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Iris
Iris
Commits
4468acd9
Commit
4468acd9
authored
Dec 15, 2015
by
Robbert Krebbers
Browse files
Misc changes to cofes.
parent
53fa71ca
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iris/cofe.v
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4468acd9
...
...
@@ 64,8 +64,8 @@ Section cofe.
Global
Instance
dist_ne
n
:
Proper
(
dist
n
==>
dist
n
==>
iff
)
(
dist
n
).
Proof
.
intros
x1
x2
?
y1
y2
?
;
split
;
intros
.
*
by
transitivity
x1
;
[
done
]
;
transitivity
y1
.
*
by
transitivity
x2
;
[
done
]
;
transitivity
y2
.
*
by
transitivity
x1
;
[

transitivity
y1
]
.
*
by
transitivity
x2
;
[

transitivity
y2
]
.
Qed
.
Global
Instance
dist_proper
n
:
Proper
((
≡
)
==>
(
≡
)
==>
iff
)
(
dist
n
).
Proof
.
...
...
@@ 84,7 +84,7 @@ Section cofe.
Proper
((
≡
)
==>
(
≡
)
==>
(
≡
))
f

100
.
Proof
.
unfold
Proper
,
respectful
;
setoid_rewrite
equiv_dist
.
by
intros
x1
x2
Hx
y1
y2
Hy
n
;
rewrite
Hx
,
Hy
.
by
intros
x1
x2
Hx
y1
y2
Hy
n
;
rewrite
(
Hx
n
)
,
(
Hy
n
)
.
Qed
.
Lemma
compl_ne
(
c1
c2
:
chain
A
)
n
:
c1
n
={
n
}=
c2
n
→
compl
c1
={
n
}=
compl
c2
.
Proof
.
intros
.
by
rewrite
(
conv_compl
c1
n
),
(
conv_compl
c2
n
).
Qed
.
...
...
@@ 140,7 +140,7 @@ End fixpoint.
Global
Opaque
fixpoint
.
(** Function space *)
Structure
cofeMor
(
A
B
:
cofeT
)
:
Type
:
=
CofeMor
{
Record
cofeMor
(
A
B
:
cofeT
)
:
Type
:
=
CofeMor
{
cofe_mor_car
:
>
A
→
B
;
cofe_mor_ne
n
:
Proper
(
dist
n
==>
dist
n
)
cofe_mor_car
}.
...
...
@@ 305,18 +305,19 @@ Section later.
Qed
.
Canonical
Structure
laterC
(
A
:
cofeT
)
:
cofeT
:
=
CofeT
(
later
A
).
Instance
later_fmap
:
FMap
later
:
=
λ
A
B
f
x
,
Later
(
f
(
later_car
x
)).
Definition
later_map
{
A
B
}
(
f
:
A
→
B
)
(
x
:
later
A
)
:
later
B
:
=
Later
(
f
(
later_car
x
)).
Instance
later_fmap_ne
`
{
Cofe
A
,
Cofe
B
}
(
f
:
A
→
B
)
:
(
∀
n
,
Proper
(
dist
n
==>
dist
n
)
f
)
→
∀
n
,
Proper
(
dist
n
==>
dist
n
)
(
fmap
f
:
later
A
→
later
B
).
∀
n
,
Proper
(
dist
n
==>
dist
n
)
(
later_map
f
).
Proof
.
intros
Hf
[
n
]
[
x
]
[
y
]
?
;
do
2
red
;
simpl
.
done
.
by
apply
Hf
.
Qed
.
Lemma
later_fmap_id
{
A
}
(
x
:
later
A
)
:
id
<$>
x
=
x
.
Lemma
later_fmap_id
{
A
}
(
x
:
later
A
)
:
later_map
id
x
=
x
.
Proof
.
by
destruct
x
.
Qed
.
Lemma
later_fmap_compose
{
A
B
C
}
(
f
:
A
→
B
)
(
g
:
B
→
C
)
(
x
:
later
A
)
:
g
∘
f
<$>
x
=
g
<$>
f
<$>
x
.
later_map
(
g
∘
f
)
x
=
later_map
g
(
later_map
f
x
)
.
Proof
.
by
destruct
x
.
Qed
.
Definition
laterC_map
{
A
B
}
(
f
:
A

n
>
B
)
:
laterC
A

n
>
laterC
B
:
=
CofeMor
(
fmap
f
:
laterC
A
→
laterC
B
).
CofeMor
(
later_map
f
).
Instance
laterC_map_contractive
(
A
B
:
cofeT
)
:
Contractive
(@
laterC_map
A
B
).
Proof
.
intros
n
f
g
Hf
n'
;
apply
Hf
.
Qed
.
End
later
.
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