Skip to content
GitLab
Menu
Projects
Groups
Snippets
Loading...
Help
Help
Support
Community forum
Keyboard shortcuts
?
Submit feedback
Contribute to GitLab
Sign in / Register
Toggle navigation
Menu
Open sidebar
Iris
Fairis
Commits
b13debed
Commit
b13debed
authored
Jan 15, 2016
by
Robbert Krebbers
Browse files
Cleanup agree and prove some additional properties.
parent
69407372
Changes
1
Hide whitespace changes
Inline
Sidebyside
Showing
1 changed file
with
25 additions
and
19 deletions
+25
19
modures/agree.v
modures/agree.v
+25
19
No files found.
modures/agree.v
View file @
b13debed
...
...
@@ 51,6 +51,11 @@ Proof.
Qed
.
Canonical
Structure
agreeC
:=
CofeT
agree_cofe_mixin
.
Lemma
agree_car_ne
(
x
y
:
agree
A
)
n
:
✓
{
n
}
x
→
x
={
n
}=
y
→
x
n
={
n
}=
y
n
.
Proof
.
by
intros
[
??
]
Hxy
;
apply
Hxy
.
Qed
.
Lemma
agree_cauchy
(
x
:
agree
A
)
n
i
:
✓
{
n
}
x
→
i
≤
n
→
x
i
={
i
}=
x
n
.
Proof
.
by
intros
[
?
Hx
];
apply
Hx
.
Qed
.
Program
Instance
agree_op
:
Op
(
agree
A
)
:=
λ
x
y
,
{
agree_car
:=
x
;
agree_is_valid
n
:=
agree_is_valid
x
n
∧
agree_is_valid
y
n
∧
x
={
n
}=
y
}
.
...
...
@@ 62,6 +67,12 @@ Instance: Commutative (≡) (@op (agree A) _).
Proof
.
intros
x
y
;
split
;
[
naive_solver

by
intros
n
(
?&?&
Hxy
);
apply
Hxy
].
Qed
.
Definition
agree_idempotent
(
x
:
agree
A
)
:
x
⋅
x
≡
x
.
Proof
.
split
;
naive_solver
.
Qed
.
Instance:
∀
n
:
nat
,
Proper
(
dist
n
==>
impl
)
(
@
validN
(
agree
A
)
_
n
).
Proof
.
intros
n
x
y
Hxy
[
?
Hx
];
split
;
[
by
apply
Hxy

intros
n
'
?
].
rewrite

(
proj2
Hxy
n
'
)
1
?
(
Hx
n
'
);
eauto
using
agree_valid_le
.
by
apply
dist_le
with
n
;
try
apply
Hxy
.
Qed
.
Instance:
∀
x
:
agree
A
,
Proper
(
dist
n
==>
dist
n
)
(
op
x
).
Proof
.
intros
n
x
y1
y2
[
Hy
'
Hy
];
split
;
[

done
].
...
...
@@ 88,9 +99,6 @@ Qed.
Definition
agree_cmra_mixin
:
CMRAMixin
(
agree
A
).
Proof
.
split
;
try
(
apply
_

done
).
*
intros
n
x
y
Hxy
[
?
Hx
];
split
;
[
by
apply
Hxy

intros
n
'
?
].
rewrite

(
proj2
Hxy
n
'
)
1
?
(
Hx
n
'
);
eauto
using
agree_valid_le
.
by
apply
dist_le
with
n
;
try
apply
Hxy
.
*
by
intros
n
x1
x2
Hx
y1
y2
Hy
.
*
intros
x
;
split
;
[
apply
agree_valid_0

].
by
intros
n
'
;
rewrite
Nat
.
le_0_r
;
intros
>
.
...
...
@@ 101,14 +109,18 @@ Proof.
*
by
intros
x
y
n
[(
?&?&?
)
?
].
*
by
intros
x
y
n
;
rewrite
agree_includedN
.
Qed
.
Lemma
agree_op_inv
(
x
y1
y2
:
agree
A
)
n
:
✓
{
n
}
x
→
x
={
n
}=
y1
⋅
y2
→
y1
={
n
}=
y2
.
Proof
.
by
intros
[
??
]
Hxy
;
apply
Hxy
.
Qed
.
Lemma
agree_op_inv
(
x1
x2
:
agree
A
)
n
:
✓
{
n
}
(
x1
⋅
x2
)
→
x1
={
n
}=
x2
.
Proof
.
intros
Hxy
;
apply
Hxy
.
Qed
.
Lemma
agree_valid_includedN
(
x
y
:
agree
A
)
n
:
✓
{
n
}
y
→
x
≼
{
n
}
y
→
x
={
n
}=
y
.
Proof
.
move
=>
Hval
[
z
Hy
];
move
:
Hval
;
rewrite
Hy
.
by
move
=>
/
agree_op_inv
>
;
rewrite
agree_idempotent
.
Qed
.
Definition
agree_cmra_extend_mixin
:
CMRAExtendMixin
(
agree
A
).
Proof
.
intros
n
x
y1
y2
?
Hx
;
exists
(
x
,
x
);
simpl
;
split
.
intros
n
x
y1
y2
Hval
Hx
;
exists
(
x
,
x
);
simpl
;
split
.
*
by
rewrite
agree_idempotent
.
*
by
rewrite
Hx
(
agree_op_inv
x
y1
y2
)
//
agree_idempotent.
*
by
move
:
Hval
;
rewrite
Hx
;
move
=>
/
agree_op_inv
>
;
rewrite
agree_idempotent
.
Qed
.
Canonical
Structure
agreeRA
:
cmraT
:=
CMRAT
agree_cofe_mixin
agree_cmra_mixin
agree_cmra_extend_mixin
.
...
...
@@ 118,15 +130,9 @@ Program Definition to_agree (x : A) : agree A :=
Solve
Obligations
with
done
.
Global
Instance
to_agree_ne
n
:
Proper
(
dist
n
==>
dist
n
)
to_agree
.
Proof
.
intros
x1
x2
Hx
;
split
;
naive_solver
eauto
using
@
dist_le
.
Qed
.
Lemma
agree_car_ne
(
x
y
:
agree
A
)
n
:
✓
{
n
}
x
→
x
={
n
}=
y
→
x
n
={
n
}=
y
n
.
Proof
.
by
intros
[
??
]
Hxy
;
apply
Hxy
.
Qed
.
Lemma
agree_cauchy
(
x
:
agree
A
)
n
i
:
n
≤
i
→
✓
{
i
}
x
→
x
n
={
n
}=
x
i
.
Proof
.
by
intros
?
[
?
Hx
];
apply
Hx
.
Qed
.
Lemma
agree_to_agree_inj
(
x
y
:
agree
A
)
a
n
:
✓
{
n
}
x
→
x
={
n
}=
to_agree
a
⋅
y
→
x
n
={
n
}=
a
.
Proof
.
by
intros
;
transitivity
((
to_agree
a
⋅
y
)
n
);
first
apply
agree_car_ne
.
Qed
.
Global
Instance
to_agree_proper
:
Proper
((
≡
)
==>
(
≡
))
to_agree
:=
ne_proper
_.
Global
Instance
to_agree_inj
n
:
Injective
(
dist
n
)
(
dist
n
)
(
to_agree
).
Proof
.
by
intros
x
y
[
_
Hxy
];
apply
Hxy
.
Qed
.
End
agree
.
Arguments
agreeC
:
clear
implicits
.
...
...
@@ 137,8 +143,8 @@ Program Definition agree_map {A B} (f : A → B) (x : agree A) : agree B :=
Solve
Obligations
with
auto
using
agree_valid_0
,
agree_valid_S
.
Lemma
agree_map_id
{
A
}
(
x
:
agree
A
)
:
agree_map
id
x
=
x
.
Proof
.
by
destruct
x
.
Qed
.
Lemma
agree_map_compose
{
A
B
C
}
(
f
:
A
→
B
)
(
g
:
B
→
C
)
(
x
:
agree
A
)
:
agree_map
(
g
∘
f
)
x
=
agree_map
g
(
agree_map
f
x
).
Lemma
agree_map_compose
{
A
B
C
}
(
f
:
A
→
B
)
(
g
:
B
→
C
)
(
x
:
agree
A
)
:
agree_map
(
g
∘
f
)
x
=
agree_map
g
(
agree_map
f
x
).
Proof
.
done
.
Qed
.
Section
agree_map
.
...
...
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