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Rice Wine
Iris
Commits
5241c33d
Commit
5241c33d
authored
Dec 28, 2016
by
Robbert Krebbers
Browse files
Apply default instance for later stripping not deep in terms.
This fixes issue
#55
.
parent
8c844e32
Changes
1
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Inline
Side-by-side
theories/proofmode/class_instances.v
View file @
5241c33d
...
...
@@ -72,53 +72,109 @@ Global Instance into_persistentP_persistent P :
Proof
.
done
.
Qed
.
(* IntoLater *)
(* The class [IntoLaterN] has only two instances:
- The default instance [IntoLaterN n P P], i.e. [▷^n P -∗ P]
- The instance [ProgIntoLaterN n P Q → IntoLaterN n P Q], where [ProgIntoLaterN]
is identical to [IntoLaterN], but computationally is supposed to make
progress, i.e. its instances should actually strip a later.
The point of using the auxilary class [ProgIntoLaterN] is to ensure that the
default instance is not applied deeply in the term, which may cause in too many
definitions being unfolded (see issue #55).
For binary connectives we have the following instances:
<<
ProgIntoLaterN n P P' IntoLaterN n Q Q'
---------------------------------------------
ProgIntoLaterN n (P /\ Q) (P' /\ Q')
ProgIntoLaterN n Q Q'
--------------------------------
IntoLaterN n (P /\ Q) (P /\ Q')
>>
That is, to make progress, a later _should_ be stripped on either the left- or
right-hand side of the binary connective. *)
Class
ProgIntoLaterN
(
n
:
nat
)
(
P
Q
:
uPred
M
)
:
=
prog_into_laterN
:
P
⊢
▷
^
n
Q
.
Global
Arguments
prog_into_laterN
_
_
_
{
_
}.
Global
Instance
into_laterN_default
n
P
:
IntoLaterN
n
P
P
|
1000
.
Proof
.
apply
laterN_intro
.
Qed
.
Global
Instance
into_laterN_progress
P
Q
:
ProgIntoLaterN
n
P
Q
→
IntoLaterN
n
P
Q
.
Proof
.
done
.
Qed
.
Global
Instance
into_laterN_later
n
P
Q
:
IntoLaterN
n
P
Q
→
IntoLaterN
(
S
n
)
(
▷
P
)
Q
.
Proof
.
by
rewrite
/
IntoLaterN
=>->.
Qed
.
Global
Instance
into_laterN_laterN
n
P
:
IntoLaterN
n
(
▷
^
n
P
)
P
.
IntoLaterN
n
P
Q
→
Prog
IntoLaterN
(
S
n
)
(
▷
P
)
Q
.
Proof
.
by
rewrite
/
IntoLaterN
/
ProgIntoLaterN
=>->.
Qed
.
Global
Instance
into_laterN_laterN
n
P
:
Prog
IntoLaterN
n
(
▷
^
n
P
)
P
.
Proof
.
done
.
Qed
.
Global
Instance
into_laterN_laterN_plus
n
m
P
Q
:
IntoLaterN
m
P
Q
→
IntoLaterN
(
n
+
m
)
(
▷
^
n
P
)
Q
.
Proof
.
rewrite
/
IntoLaterN
=>->.
by
rewrite
laterN_plus
.
Qed
.
IntoLaterN
m
P
Q
→
ProgIntoLaterN
(
n
+
m
)
(
▷
^
n
P
)
Q
.
Proof
.
rewrite
/
IntoLaterN
/
ProgIntoLaterN
=>->.
by
rewrite
laterN_plus
.
Qed
.
Global
Instance
into_laterN_and_l
n
P1
P2
Q1
Q2
:
ProgIntoLaterN
n
P1
Q1
→
IntoLaterN
n
P2
Q2
→
IntoLaterN
n
(
P1
∧
P2
)
(
Q1
∧
Q2
).
Proof
.
rewrite
/
ProgIntoLaterN
/
IntoLaterN
=>
->
->.
by
rewrite
laterN_and
.
Qed
.
Global
Instance
into_laterN_and_r
n
P
P2
Q2
:
ProgIntoLaterN
n
P2
Q2
→
ProgIntoLaterN
n
(
P
∧
P2
)
(
P
∧
Q2
).
Proof
.
rewrite
/
ProgIntoLaterN
=>
->.
by
rewrite
laterN_and
-(
laterN_intro
_
P
).
Qed
.
Global
Instance
into_laterN_and
n
P1
P2
Q1
Q2
:
IntoLaterN
n
P1
Q1
→
IntoLaterN
n
P2
Q2
→
IntoLaterN
n
(
P1
∧
P2
)
(
Q1
∧
Q2
).
Proof
.
intros
??
;
red
.
by
rewrite
laterN_and
;
apply
and_mono
.
Qed
.
Global
Instance
into_laterN_or
n
P1
P2
Q1
Q2
:
IntoLaterN
n
P1
Q1
→
IntoLaterN
n
P2
Q2
→
IntoLaterN
n
(
P1
∨
P2
)
(
Q1
∨
Q2
).
Proof
.
intros
??
;
red
.
by
rewrite
laterN_or
;
apply
or_mono
.
Qed
.
Global
Instance
into_laterN_sep
n
P1
P2
Q1
Q2
:
IntoLaterN
n
P1
Q1
→
IntoLaterN
n
P2
Q2
→
IntoLaterN
n
(
P1
∗
P2
)
(
Q1
∗
Q2
).
Global
Instance
into_laterN_or_l
n
P1
P2
Q1
Q2
:
ProgIntoLaterN
n
P1
Q1
→
IntoLaterN
n
P2
Q2
→
IntoLaterN
n
(
P1
∨
P2
)
(
Q1
∨
Q2
).
Proof
.
rewrite
/
ProgIntoLaterN
/
IntoLaterN
=>
->
->.
by
rewrite
laterN_or
.
Qed
.
Global
Instance
into_laterN_or_r
n
P
P2
Q2
:
ProgIntoLaterN
n
P2
Q2
→
ProgIntoLaterN
n
(
P
∨
P2
)
(
P
∨
Q2
).
Proof
.
rewrite
/
ProgIntoLaterN
=>
->.
by
rewrite
laterN_or
-(
laterN_intro
_
P
).
Qed
.
Global
Instance
into_laterN_sep_l
n
P1
P2
Q1
Q2
:
ProgIntoLaterN
n
P1
Q1
→
IntoLaterN
n
P2
Q2
→
IntoLaterN
n
(
P1
∗
P2
)
(
Q1
∗
Q2
).
Proof
.
intros
??
;
red
.
by
rewrite
laterN_sep
;
apply
sep_mono
.
Qed
.
Global
Instance
into_laterN_sep_r
n
P
P2
Q2
:
ProgIntoLaterN
n
P2
Q2
→
ProgIntoLaterN
n
(
P
∗
P2
)
(
P
∗
Q2
).
Proof
.
rewrite
/
ProgIntoLaterN
=>
->.
by
rewrite
laterN_sep
-(
laterN_intro
_
P
).
Qed
.
Global
Instance
into_laterN_big_sepL
n
{
A
}
(
Φ
Ψ
:
nat
→
A
→
uPred
M
)
(
l
:
list
A
)
:
(
∀
x
k
,
IntoLaterN
n
(
Φ
k
x
)
(
Ψ
k
x
))
→
IntoLaterN
n
([
∗
list
]
k
↦
x
∈
l
,
Φ
k
x
)
([
∗
list
]
k
↦
x
∈
l
,
Ψ
k
x
).
(
∀
x
k
,
Prog
IntoLaterN
n
(
Φ
k
x
)
(
Ψ
k
x
))
→
Prog
IntoLaterN
n
([
∗
list
]
k
↦
x
∈
l
,
Φ
k
x
)
([
∗
list
]
k
↦
x
∈
l
,
Ψ
k
x
).
Proof
.
rewrite
/
IntoLaterN
=>
?.
rewrite
big_sepL_laterN
.
by
apply
big_sepL_mono
.
rewrite
/
Prog
IntoLaterN
=>
?.
rewrite
big_sepL_laterN
.
by
apply
big_sepL_mono
.
Qed
.
Global
Instance
into_laterN_big_sepM
n
`
{
Countable
K
}
{
A
}
(
Φ
Ψ
:
K
→
A
→
uPred
M
)
(
m
:
gmap
K
A
)
:
(
∀
x
k
,
IntoLaterN
n
(
Φ
k
x
)
(
Ψ
k
x
))
→
IntoLaterN
n
([
∗
map
]
k
↦
x
∈
m
,
Φ
k
x
)
([
∗
map
]
k
↦
x
∈
m
,
Ψ
k
x
).
(
∀
x
k
,
Prog
IntoLaterN
n
(
Φ
k
x
)
(
Ψ
k
x
))
→
Prog
IntoLaterN
n
([
∗
map
]
k
↦
x
∈
m
,
Φ
k
x
)
([
∗
map
]
k
↦
x
∈
m
,
Ψ
k
x
).
Proof
.
rewrite
/
IntoLaterN
=>
?.
rewrite
big_sepM_laterN
;
by
apply
big_sepM_mono
.
rewrite
/
Prog
IntoLaterN
=>
?.
rewrite
big_sepM_laterN
;
by
apply
big_sepM_mono
.
Qed
.
Global
Instance
into_laterN_big_sepS
n
`
{
Countable
A
}
(
Φ
Ψ
:
A
→
uPred
M
)
(
X
:
gset
A
)
:
(
∀
x
,
IntoLaterN
n
(
Φ
x
)
(
Ψ
x
))
→
IntoLaterN
n
([
∗
set
]
x
∈
X
,
Φ
x
)
([
∗
set
]
x
∈
X
,
Ψ
x
).
(
∀
x
,
Prog
IntoLaterN
n
(
Φ
x
)
(
Ψ
x
))
→
Prog
IntoLaterN
n
([
∗
set
]
x
∈
X
,
Φ
x
)
([
∗
set
]
x
∈
X
,
Ψ
x
).
Proof
.
rewrite
/
IntoLaterN
=>
?.
rewrite
big_sepS_laterN
;
by
apply
big_sepS_mono
.
rewrite
/
Prog
IntoLaterN
=>
?.
rewrite
big_sepS_laterN
;
by
apply
big_sepS_mono
.
Qed
.
Global
Instance
into_laterN_big_sepMS
n
`
{
Countable
A
}
(
Φ
Ψ
:
A
→
uPred
M
)
(
X
:
gmultiset
A
)
:
(
∀
x
,
IntoLaterN
n
(
Φ
x
)
(
Ψ
x
))
→
IntoLaterN
n
([
∗
mset
]
x
∈
X
,
Φ
x
)
([
∗
mset
]
x
∈
X
,
Ψ
x
).
(
∀
x
,
Prog
IntoLaterN
n
(
Φ
x
)
(
Ψ
x
))
→
Prog
IntoLaterN
n
([
∗
mset
]
x
∈
X
,
Φ
x
)
([
∗
mset
]
x
∈
X
,
Ψ
x
).
Proof
.
rewrite
/
IntoLaterN
=>
?.
rewrite
big_sepMS_laterN
;
by
apply
big_sepMS_mono
.
rewrite
/
Prog
IntoLaterN
=>
?.
rewrite
big_sepMS_laterN
;
by
apply
big_sepMS_mono
.
Qed
.
(* FromLater *)
...
...
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