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Simon Spies
Iris
Commits
2709c37e
Commit
2709c37e
authored
Feb 24, 2016
by
Robbert Krebbers
Browse files
Change order of premises in heap.v to instantiate evars earlier.
parent
67102cc5
Changes
1
Hide whitespace changes
Inline
Side-by-side
heap_lang/heap.v
View file @
2709c37e
...
...
@@ -109,12 +109,12 @@ Section heap.
(** Weakest precondition *)
Lemma
wp_alloc
N
E
e
v
P
Φ
:
to_val
e
=
Some
v
→
nclose
N
⊆
E
→
P
⊑
heap_ctx
N
→
to_val
e
=
Some
v
→
P
⊑
heap_ctx
N
→
nclose
N
⊆
E
→
P
⊑
(
▷
∀
l
,
l
↦
v
-
★
Φ
(
LocV
l
))
→
P
⊑
||
Alloc
e
@
E
{{
Φ
}}.
Proof
.
rewrite
/
heap_ctx
/
heap_inv
heap_mapsto_eq
=>
??
Hctx
HP
.
rewrite
/
heap_ctx
/
heap_inv
heap_mapsto_eq
=>
??
?
HP
.
trans
(|={
E
}=>
auth_own
heap_name
∅
★
P
)%
I
.
{
by
rewrite
-
pvs_frame_r
-(
auth_empty
_
E
)
left_id
.
}
apply
wp_strip_pvs
,
(
auth_fsa
heap_inv
(
wp_fsa
(
Alloc
e
)))
...
...
@@ -135,12 +135,11 @@ Section heap.
Qed
.
Lemma
wp_load
N
E
l
v
P
Φ
:
nclose
N
⊆
E
→
P
⊑
heap_ctx
N
→
P
⊑
heap_ctx
N
→
nclose
N
⊆
E
→
P
⊑
(
▷
l
↦
v
★
▷
(
l
↦
v
-
★
Φ
v
))
→
P
⊑
||
Load
(
Loc
l
)
@
E
{{
Φ
}}.
Proof
.
rewrite
/
heap_ctx
/
heap_inv
heap_mapsto_eq
=>
HN
?
HP
Φ
.
rewrite
/
heap_ctx
/
heap_inv
heap_mapsto_eq
=>
?
?
HP
Φ
.
apply
(
auth_fsa'
heap_inv
(
wp_fsa
_
)
id
)
with
N
heap_name
{[
l
:
=
Excl
v
]}
;
simpl
;
eauto
with
I
.
rewrite
HP
Φ
{
HP
Φ
}
;
apply
sep_mono_r
,
forall_intro
=>
h
;
apply
wand_intro_l
.
...
...
@@ -153,12 +152,12 @@ Section heap.
Qed
.
Lemma
wp_store
N
E
l
v'
e
v
P
Φ
:
to_val
e
=
Some
v
→
nclose
N
⊆
E
→
P
⊑
heap_ctx
N
→
to_val
e
=
Some
v
→
P
⊑
heap_ctx
N
→
nclose
N
⊆
E
→
P
⊑
(
▷
l
↦
v'
★
▷
(
l
↦
v
-
★
Φ
(
LitV
LitUnit
)))
→
P
⊑
||
Store
(
Loc
l
)
e
@
E
{{
Φ
}}.
Proof
.
rewrite
/
heap_ctx
/
heap_inv
heap_mapsto_eq
=>
?
HN
?
HP
Φ
.
rewrite
/
heap_ctx
/
heap_inv
heap_mapsto_eq
=>
??
?
HP
Φ
.
apply
(
auth_fsa'
heap_inv
(
wp_fsa
_
)
(
alter
(
λ
_
,
Excl
v
)
l
))
with
N
heap_name
{[
l
:
=
Excl
v'
]}
;
simpl
;
eauto
with
I
.
rewrite
HP
Φ
{
HP
Φ
}
;
apply
sep_mono_r
,
forall_intro
=>
h
;
apply
wand_intro_l
.
...
...
@@ -173,12 +172,11 @@ Section heap.
Lemma
wp_cas_fail
N
E
l
v'
e1
v1
e2
v2
P
Φ
:
to_val
e1
=
Some
v1
→
to_val
e2
=
Some
v2
→
v'
≠
v1
→
nclose
N
⊆
E
→
P
⊑
heap_ctx
N
→
P
⊑
heap_ctx
N
→
nclose
N
⊆
E
→
P
⊑
(
▷
l
↦
v'
★
▷
(
l
↦
v'
-
★
Φ
(
LitV
(
LitBool
false
))))
→
P
⊑
||
Cas
(
Loc
l
)
e1
e2
@
E
{{
Φ
}}.
Proof
.
rewrite
/
heap_ctx
/
heap_inv
heap_mapsto_eq
=>???
HN
?
HP
Φ
.
rewrite
/
heap_ctx
/
heap_inv
heap_mapsto_eq
=>???
?
?
HP
Φ
.
apply
(
auth_fsa'
heap_inv
(
wp_fsa
_
)
id
)
with
N
heap_name
{[
l
:
=
Excl
v'
]}
;
simpl
;
eauto
10
with
I
.
rewrite
HP
Φ
{
HP
Φ
}
;
apply
sep_mono_r
,
forall_intro
=>
h
;
apply
wand_intro_l
.
...
...
@@ -192,12 +190,11 @@ Section heap.
Lemma
wp_cas_suc
N
E
l
e1
v1
e2
v2
P
Φ
:
to_val
e1
=
Some
v1
→
to_val
e2
=
Some
v2
→
nclose
N
⊆
E
→
P
⊑
heap_ctx
N
→
P
⊑
heap_ctx
N
→
nclose
N
⊆
E
→
P
⊑
(
▷
l
↦
v1
★
▷
(
l
↦
v2
-
★
Φ
(
LitV
(
LitBool
true
))))
→
P
⊑
||
Cas
(
Loc
l
)
e1
e2
@
E
{{
Φ
}}.
Proof
.
rewrite
/
heap_ctx
/
heap_inv
heap_mapsto_eq
=>
??
HN
?
HP
Φ
.
rewrite
/
heap_ctx
/
heap_inv
heap_mapsto_eq
=>
??
?
?
HP
Φ
.
apply
(
auth_fsa'
heap_inv
(
wp_fsa
_
)
(
alter
(
λ
_
,
Excl
v2
)
l
))
with
N
heap_name
{[
l
:
=
Excl
v1
]}
;
simpl
;
eauto
10
with
I
.
rewrite
HP
Φ
{
HP
Φ
}
;
apply
sep_mono_r
,
forall_intro
=>
h
;
apply
wand_intro_l
.
...
...
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