-
Notifications
You must be signed in to change notification settings - Fork 0
/
spec_singleElementQueue_history.v
144 lines (123 loc) · 5.55 KB
/
spec_singleElementQueue_history.v
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
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 seq_event := Init | Enq (v : Z) (n : nat) | Deq (v : Z) (n : nat).
Definition seq_state := list (event_id * Z * nat* view * eView).
Global Instance seq_event_inhabited : Inhabited seq_event := populate Init.
Local Notation history := (history seq_event).
Local Notation empty := 0 (only parsing).
Implicit Types (E : history) (st : seq_state).
Inductive seq_step : ∀ (e : event_id) (eV : omo_event seq_event) st st', Prop :=
| seq_step_Enq e eV v n
(ENQ : eV.(type) = Enq v n)
(GT : 0 < v)
(EVIEW : e ∈ eV.(eview))
: seq_step e eV [] [(e, v, n, eV.(sync), eV.(eview))]
| seq_step_Deq e eV e' v n V lV
(DEQ : eV.(type) = Deq v n)
(GT : 0 < v)
(SYNC : V ⊑ eV.(sync))
(EVIEW : {[e; e']} ∪ lV ⊆ eV.(eview))
: seq_step e eV [(e', v, n, V, lV)] []
| seq_step_Init eV
(INIT : eV.(type) = Init)
(EVIEW : eV.(eview) = {[0%nat]})
: seq_step 0%nat eV [] []
.
Global Instance seq_interpretable : Interpretable seq_event seq_state :=
{
init := [];
step := seq_step
}.
Inductive seq_perm_type := EnqP | DeqP.
Global Instance seq_perm_type_inhabited : Inhabited seq_perm_type := populate EnqP.
Definition SeqLocalT Σ : Type :=
∀ (γg : gname) (q : loc) (E : history) (M : eView), vProp Σ.
Definition SeqLocalNT Σ : Type :=
∀ (N : namespace), SeqLocalT Σ.
Definition SeqInvT Σ : Type :=
∀ (γg : gname) (q : loc) (E : history), vProp Σ.
Definition SeqPermT Σ : Type :=
∀ (γg : gname) (q : loc) (ty : seq_perm_type) (P : nat → bool), vProp Σ.
Definition new_seq_spec' {Σ} `{!noprolG Σ}
(newSEQ : val) (SeqLocal : SeqLocalNT Σ) (SeqInv : SeqInvT Σ) (SeqPerm : SeqPermT Σ) : Prop :=
∀ N tid V,
{{{ ⊒V }}}
newSEQ [] @ tid; ⊤
{{{ γg (q: loc) E M V', RET #q;
⊒V' ∗ @{V'} SeqLocal N γg q E M ∗ SeqInv γg q E ∗ SeqPerm γg q EnqP (λ _, true) ∗ SeqPerm γg q DeqP (λ _, true) ∗
⌜ E = [mkOmoEvent Init V' M] ∧ V ⊑ V' ⌝ }}}.
Definition enqueueWithTicket_spec' {Σ} `{!noprolG Σ}
(enqueueWithTicket : val) (SeqLocal : SeqLocalNT Σ) (SeqInv : SeqInvT Σ) (SeqPerm : SeqPermT Σ) : Prop :=
∀ N (DISJ: N ## histN) (q: loc) tid γg E1 M (V : view) (v : Z) (n : nat),
(* PRIVATE PRE *)
(* E1 is a snapshot of the history, locally observed by M *)
0 < v →
⊒V -∗ SeqLocal N γg q E1 M -∗ SeqPerm γg q EnqP (λ m, m =? n)%nat -∗
(* PUBLIC PRE *)
<<< ∀ E, ▷ SeqInv γg q E >>>
enqueueWithTicket [ #q; #n; #v] @ tid; ↑N
<<< ∃ V' E' M',
(* PUBLIC POST *)
▷ SeqInv γg q E' ∗
⊒V' ∗ @{V'} SeqLocal N γg q E' M' ∗
⌜ V ⊑ V' ∧
E' = E ++ [mkOmoEvent (Enq v n) V' M'] ∧ M ⊆ M' ⌝,
RET #☠, emp >>>
.
Definition dequeueWithTicket_spec' {Σ} `{!noprolG Σ}
(dequeueWithTicket : val) (SeqLocal : SeqLocalNT Σ) (SeqInv : SeqInvT Σ) (SeqPerm : SeqPermT Σ) : Prop :=
∀ N (DISJ: N ## histN) (q: loc) tid γg E1 M (V : view) (n : nat),
(* PRIVATE PRE *)
(* E1 is a snapshot of the history, locally observed by M *)
⊒V -∗ SeqLocal N γg q E1 M -∗ SeqPerm γg q DeqP (λ m, m =? n)%nat -∗
(* PUBLIC PRE *)
<<< ∀ E, ▷ SeqInv γg q E >>>
dequeueWithTicket [ #q; #n] @ tid; ↑N
<<< ∃ V' E' M' (v : Z),
(* PUBLIC POST *)
▷ SeqInv γg q E' ∗
⊒V' ∗ @{V'} SeqLocal N γg q E' M' ∗
⌜ V ⊑ V' ∧
E' = E ++ [mkOmoEvent (Deq v n) V' M'] ∧ M ⊆ M' ∧ 0 < v⌝,
RET #v, emp >>>
.
Record seq_spec {Σ} `{!noprolG Σ} := SeqSpec {
(** operations *)
newSEQ : val;
enqueueWithTicket : val;
dequeueWithTicket : val;
(** These are common elements in arbitrary history-style spec *)
(** predicates *)
SeqLocal : SeqLocalNT Σ;
SeqInv : SeqInvT Σ;
SeqPerm : SeqPermT Σ;
(** predicates properties *)
SeqInv_Objective : ∀ γg q E, Objective (SeqInv γg q E);
SeqInv_Linearizable : ∀ γg q E, SeqInv γg q E ⊢ ⌜ Linearizability E ⌝;
SeqInv_history_wf :
∀ γg q E, SeqInv γg q E ⊢ ⌜ history_wf E ⌝;
SeqInv_SeqLocal :
∀ N γg q E E' M',
SeqInv γg q E -∗ SeqLocal N γg q E' M' -∗ ⌜ E' ⊑ E ⌝;
SeqLocal_lookup :
∀ N γg q E M e V,
sync <$> E !! e = Some V → e ∈ M → SeqLocal N γg q E M -∗ ⊒V;
SeqLocal_Persistent :
∀ N γg q E M, Persistent (SeqLocal N γg q E M);
SeqPerm_Objective : ∀ γg q ty P, Objective (SeqPerm γg q ty P);
SeqPerm_Equiv : ∀ γg q ty P1 P2, (∀ n, P1 n = P2 n) → SeqPerm γg q ty P1 -∗ SeqPerm γg q ty P2;
SeqPerm_Split : ∀ γg q ty P1 P2, SeqPerm γg q ty P1 -∗ SeqPerm γg q ty (λ n, P1 n && P2 n) ∗ SeqPerm γg q ty (λ n, P1 n && negb (P2 n));
SeqPerm_Combine : ∀ γg q ty P1 P2, SeqPerm γg q ty P1 -∗ SeqPerm γg q ty P2 -∗ SeqPerm γg q ty (λ n, P1 n || P2 n);
SeqPerm_Excl : ∀ γg q ty P1 P2 n, P1 n = true → P2 n = true → SeqPerm γg q ty P1 -∗ SeqPerm γg q ty P2 -∗ False;
(**************************************************************)
(* operations specs *)
new_seq_spec : new_seq_spec' newSEQ SeqLocal SeqInv SeqPerm;
enqueueWithTicket_spec : enqueueWithTicket_spec' enqueueWithTicket SeqLocal SeqInv SeqPerm;
dequeueWithTicket_spec : dequeueWithTicket_spec' dequeueWithTicket SeqLocal SeqInv SeqPerm;
}.
Arguments seq_spec _ {_}.
Global Existing Instances SeqInv_Objective SeqLocal_Persistent SeqPerm_Objective.