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Tej Chajed
iris
Commits
d4fd7c20
Commit
d4fd7c20
authored
Feb 22, 2016
by
Ralf Jung
Browse files
hide disjointness better from the client
parent
65e4effa
Changes
1
Hide whitespace changes
Inline
Side-by-side
barrier/barrier.v
View file @
d4fd7c20
...
...
@@ -158,11 +158,12 @@ Section proof.
)%
I
.
Definition
barrier_ctx
(
γ
:
gname
)
(
l
:
loc
)
(
P
:
iProp
)
:
iProp
:
=
(
heap_ctx
heapN
★
sts_ctx
γ
N
(
barrier_inv
l
P
))%
I
.
(
■
(
heapN
⊥
N
)
★
heap_ctx
heapN
★
sts_ctx
γ
N
(
barrier_inv
l
P
))%
I
.
Global
Instance
barrier_ctx_ne
n
γ
l
:
Proper
(
dist
n
==>
dist
n
)
(
barrier_ctx
γ
l
).
Proof
.
move
=>?
?
EQ
.
rewrite
/
barrier_ctx
.
apply
sep_ne
;
first
done
.
apply
sts_ctx_ne
.
move
=>?
?
EQ
.
rewrite
/
barrier_ctx
.
apply
sep_ne
;
first
done
.
apply
sep_ne
;
first
done
.
apply
sts_ctx_ne
.
move
=>[
p
I
].
rewrite
/
barrier_inv
.
destruct
p
;
last
done
.
rewrite
/
waiting
.
by
setoid_rewrite
EQ
.
Qed
.
...
...
@@ -244,10 +245,11 @@ Section proof.
Qed
.
Lemma
newchan_spec
(
P
:
iProp
)
(
Φ
:
val
→
iProp
)
:
heapN
⊥
N
→
(
heap_ctx
heapN
★
∀
l
,
recv
l
P
★
send
l
P
-
★
Φ
(
LocV
l
))
⊑
||
newchan
'
()
{{
Φ
}}.
Proof
.
rewrite
/
newchan
.
wp_seq
.
intros
HN
.
rewrite
/
newchan
.
wp_seq
.
rewrite
-
wp_pvs
.
wp
eapply
wp_alloc
;
eauto
with
I
ndisj
.
apply
forall_intro
=>
l
.
rewrite
(
forall_elim
l
).
apply
wand_intro_l
.
rewrite
!
assoc
.
apply
pvs_wand_r
.
...
...
@@ -276,7 +278,7 @@ Section proof.
rewrite
[
barrier_ctx
_
_
_
]
lock
!
assoc
[(
_
★
locked
_
)%
I
]
comm
!
assoc
-
lock
.
rewrite
-
always_sep_dup
.
rewrite
[
barrier_ctx
_
_
_
]
lock
always_and_sep_l
-!
assoc
assoc
-
lock
.
rewrite
-
pvs_frame_l
.
apply
sep_mono_r
.
rewrite
-
pvs_frame_l
.
rewrite
/
barrier_ctx
const_equiv
//
left_id
.
apply
sep_mono_r
.
rewrite
[(
saved_prop_own
_
_
★
_
)%
I
]
comm
!
assoc
.
rewrite
-
pvs_frame_r
.
apply
sep_mono_l
.
rewrite
-
assoc
[(
▷
_
★
_
)%
I
]
comm
assoc
-
pvs_frame_r
.
...
...
@@ -292,14 +294,14 @@ Section proof.
Qed
.
Lemma
signal_spec
l
P
(
Φ
:
val
→
iProp
)
:
heapN
⊥
N
→
(
send
l
P
★
P
★
Φ
'
())
⊑
||
signal
(
LocV
l
)
{{
Φ
}}.
(
send
l
P
★
P
★
Φ
'
())
⊑
||
signal
(
LocV
l
)
{{
Φ
}}.
Proof
.
intros
Hdisj
.
rewrite
/
signal
/
send
/
barrier_ctx
.
rewrite
sep_exist_r
.
apply
exist_elim
=>
γ
.
wp_let
.
rewrite
/
signal
/
send
/
barrier_ctx
.
rewrite
sep_exist_r
.
apply
exist_elim
=>
γ
.
rewrite
-!
assoc
.
apply
const_elim_sep_l
=>?.
wp_let
.
(* I think some evars here are better than repeating *everything* *)
eapply
(
sts_fsaS
_
(
wp_fsa
_
))
with
(
N0
:
=
N
)
(
γ
0
:
=
γ
)
;
simpl
;
eauto
with
I
ndisj
.
rewrite
[(
_
★
sts_ownS
_
_
_
)%
I
]
comm
-!
assoc
.
apply
sep_mono_r
.
rewrite
!
assoc
[(
_
★
sts_ownS
_
_
_
)%
I
]
comm
-!
assoc
.
apply
sep_mono_r
.
apply
forall_intro
=>-[
p
I
].
apply
wand_intro_l
.
rewrite
-!
assoc
.
apply
const_elim_sep_l
=>
Hs
.
destruct
p
;
last
done
.
rewrite
{
1
}/
barrier_inv
=>/={
Hs
}.
rewrite
later_sep
.
...
...
@@ -319,13 +321,14 @@ Section proof.
Qed
.
Lemma
wait_spec
l
P
(
Φ
:
val
→
iProp
)
:
heapN
⊥
N
→
(
recv
l
P
★
(
P
-
★
Φ
'
()))
⊑
||
wait
(
LocV
l
)
{{
Φ
}}.
(
recv
l
P
★
(
P
-
★
Φ
'
()))
⊑
||
wait
(
LocV
l
)
{{
Φ
}}.
Proof
.
rename
P
into
R
.
intros
Hdisj
.
wp_rec
.
rename
P
into
R
.
wp_rec
.
rewrite
{
1
}/
recv
/
barrier_ctx
.
rewrite
!
sep_exist_r
.
apply
exist_elim
=>
γ
.
rewrite
!
sep_exist_r
.
apply
exist_elim
=>
P
.
rewrite
!
sep_exist_r
.
apply
exist_elim
=>
Q
.
rewrite
!
sep_exist_r
.
apply
exist_elim
=>
i
.
wp_focus
(!
_
)%
L
.
apply
exist_elim
=>
i
.
rewrite
-!
assoc
.
apply
const_elim_sep_l
=>?.
wp_focus
(!
_
)%
L
.
(* I think some evars here are better than repeating *everything* *)
eapply
(
sts_fsaS
_
(
wp_fsa
_
))
with
(
N0
:
=
N
)
(
γ
0
:
=
γ
)
;
simpl
;
eauto
with
I
ndisj
.
...
...
@@ -338,7 +341,7 @@ Section proof.
apply
wand_intro_l
.
destruct
p
.
{
(* a Low state. The comparison fails, and we recurse. *)
rewrite
-(
exist_intro
(
State
Low
I
))
-(
exist_intro
{[
Change
i
]}).
rewrite
const_equiv
/=
;
last
by
apply
rtc_refl
.
rewrite
[(
■
sts
.
steps
_
_
)%
I
]
const_equiv
/=
;
last
by
apply
rtc_refl
.
rewrite
left_id
-[(
▷
barrier_inv
_
_
_
)%
I
]
later_intro
{
3
}/
barrier_inv
.
rewrite
-!
assoc
.
apply
sep_mono_r
,
sep_mono_r
,
wand_intro_l
.
wp_op
;
first
done
.
intros
_
.
wp_if
.
rewrite
!
assoc
.
...
...
@@ -347,7 +350,8 @@ Section proof.
rewrite
-(
exist_intro
γ
)
-(
exist_intro
P
)
-(
exist_intro
Q
)
-(
exist_intro
i
).
rewrite
!
assoc
.
do
3
(
rewrite
-
pvs_frame_r
;
apply
sep_mono
;
last
(
try
apply
later_intro
;
reflexivity
)).
rewrite
[(
_
★
heap_ctx
_
)%
I
]
comm
-!
assoc
-
pvs_frame_l
.
apply
sep_mono_r
.
rewrite
[(
_
★
heap_ctx
_
)%
I
]
comm
-!
assoc
.
rewrite
const_equiv
//
left_id
-
pvs_frame_l
.
apply
sep_mono_r
.
rewrite
comm
-
pvs_frame_l
.
apply
sep_mono_r
.
apply
sts_ownS_weaken
;
eauto
using
sts
.
up_subseteq
with
sts
.
}
(* a High state: the comparison succeeds, and we perform a transition and
...
...
@@ -377,7 +381,7 @@ Section proof.
rewrite
{
1
}/
recv
/
barrier_ctx
.
rewrite
sep_exist_r
.
apply
exist_elim
=>
γ
.
rewrite
sep_exist_r
.
apply
exist_elim
=>
P
.
rewrite
sep_exist_r
.
apply
exist_elim
=>
Q
.
rewrite
sep_exist_r
.
apply
exist_elim
=>
i
.
rewrite
-
wp_pvs
.
apply
exist_elim
=>
i
.
rewrite
-!
assoc
.
apply
const_elim_sep_l
=>?.
rewrite
-
wp_pvs
.
(* I think some evars here are better than repeating *everything* *)
eapply
(
sts_fsaS
_
(
wp_fsa
_
))
with
(
N0
:
=
N
)
(
γ
0
:
=
γ
)
;
simpl
;
eauto
with
I
ndisj
.
...
...
@@ -398,7 +402,7 @@ Section proof.
(* Case I: Low state. *)
-
rewrite
-(
exist_intro
(
State
Low
({[
i1
]}
∪
({[
i2
]}
∪
(
I
∖
{[
i
]}))))).
rewrite
-(
exist_intro
({[
Change
i1
]}
∪
{[
Change
i2
]})).
rewrite
const_equiv
;
last
by
eauto
with
sts
.
rewrite
[(
■
sts
.
steps
_
_
)%
I
]
const_equiv
;
last
by
eauto
with
sts
.
rewrite
left_id
-
later_intro
{
1
3
}/
barrier_inv
.
(* FIXME ssreflect rewrite fails if there are evars around. Also, this is very slow because we don't have a proof mode. *)
rewrite
-(
waiting_split
_
_
_
Q
R1
R2
)
;
[|
done
..].
...
...
@@ -424,7 +428,8 @@ Section proof.
rewrite
-!
assoc
.
rewrite
[(
sts_ownS
_
_
_
★
_
★
_
)%
I
]
assoc
-
pvs_frame_r
.
apply
sep_mono
.
*
rewrite
-
sts_ownS_op
;
by
eauto
using
sts_own_weaken
with
sts
.
*
rewrite
{
1
}[
heap_ctx
_
]
always_sep_dup
!
assoc
[(
_
★
heap_ctx
_
)%
I
]
comm
-!
assoc
.
apply
sep_mono_r
.
*
rewrite
const_equiv
//
!
left_id
.
rewrite
{
1
}[
heap_ctx
_
]
always_sep_dup
!
assoc
[(
_
★
heap_ctx
_
)%
I
]
comm
-!
assoc
.
apply
sep_mono_r
.
rewrite
!
assoc
![(
_
★
heap_ctx
_
)%
I
]
comm
-!
assoc
.
apply
sep_mono_r
.
rewrite
{
1
}[
sts_ctx
_
_
_
]
always_sep_dup
!
assoc
[(
_
★
sts_ctx
_
_
_
)%
I
]
comm
-!
assoc
.
apply
sep_mono_r
.
rewrite
!
assoc
![(
_
★
sts_ctx
_
_
_
)%
I
]
comm
-!
assoc
.
apply
sep_mono_r
.
...
...
@@ -463,7 +468,8 @@ Section proof.
rewrite
-!
assoc
.
rewrite
[(
sts_ownS
_
_
_
★
_
★
_
)%
I
]
assoc
-
pvs_frame_r
.
apply
sep_mono
.
*
rewrite
-
sts_ownS_op
;
by
eauto
using
sts_own_weaken
with
sts
.
*
rewrite
{
1
}[
heap_ctx
_
]
always_sep_dup
!
assoc
[(
_
★
heap_ctx
_
)%
I
]
comm
-!
assoc
.
apply
sep_mono_r
.
*
rewrite
const_equiv
//
!
left_id
.
rewrite
{
1
}[
heap_ctx
_
]
always_sep_dup
!
assoc
[(
_
★
heap_ctx
_
)%
I
]
comm
-!
assoc
.
apply
sep_mono_r
.
rewrite
!
assoc
![(
_
★
heap_ctx
_
)%
I
]
comm
-!
assoc
.
apply
sep_mono_r
.
rewrite
{
1
}[
sts_ctx
_
_
_
]
always_sep_dup
!
assoc
[(
_
★
sts_ctx
_
_
_
)%
I
]
comm
-!
assoc
.
apply
sep_mono_r
.
rewrite
!
assoc
![(
_
★
sts_ctx
_
_
_
)%
I
]
comm
-!
assoc
.
apply
sep_mono_r
.
...
...
@@ -479,7 +485,7 @@ Section proof.
apply
wand_intro_l
.
rewrite
/
recv
.
rewrite
sep_exist_r
.
apply
exist_mono
=>
γ
.
rewrite
sep_exist_r
.
apply
exist_mono
=>
P
.
rewrite
sep_exist_r
.
apply
exist_mono
=>
Q
.
rewrite
sep_exist_r
.
apply
exist_mono
=>
i
.
rewrite
-!
assoc
.
apply
sep_mono_r
,
sep_mono_r
,
sep_mono_r
,
sep_mono_r
.
rewrite
-!
assoc
.
apply
sep_mono_r
,
sep_mono_r
,
sep_mono_r
,
sep_mono_r
,
sep_mono_r
.
rewrite
(
later_intro
(
P1
-
★
_
)%
I
)
-
later_sep
.
apply
later_mono
.
apply
wand_intro_l
.
rewrite
!
assoc
wand_elim_r
wand_elim_r
.
done
.
Qed
.
...
...
@@ -506,13 +512,12 @@ Section spec.
Proof
.
intros
HN
.
exists
(
λ
l
,
CofeMor
(
recv
N
heapN
l
)).
exists
(
λ
l
,
CofeMor
(
send
N
heapN
l
)).
split_and
?
;
cbn
.
-
intros
.
apply
:
always_intro
.
apply
impl_intro_l
.
rewrite
-
newchan_spec
.
-
intros
.
apply
:
always_intro
.
apply
impl_intro_l
.
rewrite
-
newchan_spec
//
.
rewrite
comm
always_and_sep_r
.
apply
sep_mono_r
.
apply
forall_intro
=>
l
.
apply
wand_intro_l
.
rewrite
right_id
-(
exist_intro
l
)
const_equiv
//
left_id
.
apply
wand_intro_l
.
rewrite
right_id
-(
exist_intro
l
)
const_equiv
//
left_id
;
done
.
-
intros
.
apply
ht_alt
.
rewrite
-
signal_spec
;
last
done
.
by
rewrite
right_id
.
-
intros
.
apply
ht_alt
.
rewrite
-
wait_spec
;
last
done
.
-
intros
.
apply
ht_alt
.
rewrite
-
signal_spec
.
by
rewrite
right_id
.
-
intros
.
apply
ht_alt
.
rewrite
-
wait_spec
.
apply
sep_intro_True_r
;
first
done
.
apply
wand_intro_l
.
eauto
with
I
.
-
intros
.
apply
ht_alt
.
rewrite
-
recv_split
.
apply
sep_intro_True_r
;
first
done
.
apply
wand_intro_l
.
eauto
with
I
.
...
...
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