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Jonas Kastberg
iris
Commits
daef264e
Commit
daef264e
authored
Oct 24, 2017
by
Robbert Krebbers
Browse files
Port the core to use the plainness modality and prove it is non-expansive.
parent
25076b74
Changes
1
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Inline
Side-by-side
theories/base_logic/lib/core.v
View file @
daef264e
...
...
@@ -3,19 +3,9 @@ From iris.proofmode Require Import tactics.
Set
Default
Proof
Using
"Type"
.
Import
uPred
.
(** The "core" of an assertion is its maximal persistent part.
It can be defined entirely within the logic... at least
in the shallow embedding.
WARNING: The function "coreP" is NOT NON-EXPANSIVE.
This is because the turnstile is not non-expansive as a function
from iProp to (discreteC Prop).
To obtain a core that's non-expansive, we would have to add another
modality to the logic: a box that removes access to *all* resources,
not just restricts access to the core.
*)
(** The "core" of an assertion is its maximal persistent part. *)
Definition
coreP
{
M
:
ucmraT
}
(
P
:
uPred
M
)
:
uPred
M
:
=
(
∀
`
(!
Persistent
Q
),
⌜
P
⊢
Q
⌝
→
Q
)%
I
.
(
∀
`
(!
Persistent
Q
),
■
(
P
→
Q
)
→
Q
)%
I
.
Instance
:
Params
(@
coreP
)
1
.
Typeclasses
Opaque
coreP
.
...
...
@@ -24,25 +14,26 @@ Section core.
Implicit
Types
P
Q
:
uPred
M
.
Lemma
coreP_intro
P
:
P
-
∗
coreP
P
.
Proof
.
rewrite
/
coreP
.
iIntros
"HP"
.
by
iIntros
(
Q
HQ
->)
.
Qed
.
Proof
.
rewrite
/
coreP
.
iIntros
"HP"
.
iIntros
(
Q
HQ
)
"HPQ"
.
by
iApply
"HPQ"
.
Qed
.
Global
Instance
coreP_persistent
P
:
Persistent
(
coreP
P
).
Proof
.
rewrite
/
coreP
.
apply
_
.
Qed
.
Global
Instance
coreP_ne
:
NonExpansive
(@
coreP
M
).
Proof
.
solve_proper
.
Qed
.
Global
Instance
coreP_proper
:
Proper
((
⊣
⊢
)
==>
(
⊣
⊢
))
(@
coreP
M
).
Proof
.
solve_proper
.
Qed
.
Global
Instance
coreP_mono
:
Proper
((
⊢
)
==>
(
⊢
))
(@
coreP
M
).
Proof
.
rewrite
/
coreP
.
iIntros
(
P
P'
?
)
"H"
;
iIntros
(
Q
?
?
).
iApply
(
"H"
$!
Q
with
"[
%
]"
).
by
etrans
.
rewrite
/
coreP
.
iIntros
(
P
P'
HP
)
"H"
;
iIntros
(
Q
?)
"#HPQ"
.
iApply
(
"H"
$!
Q
with
"[]"
).
by
rewrite
HP
.
Qed
.
Global
Instance
coreP_proper
:
Proper
((
⊣
⊢
)
==>
(
⊣
⊢
))
(@
coreP
M
).
Proof
.
intros
P
Q
.
rewrite
!
equiv_spec
=>-[??].
by
split
;
apply
coreP_mono
.
Qed
.
Lemma
coreP_elim
P
:
Persistent
P
→
coreP
P
-
∗
P
.
Proof
.
rewrite
/
coreP
.
iIntros
(?)
"HCP"
.
unshelve
iApply
(
"HCP"
$!
P
)
;
auto
.
Qed
.
Proof
.
rewrite
/
coreP
.
iIntros
(?)
"HCP"
.
iApply
(
"HCP"
$!
P
)
;
auto
.
Qed
.
Lemma
coreP_wand
P
Q
:
(
coreP
P
⊢
Q
)
↔
(
P
⊢
□
Q
).
Lemma
coreP_wand
P
Q
:
(
coreP
P
⊢
Q
)
↔
(
P
⊢
□
Q
).
Proof
.
split
.
-
iIntros
(
HP
)
"HP"
.
iDestruct
(
coreP_intro
with
"HP"
)
as
"#HcP"
.
...
...
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