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5fb53667
Commit
5fb53667
authored
Feb 02, 2016
by
Robbert Krebbers
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barrier/heap_lang.v
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barrier/heap_lang.v
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5fb53667
...
...
@@ -208,6 +208,7 @@ Proof.
Qed
.
Instance:
Injective
(
=
)
(
=
)
of_val
.
Proof
.
by
intros
??
Hv
;
apply
(
injective
Some
);
rewrite
-!
to_of_val
Hv
.
Qed
.
Instance
ectx_item_fill_inj
Ki
:
Injective
(
=
)
(
=
)
(
ectx_item_fill
Ki
).
Proof
.
destruct
Ki
;
intros
???
;
simplify_equality
'
;
auto
with
f_equal
.
Qed
.
Instance
ectx_fill_inj
K
:
Injective
(
=
)
(
=
)
(
fill
K
).
...
...
@@ -221,11 +222,13 @@ Proof.
Qed
.
Lemma
fill_not_val
K
e
:
to_val
e
=
None
→
to_val
(
fill
K
e
)
=
None
.
Proof
.
rewrite
!
eq_None_not_Some
;
eauto
using
fill_val
.
Qed
.
Lemma
values_head_stuck
e1
σ
1
e2
σ
2
ef
:
head_step
e1
σ
1
e2
σ
2
ef
→
to_val
e1
=
None
.
Proof
.
destruct
1
;
naive_solver
.
Qed
.
Lemma
values_stuck
e1
σ
1
e2
σ
2
ef
:
prim_step
e1
σ
1
e2
σ
2
ef
→
to_val
e1
=
None
.
Proof
.
intros
[
???
->
->
?
];
eauto
using
fill_not_val
,
values_head_stuck
.
Qed
.
Lemma
atomic_not_val
e
:
atomic
e
→
to_val
e
=
None
.
Proof
.
destruct
e
;
naive_solver
.
Qed
.
Lemma
atomic_fill
K
e
:
atomic
(
fill
K
e
)
→
to_val
e
=
None
→
K
=
[].
...
...
@@ -243,9 +246,11 @@ Proof.
assert
(
K
=
[])
as
->
by
eauto
10
using
atomic_fill
,
values_head_stuck
.
naive_solver
eauto
using
atomic_head_step
.
Qed
.
Lemma
head_ctx_step_val
Ki
e
σ
1
e2
σ
2
ef
:
head_step
(
ectx_item_fill
Ki
e
)
σ
1
e2
σ
2
ef
→
is_Some
(
to_val
e
).
Proof
.
destruct
Ki
;
inversion_clear
1
;
simplify_option_equality
;
eauto
.
Qed
.
Lemma
fill_item_inj
Ki1
Ki2
e1
e2
:
to_val
e1
=
None
→
to_val
e2
=
None
→
ectx_item_fill
Ki1
e1
=
ectx_item_fill
Ki2
e2
→
Ki1
=
Ki2
.
...
...
@@ -270,6 +275,7 @@ Proof.
cut
(
Ki
=
Ki
'
);
[
naive_solver
eauto
using
prefix_of_cons
|
].
eauto
using
fill_item_inj
,
values_head_stuck
,
fill_not_val
.
Qed
.
Lemma
alloc_fresh
e
v
σ
:
let
l
:=
fresh
(
dom
_
σ
)
in
to_val
e
=
Some
v
→
head_step
(
Alloc
e
)
σ
(
Loc
l
)
(
<
[
l
:=
v
]
>
σ
)
None
.
...
...
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