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f2bf449c
Commit
f2bf449c
authored
Nov 25, 2016
by
Robbert Krebbers
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Plain Diff
Tweak boxes.
No longer `put box_own_prop γ P` in the invariant, it is persistent.
parent
513b8d85
Pipeline
#3115
passed with stage
in 10 minutes and 32 seconds
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1
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base_logic/lib/boxes.v
base_logic/lib/boxes.v
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base_logic/lib/boxes.v
View file @
f2bf449c
...
...
@@ -22,10 +22,10 @@ Section box_defs.
own
γ
(
∅
:
auth
(
option
(
excl
bool
)),
Some
(
to_agree
(
Next
(
iProp_unfold
P
)))).
Definition
slice_inv
(
γ
:
slice_name
)
(
P
:
iProp
Σ
)
:
iProp
Σ
:
=
(
∃
b
,
box_own_auth
γ
(
●
Excl'
b
)
∗
box_own_prop
γ
P
∗
if
b
then
P
else
True
)%
I
.
(
∃
b
,
box_own_auth
γ
(
●
Excl'
b
)
∗
if
b
then
P
else
True
)%
I
.
Definition
slice
(
γ
:
slice_name
)
(
P
:
iProp
Σ
)
:
iProp
Σ
:
=
inv
N
(
slice_inv
γ
P
)
.
(
box_own_prop
γ
P
∗
inv
N
(
slice_inv
γ
P
))%
I
.
Definition
box
(
f
:
gmap
slice_name
bool
)
(
P
:
iProp
Σ
)
:
iProp
Σ
:
=
(
∃
Φ
:
slice_name
→
iProp
Σ
,
...
...
@@ -114,9 +114,9 @@ Lemma box_delete_empty E f P Q γ :
slice
N
γ
Q
-
∗
▷
box
N
f
P
={
E
}=
∗
∃
P'
,
▷
▷
(
P
≡
(
Q
∗
P'
))
∗
▷
box
N
(
delete
γ
f
)
P'
.
Proof
.
iIntros
(??)
"
#Hinv H"
;
iDestruct
"H"
as
(
Φ
)
"[#HeqP Hf]"
.
iIntros
(??)
"
[#HγQ Hinv] H"
.
iDestruct
"H"
as
(
Φ
)
"[#HeqP Hf]"
.
iExists
([
∗
map
]
γ
'
↦
_
∈
delete
γ
f
,
Φ
γ
'
)%
I
.
iInv
N
as
(
b
)
"
(Hγ & #HγQ &_)
"
"Hclose"
.
iInv
N
as
(
b
)
"
[Hγ _]
"
"Hclose"
.
iApply
fupd_trans_frame
;
iFrame
"Hclose"
;
iModIntro
;
iNext
.
iDestruct
(
big_sepM_delete
_
f
_
false
with
"Hf"
)
as
"[[Hγ' #[HγΦ ?]] ?]"
;
first
done
.
...
...
@@ -133,8 +133,8 @@ Lemma box_fill E f γ P Q :
f
!!
γ
=
Some
false
→
slice
N
γ
Q
-
∗
▷
Q
-
∗
▷
box
N
f
P
={
E
}=
∗
▷
box
N
(<[
γ
:
=
true
]>
f
)
P
.
Proof
.
iIntros
(??)
"#
Hinv
HQ H"
;
iDestruct
"H"
as
(
Φ
)
"[#HeqP Hf]"
.
iInv
N
as
(
b'
)
"
(>Hγ & #HγQ & _)
"
"Hclose"
.
iIntros
(??)
"#
[HγQ Hinv]
HQ H"
;
iDestruct
"H"
as
(
Φ
)
"[#HeqP Hf]"
.
iInv
N
as
(
b'
)
"
[>Hγ _]
"
"Hclose"
.
iDestruct
(
big_sepM_later
_
f
with
"Hf"
)
as
"Hf"
.
iDestruct
(
big_sepM_delete
_
f
_
false
with
"Hf"
)
as
"[[>Hγ' #[HγΦ Hinv']] ?]"
;
first
done
.
...
...
@@ -152,8 +152,8 @@ Lemma box_empty E f P Q γ :
f
!!
γ
=
Some
true
→
slice
N
γ
Q
-
∗
▷
box
N
f
P
={
E
}=
∗
▷
Q
∗
▷
box
N
(<[
γ
:
=
false
]>
f
)
P
.
Proof
.
iIntros
(??)
"#
Hinv
H"
;
iDestruct
"H"
as
(
Φ
)
"[#HeqP Hf]"
.
iInv
N
as
(
b
)
"
(>Hγ & #HγQ & HQ)
"
"Hclose"
.
iIntros
(??)
"#
[HγQ Hinv]
H"
;
iDestruct
"H"
as
(
Φ
)
"[#HeqP Hf]"
.
iInv
N
as
(
b
)
"
[>Hγ HQ]
"
"Hclose"
.
iDestruct
(
big_sepM_later
_
f
with
"Hf"
)
as
"Hf"
.
iDestruct
(
big_sepM_delete
_
f
with
"Hf"
)
as
"[[>Hγ' #[HγΦ Hinv']] ?]"
;
first
done
.
...
...
@@ -174,7 +174,7 @@ Lemma box_insert_full Q E f P :
Proof
.
iIntros
(?)
"HQ Hbox"
.
iMod
(
box_insert_empty
with
"Hbox"
)
as
(
γ
)
"(% & #Hslice & Hbox)"
.
iExists
γ
.
iFrame
"%#"
.
iMod
(
box_fill
with
"Hslice HQ Hbox"
)
.
done
.
iExists
γ
.
iFrame
"%#"
.
iMod
(
box_fill
with
"Hslice HQ Hbox"
)
;
first
done
.
by
apply
lookup_insert
.
by
rewrite
insert_insert
.
Qed
.
...
...
@@ -217,14 +217,14 @@ Proof.
iAssert
([
∗
map
]
γ↦
b
∈
f
,
▷
Φ
γ
∗
box_own_auth
γ
(
◯
Excl'
false
)
∗
box_own_prop
γ
(
Φ
γ
)
∗
inv
N
(
slice_inv
γ
(
Φ
γ
)))%
I
with
">[Hf]"
as
"[HΦ ?]"
.
{
iApply
(
fupd_big_sepM
_
_
f
)
;
iApply
(
big_sepM_impl
_
_
f
)
;
iFrame
"Hf"
.
iAlways
;
iIntros
(
γ
b
?)
"(Hγ' & #
$ & #$
)"
.
iAlways
;
iIntros
(
γ
b
?)
"(Hγ' & #
HγΦ & #Hinv
)"
.
assert
(
true
=
b
)
as
<-
by
eauto
.
iInv
N
as
(
b
)
"
(>Hγ & _ & HΦ)
"
"Hclose"
.
iInv
N
as
(
b
)
"
[>Hγ HΦ]
"
"Hclose"
.
iDestruct
(
box_own_auth_agree
γ
b
true
with
"[-]"
)
as
%->
;
first
by
iFrame
.
iMod
(
box_own_auth_update
γ
true
true
false
with
"[Hγ Hγ']"
)
as
"[Hγ $]"
;
first
by
iFrame
.
iMod
(
"Hclose"
with
"[Hγ]"
)
;
first
(
iNext
;
iExists
false
;
iFrame
;
eauto
).
by
iApply
"HΦ"
.
}
iFrame
"HγΦ Hinv"
.
by
iApply
"HΦ"
.
}
iModIntro
;
iSplitL
"HΦ"
.
-
rewrite
internal_eq_iff
later_iff
big_sepM_later
.
by
iApply
"HeqP"
.
-
iExists
Φ
;
iSplit
;
by
rewrite
big_sepM_fmap
.
...
...
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