindings are preserved
diff --git a/tests/fstar/hashmap/Primitives.fst b/tests/fstar/hashmap/Primitives.fst
index 71d75c11..3297803c 100644
--- a/tests/fstar/hashmap/Primitives.fst
+++ b/tests/fstar/hashmap/Primitives.fst
@@ -427,7 +427,7 @@ let alloc_vec_Vec_new (a : Type0) : alloc_vec_Vec a = assert_norm(length #a []
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) (x : a) : result a =
+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) =
@@ -704,6 +704,22 @@ let alloc_vec_Vec_coreopsindexIndexMutInst (t idx : Type0)
(*** 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_usize_coresliceindexSliceIndexInst a) v i ==
+ alloc_vec_Vec_index_usize v i)
+ [SMTPat (alloc_vec_Vec_index a usize (core_slice_index_usize_coresliceindexSliceIndexInst 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_usize_coresliceindexSliceIndexInst a) v i ==
+ alloc_vec_Vec_index_usize v i)
+ [SMTPat (alloc_vec_Vec_index_mut a usize (core_slice_index_usize_coresliceindexSliceIndexInst 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_usize_coresliceindexSliceIndexInst a) v i x ==