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0b7e25c2
Commit
0b7e25c2
authored
Feb 10, 2016
by
Ralf Jung
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make auth_closing less stupid
parent
05b7229d
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2
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2 changed files
with
7 additions
and
10 deletions
+7
10
algebra/auth.v
algebra/auth.v
+5
1
program_logic/auth.v
program_logic/auth.v
+2
9
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algebra/auth.v
View file @
0b7e25c2
...
...
@@ 147,8 +147,12 @@ Proof. done. Qed.
Lemma
auth_both_op
a
b
:
Auth
(
Excl
a
)
b
≡
●
a
⋅
◯
b
.
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'
:
=
∀
n
af
,
✓
{
n
}
a
→
a
≡
{
n
}
≡
a'
⋅
af
→
b
≡
{
n
}
≡
b'
⋅
af
∧
✓
{
n
}
b
.
Lemma
auth_update
a
a'
b
b'
:
(
∀
n
af
,
✓
{
n
}
a
→
a
≡
{
n
}
≡
a'
⋅
af
→
b
≡
{
n
}
≡
b'
⋅
af
∧
✓
{
n
}
b
)
→
auth_step
a
a'
b
b'
→
●
a
⋅
◯
a'
~~>
●
b
⋅
◯
b'
.
Proof
.
move
=>
Hab
[[?
]
bf1
]
n
//
=>[[
bf2
Ha
]
?]
;
do
2
red
;
simpl
in
*.
...
...
program_logic/auth.v
View file @
0b7e25c2
...
...
@@ 58,14 +58,8 @@ Section auth.
by
rewrite
sep_elim_l
.
Qed
.
(* TODO: This notion should probably be defined in algebra/,
with instances proven for the important constructions. *)
Definition
auth_step
a
b
:
=
(
∀
n
a'
af
,
✓
{
n
}
(
a
⋅
a'
)
→
a
⋅
a'
≡
{
n
}
≡
af
⋅
a
→
b
⋅
a'
≡
{
n
}
≡
b
⋅
af
∧
✓
{
n
}
(
b
⋅
a'
)).
Lemma
auth_closing
a
a'
b
γ
:
auth_step
a
b
→
auth_step
(
a
⋅
a'
)
a
(
b
⋅
a'
)
b
→
(
φ
(
b
⋅
a'
)
★
own
AuthI
γ
(
●
(
a
⋅
a'
)
⋅
◯
a
))
⊑
pvs
N
N
(
auth_inv
γ
★
auth_own
γ
b
).
Proof
.
...
...
@@ 73,8 +67,7 @@ Section auth.
rewrite
[(
_
★
φ
_
)%
I
]
commutative

associative
.
rewrite

pvs_frame_l
.
apply
sep_mono
;
first
done
.
rewrite

own_op
.
apply
own_update
.
apply
auth_update
=>
n
af
Ha
Heq
.
apply
Hstep
;
first
done
.
by
rewrite
[
af
⋅
_
]
commutative
.
by
apply
auth_update
.
Qed
.
End
auth
.
...
...
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