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Daniël Louwrink
lambda-rust
Commits
e10a713e
Commit
e10a713e
authored
4 years ago
by
Daniël Louwrink
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prove logical disabling lemma
parent
d3d87675
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theories/lang/stbor/stbor_sim.v
+57
-4
57 additions, 4 deletions
theories/lang/stbor/stbor_sim.v
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57 additions
and
4 deletions
theories/lang/stbor/stbor_sim.v
+
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−
4
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e10a713e
...
@@ -481,7 +481,7 @@ Qed.
...
@@ -481,7 +481,7 @@ Qed.
(** * Retagging (SharedRW) extend *)
(** * Retagging (SharedRW) extend *)
(** * Logical popping *)
(** * Logical popping *)
Lemma
pop_prefix
_preserve_tail
stkparsed
stklog1
stklog2
:
Lemma
log_pop
_preserve_tail
stkparsed
stklog1
stklog2
:
stklog2
`
suffix_of
`
stklog1
→
stklog2
`
suffix_of
`
stklog1
→
stack_sub_tail
stklog1
stkparsed
→
stack_sub_tail
stklog1
stkparsed
→
stack_sub_tail
stklog2
stkparsed
.
stack_sub_tail
stklog2
stkparsed
.
...
@@ -506,7 +506,7 @@ Proof.
...
@@ -506,7 +506,7 @@ Proof.
apply
stack_sub_tail_drop_both
.
eapply
IH
.
eassumption
.
apply
stack_sub_tail_drop_both
.
eapply
IH
.
eassumption
.
Qed
.
Qed
.
Lemma
pop_prefix_preserve
stkphys
stklog1
stklog2
:
Lemma
log_
pop_prefix_preserve
stkphys
stklog1
stklog2
:
stklog2
`
suffix_of
`
stklog1
→
stklog2
`
suffix_of
`
stklog1
→
stack_rel_stack
stkphys
stklog1
→
stack_rel_stack
stkphys
stklog1
→
stack_rel_stack
stkphys
stklog2
.
stack_rel_stack
stkphys
stklog2
.
...
@@ -520,12 +520,65 @@ Proof.
...
@@ -520,12 +520,65 @@ Proof.
+
rewrite
-
app_comm_cons
in
Hsuffix
.
inversion
Hsuffix
.
+
rewrite
-
app_comm_cons
in
Hsuffix
.
inversion
Hsuffix
.
eexists
;
split
;
first
apply
Hparse
.
eexists
;
split
;
first
apply
Hparse
.
apply
stack_sub_drop_shared
.
apply
stack_sub_drop_shared
.
eapply
pop_prefix
_preserve_tail
;
last
eassumption
.
eapply
log_pop
_preserve_tail
;
last
eassumption
.
by
exists
stkdead
.
by
exists
stkdead
.
-
eexists
;
split
;
first
apply
Hparse
.
-
eexists
;
split
;
first
apply
Hparse
.
apply
stack_sub_drop_shared
.
apply
stack_sub_drop_shared
.
eapply
pop_prefix
_preserve_tail
;
last
eassumption
.
eapply
log_pop
_preserve_tail
;
last
eassumption
.
by
exists
stkdead
.
by
exists
stkdead
.
Qed
.
Qed
.
(** * Logical disabling *)
(** * Logical disabling *)
Inductive
log_disable_item
:
item
→
item
→
Prop
:=
|
log_disable_item_disable
tg
:
log_disable_item
(
ItUnique
tg
)
ItDisabled
|
log_disable_item_keep
it
:
log_disable_item
it
it
.
Definition
log_disable
(
stk1
stk2
:
stack
)
:
Prop
:=
Forall2
log_disable_item
stk1
stk2
.
Lemma
log_disable_cons_inv_l
it1
stklog1
stklog2
:
log_disable
(
it1
::
stklog1
)
stklog2
→
∃
it2
stklog2'
,
log_disable_item
it1
it2
∧
log_disable
stklog1
stklog2'
∧
stklog2
=
it2
::
stklog2'
.
Proof
.
intros
Hdisable
.
rewrite
/
log_disable
in
Hdisable
.
eapply
Forall2_cons_inv_l
.
apply
Hdisable
.
Qed
.
Lemma
log_disable_preserve_tail
stklog2
stkparsed
stklog1
:
log_disable
stklog1
stklog2
→
stack_sub_tail
stklog1
stkparsed
→
stack_sub_tail
stklog2
stkparsed
.
Proof
.
intros
Hdisable
Hsub
.
generalize
dependent
stklog2
.
induction
Hsub
as
[|?
?
?
?
?
IH
|?
?
?
?
?
Hsubit
?
IH
|?
?
?
?
?
?
?
Hsubit
?
IH
];
intros
stklog2
Hdisable
.
-
inversion
Hdisable
.
apply
stack_sub_tail_empty
.
-
apply
stack_sub_tail_drop_both
.
apply
IH
.
apply
Hdisable
.
-
apply
log_disable_cons_inv_l
in
Hdisable
as
(
it3
&
stklog3
&
Hdisableit
&
Hdisable
&
->
)
.
apply
stack_sub_tail_drop_one
.
{
inversion
Hdisableit
;
subst
;
last
assumption
.
inversion
Hsubit
.
constructor
.
}
apply
IH
.
assumption
.
-
apply
log_disable_cons_inv_l
in
Hdisable
as
(
it3
&
stklog3
&
Hdisableit3
&
Hdisable
&
->
)
.
apply
log_disable_cons_inv_l
in
Hdisable
as
(
it4
&
stklog4
&
Hdisableit4
&
Hdisable
&
->
)
.
inversion
Hdisableit3
;
subst
.
apply
stack_sub_tail_keep
;
first
done
.
{
inversion
Hdisableit4
;
subst
;
last
assumption
.
inversion
Hsubit
.
constructor
.
}
apply
IH
.
assumption
.
Qed
.
Lemma
log_disable_preserve
stklog2
stkphys
stklog1
:
log_disable
stklog1
stklog2
→
stack_rel_stack
stkphys
stklog1
→
stack_rel_stack
stkphys
stklog2
.
Proof
.
intros
Hdisable
(
stkparsed
&
Hparse
&
Hsub
)
.
destruct
Hsub
.
-
eexists
;
split
;
first
apply
Hparse
.
apply
log_disable_cons_inv_l
in
Hdisable
as
(
it3
&
stklog3
&
Hdisableit3
&
Hdisable
&
->
)
.
inversion
Hdisableit3
.
apply
stack_sub_keep_shared
;
first
done
.
by
eapply
log_disable_preserve_tail
.
-
eexists
;
split
;
first
apply
Hparse
.
apply
stack_sub_drop_shared
.
by
eapply
log_disable_preserve_tail
.
Qed
.
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