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-rw-r--r--tests/fstar/hashmap/Hashmap.Clauses.Template.fst66
-rw-r--r--tests/fstar/hashmap/Hashmap.Clauses.fst61
-rw-r--r--tests/fstar/hashmap/Hashmap.Funs.fst683
-rw-r--r--tests/fstar/hashmap/Hashmap.Properties.fst3247
-rw-r--r--tests/fstar/hashmap/Hashmap.Properties.fsti267
-rw-r--r--tests/fstar/hashmap/Hashmap.Types.fst25
-rw-r--r--tests/fstar/hashmap/Makefile47
-rw-r--r--tests/fstar/hashmap/Primitives.fst287
8 files changed, 4683 insertions, 0 deletions
diff --git a/tests/fstar/hashmap/Hashmap.Clauses.Template.fst b/tests/fstar/hashmap/Hashmap.Clauses.Template.fst
new file mode 100644
index 00000000..3e51c6f1
--- /dev/null
+++ b/tests/fstar/hashmap/Hashmap.Clauses.Template.fst
@@ -0,0 +1,66 @@
+(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
+(** [hashmap]: templates for the decreases clauses *)
+module Hashmap.Clauses.Template
+open Primitives
+open Hashmap.Types
+
+#set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
+
+(** [hashmap::HashMap::{0}::allocate_slots]: decreases clause *)
+unfold
+let hash_map_allocate_slots_decreases (t : Type0) (slots : vec (list_t t))
+ (n : usize) : nat =
+ admit ()
+
+(** [hashmap::HashMap::{0}::clear_slots]: decreases clause *)
+unfold
+let hash_map_clear_slots_decreases (t : Type0) (slots : vec (list_t t))
+ (i : usize) : nat =
+ admit ()
+
+(** [hashmap::HashMap::{0}::insert_in_list]: decreases clause *)
+unfold
+let hash_map_insert_in_list_decreases (t : Type0) (key : usize) (value : t)
+ (ls : list_t t) : nat =
+ admit ()
+
+(** [core::num::u32::{9}::MAX] *)
+let core_num_u32_max_body : result u32 = Return 4294967295
+let core_num_u32_max_c : u32 = eval_global core_num_u32_max_body
+
+(** [hashmap::HashMap::{0}::move_elements_from_list]: decreases clause *)
+unfold
+let hash_map_move_elements_from_list_decreases (t : Type0)
+ (ntable : hash_map_t t) (ls : list_t t) : nat =
+ admit ()
+
+(** [hashmap::HashMap::{0}::move_elements]: decreases clause *)
+unfold
+let hash_map_move_elements_decreases (t : Type0) (ntable : hash_map_t t)
+ (slots : vec (list_t t)) (i : usize) : nat =
+ admit ()
+
+(** [hashmap::HashMap::{0}::contains_key_in_list]: decreases clause *)
+unfold
+let hash_map_contains_key_in_list_decreases (t : Type0) (key : usize)
+ (ls : list_t t) : nat =
+ admit ()
+
+(** [hashmap::HashMap::{0}::get_in_list]: decreases clause *)
+unfold
+let hash_map_get_in_list_decreases (t : Type0) (key : usize) (ls : list_t t) :
+ nat =
+ admit ()
+
+(** [hashmap::HashMap::{0}::get_mut_in_list]: decreases clause *)
+unfold
+let hash_map_get_mut_in_list_decreases (t : Type0) (key : usize)
+ (ls : list_t t) : nat =
+ admit ()
+
+(** [hashmap::HashMap::{0}::remove_from_list]: decreases clause *)
+unfold
+let hash_map_remove_from_list_decreases (t : Type0) (key : usize)
+ (ls : list_t t) : nat =
+ admit ()
+
diff --git a/tests/fstar/hashmap/Hashmap.Clauses.fst b/tests/fstar/hashmap/Hashmap.Clauses.fst
new file mode 100644
index 00000000..4f3e37e9
--- /dev/null
+++ b/tests/fstar/hashmap/Hashmap.Clauses.fst
@@ -0,0 +1,61 @@
+(** [hashmap]: the decreases clauses *)
+module Hashmap.Clauses
+open Primitives
+open FStar.List.Tot
+open Hashmap.Types
+
+#set-options "--z3rlimit 50 --fuel 0 --ifuel 1"
+
+(** [hashmap::HashMap::allocate_slots]: decreases clause *)
+unfold
+let hash_map_allocate_slots_decreases (t : Type0) (slots : vec (list_t t))
+ (n : usize) : nat = n
+
+(** [hashmap::HashMap::clear_slots]: decreases clause *)
+unfold
+let hash_map_clear_slots_decreases (t : Type0) (slots : vec (list_t t))
+ (i : usize) : nat =
+ if i < length slots then length slots - i else 0
+
+(** [hashmap::HashMap::insert_in_list]: decreases clause *)
+unfold
+let hash_map_insert_in_list_decreases (t : Type0) (key : usize) (value : t)
+ (ls : list_t t) : list_t t =
+ ls
+
+(** [hashmap::HashMap::move_elements_from_list]: decreases clause *)
+unfold
+let hash_map_move_elements_from_list_decreases (t : Type0)
+ (ntable : hash_map_t t) (ls : list_t t) : list_t t =
+ ls
+
+(** [hashmap::HashMap::move_elements]: decreases clause *)
+unfold
+let hash_map_move_elements_decreases (t : Type0) (ntable : hash_map_t t)
+ (slots : vec (list_t t)) (i : usize) : nat =
+ if i < length slots then length slots - i else 0
+
+(** [hashmap::HashMap::contains_key_in_list]: decreases clause *)
+unfold
+let hash_map_contains_key_in_list_decreases (t : Type0) (key : usize)
+ (ls : list_t t) : list_t t =
+ ls
+
+(** [hashmap::HashMap::get_in_list]: decreases clause *)
+unfold
+let hash_map_get_in_list_decreases (t : Type0) (key : usize) (ls : list_t t) :
+ list_t t =
+ ls
+
+(** [hashmap::HashMap::get_mut_in_list]: decreases clause *)
+unfold
+let hash_map_get_mut_in_list_decreases (t : Type0) (key : usize)
+ (ls : list_t t) : list_t t =
+ ls
+
+(** [hashmap::HashMap::remove_from_list]: decreases clause *)
+unfold
+let hash_map_remove_from_list_decreases (t : Type0) (key : usize)
+ (ls : list_t t) : list_t t =
+ ls
+
diff --git a/tests/fstar/hashmap/Hashmap.Funs.fst b/tests/fstar/hashmap/Hashmap.Funs.fst
new file mode 100644
index 00000000..6e67fca4
--- /dev/null
+++ b/tests/fstar/hashmap/Hashmap.Funs.fst
@@ -0,0 +1,683 @@
+(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
+(** [hashmap]: function definitions *)
+module Hashmap.Funs
+open Primitives
+include Hashmap.Types
+include Hashmap.Clauses
+
+#set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
+
+(** [hashmap::hash_key] *)
+let hash_key_fwd (k : usize) : result usize = Return k
+
+(** [hashmap::HashMap::{0}::allocate_slots] *)
+let rec hash_map_allocate_slots_fwd
+ (t : Type0) (slots : vec (list_t t)) (n : usize) :
+ Tot (result (vec (list_t t)))
+ (decreases (hash_map_allocate_slots_decreases t slots n))
+ =
+ if n = 0
+ then Return slots
+ else
+ begin match vec_push_back (list_t t) slots ListNil with
+ | Fail -> Fail
+ | Return slots0 ->
+ begin match usize_sub n 1 with
+ | Fail -> Fail
+ | Return i ->
+ begin match hash_map_allocate_slots_fwd t slots0 i with
+ | Fail -> Fail
+ | Return v -> Return v
+ end
+ end
+ end
+
+(** [hashmap::HashMap::{0}::new_with_capacity] *)
+let hash_map_new_with_capacity_fwd
+ (t : Type0) (capacity : usize) (max_load_dividend : usize)
+ (max_load_divisor : usize) :
+ result (hash_map_t t)
+ =
+ let v = vec_new (list_t t) in
+ begin match hash_map_allocate_slots_fwd t v capacity with
+ | Fail -> Fail
+ | Return slots ->
+ begin match usize_mul capacity max_load_dividend with
+ | Fail -> Fail
+ | Return i ->
+ begin match usize_div i max_load_divisor with
+ | Fail -> Fail
+ | Return i0 ->
+ Return (Mkhash_map_t 0 (max_load_dividend, max_load_divisor) i0 slots)
+ end
+ end
+ end
+
+(** [hashmap::HashMap::{0}::new] *)
+let hash_map_new_fwd (t : Type0) : result (hash_map_t t) =
+ begin match hash_map_new_with_capacity_fwd t 32 4 5 with
+ | Fail -> Fail
+ | Return hm -> Return hm
+ end
+
+(** [hashmap::HashMap::{0}::clear_slots] *)
+let rec hash_map_clear_slots_fwd_back
+ (t : Type0) (slots : vec (list_t t)) (i : usize) :
+ Tot (result (vec (list_t t)))
+ (decreases (hash_map_clear_slots_decreases t slots i))
+ =
+ let i0 = vec_len (list_t t) slots in
+ if i < i0
+ then
+ begin match vec_index_mut_back (list_t t) slots i ListNil with
+ | Fail -> Fail
+ | Return slots0 ->
+ begin match usize_add i 1 with
+ | Fail -> Fail
+ | Return i1 ->
+ begin match hash_map_clear_slots_fwd_back t slots0 i1 with
+ | Fail -> Fail
+ | Return slots1 -> Return slots1
+ end
+ end
+ end
+ else Return slots
+
+(** [hashmap::HashMap::{0}::clear] *)
+let hash_map_clear_fwd_back
+ (t : Type0) (self : hash_map_t t) : result (hash_map_t t) =
+ begin match hash_map_clear_slots_fwd_back t self.hash_map_slots 0 with
+ | Fail -> Fail
+ | Return v ->
+ Return (Mkhash_map_t 0 self.hash_map_max_load_factor self.hash_map_max_load
+ v)
+ end
+
+(** [hashmap::HashMap::{0}::len] *)
+let hash_map_len_fwd (t : Type0) (self : hash_map_t t) : result usize =
+ Return self.hash_map_num_entries
+
+(** [hashmap::HashMap::{0}::insert_in_list] *)
+let rec hash_map_insert_in_list_fwd
+ (t : Type0) (key : usize) (value : t) (ls : list_t t) :
+ Tot (result bool)
+ (decreases (hash_map_insert_in_list_decreases t key value ls))
+ =
+ begin match ls with
+ | ListCons ckey cvalue ls0 ->
+ if ckey = key
+ then Return false
+ else
+ begin match hash_map_insert_in_list_fwd t key value ls0 with
+ | Fail -> Fail
+ | Return b -> Return b
+ end
+ | ListNil -> Return true
+ end
+
+(** [hashmap::HashMap::{0}::insert_in_list] *)
+let rec hash_map_insert_in_list_back
+ (t : Type0) (key : usize) (value : t) (ls : list_t t) :
+ Tot (result (list_t t))
+ (decreases (hash_map_insert_in_list_decreases t key value ls))
+ =
+ begin match ls with
+ | ListCons ckey cvalue ls0 ->
+ if ckey = key
+ then Return (ListCons ckey value ls0)
+ else
+ begin match hash_map_insert_in_list_back t key value ls0 with
+ | Fail -> Fail
+ | Return ls1 -> Return (ListCons ckey cvalue ls1)
+ end
+ | ListNil -> let l = ListNil in Return (ListCons key value l)
+ end
+
+(** [hashmap::HashMap::{0}::insert_no_resize] *)
+let hash_map_insert_no_resize_fwd_back
+ (t : Type0) (self : hash_map_t t) (key : usize) (value : t) :
+ result (hash_map_t t)
+ =
+ begin match hash_key_fwd key with
+ | Fail -> Fail
+ | Return hash ->
+ let i = vec_len (list_t t) self.hash_map_slots in
+ begin match usize_rem hash i with
+ | Fail -> Fail
+ | Return hash_mod ->
+ begin match vec_index_mut_fwd (list_t t) self.hash_map_slots hash_mod
+ with
+ | Fail -> Fail
+ | Return l ->
+ begin match hash_map_insert_in_list_fwd t key value l with
+ | Fail -> Fail
+ | Return inserted ->
+ if inserted
+ then
+ begin match usize_add self.hash_map_num_entries 1 with
+ | Fail -> Fail
+ | Return i0 ->
+ begin match hash_map_insert_in_list_back t key value l with
+ | Fail -> Fail
+ | Return l0 ->
+ begin match
+ vec_index_mut_back (list_t t) self.hash_map_slots hash_mod l0
+ with
+ | Fail -> Fail
+ | Return v ->
+ Return (Mkhash_map_t i0 self.hash_map_max_load_factor
+ self.hash_map_max_load v)
+ end
+ end
+ end
+ else
+ begin match hash_map_insert_in_list_back t key value l with
+ | Fail -> Fail
+ | Return l0 ->
+ begin match
+ vec_index_mut_back (list_t t) self.hash_map_slots hash_mod l0
+ with
+ | Fail -> Fail
+ | Return v ->
+ Return (Mkhash_map_t self.hash_map_num_entries
+ self.hash_map_max_load_factor self.hash_map_max_load v)
+ end
+ end
+ end
+ end
+ end
+ end
+
+(** [core::num::u32::{9}::MAX] *)
+let core_num_u32_max_body : result u32 = Return 4294967295
+let core_num_u32_max_c : u32 = eval_global core_num_u32_max_body
+
+(** [hashmap::HashMap::{0}::move_elements_from_list] *)
+let rec hash_map_move_elements_from_list_fwd_back
+ (t : Type0) (ntable : hash_map_t t) (ls : list_t t) :
+ Tot (result (hash_map_t t))
+ (decreases (hash_map_move_elements_from_list_decreases t ntable ls))
+ =
+ begin match ls with
+ | ListCons k v tl ->
+ begin match hash_map_insert_no_resize_fwd_back t ntable k v with
+ | Fail -> Fail
+ | Return ntable0 ->
+ begin match hash_map_move_elements_from_list_fwd_back t ntable0 tl with
+ | Fail -> Fail
+ | Return ntable1 -> Return ntable1
+ end
+ end
+ | ListNil -> Return ntable
+ end
+
+(** [hashmap::HashMap::{0}::move_elements] *)
+let rec hash_map_move_elements_fwd_back
+ (t : Type0) (ntable : hash_map_t t) (slots : vec (list_t t)) (i : usize) :
+ Tot (result ((hash_map_t t) & (vec (list_t t))))
+ (decreases (hash_map_move_elements_decreases t ntable slots i))
+ =
+ let i0 = vec_len (list_t t) slots in
+ if i < i0
+ then
+ begin match vec_index_mut_fwd (list_t t) slots i with
+ | Fail -> Fail
+ | Return l ->
+ let ls = mem_replace_fwd (list_t t) l ListNil in
+ begin match hash_map_move_elements_from_list_fwd_back t ntable ls with
+ | Fail -> Fail
+ | Return ntable0 ->
+ let l0 = mem_replace_back (list_t t) l ListNil in
+ begin match vec_index_mut_back (list_t t) slots i l0 with
+ | Fail -> Fail
+ | Return slots0 ->
+ begin match usize_add i 1 with
+ | Fail -> Fail
+ | Return i1 ->
+ begin match hash_map_move_elements_fwd_back t ntable0 slots0 i1
+ with
+ | Fail -> Fail
+ | Return (ntable1, slots1) -> Return (ntable1, slots1)
+ end
+ end
+ end
+ end
+ end
+ else Return (ntable, slots)
+
+(** [hashmap::HashMap::{0}::try_resize] *)
+let hash_map_try_resize_fwd_back
+ (t : Type0) (self : hash_map_t t) : result (hash_map_t t) =
+ begin match scalar_cast U32 Usize core_num_u32_max_c with
+ | Fail -> Fail
+ | Return max_usize ->
+ let capacity = vec_len (list_t t) self.hash_map_slots in
+ begin match usize_div max_usize 2 with
+ | Fail -> Fail
+ | Return n1 ->
+ let (i, i0) = self.hash_map_max_load_factor in
+ begin match usize_div n1 i with
+ | Fail -> Fail
+ | Return i1 ->
+ if capacity <= i1
+ then
+ begin match usize_mul capacity 2 with
+ | Fail -> Fail
+ | Return i2 ->
+ begin match hash_map_new_with_capacity_fwd t i2 i i0 with
+ | Fail -> Fail
+ | Return ntable ->
+ begin match
+ hash_map_move_elements_fwd_back t ntable self.hash_map_slots 0
+ with
+ | Fail -> Fail
+ | Return (ntable0, _) ->
+ Return (Mkhash_map_t self.hash_map_num_entries (i, i0)
+ ntable0.hash_map_max_load ntable0.hash_map_slots)
+ end
+ end
+ end
+ else
+ Return (Mkhash_map_t self.hash_map_num_entries (i, i0)
+ self.hash_map_max_load self.hash_map_slots)
+ end
+ end
+ end
+
+(** [hashmap::HashMap::{0}::insert] *)
+let hash_map_insert_fwd_back
+ (t : Type0) (self : hash_map_t t) (key : usize) (value : t) :
+ result (hash_map_t t)
+ =
+ begin match hash_map_insert_no_resize_fwd_back t self key value with
+ | Fail -> Fail
+ | Return self0 ->
+ begin match hash_map_len_fwd t self0 with
+ | Fail -> Fail
+ | Return i ->
+ if i > self0.hash_map_max_load
+ then
+ begin match hash_map_try_resize_fwd_back t self0 with
+ | Fail -> Fail
+ | Return self1 -> Return self1
+ end
+ else Return self0
+ end
+ end
+
+(** [hashmap::HashMap::{0}::contains_key_in_list] *)
+let rec hash_map_contains_key_in_list_fwd
+ (t : Type0) (key : usize) (ls : list_t t) :
+ Tot (result bool)
+ (decreases (hash_map_contains_key_in_list_decreases t key ls))
+ =
+ begin match ls with
+ | ListCons ckey x ls0 ->
+ if ckey = key
+ then Return true
+ else
+ begin match hash_map_contains_key_in_list_fwd t key ls0 with
+ | Fail -> Fail
+ | Return b -> Return b
+ end
+ | ListNil -> Return false
+ end
+
+(** [hashmap::HashMap::{0}::contains_key] *)
+let hash_map_contains_key_fwd
+ (t : Type0) (self : hash_map_t t) (key : usize) : result bool =
+ begin match hash_key_fwd key with
+ | Fail -> Fail
+ | Return hash ->
+ let i = vec_len (list_t t) self.hash_map_slots in
+ begin match usize_rem hash i with
+ | Fail -> Fail
+ | Return hash_mod ->
+ begin match vec_index_fwd (list_t t) self.hash_map_slots hash_mod with
+ | Fail -> Fail
+ | Return l ->
+ begin match hash_map_contains_key_in_list_fwd t key l with
+ | Fail -> Fail
+ | Return b -> Return b
+ end
+ end
+ end
+ end
+
+(** [hashmap::HashMap::{0}::get_in_list] *)
+let rec hash_map_get_in_list_fwd
+ (t : Type0) (key : usize) (ls : list_t t) :
+ Tot (result t) (decreases (hash_map_get_in_list_decreases t key ls))
+ =
+ begin match ls with
+ | ListCons ckey cvalue ls0 ->
+ if ckey = key
+ then Return cvalue
+ else
+ begin match hash_map_get_in_list_fwd t key ls0 with
+ | Fail -> Fail
+ | Return x -> Return x
+ end
+ | ListNil -> Fail
+ end
+
+(** [hashmap::HashMap::{0}::get] *)
+let hash_map_get_fwd
+ (t : Type0) (self : hash_map_t t) (key : usize) : result t =
+ begin match hash_key_fwd key with
+ | Fail -> Fail
+ | Return hash ->
+ let i = vec_len (list_t t) self.hash_map_slots in
+ begin match usize_rem hash i with
+ | Fail -> Fail
+ | Return hash_mod ->
+ begin match vec_index_fwd (list_t t) self.hash_map_slots hash_mod with
+ | Fail -> Fail
+ | Return l ->
+ begin match hash_map_get_in_list_fwd t key l with
+ | Fail -> Fail
+ | Return x -> Return x
+ end
+ end
+ end
+ end
+
+(** [hashmap::HashMap::{0}::get_mut_in_list] *)
+let rec hash_map_get_mut_in_list_fwd
+ (t : Type0) (key : usize) (ls : list_t t) :
+ Tot (result t) (decreases (hash_map_get_mut_in_list_decreases t key ls))
+ =
+ begin match ls with
+ | ListCons ckey cvalue ls0 ->
+ if ckey = key
+ then Return cvalue
+ else
+ begin match hash_map_get_mut_in_list_fwd t key ls0 with
+ | Fail -> Fail
+ | Return x -> Return x
+ end
+ | ListNil -> Fail
+ end
+
+(** [hashmap::HashMap::{0}::get_mut_in_list] *)
+let rec hash_map_get_mut_in_list_back
+ (t : Type0) (key : usize) (ls : list_t t) (ret : t) :
+ Tot (result (list_t t))
+ (decreases (hash_map_get_mut_in_list_decreases t key ls))
+ =
+ begin match ls with
+ | ListCons ckey cvalue ls0 ->
+ if ckey = key
+ then Return (ListCons ckey ret ls0)
+ else
+ begin match hash_map_get_mut_in_list_back t key ls0 ret with
+ | Fail -> Fail
+ | Return ls1 -> Return (ListCons ckey cvalue ls1)
+ end
+ | ListNil -> Fail
+ end
+
+(** [hashmap::HashMap::{0}::get_mut] *)
+let hash_map_get_mut_fwd
+ (t : Type0) (self : hash_map_t t) (key : usize) : result t =
+ begin match hash_key_fwd key with
+ | Fail -> Fail
+ | Return hash ->
+ let i = vec_len (list_t t) self.hash_map_slots in
+ begin match usize_rem hash i with
+ | Fail -> Fail
+ | Return hash_mod ->
+ begin match vec_index_mut_fwd (list_t t) self.hash_map_slots hash_mod
+ with
+ | Fail -> Fail
+ | Return l ->
+ begin match hash_map_get_mut_in_list_fwd t key l with
+ | Fail -> Fail
+ | Return x -> Return x
+ end
+ end
+ end
+ end
+
+(** [hashmap::HashMap::{0}::get_mut] *)
+let hash_map_get_mut_back
+ (t : Type0) (self : hash_map_t t) (key : usize) (ret : t) :
+ result (hash_map_t t)
+ =
+ begin match hash_key_fwd key with
+ | Fail -> Fail
+ | Return hash ->
+ let i = vec_len (list_t t) self.hash_map_slots in
+ begin match usize_rem hash i with
+ | Fail -> Fail
+ | Return hash_mod ->
+ begin match vec_index_mut_fwd (list_t t) self.hash_map_slots hash_mod
+ with
+ | Fail -> Fail
+ | Return l ->
+ begin match hash_map_get_mut_in_list_back t key l ret with
+ | Fail -> Fail
+ | Return l0 ->
+ begin match
+ vec_index_mut_back (list_t t) self.hash_map_slots hash_mod l0 with
+ | Fail -> Fail
+ | Return v ->
+ Return (Mkhash_map_t self.hash_map_num_entries
+ self.hash_map_max_load_factor self.hash_map_max_load v)
+ end
+ end
+ end
+ end
+ end
+
+(** [hashmap::HashMap::{0}::remove_from_list] *)
+let rec hash_map_remove_from_list_fwd
+ (t : Type0) (key : usize) (ls : list_t t) :
+ Tot (result (option t))
+ (decreases (hash_map_remove_from_list_decreases t key ls))
+ =
+ begin match ls with
+ | ListCons ckey x tl ->
+ if ckey = key
+ then
+ let mv_ls = mem_replace_fwd (list_t t) (ListCons ckey x tl) ListNil in
+ begin match mv_ls with
+ | ListCons i cvalue tl0 -> Return (Some cvalue)
+ | ListNil -> Fail
+ end
+ else
+ begin match hash_map_remove_from_list_fwd t key tl with
+ | Fail -> Fail
+ | Return opt -> Return opt
+ end
+ | ListNil -> Return None
+ end
+
+(** [hashmap::HashMap::{0}::remove_from_list] *)
+let rec hash_map_remove_from_list_back
+ (t : Type0) (key : usize) (ls : list_t t) :
+ Tot (result (list_t t))
+ (decreases (hash_map_remove_from_list_decreases t key ls))
+ =
+ begin match ls with
+ | ListCons ckey x tl ->
+ if ckey = key
+ then
+ let mv_ls = mem_replace_fwd (list_t t) (ListCons ckey x tl) ListNil in
+ begin match mv_ls with
+ | ListCons i cvalue tl0 -> Return tl0
+ | ListNil -> Fail
+ end
+ else
+ begin match hash_map_remove_from_list_back t key tl with
+ | Fail -> Fail
+ | Return tl0 -> Return (ListCons ckey x tl0)
+ end
+ | ListNil -> Return ListNil
+ end
+
+(** [hashmap::HashMap::{0}::remove] *)
+let hash_map_remove_fwd
+ (t : Type0) (self : hash_map_t t) (key : usize) : result (option t) =
+ begin match hash_key_fwd key with
+ | Fail -> Fail
+ | Return hash ->
+ let i = vec_len (list_t t) self.hash_map_slots in
+ begin match usize_rem hash i with
+ | Fail -> Fail
+ | Return hash_mod ->
+ begin match vec_index_mut_fwd (list_t t) self.hash_map_slots hash_mod
+ with
+ | Fail -> Fail
+ | Return l ->
+ begin match hash_map_remove_from_list_fwd t key l with
+ | Fail -> Fail
+ | Return x ->
+ begin match x with
+ | None -> Return None
+ | Some x0 ->
+ begin match usize_sub self.hash_map_num_entries 1 with
+ | Fail -> Fail
+ | Return _ -> Return (Some x0)
+ end
+ end
+ end
+ end
+ end
+ end
+
+(** [hashmap::HashMap::{0}::remove] *)
+let hash_map_remove_back
+ (t : Type0) (self : hash_map_t t) (key : usize) : result (hash_map_t t) =
+ begin match hash_key_fwd key with
+ | Fail -> Fail
+ | Return hash ->
+ let i = vec_len (list_t t) self.hash_map_slots in
+ begin match usize_rem hash i with
+ | Fail -> Fail
+ | Return hash_mod ->
+ begin match vec_index_mut_fwd (list_t t) self.hash_map_slots hash_mod
+ with
+ | Fail -> Fail
+ | Return l ->
+ begin match hash_map_remove_from_list_fwd t key l with
+ | Fail -> Fail
+ | Return x ->
+ begin match x with
+ | None ->
+ begin match hash_map_remove_from_list_back t key l with
+ | Fail -> Fail
+ | Return l0 ->
+ begin match
+ vec_index_mut_back (list_t t) self.hash_map_slots hash_mod l0
+ with
+ | Fail -> Fail
+ | Return v ->
+ Return (Mkhash_map_t self.hash_map_num_entries
+ self.hash_map_max_load_factor self.hash_map_max_load v)
+ end
+ end
+ | Some x0 ->
+ begin match usize_sub self.hash_map_num_entries 1 with
+ | Fail -> Fail
+ | Return i0 ->
+ begin match hash_map_remove_from_list_back t key l with
+ | Fail -> Fail
+ | Return l0 ->
+ begin match
+ vec_index_mut_back (list_t t) self.hash_map_slots hash_mod l0
+ with
+ | Fail -> Fail
+ | Return v ->
+ Return (Mkhash_map_t i0 self.hash_map_max_load_factor
+ self.hash_map_max_load v)
+ end
+ end
+ end
+ end
+ end
+ end
+ end
+ end
+
+(** [hashmap::test1] *)
+let test1_fwd : result unit =
+ begin match hash_map_new_fwd u64 with
+ | Fail -> Fail
+ | Return hm ->
+ begin match hash_map_insert_fwd_back u64 hm 0 42 with
+ | Fail -> Fail
+ | Return hm0 ->
+ begin match hash_map_insert_fwd_back u64 hm0 128 18 with
+ | Fail -> Fail
+ | Return hm1 ->
+ begin match hash_map_insert_fwd_back u64 hm1 1024 138 with
+ | Fail -> Fail
+ | Return hm2 ->
+ begin match hash_map_insert_fwd_back u64 hm2 1056 256 with
+ | Fail -> Fail
+ | Return hm3 ->
+ begin match hash_map_get_fwd u64 hm3 128 with
+ | Fail -> Fail
+ | Return i ->
+ if not (i = 18)
+ then Fail
+ else
+ begin match hash_map_get_mut_back u64 hm3 1024 56 with
+ | Fail -> Fail
+ | Return hm4 ->
+ begin match hash_map_get_fwd u64 hm4 1024 with
+ | Fail -> Fail
+ | Return i0 ->
+ if not (i0 = 56)
+ then Fail
+ else
+ begin match hash_map_remove_fwd u64 hm4 1024 with
+ | Fail -> Fail
+ | Return x ->
+ begin match x with
+ | None -> Fail
+ | Some x0 ->
+ if not (x0 = 56)
+ then Fail
+ else
+ begin match hash_map_remove_back u64 hm4 1024 with
+ | Fail -> Fail
+ | Return hm5 ->
+ begin match hash_map_get_fwd u64 hm5 0 with
+ | Fail -> Fail
+ | Return i1 ->
+ if not (i1 = 42)
+ then Fail
+ else
+ begin match hash_map_get_fwd u64 hm5 128 with
+ | Fail -> Fail
+ | Return i2 ->
+ if not (i2 = 18)
+ then Fail
+ else
+ begin match hash_map_get_fwd u64 hm5 1056
+ with
+ | Fail -> Fail
+ | Return i3 ->
+ if not (i3 = 256)
+ then Fail
+ else Return ()
+ end
+ end
+ end
+ end
+ end
+ end
+ end
+ end
+ end
+ end
+ end
+ end
+ end
+ end
+
+(** Unit test for [hashmap::test1] *)
+let _ = assert_norm (test1_fwd = Return ())
+
diff --git a/tests/fstar/hashmap/Hashmap.Properties.fst b/tests/fstar/hashmap/Hashmap.Properties.fst
new file mode 100644
index 00000000..21a46c73
--- /dev/null
+++ b/tests/fstar/hashmap/Hashmap.Properties.fst
@@ -0,0 +1,3247 @@
+(** Properties about the hashmap *)
+module Hashmap.Properties
+open Primitives
+open FStar.List.Tot
+open FStar.Mul
+open Hashmap.Types
+open Hashmap.Clauses
+open Hashmap.Funs
+
+#set-options "--z3rlimit 50 --fuel 0 --ifuel 1"
+
+let _align_fsti = ()
+
+/// The proofs:
+/// ===========
+///
+/// The proof strategy is to do exactly as with Low* proofs (we initially tried to
+/// prove more properties in one go, but it was a mistake):
+/// - prove that, under some preconditions, the low-level functions translated
+/// from Rust refine some higher-level functions
+/// - do functional proofs about those high-level functions to prove interesting
+/// properties about the hash map operations, and invariant preservation
+/// - combine everything
+///
+/// The fact that we work in a pure setting allows us to be more modular than when
+/// working with effects. For instance we can do a case disjunction (see the proofs
+/// for insert, which study the cases where the key is already/not in the hash map
+/// in separate proofs - we had initially tried to do them in one step: it is doable
+/// but requires some work, and the F* response time quickly becomes annoying while
+/// making progress, so we split them). We can also easily prove a refinement lemma,
+/// study the model, *then* combine those to also prove that the low-level function
+/// preserves the invariants, rather than do everything at once as is usually the
+/// case when doing intrinsic proofs with effects (I remember that having to prove
+/// invariants in one go *and* a refinement step, even small, can be extremely
+/// difficult in Low*).
+
+
+(*** Utilities *)
+
+/// We need many small helpers and lemmas, mostly about lists (and the ones we list
+/// here are not in the standard F* library).
+
+val index_append_lem (#a : Type0) (ls0 ls1 : list a) (i : nat{i < length ls0 + length ls1}) :
+ Lemma (
+ (i < length ls0 ==> index (ls0 @ ls1) i == index ls0 i) /\
+ (i >= length ls0 ==> index (ls0 @ ls1) i == index ls1 (i - length ls0)))
+ [SMTPat (index (ls0 @ ls1) i)]
+
+#push-options "--fuel 1"
+let rec index_append_lem #a ls0 ls1 i =
+ match ls0 with
+ | [] -> ()
+ | x :: ls0' ->
+ if i = 0 then ()
+ else index_append_lem ls0' ls1 (i-1)
+#pop-options
+
+val index_map_lem (#a #b: Type0) (f : a -> Tot b) (ls : list a)
+ (i : nat{i < length ls}) :
+ Lemma (
+ index (map f ls) i == f (index ls i))
+ [SMTPat (index (map f ls) i)]
+
+#push-options "--fuel 1"
+let rec index_map_lem #a #b f ls i =
+ match ls with
+ | [] -> ()
+ | x :: ls' ->
+ if i = 0 then ()
+ else index_map_lem f ls' (i-1)
+#pop-options
+
+val for_all_append (#a : Type0) (f : a -> Tot bool) (ls0 ls1 : list a) :
+ Lemma (for_all f (ls0 @ ls1) = (for_all f ls0 && for_all f ls1))
+
+#push-options "--fuel 1"
+let rec for_all_append #a f ls0 ls1 =
+ match ls0 with
+ | [] -> ()
+ | x :: ls0' ->
+ for_all_append f ls0' ls1
+#pop-options
+
+/// Filter a list, stopping after we removed one element
+val filter_one (#a : Type) (f : a -> bool) (ls : list a) : list a
+
+let rec filter_one #a f ls =
+ match ls with
+ | [] -> []
+ | x :: ls' -> if f x then x :: filter_one f ls' else ls'
+
+val find_append (#a : Type) (f : a -> bool) (ls0 ls1 : list a) :
+ Lemma (
+ find f (ls0 @ ls1) ==
+ begin match find f ls0 with
+ | Some x -> Some x
+ | None -> find f ls1
+ end)
+
+#push-options "--fuel 1"
+let rec find_append #a f ls0 ls1 =
+ match ls0 with
+ | [] -> ()
+ | x :: ls0' ->
+ if f x then
+ begin
+ assert(ls0 @ ls1 == x :: (ls0' @ ls1));
+ assert(find f (ls0 @ ls1) == find f (x :: (ls0' @ ls1)));
+ // Why do I have to do this?! Is it because of subtyping??
+ assert(
+ match find f (ls0 @ ls1) with
+ | Some x' -> x' == x
+ | None -> False)
+ end
+ else find_append f ls0' ls1
+#pop-options
+
+val length_flatten_update :
+ #a:Type
+ -> ls:list (list a)
+ -> i:nat{i < length ls}
+ -> x:list a ->
+ Lemma (
+ // We want this property:
+ // ```
+ // length (flatten (list_update ls i x)) =
+ // length (flatten ls) - length (index ls i) + length x
+ // ```
+ length (flatten (list_update ls i x)) + length (index ls i) =
+ length (flatten ls) + length x)
+
+#push-options "--fuel 1"
+let rec length_flatten_update #a ls i x =
+ match ls with
+ | x' :: ls' ->
+ assert(flatten ls == x' @ flatten ls'); // Triggers patterns
+ assert(length (flatten ls) == length x' + length (flatten ls'));
+ if i = 0 then
+ begin
+ let ls1 = x :: ls' in
+ assert(list_update ls i x == ls1);
+ assert(flatten ls1 == x @ flatten ls'); // Triggers patterns
+ assert(length (flatten ls1) == length x + length (flatten ls'));
+ ()
+ end
+ else
+ begin
+ length_flatten_update ls' (i-1) x;
+ let ls1 = x' :: list_update ls' (i-1) x in
+ assert(flatten ls1 == x' @ flatten (list_update ls' (i-1) x)) // Triggers patterns
+ end
+#pop-options
+
+val length_flatten_index :
+ #a:Type
+ -> ls:list (list a)
+ -> i:nat{i < length ls} ->
+ Lemma (
+ length (flatten ls) >= length (index ls i))
+
+#push-options "--fuel 1"
+let rec length_flatten_index #a ls i =
+ match ls with
+ | x' :: ls' ->
+ assert(flatten ls == x' @ flatten ls'); // Triggers patterns
+ assert(length (flatten ls) == length x' + length (flatten ls'));
+ if i = 0 then ()
+ else length_flatten_index ls' (i-1)
+#pop-options
+
+val forall_index_equiv_list_for_all
+ (#a : Type) (pred : a -> Tot bool) (ls : list a) :
+ Lemma ((forall (i:nat{i < length ls}). pred (index ls i)) <==> for_all pred ls)
+
+#push-options "--fuel 1"
+let rec forall_index_equiv_list_for_all pred ls =
+ match ls with
+ | [] -> ()
+ | x :: ls' ->
+ assert(forall (i:nat{i < length ls'}). index ls' i == index ls (i+1));
+ assert(forall (i:nat{0 < i /\ i < length ls}). index ls i == index ls' (i-1));
+ assert(index ls 0 == x);
+ forall_index_equiv_list_for_all pred ls'
+#pop-options
+
+val find_update:
+ #a:Type
+ -> f:(a -> Tot bool)
+ -> ls:list a
+ -> x:a
+ -> ls':list a{length ls' == length ls}
+#push-options "--fuel 1"
+let rec find_update #a f ls x =
+ match ls with
+ | [] -> []
+ | hd::tl ->
+ if f hd then x :: tl else hd :: find_update f tl x
+#pop-options
+
+val pairwise_distinct : #a:eqtype -> ls:list a -> Tot bool
+let rec pairwise_distinct (#a : eqtype) (ls : list a) : Tot bool =
+ match ls with
+ | [] -> true
+ | x :: ls' -> List.Tot.for_all (fun y -> x <> y) ls' && pairwise_distinct ls'
+
+val pairwise_rel : #a:Type -> pred:(a -> a -> Tot bool) -> ls:list a -> Tot bool
+let rec pairwise_rel #a pred ls =
+ match ls with
+ | [] -> true
+ | x :: ls' ->
+ for_all (pred x) ls' && pairwise_rel pred ls'
+
+#push-options "--fuel 1"
+let rec flatten_append (#a : Type) (l1 l2: list (list a)) :
+ Lemma (flatten (l1 @ l2) == flatten l1 @ flatten l2) =
+ match l1 with
+ | [] -> ()
+ | x :: l1' ->
+ flatten_append l1' l2;
+ append_assoc x (flatten l1') (flatten l2)
+#pop-options
+
+/// We don't use anonymous functions as parameters to other functions, but rather
+/// introduce auxiliary functions instead: otherwise we can't reason (because
+/// F*'s encoding to the SMT is imprecise for functions)
+let fst_is_disctinct (#a : eqtype) (#b : Type0) (p0 : a & b) (p1 : a & b) : Type0 =
+ fst p0 <> fst p1
+
+(*** Lemmas about Primitives *)
+/// TODO: move those lemmas
+
+// TODO: rename to 'insert'?
+val list_update_index_dif_lem
+ (#a : Type0) (ls : list a) (i : nat{i < length ls}) (x : a)
+ (j : nat{j < length ls}) :
+ Lemma (requires (j <> i))
+ (ensures (index (list_update ls i x) j == index ls j))
+ [SMTPat (index (list_update ls i x) j)]
+
+#push-options "--fuel 1"
+let rec list_update_index_dif_lem #a ls i x j =
+ match ls with
+ | x' :: ls ->
+ if i = 0 then ()
+ else if j = 0 then ()
+ else
+ list_update_index_dif_lem ls (i-1) x (j-1)
+#pop-options
+
+val map_list_update_lem
+ (#a #b: Type0) (f : a -> Tot b)
+ (ls : list a) (i : nat{i < length ls}) (x : a) :
+ Lemma (list_update (map f ls) i (f x) == map f (list_update ls i x))
+ [SMTPat (list_update (map f ls) i (f x))]
+
+#push-options "--fuel 1"
+let rec map_list_update_lem #a #b f ls i x =
+ match ls with
+ | x' :: ls' ->
+ if i = 0 then ()
+ else map_list_update_lem f ls' (i-1) x
+#pop-options
+
+(*** Invariants, models *)
+
+(**** Internals *)
+/// The following invariants, models, representation functions... are mostly
+/// for the purpose of the proofs.
+
+let is_pos_usize (n : nat) : Type0 = 0 < n /\ n <= usize_max
+type pos_usize = x:usize{x > 0}
+
+type binding (t : Type0) = key & t
+
+type slots_t (t : Type0) = vec (list_t t)
+
+/// We represent hash maps as associative lists
+type assoc_list (t : Type0) = list (binding t)
+
+/// Representation function for [list_t]
+let rec list_t_v (#t : Type0) (ls : list_t t) : assoc_list t =
+ match ls with
+ | ListNil -> []
+ | ListCons k v tl -> (k,v) :: list_t_v tl
+
+let list_t_len (#t : Type0) (ls : list_t t) : nat = length (list_t_v ls)
+let list_t_index (#t : Type0) (ls : list_t t) (i : nat{i < list_t_len ls}) : binding t =
+ index (list_t_v ls) i
+
+type slot_s (t : Type0) = list (binding t)
+type slots_s (t : Type0) = list (slot_s t)
+
+type slot_t (t : Type0) = list_t t
+let slot_t_v #t = list_t_v #t
+
+/// Representation function for the slots.
+let slots_t_v (#t : Type0) (slots : slots_t t) : slots_s t =
+ map slot_t_v slots
+
+/// Representation function for the slots, seen as an associative list.
+let slots_t_al_v (#t : Type0) (slots : slots_t t) : assoc_list t =
+ flatten (map list_t_v slots)
+
+/// High-level type for the hash-map, seen as a list of associative lists (one
+/// list per slot). This is the representation we use most, internally. Note that
+/// we later introduce a [map_s] representation, which is the one used in the
+/// lemmas shown to the user.
+type hash_map_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)}
+
+/// 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 [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)
+
+// '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)}
+
+let hash_key (k : key) : hash =
+ Return?.v (hash_key_fwd k)
+
+let hash_mod_key (k : key) (len : usize{len > 0}) : hash =
+ (hash_key k) % len
+
+let not_same_key (#t : Type0) (k : key) (b : binding t) : bool = fst b <> k
+let same_key (#t : Type0) (k : key) (b : binding t) : bool = fst b = k
+
+// We take a [nat] instead of a [hash] on purpose
+let same_hash_mod_key (#t : Type0) (len : usize{len > 0}) (h : nat) (b : binding t) : bool =
+ hash_mod_key (fst b) len = h
+
+let binding_neq (#t : Type0) (b0 b1 : binding t) : bool = fst b0 <> fst b1
+
+let hash_map_t_len_s (#t : Type0) (hm : hash_map_t t) : nat =
+ hm.hash_map_num_entries
+
+let assoc_list_find (#t : Type0) (k : key) (slot : assoc_list t) : option t =
+ match find (same_key k) slot with
+ | None -> None
+ | Some (_, v) -> Some v
+
+let slot_s_find (#t : Type0) (k : key) (slot : list (binding t)) : option t =
+ assoc_list_find k slot
+
+let slot_t_find_s (#t : Type0) (k : key) (slot : list_t t) : option t =
+ slot_s_find k (slot_t_v slot)
+
+// This is a simpler version of the "find" function, which captures the essence
+// of what happens and operates on [hash_map_s].
+let hash_map_s_find
+ (#t : Type0) (hm : hash_map_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) :
+ nat =
+ length (flatten hm)
+
+// Same as above, but operates on [hash_map_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
+// 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 i = hash_mod_key k (length slots) in
+ let slot = index slots i in
+ slot_t_find_s k slot
+
+/// Invariants for the slots
+
+let slot_s_inv
+ (#t : Type0) (len : usize{len > 0}) (i : usize) (slot : list (binding t)) : bool =
+ // All the bindings are in the proper slot
+ for_all (same_hash_mod_key len i) slot &&
+ // All the keys are pairwise distinct
+ pairwise_rel binding_neq slot
+
+let slot_t_inv (#t : Type0) (len : usize{len > 0}) (i : usize) (slot : list_t t) : bool =
+ slot_s_inv len i (slot_t_v slot)
+
+let slots_s_inv (#t : Type0) (slots : slots_s t{length slots <= usize_max}) : Type0 =
+ forall(i:nat{i < length slots}).
+ {:pattern index slots i}
+ slot_s_inv (length slots) i (index slots i)
+
+// At some point we tried to rewrite this in terms of [slots_s_inv]. However it
+// made a lot of proofs fail because those proofs relied on the [index_map_lem]
+// pattern. We tried writing others lemmas with patterns (like [slots_s_inv]
+// implies [slots_t_inv]) but it didn't succeed, so we keep things as they are.
+let slots_t_inv (#t : Type0) (slots : slots_t t{length slots <= usize_max}) : Type0 =
+ forall(i:nat{i < length slots}).
+ {:pattern index slots i}
+ slot_t_inv (length slots) i (index slots i)
+
+let hash_map_s_inv (#t : Type0) (hm : hash_map_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
+ // [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 /\
+ // Slots invariant
+ slots_t_inv hm.hash_map_slots /\
+ // The capacity must be > 0 (otherwise we can't resize, because we
+ // multiply the capacity by two!)
+ length hm.hash_map_slots > 0 /\
+ // Load computation
+ begin
+ let capacity = length hm.hash_map_slots in
+ let (dividend, divisor) = hm.hash_map_max_load_factor in
+ 0 < dividend /\ dividend < divisor /\
+ capacity * dividend >= divisor /\
+ hm.hash_map_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
+
+/// 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 =
+ // Base invariant
+ hash_map_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
+ 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
+
+/// 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
+
+(*** Overloading *)
+
+let hash_map_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))
+ (ensures (slots_t_inv slots))
+
+#push-options "--fuel 1"
+let slots_t_all_nil_inv_lem #t slots = ()
+#pop-options
+
+val slots_t_al_v_all_nil_is_empty_lem
+ (#t : Type0) (slots : vec (list_t t)) :
+ Lemma (requires (forall (i:nat{i < length slots}). index slots i == ListNil))
+ (ensures (slots_t_al_v slots == []))
+
+#push-options "--fuel 1"
+let rec slots_t_al_v_all_nil_is_empty_lem #t slots =
+ match slots with
+ | [] -> ()
+ | s :: slots' ->
+ assert(forall (i:nat{i < length slots'}). index slots' i == index slots (i+1));
+ slots_t_al_v_all_nil_is_empty_lem #t slots';
+ assert(slots_t_al_v slots == list_t_v s @ slots_t_al_v slots');
+ assert(slots_t_al_v slots == list_t_v s);
+ assert(index slots 0 == ListNil)
+#pop-options
+
+/// [allocate_slots]
+val hash_map_allocate_slots_fwd_lem
+ (t : Type0) (slots : vec (list_t t)) (n : usize) :
+ Lemma
+ (requires (length slots + n <= usize_max))
+ (ensures (
+ match hash_map_allocate_slots_fwd 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_decreases t slots n))
+
+#push-options "--fuel 1"
+let rec hash_map_allocate_slots_fwd_lem t slots n =
+ begin match n with
+ | 0 -> ()
+ | _ ->
+ begin match vec_push_back (list_t t) slots ListNil 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
+ | 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)
+ end
+ end
+ end
+ end
+#pop-options
+
+(*** new_with_capacity *)
+/// Under proper conditions, [new_with_capacity] doesn't fail and returns an empty hash map.
+val hash_map_new_with_capacity_fwd_lem
+ (t : Type0) (capacity : usize)
+ (max_load_dividend : usize) (max_load_divisor : usize) :
+ Lemma
+ (requires (
+ 0 < max_load_dividend /\
+ max_load_dividend < max_load_divisor /\
+ 0 < capacity /\
+ capacity * max_load_dividend >= max_load_divisor /\
+ capacity * max_load_dividend <= usize_max))
+ (ensures (
+ match hash_map_new_with_capacity_fwd t capacity max_load_dividend max_load_divisor with
+ | Fail -> False
+ | Return hm ->
+ // The hash map invariant is satisfied
+ hash_map_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 /\
+ // 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 /\
+ // The hash map has 0 values
+ hash_map_t_len_s hm = 0 /\
+ // It contains no bindings
+ (forall k. hash_map_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)))
+
+#push-options "--z3rlimit 50 --fuel 1"
+let hash_map_new_with_capacity_fwd_lem (t : Type0) (capacity : usize)
+ (max_load_dividend : usize) (max_load_divisor : usize) =
+ let v = 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
+ | Fail -> assert(False)
+ | Return v0 ->
+ begin match usize_mul capacity max_load_dividend with
+ | Fail -> assert(False)
+ | Return i ->
+ begin match usize_div i max_load_divisor with
+ | Fail -> assert(False)
+ | Return i0 ->
+ let hm = Mkhash_map_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
+ end
+ end
+ end
+#pop-options
+
+(*** new *)
+
+/// [new] doesn't fail and returns an empty hash map
+val hash_map_new_fwd_lem_aux (t : Type0) :
+ Lemma
+ (ensures (
+ match hash_map_new_fwd t with
+ | Fail -> False
+ | Return hm ->
+ // The hash map invariant is satisfied
+ hash_map_t_inv hm /\
+ // The hash map has 0 values
+ hash_map_t_len_s hm = 0 /\
+ // It contains no bindings
+ (forall k. hash_map_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
+ | 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
+
+(*** clear_slots *)
+/// [clear_slots] doesn't fail and simply clears the slots starting at index i
+#push-options "--fuel 1"
+let rec hash_map_clear_slots_fwd_back_lem
+ (t : Type0) (slots : vec (list_t t)) (i : usize) :
+ Lemma
+ (ensures (
+ match hash_map_clear_slots_fwd_back 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_slots_decreases t slots i))
+ =
+ let i0 = 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
+ | Fail -> ()
+ | Return v ->
+ begin match usize_add i 1 with
+ | Fail -> ()
+ | Return i1 ->
+ hash_map_clear_slots_fwd_back_lem t v i1;
+ begin match hash_map_clear_slots_fwd_back 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)
+ end
+ end
+ end
+ else ()
+#pop-options
+
+(*** clear *)
+/// [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) :
+ Lemma
+ (requires (hash_map_t_base_inv self))
+ (ensures (
+ match hash_map_clear_fwd_back t self with
+ | Fail -> False
+ | Return hm ->
+ // The hash map invariant is satisfied
+ hash_map_t_base_inv hm /\
+ // We preserved the parameters
+ hash_map_t_same_params hm self /\
+ // The hash map has 0 values
+ hash_map_t_len_s hm = 0 /\
+ // It contains no bindings
+ (forall k. hash_map_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_slots_fwd_back_lem t v 0;
+ begin match hash_map_clear_slots_fwd_back 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)
+ end
+#pop-options
+
+let hash_map_clear_fwd_back_lem #t self = hash_map_clear_fwd_back_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 = ()
+
+
+(*** 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
+ (t : Type0) (key : usize) (value : t) (ls : list_t t) :
+ Lemma
+ (ensures (
+ match hash_map_insert_in_list_fwd t key value ls with
+ | Fail -> False
+ | Return b ->
+ b <==> (slot_t_find_s key ls == None)))
+ (decreases (hash_map_insert_in_list_decreases t key value ls))
+
+#push-options "--fuel 1"
+let rec hash_map_insert_in_list_fwd_lem t key value ls =
+ begin match ls with
+ | ListCons 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
+ | Fail -> ()
+ | Return b0 -> ()
+ end
+ | ListNil ->
+ assert(list_t_v ls == []);
+ assert_norm(find (same_key #t key) [] == None)
+ end
+#pop-options
+
+(**** insert_in_list'back *)
+
+/// The proofs about [insert_in_list] backward are easier to do in several steps:
+/// extrinsic proofs to the rescue!
+/// We first prove that [insert_in_list] refines the function we wrote above, then
+/// use this function to prove the invariants, etc.
+
+/// We write a helper which "captures" what [insert_in_list] does.
+/// We then reason about this helper to prove the high-level properties we want
+/// (functional properties, preservation of invariants, etc.).
+let hash_map_insert_in_list_s
+ (#t : Type0) (key : usize) (value : t) (ls : list (binding t)) :
+ list (binding t) =
+ // Check if there is already a binding for the key
+ match find (same_key key) ls with
+ | None ->
+ // No binding: append the binding to the end
+ ls @ [(key,value)]
+ | Some _ ->
+ // There is already a binding: update it
+ find_update (same_key key) ls (key,value)
+
+/// [insert_in_list]: if the key is not in the map, appends a new bindings (functional version)
+val hash_map_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
+ | Fail -> False
+ | Return ls' ->
+ list_t_v ls' == list_t_v ls @ [(key,value)]))
+ (decreases (hash_map_insert_in_list_decreases t key value ls))
+
+#push-options "--fuel 1"
+let rec hash_map_insert_in_list_back_lem_append_s t key value ls =
+ begin match ls with
+ | ListCons 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
+ | Fail -> ()
+ | Return l -> ()
+ end
+ | ListNil -> ()
+ 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
+ (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
+ | 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_decreases t key value ls))
+
+#push-options "--fuel 1"
+let rec hash_map_insert_in_list_back_lem_update_s t key value ls =
+ begin match ls with
+ | ListCons 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
+ | Fail -> ()
+ | Return l -> ()
+ end
+ | ListNil -> ()
+ end
+#pop-options
+
+/// Put everything together
+val hash_map_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
+ | Fail -> False
+ | Return ls' ->
+ list_t_v ls' == hash_map_insert_in_list_s key value (list_t_v ls)))
+
+let hash_map_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
+
+(**** 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].
+///
+/// Note that in F* we can't have recursive proofs inside of other proofs, contrary
+/// to Coq, which makes it a bit cumbersome to prove auxiliary results like the
+/// following ones...
+
+(** Auxiliary lemmas: append case *)
+
+val slot_t_v_for_all_binding_neq_append_lem
+ (t : Type0) (key : usize) (value : t) (ls : list (binding t)) (b : binding t) :
+ Lemma
+ (requires (
+ fst b <> key /\
+ for_all (binding_neq b) ls /\
+ slot_s_find key ls == None))
+ (ensures (
+ for_all (binding_neq b) (ls @ [(key,value)])))
+
+#push-options "--fuel 1"
+let rec slot_t_v_for_all_binding_neq_append_lem t key value ls b =
+ match ls with
+ | [] -> ()
+ | (ck, cv) :: cls ->
+ slot_t_v_for_all_binding_neq_append_lem t key value cls b
+#pop-options
+
+val slot_s_inv_not_find_append_end_inv_lem
+ (t : Type0) (len : usize{len > 0}) (key : usize) (value : t) (ls : list (binding t)) :
+ Lemma
+ (requires (
+ slot_s_inv len (hash_mod_key key len) ls /\
+ slot_s_find key ls == None))
+ (ensures (
+ let ls' = ls @ [(key,value)] in
+ slot_s_inv len (hash_mod_key key len) ls' /\
+ (slot_s_find key ls' == Some value) /\
+ (forall k'. k' <> key ==> slot_s_find k' ls' == slot_s_find k' ls)))
+
+#push-options "--fuel 1"
+let rec slot_s_inv_not_find_append_end_inv_lem t len key value ls =
+ match ls with
+ | [] -> ()
+ | (ck, cv) :: cls ->
+ slot_s_inv_not_find_append_end_inv_lem t len key value cls;
+ let h = hash_mod_key key len in
+ let ls' = ls @ [(key,value)] in
+ assert(for_all (same_hash_mod_key len h) ls');
+ slot_t_v_for_all_binding_neq_append_lem t key value cls (ck, cv);
+ assert(pairwise_rel binding_neq ls');
+ assert(slot_s_inv len h ls')
+#pop-options
+
+/// [insert_in_list]: if the key is not in the map, appends a new bindings
+val hash_map_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
+ ls' == ls @ [(key,value)] /\
+ // The invariant is preserved
+ slot_s_inv len (hash_mod_key key len) ls' /\
+ // [key] maps to [value]
+ slot_s_find key ls' == Some value /\
+ // The other bindings are preserved
+ (forall k'. k' <> key ==> slot_s_find k' ls' == slot_s_find k' ls)))
+
+let hash_map_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
+ (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
+ | Fail -> False
+ | Return ls' ->
+ list_t_v ls' == list_t_v ls @ [(key,value)] /\
+ // The invariant is preserved
+ slot_t_inv len (hash_mod_key key len) ls' /\
+ // [key] maps to [value]
+ slot_t_find_s key ls' == Some value /\
+ // The other bindings are preserved
+ (forall k'. k' <> key ==> slot_t_find_s k' ls' == slot_t_find_s k' ls)))
+
+let 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)
+
+(** Auxiliary lemmas: update case *)
+
+val slot_s_find_update_for_all_binding_neq_append_lem
+ (t : Type0) (key : usize) (value : t) (ls : list (binding t)) (b : binding t) :
+ Lemma
+ (requires (
+ fst b <> key /\
+ for_all (binding_neq b) ls))
+ (ensures (
+ let ls' = find_update (same_key key) ls (key, value) in
+ for_all (binding_neq b) ls'))
+
+#push-options "--fuel 1"
+let rec slot_s_find_update_for_all_binding_neq_append_lem t key value ls b =
+ match ls with
+ | [] -> ()
+ | (ck, cv) :: cls ->
+ slot_s_find_update_for_all_binding_neq_append_lem t key value cls b
+#pop-options
+
+/// Annoying auxiliary lemma we have to prove because there is no way to reason
+/// properly about closures.
+/// I'm really enjoying my time.
+val for_all_binding_neq_value_indep
+ (#t : Type0) (key : key) (v0 v1 : t) (ls : list (binding t)) :
+ Lemma (for_all (binding_neq (key,v0)) ls = for_all (binding_neq (key,v1)) ls)
+
+#push-options "--fuel 1"
+let rec for_all_binding_neq_value_indep #t key v0 v1 ls =
+ match ls with
+ | [] -> ()
+ | _ :: ls' -> for_all_binding_neq_value_indep #t key v0 v1 ls'
+#pop-options
+
+val slot_s_inv_find_append_end_inv_lem
+ (t : Type0) (len : usize{len > 0}) (key : usize) (value : t) (ls : list (binding t)) :
+ Lemma
+ (requires (
+ slot_s_inv len (hash_mod_key key len) ls /\
+ Some? (slot_s_find key ls)))
+ (ensures (
+ let ls' = find_update (same_key key) ls (key, value) in
+ slot_s_inv len (hash_mod_key key len) ls' /\
+ (slot_s_find key ls' == Some value) /\
+ (forall k'. k' <> key ==> slot_s_find k' ls' == slot_s_find k' ls)))
+
+#push-options "--z3rlimit 50 --fuel 1"
+let rec slot_s_inv_find_append_end_inv_lem t len key value ls =
+ match ls with
+ | [] -> ()
+ | (ck, cv) :: cls ->
+ let h = hash_mod_key key len in
+ let ls' = find_update (same_key key) ls (key, value) in
+ if ck = key then
+ begin
+ assert(ls' == (ck,value) :: cls);
+ assert(for_all (same_hash_mod_key len h) ls');
+ // For pairwise_rel: binding_neq (ck, value) is actually independent
+ // of `value`. Slightly annoying to prove in F*...
+ assert(for_all (binding_neq (ck,cv)) cls);
+ for_all_binding_neq_value_indep key cv value cls;
+ assert(for_all (binding_neq (ck,value)) cls);
+ assert(pairwise_rel binding_neq ls');
+ assert(slot_s_inv len (hash_mod_key key len) ls')
+ end
+ else
+ begin
+ slot_s_inv_find_append_end_inv_lem t len key value cls;
+ assert(for_all (same_hash_mod_key len h) ls');
+ slot_s_find_update_for_all_binding_neq_append_lem t key value cls (ck, cv);
+ assert(pairwise_rel binding_neq ls');
+ assert(slot_s_inv len h ls')
+ end
+#pop-options
+
+/// [insert_in_list]: if the key is in the map, update the bindings
+val hash_map_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
+ ls' == find_update (same_key key) ls (key,value) /\
+ // The invariant is preserved
+ slot_s_inv len (hash_mod_key key len) ls' /\
+ // [key] maps to [value]
+ slot_s_find key ls' == Some value /\
+ // The other bindings are preserved
+ (forall k'. k' <> key ==> slot_s_find k' ls' == slot_s_find k' ls)))
+
+let hash_map_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
+ (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
+ | Fail -> False
+ | Return ls' ->
+ let als = list_t_v ls in
+ list_t_v ls' == find_update (same_key key) als (key,value) /\
+ // The invariant is preserved
+ slot_t_inv len (hash_mod_key key len) ls' /\
+ // [key] maps to [value]
+ slot_t_find_s key ls' == Some value /\
+ // The other bindings are preserved
+ (forall k'. k' <> key ==> slot_t_find_s k' ls' == slot_t_find_s k' ls)))
+
+let 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)
+
+(** Final lemmas about [insert_in_list] *)
+
+/// High-level version
+val hash_map_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
+ // The invariant is preserved
+ slot_s_inv len (hash_mod_key key len) ls' /\
+ // [key] maps to [value]
+ slot_s_find key ls' == Some value /\
+ // The other bindings are preserved
+ (forall k'. k' <> key ==> slot_s_find k' ls' == slot_s_find k' ls) /\
+ // The length is incremented, iff we inserted a new key
+ (match slot_s_find key ls with
+ | None -> length ls' = length ls + 1
+ | Some _ -> length ls' = length ls)))
+
+let hash_map_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
+ | Some _ ->
+ hash_map_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
+ (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
+ | Fail -> False
+ | Return ls' ->
+ // The invariant is preserved
+ slot_t_inv len (hash_mod_key key len) ls' /\
+ // [key] maps to [value]
+ slot_t_find_s key ls' == Some value /\
+ // The other bindings are preserved
+ (forall k'. k' <> key ==> slot_t_find_s k' ls' == slot_t_find_s k' ls) /\
+ // The length is incremented, iff we inserted a new key
+ (match slot_t_find_s key ls with
+ | None ->
+ list_t_v ls' == list_t_v ls @ [(key,value)] /\
+ list_t_len ls' = list_t_len ls + 1
+ | Some _ ->
+ list_t_v ls' == find_update (same_key key) (list_t_v ls) (key,value) /\
+ list_t_len ls' = list_t_len ls)))
+ (decreases (hash_map_insert_in_list_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)
+
+(*** 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
+/// 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)
+ (key : usize) (value : t) :
+ hash_map_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 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)
+ (key : usize) (value : t) :
+ result (hash_map_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
+ else Return (hash_map_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) :
+ Lemma
+ (requires (
+ hash_map_t_base_inv self /\
+ hash_map_s_len (hash_map_t_v self) = hash_map_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
+ 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
+ | _ -> False
+ end))
+
+let hash_map_insert_no_resize_fwd_back_lem_s t self key value =
+ begin match hash_key_fwd 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 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
+ | 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
+ | 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;
+ 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
+ | Fail -> ()
+ | Return l0 ->
+ begin match vec_index_mut_back (list_t t) 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
+ 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)
+ end
+ end
+ end
+ else
+ begin
+ match hash_map_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
+ | 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
+ 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)
+ end
+ end
+ end
+ end
+ end
+ end
+
+(**** 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 =
+ // [key] maps to [value]
+ hash_map_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')
+
+let insert_post (#t : Type0) (hm : hash_map_s_nes t)
+ (key : usize) (value : t) (hm' : hash_map_s_nes t) : Type0 =
+ // The invariant is preserved
+ hash_map_s_inv hm' /\
+ // [key] maps to [value] and the other bindings are preserved
+ hash_map_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)
+
+val hash_map_insert_no_fail_s_lem
+ (#t : Type0) (hm : hash_map_s_nes t)
+ (key : usize) (value : t) :
+ Lemma
+ (requires (hash_map_s_inv hm))
+ (ensures (
+ let hm' = hash_map_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 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
+ length_flatten_update hm i slot'
+
+val hash_map_insert_no_resize_s_lem
+ (#t : Type0) (hm : hash_map_s_nes t)
+ (key : usize) (value : t) :
+ Lemma
+ (requires (hash_map_s_inv hm))
+ (ensures (
+ match hash_map_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)
+ | Return hm' ->
+ insert_post hm key value hm'))
+
+let hash_map_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
+
+
+(**** 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)
+ (key : usize) (value : t) :
+ Lemma (requires (hash_map_s_inv hm))
+ (ensures (
+ match hash_map_insert_no_resize_s hm key value with
+ | Fail -> True
+ | Return hm' ->
+ hash_map_s_find hm' key == Some value))
+
+let hash_map_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 ()
+ else
+ begin
+ let hm' = Return?.v (hash_map_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
+ end
+
+val hash_map_insert_no_resize_s_get_diff_lem
+ (#t : Type0) (hm : hash_map_s t)
+ (key : usize) (value : t) (key' : usize{key' <> key}) :
+ Lemma (requires (hash_map_s_inv hm))
+ (ensures (
+ match hash_map_insert_no_resize_s hm key value with
+ | Fail -> True
+ | Return hm' ->
+ hash_map_s_find hm' key' == hash_map_s_find hm key'))
+
+let hash_map_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 ()
+ else
+ begin
+ let hm' = Return?.v (hash_map_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;
+ let i' = hash_mod_key key' len in
+ if i <> i' then ()
+ else
+ begin
+ ()
+ end
+ end
+
+
+(*** move_elements_from_list *)
+
+/// Having a great time here: if we use `result (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.
+/// I guess it comes from F*'s poor subtyping.
+/// Followingly, I'm not taking any chance and using [result_hash_map_s]
+/// everywhere.
+type result_hash_map_s_nes (t : Type0) : Type0 =
+ res:result (hash_map_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)
+ (ls : slot_s t) :
+ // Do *NOT* use `result (hash_map_s t)`
+ Tot (result_hash_map_s_nes t)
+ (decreases ls) =
+ match ls with
+ | [] -> Return hm
+ | (key, value) :: ls' ->
+ match hash_map_insert_no_resize_s hm key value with
+ | Fail -> Fail
+ | Return hm' ->
+ hash_map_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))
+ (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)
+ 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
+ | _ -> False))
+ (decreases (hash_map_move_elements_from_list_decreases t ntable ls))
+
+#push-options "--fuel 1"
+let rec hash_map_move_elements_from_list_fwd_back_lem t ntable ls =
+ begin match ls with
+ | ListCons 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
+ | 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
+ | Fail -> ()
+ | Return h0 -> ()
+ end
+ end
+ | ListNil -> ()
+ end
+#pop-options
+
+(*** move_elements *)
+
+(**** move_elements: refinement 0 *)
+/// The proof for [hash_map_move_elements_fwd_back_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
+/// 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].
+
+/// [hash_map_move_elements_fwd] 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
+/// 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))
+ (i : usize{i <= length slots /\ length slots <= usize_max}) :
+ Pure (result ((hash_map_t t) & (vec (list_t t))))
+ (requires (True))
+ (ensures (fun res ->
+ match res, hash_map_move_elements_fwd_back t ntable slots i with
+ | Fail, Fail -> True
+ | Return (ntable1, slots1), Return (ntable2, slots2) ->
+ ntable1 == ntable2 /\
+ slots1 == slots2
+ | _ -> False))
+ (decreases (hash_map_move_elements_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
+ | Fail -> Fail
+ | Return hm' ->
+ let slots' = list_update slots i ListNil in
+ hash_map_move_elements_s_simpl t hm' slots' (i+1)
+ end
+ else Return (ntable, slots)
+#pop-options
+
+(**** move_elements: refinement 1 *)
+/// We prove a second refinement lemma: calling [move_elements] refines a function
+/// which, for every slot, moves the element out of the slot. This first model is
+/// almost exactly the translated function, it just uses `list` instead of `list_t`.
+
+// Note that we ignore the returned slots (we thus don't return a pair:
+// only the new hash map in which we moved the elements from the slots):
+// this returned value is not used.
+let rec hash_map_move_elements_s
+ (#t : Type0) (hm : hash_map_s_nes t)
+ (slots : slots_s t) (i : usize{i <= length slots /\ length slots <= usize_max}) :
+ Tot (result_hash_map_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
+ | Fail -> Fail
+ | Return hm' ->
+ let slots' = list_update slots i [] in
+ hash_map_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}) :
+ Lemma
+ (requires (
+ hash_map_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
+ 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
+ | _ -> False))
+ (decreases (length slots - i))
+
+// This proof was super unstable for some reasons.
+//
+// For instance, using the [hash_map_s_nes] type abbreviation
+// in some of the above definitions led to a failure (while it was just a type
+// abbreviation: the signatures were the same if we unfolded this type). This
+// behaviour led me to the hypothesis that maybe it made F*'s type inference
+// end up with a different result, which combined with its poor support for
+// subtyping made the proof failed.
+//
+// However, later, unwrapping a definition led to another failure.
+//
+// I thus tried to manually unfold some postconditions because it
+// seemed to work for [hash_map_move_elements_fwd_back_lem] but it didn't
+// succeed.
+//
+// I tried to increase the ifuel to 2, 3: it didn't work, and I fell back to
+// other methods. Finally out of angriness I swiched the ifuel to 4 for no
+// specific reason: everything worked fine.
+//
+// I have *no clue* why 4 is the magic number. Also: it fails if I remove
+// the unfolded postconditions (meaning I would probably need to increase
+// the ifuel to unreasonable amounts).
+//
+// Finally, as I had succeeded in fixing the proof, I thought that maybe the
+// initial problem with the type abbreviations was fixed: I thus tried to use
+// them. Of course, it made the proof fail again, and this time no ifuel setting
+// seemed to work.
+//
+// At this point I was just fed up and leave things as they were, without trying
+// to cleanup the previous definitions.
+//
+// Finally, even later it broke, again, at which point I had no choice but to
+// introduce an even simpler refinement proof (with [hash_map_move_elements_s_simpl]).
+// Doing this allowed me to see that maybe the problem came from the fact that
+// Z3 had to prove that `list_t_v ListNil == []` at some point, so I added the
+// corresponding assertion and miraculously everything becamse stable... I then
+// removed all the postconditions I had manually instanciated and inserted in
+// the proof, and which took a lot of place.
+// I still have no clue why `ifuel 4` made it work earlier.
+//
+// The terrible thing is that this refinement proof is conceptually super simple:
+// - there are maybe two arithmetic proofs, which are directly solved by the
+// precondition
+// - we need to prove the call to [hash_map_move_elements_from_list_fwd_back]
+// refines its model: this is proven by another refinement lemma we proved above
+// - there is the recursive call (trivial)
+#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 b = i < i0 in
+ if b
+ then
+ begin match vec_index_mut_fwd (list_t t) slots i with
+ | Fail -> ()
+ | Return l ->
+ let l0 = mem_replace_fwd (list_t t) l ListNil 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
+ | 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
+ | 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
+ | Fail ->
+ assert(hash_map_move_elements_fwd_back t ntable slots i == Fail);
+ ()
+ | Return (ntable', v0) -> ()
+ end
+ end
+ end
+ end
+ end
+ else ()
+#pop-options
+
+
+(**** move_elements: refinement 2 *)
+/// We prove a second refinement lemma: calling [move_elements] refines a function
+/// which moves every binding of the hash map seen as *one* associative list
+/// (and not a list of lists).
+
+/// [ntable] is the hash map to which we move the elements
+/// [slots] is the current hash map, from which we remove the elements, and seen
+/// as a "flat" associative list (and not a list of lists)
+/// This is actually exactly [hash_map_move_elements_from_list_s]...
+let rec hash_map_move_elements_s_flat
+ (#t : Type0) (ntable : hash_map_s_nes t)
+ (slots : assoc_list t) :
+ Tot (result_hash_map_s_nes t)
+ (decreases slots) =
+ match slots with
+ | [] -> Return ntable
+ | (k,v) :: slots' ->
+ match hash_map_insert_no_resize_s ntable k v with
+ | Fail -> Fail
+ | Return ntable' ->
+ hash_map_move_elements_s_flat ntable' slots'
+
+/// The refinment lemmas
+/// First, auxiliary helpers.
+
+/// Flatten a list of lists, starting at index i
+val flatten_i :
+ #a:Type
+ -> l:list (list a)
+ -> i:nat{i <= length l}
+ -> Tot (list a) (decreases (length l - i))
+
+let rec flatten_i l i =
+ if i < length l then
+ index l i @ flatten_i l (i+1)
+ else []
+
+let _ = assert(let l = [1;2] in l == hd l :: tl l)
+
+val flatten_i_incr :
+ #a:Type
+ -> l:list (list a)
+ -> i:nat{Cons? l /\ i+1 <= length l} ->
+ Lemma
+ (ensures (
+ (**) assert_norm(length (hd l :: tl l) == 1 + length (tl l));
+ flatten_i l (i+1) == flatten_i (tl l) i))
+ (decreases (length l - (i+1)))
+
+#push-options "--fuel 1"
+let rec flatten_i_incr l i =
+ let x :: tl = l in
+ if i + 1 < length l then
+ begin
+ assert(flatten_i l (i+1) == index l (i+1) @ flatten_i l (i+2));
+ flatten_i_incr l (i+1);
+ assert(flatten_i l (i+2) == flatten_i tl (i+1));
+ assert(index l (i+1) == index tl i)
+ end
+ else ()
+#pop-options
+
+val flatten_0_is_flatten :
+ #a:Type
+ -> l:list (list a) ->
+ Lemma
+ (ensures (flatten_i l 0 == flatten l))
+
+#push-options "--fuel 1"
+let rec flatten_0_is_flatten #a l =
+ match l with
+ | [] -> ()
+ | x :: l' ->
+ flatten_i_incr l 0;
+ flatten_0_is_flatten l'
+#pop-options
+
+/// Auxiliary lemma
+val flatten_nil_prefix_as_flatten_i :
+ #a:Type
+ -> l:list (list a)
+ -> i:nat{i <= length l} ->
+ Lemma (requires (forall (j:nat{j < i}). index l j == []))
+ (ensures (flatten l == flatten_i l i))
+
+#push-options "--fuel 1"
+let rec flatten_nil_prefix_as_flatten_i #a l i =
+ if i = 0 then flatten_0_is_flatten l
+ else
+ begin
+ let x :: l' = l in
+ assert(index l 0 == []);
+ assert(x == []);
+ assert(flatten l == flatten l');
+ flatten_i_incr l (i-1);
+ assert(flatten_i l i == flatten_i l' (i-1));
+ assert(forall (j:nat{j < length l'}). index l' j == index l (j+1));
+ flatten_nil_prefix_as_flatten_i l' (i-1);
+ assert(flatten l' == flatten_i l' (i-1))
+ end
+#pop-options
+
+/// The proof is trivial, the functions are the same.
+/// Just keeping two definitions to allow changes...
+val hash_map_move_elements_from_list_s_as_flat_lem
+ (#t : Type0) (hm : hash_map_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))
+ (decreases ls)
+
+#push-options "--fuel 1"
+let rec hash_map_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
+ | Fail -> ()
+ | Return hm' ->
+ hash_map_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
+ | Fail -> Fail
+ | Return hm1 -> hash_map_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) :
+ Lemma
+ (ensures (
+ match hash_map_move_elements_s_flat_comp hm slot0 slot1,
+ hash_map_move_elements_s_flat hm (slot0 @ slot1)
+ with
+ | Fail, Fail -> True
+ | Return hm1, Return hm2 -> hm1 == hm2
+ | _ -> False))
+ (decreases (slot0))
+
+#push-options "--fuel 1"
+let rec hash_map_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
+ | Fail -> ()
+ | Return hm' ->
+ hash_map_move_elements_s_flat_append_lem hm' slot0' slot1
+#pop-options
+
+val flatten_i_same_suffix (#a : Type) (l0 l1 : list (list a)) (i : nat) :
+ Lemma
+ (requires (
+ i <= length l0 /\
+ length l0 = length l1 /\
+ (forall (j:nat{i <= j /\ j < length l0}). index l0 j == index l1 j)))
+ (ensures (flatten_i l0 i == flatten_i l1 i))
+ (decreases (length l0 - i))
+
+#push-options "--fuel 1"
+let rec flatten_i_same_suffix #a l0 l1 i =
+ if i < length l0 then
+ flatten_i_same_suffix l0 l1 (i+1)
+ else ()
+#pop-options
+
+/// Refinement lemma:
+/// [hash_map_move_elements_s] refines [hash_map_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)
+ (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)
+ with
+ | Fail, Fail -> True
+ | Return hm, Return hm' -> hm == hm'
+ | _ -> False))
+ (decreases (length slots - i))
+
+#push-options "--fuel 1"
+let rec hash_map_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
+ | 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(hash_map_move_elements_s_flat hm (flatten_i slots i) == Fail)
+ | 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));
+ ()
+ end
+ else ()
+#pop-options
+
+let assoc_list_inv (#t : Type0) (al : assoc_list t) : Type0 =
+ // All the keys are pairwise distinct
+ pairwise_rel binding_neq al
+
+let disjoint_hm_al_on_key
+ (#t : Type0) (hm : 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
+ | 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 =
+ 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) :
+ option t =
+ match hash_map_s_find hm k with
+ | Some b -> Some b
+ | None -> assoc_list_find k al
+
+/// Auxiliary lemma
+val for_all_binding_neq_find_lem (#t : Type0) (k : key) (v : t) (al : assoc_list t) :
+ Lemma (requires (for_all (binding_neq (k,v)) al))
+ (ensures (assoc_list_find k al == None))
+
+#push-options "--fuel 1"
+let rec for_all_binding_neq_find_lem #t k v al =
+ match al with
+ | [] -> ()
+ | b :: al' -> for_all_binding_neq_find_lem k v al'
+#pop-options
+
+val hash_map_move_elements_s_flat_lem
+ (#t : Type0) (hm : hash_map_s_nes t) (al : assoc_list t) :
+ Lemma
+ (requires (
+ // Invariants
+ hash_map_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))
+ (ensures (
+ match hash_map_move_elements_s_flat hm al with
+ | Fail -> False // We can't fail
+ | Return hm' ->
+ // The invariant is preserved
+ hash_map_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))
+ (decreases al)
+
+#restart-solver
+#push-options "--z3rlimit 200 --fuel 1"
+let rec hash_map_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
+ | Fail -> ()
+ | Return hm' ->
+ assert(hash_map_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);
+ 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(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'
+#pop-options
+
+/// We need to prove that the invariants on the "low-level" representations of
+/// the hash map imply the invariants on the "high-level" representations.
+
+val slots_t_inv_implies_slots_s_inv
+ (#t : Type0) (slots : slots_t t{length slots <= usize_max}) :
+ Lemma (requires (slots_t_inv slots))
+ (ensures (slots_s_inv (slots_t_v slots)))
+
+let slots_t_inv_implies_slots_s_inv #t slots =
+ // Ok, works fine: this lemma was useless.
+ // Problem is: I can never really predict for sure with F*...
+ ()
+
+val 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)))
+
+let hash_map_t_base_inv_implies_hash_map_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
+ (#t : Type0) (len : usize{len > 0}) (offset : usize)
+ (hm : hash_map_s t{offset + length hm <= usize_max}) : Type0 =
+ forall(i:nat{i < length hm}). {:pattern index hm i} slot_s_inv len (offset + i) (index hm i)
+
+/// Auxiliary lemma.
+/// If a binding comes from a slot i, then its key is different from the keys
+/// of the bindings in the other slots (because the hashes of the keys are distinct).
+val binding_in_previous_slot_implies_neq
+ (#t : Type0) (len : usize{len > 0})
+ (i : usize) (b : binding t)
+ (offset : usize{i < offset})
+ (slots : hash_map_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))
+ (ensures (
+ for_all (binding_neq b) (flatten slots)))
+ (decreases slots)
+
+#push-options "--z3rlimit 100 --fuel 1"
+let rec binding_in_previous_slot_implies_neq #t len i b offset slots =
+ match slots with
+ | [] -> ()
+ | s :: slots' ->
+ assert(slot_s_inv len offset (index slots 0)); // Triggers patterns
+ assert(slot_s_inv len offset s);
+ // Proving TARGET. We use quantifiers.
+ assert(for_all (same_hash_mod_key len offset) s);
+ forall_index_equiv_list_for_all (same_hash_mod_key len offset) s;
+ assert(forall (i:nat{i < length s}). same_hash_mod_key len offset (index s i));
+ let aux (i:nat{i < length s}) :
+ Lemma
+ (requires (same_hash_mod_key len offset (index s i)))
+ (ensures (binding_neq b (index s i)))
+ [SMTPat (index s i)] = ()
+ in
+ assert(forall (i:nat{i < length s}). binding_neq b (index s i));
+ forall_index_equiv_list_for_all (binding_neq b) s;
+ assert(for_all (binding_neq b) s); // TARGET
+ //
+ assert(forall (i:nat{i < length slots'}). index slots' i == index slots (i+1)); // Triggers instantiations
+ binding_in_previous_slot_implies_neq len i b (offset+1) slots';
+ for_all_append (binding_neq b) s (flatten slots')
+#pop-options
+
+val partial_hash_map_s_inv_implies_assoc_list_lem
+ (#t : Type0) (len : usize{len > 0}) (offset : usize)
+ (hm : hash_map_s t{offset + length hm <= usize_max}) :
+ Lemma
+ (requires (
+ partial_hash_map_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 =
+ match hm with
+ | [] -> ()
+ | slot :: hm' ->
+ assert(flatten hm == slot @ flatten hm');
+ assert(forall (i:nat{i < length hm'}). index hm' i == index hm (i+1)); // Triggers instantiations
+ match slot with
+ | [] ->
+ assert(flatten hm == flatten hm');
+ assert(partial_hash_map_s_inv len (offset+1) hm'); // Triggers instantiations
+ partial_hash_map_s_inv_implies_assoc_list_lem len (offset+1) hm'
+ | x :: slot' ->
+ assert(flatten (slot' :: hm') == slot' @ flatten hm');
+ let hm'' = slot' :: hm' in
+ assert(forall (i:nat{0 < i /\ i < length hm''}). index hm'' i == index hm i); // Triggers instantiations
+ assert(forall (i:nat{0 < i /\ i < length hm''}). slot_s_inv len (offset + i) (index hm'' i));
+ assert(index hm 0 == slot); // Triggers instantiations
+ assert(slot_s_inv len offset slot);
+ assert(slot_s_inv len offset slot');
+ assert(partial_hash_map_s_inv len offset hm'');
+ partial_hash_map_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');
+ 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))
+ (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
+
+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)))
+
+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)
+
+/// 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})
+ (al : assoc_list t) : Type0 =
+ (forall (k:key). hash_map_t_find_s ntable k == assoc_list_find k al)
+
+let partial_hash_map_s_find
+ (#t : Type0) (len : usize{len > 0}) (offset : usize)
+ (hm : hash_map_s_nes t{offset + length hm = len})
+ (k : key{hash_mod_key k len >= offset}) : option t =
+ let i = hash_mod_key k len in
+ let slot = index hm (i - offset) in
+ slot_s_find k slot
+
+val not_same_hash_key_not_found_in_slot
+ (#t : Type0) (len : usize{len > 0})
+ (k : key)
+ (i : usize)
+ (slot : slot_s t) :
+ Lemma
+ (requires (
+ hash_mod_key k len <> i /\
+ slot_s_inv len i slot))
+ (ensures (slot_s_find k slot == None))
+
+#push-options "--fuel 1"
+let rec not_same_hash_key_not_found_in_slot #t len k i slot =
+ match slot with
+ | [] -> ()
+ | (k',v) :: slot' -> not_same_hash_key_not_found_in_slot len k i slot'
+#pop-options
+
+/// Small variation of [binding_in_previous_slot_implies_neq]: if the hash of
+/// a key links it to a previous slot, it can't be found in the slots after.
+val key_in_previous_slot_implies_not_found
+ (#t : Type0) (len : usize{len > 0})
+ (k : key)
+ (offset : usize)
+ (slots : hash_map_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))
+ (ensures (
+ assoc_list_find k (flatten slots) == None))
+ (decreases slots)
+
+#push-options "--fuel 1"
+let rec key_in_previous_slot_implies_not_found #t len k offset slots =
+ match slots with
+ | [] -> ()
+ | slot :: slots' ->
+ find_append (same_key k) slot (flatten slots');
+ assert(index slots 0 == slot); // Triggers instantiations
+ not_same_hash_key_not_found_in_slot #t len k offset slot;
+ assert(assoc_list_find k slot == None);
+ assert(forall (i:nat{i < length slots'}). index slots' i == index slots (i+1)); // Triggers instantiations
+ key_in_previous_slot_implies_not_found len k (offset+1) slots'
+#pop-options
+
+val partial_hash_map_s_is_assoc_list_lem
+ (#t : Type0) (len : usize{len > 0}) (offset : usize)
+ (hm : hash_map_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))
+ (ensures (
+ partial_hash_map_s_find len offset hm k == assoc_list_find k (flatten hm)))
+ (decreases hm)
+// (decreases (length hm + length (flatten hm)))
+
+#push-options "--fuel 1"
+let rec partial_hash_map_s_is_assoc_list_lem #t len offset hm k =
+ match hm with
+ | [] -> ()
+ | slot :: hm' ->
+ let h = hash_mod_key k len in
+ let i = h - offset in
+ if i = 0 then
+ begin
+ // We must look in the current slot
+ assert(partial_hash_map_s_find len offset hm k == slot_s_find k slot);
+ find_append (same_key k) slot (flatten hm');
+ assert(forall (i:nat{i < length hm'}). index hm' i == index hm (i+1)); // Triggers instantiations
+ key_in_previous_slot_implies_not_found #t len k (offset+1) hm';
+ assert( // Of course, writing `== None` doesn't work...
+ match find (same_key k) (flatten hm') with
+ | None -> True
+ | Some _ -> False);
+ assert(
+ find (same_key k) (flatten hm) ==
+ begin match find (same_key k) slot with
+ | Some x -> Some x
+ | None -> find (same_key k) (flatten hm')
+ end);
+ ()
+ end
+ else
+ begin
+ // We must ignore the current slot
+ assert(partial_hash_map_s_find len offset hm k ==
+ partial_hash_map_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
+ 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)))
+
+let hash_map_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
+ let len = length hm_v in
+ partial_hash_map_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)) :
+ Lemma
+ (requires (
+ let al = flatten (slots_t_v slots) in
+ hash_map_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)))
+ (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
+ with
+ | Return (ntable', _), Return ntable'_v ->
+ // The invariant is preserved
+ hash_map_t_base_inv ntable' /\
+ // We preserved the parameters
+ hash_map_t_same_params ntable' ntable /\
+ // The table has the same number of slots
+ length ntable'.hash_map_slots = length ntable.hash_map_slots /\
+ // The count is good
+ hash_map_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 /\
+ // 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
+ | _ -> False // We can only succeed
+ ))
+
+// Weird, dirty things happen below.
+// Manually unfolding some postconditions allowed to make the proof pass,
+// and also revealed the reason why some proofs failed with "Unknown assertion
+// failed" (resulting in the call to [flatten_0_is_flatten] for instance).
+// I think manually unfolding the postconditions allowed to account for the
+// lack of ifuel (this kind of proofs is annoying, really).
+#restart-solver
+#push-options "--z3rlimit 100"
+let hash_map_move_elements_fwd_back_lem t ntable slots =
+ let ntable_v = hash_map_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;
+ begin
+ match hash_map_move_elements_fwd_back t ntable slots 0,
+ hash_map_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(False)
+ end;
+ hash_map_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)
+ 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
+ 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(False)
+#pop-options
+
+(*** try_resize *)
+
+/// High-level model 1.
+/// This is one is slightly "crude": we just simplify a bit the function.
+
+let hash_map_try_resize_s_simpl
+ (#t : Type0)
+ (hm : hash_map_t t) :
+ Pure (result (hash_map_t t))
+ (requires (
+ let (divid, divis) = hm.hash_map_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
+ 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
+ | Fail -> Fail
+ | Return ntable ->
+ match hash_map_move_elements_fwd_back t ntable hm.hash_map_slots 0 with
+ | Fail -> Fail
+ | Return (ntable', _) ->
+ let hm =
+ { hm with hash_map_slots = ntable'.hash_map_slots;
+ hash_map_max_load = ntable'.hash_map_max_load }
+ in
+ Return hm
+ end
+ else Return hm
+
+// I had made a mistake when writing the above definition: I had used `ntable`
+// instead of `ntable'` in the last assignments. Of course, Z3 failed to prove
+// the equality `hm1 == hm2`, and as I couldn't spot immediately the mistake,
+// I had to resort to the good old "test every field" trick, by replacing
+// `hm1 == hm2` with:
+// ```
+// hm1.hash_map_num_entries == hm2.hash_map_num_entries /\
+// hm1.hash_map_max_load_factor == hm2.hash_map_max_load_factor /\
+// hm1.hash_map_max_load == hm2.hash_map_max_load /\
+// hm1.hash_map_slots == hm2.hash_map_slots
+// ```
+// Once again, if I had had access to a context, I would have seen the error
+// immediately.
+val hash_map_try_resize_fwd_back_lem_refin
+ (t : Type0) (self : hash_map_t t) :
+ Lemma
+ (requires (
+ let (divid, divis) = self.hash_map_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
+ with
+ | Fail, Fail -> True
+ | Return hm1, Return hm2 -> hm1 == hm2
+ | _ -> False))
+
+let hash_map_try_resize_fwd_back_lem_refin t self = ()
+
+/// Isolating arithmetic proofs
+
+let gt_lem0 (n m q : nat) :
+ Lemma (requires (m > 0 /\ n > q))
+ (ensures (n * m > q * m)) = ()
+
+let ge_lem0 (n m q : nat) :
+ Lemma (requires (m > 0 /\ n >= q))
+ (ensures (n * m >= q * m)) = ()
+
+let gt_ge_trans (n m p : nat) :
+ Lemma (requires (n > m /\ m >= p)) (ensures (n > p)) = ()
+
+let ge_trans (n m p : nat) :
+ Lemma (requires (n >= m /\ m >= p)) (ensures (n >= p)) = ()
+
+#push-options "--z3rlimit 200"
+let gt_lem1 (n m q : nat) :
+ Lemma (requires (m > 0 /\ n > q / m)) (ensures (n * m > q)) =
+ assert(n >= q / m + 1);
+ ge_lem0 n m (q / m + 1);
+ assert(n * m >= (q / m) * m + m)
+#pop-options
+
+let gt_lem2 (n m p q : nat) :
+ Lemma (requires (m > 0 /\ p > 0 /\ n > (q / m) / p)) (ensures (n * m * p > q)) =
+ gt_lem1 n p (q / m);
+ assert(n * p > q / m);
+ gt_lem1 (n * p) m q
+
+let ge_lem1 (n m q : nat) :
+ Lemma (requires (n >= m /\ q > 0))
+ (ensures (n / q >= m / q)) =
+ FStar.Math.Lemmas.lemma_div_le m n q
+
+#restart-solver
+#push-options "--z3rlimit 200"
+let times_divid_lem (n m p : pos) : Lemma ((n * m) / p >= n * (m / p))
+ =
+ FStar.Math.Lemmas.multiply_fractions m p;
+ assert(m >= (m / p) * p);
+ assert(n * m >= n * (m / p) * p); //
+ ge_lem1 (n * m) (n * (m / p) * p) p;
+ assert((n * m) / p >= (n * (m / p) * p) / p);
+ assert(n * (m / p) * p = (n * (m / p)) * p);
+ FStar.Math.Lemmas.cancel_mul_div (n * (m / p)) p;
+ assert(((n * (m / p)) * p) / p = n * (m / p))
+#pop-options
+
+/// The good old arithmetic proofs and their unstability...
+/// At some point I thought it was stable because it worked with `--quake 100`.
+/// Of course, it broke the next time I checked the file...
+/// It seems things are ok when we check this proof on its own, but not when
+/// it is sent at the same time as the one above (though we put #restart-solver!).
+/// I also tried `--quake 1/100` to no avail: it seems that when Z3 decides to
+/// fail the first one, it fails them all. I inserted #restart-solver before
+/// the previous lemma to see if it had an effect (of course not).
+val new_max_load_lem
+ (len : usize) (capacity : usize{capacity > 0})
+ (divid : usize{divid > 0}) (divis : usize{divis > 0}) :
+ Lemma
+ (requires (
+ let max_load = (capacity * divid) / divis in
+ let ncapacity = 2 * capacity in
+ let nmax_load = (ncapacity * divid) / divis in
+ capacity > 0 /\ 0 < divid /\ divid < divis /\
+ capacity * divid >= divis /\
+ len = max_load + 1))
+ (ensures (
+ let max_load = (capacity * divid) / divis in
+ let ncapacity = 2 * capacity in
+ let nmax_load = (ncapacity * divid) / divis in
+ len <= nmax_load))
+
+let mul_assoc (a b c : nat) : Lemma (a * b * c == a * (b * c)) = ()
+
+let ge_lem2 (a b c d : nat) : Lemma (requires (a >= b + c /\ c >= d)) (ensures (a >= b + d)) = ()
+let ge_div_lem1 (a b : nat) : Lemma (requires (a >= b /\ b > 0)) (ensures (a / b >= 1)) = ()
+
+#restart-solver
+#push-options "--z3rlimit 100 --z3cliopt smt.arith.nl=false"
+let new_max_load_lem len capacity divid divis =
+ FStar.Math.Lemmas.paren_mul_left 2 capacity divid;
+ mul_assoc 2 capacity divid;
+ // The following assertion often breaks though it is given by the above
+ // lemma. I really don't know what to do (I deactivated non-linear
+ // arithmetic and added the previous lemma call, moved the assertion up,
+ // boosted the rlimit...).
+ assert(2 * capacity * divid == 2 * (capacity * divid));
+ let max_load = (capacity * divid) / divis in
+ let ncapacity = 2 * capacity in
+ let nmax_load = (ncapacity * divid) / divis in
+ assert(nmax_load = (2 * capacity * divid) / divis);
+ times_divid_lem 2 (capacity * divid) divis;
+ assert((2 * (capacity * divid)) / divis >= 2 * ((capacity * divid) / divis));
+ assert(nmax_load >= 2 * ((capacity * divid) / divis));
+ assert(nmax_load >= 2 * max_load);
+ assert(nmax_load >= max_load + max_load);
+ ge_div_lem1 (capacity * divid) divis;
+ ge_lem2 nmax_load max_load max_load 1;
+ assert(nmax_load >= max_load + 1)
+#pop-options
+
+val hash_map_try_resize_s_simpl_lem (#t : Type0) (hm : hash_map_t t) :
+ Lemma
+ (requires (
+ // The base invariant is satisfied
+ hash_map_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)
+ ))
+ (ensures (
+ match hash_map_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' /\
+ // 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)))
+
+#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
+ 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
+ | Fail -> ()
+ | Return ntable ->
+ let slots = hm.hash_map_slots in
+ let al = flatten (slots_t_v slots) in
+ // Proving that: length al = hm.hash_map_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(length al <= usize_max);
+ hash_map_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
+ | Fail -> ()
+ | Return (ntable', _) ->
+ hash_map_is_assoc_list_lem hm;
+ assert(hash_map_is_assoc_list hm (hash_map_t_al_v hm));
+ let hm' =
+ { hm with hash_map_slots = ntable'.hash_map_slots;
+ hash_map_max_load = ntable'.hash_map_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')
+ end
+ else
+ begin
+ gt_lem2 capacity 2 divid usize_max;
+ assert(capacity * 2 * divid > usize_max)
+ 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
+
+/// The final lemma about [try_resize]
+val hash_map_try_resize_fwd_back_lem (#t : Type0) (hm : hash_map_t t) :
+ Lemma
+ (requires (
+ hash_map_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)))
+ (ensures (
+ match hash_map_try_resize_fwd_back 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' /\
+ // The length is the same
+ hash_map_t_len_s hm' = hash_map_t_len_s hm /\
+ // It contains the same bindings as the initial map
+ hash_map_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
+
+(*** 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
+ | Fail -> Fail
+ | Return hm' ->
+ if hash_map_t_len_s hm' > hm'.hash_map_max_load then
+ hash_map_try_resize_fwd_back t hm'
+ else Return hm'
+
+val hash_map_insert_fwd_back_lem_refin
+ (t : Type0) (self : hash_map_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
+ with
+ | Fail, Fail -> True
+ | Return hm1, Return hm2 -> hm1 == hm2
+ | _ -> False))
+
+let hash_map_insert_fwd_back_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) :
+ 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''))
+ (ensures (
+ hash_map_s_updated_binding (hash_map_t_v self) key
+ (Some value) (hash_map_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))
+ (ensures (
+ match hash_map_insert_fwd_back 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)
+ | Return hm' ->
+ // The invariant is preserved
+ hash_map_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') /\
+ // 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)))
+
+#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
+ | 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]
+ assert(insert_post self_v key value hm'_v);
+ // Expanding [insert_post]
+ assert(hash_map_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
+ 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
+ // Proving the post
+ assert(hash_map_t_inv hm'');
+ hash_map_insert_fwd_back_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)
+ 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
+
+(*** contains_key *)
+
+(**** contains_key_in_list *)
+
+val hash_map_contains_key_in_list_fwd_lem
+ (#t : Type0) (key : usize) (ls : list_t t) :
+ Lemma
+ (ensures (
+ match hash_map_contains_key_in_list_fwd 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 =
+ match ls with
+ | ListCons 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
+ | Fail -> ()
+ | Return b0 -> ()
+ end
+ | ListNil -> ()
+#pop-options
+
+(**** contains_key *)
+
+val hash_map_contains_key_fwd_lem_aux
+ (#t : Type0) (self : hash_map_t_nes t) (key : usize) :
+ Lemma
+ (ensures (
+ match hash_map_contains_key_fwd t self key with
+ | Fail -> False
+ | Return b -> b = Some? (hash_map_t_find_s self key)))
+
+let hash_map_contains_key_fwd_lem_aux #t self key =
+ begin match hash_key_fwd key with
+ | Fail -> ()
+ | Return i ->
+ let v = self.hash_map_slots in
+ let i0 = 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
+ | 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
+ | Fail -> ()
+ | Return b -> ()
+ end
+ end
+ end
+ 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
+
+(*** get *)
+
+(**** get_in_list *)
+
+val hash_map_get_in_list_fwd_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
+ | 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 =
+ begin match ls with
+ | ListCons 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
+ | Fail -> ()
+ | Return x -> ()
+ end
+ | ListNil -> ()
+ end
+#pop-options
+
+(**** get *)
+
+val hash_map_get_fwd_lem_aux
+ (#t : Type0) (self : hash_map_t_nes t) (key : usize) :
+ Lemma
+ (ensures (
+ match hash_map_get_fwd t self key, hash_map_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
+ | Fail -> ()
+ | Return i ->
+ let v = self.hash_map_slots in
+ let i0 = 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
+ | Fail -> ()
+ | Return l ->
+ begin
+ hash_map_get_in_list_fwd_lem key l;
+ match hash_map_get_in_list_fwd t key l with
+ | Fail -> ()
+ | Return x -> ()
+ end
+ end
+ end
+ end
+
+/// .fsti
+let hash_map_get_fwd_lem #t self key = hash_map_get_fwd_lem_aux #t self key
+
+(*** get_mut'fwd *)
+
+
+(**** get_mut_in_list'fwd *)
+
+val hash_map_get_mut_in_list_fwd_lem
+ (#t : Type0) (key : usize) (ls : list_t t) :
+ Lemma
+ (ensures (
+ match hash_map_get_mut_in_list_fwd 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_mut_in_list_fwd_lem #t key ls =
+ begin match ls with
+ | ListCons ckey cvalue ls0 ->
+ let b = ckey = key in
+ if b
+ then ()
+ else
+ begin
+ hash_map_get_mut_in_list_fwd_lem key ls0;
+ match hash_map_get_mut_in_list_fwd t key ls0 with
+ | Fail -> ()
+ | Return x -> ()
+ end
+ | ListNil -> ()
+ end
+#pop-options
+
+(**** get_mut'fwd *)
+
+val hash_map_get_mut_fwd_lem_aux
+ (#t : Type0) (self : hash_map_t_nes t) (key : usize) :
+ Lemma
+ (ensures (
+ match hash_map_get_mut_fwd t self key, hash_map_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
+ | Fail -> ()
+ | Return i ->
+ let v = self.hash_map_slots in
+ let i0 = 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
+ | Fail -> ()
+ | Return l ->
+ begin
+ hash_map_get_mut_in_list_fwd_lem key l;
+ match hash_map_get_mut_in_list_fwd t key l with
+ | Fail -> ()
+ | Return x -> ()
+ end
+ end
+ end
+ end
+
+let hash_map_get_mut_fwd_lem #t self key =
+ hash_map_get_mut_fwd_lem_aux #t self key
+
+(*** get_mut'back *)
+
+(**** get_mut_in_list'back *)
+
+val hash_map_get_mut_in_list_back_lem
+ (#t : Type0) (key : usize) (ls : list_t t) (ret : t) :
+ Lemma
+ (requires (Some? (slot_t_find_s key ls)))
+ (ensures (
+ match hash_map_get_mut_in_list_back t key ls 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_back_lem #t key ls ret =
+ begin match ls with
+ | ListCons ckey cvalue ls0 ->
+ let b = ckey = key in
+ if b
+ then let ls1 = ListCons ckey ret ls0 in ()
+ else
+ begin
+ hash_map_get_mut_in_list_back_lem key ls0 ret;
+ match hash_map_get_mut_in_list_back t key ls0 ret with
+ | Fail -> ()
+ | Return l -> let ls1 = ListCons ckey cvalue l in ()
+ end
+ | ListNil -> ()
+ 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})
+ (key : usize) (ret : t) :
+ Lemma
+ (requires (Some? (hash_map_t_find_s self key)))
+ (ensures (
+ match hash_map_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))
+
+let hash_map_get_mut_back_lem_refin #t self key ret =
+ begin match hash_key_fwd 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
+ begin match usize_rem i i2 with
+ | Fail -> ()
+ | Return hash_mod ->
+ begin match vec_index_mut_fwd (list_t t) v hash_mod with
+ | Fail -> ()
+ | Return l ->
+ begin
+ hash_map_get_mut_in_list_back_lem key l ret;
+ match hash_map_get_mut_in_list_back t key l ret with
+ | Fail -> ()
+ | Return l0 ->
+ begin match vec_index_mut_back (list_t t) v hash_mod l0 with
+ | Fail -> ()
+ | Return v0 -> let self0 = Mkhash_map_t i0 p i1 v0 in ()
+ end
+ end
+ end
+ end
+ end
+
+/// Final lemma
+val hash_map_get_mut_back_lem_aux
+ (#t : Type0) (hm : hash_map_t t)
+ (key : usize) (ret : t) :
+ Lemma
+ (requires (
+ hash_map_t_inv hm /\
+ Some? (hash_map_t_find_s hm key)))
+ (ensures (
+ match hash_map_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 /\
+ // The invariant is preserved
+ hash_map_t_inv hm' /\
+ // The length is preserved
+ hash_map_t_len_s hm' = hash_map_t_len_s hm /\
+ // [key] maps to [value]
+ hash_map_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')))
+
+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
+ | Fail -> assert(False)
+ | Return hm' ->
+ hash_map_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
+
+(*** remove'fwd *)
+
+val hash_map_remove_from_list_fwd_lem
+ (#t : Type0) (key : usize) (ls : list_t t) :
+ Lemma
+ (ensures (
+ match hash_map_remove_from_list_fwd 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 =
+ begin match ls with
+ | ListCons 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
+ begin match mv_ls with
+ | ListCons i cvalue tl0 -> ()
+ | ListNil -> ()
+ end
+ else
+ begin
+ hash_map_remove_from_list_fwd_lem key tl;
+ match hash_map_remove_from_list_fwd t key tl with
+ | Fail -> ()
+ | Return opt -> ()
+ end
+ | ListNil -> ()
+ end
+#pop-options
+
+val hash_map_remove_fwd_lem_aux
+ (#t : Type0) (self : hash_map_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))
+ (ensures (
+ match hash_map_remove_fwd t self key with
+ | Fail -> False
+ | Return opt_x -> opt_x == hash_map_t_find_s self key))
+
+let hash_map_remove_fwd_lem_aux #t self key =
+ begin match hash_key_fwd 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
+ begin match usize_rem i i1 with
+ | Fail -> ()
+ | Return hash_mod ->
+ begin match vec_index_mut_fwd (list_t t) 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
+ | Fail -> ()
+ | Return x ->
+ begin match x with
+ | None -> ()
+ | Some x0 ->
+ begin
+ assert(l == index v hash_mod);
+ assert(length (list_t_v #t l) > 0);
+ length_flatten_index (hash_map_t_v self) hash_mod;
+ match usize_sub i0 1 with
+ | Fail -> ()
+ | Return _ -> ()
+ end
+ end
+ end
+ end
+ end
+ end
+
+/// .fsti
+let hash_map_remove_fwd_lem #t self key = hash_map_remove_fwd_lem_aux #t self key
+
+(*** remove'back *)
+
+(**** Refinement proofs *)
+
+/// High-level model for [remove_from_list'back]
+let hash_map_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
+ (#t : Type0) (key : usize) (ls : list_t t) :
+ Lemma
+ (ensures (
+ match hash_map_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) /\
+ // The length is decremented, iff the key was in the slot
+ (let len = length (list_t_v ls) in
+ let len' = length (list_t_v ls') in
+ match slot_s_find key (list_t_v ls) with
+ | None -> len = len'
+ | Some _ -> len = len' + 1)))
+
+#push-options "--fuel 1"
+let rec hash_map_remove_from_list_back_lem_refin #t key ls =
+ begin match ls with
+ | ListCons 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
+ begin match mv_ls with
+ | ListCons i cvalue tl0 -> ()
+ | ListNil -> ()
+ end
+ else
+ begin
+ hash_map_remove_from_list_back_lem_refin key tl;
+ match hash_map_remove_from_list_back t key tl with
+ | Fail -> ()
+ | Return l -> let ls0 = ListCons ckey x l in ()
+ end
+ | ListNil -> ()
+ 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 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
+ list_update self hash slot'
+
+/// Refinement lemma
+val hash_map_remove_back_lem_refin
+ (#t : Type0) (self : hash_map_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))
+ (ensures (
+ match hash_map_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 /\
+ // 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
+ | None -> len = len'
+ | Some _ -> len = len' + 1)))
+
+let hash_map_remove_back_lem_refin #t self key =
+ begin match hash_key_fwd 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
+ begin match usize_rem i i2 with
+ | Fail -> ()
+ | Return hash_mod ->
+ begin match vec_index_mut_fwd (list_t t) 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
+ | 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
+ | 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
+ | Fail -> ()
+ | Return v0 -> ()
+ end
+ end
+ | Some x0 ->
+ begin
+ assert(l == index v hash_mod);
+ assert(length (list_t_v #t l) > 0);
+ length_flatten_index (hash_map_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
+ | 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
+ | Fail -> ()
+ | Return v0 -> ()
+ end
+ end
+ end
+ end
+ end
+ end
+ end
+ end
+
+(**** Invariants, high-level properties *)
+
+val hash_map_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
+ slot_s_inv len i slot' /\
+ slot_s_find k slot' == None /\
+ (forall (k':key{k' <> k}). slot_s_find k' slot' == slot_s_find k' slot) /\
+ // This postcondition is necessary to prove that the invariant is preserved
+ // in the recursive calls. This allows us to do the proof in one go.
+ (forall (b:binding t). for_all (binding_neq b) slot ==> for_all (binding_neq b) slot')
+ ))
+
+#push-options "--fuel 1"
+let rec hash_map_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
+ assert(for_all (same_hash_mod_key len i) ((k',v)::slot''));
+ assert(for_all (binding_neq (k',v)) slot'); // Triggers instanciation
+ assert(for_all (binding_neq (k',v)) slot'')
+ end
+ else
+ begin
+ assert(for_all (binding_neq (k',v)) slot');
+ for_all_binding_neq_find_lem key v slot'
+ end
+#pop-options
+
+val hash_map_remove_s_lem
+ (#t : Type0) (self : hash_map_s_nes t) (key : usize) :
+ Lemma
+ (requires (hash_map_s_inv self))
+ (ensures (
+ let hm' = hash_map_remove_s self key in
+ // The invariant is preserved
+ hash_map_s_inv hm' /\
+ // We updated the binding
+ hash_map_s_updated_binding self key None hm'))
+
+let hash_map_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
+ let hm' = list_update self hash slot' in
+ assert(hash_map_s_inv self)
+
+/// Final lemma about [remove'back]
+val hash_map_remove_back_lem_aux
+ (#t : Type0) (self : hash_map_t t) (key : usize) :
+ Lemma
+ (requires (hash_map_t_inv self))
+ (ensures (
+ match hash_map_remove_back t self key with
+ | Fail -> False
+ | Return hm' ->
+ hash_map_t_inv self /\
+ hash_map_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 /\
+ // 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
+ | 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
+
+/// .fsti
+let hash_map_remove_back_lem #t self key =
+ hash_map_remove_back_lem_aux #t self key
diff --git a/tests/fstar/hashmap/Hashmap.Properties.fsti b/tests/fstar/hashmap/Hashmap.Properties.fsti
new file mode 100644
index 00000000..756ae687
--- /dev/null
+++ b/tests/fstar/hashmap/Hashmap.Properties.fsti
@@ -0,0 +1,267 @@
+(** Properties about the hashmap *)
+module Hashmap.Properties
+open Primitives
+open FStar.List.Tot
+open FStar.Mul
+open Hashmap.Types
+open Hashmap.Clauses
+open Hashmap.Funs
+
+#set-options "--z3rlimit 50 --fuel 0 --ifuel 1"
+
+// Small trick to align the .fst and the .fsti
+val _align_fsti : unit
+
+(*** Utilities *)
+
+type key : eqtype = usize
+
+type hash : eqtype = usize
+
+val hash_map_t_inv (#t : Type0) (hm : hash_map_t t) : Type0
+
+val len_s (#t : Type0) (hm : hash_map_t t) : nat
+
+val find_s (#t : Type0) (hm : hash_map_t t) (k : key) : option t
+
+(*** Overloading *)
+
+/// Upon inserting *new* entries in the hash map, the slots vector is resized
+/// whenever we reach the max load, unless we can't resize anymore because
+/// there are already too many entries. This way, we maintain performance by
+/// limiting the hash collisions.
+/// This is expressed by the following property, which is maintained in the hash
+/// map invariant.
+val hash_map_not_overloaded_lem (#t : Type0) (hm : hash_map_t t) :
+ Lemma
+ (requires (hash_map_t_inv hm))
+ (ensures (
+ // The capacity is the number of slots
+ let capacity = length hm.hash_map_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
+ // technicality: this postcondition won't typecheck if we don't reveal
+ // that divisor > 0 (because of the division)
+ divisor > 0 /\
+ begin
+ // The max load, computed as a fraction of the capacity
+ let max_load = (capacity * dividend) / divisor in
+ // The number of entries inserted in the map is given by [len_s] (see
+ // the functional correctness lemmas, which state how this number evolves):
+ let len = len_s hm in
+ // We prove that:
+ // - either the number of entries is <= than the max load threshold
+ len <= max_load
+ // - or we couldn't resize the map, because then the arithmetic computations
+ // would overflow (note that we always multiply the number of slots by 2)
+ || 2* capacity * dividend > usize_max
+ end))
+
+(*** Functional correctness *)
+(**** [new'fwd] *)
+
+/// [new] doesn't fail and returns an empty hash map
+val hash_map_new_fwd_lem (t : Type0) :
+ Lemma
+ (ensures (
+ match hash_map_new_fwd t with
+ | Fail -> False
+ | Return hm ->
+ // The hash map invariant is satisfied
+ hash_map_t_inv hm /\
+ // The hash map has a length of 0
+ len_s hm = 0 /\
+ // It contains no bindings
+ (forall k. find_s hm k == None)))
+
+(**** [clear] *)
+
+/// [clear] doesn't fail and turns the hash map into an empty map
+val hash_map_clear_fwd_back_lem
+ (#t : Type0) (self : hash_map_t t) :
+ Lemma
+ (requires (hash_map_t_inv self))
+ (ensures (
+ match hash_map_clear_fwd_back t self with
+ | Fail -> False
+ | Return hm ->
+ // The hash map invariant is satisfied
+ hash_map_t_inv hm /\
+ // The hash map has a length of 0
+ len_s hm = 0 /\
+ // It contains no bindings
+ (forall k. find_s hm k == None)))
+
+(**** [len] *)
+
+/// [len] can't fail and returns the length (the number of elements) of the hash map
+val hash_map_len_fwd_lem (#t : Type0) (self : hash_map_t t) :
+ Lemma
+ (requires (hash_map_t_inv self))
+ (ensures (
+ match hash_map_len_fwd t self with
+ | Fail -> False
+ | Return l -> l = len_s self))
+
+
+(**** [insert'fwd_back] *)
+
+/// The backward function for [insert] (note it is named "...insert'fwd_back" because
+/// the forward function doesn't return anything, and was thus filtered - in a
+/// sense the effect of applying the forward function then the backward function is
+/// entirely encompassed by the effect of the backward function alone).
+///
+/// [insert'fwd_back] simply inserts a binding.
+val hash_map_insert_fwd_back_lem
+ (#t : Type0) (self : hash_map_t t) (key : usize) (value : t) :
+ Lemma
+ (requires (hash_map_t_inv self))
+ (ensures (
+ match hash_map_insert_fwd_back t self key value with
+ | Fail ->
+ // We can fail only if:
+ // - the key is not in the map and we thus need to add it
+ None? (find_s self key) /\
+ // - and we are already saturated (we can't increment the internal counter)
+ len_s self = usize_max
+ | Return hm' ->
+ // The invariant is preserved
+ hash_map_t_inv hm' /\
+ // [key] maps to [value]
+ find_s hm' key == Some value /\
+ // The other bindings are preserved
+ (forall k'. k' <> key ==> find_s hm' k' == find_s self k') /\
+ begin
+ // The length is incremented, iff we inserted a new key
+ match find_s self key with
+ | None -> len_s hm' = len_s self + 1
+ | Some _ -> len_s hm' = len_s self
+ end))
+
+
+(**** [contains_key] *)
+
+/// [contains_key'fwd] can't fail and returns `true` if and only if there is
+/// a binding for key [key]
+val hash_map_contains_key_fwd_lem
+ (#t : Type0) (self : hash_map_t t) (key : usize) :
+ Lemma
+ (requires (hash_map_t_inv self))
+ (ensures (
+ match hash_map_contains_key_fwd 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) :
+ Lemma
+ (requires (hash_map_t_inv self))
+ (ensures (
+ match hash_map_get_fwd t self key, find_s self key with
+ | Fail, None -> True
+ | Return x, Some x' -> x == x'
+ | _ -> False))
+
+(**** [get_mut'fwd] *)
+
+/// [get_mut'fwd] returns (a mutable borrow to) the binding for key [key].
+///
+/// The *forward* function models the action of getting a borrow to an element
+/// in Rust, which gives the possibility of modifying this element in place. Then,
+/// upon ending the borrow, the effect of the modification is modelled in the
+/// translation through a call to the backward function.
+val hash_map_get_mut_fwd_lem
+ (#t : Type0) (self : hash_map_t t) (key : usize) :
+ Lemma
+ (requires (hash_map_t_inv self))
+ (ensures (
+ match hash_map_get_mut_fwd t self key, find_s self key with
+ | Fail, None -> True
+ | Return x, Some x' -> x == x'
+ | _ -> False))
+
+
+(**** [get_mut'back] *)
+
+/// [get_mut'back] updates the binding for key [key], without failing.
+/// A call to [get_mut'back] must follow a call to [get_mut'fwd], which gives
+/// us that there must be a binding for key [key] in the map (otherwise we
+/// can't prove the absence of failure).
+val hash_map_get_mut_back_lem
+ (#t : Type0) (hm : hash_map_t t) (key : usize) (ret : t) :
+ Lemma
+ (requires (
+ hash_map_t_inv hm /\
+ // A call to the backward function must follow a call to the forward
+ // function, whose success gives us that there is a binding for the key.
+ // In the case of *forward* functions, "success" has to be understood as
+ // the absence of panics. When translating code from Rust to pure lambda
+ // calculus, we have the property that the generated calls to the backward
+ // functions can't fail (because their are preceded by calls to forward
+ // functions, which must then have succeeded before): for a backward function,
+ // "failure" is to be understood as the semantics getting stuck.
+ // This is of course true unless we filtered the call to the forward function
+ // because its effect is encompassed by the backward function, as with
+ // [hash_map_clear_fwd_back]).
+ Some? (find_s hm key)))
+ (ensures (
+ match hash_map_get_mut_back t hm key ret with
+ | Fail -> False // Can't fail
+ | Return hm' ->
+ // The invariant is preserved
+ hash_map_t_inv hm' /\
+ // The length is preserved
+ len_s hm' = len_s hm /\
+ // [key] maps to the update value, [ret]
+ find_s hm' key == Some ret /\
+ // The other bindings are preserved
+ (forall k'. k' <> key ==> find_s hm' k' == find_s hm k')))
+
+(**** [remove'fwd] *)
+
+/// [remove'fwd] returns the (optional) element which has been removed from the map
+/// (the rust function *moves* it out of the map). Note that the effect of the update
+/// on the map is modelles through the call to [remove'back] ([remove] takes a
+/// mutable borrow to the hash map as parameter).
+val hash_map_remove_fwd_lem
+ (#t : Type0) (self : hash_map_t t) (key : usize) :
+ Lemma
+ (requires (hash_map_t_inv self))
+ (ensures (
+ match hash_map_remove_fwd t self key with
+ | Fail -> False
+ | Return opt_x -> opt_x == find_s self key))
+
+
+(**** [remove'back] *)
+
+/// The hash map given as parameter to [remove] is given through a mutable borrow:
+/// hence the backward function which gives back the updated map, without the
+/// binding.
+val hash_map_remove_back_lem
+ (#t : Type0) (self : hash_map_t t) (key : usize) :
+ Lemma
+ (requires (hash_map_t_inv self))
+ (ensures (
+ match hash_map_remove_back t self key with
+ | Fail -> False
+ | Return hm' ->
+ // The invariant is preserved
+ hash_map_t_inv self /\
+ // The binding for [key] is not there anymore
+ find_s hm' key == None /\
+ // The other bindings are preserved
+ (forall k'. k' <> key ==> find_s hm' k' == find_s self k') /\
+ begin
+ // The length is decremented iff the key was in the map
+ let len = len_s self in
+ let len' = len_s hm' in
+ match find_s self key with
+ | None -> len = len'
+ | Some _ -> len = len' + 1
+ end))
diff --git a/tests/fstar/hashmap/Hashmap.Types.fst b/tests/fstar/hashmap/Hashmap.Types.fst
new file mode 100644
index 00000000..d53b8a42
--- /dev/null
+++ b/tests/fstar/hashmap/Hashmap.Types.fst
@@ -0,0 +1,25 @@
+(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
+(** [hashmap]: type definitions *)
+module Hashmap.Types
+open Primitives
+
+#set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
+
+(** [hashmap::List] *)
+type list_t (t : Type0) =
+| ListCons : usize -> t -> list_t t -> list_t t
+| ListNil : list_t t
+
+(** [hashmap::HashMap] *)
+type hash_map_t (t : Type0) =
+{
+ hash_map_num_entries : usize;
+ hash_map_max_load_factor : (usize & usize);
+ hash_map_max_load : usize;
+ hash_map_slots : vec (list_t t);
+}
+
+(** [core::num::u32::{9}::MAX] *)
+let core_num_u32_max_body : result u32 = Return 4294967295
+let core_num_u32_max_c : u32 = eval_global core_num_u32_max_body
+
diff --git a/tests/fstar/hashmap/Makefile b/tests/fstar/hashmap/Makefile
new file mode 100644
index 00000000..a16b0edb
--- /dev/null
+++ b/tests/fstar/hashmap/Makefile
@@ -0,0 +1,47 @@
+INCLUDE_DIRS = .
+
+FSTAR_INCLUDES = $(addprefix --include ,$(INCLUDE_DIRS))
+
+FSTAR_HINTS ?= --use_hints --use_hint_hashes --record_hints
+
+FSTAR_OPTIONS = $(FSTAR_HINTS) \
+ --cache_checked_modules $(FSTAR_INCLUDES) --cmi \
+ --warn_error '+241@247+285-274' \
+
+FSTAR_NO_FLAGS = fstar.exe --already_cached 'Prims FStar LowStar Steel' --odir obj --cache_dir obj
+
+FSTAR = $(FSTAR_NO_FLAGS) $(FSTAR_OPTIONS)
+
+# The F* roots are used to compute the dependency graph, and generate the .depend file
+FSTAR_ROOTS ?= $(wildcard *.fst *.fsti)
+
+# Build all the files
+all: $(addprefix obj/,$(addsuffix .checked,$(FSTAR_ROOTS)))
+
+# This is the right way to ensure the .depend file always gets re-built.
+ifeq (,$(filter %-in,$(MAKECMDGOALS)))
+ifndef NODEPEND
+ifndef MAKE_RESTARTS
+.depend: .FORCE
+ $(FSTAR_NO_FLAGS) --dep full $(notdir $(FSTAR_ROOTS)) > $@
+
+.PHONY: .FORCE
+.FORCE:
+endif
+endif
+
+include .depend
+endif
+
+# For the interactive mode
+%.fst-in %.fsti-in:
+ @echo $(FSTAR_OPTIONS)
+
+# Generete the .checked files in batch mode
+%.checked:
+ $(FSTAR) $(FSTAR_OPTIONS) $< && \
+ touch -c $@
+
+.PHONY: clean
+clean:
+ rm -f obj/*
diff --git a/tests/fstar/hashmap/Primitives.fst b/tests/fstar/hashmap/Primitives.fst
new file mode 100644
index 00000000..96138e46
--- /dev/null
+++ b/tests/fstar/hashmap/Primitives.fst
@@ -0,0 +1,287 @@
+/// This file lists primitive and assumed functions and types
+module Primitives
+open FStar.Mul
+open FStar.List.Tot
+
+#set-options "--z3rlimit 15 --fuel 0 --ifuel 1"
+
+(*** Utilities *)
+val list_update (#a : Type0) (ls : list a) (i : nat{i < length ls}) (x : a) :
+ ls':list a{
+ length ls' = length ls /\
+ index ls' i == x
+ }
+#push-options "--fuel 1"
+let rec list_update #a ls i x =
+ match ls with
+ | x' :: ls -> if i = 0 then x :: ls else x' :: list_update ls (i-1) x
+#pop-options
+
+(*** Result *)
+type result (a : Type0) : Type0 =
+| Return : v:a -> result a
+| Fail : result a
+
+// Monadic bind and return.
+// Re-definining those allows us to customize the result of the monadic notations
+// like: `y <-- f x;`
+let return (#a : Type0) (x:a) : result a = Return x
+let bind (#a #b : Type0) (m : result a) (f : a -> result b) : result b =
+ match m with
+ | Return x -> f x
+ | Fail -> Fail
+
+// Monadic assert(...)
+let massert (b:bool) : result unit = if b then Return () else Fail
+
+// Normalize and unwrap a successful result (used for globals).
+let eval_global (#a : Type0) (x : result a{Return? (normalize_term x)}) : a = Return?.v x
+
+(*** Misc *)
+type char = FStar.Char.char
+type string = string
+
+let mem_replace_fwd (a : Type0) (x : a) (y : a) : a = x
+let mem_replace_back (a : Type0) (x : a) (y : a) : a = y
+
+(*** Scalars *)
+/// Rk.: most of the following code was at least partially generated
+
+let isize_min : int = -9223372036854775808 // TODO: should be opaque
+let isize_max : int = 9223372036854775807 // TODO: should be opaque
+let i8_min : int = -128
+let i8_max : int = 127
+let i16_min : int = -32768
+let i16_max : int = 32767
+let i32_min : int = -2147483648
+let i32_max : int = 2147483647
+let i64_min : int = -9223372036854775808
+let i64_max : int = 9223372036854775807
+let i128_min : int = -170141183460469231731687303715884105728
+let i128_max : int = 170141183460469231731687303715884105727
+let usize_min : int = 0
+let usize_max : int = 4294967295 // TODO: should be opaque
+let u8_min : int = 0
+let u8_max : int = 255
+let u16_min : int = 0
+let u16_max : int = 65535
+let u32_min : int = 0
+let u32_max : int = 4294967295
+let u64_min : int = 0
+let u64_max : int = 18446744073709551615
+let u128_min : int = 0
+let u128_max : int = 340282366920938463463374607431768211455
+
+type scalar_ty =
+| Isize
+| I8
+| I16
+| I32
+| I64
+| I128
+| Usize
+| U8
+| U16
+| U32
+| U64
+| U128
+
+let scalar_min (ty : scalar_ty) : int =
+ match ty with
+ | Isize -> isize_min
+ | I8 -> i8_min
+ | I16 -> i16_min
+ | I32 -> i32_min
+ | I64 -> i64_min
+ | I128 -> i128_min
+ | Usize -> usize_min
+ | U8 -> u8_min
+ | U16 -> u16_min
+ | U32 -> u32_min
+ | U64 -> u64_min
+ | U128 -> u128_min
+
+let scalar_max (ty : scalar_ty) : int =
+ match ty with
+ | Isize -> isize_max
+ | I8 -> i8_max
+ | I16 -> i16_max
+ | I32 -> i32_max
+ | I64 -> i64_max
+ | I128 -> i128_max
+ | Usize -> usize_max
+ | U8 -> u8_max
+ | U16 -> u16_max
+ | U32 -> u32_max
+ | U64 -> u64_max
+ | U128 -> u128_max
+
+type scalar (ty : scalar_ty) : eqtype = x:int{scalar_min ty <= x && x <= scalar_max ty}
+
+let mk_scalar (ty : scalar_ty) (x : int) : result (scalar ty) =
+ if scalar_min ty <= x && scalar_max ty >= x then Return x else Fail
+
+let scalar_neg (#ty : scalar_ty) (x : scalar ty) : result (scalar ty) = mk_scalar ty (-x)
+
+let scalar_div (#ty : scalar_ty) (x : scalar ty) (y : scalar ty) : result (scalar ty) =
+ if y <> 0 then mk_scalar ty (x / y) else Fail
+
+/// The remainder operation
+let int_rem (x : int) (y : int{y <> 0}) : int =
+ if x >= 0 then (x % y) else -(x % y)
+
+(* Checking consistency with Rust *)
+let _ = assert_norm(int_rem 1 2 = 1)
+let _ = assert_norm(int_rem (-1) 2 = -1)
+let _ = assert_norm(int_rem 1 (-2) = 1)
+let _ = assert_norm(int_rem (-1) (-2) = -1)
+
+let scalar_rem (#ty : scalar_ty) (x : scalar ty) (y : scalar ty) : result (scalar ty) =
+ if y <> 0 then mk_scalar ty (int_rem x y) else Fail
+
+let scalar_add (#ty : scalar_ty) (x : scalar ty) (y : scalar ty) : result (scalar ty) =
+ mk_scalar ty (x + y)
+
+let scalar_sub (#ty : scalar_ty) (x : scalar ty) (y : scalar ty) : result (scalar ty) =
+ mk_scalar ty (x - y)
+
+let scalar_mul (#ty : scalar_ty) (x : scalar ty) (y : scalar ty) : result (scalar ty) =
+ mk_scalar ty (x * y)
+
+(** Cast an integer from a [src_ty] to a [tgt_ty] *)
+// TODO: check the semantics of casts in Rust
+let scalar_cast (src_ty : scalar_ty) (tgt_ty : scalar_ty) (x : scalar src_ty) : result (scalar tgt_ty) =
+ mk_scalar tgt_ty x
+
+/// The scalar types
+type isize : eqtype = scalar Isize
+type i8 : eqtype = scalar I8
+type i16 : eqtype = scalar I16
+type i32 : eqtype = scalar I32
+type i64 : eqtype = scalar I64
+type i128 : eqtype = scalar I128
+type usize : eqtype = scalar Usize
+type u8 : eqtype = scalar U8
+type u16 : eqtype = scalar U16
+type u32 : eqtype = scalar U32
+type u64 : eqtype = scalar U64
+type u128 : eqtype = scalar U128
+
+/// Negation
+let isize_neg = scalar_neg #Isize
+let i8_neg = scalar_neg #I8
+let i16_neg = scalar_neg #I16
+let i32_neg = scalar_neg #I32
+let i64_neg = scalar_neg #I64
+let i128_neg = scalar_neg #I128
+
+/// Division
+let isize_div = scalar_div #Isize
+let i8_div = scalar_div #I8
+let i16_div = scalar_div #I16
+let i32_div = scalar_div #I32
+let i64_div = scalar_div #I64
+let i128_div = scalar_div #I128
+let usize_div = scalar_div #Usize
+let u8_div = scalar_div #U8
+let u16_div = scalar_div #U16
+let u32_div = scalar_div #U32
+let u64_div = scalar_div #U64
+let u128_div = scalar_div #U128
+
+/// Remainder
+let isize_rem = scalar_rem #Isize
+let i8_rem = scalar_rem #I8
+let i16_rem = scalar_rem #I16
+let i32_rem = scalar_rem #I32
+let i64_rem = scalar_rem #I64
+let i128_rem = scalar_rem #I128
+let usize_rem = scalar_rem #Usize
+let u8_rem = scalar_rem #U8
+let u16_rem = scalar_rem #U16
+let u32_rem = scalar_rem #U32
+let u64_rem = scalar_rem #U64
+let u128_rem = scalar_rem #U128
+
+/// Addition
+let isize_add = scalar_add #Isize
+let i8_add = scalar_add #I8
+let i16_add = scalar_add #I16
+let i32_add = scalar_add #I32
+let i64_add = scalar_add #I64
+let i128_add = scalar_add #I128
+let usize_add = scalar_add #Usize
+let u8_add = scalar_add #U8
+let u16_add = scalar_add #U16
+let u32_add = scalar_add #U32
+let u64_add = scalar_add #U64
+let u128_add = scalar_add #U128
+
+/// Substraction
+let isize_sub = scalar_sub #Isize
+let i8_sub = scalar_sub #I8
+let i16_sub = scalar_sub #I16
+let i32_sub = scalar_sub #I32
+let i64_sub = scalar_sub #I64
+let i128_sub = scalar_sub #I128
+let usize_sub = scalar_sub #Usize
+let u8_sub = scalar_sub #U8
+let u16_sub = scalar_sub #U16
+let u32_sub = scalar_sub #U32
+let u64_sub = scalar_sub #U64
+let u128_sub = scalar_sub #U128
+
+/// Multiplication
+let isize_mul = scalar_mul #Isize
+let i8_mul = scalar_mul #I8
+let i16_mul = scalar_mul #I16
+let i32_mul = scalar_mul #I32
+let i64_mul = scalar_mul #I64
+let i128_mul = scalar_mul #I128
+let usize_mul = scalar_mul #Usize
+let u8_mul = scalar_mul #U8
+let u16_mul = scalar_mul #U16
+let u32_mul = scalar_mul #U32
+let u64_mul = scalar_mul #U64
+let u128_mul = scalar_mul #U128
+
+(*** Vector *)
+type vec (a : Type0) = v:list a{length v <= usize_max}
+
+let vec_new (a : Type0) : vec a = assert_norm(length #a [] == 0); []
+let vec_len (a : Type0) (v : vec a) : usize = length v
+
+// The **forward** function shouldn't be used
+let vec_push_fwd (a : Type0) (v : vec a) (x : a) : unit = ()
+let vec_push_back (a : Type0) (v : vec a) (x : a) :
+ Pure (result (vec a))
+ (requires True)
+ (ensures (fun res ->
+ match res with
+ | Fail -> True
+ | Return v' -> length v' = length v + 1)) =
+ if length v < usize_max then begin
+ (**) assert_norm(length [x] == 1);
+ (**) append_length v [x];
+ (**) assert(length (append v [x]) = length v + 1);
+ Return (append v [x])
+ end
+ else Fail
+
+// The **forward** function shouldn't be used
+let vec_insert_fwd (a : Type0) (v : vec a) (i : usize) (x : a) : result unit =
+ if i < length v then Return () else Fail
+let vec_insert_back (a : Type0) (v : vec a) (i : usize) (x : a) : result (vec a) =
+ if i < length v then Return (list_update v i x) else Fail
+
+// The **backward** function shouldn't be used
+let vec_index_fwd (a : Type0) (v : vec a) (i : usize) : result a =
+ if i < length v then Return (index v i) else Fail
+let vec_index_back (a : Type0) (v : vec a) (i : usize) (x : a) : result unit =
+ if i < length v then Return () else Fail
+
+let vec_index_mut_fwd (a : Type0) (v : vec a) (i : usize) : result a =
+ if i < length v then Return (index v i) else Fail
+let vec_index_mut_back (a : Type0) (v : vec a) (i : usize) (nx : a) : result (vec a) =
+ if i < length v then Return (list_update v i nx) else Fail
+
generated by cgit v1.2.3 (git 2.25.1) at 2024-10-18 21:34:33 +0000