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FP
Stacked Borrows Coq
Commits
d881c0ba
Commit
d881c0ba
authored
Aug 19, 2019
by
Hai Dang
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clean up
parent
c3402c2b
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123 deletions
+1
-123
theories/sim/cmra.v
theories/sim/cmra.v
+0
-122
theories/sim/refl.v
theories/sim/refl.v
+1
-1
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theories/sim/cmra.v
View file @
d881c0ba
...
...
@@ -546,125 +546,3 @@ Proof. by rewrite lookup_insert. Qed.
Lemma
res_tag_lookup_ne
(
k
:
tag_kind
)
(
h
:
heaplet
)
(
t
t
'
:
ptr_id
)
(
NEQ
:
t
'
≠
t
)
:
(
res_tag
t
k
h
).(
rtm
)
!!
t
'
≡
None
.
Proof
.
by
rewrite
lookup_insert_ne
.
Qed
.
(
**
res_mapsto
*
)
(
*
Lemma
res_loc_lookup
l
n
t
:
(
res_loc
l
n
t
).(
rlm
)
!!
t
≡
Some
(
Excl
$
locs_seq
l
n
).
Proof
.
rewrite
/=
lookup_fmap
lookup_insert
//. Qed.
Lemma
res_mapsto_llookup
l
v
t
:
(
res_mapsto
l
v
t
).(
rlm
)
!!
t
≡
Some
(
Excl
$
locs_seq
l
(
length
v
)).
Proof
.
rewrite
lookup_op
res_loc_lookup
//. Qed.
Lemma
res_mapsto_llookup_ne
l
v
t
t1
:
t1
≠
t
→
(
res_mapsto
l
v
t
).(
rlm
)
!!
t1
=
None
.
Proof
.
intros
.
rewrite
/
res_mapsto
/=
/
to_lmUR
right_id_L
lookup_fmap
lookup_insert_ne
//.
Qed
.
Lemma
res_mapsto_llookup_eq
l
v
t
t1
ls1
:
(
res_mapsto
l
v
t
).(
rlm
)
!!
t1
≡
Some
(
Excl
ls1
)
→
t1
=
t
∧
ls1
=
locs_seq
l
(
length
v
).
Proof
.
case
(
decide
(
t1
=
t
))
=>
?
;
[
subst
t1
|
].
-
rewrite
res_mapsto_llookup
.
intros
.
by
simplify_eq
.
-
rewrite
res_mapsto_llookup_ne
//. by inversion 1.
Qed
.
Lemma
res_mapsto_tlookup
l
v
(
t
:
ptr_id
)
:
(
res_mapsto
l
v
t
).(
rtm
)
!!
t
≡
Some
(
to_tgkR
tkUnique
,
to_agree
<
$
>
(
write_hpl
l
v
∅
)).
Proof
.
by
rewrite
lookup_op
/=
lookup_empty
left_id
lookup_insert
.
Qed
.
Lemma
res_mapsto_tlookup_ne
l
v
(
t
t
'
:
ptr_id
)
(
NEQ
:
t
'
≠
t
)
:
(
res_mapsto
l
v
t
).(
rtm
)
!!
t
'
≡
None
.
Proof
.
by
rewrite
lookup_op
/=
lookup_empty
left_id
lookup_insert_ne
.
Qed
.
(
**
allocating
locals
*
)
Lemma
res_loc_alloc_local_update
(
lm
:
lmapUR
)
(
t
:
ptr_id
)
ls
:
lm
!!
t
=
None
→
(
lm
,
ε
)
~
l
~>
(
lm
⋅
(
to_lmUR
{
[
t
:=
ls
]
}
),
(
to_lmUR
{
[
t
:=
ls
]
}
)).
Proof
.
intros
FRESH
.
rewrite
/
to_lmUR
fmap_insert
fmap_empty
insert_empty
(
cmra_comm
_
{
[
t
:=
_
]
}
)
-
insert_singleton_op
//.
by
apply
alloc_local_update
.
Qed
.
Lemma
res_mapsto_alloc_local_update
r
l
v
t
:
r
.(
rtm
)
!!
t
=
None
→
r
.(
rlm
)
!!
t
=
None
→
(
r
,
ε
)
~
l
~>
(
r
⋅
res_mapsto
l
v
t
,
res_mapsto
l
v
t
).
Proof
.
intros
FRESH1
FRESH2
.
destruct
r
as
[[
tm
cm
]
lm
].
rewrite
/
res_mapsto
(
cmra_comm
(
res_loc
_
_
_
)).
etrans
.
-
by
apply
(
res_tag_alloc_local_update
_
t
tkUnique
(
write_hpl
l
v
∅
)).
-
rewrite
!
pair_op
!
right_id
left_id
/=
.
by
apply
prod_local_update_2
,
res_loc_alloc_local_update
.
Qed
.
(
**
deallocating
locals
*
)
Lemma
res_loc_dealloc_local_update
(
lm
:
lmapUR
)
t
ls
:
lm
!!
t
=
None
→
(
lm
⋅
(
to_lmUR
{
[
t
:=
ls
]
}
),
to_lmUR
{
[
t
:=
ls
]
}
)
~
l
~>
(
lm
,
ε
).
Proof
.
intros
?
.
rewrite
/
to_lmUR
fmap_insert
fmap_empty
insert_empty
(
cmra_comm
_
{
[
t
:=
_
]
}
)
-
insert_singleton_op
;
[
|
done
].
etrans
.
-
eapply
(
delete_local_update_cancelable
_
_
t
);
[
|
by
rewrite
lookup_insert
..].
apply
_.
-
rewrite
2
!
delete_insert_delete
delete_empty
delete_notin
//.
Qed
.
Lemma
res_mapsto_res_tag
(
r
:
resUR
)
l
v
t
k
'
h
'
(
NONE1
:
r
.(
rlm
)
!!
t
=
None
)
(
NONE2
:
r
.(
rtm
)
!!
t
=
None
)
:
(
r
⋅
res_mapsto
l
v
t
,
res_mapsto
l
v
t
)
~
l
~>
(
r
⋅
res_tag
t
k
'
h
'
,
res_tag
t
k
'
h
'
).
Proof
.
rewrite
/
res_mapsto
.
destruct
r
as
[[
tm
cm
]
lm
].
rewrite
(
cmra_comm
(
res_loc
_
_
_
))
cmra_assoc
.
etrans
.
-
apply
prod_local_update_2
.
rewrite
/=
right_id
left_id
.
by
apply
res_loc_dealloc_local_update
.
-
rewrite
!
pair_op
/=
!
right_id
.
apply
prod_local_update_1
,
prod_local_update_1
.
rewrite
/=
.
by
apply
(
res_tag_uniq_insert_local_update_inner
_
_
k
'
).
Qed
.
(
**
updating
locals
*
)
Lemma
res_mapsto_1_insert_local_update
(
r
:
resUR
)
(
l
:
loc
)
s1
s2
(
t
:
ptr_id
)
(
NONE
:
r
.(
rtm
)
!!
t
=
None
)
:
(
r
⋅
res_mapsto
l
[
s1
]
t
,
res_mapsto
l
[
s1
]
t
)
~
l
~>
(
r
⋅
res_mapsto
l
[
s2
]
t
,
res_mapsto
l
[
s2
]
t
).
Proof
.
intros
.
rewrite
/
res_mapsto
cmra_assoc
.
etrans
.
-
eapply
res_tag_1_insert_local_update_r
.
by
rewrite
lookup_op
NONE
/=
lookup_empty
right_id_L
.
-
rewrite
-
(
cmra_assoc
r
)
2
!
(
cmra_comm
(
res_loc
_
_
_
))
2
!
cmra_assoc
/=
insert_empty
//.
Qed
.
Lemma
res_mapsto_tdom
l
v
t
:
dom
(
gset
nat
)
(
res_mapsto
l
v
t
).(
rtm
)
≡
{
[
t
]
}
.
Proof
.
intros
t1
.
rewrite
elem_of_dom
/
res_mapsto
lookup_op
/=
left_id
elem_of_singleton
.
case
(
decide
(
t1
=
t
))
=>
?
.
-
subst
t1
.
rewrite
lookup_insert
.
naive_solver
.
-
rewrite
lookup_insert_ne
// lookup_empty. split; [by destruct 1|done].
Qed
.
Lemma
res_mapsto_ldom
l
v
t
:
dom
(
gset
nat
)
(
res_mapsto
l
v
t
).(
rlm
)
≡
{
[
t
]
}
.
Proof
.
intros
t1
.
rewrite
elem_of_dom
/
res_mapsto
lookup_op
/=
right_id
elem_of_singleton
/
to_lmUR
lookup_fmap
.
case
(
decide
(
t1
=
t
))
=>
?
.
-
subst
t1
.
rewrite
lookup_insert
.
naive_solver
.
-
rewrite
lookup_insert_ne
// lookup_empty. split; [by destruct 1|done].
Qed
.
*
)
theories/sim/refl.v
View file @
d881c0ba
...
...
@@ -313,7 +313,7 @@ Proof using Type*.
eapply
(
Forall_lookup_1
_
_
_
_
H
Hlk
).
+
eapply
(
Forall_lookup_1
_
_
_
_
Hwf2
Hlk
).
+
eauto
.
Q
ed
.
Admitt
ed
.
End
sem
.
...
...
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