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a6f31142
Commit
a6f31142
authored
Jan 25, 2016
by
Ralf Jung
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strengthen adequacy: allow ownership of an arbitrary valid ghost in the beginning
parent
951d8927
Changes
2
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2 changed files
with
34 additions
and
21 deletions
+34
-21
iris/adequacy.v
iris/adequacy.v
+30
-18
iris/wsat.v
iris/wsat.v
+4
-3
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iris/adequacy.v
View file @
a6f31142
...
...
@@ -63,46 +63,58 @@ Proof.
apply
Hht
with
r1
(
k
+
n
)
;
eauto
using
@
ra_included_unit
.
by
destruct
(
k
+
n
).
Qed
.
Theorem
ht_adequacy_result
E
φ
e
v
t2
σ
1
σ
2
:
{{
ownP
σ
1
}}
e
@
E
{{
λ
v'
,
■
φ
v'
}}
→
Lemma
ht_adequacy_own
Q
e1
t2
σ
1
m
σ
2
:
✓
m
→
{{
ownP
σ
1
★
ownG
m
}}
e1
@
coPset_all
{{
Q
}}
→
rtc
step
([
e1
],
σ
1
)
(
t2
,
σ
2
)
→
∃
rs2
Qs'
,
wptp
3
t2
((
λ
v
,
pvs
coPset_all
coPset_all
(
Q
v
))
::
Qs'
)
rs2
∧
wsat
3
coPset_all
σ
2
(
big_op
rs2
).
Proof
.
intros
Hv
?
[
k
?]%
rtc_nsteps
.
eapply
ht_adequacy_steps
with
(
r1
:
=
(
Res
∅
(
Excl
σ
1
)
m
))
;
eauto
;
[|].
-
by
rewrite
Nat
.
add_comm
;
apply
wsat_init
,
cmra_valid_validN
.
-
exists
(
Res
∅
(
Excl
σ
1
)
∅
),
(
Res
∅
∅
m
).
split_ands
.
+
by
rewrite
/
op
/
cmra_op
/=
/
res_op
/=
!
ra_empty_l
ra_empty_r
.
+
by
rewrite
/
uPred_holds
/=.
+
by
apply
ownG_spec
.
Qed
.
Theorem
ht_adequacy_result
E
φ
e
v
t2
σ
1
m
σ
2
:
✓
m
→
{{
ownP
σ
1
★
ownG
m
}}
e
@
E
{{
λ
v'
,
■
φ
v'
}}
→
rtc
step
([
e
],
σ
1
)
(
of_val
v
::
t2
,
σ
2
)
→
φ
v
.
Proof
.
intros
?
[
k
?]%
rtc_nstep
s
.
destruct
(
ht_adequacy_
steps
(
ownP
σ
1
)
(
λ
v'
,
■
φ
v'
)%
I
k
2
e
(
of_val
v
::
t2
)
σ
1
σ
2
(
Res
∅
(
Excl
σ
1
)
∅
))
as
(
rs2
&
Qs
&
Hwptp
&?)
;
auto
.
intros
Hv
?
H
s
.
destruct
(
ht_adequacy_
own
(
λ
v'
,
■
φ
v'
)%
I
e
(
of_val
v
::
t2
)
σ
1
m
σ
2
)
as
(
rs2
&
Qs
&
Hwptp
&?)
;
auto
.
{
by
rewrite
-(
ht_mask_weaken
E
coPset_all
).
}
{
rewrite
Nat
.
add_comm
;
apply
wsat_init
.
}
{
by
rewrite
/
uPred_holds
/=.
}
inversion
Hwptp
as
[|??
r
??
rs
Hwp
_
]
;
clear
Hwptp
;
subst
.
apply
wp_value_inv
in
Hwp
;
destruct
(
Hwp
(
big_op
rs
)
2
∅
σ
2
)
as
[
r'
[]]
;
auto
.
apply
wp_value_inv
in
Hwp
;
destruct
(
Hwp
(
big_op
rs
)
3
∅
σ
2
)
as
[
r'
[]]
;
auto
.
by
rewrite
right_id_L
.
Qed
.
Lemma
ht_adequacy_reducible
E
Q
e1
e2
t2
σ
1
σ
2
:
{{
ownP
σ
1
}}
e1
@
E
{{
Q
}}
→
Lemma
ht_adequacy_reducible
E
Q
e1
e2
t2
σ
1
m
σ
2
:
✓
m
→
{{
ownP
σ
1
★
ownG
m
}}
e1
@
E
{{
Q
}}
→
rtc
step
([
e1
],
σ
1
)
(
t2
,
σ
2
)
→
e2
∈
t2
→
to_val
e2
=
None
→
reducible
e2
σ
2
.
Proof
.
intros
?
[
k
?]%
rtc_nsteps
[
i
?]%
elem_of_list_lookup
He
.
destruct
(
ht_adequacy_steps
(
ownP
σ
1
)
Q
k
3 e1
t2
σ
1
σ
2
(
Res
∅
(
Excl
σ
1
)
∅
))
as
(
rs2
&
Qs
&?&?)
;
auto
.
intros
Hv
?
Hs
[
i
?]%
elem_of_list_lookup
He
.
destruct
(
ht_adequacy_own
Q
e1
t2
σ
1
m
σ
2
)
as
(
rs2
&
Qs
&?&?)
;
auto
.
{
by
rewrite
-(
ht_mask_weaken
E
coPset_all
).
}
{
rewrite
Nat
.
add_comm
;
apply
wsat_init
.
}
{
by
rewrite
/
uPred_holds
/=.
}
destruct
(
Forall3_lookup_l
(
λ
e
Q
r
,
wp
coPset_all
e
Q
3
r
)
t2
(
pvs
coPset_all
coPset_all
∘
Q
::
Qs
)
rs2
i
e2
)
as
(
Q'
&
r2
&?&?&
Hwp
)
;
auto
.
destruct
(
wp_step_inv
coPset_all
∅
Q'
e2
2
3
σ
2
r2
(
big_op
(
delete
i
rs2
)))
;
rewrite
?right_id_L
?big_op_delete
;
auto
.
Qed
.
Theorem
ht_adequacy_safe
E
Q
e1
t2
σ
1
σ
2
:
{{
ownP
σ
1
}}
e1
@
E
{{
Q
}}
→
Theorem
ht_adequacy_safe
E
Q
e1
t2
σ
1
m
σ
2
:
✓
m
→
{{
ownP
σ
1
★
ownG
m
}}
e1
@
E
{{
Q
}}
→
rtc
step
([
e1
],
σ
1
)
(
t2
,
σ
2
)
→
Forall
(
λ
e
,
is_Some
(
to_val
e
))
t2
∨
∃
t3
σ
3
,
step
(
t2
,
σ
2
)
(
t3
,
σ
3
).
Proof
.
intros
.
destruct
(
decide
(
Forall
(
λ
e
,
is_Some
(
to_val
e
))
t2
))
as
[|
Ht2
]
;
[
by
left
|].
apply
(
not_Forall_Exists
_
),
Exists_exists
in
Ht2
;
destruct
Ht2
as
(
e2
&?&
He2
).
destruct
(
ht_adequacy_reducible
E
Q
e1
e2
t2
σ
1
σ
2
)
as
(
e3
&
σ
3
&
ef
&?)
;
destruct
(
ht_adequacy_reducible
E
Q
e1
e2
t2
σ
1
m
σ
2
)
as
(
e3
&
σ
3
&
ef
&?)
;
rewrite
?eq_None_not_Some
;
auto
.
destruct
(
elem_of_list_split
t2
e2
)
as
(
t2'
&
t2''
&->)
;
auto
.
right
;
exists
(
t2'
++
e3
::
t2''
++
option_list
ef
),
σ
3
;
econstructor
;
eauto
.
...
...
iris/wsat.v
View file @
a6f31142
...
...
@@ -63,11 +63,12 @@ Proof.
destruct
n
;
[
intros
;
apply
cmra_valid_0
|
intros
[
rs
?]].
eapply
cmra_valid_op_l
,
wsat_pre_valid
;
eauto
.
Qed
.
Lemma
wsat_init
k
E
σ
:
wsat
(
S
k
)
E
σ
(
Res
∅
(
Excl
σ
)
∅
).
Lemma
wsat_init
k
E
σ
m
:
✓
{
S
k
}
m
→
wsat
(
S
k
)
E
σ
(
Res
∅
(
Excl
σ
)
m
).
Proof
.
exists
∅
;
constructor
;
auto
.
intros
Hv
.
exists
∅
;
constructor
;
auto
.
*
rewrite
big_opM_empty
right_id
.
split_ands'
;
try
(
apply
cmra_valid_validN
,
ra_empty_valid
)
;
constructor
.
split_ands'
;
try
(
apply
cmra_valid_validN
,
ra_empty_valid
)
;
constructor
||
apply
Hv
.
*
by
intros
i
;
rewrite
lookup_empty
=>-[??].
*
intros
i
P
?
;
rewrite
/=
(
left_id
_
_
)
lookup_empty
;
inversion_clear
1
.
Qed
.
...
...
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