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Simon Spies
Iris
Commits
5a291902
Commit
5a291902
authored
Jun 12, 2017
by
Robbert Krebbers
Browse files
Show that the fancy update can be encoded in terms of the view shift.
parent
6b68b171
Changes
2
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5a291902
...
...
@@ -51,6 +51,7 @@ theories/base_logic/lib/counter_examples.v
theories/base_logic/lib/fractional.v
theories/base_logic/lib/gen_heap.v
theories/base_logic/lib/core.v
theories/base_logic/lib/fancy_updates_from_vs.v
theories/program_logic/adequacy.v
theories/program_logic/lifting.v
theories/program_logic/weakestpre.v
...
...
theories/base_logic/lib/fancy_updates_from_vs.v
0 → 100644
View file @
5a291902
(* This file shows that the fancy update can be encoded in terms of the
view shift, and that the laws of the fancy update can be derived from the
laws of the view shift. *)
From
iris
.
proofmode
Require
Import
tactics
.
From
stdpp
Require
Export
coPset
.
Set
Default
Proof
Using
"Type*"
.
Section
fupd
.
Context
{
M
}
(
vs
:
coPset
→
coPset
→
uPred
M
→
uPred
M
→
uPred
M
).
Notation
"P ={ E1 , E2 }=> Q"
:
=
(
vs
E1
E2
P
Q
)
(
at
level
99
,
E1
,
E2
at
level
50
,
Q
at
level
200
,
format
"P ={ E1 , E2 }=> Q"
)
:
uPred_scope
.
Context
(
vs_ne
:
∀
E1
E2
,
NonExpansive2
(
vs
E1
E2
)).
Context
(
vs_persistent
:
∀
E1
E2
P
Q
,
PersistentP
(
P
={
E1
,
E2
}=>
Q
)).
Context
(
vs_impl
:
∀
E
P
Q
,
□
(
P
→
Q
)
⊢
P
={
E
,
E
}=>
Q
).
Context
(
vs_transitive
:
∀
E1
E2
E3
P
Q
R
,
(
P
={
E1
,
E2
}=>
Q
)
∧
(
Q
={
E2
,
E3
}=>
R
)
⊢
P
={
E1
,
E3
}=>
R
).
Context
(
vs_mask_frame_r
:
∀
E1
E2
Ef
P
Q
,
E1
⊥
Ef
→
(
P
={
E1
,
E2
}=>
Q
)
⊢
P
={
E1
∪
Ef
,
E2
∪
Ef
}=>
Q
).
Context
(
vs_frame_r
:
∀
E1
E2
P
Q
R
,
(
P
={
E1
,
E2
}=>
Q
)
⊢
P
∗
R
={
E1
,
E2
}=>
Q
∗
R
).
Context
(
vs_exists
:
∀
{
A
}
E1
E2
(
Φ
:
A
→
uPred
M
)
Q
,
(
∀
x
,
Φ
x
={
E1
,
E2
}=>
Q
)
⊢
(
∃
x
,
Φ
x
)
={
E1
,
E2
}=>
Q
).
Context
(
vs_persistent_intro_r
:
∀
E1
E2
P
Q
R
,
PersistentP
R
→
(
R
-
∗
(
P
={
E1
,
E2
}=>
Q
))
⊢
P
∗
R
={
E1
,
E2
}=>
Q
).
Definition
fupd
(
E1
E2
:
coPset
)
(
P
:
uPred
M
)
:
uPred
M
:
=
(
∃
R
,
R
∗
vs
E1
E2
R
P
)%
I
.
Notation
"|={ E1 , E2 }=> Q"
:
=
(
fupd
E1
E2
Q
)
(
at
level
99
,
E1
,
E2
at
level
50
,
Q
at
level
200
,
format
"|={ E1 , E2 }=> Q"
)
:
uPred_scope
.
Global
Instance
fupd_ne
E1
E2
:
NonExpansive
(@
fupd
E1
E2
).
Proof
.
solve_proper
.
Qed
.
Lemma
fupd_intro
E
P
:
P
⊢
|={
E
,
E
}=>
P
.
Proof
.
iIntros
"HP"
.
iExists
P
.
iFrame
"HP"
.
iApply
vs_impl
;
auto
.
Qed
.
Lemma
fupd_mono
E1
E2
P
Q
:
(
P
⊢
Q
)
→
(|={
E1
,
E2
}=>
P
)
⊢
|={
E1
,
E2
}=>
Q
.
Proof
.
iIntros
(
HPQ
)
;
iDestruct
1
as
(
R
)
"[HR Hvs]"
.
iExists
R
;
iFrame
"HR"
.
iApply
(
vs_transitive
with
"[$Hvs]"
).
iApply
vs_impl
.
iIntros
"!# HP"
.
by
iApply
HPQ
.
Qed
.
Lemma
fupd_trans
E1
E2
E3
P
:
(|={
E1
,
E2
}=>
|={
E2
,
E3
}=>
P
)
⊢
|={
E1
,
E3
}=>
P
.
Proof
.
iDestruct
1
as
(
R
)
"[HR Hvs]"
.
iExists
R
.
iFrame
"HR"
.
iApply
(
vs_transitive
with
"[$Hvs]"
).
clear
R
.
iApply
vs_exists
;
iIntros
(
R
).
iApply
vs_persistent_intro_r
;
iIntros
"Hvs"
.
iApply
(
vs_transitive
with
"[$Hvs]"
).
iApply
vs_impl
;
auto
.
Qed
.
Lemma
fupd_mask_frame_r
E1
E2
Ef
P
:
E1
⊥
Ef
→
(|={
E1
,
E2
}=>
P
)
⊢
|={
E1
∪
Ef
,
E2
∪
Ef
}=>
P
.
Proof
.
iIntros
(
HE
)
;
iDestruct
1
as
(
R
)
"[HR Hvs]"
.
iExists
R
;
iFrame
"HR"
.
by
iApply
vs_mask_frame_r
.
Qed
.
Lemma
fupd_frame_r
E1
E2
P
Q
:
(|={
E1
,
E2
}=>
P
)
∗
Q
⊢
|={
E1
,
E2
}=>
P
∗
Q
.
Proof
.
iIntros
"[Hvs HQ]"
.
iDestruct
"Hvs"
as
(
R
)
"[HR Hvs]"
.
iExists
(
R
∗
Q
)%
I
.
iFrame
"HR HQ"
.
by
iApply
vs_frame_r
.
Qed
.
End
fupd
.
\ No newline at end of file
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