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Tej Chajed
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 nonexpansive.
parent
25076b74
Changes
1
Show whitespace changes
Inline
Sidebyside
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 NONEXPANSIVE.
This is because the turnstile is not nonexpansive as a function
from iProp to (discreteC Prop).
To obtain a core that's nonexpansive, 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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