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Dan Frumin
ReLoC-v1
Commits
16093667
Commit
16093667
authored
May 23, 2016
by
Amin Timany
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Update to work with the newest iris master
parent
a3479c77
Changes
1
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1 changed file
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24 additions
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19 deletions
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-19
F_mu_ref_par/rules_binary.v
F_mu_ref_par/rules_binary.v
+24
-19
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F_mu_ref_par/rules_binary.v
View file @
16093667
...
...
@@ -15,7 +15,7 @@ Section lang_rules.
Global
Instance
tpool_singleton
:
SingletonM
nat
(
fracR
(
dec_agreeR
expr
))
tpoolR
.
Proof
.
typeclasses
eauto
.
Defined
.
Proof
.
eapply
@
list_singletonM
,
frac_empty
.
Defined
.
Global
Instance
tpool_Empty
:
Empty
(
fracR
(
dec_agreeR
expr
)).
Proof
.
apply
frac_empty
.
Defined
.
...
...
@@ -164,9 +164,9 @@ Section lang_rules.
apply
Forall_lookup
=>
i
x
H2
.
destruct
(
eq_nat_dec
j
i
);
[
subst
|
].
-
assert
(
H3
:=
proj1
(
Forall_lookup
_
_
)
H1
i
).
cbn
in
H3
.
rewrite
list_
op_lookup
in
H2
.
rewrite
list_op_looku
p
in
H3
.
rewrite
list_
Singleton_lookup
in
H2
.
rewrite
list_
Singleton_lookup
in
H3
.
rewrite
list_
lookup_op
in
H2
.
rewrite
list_lookup_o
p
in
H3
.
rewrite
list_
lookup_singletonM
in
H2
.
rewrite
list_
lookup_singletonM
in
H3
.
match
goal
with
[
H
:
Some
_
⋅
?
B
=
Some
_
,
H
'
:
forall
x
,
Some
_
⋅
?
B
=
Some
x
→
_
|-
_
]
=>
destruct
B
as
[
y
|
]
...
...
@@ -178,10 +178,10 @@ Section lang_rules.
repeat
constructor
;
auto
.
+
inversion
H2
.
repeat
constructor
;
auto
.
-
assert
(
H3
:=
proj1
(
Forall_lookup
_
_
)
H1
i
).
cbn
in
H3
.
rewrite
list_
op_lookup
in
H2
.
rewrite
list_op_looku
p
in
H3
.
edestruct
(
list_
Singleton_lookup_2
j
i
)
with
rewrite
list_
lookup_op
in
H2
.
rewrite
list_lookup_o
p
in
H3
.
edestruct
(
list_
lookup_singletonM_ne
j
i
)
with
(
Frac
1
(
DecAgree
e
)
:
fracR
(
dec_agreeR
_
))
as
[
H4
|
H4
];
trivial
;
edestruct
(
list_
Singleton_lookup_2
j
i
)
edestruct
(
list_
lookup_singletonM_ne
j
i
)
with
(
Frac
1
(
DecAgree
e
'
)
:
fracR
(
dec_agreeR
_
))
as
[
H5
|
H5
];
trivial
;
rewrite
H4
in
H3
;
rewrite
H5
in
H2
;
match
goal
with
...
...
@@ -245,7 +245,7 @@ Section lang_rules.
Qed
.
Lemma
list_op_units
k
tp
:
of_tpool
(
rep
eat
∅
k
⋅
tp
)
=
of_tpool
tp
.
of_tpool
(
rep
licate
k
∅
⋅
tp
)
=
of_tpool
tp
.
Proof
.
revert
k
;
induction
tp
as
[
|
x
tp
]
=>
k
.
-
destruct
k
;
simpl
;
trivial
.
induction
k
;
simpl
;
trivial
.
...
...
@@ -253,6 +253,11 @@ Section lang_rules.
destruct
x
;
simpl
;
[
|
apply
IHtp
].
rewrite
IHtp
;
trivial
.
Qed
.
Local
Ltac
rewrite_list_lemma
L
:=
let
W
:=
fresh
in
set
(
W
:=
L
);
unfold
op
,
cmra_op
in
W
;
simpl
in
W
;
rewrite
W
;
clear
W
.
Lemma
tpool_conv
j
e
tp
:
✓
(
{
[
j
:=
(
Frac
1
(
DecAgree
e
:
dec_agreeR
_
))
]
}
⋅
tp
)
→
∃
l1
l2
,
(
∀
e
'
,
of_tpool
(
{
[
j
:=
(
Frac
1
(
DecAgree
e
'
:
dec_agreeR
_
))
]
}
⋅
tp
)
...
...
@@ -268,7 +273,7 @@ Section lang_rules.
-
exists
[];
exists
[];
split
.
+
intros
e
'
.
clear
H
.
induction
j
;
simpl
;
trivial
;
simpl
in
*
.
rewrite
list_op_nil
in
IHj
;
trivial
.
rewrite
->
cmra_comm
in
IHj
;
trivial
.
+
intros
e
'
k
e
''
H1
H2
;
simpl
in
*
.
replace
[]
with
(
∅
:
tpoolR
)
by
trivial
;
rewrite
right_id
.
apply
of_tpool_2_singletons
;
auto
with
omega
.
...
...
@@ -278,10 +283,10 @@ Section lang_rules.
*
intros
e
'
;
simpl
;
trivial
.
*
intros
e
'
k
e
''
Hc1
Hc2
.
destruct
k
;
auto
with
omega
.
simpl
;
apply
(
f_equal
(
cons
_
)).
set
(
W
:=
@
list_op_app
);
unfold
op
,
cmra_op
in
W
;
simpl
in
W
;
rewrite
W
;
clear
W
.
rewrite
of_tpool_app
list_op_units
;
trivial
.
rewrite
rep
eat
_length
.
unfold
op
,
cmra_op
.
rewrite_list_lemma
@
list_op_app
.
rewrite_list_lemma
of_tpool_app
.
rewrite
list_op_units
;
trivial
.
rewrite
rep
licate
_length
.
match
type
of
Hc2
with
_
>
S
?
A
=>
match
goal
with
(
*
A
and
B
are
convertible
!
*
)
...
...
@@ -312,13 +317,13 @@ Section lang_rules.
intros
H
.
replace
(
{
[
j
:=
Frac
1
(
DecAgree
e
'
)]
}
:
tpoolR
)
with
(
alter
(
λ
_
:
fracR
(
dec_agreeR
expr
),
Frac
1
(
DecAgree
e
'
))
j
{
[
j
:=
Frac
1
(
DecAgree
e
)]
}
)
by
(
by
rewrite
list_alter_singleton
).
{
[
j
:=
Frac
1
(
DecAgree
e
)]
}
)
by
(
by
rewrite
list_alter_singleton
M
).
apply
(
@
auth_local_update_l
_
_
_
_
_
(
@
prod_LocalUpdate
_
heapR
_
_
_
_
_
(
local_update_id
))).
-
split
;
trivial
.
eexists
(
Frac
1
_
);
by
rewrite
list_
Singleton_lookup
;
split
.
-
simpl
.
rewrite
list_alter_singleton
.
by
rewrite
list_
lookup_singletonM
;
split
.
-
simpl
.
rewrite
list_alter_singleton
M
.
inversion
H
;
constructor
;
simpl
in
*
;
trivial
.
eapply
tpool_update_valid
;
eauto
.
Qed
.
...
...
@@ -334,9 +339,9 @@ Section lang_rules.
List
.
length
{
[
j
:=
Frac
1
(
DecAgree
e
)]
}
=
S
j
.
Proof
.
induction
j
;
simpl
;
eauto
with
f_equal
.
Qed
.
Lemma
tpool_valid_units
j
:
✓
(
rep
eat
∅
j
).
Lemma
tpool_valid_units
j
:
✓
(
rep
licate
j
∅
).
Proof
.
induction
j
;
repeat
constructor
;
auto
.
Qed
.
Lemma
tpool_valid_prepend_units_valid
j
th
:
✓
th
→
✓
(
rep
eat
∅
j
⋅
th
).
Lemma
tpool_valid_prepend_units_valid
j
th
:
✓
th
→
✓
(
rep
licate
j
∅
⋅
th
).
Proof
.
revert
th
;
induction
j
=>
th
H
.
-
destruct
th
;
inversion
H
;
constructor
;
trivial
.
...
...
@@ -360,7 +365,7 @@ Section lang_rules.
rewrite
list_op_app
.
-
apply
Forall_app
;
split
;
[
|
repeat
constructor
;
auto
].
apply
tpool_valid_prepend_units_valid
;
trivial
.
-
rewrite
list_op_length
tpool_singleton_length
rep
eat
_length
.
lia
.
-
rewrite
list_op_length
tpool_singleton_length
rep
licate
_length
.
lia
.
Qed
.
Lemma
thread_alloc_update
k
j
e
e
'
h
ρ
:
...
...
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