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998df552
Commit
998df552
authored
Feb 23, 2016
by
Ralf Jung
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implement dec_agree (no lemmas about it yet)
parent
d3700ebd
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#92
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998df552
...
...
@@ -47,6 +47,7 @@ algebra/base.v
algebra/dra.v
algebra/cofe_solver.v
algebra/agree.v
algebra/dec_agree.v
algebra/excl.v
algebra/iprod.v
algebra/functor.v
...
...
algebra/dec_agree.v
0 → 100644
View file @
998df552
From
algebra
Require
Export
cmra
.
From
algebra
Require
Import
functor
upred
.
Local
Arguments
validN
_
_
_
!
_
/.
Local
Arguments
valid
_
_
!
_
/.
Local
Arguments
op
_
_
_
!
_
/.
Local
Arguments
unit
_
_
!
_
/.
(* This is isomorphic to optiob, but has a very different RA structure. *)
Inductive
dec_agree
(
A
:
Type
)
:
Type
:
=
|
DecAgree
:
A
→
dec_agree
A
|
DecAgreeBot
:
dec_agree
A
.
Arguments
DecAgree
{
_
}
_
.
Arguments
DecAgreeBot
{
_
}.
Section
dec_agree
.
Context
{
A
:
Type
}
`
{
∀
x
y
:
A
,
Decision
(
x
=
y
)}.
Instance
dec_agree_valid
:
Valid
(
dec_agree
A
)
:
=
λ
x
,
if
x
is
DecAgree
_
then
True
else
False
.
Instance
dec_agree_equiv
:
Equiv
(
dec_agree
A
)
:
=
equivL
.
Canonical
Structure
dec_agreeC
:
cofeT
:
=
leibnizC
(
dec_agree
A
).
Instance
dec_agree_op
:
Op
(
dec_agree
A
)
:
=
λ
x
y
,
match
x
,
y
with
|
DecAgree
a
,
DecAgree
b
=>
if
decide
(
a
=
b
)
then
DecAgree
a
else
DecAgreeBot
|
_
,
_
=>
DecAgreeBot
end
.
Instance
dec_agree_unit
:
Unit
(
dec_agree
A
)
:
=
id
.
Instance
dec_agree_minus
:
Minus
(
dec_agree
A
)
:
=
λ
x
y
,
x
.
Definition
dec_agree_ra
:
RA
(
dec_agree
A
).
Proof
.
split
.
-
apply
_
.
-
apply
_
.
-
apply
_
.
-
apply
_
.
-
intros
[?|]
[?|]
[?|]
;
simpl
;
repeat
(
case_match
;
simpl
)
;
subst
;
congruence
.
-
intros
[?|]
[?|]
;
simpl
;
repeat
(
case_match
;
simpl
)
;
try
subst
;
congruence
.
-
intros
[?|]
;
simpl
;
repeat
(
case_match
;
simpl
)
;
try
subst
;
congruence
.
-
intros
[?|]
;
simpl
;
repeat
(
case_match
;
simpl
)
;
try
subst
;
congruence
.
-
intros
[?|]
[?|]
?
;
simpl
;
done
.
-
intros
[?|]
[?|]
?
;
simpl
;
done
.
-
intros
[?|]
[?|]
[[?|]]
;
simpl
;
repeat
(
case_match
;
simpl
)
;
subst
;
try
congruence
;
[].
case
=>
EQ
.
destruct
EQ
.
done
.
Qed
.
Canonical
Structure
dec_agreeRA
:
cmraT
:
=
discreteRA
dec_agree_ra
.
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