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FP
irisatomic
Commits
3b6db97b
Commit
3b6db97b
authored
Sep 20, 2016
by
Zhen Zhang
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doOp tentative
parent
637f31c7
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3b6db97b
...
...
@@ 185,42 +185,52 @@ Section proof.
iApply
(
"HΦ"
with
"Ho2 Ho3 Hfrag Hx2"
).
Admitted
.
Definition
doOp_triple
(
f
:
val
)
p
γ
x
γ
1
γ
2
γ
3
γ
4
Q
:
iProp
Σ
:=
atomic_triple
(
fun
_
:
()
=>
p_inv
γ
x
γ
1
γ
2
γ
3
γ
4
p
Q
★
(
own
γ
2
(
Excl
())
∨
own
γ
1
(
Excl
()))
★
□
(
∀
x
:
val
,
WP
f
x
{{
v
,
■
Q
x
v
}}
))
%
I
(
fun
_
ret
=>
(
own
γ
2
(
Excl
())
∨
own
γ
1
(
Excl
()))
★
ret
=
#()
★
p_inv
γ
x
γ
1
γ
2
γ
3
γ
4
p
Q
)
%
I
(
nclose
heapN
)
⊤
(
doOp
f
#
p
).
Lemma
doOp_spec
(
f
:
val
)
p
γ
x
γ
1
γ
2
γ
3
γ
4
R
:
heapN
⊥
N
→
heap_ctx
⊢
doOp_triple
f
p
γ
x
γ
1
γ
2
γ
3
γ
4
R
.
Definition
pinv_sub
RI
γ
x
γ
1
γ
2
γ
3
γ
4
p
Q
:=
(
RI
⊣⊢
∃
Rf
,
Rf
★
p_inv
γ
x
γ
1
γ
2
γ
3
γ
4
p
Q
)
%
I
.
Lemma
doOp_spec
Φ
(
f
:
val
)
(
RI
:
iProp
Σ
)
γ
x
γ
1
γ
2
γ
3
γ
4
p
Q
`
{
TimelessP
_
RI
}:
heapN
⊥
N
→
pinv_sub
RI
γ
x
γ
1
γ
2
γ
3
γ
4
p
Q
→
heap_ctx
★
inv
N
RI
★
own
γ
2
(
Excl
())
★
□
(
∀
x
:
val
,
WP
f
x
{{
v
,
■
Q
x
v
}}
)
%
I
★
(
own
γ
2
(
Excl
())

★
Φ
#())
⊢
WP
doOp
f
#
p
{{
Φ
}}
.
Proof
.
iIntros
(
HN
)
"#Hh"
.
rewrite
/
doOp_triple
/
atomic_triple
.
iIntros
(
P
Q
)
"#Hvs"
.
iIntros
"!# HP"
.
wp_rec
.
wp_let
.
wp_bind
(
!
_
)
%
E
.
iVs
(
"Hvs"
with
"HP"
)
as
(
xs
)
"[[Hp [[Ho2  Ho1] #Hf]] Hvs']"
.

rewrite
/
p_inv
.
iDestruct
"Hp"
as
"[Hp  [Hp  [Hp  Hp]]]"
.
+
iDestruct
"Hp"
as
(
y
)
"(Hp & Ho1 & Ho3)"
.
wp_load
.
iDestruct
"Hvs'"
as
"[_ Hvs']"
.
iVs
(
"Hvs'"
$
!
#()
with
"[]"
)
as
"HQ"
.
{
iSplitL
"Ho2"
;
first
by
iLeft
.
iSplitR
;
first
auto
.
iLeft
.
iExists
y
.
by
iFrame
.
}
iVsIntro
.
wp_match
.
eauto
.
+
iDestruct
"Hp"
as
(
x
)
"(Hp & Hx & Ho1 & Ho4)"
.
wp_load
.
iAssert
(
=
r
=>
own
γ
x
(((
1
/
4
)
%
Qp
,
DecAgree
x
)
⋅
((
1
/
4
)
%
Qp
,
DecAgree
x
)))
%
I
with
"[Hx]"
as
"==>[Hx1 Hx2]"
.
{
iDestruct
(
own_update
with
"Hx"
)
as
"Hx"
;
last
by
iAssumption
.
replace
((
1
/
2
)
%
Qp
)
with
(
1
/
4
+
1
/
4
)
%
Qp
;
last
by
apply
Qp_div_S
.
by
apply
pair_l_frac_op
'
.
}
iDestruct
"Hvs'"
as
"[Hvs' _]"
.
iVs
(
"Hvs'"
with
"[]"
)
as
"HP"
.
{
iSplitR
"Ho1"
;
last
auto
.
iRight
.
iRight
.
iLeft
.
iExists
x
.
by
iFrame
.
}
iVsIntro
.
wp_match
.
\ No newline at end of file
iIntros
(
HN
Hsub
)
"(#Hh & #HRI & Ho2 & #Hf & HΦ)"
.
wp_seq
.
wp_let
.
wp_bind
(
!
_
)
%
E
.
iInv
N
as
">H"
"Hclose"
.
iDestruct
(
Hsub
with
"H"
)
as
(
Rf
)
"[HRf [Hp  [Hp  [Hp  Hp]]]]"
.

iDestruct
"Hp"
as
(
y
)
"(Hp & Ho1 & Ho3)"
.
wp_load
.
iVs
(
"Hclose"
with
"[HRf Hp Ho1 Ho3]"
).
{
iNext
.
iApply
Hsub
.
iExists
Rf
.
iFrame
"HRf"
.
iLeft
.
iExists
y
.
by
iFrame
.
}
iVsIntro
.
wp_match
.
by
iApply
"HΦ"
.

iDestruct
"Hp"
as
(
x
)
"(Hp & Hx & Ho1 & Ho4)"
.
wp_load
.
iAssert
(
=
r
=>
own
γ
x
(((
1
/
4
)
%
Qp
,
DecAgree
x
)
⋅
((
1
/
4
)
%
Qp
,
DecAgree
x
)))
%
I
with
"[Hx]"
as
"==>[Hx1 Hx2]"
.
{
iDestruct
(
own_update
with
"Hx"
)
as
"Hx"
;
last
by
iAssumption
.
replace
((
1
/
2
)
%
Qp
)
with
(
1
/
4
+
1
/
4
)
%
Qp
;
last
by
apply
Qp_div_S
.
by
apply
pair_l_frac_op
'
.
}
iVs
(
"Hclose"
with
"[HRf Hp Hx1 Ho2 Ho4]"
).
{
iNext
.
iApply
Hsub
.
iExists
Rf
.
iFrame
"HRf"
.
iRight
.
iRight
.
iLeft
.
iExists
x
.
by
iFrame
.
}
iVsIntro
.
wp_match
.
wp_bind
(
f
_
).
iApply
wp_wand_r
.
iSplitR
;
first
by
iApply
"Hf"
.
iIntros
(
y
)
"%"
.
iInv
N
as
">H"
"Hclose"
.
iDestruct
(
Hsub
with
"H"
)
as
(
Rf
'
)
"[HRf [Hp  [Hp  [Hp  Hp]]]]"
.
+
admit
.
+
admit
.
+
iDestruct
"Hp"
as
(
x
'
)
"(Hp & Hx & Ho2 & Ho4)"
.
destruct
(
decide
(
x
=
x
'
))
as
[
>
Hneq
];
last
by
admit
.
iCombine
"Hx2"
"Hx"
as
"Hx"
.
iDestruct
(
own_update
with
"Hx"
)
as
"==>Hx"
;
first
by
apply
pair_l_frac_op
.
rewrite
Qp_div_S
.
wp_store
.
iVs
(
"Hclose"
with
"[HRf Hp Hx Ho1 Ho4]"
).
{
iNext
.
iApply
Hsub
.
iExists
Rf
'
.
iFrame
"HRf"
.
iRight
.
iRight
.
iRight
.
iExists
x
'
,
y
.
by
iFrame
.
}
iVsIntro
.
by
iApply
"HΦ"
.
+
admit
.

admit
.

admit
.
Admitted
.
\ No newline at end of file
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