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FP
irisatomic
Commits
d344c353
Commit
d344c353
authored
Sep 08, 2016
by
Zhen Zhang
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srv ... token exchange is too complex
parent
b2ba5bcb
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srv.v
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srv.v
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d344c353
...
...
@@ 16,7 +16,7 @@ Definition srv : val :=
Definition
wait
:
val
:=
rec:
"wait"
"p"
:=
match:
!
"p"
with
InjR
"r"
=>
"
p"
<
InjR
#
0
;;
"
r"
InjR
"r"
=>
"r"

InjL
"_"
=>
"wait"
"p"
end
.
...
...
@@ 60,38 +60,53 @@ Section proof.
Context
`
{!
heapG
Σ
,
!
lockG
Σ
,
!
srvG
Σ
}
(
N
:
namespace
).
Definition
srv_inv
(
γ
x
γ
1
γ
2
γ
3
:
gname
)
(
p
:
loc
)
(
γ
x
γ
1
γ
2
γ
3
γ
4
γ
5
:
gname
)
(
p
:
loc
)
(
Q
:
val
→
val
→
Prop
)
:
iProp
Σ
:=
((
∃
(
x
:
val
),
p
↦
InjRV
x
★
own
γ
1
(
Excl
()))
∨
(
∃
(
x
:
val
),
p
↦
InjLV
x
★
own
γ
x
((
1
/
2
)
%
Qp
,
DecAgree
x
)
★
own
γ
2
(
Excl
()))
∨
(
∃
(
x
y
:
val
),
p
↦
InjRV
y
★
own
γ
x
((
1
/
2
)
%
Qp
,
DecAgree
x
)
★
■
Q
x
y
★
own
γ
3
(
Excl
())))
%
I
.
((
∃
(
x
:
val
),
p
↦
InjRV
x
★
own
γ
1
(
Excl
())
★
own
γ
3
(
Excl
()))
∨
(
∃
(
x
y
:
val
),
p
↦
InjRV
y
★
own
γ
x
((
1
/
2
)
%
Qp
,
DecAgree
x
)
★
■
Q
x
y
★
own
γ
2
(
Excl
())
★
own
γ
3
(
Excl
()))
∨
(
∃
(
x
:
val
),
p
↦
InjLV
x
★
own
γ
x
((
1
/
2
)
%
Qp
,
DecAgree
x
)
★
own
γ
5
(
Excl
())
★
own
γ
3
(
Excl
()))
∨
(
∃
(
x
:
val
),
p
↦
InjLV
x
★
own
γ
x
((
1
/
2
)
%
Qp
,
DecAgree
x
)
★
own
γ
5
(
Excl
())
★
own
γ
4
(
Excl
())))
%
I
.
Lemma
srv_inv_timeless
γ
x
γ
1
γ
2
γ
3
p
Q
:
TimelessP
(
srv_inv
γ
x
γ
1
γ
2
γ
3
p
Q
).
Lemma
srv_inv_timeless
γ
x
γ
1
γ
2
γ
3
γ
4
γ
5
p
Q
:
TimelessP
(
srv_inv
γ
x
γ
1
γ
2
γ
3
γ
4
γ
5
p
Q
).
Proof
.
apply
_.
Qed
.
Lemma
wait_spec
(
Φ
:
val
→
iProp
Σ
)
(
Q
:
val
→
val
→
Prop
)
x
γ
x
γ
1
γ
2
γ
3
p
:
Lemma
wait_spec
(
Φ
:
val
→
iProp
Σ
)
(
Q
:
val
→
val
→
Prop
)
x
γ
x
γ
1
γ
2
γ
3
γ
4
γ
5
p
:
heapN
⊥
N
→
heap_ctx
★
inv
N
(
srv_inv
γ
x
γ
1
γ
2
γ
3
p
Q
)
★
own
γ
x
((
1
/
2
)
%
Qp
,
DecAgree
x
)
★
own
γ
1
(
Excl
())
★
own
γ
3
(
Excl
())
★
(
∀
y
,
own
γ
1
(
Excl
())
★
own
γ
2
(
Excl
())

★
own
γ
x
(
1
%
Qp
,
DecAgree
x
)

★
■
Q
x
y

★
Φ
y
)
heap_ctx
★
inv
N
(
srv_inv
γ
x
γ
1
γ
2
γ
3
γ
4
γ
5
p
Q
)
★
own
γ
x
((
1
/
2
)
%
Qp
,
DecAgree
x
)
★
own
γ
1
(
Excl
())
★
own
γ
5
(
Excl
())
★
(
∀
y
,
own
γ
2
(
Excl
())

★
own
γ
x
(
1
%
Qp
,
DecAgree
x
)

★
■
Q
x
y

★
Φ
y
)
⊢
WP
wait
#
p
{{
Φ
}}
.
Proof
.
iIntros
(
HN
)
"(#Hh & #Hsrv & Hx & Hempty & Hfinished & HΦ)"
.
iL
ö
b
as
"IH"
.
wp_rec
.
wp_bind
(
!
#
p
)
%
E
.
iInv
N
as
">[Hinv[Hinv
Hinv
]]"
"Hclose"
.
+
iExFalso
.
iDestruct
"Hinv"
as
(
?
)
"[_ Ho1
]"
.
iInv
N
as
">[Hinv[Hinv
[HinvHinv]
]]"
"Hclose"
.

iExFalso
.
iDestruct
"Hinv"
as
(
?
)
"[_ [Ho1 _]
]"
.
iCombine
"Hempty"
"Ho1"
as
"Hempty"
.
by
iDestruct
(
own_valid
with
"Hempty"
)
as
"%"
.
+
iDestruct
"Hinv"
as
(
x
'
)
"(Hp & Hx' & Hissued)"
.
wp_load
.
iVs
(
"Hclose"
with
"[Hp Hx' Hissued]"
).
{
iNext
.
iRight
.
iLeft
.
iExists
x
'
.
by
iFrame
.
}
iVsIntro
.
wp_match
.
by
iApply
(
"IH"
with
"Hx Hempty Hfinished"
).
+
iDestruct
"Hinv"
as
(
x
'
y
'
)
"(Hp & Hx' & % & Ho3)"
.
iCombine
"Hfinished"
"Ho3"
as
"Hfinished"
.
by
iDestruct
(
own_valid
with
"Hfinished"
)
as
"%"
.
Qed
.
by
iDestruct
(
own_valid
with
"Hempty"
)
as
"%"
.

iDestruct
"Hinv"
as
(
x
'
y
'
)
"(Hp & Hx' & % & Ho2 & Ho3)"
.
destruct
(
decide
(
x
=
x
'
))
as
[
>
Hneq
].
+
wp_load
.
iVs
(
"Hclose"
with
"[Hp Hx' Ho2 Ho3]"
).
{
iNext
.
rewrite
/
srv_inv
.
iRight
.
iLeft
.
iExists
x
'
,
y
'
.
by
iFrame
.
}
iVsIntro
.
wp_match
.
iInv
N
as
">[Hinv[Hinv[HinvHinv]]]"
"Hclose"
.
*
admit
.
*
iDestruct
"Hinv"
as
(
x
''
y
''
)
"(Hp & Hx'' & % & Ho2 & Ho3)"
.
iVs
(
"Hclose"
with
"[Hp Hempty Ho3]"
).
{
iNext
.
rewrite
/
srv_inv
.
iLeft
.
iExists
y
''
.
by
iFrame
.
}
destruct
(
decide
(
x
'
=
x
''
))
as
[
>
Hneq
].
{
iCombine
"Hx"
"Hx''"
as
"Hx"
.
iDestruct
(
own_update
with
"Hx"
)
as
"==>Hx"
;
first
by
apply
pair_l_frac_op
.
by
iApply
(
"HΦ"
with
"Ho2 Hx"
).
}
{
admit
.
}
*
admit
.
*
admit
.
+
admit
.

admit
.

admit
.
Admitted
.
Lemma
mk_srv_spec
(
f
:
val
)
Q
:
heapN
⊥
N
→
...
...
@@ 102,57 +117,85 @@ Section proof.
wp_let
.
wp_alloc
p
as
"Hp"
.
iVs
(
own_alloc
(
Excl
()))
as
(
γ
1
)
"Hempty"
;
first
done
.
iVs
(
own_alloc
(
Excl
()))
as
(
γ
2
)
"Hissued"
;
first
done
.
iVs
(
own_alloc
(
Excl
()))
as
(
γ
3
)
"Hfinished"
;
first
done
.
iVs
(
own_alloc
(
Excl
()))
as
(
γ
3
)
"Hblack"
;
first
done
.
iVs
(
own_alloc
(
Excl
()))
as
(
γ
4
)
"Hwhite"
;
first
done
.
iVs
(
own_alloc
(
Excl
()))
as
(
γ
5
)
"Hfinished"
;
first
done
.
iVs
(
own_alloc
(
1
%
Qp
,
DecAgree
#
0
))
as
(
γ
x
)
"Hx"
;
first
done
.
iVs
(
inv_alloc
N
_
(
srv_inv
γ
x
γ
1
γ
2
γ
3
p
Q
)
with
"[Hp Hempty
]"
)
as
"#?"
.
iVs
(
inv_alloc
N
_
(
srv_inv
γ
x
γ
1
γ
2
γ
3
γ
4
γ
5
p
Q
)
with
"[Hp Hempty Hblack
]"
)
as
"#?"
.
{
iNext
.
rewrite
/
srv_inv
.
iLeft
.
iExists
#
0.
by
iFrame
.
}
(
*
iVs
(
inv_alloc
N
_
(
own
γ
3
(
Excl
())
∨
own
γ
4
(
Excl
()))
%
I
with
"[Hwhite]"
)
as
"#Hsinv"
.
*
)
(
*
{
iNext
.
by
iRight
.
}
*
)
wp_let
.
wp_bind
(
newlock
_
).
iApply
newlock_spec
=>
//. iFrame "Hh".
iAssert
(
∃
x
,
own
γ
x
(
1
%
Qp
,
DecAgree
x
)
★
own
γ
2
(
Excl
())
★
own
γ
3
(
Excl
()))
%
I
with
"[Hissued Hfinished Hx]"
as
"Hinv"
.
iAssert
(
∃
x
,
own
γ
x
(
1
%
Qp
,
DecAgree
x
)
★
own
γ
2
(
Excl
())
★
own
γ
5
(
Excl
()))
%
I
with
"[Hissued Hfinished Hx]"
as
"Hinv"
.
{
iExists
#
0.
by
iFrame
.
}
iFrame
"Hinv"
.
iIntros
(
lk
γ
lk
)
"#Hlk"
.
wp_let
.
wp_apply
wp_fork
.
iSplit
L
.

(
*
client
closure
*
)
iVsIntro
.
wp_seq
.
iVsIntro
.
iAlways
.
iIntros
(
x
).
wp_let
.
wp_bind
(
acquire
_
).
iApply
acquire_spec
.
iFrame
"Hlk"
.
iIntros
"Hlked Ho"
.
iDestruct
"Ho"
as
(
x
'
)
"[Hx [Hissued Hfinished]]"
.
wp_seq
.
wp_bind
(
_
<
_
)
%
E
.
iInv
N
as
">Hinv"
"Hclose"
.
rewrite
/
srv_inv
.
iDestruct
"Hinv"
as
"[Hinv[HinvHinv]]"
.
+
iDestruct
"Hinv"
as
(
x
''
)
"[Hp Hempty]"
.
wp_store
.
iAssert
(
=
r
=>
own
γ
x
(
1
%
Qp
,
DecAgree
x
))
%
I
with
"[Hx]"
as
"Ho"
.
{
iDestruct
(
own_update
with
"Hx"
)
as
"Hx"
;
last
by
iAssumption
.
apply
cmra_update_exclusive
.
done
.
}
iVs
"Ho"
.
iDestruct
(
own_update
with
"Ho"
)
as
"==>[Ho1 Ho2]"
;
first
by
apply
pair_l_frac_op
'
.
iVs
(
"Hclose"
with
"[Hp Hissued Ho1]"
).
{
rewrite
/
locked
.
iNext
.
iRight
.
iLeft
.
iExists
x
.
by
iFrame
.
}
iVsIntro
.
wp_seq
.
wp_bind
(
wait
_
).
iApply
(
wait_spec
with
"[Hempty Hfinished Ho2 Hlked]"
);
first
by
done
.
{
iFrame
"Hh"
.
iFrame
"#"
.
iFrame
.
iIntros
(
y3
)
"[Hempty Hissued] Hx %"
.
wp_let
.
wp_bind
(
release
_
).
iApply
pvs_wp
.
iInv
N
as
">[Hinv[HinvHinv]]"
"Hclose"
.

admit
.

admit
.

iDestruct
"Hinv"
as
(
x4
y4
)
"(Hp & _ & _ & Hfinished)"
.
iVs
(
"Hclose"
with
"[Hp Hempty]"
).
{
iNext
.
iLeft
.
iExists
y4
.
by
iFrame
.
}
iApply
release_spec
.
iFrame
"Hlk Hlked"
.
iSplitL
"Hissued Hfinished Hx"
.
{
iExists
x
.
by
iFrame
.
}
by
wp_seq
.
}
+
admit
.
+
admit
.
iSplit
R
"Hwhite"
.

(
*
(
*
client
closure
*
)
*
)
(
*
iVsIntro
.
wp_seq
.
iVsIntro
.
*
)
(
*
iAlways
.
iIntros
(
x
).
*
)
(
*
wp_let
.
wp_bind
(
acquire
_
).
iApply
acquire_spec
.
*
)
(
*
iFrame
"Hlk"
.
iIntros
"Hlked Ho"
.
*
)
(
*
iDestruct
"Ho"
as
(
x
'
)
"[Hx [Hissued Hfinished]]"
.
*
)
(
*
wp_seq
.
wp_bind
(
_
<
_
)
%
E
.
*
)
(
*
iInv
N
as
">Hinv"
"Hclose"
.
*
)
(
*
rewrite
/
srv_inv
.
*
)
(
*
iDestruct
"Hinv"
as
"[Hinv[HinvHinv]]"
.
*
)
(
*
+
iDestruct
"Hinv"
as
(
x
''
)
"[Hp Hempty]"
.
*
)
(
*
wp_store
.
*
)
(
*
iAssert
(
=
r
=>
own
γ
x
(
1
%
Qp
,
DecAgree
x
))
%
I
with
"[Hx]"
as
"Ho"
.
*
)
(
*
{
iDestruct
(
own_update
with
"Hx"
)
as
"Hx"
;
last
by
iAssumption
.
*
)
(
*
apply
cmra_update_exclusive
.
done
.
}
*
)
(
*
iVs
"Ho"
.
iDestruct
(
own_update
with
"Ho"
)
as
"==>[Ho1 Ho2]"
;
first
by
apply
pair_l_frac_op
'
.
*
)
(
*
iVs
(
"Hclose"
with
"[Hp Hissued Ho1]"
).
*
)
(
*
{
rewrite
/
locked
.
iNext
.
iRight
.
iLeft
.
*
)
(
*
iExists
x
.
by
iFrame
.
}
*
)
(
*
iVsIntro
.
wp_seq
.
*
)
(
*
wp_bind
(
wait
_
).
*
)
(
*
iApply
(
wait_spec
with
"[Hempty Hfinished Ho2 Hlked]"
);
first
by
done
.
*
)
(
*
{
iFrame
"Hh"
.
iFrame
"#"
.
iFrame
.
*
)
(
*
iIntros
(
y3
)
"[Hempty Hissued] Hx %"
.
*
)
(
*
wp_let
.
wp_bind
(
release
_
).
*
)
(
*
iApply
pvs_wp
.
*
)
(
*
iInv
N
as
">[Hinv[HinvHinv]]"
"Hclose"
.
*
)
(
*

admit
.
*
)
(
*

admit
.
*
)
(
*

iDestruct
"Hinv"
as
(
x4
y4
)
"(Hp & _ & _ & Hfinished)"
.
*
)
(
*
iVs
(
"Hclose"
with
"[Hp Hempty]"
).
*
)
(
*
{
iNext
.
iLeft
.
iExists
y4
.
by
iFrame
.
}
*
)
(
*
iApply
release_spec
.
*
)
(
*
iFrame
"Hlk Hlked"
.
*
)
(
*
iSplitL
"Hissued Hfinished Hx"
.
*
)
(
*
{
iExists
x
.
by
iFrame
.
}
*
)
(
*
by
wp_seq
.
*
)
(
*
}
*
)
(
*
+
admit
.
*
)
(
*
+
admit
.
*
)
admit
.

(
*
server
side
*
)
iL
ö
b
as
"IH"
.
wp_rec
.
wp_let
.
wp_bind
(
!
_
)
%
E
.
iInv
N
as
">[Hinv[Hinv[HinvHinv]]]"
"Hclose"
.
+
iDestruct
"Hinv"
as
(
x
)
"[Hp Hrest]"
.
wp_load
.
iVs
(
"Hclose"
with
"[Hp Hrest]"
).
{
iNext
.
rewrite
/
srv_inv
.
iLeft
.
iExists
x
.
by
iFrame
.
}
iVsIntro
.
wp_match
.
by
iApply
"IH"
.
+
iDestruct
"Hinv"
as
(
x
y
)
"[Hp Hrest]"
.
wp_load
.
iVs
(
"Hclose"
with
"[Hp Hrest]"
).
{
iNext
.
rewrite
/
srv_inv
.
iRight
.
iLeft
.
iExists
x
,
y
.
by
iFrame
.
}
iVsIntro
.
wp_match
.
by
iApply
"IH"
.
+
iDestruct
"Hinv"
as
(
x
)
"(Hp & Hx & Hfinished & Hblack)"
.
wp_load
.
iVs
(
"Hclose"
with
"[Hp Hx Hfinished Hwhite]"
).
{
iNext
.
rewrite
/
srv_inv
.
iRight
.
iRight
.
iRight
.
iExists
x
.
by
iFrame
.
}
iVsIntro
.
wp_match
.
wp_bind
(
_
<
_
)
%
E
.
iApply
pvs_wp
.
iInv
N
as
">[Hinv[Hinv[HinvHinv]]]"
"Hclose"
.
*
admit
.
*
admit
.
*
admit
.
*
iDestruct
"Hinv"
as
(
x
'
)
"(Hp & Hx & Hfinished & Hwhite)"
.
iVs
(
"Hclose"
with
"[Hp Hx Hfinished Hblack]"
).
Admitted
.
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