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Rodolphe Lepigre
Iris
Commits
126aef31
Commit
126aef31
authored
Aug 25, 2016
by
Robbert Krebbers
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Cancelable invariants.
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622800da
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program_logic/cancelable_invariants.v
program_logic/cancelable_invariants.v
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View file @
126aef31
...
...
@@ -85,6 +85,7 @@ program_logic/boxes.v
program_logic/counter_examples.v
program_logic/iris.v
program_logic/thread_local.v
program_logic/cancelable_invariants.v
heap_lang/lang.v
heap_lang/tactics.v
heap_lang/wp_tactics.v
...
...
program_logic/cancelable_invariants.v
0 → 100644
View file @
126aef31
From
iris
.
program_logic
Require
Export
invariants
.
From
iris
.
algebra
Require
Export
frac
.
From
iris
.
proofmode
Require
Import
invariants
tactics
.
Import
uPred
.
Class
cinvG
Σ
:
=
cinv_inG
:
>
inG
Σ
fracR
.
Section
defs
.
Context
`
{
irisG
Λ
Σ
,
cinvG
Σ
}.
Definition
cinv_own
(
γ
:
gname
)
(
p
:
frac
)
:
iProp
Σ
:
=
own
γ
p
.
Definition
cinv
(
N
:
namespace
)
(
γ
:
gname
)
(
P
:
iProp
Σ
)
:
iProp
Σ
:
=
inv
N
(
P
∨
cinv_own
γ
1
%
Qp
)%
I
.
End
defs
.
Instance
:
Params
(@
cinv
)
6
.
Typeclasses
Opaque
cinv_own
cinv
.
Section
proofs
.
Context
`
{
irisG
Λ
Σ
,
cinvG
Σ
}.
Global
Instance
cinv_own_timeless
γ
p
:
TimelessP
(
cinv_own
γ
p
).
Proof
.
rewrite
/
cinv_own
;
apply
_
.
Qed
.
Global
Instance
cinv_ne
N
γ
n
:
Proper
(
dist
n
==>
dist
n
)
(
cinv
N
γ
).
Proof
.
solve_proper
.
Qed
.
Global
Instance
cinv_proper
N
γ
:
Proper
((
≡
)
==>
(
≡
))
(
cinv
N
γ
).
Proof
.
apply
(
ne_proper
_
).
Qed
.
Global
Instance
cinv_persistent
N
γ
P
:
PersistentP
(
cinv
N
γ
P
).
Proof
.
rewrite
/
cinv
;
apply
_
.
Qed
.
Lemma
cinv_own_op
γ
q1
q2
:
cinv_own
γ
q1
★
cinv_own
γ
q2
⊣
⊢
cinv_own
γ
(
q1
+
q2
).
Proof
.
by
rewrite
/
cinv_own
own_op
.
Qed
.
Lemma
cinv_own_half
γ
q
:
cinv_own
γ
(
q
/
2
)
★
cinv_own
γ
(
q
/
2
)
⊣
⊢
cinv_own
γ
q
.
Proof
.
by
rewrite
cinv_own_op
Qp_div_2
.
Qed
.
Lemma
cinv_own_valid
γ
q1
q2
:
cinv_own
γ
q1
★
cinv_own
γ
q2
⊢
✓
(
q1
+
q2
)%
Qp
.
Proof
.
rewrite
/
cinv_own
-
own_op
own_valid
.
by
iIntros
"% !%"
.
Qed
.
Lemma
cinv_own_1_l
γ
q
:
cinv_own
γ
1
★
cinv_own
γ
q
⊢
False
.
Proof
.
rewrite
cinv_own_valid
.
by
iIntros
(?%(
exclusive_l
1
%
Qp
)).
Qed
.
Lemma
cinv_alloc
E
N
P
:
▷
P
={
E
}=>
∃
γ
,
cinv
N
γ
P
★
cinv_own
γ
1
.
Proof
.
rewrite
/
cinv
/
cinv_own
.
iIntros
"HP"
.
iVs
(
own_alloc
1
%
Qp
)
as
(
γ
)
"H1"
;
first
done
.
iVs
(
inv_alloc
N
_
(
P
∨
own
γ
1
%
Qp
)%
I
with
"[HP]"
)
;
eauto
.
Qed
.
Lemma
cinv_cancel
E
N
γ
P
:
nclose
N
⊆
E
→
cinv
N
γ
P
⊢
cinv_own
γ
1
={
E
}=
★
▷
P
.
Proof
.
rewrite
/
cinv
.
iIntros
(?)
"#Hinv Hγ"
.
iInv
N
as
"[$|>Hγ']"
"Hclose"
;
first
iApply
"Hclose"
;
eauto
.
iDestruct
(
cinv_own_1_l
with
"[Hγ Hγ']"
)
as
%[].
by
iFrame
.
Qed
.
Lemma
cinv_open
E
N
γ
p
P
:
nclose
N
⊆
E
→
cinv
N
γ
P
⊢
cinv_own
γ
p
={
E
,
E
∖
N
}=
★
▷
P
★
cinv_own
γ
p
★
(
▷
P
={
E
∖
N
,
E
}=
★
True
).
Proof
.
rewrite
/
cinv
.
iIntros
(?)
"#Hinv Hγ"
.
iInv
N
as
"[$|>Hγ']"
"Hclose"
.
-
iIntros
"!==> {$Hγ} HP"
.
iApply
"Hclose"
;
eauto
.
-
iDestruct
(
cinv_own_1_l
with
"[Hγ Hγ']"
)
as
%[].
by
iFrame
.
Qed
.
End
proofs
.
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