Skip to content
GitLab
Projects
Groups
Snippets
Help
Loading...
Help
What's new
7
Help
Support
Community forum
Keyboard shortcuts
?
Submit feedback
Contribute to GitLab
Sign in / Register
Toggle navigation
Open sidebar
Iris
Iris
Commits
2c1b15dc
Commit
2c1b15dc
authored
Feb 11, 2016
by
Ralf Jung
Browse files
Options
Browse Files
Download
Email Patches
Plain Diff
auth comments
parent
03863370
Changes
1
Hide whitespace changes
Inline
Side-by-side
Showing
1 changed file
with
14 additions
and
15 deletions
+14
-15
algebra/auth.v
algebra/auth.v
+14
-15
No files found.
algebra/auth.v
View file @
2c1b15dc
...
@@ -147,12 +147,8 @@ Proof. done. Qed.
...
@@ -147,12 +147,8 @@ Proof. done. Qed.
Lemma
auth_both_op
a
b
:
Auth
(
Excl
a
)
b
≡
●
a
⋅
◯
b
.
Lemma
auth_both_op
a
b
:
Auth
(
Excl
a
)
b
≡
●
a
⋅
◯
b
.
Proof
.
by
rewrite
/
op
/
auth_op
/=
left_id
.
Qed
.
Proof
.
by
rewrite
/
op
/
auth_op
/=
left_id
.
Qed
.
(* FIXME tentative name. Or maybe remove this notion entirely. *)
Definition
auth_step
(
a
a'
b
b'
:
A
)
:
Prop
:
=
∀
n
af
,
✓
{
n
}
a
→
a
≡
{
n
}
≡
a'
⋅
af
→
b
≡
{
n
}
≡
b'
⋅
af
∧
✓
{
n
}
b
.
Lemma
auth_update
a
a'
b
b'
:
Lemma
auth_update
a
a'
b
b'
:
auth_step
a
a'
b
b'
→
(
∀
n
af
,
✓
{
n
}
a
→
a
≡
{
n
}
≡
a'
⋅
af
→
b
≡
{
n
}
≡
b'
⋅
af
∧
✓
{
n
}
b
)
→
●
a
⋅
◯
a'
~~>
●
b
⋅
◯
b'
.
●
a
⋅
◯
a'
~~>
●
b
⋅
◯
b'
.
Proof
.
Proof
.
move
=>
Hab
[[?|
|]
bf1
]
n
//
=>-[[
bf2
Ha
]
?]
;
do
2
red
;
simpl
in
*.
move
=>
Hab
[[?|
|]
bf1
]
n
//
=>-[[
bf2
Ha
]
?]
;
do
2
red
;
simpl
in
*.
...
@@ -161,20 +157,11 @@ Proof.
...
@@ -161,20 +157,11 @@ Proof.
split
;
[
by
rewrite
Ha'
left_id
associative
;
apply
cmra_includedN_l
|
done
].
split
;
[
by
rewrite
Ha'
left_id
associative
;
apply
cmra_includedN_l
|
done
].
Qed
.
Qed
.
(* FIXME: are the following lemmas derivable from each other? *)
Lemma
auth_local_update_l
f
`
{!
LocalUpdate
P
f
}
a
a'
:
P
a
→
✓
(
f
a
⋅
a'
)
→
●
(
a
⋅
a'
)
⋅
◯
a
~~>
●
(
f
a
⋅
a'
)
⋅
◯
f
a
.
Proof
.
intros
;
apply
auth_update
=>
n
af
?
EQ
;
split
;
last
done
.
by
rewrite
-(
local_updateN
f
)
//
EQ
-(
local_updateN
f
)
//
-
EQ
.
Qed
.
Lemma
auth_local_update
f
`
{!
LocalUpdate
P
f
}
a
a'
:
Lemma
auth_local_update
f
`
{!
LocalUpdate
P
f
}
a
a'
:
P
a
→
✓
(
f
a'
)
→
P
a
→
✓
(
f
a'
)
→
●
a'
⋅
◯
a
~~>
●
f
a'
⋅
◯
f
a
.
●
a'
⋅
◯
a
~~>
●
f
a'
⋅
◯
f
a
.
Proof
.
Proof
.
intros
;
apply
auth_update
=>
n
af
?
EQ
;
split
;
last
done
.
intros
.
apply
auth_update
=>
n
af
?
EQ
;
split
;
last
done
.
by
rewrite
EQ
(
local_updateN
f
)
//
-
EQ
.
by
rewrite
EQ
(
local_updateN
f
)
//
-
EQ
.
Qed
.
Qed
.
...
@@ -185,6 +172,18 @@ Lemma auth_update_op_r a a' b :
...
@@ -185,6 +172,18 @@ Lemma auth_update_op_r a a' b :
✓
(
a
⋅
b
)
→
●
a
⋅
◯
a'
~~>
●
(
a
⋅
b
)
⋅
◯
(
a'
⋅
b
).
✓
(
a
⋅
b
)
→
●
a
⋅
◯
a'
~~>
●
(
a
⋅
b
)
⋅
◯
(
a'
⋅
b
).
Proof
.
rewrite
-!(
commutative
_
b
)
;
apply
auth_update_op_l
.
Qed
.
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
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
.
Proof
.
intros
.
apply
auth_update
=>
n
af
?
EQ
;
split
;
last
done
.
by
rewrite
-(
local_updateN
f
)
//
EQ
-(
local_updateN
f
)
//
-
EQ
.
Qed
.
End
cmra
.
End
cmra
.
Arguments
authRA
:
clear
implicits
.
Arguments
authRA
:
clear
implicits
.
...
...
Write
Preview
Markdown
is supported
0%
Try again
or
attach a new file
.
Attach a file
Cancel
You are about to add
0
people
to the discussion. Proceed with caution.
Finish editing this message first!
Cancel
Please
register
or
sign in
to comment