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iris
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Tej Chajed
iris
Commits
548a5de9
Commit
548a5de9
authored
8 years ago
by
Zhen Zhang
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use pair of ref in ticket lock
parent
59a8f5bf
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heap_lang/lib/ticket_lock.v
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heap_lang/lib/ticket_lock.v
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548a5de9
...
...
@@ -7,26 +7,27 @@ From iris.algebra Require Import gset.
Import
uPred
.
Definition
wait_loop
:
val
:=
rec
:
"wait_loop"
"x"
"l"
:=
let
:
"o"
:=
Fst
!
"l
"
in
rec
:
"wait_loop"
"x"
"l
ock
"
:=
let
:
"o"
:=
!
(
Fst
"l
ock"
)
in
if
:
"x"
=
"o"
then
#
()
(* my turn *)
else
"wait_loop"
"x"
"l"
.
else
"wait_loop"
"x"
"lock"
.
Definition
newlock
:
val
:=
λ
:
<>
,
(
(* owner *)
ref
#
0
,
(* next *)
ref
#
0
)
.
Definition
newlock
:
val
:=
λ
:
<>
,
ref
(
(* owner *)
#
0
,
(* next *)
#
0
)
.
Definition
acquire
:
val
:=
rec
:
"acquire"
"l"
:=
let
:
"
oldl
"
:=
!
"l"
in
if
:
CAS
"l"
"oldl"
(
Fst
"oldl"
,
Snd
"oldl
"
+
#
1
)
then
wait_loop
(
Snd
"oldl"
)
"l
"
else
"acquire"
"l"
.
rec
:
"acquire"
"l
ock
"
:=
let
:
"
n
"
:=
!
(
Snd
"lock"
)
in
if
:
CAS
(
Snd
"lock"
)
"n"
(
"n
"
+
#
1
)
then
wait_loop
"n"
"lock
"
else
"acquire"
"l
ock
"
.
Definition
release
:
val
:=
rec
:
"release"
"l"
:=
let
:
"o
ldl
"
:=
!
"l"
in
if
:
CAS
"l"
"oldl"
(
Fst
"oldl"
+
#
1
,
Snd
"oldl"
)
rec
:
"release"
"l
ock
"
:=
let
:
"o"
:=
!
(
Fst
"lock"
)
in
if
:
CAS
(
Fst
"lock"
)
"o"
(
"o"
+
#
1
)
then
#
()
else
"release"
"l"
.
else
"release"
"l
ock
"
.
Global
Opaque
newlock
acquire
release
wait_loop
.
...
...
@@ -42,28 +43,29 @@ Instance subG_tlockΣ {Σ} : subG tlockΣ Σ → tlockG Σ.
Proof
.
intros
[?
[?
%
subG_inG
_]
%
subG_inv
]
%
subG_inv
.
split
;
apply
_
.
Qed
.
Section
proof
.
Context
`{
!
heapG
Σ
,
!
tlockG
Σ
}
(
N
:
namespace
)
.
Context
`{
!
heapG
Σ
,
!
tlockG
Σ
}
(
N
:
namespace
)
(
HN
:
heapN
⊥
N
)
.
Definition
tickets_inv
(
n
:
nat
)
(
gs
:
gset_disjUR
nat
)
:
iProp
Σ
:=
(
gs
=
GSet
(
seq_set
0
n
))
%
I
.
Definition
lock_inv
(
γ1
γ2
:
gname
)
(
l
:
loc
)
(
R
:
iProp
Σ
)
:
iProp
Σ
:=
(
∃
o
n
:
nat
,
l
↦
(
#
o
,
#
n
)
★
auth_inv
γ1
(
tickets_inv
n
)
★
((
own
γ2
(
Excl
())
★
R
)
∨
auth_own
γ1
(
GSet
{[
o
]})))
%
I
.
Definition
lock_inv
(
γ1
γ2
:
gname
)
(
lo
ln
:
loc
)
(
R
:
iProp
Σ
)
:
iProp
Σ
:=
(
∃
(
o
n
:
nat
),
lo
↦
#
o
★
ln
↦
#
n
★
auth_inv
γ1
(
tickets_inv
n
)
★
((
own
γ2
(
Excl
())
★
R
)
∨
auth_own
γ1
(
GSet
{[
o
]})))
%
I
.
Definition
is_lock
(
l
:
loc
)
(
R
:
iProp
Σ
)
:
iProp
Σ
:=
(
∃
γ1
γ2
,
heapN
⊥
N
∧
heap_ctx
∧
inv
N
(
lock_inv
γ1
γ2
l
R
))
%
I
.
Definition
is_lock
(
l
:
val
)
(
R
:
iProp
Σ
)
:
iProp
Σ
:=
(
∃
γ1
γ2
(
lo
ln
:
loc
),
heap_ctx
∧
l
=
(
#
lo
,
#
ln
)
%
V
∧
inv
N
(
lock_inv
γ1
γ2
l
o
ln
R
))
%
I
.
Definition
issued
(
l
:
loc
)
(
x
:
nat
)
(
R
:
iProp
Σ
)
:
iProp
Σ
:=
(
∃
γ1
γ2
,
heapN
⊥
N
∧
heap_ctx
∧
inv
N
(
lock_inv
γ1
γ2
l
R
)
∧
auth_own
γ1
(
GSet
{[
x
]}))
%
I
.
Definition
issued
(
l
:
val
)
(
x
:
nat
)
(
R
:
iProp
Σ
)
:
iProp
Σ
:=
(
∃
γ1
γ2
(
lo
ln
:
loc
),
heap_ctx
∧
l
=
(
#
lo
,
#
ln
)
%
V
∧
inv
N
(
lock_inv
γ1
γ2
l
o
ln
R
)
∧
auth_own
γ1
(
GSet
{[
x
]}))
%
I
.
Definition
locked
(
l
:
loc
)
(
R
:
iProp
Σ
)
:
iProp
Σ
:=
(
∃
γ1
γ2
,
heapN
⊥
N
∧
heap_ctx
∧
inv
N
(
lock_inv
γ1
γ2
l
R
)
∧
own
γ2
(
Excl
()))
%
I
.
Definition
locked
(
l
:
val
)
(
R
:
iProp
Σ
)
:
iProp
Σ
:=
(
∃
γ1
γ2
(
lo
ln
:
loc
),
heap_ctx
∧
l
=
(
#
lo
,
#
ln
)
%
V
∧
inv
N
(
lock_inv
γ1
γ2
l
o
ln
R
)
∧
own
γ2
(
Excl
()))
%
I
.
Global
Instance
lock_inv_ne
n
γ1
γ2
l
:
Proper
(
dist
n
==>
dist
n
)
(
lock_inv
γ1
γ2
l
)
.
Global
Instance
lock_inv_ne
n
γ1
γ2
l
o
ln
:
Proper
(
dist
n
==>
dist
n
)
(
lock_inv
γ1
γ2
l
o
ln
)
.
Proof
.
solve_proper
.
Qed
.
Global
Instance
is_lock_ne
n
l
:
Proper
(
dist
n
==>
dist
n
)
(
is_lock
l
)
.
Proof
.
solve_proper
.
Qed
.
...
...
@@ -74,14 +76,13 @@ Global Instance is_lock_persistent l R : PersistentP (is_lock l R).
Proof
.
apply
_
.
Qed
.
Lemma
newlock_spec
(
R
:
iProp
Σ
)
Φ
:
heapN
⊥
N
→
heap_ctx
★
R
★
(
∀
l
,
is_lock
l
R
-★
Φ
#
l
)
⊢
WP
newlock
#
()
{{
Φ
}}
.
heap_ctx
★
R
★
(
∀
l
,
is_lock
l
R
-★
Φ
l
)
⊢
WP
newlock
#
()
{{
Φ
}}
.
Proof
.
iIntros
(?)
"(#Hh & HR & HΦ)"
.
rewrite
/
newlock
.
wp_seq
.
wp_alloc
l
as
"Hl"
.
iIntros
"(#Hh & HR & HΦ)"
.
rewrite
/
newlock
.
wp_seq
.
wp_alloc
l
o
as
"Hl
o"
.
wp_alloc
ln
as
"Hln
"
.
iVs
(
own_alloc
(
Excl
()))
as
(
γ2
)
"Hγ2"
;
first
done
.
iVs
(
own_alloc_strong
(
Auth
(
Excl'
∅
)
∅
)
{[
γ2
]})
as
(
γ1
)
"[% Hγ1]"
;
first
done
.
iVs
(
inv_alloc
N
_
(
lock_inv
γ1
γ2
l
R
)
with
"[-HΦ]"
)
.
iVs
(
inv_alloc
N
_
(
lock_inv
γ1
γ2
l
o
ln
R
)
with
"[-HΦ]"
)
.
{
iNext
.
rewrite
/
lock_inv
.
iExists
0
%
nat
,
0
%
nat
.
iFrame
.
...
...
@@ -93,90 +94,90 @@ Proof.
by
iFrame
.
}
iVsIntro
.
iApply
"HΦ"
.
iExists
γ1
,
γ2
.
iExists
γ1
,
γ2
,
lo
,
ln
.
iSplit
;
by
auto
.
Qed
.
Lemma
wait_loop_spec
l
x
R
(
Φ
:
val
→
iProp
Σ
)
:
issued
l
x
R
★
(
∀
l
,
locked
l
R
-★
R
-★
Φ
#
())
⊢
WP
wait_loop
#
x
#
l
{{
Φ
}}
.
issued
l
x
R
★
(
∀
l
,
locked
l
R
-★
R
-★
Φ
#
())
⊢
WP
wait_loop
#
x
l
{{
Φ
}}
.
Proof
.
iIntros
"[Hl HΦ]"
.
iDestruct
"Hl"
as
(
γ1
γ2
)
"(
%
&
#?
& #? & Ht)"
.
iLöb
as
"IH"
.
wp_rec
.
wp_let
.
wp_bind
(
!
_)
%
E
.
iInv
N
as
(
o
n
)
"[Hl Ha]"
"Hclose"
.
iIntros
"[Hl HΦ]"
.
iDestruct
"Hl"
as
(
γ1
γ2
lo
ln
)
"(
#?
&
%
& #? & Ht)"
.
iLöb
as
"IH"
.
wp_rec
.
subst
.
wp_let
.
wp_proj
.
wp_bind
(
!
_)
%
E
.
iInv
N
as
(
o
n
)
"[Hl
o [Hln
Ha]
]
"
"Hclose"
.
wp_load
.
destruct
(
decide
(
x
=
o
))
as
[
->
|
Hneq
]
.
-
iDestruct
"Ha"
as
"[Hainv [[Ho HR] | Haown]]"
.
+
iVs
(
"Hclose"
with
"[Hl Hainv Ht]"
)
.
+
iVs
(
"Hclose"
with
"[Hl
o Hln
Hainv Ht]"
)
.
{
iNext
.
iExists
o
,
n
.
iFrame
.
eauto
.
}
iVsIntro
.
wp_proj
.
wp_let
.
wp_op
=>[_|[]]
//.
iVsIntro
.
wp_let
.
wp_op
=>[_|[]]
//.
wp_if
.
iVsIntro
.
iApply
(
"HΦ"
with
"[-HR] HR"
)
.
iExists
γ1
,
γ2
;
eauto
.
iApply
(
"HΦ"
with
"[-HR] HR"
)
.
iExists
γ1
,
γ2
,
lo
,
ln
;
eauto
.
+
iExFalso
.
iCombine
"Ht"
"Haown"
as
"Haown"
.
iDestruct
(
auth_own_valid
with
"Haown"
)
as
%
?
%
gset_disj_valid_op
.
set_solver
.
-
iVs
(
"Hclose"
with
"[Hl Ha]"
)
.
-
iVs
(
"Hclose"
with
"[Hl
o Hln
Ha]"
)
.
{
iNext
.
iExists
o
,
n
.
by
iFrame
.
}
iVsIntro
.
wp_proj
.
wp_let
.
wp_op
=>?;
first
omega
.
iVsIntro
.
wp_let
.
wp_op
=>?;
first
omega
.
wp_if
.
by
iApply
(
"IH"
with
"Ht"
)
.
Qed
.
Lemma
acquire_spec
l
R
(
Φ
:
val
→
iProp
Σ
)
:
is_lock
l
R
★
(
∀
l
,
locked
l
R
-★
R
-★
Φ
#
())
⊢
WP
acquire
#
l
{{
Φ
}}
.
is_lock
l
R
★
(
∀
l
,
locked
l
R
-★
R
-★
Φ
#
())
⊢
WP
acquire
l
{{
Φ
}}
.
Proof
.
iIntros
"[Hl HΦ]"
.
iDestruct
"Hl"
as
(
γ1
γ2
)
"(
%
&
#?
& #?)"
.
iLöb
as
"IH"
.
wp_rec
.
wp_bind
(
!
_)
%
E
.
iInv
N
as
(
o
n
)
"[Hl Ha]"
"Hclose"
.
wp_load
.
iVs
(
"Hclose"
with
"[Hl Ha]"
)
.
iIntros
"[Hl HΦ]"
.
iDestruct
"Hl"
as
(
γ1
γ2
lo
ln
)
"(
#?
&
%
& #?)"
.
iLöb
as
"IH"
.
wp_rec
.
wp_bind
(
!
_)
%
E
.
subst
.
wp_proj
.
iInv
N
as
(
o
n
)
"[Hl
o [Hln
Ha]
]
"
"Hclose"
.
wp_load
.
iVs
(
"Hclose"
with
"[Hl
o Hln
Ha]"
)
.
{
iNext
.
iExists
o
,
n
.
by
iFrame
.
}
iVsIntro
.
wp_let
.
wp_proj
.
wp_proj
.
wp_op
.
iVsIntro
.
wp_let
.
wp_proj
.
wp_op
.
wp_bind
(
CAS
_
_
_)
.
iInv
N
as
(
o'
n'
)
"[Hl [Hainv Haown]]"
"Hclose"
.
destruct
(
decide
(
(
#
o'
,
#
n'
)
=
(
#
o
,
#
n
))
)
%
V
as
[[
=
->%
Nat2Z
.
inj
->%
Nat2Z
.
inj
]
|
Hneq
]
.
iInv
N
as
(
o'
n'
)
"[Hl
o' [Hln'
[Hainv Haown]]
]
"
"Hclose"
.
destruct
(
decide
(
#
n'
=
#
n
))
%
V
as
[[
=
->%
Nat2Z
.
inj
]
|
Hneq
]
.
-
wp_cas_suc
.
iDestruct
"Hainv"
as
(
s
)
"[Ho %]"
;
subst
.
iVs
(
own_update
with
"Ho"
)
as
"Ho"
.
{
eapply
auth_update_no_frag
,
(
gset_alloc_empty_local_update
n
)
.
rewrite
elem_of_seq_set
;
omega
.
}
iDestruct
"Ho"
as
"[Hofull Hofrag]"
.
iVs
(
"Hclose"
with
"[Hl Haown Hofull]"
)
.
iVs
(
"Hclose"
with
"[Hl
o' Hln'
Haown Hofull]"
)
.
{
rewrite
gset_disj_union
;
last
by
apply
(
seq_set_S_disjoint
0
)
.
rewrite
-
(
seq_set_S_union_L
0
)
.
iNext
.
iExists
o
,
(
S
n
)
%
nat
.
iNext
.
iExists
o
'
,
(
S
n
)
%
nat
.
rewrite
Nat2Z
.
inj_succ
-
Z
.
add_1_r
.
iFrame
.
iExists
(
GSet
(
seq_set
0
(
S
n
)))
.
by
iFrame
.
}
iVsIntro
.
wp_if
.
wp_proj
.
iApply
wait_loop_spec
.
iVsIntro
.
wp_if
.
iApply
(
wait_loop_spec
(
#
lo
,
#
ln
))
.
iSplitR
"HΦ"
;
last
by
done
.
rewrite
/
issued
/
auth_own
;
eauto
10
.
-
wp_cas_fail
.
iVs
(
"Hclose"
with
"[Hl Hainv Haown]"
)
.
iVs
(
"Hclose"
with
"[Hl
o' Hln'
Hainv Haown]"
)
.
{
iNext
.
iExists
o'
,
n'
.
by
iFrame
.
}
iVsIntro
.
wp_if
.
by
iApply
"IH"
.
Qed
.
Lemma
release_spec
R
l
(
Φ
:
val
→
iProp
Σ
):
locked
l
R
★
R
★
Φ
#
()
⊢
WP
release
#
l
{{
Φ
}}
.
locked
l
R
★
R
★
Φ
#
()
⊢
WP
release
l
{{
Φ
}}
.
Proof
.
iIntros
"(Hl & HR & HΦ)"
;
iDestruct
"Hl"
as
(
γ1
γ2
)
"(
%
&
#?
& #? & Hγ)"
.
iLöb
as
"IH"
.
wp_rec
.
wp_bind
(
!
_)
%
E
.
iInv
N
as
(
o
n
)
"[Hl Hr]"
"Hclose"
.
wp_load
.
iVs
(
"Hclose"
with
"[Hl Hr]"
)
.
iIntros
"(Hl & HR & HΦ)"
;
iDestruct
"Hl"
as
(
γ1
γ2
lo
ln
)
"(
#?
&
%
& #? & Hγ)"
.
iLöb
as
"IH"
.
wp_rec
.
subst
.
wp_proj
.
wp_bind
(
!
_)
%
E
.
iInv
N
as
(
o
n
)
"[Hl
o [Hln
Hr]
]
"
"Hclose"
.
wp_load
.
iVs
(
"Hclose"
with
"[Hl
o Hln
Hr]"
)
.
{
iNext
.
iExists
o
,
n
.
by
iFrame
.
}
iVsIntro
.
wp_let
.
wp_bind
(
CAS
_
_
_
)
.
wp_proj
.
wp_op
.
wp_proj
.
iInv
N
as
(
o'
n'
)
"[Hl Hr]"
"Hclose"
.
destruct
(
decide
(
(
#
o'
,
#
n'
)
=
(
#
o
,
#
n
)
))
%
V
as
[[
=
->%
Nat2Z
.
inj
->%
Nat2Z
.
inj
]
|
Hneq
]
.
wp_proj
.
wp_op
.
iInv
N
as
(
o'
n'
)
"[Hl
o' [Hln'
Hr]
]
"
"Hclose"
.
destruct
(
decide
(
#
o'
=
#
o
))
%
V
as
[[
=
->%
Nat2Z
.
inj
]
|
Hneq
]
.
-
wp_cas_suc
.
iDestruct
"Hr"
as
"[Hainv [[Ho _] | Hown]]"
.
+
iExFalso
.
iCombine
"Hγ"
"Ho"
as
"Ho"
.
iDestruct
(
own_valid
with
"#Ho"
)
as
%
[]
.
+
iVs
(
"Hclose"
with
"[Hl HR Hγ Hainv]"
)
.
{
iNext
.
iExists
(
o
+
1
)
%
nat
,
n
%
nat
.
+
iVs
(
"Hclose"
with
"[Hl
o' Hln'
HR Hγ Hainv]"
)
.
{
iNext
.
iExists
(
o
+
1
)
%
nat
,
n
'
%
nat
.
iFrame
.
rewrite
Nat2Z
.
inj_add
.
iFrame
.
iLeft
;
by
iFrame
.
}
iVsIntro
.
by
wp_if
.
-
wp_cas_fail
.
iVs
(
"Hclose"
with
"[Hl Hr]"
)
.
-
wp_cas_fail
.
iVs
(
"Hclose"
with
"[Hl
o' Hln'
Hr]"
)
.
{
iNext
.
iExists
o'
,
n'
.
by
iFrame
.
}
iVsIntro
.
wp_if
.
by
iApply
(
"IH"
with
"Hγ HR"
)
.
Qed
.
...
...
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