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spec_elim_composition.v
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spec_elim_composition.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.stack Require Export stack_event_omo.
From gpfsl.examples.omo Require Export omo omo_preds append_only_loc.
Require Import iris.prelude.options.
Local Open Scope Z_scope.
Local Notation history := (history sevent_hist).
Implicit Types (E : history) (stk : stack_state).
Local Notation EMPTY := 0 (only parsing).
Local Notation FAIL_RACE := (-1) (only parsing).
Definition StackLocalT Σ : Type :=
∀ (γg : gname) (s : loc) (M : eView), vProp Σ.
Definition StackLocalNT Σ : Type :=
∀ (N : namespace), StackLocalT Σ.
Definition StackInvT Σ : Type :=
∀ (γg γs : gname) (s : loc) (E : history) (omo : omoT) (stlist : list stack_state), vProp Σ.
Definition new_stack_spec' {Σ} `{!noprolG Σ, !omoGeneralG Σ}
(new_stack : val) (StackLocal : StackLocalNT Σ) (StackInv : StackInvT Σ) : Prop :=
∀ N tid V,
{{{ ⊒V }}}
new_stack [] @ tid; ⊤
{{{ γg γs (s: loc) M V', RET #s;
let eVinit := mkOmoEvent Init V' M in
let E := [eVinit] in
let stinit : stack_state := [] in
⊒V' ∗ StackInv γg γs s E (omo_append_w [] 0%nat []) [stinit] ∗ @{V'} StackLocal N γg s M ∗
OmoTokenW γg 0%nat ∗
⌜ V ⊑ V' ⌝}}}.
Definition try_push_spec' {Σ} `{!noprolG Σ, !omoGeneralG Σ}
(try_push : val) (StackLocal : StackLocalNT Σ) (StackInv : StackInvT Σ) : Prop :=
∀ N (DISJ: N ## histN) (s: loc) tid γg M (V : view) (v : Z) (Posx: 0 < v),
(* PRIVATE PRE *)
⊒V -∗ StackLocal N γg s M -∗
(* PUBLIC PRE *)
<<< ∀ γs E omo stlist, ▷ StackInv γg γs s E omo stlist >>>
try_push [ #s ; #v] @ tid; ↑N
<<< ∃ (b: bool) V' γs' E' omo' stlist' M',
(* PUBLIC POST *)
⊒V' ∗ ▷ StackInv γg γs' s E' omo' stlist' ∗ @{V'} StackLocal N γg s M' ∗
if b then (
(* successful case *)
⌜ E' = E ++ [mkOmoEvent (Push v) V' M']
∧ (∃ gen, omo' = omo_insert_w omo gen (length E) [])
∧ V ⊑ V' ∧ M ⊆ M' ⌝ ∗
OmoUB γg M (length E) ∗
OmoTokenW γg (length E)
) else (
(* FAIL_RACE case *)
⌜ γs' = γs ∧ E' = E ∧ omo' = omo ∧ stlist' = stlist ∧ M' = M ⌝
),
RET #b, emp >>>
.
Definition push_spec' {Σ} `{!noprolG Σ, !omoGeneralG Σ}
(push : val) (StackLocal : StackLocalNT Σ) (StackInv : StackInvT Σ) : Prop :=
∀ N (DISJ: N ## histN) (s: loc) tid γg M (V : view) (v : Z) (Posx: 0 < v),
(* PRIVATE PRE *)
⊒V -∗ StackLocal N γg s M -∗
(* PUBLIC PRE *)
<<< ∀ γs E omo stlist, ▷ StackInv γg γs s E omo stlist >>>
push [ #s ; #v] @ tid; ↑N
<<< ∃ V' γs' omo' stlist' M',
(* PUBLIC POST *)
let eVpush := mkOmoEvent (Push v) V' M' in
let E' := E ++ [eVpush] in
⊒V' ∗ ▷ StackInv γg γs' s E' omo' stlist' ∗ @{V'} StackLocal N γg s M' ∗
OmoUB γg M (length E) ∗
OmoTokenW γg (length E) ∗
⌜ (∃ gen, omo' = omo_insert_w omo gen (length E) [])
∧ V ⊑ V' ∧ M ⊆ M' ⌝,
RET #☠, emp >>>
.
Definition try_pop_spec' {Σ} `{!noprolG Σ, !omoGeneralG Σ}
(try_pop : val) (StackLocal : StackLocalNT Σ) (StackInv : StackInvT Σ) : Prop :=
∀ N (DISJ: N ## histN) (s: loc) tid γg M V,
(* PRIVATE PRE *)
⊒V -∗ StackLocal N γg s M -∗
(* PUBLIC PRE *)
<<< ∀ γs E omo stlist, ▷ StackInv γg γs s E omo stlist >>>
try_pop [ #s] @ tid; ↑N
<<< ∃ (v : Z) V' γs' E' omo' stlist' M',
(* PUBLIC POST *)
⊒V' ∗ ▷ StackInv γg γs' s E' omo' stlist' ∗ @{V'} StackLocal N γg s M' ∗
if (decide (v = FAIL_RACE)) then (
(* FAIL_RACE case *)
⌜ γs' = γs ∧ E' = E ∧ omo' = omo ∧ stlist' = stlist ∧ M' = M ⌝
) else (
⌜ V ⊑ V' ∧ M ⊆ M' ⌝ ∗
OmoUB γg M (length E) ∗
if (decide (v = EMPTY)) then ( (* EMPTY case *)
⌜ E' = E ++ [mkOmoEvent EmpPop V' M'] ∧ stlist' = stlist ∧ γs' = γs
∧ (∃ gen, omo' = omo_insert_r omo gen (length E) ∧ (gen < length omo)%nat) ⌝ ∗
OmoTokenR γg (length E)
) else ( (* successful case *)
⌜ E' = E ++ [mkOmoEvent (Pop v) V' M'] ∧ (∃ gen, omo' = omo_insert_w omo gen (length E) []) ⌝ ∗
OmoTokenW γg (length E)
)
),
RET #v , emp >>>
.
Definition pop_spec' {Σ} `{!noprolG Σ, !omoGeneralG Σ}
(pop : val) (StackLocal : StackLocalNT Σ) (StackInv : StackInvT Σ) : Prop :=
∀ N (DISJ: N ## histN) (s: loc) tid γg M V,
(* PRIVATE PRE *)
⊒V -∗ StackLocal N γg s M -∗
(* PUBLIC PRE *)
<<< ∀ γs E omo stlist, ▷ StackInv γg γs s E omo stlist >>>
pop [ #s] @ tid; ↑N
<<< ∃ (v : Z) V' γs' E' omo' stlist' M',
(* PUBLIC POST *)
⊒V' ∗ ▷ StackInv γg γs' s E' omo' stlist' ∗ @{V'} StackLocal N γg s M' ∗
⌜ V ⊑ V' ∧ M ⊆ M' ⌝ ∗
OmoUB γg M (length E) ∗
if (decide (v = EMPTY)) then ( (* EMPTY case *)
⌜ E' = E ++ [mkOmoEvent EmpPop V' M'] ∧ stlist' = stlist ∧ γs' = γs
∧ (∃ gen, omo' = omo_insert_r omo gen (length E) ∧ (gen < length omo)%nat) ⌝ ∗
OmoTokenR γg (length E)
) else ( (* successful case *)
⌜ E' = E ++ [mkOmoEvent (Pop v) V' M'] ∧ (∃ gen, omo' = omo_insert_w omo gen (length E) []) ⌝ ∗
OmoTokenW γg (length E)
),
RET #v, emp >>>
.
Record stack_spec {Σ} `{!noprolG Σ, !omoGeneralG Σ, !omoSpecificG Σ sevent_hist stack_state} := StackSpec {
(** operations *)
new_stack : val;
try_push : val;
push : val;
try_pop : val;
pop : val;
(** These are common elements in arbitrary composable linearizability spec *)
(** predicates *)
StackLocal : StackLocalNT Σ;
StackInv : StackInvT Σ;
(** predicates properties *)
StackInv_Objective : ∀ γg γs s E omo stlist, Objective (StackInv γg γs s E omo stlist);
StackInv_Timeless : ∀ γg γs s E omo stlist, Timeless (StackInv γg γs s E omo stlist);
StackInv_Linearizable : ∀ γg γs s E omo stlist, StackInv γg γs s E omo stlist ⊢ ⌜ Linearizability_omo E omo stlist ⌝;
StackInv_OmoAuth_acc : ∀ γg γs s E omo stlist,
StackInv γg γs s E omo stlist ⊢ OmoAuth γg γs (1/2)%Qp E omo stlist _ ∗ (OmoAuth γg γs (1/2)%Qp E omo stlist _ -∗ StackInv γg γs s E omo stlist);
StackLocal_OmoEview : ∀ N γg s M, StackLocal N γg s M ⊢ OmoEview γg M;
StackLocal_Eview_update : ∀ N γg s M1 M2, StackLocal N γg s M1 -∗ OmoEview γg M2 -∗ StackLocal N γg s (M1 ∪ M2);
StackLocal_Persistent :
∀ N γg s M, Persistent (StackLocal N γg s M);
(**************************************************************)
(* operations specs *)
new_stack_spec : new_stack_spec' new_stack StackLocal StackInv;
try_push_spec : try_push_spec' try_push StackLocal StackInv;
push_spec : push_spec' push StackLocal StackInv;
try_pop_spec : try_pop_spec' try_pop StackLocal StackInv;
pop_spec : pop_spec' pop StackLocal StackInv;
}.
Arguments stack_spec _ {_ _ _}.
Global Existing Instances StackInv_Objective StackInv_Timeless StackLocal_Persistent.