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Iris
Fairis
Commits
245e0349
Commit
245e0349
authored
Mar 11, 2016
by
Ralf Jung
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start working on a one_shot construction
parent
a56e6ab8
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_CoqProject
_CoqProject
+1
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algebra/frac.v
algebra/frac.v
+4
5
algebra/one_shot.v
algebra/one_shot.v
+93
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_CoqProject
View file @
245e0349
...
...
@@ 54,6 +54,7 @@ algebra/upred.v
algebra/upred_tactics.v
algebra/upred_big_op.v
algebra/frac.v
algebra/one_shot.v
program_logic/model.v
program_logic/adequacy.v
program_logic/hoare_lifting.v
...
...
algebra/frac.v
View file @
245e0349
...
...
@@ 4,11 +4,10 @@ From iris.algebra Require Import upred.
Local
Arguments
validN
_
_
_
!
_
/
.
Local
Arguments
valid
_
_
!
_
/
.
Inductive
frac
(
A
:
Type
)
:=

Frac
:
Qp
→
A
→
frac
A

FracUnit
:
frac
A
.
Arguments
Frac
{
_
}
_
_.
Arguments
FracUnit
{
_
}
.
Inductive
frac
{
A
:
Type
}
:=

Frac
:
Qp
→
A
→
frac

FracUnit
:
frac
.
Arguments
frac
_
:
clear
implicits
.
Instance
maybe_Frac
{
A
}
:
Maybe2
(
@
Frac
A
)
:=
λ
x
,
match
x
with
Frac
q
a
=>
Some
(
q
,
a
)

_
=>
None
end
.
Instance:
Params
(
@
Frac
)
2.
...
...
algebra/one_shot.v
0 → 100644
View file @
245e0349
From
iris
.
algebra
Require
Export
cmra
.
From
iris
.
algebra
Require
Import
upred
.
Local
Arguments
validN
_
_
_
!
_
/
.
Local
Arguments
valid
_
_
!
_
/
.
Inductive
one_shot
{
A
:
Type
}
:=

OneShotPending
:
one_shot

Shot
:
A
→
one_shot

OneShotUnit
:
one_shot

OneShotBot
:
one_shot
.
Arguments
one_shot
_
:
clear
implicits
.
Instance
maybe_Shot
{
A
}
:
Maybe
(
@
Shot
A
)
:=
λ
x
,
match
x
with
Shot
a
=>
Some
a

_
=>
None
end
.
Instance:
Params
(
@
Shot
)
1.
Section
cofe
.
Context
{
A
:
cofeT
}
.
Implicit
Types
a
b
:
A
.
Implicit
Types
x
y
:
one_shot
A
.
(
*
Cofe
*
)
Inductive
one_shot_equiv
:
Equiv
(
one_shot
A
)
:=

OneShotPending_equiv
:
OneShotPending
≡
OneShotPending

OneShot_equiv
a
b
:
a
≡
b
→
Shot
a
≡
Shot
b

OneShotUnit_equiv
:
OneShotUnit
≡
OneShotUnit

OneShotBot_equiv
:
OneShotBot
≡
OneShotBot
.
Existing
Instance
one_shot_equiv
.
Inductive
one_shot_dist
:
Dist
(
one_shot
A
)
:=

OneShotPending_dist
n
:
OneShotPending
≡
{
n
}
≡
OneShotPending

OneShot_dist
n
a
b
:
a
≡
{
n
}
≡
b
→
Shot
a
≡
{
n
}
≡
Shot
b

OneShotUnit_dist
n
:
OneShotUnit
≡
{
n
}
≡
OneShotUnit

OneShotBot_dist
n
:
OneShotBot
≡
{
n
}
≡
OneShotBot
.
Existing
Instance
one_shot_dist
.
Global
Instance
One_Shot_ne
n
:
Proper
(
dist
n
==>
dist
n
)
(
@
Shot
A
).
Proof
.
by
constructor
.
Qed
.
Global
Instance
One_Shot_proper
:
Proper
((
≡
)
==>
(
≡
))
(
@
Shot
A
).
Proof
.
by
constructor
.
Qed
.
Global
Instance
One_Shot_inj
:
Inj
(
≡
)
(
≡
)
(
@
Shot
A
).
Proof
.
by
inversion_clear
1.
Qed
.
Global
Instance
One_Shot_dist_inj
n
:
Inj
(
dist
n
)
(
dist
n
)
(
@
Shot
A
).
Proof
.
by
inversion_clear
1.
Qed
.
Program
Definition
one_shot_chain
(
c
:
chain
(
one_shot
A
))
(
a
:
A
)
(
H
:
maybe
Shot
(
c
0
)
=
Some
a
)
:
chain
A
:=
{
chain_car
n
:=
match
c
n
return
_
with
Shot
b
=>
b

_
=>
a
end
}
.
Next
Obligation
.
intros
c
a
?
n
i
?
;
simpl
.
destruct
(
c
0
)
eqn
:?
;
simplify_eq
/=
.
by
feed
inversion
(
chain_cauchy
c
n
i
).
Qed
.
Instance
one_shot_compl
:
Compl
(
one_shot
A
)
:=
λ
c
,
match
Some_dec
(
maybe
Shot
(
c
0
))
with

inleft
(
exist
a
H
)
=>
Shot
(
compl
(
one_shot_chain
c
a
H
))

inright
_
=>
c
0
end
.
Definition
one_shot_cofe_mixin
:
CofeMixin
(
one_shot
A
).
Proof
.
split
.

intros
mx
my
;
split
.
+
by
destruct
1
;
subst
;
constructor
;
try
apply
equiv_dist
.
+
intros
Hxy
;
feed
inversion
(
Hxy
0
);
subst
;
constructor
;
try
done
.
apply
equiv_dist
=>
n
;
by
feed
inversion
(
Hxy
n
).

intros
n
;
split
.
+
by
intros
[

a


];
constructor
.
+
by
destruct
1
;
constructor
.
+
destruct
1
;
inversion_clear
1
;
constructor
;
etrans
;
eauto
.

by
inversion_clear
1
;
constructor
;
done

apply
dist_S
.

intros
n
c
;
unfold
compl
,
one_shot_compl
.
destruct
(
Some_dec
(
maybe
Shot
(
c
0
)))
as
[[
a
Hx
]

].
{
assert
(
c
0
=
Shot
a
)
by
(
by
destruct
(
c
0
);
simplify_eq
/=
).
assert
(
∃
b
,
c
n
=
Shot
b
)
as
[
y
Hy
].
{
feed
inversion
(
chain_cauchy
c
0
n
);
eauto
with
lia
congruence
f_equal
.
}
rewrite
Hy
;
constructor
;
auto
.
by
rewrite
(
conv_compl
n
(
one_shot_chain
c
a
Hx
))
/=
Hy
.
}
feed
inversion
(
chain_cauchy
c
0
n
);
first
lia
;
constructor
;
destruct
(
c
0
);
simplify_eq
/=
.
Qed
.
Canonical
Structure
one_shotC
:
cofeT
:=
CofeT
one_shot_cofe_mixin
.
Global
Instance
one_shot_discrete
:
Discrete
A
→
Discrete
one_shotC
.
Proof
.
by
inversion_clear
2
;
constructor
;
done

apply
(
timeless
_
).
Qed
.
Global
Instance
one_shot_leibniz
:
LeibnizEquiv
A
→
LeibnizEquiv
(
one_shot
A
).
Proof
.
by
destruct
2
;
f_equal
;
done

apply
leibniz_equiv
.
Qed
.
Global
Instance
Shot_timeless
(
a
:
A
)
:
Timeless
a
→
Timeless
(
Shot
a
).
Proof
.
by
inversion_clear
2
;
constructor
;
done

apply
(
timeless
_
).
Qed
.
Global
Instance
OneShotUnit_timeless
:
Timeless
(
@
OneShotUnit
A
).
Proof
.
by
inversion_clear
1
;
constructor
.
Qed
.
End
cofe
.
Arguments
one_shotC
:
clear
implicits
.
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