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Rice Wine
Iris
Commits
6d0aa4f2
Commit
6d0aa4f2
authored
Feb 09, 2017
by
Robbert Krebbers
Browse files
Easier way to construct OFEs that are isomorphic to an existing OFE.
parent
8b9f59ab
Changes
3
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Inline
Side-by-side
theories/algebra/auth.v
View file @
6d0aa4f2
...
...
@@ -37,25 +37,13 @@ Global Instance own_proper : Proper ((≡) ==> (≡)) (@auth_own A).
Proof
.
by
destruct
1
.
Qed
.
Definition
auth_ofe_mixin
:
OfeMixin
(
auth
A
).
Proof
.
split
.
-
intros
x
y
;
unfold
dist
,
auth_dist
,
equiv
,
auth_equiv
.
rewrite
!
equiv_dist
;
naive_solver
.
-
intros
n
;
split
.
+
by
intros
?
;
split
.
+
by
intros
??
[??]
;
split
;
symmetry
.
+
intros
???
[??]
[??]
;
split
;
etrans
;
eauto
.
-
by
intros
?
[??]
[??]
[??]
;
split
;
apply
dist_S
.
Qed
.
Proof
.
by
apply
(
iso_ofe_mixin
(
λ
x
,
(
authoritative
x
,
auth_own
x
))).
Qed
.
Canonical
Structure
authC
:
=
OfeT
(
auth
A
)
auth_ofe_mixin
.
Definition
auth_compl
`
{
Cofe
A
}
:
Compl
authC
:
=
λ
c
,
Auth
(
compl
(
chain_map
authoritative
c
))
(
compl
(
chain_map
auth_own
c
)).
Global
Program
Instance
auth_cofe
`
{
Cofe
A
}
:
Cofe
authC
:
=
{|
compl
:
=
auth_compl
|}.
Next
Obligation
.
intros
?
n
c
;
split
.
apply
(
conv_compl
n
(
chain_map
authoritative
c
)).
apply
(
conv_compl
n
(
chain_map
auth_own
c
)).
Global
Instance
auth_cofe
`
{
Cofe
A
}
:
Cofe
authC
.
Proof
.
apply
(
iso_cofe
(
λ
y
:
_
*
_
,
Auth
(
y
.
1
)
(
y
.
2
))
(
λ
x
,
(
authoritative
x
,
auth_own
x
)))
;
by
repeat
intro
.
Qed
.
Global
Instance
Auth_timeless
a
b
:
...
...
theories/algebra/excl.v
View file @
6d0aa4f2
...
...
@@ -46,29 +46,16 @@ Proof. by inversion_clear 1. Qed.
Definition
excl_ofe_mixin
:
OfeMixin
(
excl
A
).
Proof
.
split
.
-
intros
x
y
;
split
;
[
by
destruct
1
;
constructor
;
apply
equiv_dist
|].
intros
Hxy
;
feed
inversion
(
Hxy
1
)
;
subst
;
constructor
;
apply
equiv_dist
.
by
intros
n
;
feed
inversion
(
Hxy
n
).
-
intros
n
;
split
.
+
by
intros
[]
;
constructor
.
+
by
destruct
1
;
constructor
.
+
destruct
1
;
inversion_clear
1
;
constructor
;
etrans
;
eauto
.
-
by
inversion_clear
1
;
constructor
;
apply
dist_S
.
apply
(
iso_ofe_mixin
(
maybe
Excl
)).
-
by
intros
[
a
|]
[
b
|]
;
split
;
inversion_clear
1
;
constructor
.
-
by
intros
n
[
a
|]
[
b
|]
;
split
;
inversion_clear
1
;
constructor
.
Qed
.
Canonical
Structure
exclC
:
ofeT
:
=
OfeT
(
excl
A
)
excl_ofe_mixin
.
Program
Definition
excl_chain
(
c
:
chain
exclC
)
(
a
:
A
)
:
chain
A
:
=
{|
chain_car
n
:
=
match
c
n
return
_
with
Excl
y
=>
y
|
_
=>
a
end
|}.
Next
Obligation
.
intros
c
a
n
i
?
;
simpl
.
by
destruct
(
chain_cauchy
c
n
i
).
Qed
.
Definition
excl_compl
`
{
Cofe
A
}
:
Compl
exclC
:
=
λ
c
,
match
c
0
with
Excl
a
=>
Excl
(
compl
(
excl_chain
c
a
))
|
x
=>
x
end
.
Global
Program
Instance
excl_cofe
`
{
Cofe
A
}
:
Cofe
exclC
:
=
{|
compl
:
=
excl_compl
|}.
Next
Obligation
.
intros
?
n
c
;
rewrite
/
compl
/
excl_compl
.
feed
inversion
(
chain_cauchy
c
0
n
)
;
auto
with
omega
.
rewrite
(
conv_compl
n
(
excl_chain
c
_
))
/=.
destruct
(
c
n
)
;
naive_solver
.
Global
Instance
excl_cofe
`
{
Cofe
A
}
:
Cofe
exclC
.
Proof
.
apply
(
iso_cofe
(
from_option
Excl
ExclBot
)
(
maybe
Excl
))
;
[
by
destruct
1
;
constructor
..|
by
intros
[]
;
constructor
].
Qed
.
Global
Instance
excl_discrete
:
Discrete
A
→
Discrete
exclC
.
...
...
theories/algebra/ofe.v
View file @
6d0aa4f2
...
...
@@ -553,6 +553,26 @@ Section unit.
Proof
.
done
.
Qed
.
End
unit
.
Lemma
iso_ofe_mixin
{
A
:
ofeT
}
`
{
Equiv
B
,
Dist
B
}
(
g
:
B
→
A
)
(
g_equiv
:
∀
y1
y2
,
y1
≡
y2
↔
g
y1
≡
g
y2
)
(
g_dist
:
∀
n
y1
y2
,
y1
≡
{
n
}
≡
y2
↔
g
y1
≡
{
n
}
≡
g
y2
)
:
OfeMixin
B
.
Proof
.
split
.
-
intros
y1
y2
.
rewrite
g_equiv
.
setoid_rewrite
g_dist
.
apply
equiv_dist
.
-
split
.
+
intros
y
.
by
apply
g_dist
.
+
intros
y1
y2
.
by
rewrite
!
g_dist
.
+
intros
y1
y2
y3
.
rewrite
!
g_dist
.
intros
??
;
etrans
;
eauto
.
-
intros
n
y1
y2
.
rewrite
!
g_dist
.
apply
dist_S
.
Qed
.
Program
Definition
iso_cofe
{
A
B
:
ofeT
}
`
{
Cofe
A
}
(
f
:
A
→
B
)
(
g
:
B
→
A
)
`
(!
NonExpansive
g
,
!
NonExpansive
f
)
(
fg
:
∀
y
,
f
(
g
y
)
≡
y
)
:
Cofe
B
:
=
{|
compl
c
:
=
f
(
compl
(
chain_map
g
c
))
|}.
Next
Obligation
.
intros
A
B
?
f
g
??
fg
n
c
.
by
rewrite
/=
conv_compl
/=
fg
.
Qed
.
(** Product *)
Section
product
.
Context
{
A
B
:
ofeT
}.
...
...
@@ -1084,14 +1104,7 @@ Section sigma.
Global
Instance
proj1_sig_ne
:
NonExpansive
(@
proj1_sig
_
P
).
Proof
.
by
intros
n
[
a
Ha
]
[
b
Hb
]
?.
Qed
.
Definition
sig_ofe_mixin
:
OfeMixin
(
sig
P
).
Proof
.
split
.
-
intros
[
a
?]
[
b
?].
rewrite
/
dist
/
sig_dist
/
equiv
/
sig_equiv
/=.
apply
equiv_dist
.
-
intros
n
.
rewrite
/
dist
/
sig_dist
.
split
;
[
intros
[]|
intros
[]
[]|
intros
[]
[]
[]]=>
//=
->
//.
-
intros
n
[
a
?]
[
b
?].
rewrite
/
dist
/
sig_dist
/=.
apply
dist_S
.
Qed
.
Proof
.
by
apply
(
iso_ofe_mixin
proj1_sig
).
Qed
.
Canonical
Structure
sigC
:
ofeT
:
=
OfeT
(
sig
P
)
sig_ofe_mixin
.
(* FIXME: WTF, it seems that within these braces {...} the ofe argument of LimitPreserving
...
...
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