Skip to content
GitLab
Projects
Groups
Snippets
Help
Loading...
Help
Help
Support
Community forum
Keyboard shortcuts
?
Submit feedback
Contribute to GitLab
Sign in / Register
Toggle navigation
I
irisatomic
Project overview
Project overview
Details
Activity
Releases
Repository
Repository
Files
Commits
Branches
Tags
Contributors
Graph
Compare
Issues
3
Issues
3
List
Boards
Labels
Service Desk
Milestones
Merge Requests
0
Merge Requests
0
CI / CD
CI / CD
Pipelines
Jobs
Schedules
Operations
Operations
Incidents
Environments
Analytics
Analytics
CI / CD
Repository
Value Stream
Wiki
Wiki
Members
Members
Collapse sidebar
Close sidebar
Activity
Graph
Create a new issue
Jobs
Commits
Issue Boards
Open sidebar
FP
irisatomic
Commits
d344c353
Commit
d344c353
authored
Sep 08, 2016
by
Zhen Zhang
Browse files
Options
Browse Files
Download
Email Patches
Plain Diff
srv ... token exchange is too complex
parent
b2ba5bcb
Changes
1
Hide whitespace changes
Inline
Sidebyside
Showing
1 changed file
with
110 additions
and
67 deletions
+110
67
srv.v
srv.v
+110
67
No files found.
srv.v
View file @
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
.
Write
Preview
Markdown
is supported
0%
Try again
or
attach a new file
.
Attach a file
Cancel
You are about to add
0
people
to the discussion. Proceed with caution.
Finish editing this message first!
Cancel
Please
register
or
sign in
to comment