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(** Properties about the hashmap written on disk *)
module HashmapMain.Properties
open Primitives
open HashmapMain.Funs
#set-options "--z3rlimit 50 --fuel 0 --ifuel 1"
/// Below, we focus on the functions to read from disk/write to disk to showcase
/// how such reasoning which mixes opaque functions together with a state-error
/// monad can be performed.
(*** Hypotheses *)
/// [state_v] gives us the hash map currently stored on disk
assume
val state_v : state -> hashmap_hash_map_t u64
/// [serialize] updates the hash map stored on disk
assume
val serialize_lem (hm : hashmap_hash_map_t u64) (st : state) : Lemma (
match hashmap_utils_serialize_fwd hm st with
| Fail -> True
| Return (st', ()) -> state_v st' == hm)
[SMTPat (hashmap_utils_serialize_fwd hm st)]
/// [deserialize] gives us the hash map stored on disk, without updating it
assume
val deserialize_lem (st : state) : Lemma (
match hashmap_utils_deserialize_fwd st with
| Fail -> True
| Return (st', hm) -> hm == state_v st /\ st' == st)
[SMTPat (hashmap_utils_deserialize_fwd st)]
(*** Lemmas *)
/// The obvious lemma about [insert_on_disk]: the updated hash map stored on disk
/// is exactly the hash map produced from inserting the binding ([key], [value])
/// in the hash map previously stored on disk.
val insert_on_disk_fwd_lem (key : usize) (value : u64) (st : state) : Lemma (
match insert_on_disk_fwd key value st with
| Fail -> True
| Return (st', ()) ->
let hm = state_v st in
match hashmap_hash_map_insert_fwd_back u64 hm key value with
| Fail -> False
| Return hm' -> hm' == state_v st')
let insert_on_disk_fwd_lem key value st = ()
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