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1c87b96a
Commit
1c87b96a
authored
May 25, 2016
by
Robbert Krebbers
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Define dist on option using option_Forall2.
parent
0b8de700
Changes
3
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3 changed files
with
7 additions
and
12 deletions
+7
-12
algebra/cofe.v
algebra/cofe.v
+4
-9
algebra/list.v
algebra/list.v
+2
-2
program_logic/ownership.v
program_logic/ownership.v
+1
-1
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algebra/cofe.v
View file @
1c87b96a
...
...
@@ -454,13 +454,10 @@ Canonical Structure boolC := leibnizC bool.
Section
option
.
Context
{
A
:
cofeT
}.
Inductive
option_dist'
(
n
:
nat
)
:
relation
(
option
A
)
:
=
|
Some_dist
x
y
:
x
≡
{
n
}
≡
y
→
option_dist'
n
(
Some
x
)
(
Some
y
)
|
None_dist
:
option_dist'
n
None
None
.
Instance
option_dist
:
Dist
(
option
A
)
:
=
option_dist'
.
Instance
option_dist
:
Dist
(
option
A
)
:
=
λ
n
,
option_Forall2
(
dist
n
).
Lemma
dist_option_Forall2
n
mx
my
:
mx
≡
{
n
}
≡
my
↔
option_Forall2
(
dist
n
)
mx
my
.
Proof
.
split
;
destruct
1
;
constructor
;
auto
.
Qed
.
Proof
.
done
.
Qed
.
Program
Definition
option_chain
(
c
:
chain
(
option
A
))
(
x
:
A
)
:
chain
A
:
=
{|
chain_car
n
:
=
from_option
x
(
c
n
)
|}.
...
...
@@ -474,10 +471,7 @@ Section option.
-
intros
mx
my
;
split
;
[
by
destruct
1
;
constructor
;
apply
equiv_dist
|].
intros
Hxy
;
destruct
(
Hxy
0
)
;
constructor
;
apply
equiv_dist
.
by
intros
n
;
feed
inversion
(
Hxy
n
).
-
intros
n
;
split
.
+
by
intros
[
x
|]
;
constructor
.
+
by
destruct
1
;
constructor
.
+
destruct
1
;
inversion_clear
1
;
constructor
;
etrans
;
eauto
.
-
apply
_
.
-
destruct
1
;
constructor
;
by
apply
dist_S
.
-
intros
n
c
;
rewrite
/
compl
/
option_compl
.
feed
inversion
(
chain_cauchy
c
0
n
)
;
first
auto
with
lia
;
constructor
.
...
...
@@ -503,6 +497,7 @@ Section option.
Proof
.
by
intros
?
;
inversion_clear
1
;
constructor
;
apply
timeless
.
Qed
.
End
option
.
Typeclasses
Opaque
option_dist
.
Arguments
optionC
:
clear
implicits
.
Instance
option_fmap_ne
{
A
B
:
cofeT
}
(
f
:
A
→
B
)
n
:
...
...
algebra/list.v
View file @
1c87b96a
...
...
@@ -62,8 +62,8 @@ Proof.
destruct
(
c
0
)
as
[|
x
l
]
eqn
:
Hc0
at
1
.
{
by
destruct
(
chain_cauchy
c
0
n
)
;
auto
with
omega
.
}
rewrite
-(
λ
H
,
length_ne
_
_
_
(
chain_cauchy
c
0
n
H
))
;
last
omega
.
apply
Forall2_lookup
=>
i
;
apply
dist_option_Forall2
.
rewrite
list_lookup_fmap
.
destruct
(
decide
(
i
<
length
(
c
n
)))
;
last
first
.
apply
Forall2_lookup
=>
i
.
rewrite
-
dist_option_Forall2
list_lookup_fmap
.
destruct
(
decide
(
i
<
length
(
c
n
)))
;
last
first
.
{
rewrite
lookup_seq_ge
?lookup_ge_None_2
;
auto
with
omega
.
}
rewrite
lookup_seq
//=
(
conv_compl
n
(
list_chain
c
_
_
))
/=.
by
destruct
(
lookup_lt_is_Some_2
(
c
n
)
i
)
as
[?
->].
...
...
program_logic/ownership.v
View file @
1c87b96a
...
...
@@ -64,7 +64,7 @@ Proof.
intros
(?&?&?).
rewrite
/
ownI
;
uPred
.
unseal
.
rewrite
/
uPred_holds
/=
res_includedN
/=
singleton_includedN
;
split
.
-
intros
[(
P'
&
Hi
&
HP
)
_
]
;
rewrite
Hi
.
apply
Some_dist
,
symmetry
,
agree_valid_includedN
;
last
done
.
constructor
;
symmetry
;
apply
agree_valid_includedN
;
last
done
.
by
apply
lookup_validN_Some
with
(
wld
r
)
i
.
-
intros
?
;
split_and
?
;
try
apply
cmra_unit_leastN
;
eauto
.
Qed
.
...
...
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