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68445e22
Commit
68445e22
authored
Sep 12, 2016
by
Zhen Zhang
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better spec
parent
b9c66be3
Changes
1
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1 changed file
with
63 additions
and
9 deletions
+63
9
treiber_stack.v
treiber_stack.v
+63
9
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treiber_stack.v
View file @
68445e22
...
...
@@ 27,7 +27,7 @@ Definition pop: val :=
end
.
Section
proof
.
Context
`
{!
heapG
Σ
}
(
N
:
namespace
)
(
R
:
val
→
iProp
Σ
)
`
{
∀
v
,
TimelessP
(
R
v
)}
.
Context
`
{!
heapG
Σ
}
(
N
:
namespace
)
(
R
:
val
→
iProp
Σ
).
Fixpoint
is_stack'
(
hd
:
loc
)
(
xs
:
list
val
)
:
iProp
Σ
:
=
match
xs
with
...
...
@@ 35,9 +35,50 @@ Section proof.

x
::
xs
=>
(
∃
(
hd'
:
loc
)
q
,
hd
↦
{
q
}
SOMEV
(
x
,
#
hd'
)
★
□
R
x
★
is_stack'
hd'
xs
)%
I
end
.
Definition
is_stack
(
s
:
loc
)
xs
:
iProp
Σ
:
=
(
∃
hd
:
loc
,
s
↦
#
hd
★
is_stack'
hd
xs
)%
I
.
(* how can we prove that it is persistent? *)
Lemma
dup_is_stack'
:
∀
xs
hd
,
heap_ctx
★
is_stack'
hd
xs
⊢
is_stack'
hd
xs
★
is_stack'
hd
xs
.
Proof
.
induction
xs
as
[
y
xs'
IHxs'
].

iIntros
(
hd
)
"(#? & Hs)"
.
simpl
.
iDestruct
"Hs"
as
(
q
)
"[Hhd Hhd']"
.
iSplitL
"Hhd"
;
eauto
.

iIntros
(
hd
)
"(#? & Hs)"
.
simpl
.
iDestruct
"Hs"
as
(
hd'
q
)
"([Hhd Hhd'] & #HR & Hs')"
.
iDestruct
(
IHxs'
with
"[Hs']"
)
as
"[Hs1 Hs2]"
;
first
by
iFrame
.
iSplitL
"Hhd Hs1"
;
iExists
hd'
,
(
q
/
2
)%
Qp
;
by
iFrame
.
Qed
.
Definition
is_some_stack
(
s
:
loc
)
:
iProp
Σ
:
=
(
∃
xs
,
is_stack
s
xs
)%
I
.
Lemma
uniq_is_stack'
:
∀
xs
ys
hd
,
heap_ctx
★
is_stack'
hd
xs
★
is_stack'
hd
ys
⊢
xs
=
ys
.
Proof
.
induction
xs
as
[
x
xs'
IHxs'
].

induction
ys
as
[
y
ys'
IHys'
].
+
auto
.
+
iIntros
(
hd
)
"(#? & Hxs & Hys)"
.
simpl
.
iDestruct
"Hys"
as
(
hd'
?)
"(Hhd & #Hy & Hys')"
.
iExFalso
.
iDestruct
"Hxs"
as
(?)
"Hhd'"
.
iDestruct
(
heap_mapsto_op_1
with
"[Hhd Hhd']"
)
as
"[% _]"
.
{
iSplitL
"Hhd"
;
done
.
}
done
.

induction
ys
as
[
y
ys'
IHys'
].
+
iIntros
(
hd
)
"(#? & Hxs & Hys)"
.
simpl
.
iExFalso
.
iDestruct
"Hxs"
as
(?
?)
"(Hhd & _ & _)"
.
iDestruct
"Hys"
as
(?)
"Hhd'"
.
iDestruct
(
heap_mapsto_op_1
with
"[Hhd Hhd']"
)
as
"[% _]"
.
{
iSplitL
"Hhd"
;
done
.
}
done
.
+
iIntros
(
hd
)
"(#? & Hxs & Hys)"
.
simpl
.
iDestruct
"Hxs"
as
(?
?)
"(Hhd & _ & Hxs')"
.
iDestruct
"Hys"
as
(?
?)
"(Hhd' & _ & Hys')"
.
iDestruct
(
heap_mapsto_op_1
with
"[Hhd Hhd']"
)
as
"[% _]"
.
{
iSplitL
"Hhd"
;
done
.
}
inversion
H3
.
(* FIXME: name *)
subst
.
iDestruct
(
IHxs'
with
"[Hxs' Hys']"
)
as
"%"
;
first
by
iFrame
.
by
subst
.
Qed
.
Definition
is_stack
(
s
:
loc
)
xs
:
iProp
Σ
:
=
(
∃
hd
:
loc
,
s
↦
#
hd
★
is_stack'
hd
xs
)%
I
.
Lemma
new_stack_spec
:
∀
(
Φ
:
val
→
iProp
Σ
),
...
...
@@ 87,8 +128,8 @@ Section proof.
Definition
pop_triple
(
s
:
loc
)
:
=
atomic_triple
(
fun
xs
=>
is_stack
s
xs
)%
I
(
fun
xs
ret
=>
(
ret
=
NONEV
∧
xs
=
[]
∧
is_stack
s
[])
∨
(
∃
x
,
ret
=
SOMEV
x
★
□
R
x
))%
I
(* FIXME: we can give a stronger one *)
(
fun
xs
ret
=>
(
ret
=
NONEV
★
xs
=
[]
★
is_stack
s
[])
∨
(
∃
x
xs'
,
ret
=
SOMEV
x
★
□
R
x
★
xs
=
x
::
xs'
★
is_stack
s
xs'
))%
I
(
nclose
heapN
)
⊤
(
pop
#
s
).
...
...
@@ 113,16 +154,30 @@ Section proof.
iVsIntro
.
by
iExists
[].

simpl
.
iDestruct
"Hxs"
as
(
hd
)
"[Hs Hhd]"
.
simpl
.
iDestruct
"Hhd"
as
(
hd'
q
)
"([Hhd Hhd'] & #Hy' & Hxs')"
.
iDestruct
(
dup_is_stack'
with
"[Hxs']"
)
as
"[Hxs1 Hxs2]"
;
first
by
iFrame
.
wp_load
.
iDestruct
"Hvs'"
as
"[Hvs' _]"
.
iVs
(
"Hvs'"
with
"[Hhd]"
)
as
"HP"
.
iVs
(
"Hvs'"
with
"[Hhd
Hxs1
]"
)
as
"HP"
.
{
iExists
hd
.
iFrame
.
iExists
hd'
,
(
q
/
2
)%
Qp
.
by
iFrame
.
}
iVsIntro
.
wp_let
.
wp_load
.
wp_match
.
wp_proj
.
wp_bind
(
CAS
_
_
_
).
iVs
(
"Hvs"
with
"HP"
)
as
(
xs
)
"[Hxs Hvs']"
.
iDestruct
"Hxs"
as
(
hd''
)
"[Hs Hhd'']"
.
destruct
(
decide
(
hd
=
hd''
))
as
[>
Hneq
].
+
wp_cas_suc
.
iDestruct
"Hvs'"
as
"[_ Hvs']"
.
iVs
(
"Hvs'"
$!
(
SOMEV
y'
)
with
"[]"
)
as
"HQ"
.
{
iRight
.
eauto
.
}
iVs
(
"Hvs'"
$!
(
SOMEV
y'
)
with
"[]"
)
as
"HQ"
.
{
iRight
.
rewrite
/
is_stack
.
iExists
y'
,
xs'
.
destruct
xs
as
[
x'
xs''
].

simpl
.
iDestruct
"Hhd''"
as
(?)
"H"
.
iExFalso
.
iDestruct
(
heap_mapsto_op_1
with
"[Hhd H]"
)
as
"[% _]"
.
{
iSplitL
"Hhd"
;
done
.
}
done
.

simpl
.
iDestruct
"Hhd''"
as
(
hd'''
?)
"(Hhd'' & _ & Hxs'')"
.
iDestruct
(
heap_mapsto_op_1
with
"[Hhd Hhd'']"
)
as
"[% _]"
.
{
iSplitL
"Hhd"
;
done
.
}
inversion
H0
.
(* FIXME: bad naming *)
subst
.
iDestruct
(
uniq_is_stack'
with
"[Hxs1 Hxs'']"
)
as
"%"
;
first
by
iFrame
.
subst
.
repeat
(
iSplitR
"Hxs1 Hs"
;
first
done
).
iExists
hd'''
.
by
iFrame
.
}
iVsIntro
.
wp_if
.
wp_proj
.
eauto
.
+
wp_cas_fail
.
iDestruct
"Hvs'"
as
"[Hvs' _]"
.
iVs
(
"Hvs'"
with
"[]"
)
as
"HP"
.
...
...
@@ 131,4 +186,3 @@ Section proof.
Qed
.
End
proof
.
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