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560bd3a9
Commit
560bd3a9
authored
Feb 11, 2016
by
Ralf Jung
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change naming conventions for LocalUpdates: L is the function, Lv the validity
parent
88c1dd29
Changes
3
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3 changed files
with
20 additions
and
20 deletions
+20
-20
algebra/auth.v
algebra/auth.v
+9
-9
algebra/cmra.v
algebra/cmra.v
+8
-8
algebra/fin_maps.v
algebra/fin_maps.v
+3
-3
No files found.
algebra/auth.v
View file @
560bd3a9
...
...
@@ -157,12 +157,12 @@ Proof.
split
;
[
by
rewrite
Ha'
left_id
associative
;
apply
cmra_includedN_l
|
done
].
Qed
.
Lemma
auth_local_update
f
`
{!
LocalUpdate
P
f
}
a
a'
:
P
a
→
✓
(
f
a'
)
→
●
a'
⋅
◯
a
~~>
●
f
a'
⋅
◯
f
a
.
Lemma
auth_local_update
L
`
{!
LocalUpdate
Lv
L
}
a
a'
:
Lv
a
→
✓
(
L
a'
)
→
●
a'
⋅
◯
a
~~>
●
L
a'
⋅
◯
L
a
.
Proof
.
intros
.
apply
auth_update
=>
n
af
?
EQ
;
split
;
last
done
.
by
rewrite
EQ
(
local_updateN
f
)
//
-
EQ
.
by
rewrite
EQ
(
local_updateN
L
)
//
-
EQ
.
Qed
.
Lemma
auth_update_op_l
a
a'
b
:
...
...
@@ -173,15 +173,15 @@ Lemma auth_update_op_r a a' b :
Proof
.
rewrite
-!(
commutative
_
b
)
;
apply
auth_update_op_l
.
Qed
.
(* This does not seem to follow from auth_local_update.
The trouble is that given ✓ (
f
a ⋅ a'),
P
a
The trouble is that given ✓ (
L
a ⋅ a'),
Lv
a
we need ✓ (a ⋅ a'). I think this should hold for every local update,
but adding an extra axiom to local updates just for this is silly. *)
Lemma
auth_local_update_l
f
`
{!
LocalUpdate
P
f
}
a
a'
:
P
a
→
✓
(
f
a
⋅
a'
)
→
●
(
a
⋅
a'
)
⋅
◯
a
~~>
●
(
f
a
⋅
a'
)
⋅
◯
f
a
.
Lemma
auth_local_update_l
L
`
{!
LocalUpdate
Lv
L
}
a
a'
:
Lv
a
→
✓
(
L
a
⋅
a'
)
→
●
(
a
⋅
a'
)
⋅
◯
a
~~>
●
(
L
a
⋅
a'
)
⋅
◯
L
a
.
Proof
.
intros
.
apply
auth_update
=>
n
af
?
EQ
;
split
;
last
done
.
by
rewrite
-(
local_updateN
f
)
//
EQ
-(
local_updateN
f
)
//
-
EQ
.
by
rewrite
-(
local_updateN
L
)
//
EQ
-(
local_updateN
L
)
//
-
EQ
.
Qed
.
End
cmra
.
...
...
algebra/cmra.v
View file @
560bd3a9
...
...
@@ -137,9 +137,9 @@ Class CMRAMonotone {A B : cmraT} (f : A → B) := {
}.
(** * Local updates *)
Class
LocalUpdate
{
A
:
cmraT
}
(
P
:
A
→
Prop
)
(
f
:
A
→
A
)
:
=
{
local_update_ne
n
:
>
Proper
(
dist
n
==>
dist
n
)
f
;
local_updateN
n
x
y
:
P
x
→
✓
{
n
}
(
x
⋅
y
)
→
f
(
x
⋅
y
)
≡
{
n
}
≡
f
x
⋅
y
Class
LocalUpdate
{
A
:
cmraT
}
(
Lv
:
A
→
Prop
)
(
L
:
A
→
A
)
:
=
{
local_update_ne
n
:
>
Proper
(
dist
n
==>
dist
n
)
L
;
local_updateN
n
x
y
:
Lv
x
→
✓
{
n
}
(
x
⋅
y
)
→
L
(
x
⋅
y
)
≡
{
n
}
≡
L
x
⋅
y
}.
Arguments
local_updateN
{
_
_
}
_
{
_
}
_
_
_
_
_
.
...
...
@@ -322,13 +322,13 @@ Section identity.
End
identity
.
(** ** Local updates *)
Global
Instance
local_update_proper
P
(
f
:
A
→
A
)
:
LocalUpdate
P
f
→
Proper
((
≡
)
==>
(
≡
))
f
.
Global
Instance
local_update_proper
Lv
(
L
:
A
→
A
)
:
LocalUpdate
Lv
L
→
Proper
((
≡
)
==>
(
≡
))
L
.
Proof
.
intros
;
apply
(
ne_proper
_
).
Qed
.
Lemma
local_update
f
`
{!
LocalUpdate
P
f
}
x
y
:
P
x
→
✓
(
x
⋅
y
)
→
f
(
x
⋅
y
)
≡
f
x
⋅
y
.
Proof
.
by
rewrite
equiv_dist
=>??
n
;
apply
(
local_updateN
f
).
Qed
.
Lemma
local_update
L
`
{!
LocalUpdate
Lv
L
}
x
y
:
Lv
x
→
✓
(
x
⋅
y
)
→
L
(
x
⋅
y
)
≡
L
x
⋅
y
.
Proof
.
by
rewrite
equiv_dist
=>??
n
;
apply
(
local_updateN
L
).
Qed
.
Global
Instance
local_update_op
x
:
LocalUpdate
(
λ
_
,
True
)
(
op
x
).
Proof
.
split
.
apply
_
.
by
intros
n
y1
y2
_
_;
rewrite
associative
.
Qed
.
...
...
algebra/fin_maps.v
View file @
560bd3a9
...
...
@@ -288,14 +288,14 @@ End freshness.
(* Deallocation is not a local update. The trouble is that if we own {[ i ↦ x ]},
then the frame could always own "unit x", and prevent deallocation. *)
Global
Instance
map_alter_update
`
{!
LocalUpdate
P
f
}
i
:
LocalUpdate
(
λ
m
,
∃
x
,
m
!!
i
=
Some
x
∧
P
x
)
(
alter
f
i
).
Global
Instance
map_alter_update
`
{!
LocalUpdate
Lv
L
}
i
:
LocalUpdate
(
λ
m
,
∃
x
,
m
!!
i
=
Some
x
∧
Lv
x
)
(
alter
L
i
).
Proof
.
split
;
first
apply
_
.
intros
n
m1
m2
(
x
&
Hix
&?)
Hm
j
;
destruct
(
decide
(
i
=
j
))
as
[->|].
-
rewrite
lookup_alter
!
lookup_op
lookup_alter
Hix
/=.
move
:
(
Hm
j
)
;
rewrite
lookup_op
Hix
.
case
:
(
m2
!!
j
)=>[
y
|]
//=
;
constructor
.
by
apply
(
local_updateN
f
).
case
:
(
m2
!!
j
)=>[
y
|]
//=
;
constructor
.
by
apply
(
local_updateN
L
).
-
by
rewrite
lookup_op
!
lookup_alter_ne
//
lookup_op
.
Qed
.
End
properties
.
...
...
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