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Iris
Fairis
Commits
a121e077
Commit
a121e077
authored
Dec 21, 2015
by
Robbert Krebbers
Browse files
Contractive and nonexpansiveness properties of later.
parent
457cf079
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modures/cofe.v
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a121e077
...
...
@@ 278,8 +278,10 @@ Canonical Structure boolC := leibnizC bool.
(
**
Later
*
)
Inductive
later
(
A
:
Type
)
:
Type
:=
Later
{
later_car
:
A
}
.
Add
Printing
Constructor
later
.
Arguments
Later
{
_
}
_.
Arguments
later_car
{
_
}
_.
Section
later
.
Instance
later_equiv
`
{
Equiv
A
}
:
Equiv
(
later
A
)
:=
λ
x
y
,
later_car
x
≡
later_car
y
.
...
...
@@ 305,12 +307,14 @@ Section later.
Qed
.
Canonical
Structure
laterC
(
A
:
cofeT
)
:
cofeT
:=
CofeT
(
later
A
).
Global
Instance
Later_contractive
`
{
Dist
A
}
:
Contractive
(
@
Later
A
).
Proof
.
by
intros
n
??
.
Qed
.
Definition
later_map
{
A
B
}
(
f
:
A
→
B
)
(
x
:
later
A
)
:
later
B
:=
Later
(
f
(
later_car
x
)).
Instance
later_
f
map_ne
`
{
Cofe
A
,
Cofe
B
}
(
f
:
A
→
B
)
:
(
∀
n
,
Proper
(
dist
n
==>
dist
n
)
f
)
→
∀
n
,
Proper
(
dist
n
==>
dist
n
)
(
later_map
f
).
Proof
.
intros
Hf
[

n
]
[
x
]
[
y
]
?
;
do
2
red
;
simpl
.
done
.
by
apply
Hf
.
Qed
.
Global
Instance
later_map_ne
`
{
Cofe
A
,
Cofe
B
}
(
f
:
A
→
B
)
n
:
Proper
(
dist
(
pred
n
)
==>
dist
(
pred
n
)
)
f
→
Proper
(
dist
n
==>
dist
n
)
(
later_map
f
)

0
.
Proof
.
destruct
n
as
[

n
];
intros
Hf
[
x
]
[
y
]
?
;
do
2
red
;
simpl
;
auto
.
Qed
.
Lemma
later_fmap_id
{
A
}
(
x
:
later
A
)
:
later_map
id
x
=
x
.
Proof
.
by
destruct
x
.
Qed
.
Lemma
later_fmap_compose
{
A
B
C
}
(
f
:
A
→
B
)
(
g
:
B
→
C
)
(
x
:
later
A
)
:
...
...
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