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Dan Frumin
ReLoC-v1
Commits
d0a6e8d0
Commit
d0a6e8d0
authored
Jan 15, 2018
by
Dan Frumin
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Use the most general rule for FAI in the ticket lock proof
parent
b3b1911c
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1
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theories/tests/relatomic.v
theories/tests/relatomic.v
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theories/tests/relatomic.v
View file @
d0a6e8d0
...
...
@@ -71,9 +71,9 @@ Section contents.
Lemma
FAI_atomic
R1
R2
Γ
E1
E2
K
x
t
τ
Δ
:
R2
-
∗
□
(
|={
E1
,
E2
}=>
∃
n
:
nat
,
x
↦ᵢ
#
n
∗
R1
n
∗
(
x
↦ᵢ
#
n
∗
R1
n
={
E2
,
E1
}=
∗
True
)
∧
(
x
↦ᵢ
#(
S
n
)
∗
R1
n
-
∗
R2
-
∗
{
E2
,
E1
;
Δ
;
Γ
}
⊨
fill
K
#
n
≤
log
≤
t
:
τ
))
(
(
∃
(
m
:
nat
),
x
↦ᵢ
#
m
∗
R1
m
)
={
E2
,
E1
}=
∗
True
)
∧
(
∀
m
,
x
↦ᵢ
#(
S
m
)
∗
R1
m
-
∗
R2
-
∗
{
E2
,
E1
;
Δ
;
Γ
}
⊨
fill
K
#
m
≤
log
≤
t
:
τ
))
-
∗
(
{
E1
;
Δ
;
Γ
}
⊨
fill
K
(
FAI
#
x
)
≤
log
≤
t
:
τ
).
Proof
.
iIntros
"HR2 #H"
.
...
...
@@ -87,7 +87,7 @@ Section contents.
iExists
#
n
.
iFrame
.
iNext
.
iIntros
"Hx"
.
iDestruct
"Hrev"
as
"[Hrev _]"
.
iMod
(
"Hrev"
with
"[HR Hx]"
)
as
"_"
.
{
by
iFrame
.
}
{
iExists
_.
by
iFrame
.
}
rel_rec_l
.
rel_op_l
.
rel_cas_l_atomic
.
iMod
"H"
as
(
n
'
)
"[Hx [HR HQ]]"
.
iModIntro
.
...
...
@@ -104,7 +104,7 @@ Section contents.
rel_if_l
.
iDestruct
"HQ"
as
"[HQ _]"
.
iMod
(
"HQ"
with
"[Hx HR]"
)
as
"_"
.
{
by
iFrame
.
}
{
iExists
_.
by
iFrame
.
}
unlock
FAI
.
by
iApply
"IH"
.
Qed
.
...
...
@@ -225,7 +225,7 @@ Section contents.
rel_let_l
.
repeat
rel_proj_l
.
(
*
rel_apply_l
(
FAI_atomic
).
*
)
rel_bind_l
(
FAI
#
ln
).
iApply
(
FAI_atomic
(
fun
_
=>
True
)
%
I
True
%
I
);
first
done
.
iApply
(
FAI_atomic
(
fun
n
=>
own
γ
(
●
GSet
(
seq_set
0
n
))
)
%
I
True
%
I
);
first
done
.
iAlways
.
iInv
N
as
(
P
)
"[>HP Hpool]"
"Hcl"
.
iDestruct
(
lockPool_lookup
with
"HP Hls"
)
as
%
Hls
.
...
...
@@ -233,17 +233,15 @@ Section contents.
rewrite
{
1
}/
lockInv
.
iDestruct
"Hlk"
as
(
o
n
b
)
"(>Hlo & >Hln & >Hseq & Hl' & Hrest)"
.
iModIntro
.
iExists
_
;
iFrame
.
iSplitR
;
first
done
.
iSplit
.
-
iIntros
"[Hln ?]"
.
iMod
(
"Hcl"
with
"[-]"
)
as
"_"
.
{
iNext
.
iExists
P
;
iFrame
.
iApply
"Hpool"
.
iExists
_
,
_
,
_
;
iFrame
.
iFrame
"Hrest"
.
}
done
.
-
iIntros
"[Hln ?] _"
.
-
iDestruct
1
as
(
m
)
"[Hln ?]"
.
iApply
(
"Hcl"
with
"[-]"
).
iNext
.
iExists
P
;
iFrame
.
iApply
"Hpool"
.
iExists
_
,
_
,
_
;
by
iFrame
.
-
iIntros
(
m
)
"[Hln Hseq] _"
.
iMod
(
own_update
with
"Hseq"
)
as
"[Hseq Hticket]"
.
{
eapply
auth_update_alloc
.
eapply
(
gset_disj_alloc_empty_local_update
_
{
[
n
]
}
).
eapply
(
gset_disj_alloc_empty_local_update
_
{
[
m
]
}
).
apply
(
seq_set_S_disjoint
0
).
}
rewrite
-
(
seq_set_S_union_L
0
).
iMod
(
"Hcl"
with
"[-Hticket]"
)
as
"_"
.
...
...
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