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4c1a0469
Commit
4c1a0469
authored
Jun 16, 2016
by
Robbert Krebbers
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Make exclusive stuff more consistent.
parent
4397cde3
Changes
3
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3 changed files
with
22 additions
and
17 deletions
+22
-17
algebra/cmra.v
algebra/cmra.v
+19
-14
algebra/updates.v
algebra/updates.v
+2
-2
heap_lang/heap.v
heap_lang/heap.v
+1
-1
No files found.
algebra/cmra.v
View file @
4c1a0469
...
...
@@ -128,8 +128,8 @@ Class Persistent {A : cmraT} (x : A) := persistent : pcore x ≡ Some x.
Arguments
persistent
{
_
}
_
{
_
}.
(** * Exclusive elements (i.e., elements that cannot have a frame). *)
Class
Exclusive
{
A
:
cmraT
}
(
x
:
A
)
:
=
exclusive0_
r
:
∀
y
,
✓
{
0
}
(
x
⋅
y
)
→
False
.
Arguments
exclusive0_
r
{
_
}
_
{
_
}
_
_
.
Class
Exclusive
{
A
:
cmraT
}
(
x
:
A
)
:
=
exclusive0_
l
y
:
✓
{
0
}
(
x
⋅
y
)
→
False
.
Arguments
exclusive0_
l
{
_
}
_
{
_
}
_
_
.
(** * CMRAs whose core is total *)
(** The function [core] may return a dummy when used on CMRAs without total
...
...
@@ -318,16 +318,14 @@ Lemma persistent_dup x `{!Persistent x} : x ≡ x ⋅ x.
Proof
.
by
apply
cmra_pcore_dup'
with
x
.
Qed
.
(** ** Exclusive elements *)
Lemma
exclusiveN_r
x
`
{!
Exclusive
x
}
:
∀
(
n
:
nat
)
(
y
:
A
),
✓
{
n
}
(
x
⋅
y
)
→
False
.
Proof
.
intros
???%
cmra_validN_le
%
exclusive0_r
;
auto
with
arith
.
Qed
.
Lemma
exclusiveN_l
x
`
{!
Exclusive
x
}
:
∀
(
n
:
nat
)
(
y
:
A
),
✓
{
n
}
(
y
⋅
x
)
→
False
.
Proof
.
intros
??.
rewrite
comm
.
by
apply
exclusiveN_r
.
Qed
.
Lemma
exclusive_r
x
`
{!
Exclusive
x
}
:
∀
(
y
:
A
),
✓
(
x
⋅
y
)
→
False
.
Proof
.
by
intros
?
?%
cmra_valid_validN
%(
exclusiveN_r
_
0
).
Qed
.
Lemma
exclusive_l
x
`
{!
Exclusive
x
}
:
∀
(
y
:
A
),
✓
(
y
⋅
x
)
→
False
.
Proof
.
by
intros
?
?%
cmra_valid_validN
%(
exclusiveN_l
_
0
).
Qed
.
Lemma
exclusiveN_l
n
x
`
{!
Exclusive
x
}
y
:
✓
{
n
}
(
x
⋅
y
)
→
False
.
Proof
.
intros
?%
cmra_validN_le
%
exclusive0_l
;
auto
with
arith
.
Qed
.
Lemma
exclusiveN_r
n
x
`
{!
Exclusive
x
}
y
:
✓
{
n
}
(
y
⋅
x
)
→
False
.
Proof
.
rewrite
comm
.
by
apply
exclusiveN_l
.
Qed
.
Lemma
exclusive_l
x
`
{!
Exclusive
x
}
y
:
✓
(
x
⋅
y
)
→
False
.
Proof
.
by
move
/
cmra_valid_validN
/(
_
0
)
/
exclusive0_l
.
Qed
.
Lemma
exclusive_r
x
`
{!
Exclusive
x
}
y
:
✓
(
y
⋅
x
)
→
False
.
Proof
.
rewrite
comm
.
by
apply
exclusive_l
.
Qed
.
(** ** Order *)
Lemma
cmra_included_includedN
n
x
y
:
x
≼
y
→
x
≼
{
n
}
y
.
...
...
@@ -868,9 +866,9 @@ Section prod.
Proof
.
by
rewrite
/
Persistent
prod_pcore_Some'
.
Qed
.
Global
Instance
pair_exclusive_l
x
y
:
Exclusive
x
→
Exclusive
(
x
,
y
).
Proof
.
by
intros
?[][?%
exclusive0_
r
].
Qed
.
Proof
.
by
intros
?[][?%
exclusive0_
l
].
Qed
.
Global
Instance
pair_exclusive_r
x
y
:
Exclusive
y
→
Exclusive
(
x
,
y
).
Proof
.
by
intros
?[][??%
exclusive0_
r
].
Qed
.
Proof
.
by
intros
?[][??%
exclusive0_
l
].
Qed
.
End
prod
.
Arguments
prodR
:
clear
implicits
.
...
...
@@ -1045,6 +1043,13 @@ Section option.
Global
Instance
option_persistent
(
mx
:
option
A
)
:
(
∀
x
:
A
,
Persistent
x
)
→
Persistent
mx
.
Proof
.
intros
.
destruct
mx
;
apply
_
.
Qed
.
Lemma
exclusiveN_Some_l
n
x
`
{!
Exclusive
x
}
my
:
✓
{
n
}
(
Some
x
⋅
my
)
→
my
=
None
.
Proof
.
destruct
my
.
move
=>
/(
exclusiveN_l
_
x
)
[].
done
.
Qed
.
Lemma
exclusiveN_Some_r
n
x
`
{!
Exclusive
x
}
my
:
✓
{
n
}
(
my
⋅
Some
x
)
→
my
=
None
.
Proof
.
rewrite
comm
.
by
apply
exclusiveN_Some_l
.
Qed
.
End
option
.
Arguments
optionR
:
clear
implicits
.
...
...
algebra/updates.v
View file @
4c1a0469
...
...
@@ -56,7 +56,7 @@ Proof. split; auto with typeclass_instances. Qed.
Global
Instance
exclusive_local_update
y
:
LocalUpdate
Exclusive
(
λ
_
,
y
)
|
1000
.
Proof
.
split
.
apply
_
.
by
intros
?????%
exclusiveN_
r
.
Qed
.
Proof
.
split
.
apply
_
.
by
intros
?????%
exclusiveN_
l
.
Qed
.
(** ** Frame preserving updates *)
Lemma
cmra_update_updateP
x
y
:
x
~~>
y
↔
x
~~>
:
(
y
=).
...
...
@@ -83,7 +83,7 @@ Proof.
Qed
.
Lemma
cmra_update_exclusive
`
{!
Exclusive
x
}
y
:
✓
y
→
x
~~>
y
.
Proof
.
move
=>??[
z
|]=>[/
exclusiveN_
r
[]|
_
].
by
apply
cmra_valid_validN
.
Qed
.
Proof
.
move
=>??[
z
|]=>[/
exclusiveN_
l
[]|
_
].
by
apply
cmra_valid_validN
.
Qed
.
Lemma
cmra_updateP_op
(
P1
P2
Q
:
A
→
Prop
)
x1
x2
:
x1
~~>
:
P1
→
x2
~~>
:
P2
→
(
∀
y1
y2
,
P1
y1
→
P2
y2
→
Q
(
y1
⋅
y2
))
→
...
...
heap_lang/heap.v
View file @
4c1a0469
...
...
@@ -89,7 +89,7 @@ Section heap.
Proof
.
intros
Hv
l'
;
move
:
(
Hv
l'
).
destruct
(
decide
(
l'
=
l
))
as
[->|].
-
rewrite
!
lookup_op
!
lookup_singleton
.
by
case
:
(
h
!!
l
)=>
[
x
|]
//
/
Some_valid
/
exclusive_
r
.
by
case
:
(
h
!!
l
)=>
[
x
|]
//
/
Some_valid
/
exclusive_
l
.
-
by
rewrite
!
lookup_op
!
lookup_singleton_ne
.
Qed
.
Hint
Resolve
heap_store_valid
.
...
...
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