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spec_mpmcqueue_history.v
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spec_mpmcqueue_history.v
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From gpfsl.examples Require Import sflib.
From stdpp Require Import namespaces.
From gpfsl.logic Require Import logatom.
From gpfsl.examples.omo Require Export omo omo_preds append_only_loc.
Require Import iris.prelude.options.
Local Open Scope Z_scope.
Inductive qevent := Init | Enq (v : Z) | Deq (v : Z). (* No EmpDeq in Folly queue *)
Definition queue_state := list (event_id * Z * view * eView).
Global Instance qevent_inhabited : Inhabited qevent := populate Init.
Local Notation history := (history qevent).
Implicit Types (E : history) (qu : queue_state).
(* Build queue state with the events in the given order *)
Inductive queue_step : ∀ (e : event_id) (eV : omo_event qevent) qu qu', Prop :=
| queue_step_Enq u uV v qu
(ENQ : uV.(type) = Enq v)
(NZ : 0 < v)
(EVIEW : u ∈ uV.(eview))
: queue_step u uV qu (qu ++ [(u, v, uV.(sync), uV.(eview))])
| queue_step_Deq u o oV v V lV qu
(DEQ : oV.(type) = Deq v)
(NZ : 0 < v)
(SYNC : V ⊑ oV.(sync))
(EVIEW : {[o; u]} ∪ lV ⊆ oV.(eview))
: queue_step o oV ((u, v, V, lV) :: qu) qu
| queue_step_Init eV
(INIT : eV.(type) = Init)
(EVIEW : eV.(eview) = {[0%nat]})
: queue_step 0%nat eV [] []
.
Global Instance queue_interpretable : Interpretable qevent queue_state :=
{
init := [];
step := queue_step
}.
Definition QueueLocalT Σ : Type :=
∀ (N : namespace) (γg : gname) (q : loc) (E : history) (M : eView), vProp Σ.
Definition QueueInvT Σ : Type :=
∀ (γg : gname) (q : loc) (E : history), vProp Σ.
Definition new_queue_spec' {Σ} `{!noprolG Σ}
(newQueue : val) (QueueLocal : QueueLocalT Σ) (QueueInv : QueueInvT Σ) : Prop :=
∀ N tid (sz : nat),
(0 < sz)%nat →
{{{ True }}}
newQueue [ #sz] @ tid; ⊤
{{{ γg (q: loc) V E M, RET #q;
⊒V ∗ @{V} QueueLocal N γg q E M ∗ QueueInv γg q E ∗
⌜ E = [mkOmoEvent Init V M] ⌝ }}}.
Definition enqueue_spec' {Σ} `{!noprolG Σ}
(enqueue : val) (QueueLocal : QueueLocalT Σ) (QueueInv : QueueInvT Σ) : Prop :=
∀ N (DISJ: N ## histN) (q: loc) tid γg E1 M (V : view) (v : Z) (Posx: 0 < v),
(* PRIVATE PRE *)
(* E1 is a snapshot of the history, locally observed by M *)
⊒V -∗ QueueLocal N γg q E1 M -∗
(* PUBLIC PRE *)
<<< ∀ E, ▷ QueueInv γg q E >>>
enqueue [ #q ; #v] @ tid; ↑N
<<< ∃ V' E' M',
(* PUBLIC POST *)
▷ QueueInv γg q E' ∗
⊒V' ∗ @{V'} QueueLocal N γg q E' M' ∗
⌜ V ⊑ V' ∧
E' = E ++ [mkOmoEvent (Enq v) V' M'] ∧ M ⊆ M' ⌝,
RET #☠, emp >>>
.
Definition dequeue_spec' {Σ} `{!noprolG Σ}
(dequeue : val) (QueueLocal : QueueLocalT Σ) (QueueInv : QueueInvT Σ) : Prop :=
∀ N (DISJ: N ## histN) (q: loc) tid γg E1 M V,
(* PRIVATE PRE *)
⊒V -∗ QueueLocal N γg q E1 M -∗
(* PUBLIC PRE *)
<<< ∀ E, ▷ QueueInv γg q E >>>
dequeue [ #q] @ tid; ↑N
<<< ∃ (v: Z) V' E' M',
(* PUBLIC POST *)
▷ QueueInv γg q E' ∗
⊒V' ∗ @{V'} QueueLocal N γg q E' M' ∗
⌜ V ⊑ V' ∧
E' = E ++ [mkOmoEvent (Deq v) V' M'] ∧ M ⊆ M' ∧ 0 < v ⌝,
RET #v, emp >>>
.
Record mpmcqueue_spec {Σ} `{!noprolG Σ} := MpmcQueueSpec {
(** operations *)
newQueue : val;
enqueue : val;
dequeue : val;
(** predicates *)
QueueLocal : QueueLocalT Σ;
QueueInv : QueueInvT Σ;
(** predicates properties *)
QueueInv_Objective : ∀ γg s E, Objective (QueueInv γg s E);
QueueInv_Timeless : ∀ γg s E, Timeless (QueueInv γg s E);
QueueInv_Linearizable : ∀ γg s E, QueueInv γg s E ⊢ ⌜ Linearizability E ⌝;
QueueInv_history_wf :
∀ γg s E, QueueInv γg s E ⊢ ⌜ history_wf E ⌝;
QueueInv_QueueLocal :
∀ N γg q E E' M',
QueueInv γg q E -∗ QueueLocal N γg q E' M' -∗ ⌜ E' ⊑ E ⌝;
QueueLocal_lookup :
∀ N γg q E M e V,
sync <$> E !! e = Some V → e ∈ M → QueueLocal N γg q E M -∗ ⊒V;
QueueLocal_Persistent :
∀ N γg q E M, Persistent (QueueLocal N γg q E M);
(* operations specs *)
new_queue_spec : new_queue_spec' newQueue QueueLocal QueueInv;
enqueue_spec : enqueue_spec' enqueue QueueLocal QueueInv;
dequeue_spec : dequeue_spec' dequeue QueueLocal QueueInv;
}.
Arguments mpmcqueue_spec _ {_}.
Global Existing Instances QueueInv_Objective QueueInv_Timeless QueueLocal_Persistent.