diff options
Diffstat (limited to 'tests/hashmap')
| -rw-r--r-- | tests/hashmap/Hashmap.Clauses.Template.fst | 66 | ||||
| -rw-r--r-- | tests/hashmap/Hashmap.Clauses.fst | 61 | ||||
| -rw-r--r-- | tests/hashmap/Hashmap.Funs.fst | 683 | ||||
| -rw-r--r-- | tests/hashmap/Hashmap.Properties.fst | 3247 | ||||
| -rw-r--r-- | tests/hashmap/Hashmap.Properties.fsti | 267 | ||||
| -rw-r--r-- | tests/hashmap/Hashmap.Types.fst | 25 | ||||
| -rw-r--r-- | tests/hashmap/Makefile | 47 | ||||
| -rw-r--r-- | tests/hashmap/Primitives.fst | 287 |
8 files changed, 0 insertions, 4683 deletions
diff --git a/tests/hashmap/Hashmap.Clauses.Template.fst b/tests/hashmap/Hashmap.Clauses.Template.fst deleted file mode 100644 index 3e51c6f1..00000000 --- a/tests/hashmap/Hashmap.Clauses.Template.fst +++ /dev/null @@ -1,66 +0,0 @@ -(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *) -(** [hashmap]: templates for the decreases clauses *) -module Hashmap.Clauses.Template -open Primitives -open Hashmap.Types - -#set-options "--z3rlimit 50 --fuel 1 --ifuel 1" - -(** [hashmap::HashMap::{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/hashmap/Hashmap.Clauses.fst b/tests/hashmap/Hashmap.Clauses.fst deleted file mode 100644 index 4f3e37e9..00000000 --- a/tests/hashmap/Hashmap.Clauses.fst +++ /dev/null @@ -1,61 +0,0 @@ -(** [hashmap]: the decreases clauses *) -module Hashmap.Clauses -open Primitives -open FStar.List.Tot -open Hashmap.Types - -#set-options "--z3rlimit 50 --fuel 0 --ifuel 1" - -(** [hashmap::HashMap::allocate_slots]: decreases clause *) -unfold -let 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/hashmap/Hashmap.Funs.fst b/tests/hashmap/Hashmap.Funs.fst deleted file mode 100644 index 6e67fca4..00000000 --- a/tests/hashmap/Hashmap.Funs.fst +++ /dev/null @@ -1,683 +0,0 @@ -(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *) -(** [hashmap]: function definitions *) -module Hashmap.Funs -open Primitives -include Hashmap.Types -include Hashmap.Clauses - -#set-options "--z3rlimit 50 --fuel 1 --ifuel 1" - -(** [hashmap::hash_key] *) -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/hashmap/Hashmap.Properties.fst b/tests/hashmap/Hashmap.Properties.fst deleted file mode 100644 index 21a46c73..00000000 --- a/tests/hashmap/Hashmap.Properties.fst +++ /dev/null @@ -1,3247 +0,0 @@ -(** Properties about the hashmap *) -module Hashmap.Properties -open Primitives -open FStar.List.Tot -open FStar.Mul -open Hashmap.Types -open Hashmap.Clauses -open Hashmap.Funs - -#set-options "--z3rlimit 50 --fuel 0 --ifuel 1" - -let _align_fsti = () - -/// The proofs: -/// =========== -/// -/// The proof strategy is to do exactly as with Low* proofs (we initially tried to -/// prove more properties in one go, but it was a mistake): -/// - prove that, under some preconditions, the low-level functions translated -/// from Rust refine some higher-level functions -/// - do functional proofs about those high-level functions to prove interesting -/// properties about the hash map operations, and invariant preservation -/// - combine everything -/// -/// The fact that we work in a pure setting allows us to be more modular than when -/// working with effects. For instance we can do a case disjunction (see the proofs -/// for insert, which study the cases where the key is already/not in the hash map -/// in separate proofs - we had initially tried to do them in one step: it is doable -/// but requires some work, and the F* response time quickly becomes annoying while -/// making progress, so we split them). We can also easily prove a refinement lemma, -/// study the model, *then* combine those to also prove that the low-level function -/// preserves the invariants, rather than do everything at once as is usually the -/// case when doing intrinsic proofs with effects (I remember that having to prove -/// invariants in one go *and* a refinement step, even small, can be extremely -/// difficult in Low*). - - -(*** Utilities *) - -/// We need many small helpers and lemmas, mostly about lists (and the ones we list -/// here are not in the standard F* library). - -val index_append_lem (#a : Type0) (ls0 ls1 : list a) (i : nat{i < length ls0 + length ls1}) : - Lemma ( - (i < length ls0 ==> index (ls0 @ ls1) i == index ls0 i) /\ - (i >= length ls0 ==> index (ls0 @ ls1) i == index ls1 (i - length ls0))) - [SMTPat (index (ls0 @ ls1) i)] - -#push-options "--fuel 1" -let rec index_append_lem #a ls0 ls1 i = - match ls0 with - | [] -> () - | x :: ls0' -> - if i = 0 then () - else index_append_lem ls0' ls1 (i-1) -#pop-options - -val index_map_lem (#a #b: Type0) (f : a -> Tot b) (ls : list a) - (i : nat{i < length ls}) : - Lemma ( - index (map f ls) i == f (index ls i)) - [SMTPat (index (map f ls) i)] - -#push-options "--fuel 1" -let rec index_map_lem #a #b f ls i = - match ls with - | [] -> () - | x :: ls' -> - if i = 0 then () - else index_map_lem f ls' (i-1) -#pop-options - -val for_all_append (#a : Type0) (f : a -> Tot bool) (ls0 ls1 : list a) : - Lemma (for_all f (ls0 @ ls1) = (for_all f ls0 && for_all f ls1)) - -#push-options "--fuel 1" -let rec for_all_append #a f ls0 ls1 = - match ls0 with - | [] -> () - | x :: ls0' -> - for_all_append f ls0' ls1 -#pop-options - -/// Filter a list, stopping after we removed one element -val filter_one (#a : Type) (f : a -> bool) (ls : list a) : list a - -let rec filter_one #a f ls = - match ls with - | [] -> [] - | x :: ls' -> if f x then x :: filter_one f ls' else ls' - -val find_append (#a : Type) (f : a -> bool) (ls0 ls1 : list a) : - Lemma ( - find f (ls0 @ ls1) == - begin match find f ls0 with - | Some x -> Some x - | None -> find f ls1 - end) - -#push-options "--fuel 1" -let rec find_append #a f ls0 ls1 = - match ls0 with - | [] -> () - | x :: ls0' -> - if f x then - begin - assert(ls0 @ ls1 == x :: (ls0' @ ls1)); - assert(find f (ls0 @ ls1) == find f (x :: (ls0' @ ls1))); - // Why do I have to do this?! Is it because of subtyping?? - assert( - match find f (ls0 @ ls1) with - | Some x' -> x' == x - | None -> False) - end - else find_append f ls0' ls1 -#pop-options - -val length_flatten_update : - #a:Type - -> ls:list (list a) - -> i:nat{i < length ls} - -> x:list a -> - Lemma ( - // We want this property: - // ``` - // length (flatten (list_update ls i x)) = - // length (flatten ls) - length (index ls i) + length x - // ``` - length (flatten (list_update ls i x)) + length (index ls i) = - length (flatten ls) + length x) - -#push-options "--fuel 1" -let rec length_flatten_update #a ls i x = - match ls with - | x' :: ls' -> - assert(flatten ls == x' @ flatten ls'); // Triggers patterns - assert(length (flatten ls) == length x' + length (flatten ls')); - if i = 0 then - begin - let ls1 = x :: ls' in - assert(list_update ls i x == ls1); - assert(flatten ls1 == x @ flatten ls'); // Triggers patterns - assert(length (flatten ls1) == length x + length (flatten ls')); - () - end - else - begin - length_flatten_update ls' (i-1) x; - let ls1 = x' :: list_update ls' (i-1) x in - assert(flatten ls1 == x' @ flatten (list_update ls' (i-1) x)) // Triggers patterns - end -#pop-options - -val length_flatten_index : - #a:Type - -> ls:list (list a) - -> i:nat{i < length ls} -> - Lemma ( - length (flatten ls) >= length (index ls i)) - -#push-options "--fuel 1" -let rec length_flatten_index #a ls i = - match ls with - | x' :: ls' -> - assert(flatten ls == x' @ flatten ls'); // Triggers patterns - assert(length (flatten ls) == length x' + length (flatten ls')); - if i = 0 then () - else length_flatten_index ls' (i-1) -#pop-options - -val forall_index_equiv_list_for_all - (#a : Type) (pred : a -> Tot bool) (ls : list a) : - Lemma ((forall (i:nat{i < length ls}). pred (index ls i)) <==> for_all pred ls) - -#push-options "--fuel 1" -let rec forall_index_equiv_list_for_all pred ls = - match ls with - | [] -> () - | x :: ls' -> - assert(forall (i:nat{i < length ls'}). index ls' i == index ls (i+1)); - assert(forall (i:nat{0 < i /\ i < length ls}). index ls i == index ls' (i-1)); - assert(index ls 0 == x); - forall_index_equiv_list_for_all pred ls' -#pop-options - -val find_update: - #a:Type - -> f:(a -> Tot bool) - -> ls:list a - -> x:a - -> ls':list a{length ls' == length ls} -#push-options "--fuel 1" -let rec find_update #a f ls x = - match ls with - | [] -> [] - | hd::tl -> - if f hd then x :: tl else hd :: find_update f tl x -#pop-options - -val pairwise_distinct : #a:eqtype -> ls:list a -> Tot bool -let rec pairwise_distinct (#a : eqtype) (ls : list a) : Tot bool = - match ls with - | [] -> true - | x :: ls' -> List.Tot.for_all (fun y -> x <> y) ls' && pairwise_distinct ls' - -val pairwise_rel : #a:Type -> pred:(a -> a -> Tot bool) -> ls:list a -> Tot bool -let rec pairwise_rel #a pred ls = - match ls with - | [] -> true - | x :: ls' -> - for_all (pred x) ls' && pairwise_rel pred ls' - -#push-options "--fuel 1" -let rec flatten_append (#a : Type) (l1 l2: list (list a)) : - Lemma (flatten (l1 @ l2) == flatten l1 @ flatten l2) = - match l1 with - | [] -> () - | x :: l1' -> - flatten_append l1' l2; - append_assoc x (flatten l1') (flatten l2) -#pop-options - -/// We don't use anonymous functions as parameters to other functions, but rather -/// introduce auxiliary functions instead: otherwise we can't reason (because -/// F*'s encoding to the SMT is imprecise for functions) -let fst_is_disctinct (#a : eqtype) (#b : Type0) (p0 : a & b) (p1 : a & b) : Type0 = - fst p0 <> fst p1 - -(*** Lemmas about Primitives *) -/// TODO: move those lemmas - -// TODO: rename to 'insert'? -val list_update_index_dif_lem - (#a : Type0) (ls : list a) (i : nat{i < length ls}) (x : a) - (j : nat{j < length ls}) : - Lemma (requires (j <> i)) - (ensures (index (list_update ls i x) j == index ls j)) - [SMTPat (index (list_update ls i x) j)] - -#push-options "--fuel 1" -let rec list_update_index_dif_lem #a ls i x j = - match ls with - | x' :: ls -> - if i = 0 then () - else if j = 0 then () - else - list_update_index_dif_lem ls (i-1) x (j-1) -#pop-options - -val map_list_update_lem - (#a #b: Type0) (f : a -> Tot b) - (ls : list a) (i : nat{i < length ls}) (x : a) : - Lemma (list_update (map f ls) i (f x) == map f (list_update ls i x)) - [SMTPat (list_update (map f ls) i (f x))] - -#push-options "--fuel 1" -let rec map_list_update_lem #a #b f ls i x = - match ls with - | x' :: ls' -> - if i = 0 then () - else map_list_update_lem f ls' (i-1) x -#pop-options - -(*** Invariants, models *) - -(**** Internals *) -/// The following invariants, models, representation functions... are mostly -/// for the purpose of the proofs. - -let is_pos_usize (n : nat) : Type0 = 0 < n /\ n <= usize_max -type pos_usize = x:usize{x > 0} - -type binding (t : Type0) = key & t - -type slots_t (t : Type0) = 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/hashmap/Hashmap.Properties.fsti b/tests/hashmap/Hashmap.Properties.fsti deleted file mode 100644 index 756ae687..00000000 --- a/tests/hashmap/Hashmap.Properties.fsti +++ /dev/null @@ -1,267 +0,0 @@ -(** Properties about the hashmap *) -module Hashmap.Properties -open Primitives -open FStar.List.Tot -open FStar.Mul -open Hashmap.Types -open Hashmap.Clauses -open Hashmap.Funs - -#set-options "--z3rlimit 50 --fuel 0 --ifuel 1" - -// Small trick to align the .fst and the .fsti -val _align_fsti : unit - -(*** Utilities *) - -type key : eqtype = usize - -type hash : eqtype = usize - -val 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/hashmap/Hashmap.Types.fst b/tests/hashmap/Hashmap.Types.fst deleted file mode 100644 index d53b8a42..00000000 --- a/tests/hashmap/Hashmap.Types.fst +++ /dev/null @@ -1,25 +0,0 @@ -(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *) -(** [hashmap]: type definitions *) -module Hashmap.Types -open Primitives - -#set-options "--z3rlimit 50 --fuel 1 --ifuel 1" - -(** [hashmap::List] *) -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/hashmap/Makefile b/tests/hashmap/Makefile deleted file mode 100644 index a16b0edb..00000000 --- a/tests/hashmap/Makefile +++ /dev/null @@ -1,47 +0,0 @@ -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/hashmap/Primitives.fst b/tests/hashmap/Primitives.fst deleted file mode 100644 index 96138e46..00000000 --- a/tests/hashmap/Primitives.fst +++ /dev/null @@ -1,287 +0,0 @@ -/// This file lists primitive and assumed functions and types -module Primitives -open FStar.Mul -open FStar.List.Tot - -#set-options "--z3rlimit 15 --fuel 0 --ifuel 1" - -(*** Utilities *) -val list_update (#a : Type0) (ls : list a) (i : nat{i < length ls}) (x : a) : - ls':list a{ - length ls' = length ls /\ - index ls' i == x - } -#push-options "--fuel 1" -let rec list_update #a ls i x = - match ls with - | x' :: ls -> if i = 0 then x :: ls else x' :: list_update ls (i-1) x -#pop-options - -(*** Result *) -type 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 - |