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(** Properties about the hashmap written on disk *)
module Hashmap.Properties
open Primitives
open Hashmap.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_t u64
/// [serialize] updates the hash map stored on disk
assume
val serialize_lem (hm : hashMap_t u64) (st : state) : Lemma (
match utils_serialize hm st with
| Fail _ -> True
| Ok (st', ()) -> state_v st' == hm)
[SMTPat (utils_serialize hm st)]
/// [deserialize] gives us the hash map stored on disk, without updating it
assume
val deserialize_lem (st : state) : Lemma (
match utils_deserialize st with
| Fail _ -> True
| Ok (st', hm) -> hm == state_v st /\ st' == st)
[SMTPat (utils_deserialize 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_lem (key : usize) (value : u64) (st : state) : Lemma (
match insert_on_disk key value st with
| Fail _ -> True
| Ok (st', ()) ->
let hm = state_v st in
match hashMap_insert u64 hm key value with
| Fail _ -> False
| Ok hm' -> hm' == state_v st')
let insert_on_disk_lem key value st = ()
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