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Simon Spies
examples
Commits
30b963ae
Commit
30b963ae
authored
Mar 07, 2018
by
Ralf Jung
Browse files
update concurrent_stack4
parent
8cd27e65
Changes
1
Hide whitespace changes
Inline
Sidebyside
theories/concurrent_stacks/concurrent_stack4.v
View file @
30b963ae
...
...
@@ 2,7 +2,7 @@ From iris.program_logic Require Export weakestpre hoare.
From
iris
.
heap_lang
Require
Export
lang
proofmode
notation
.
From
iris
.
algebra
Require
Import
excl
.
(** Stack
4
:
With h
elping,
(weak)
viewshift spec. *)
(** Stack
3
:
H
elping, viewshift spec. *)
Definition
mk_offer
:
val
:
=
λ
:
"v"
,
(
"v"
,
ref
#
0
).
...
...
@@ 67,7 +67,7 @@ Section side_channel.
Implicit
Types
l
:
loc
.
Definition
stages
γ
(
P
:
list
val
→
iProp
Σ
)
(
Q
:
iProp
Σ
)
l
(
v
:
val
)
:
=
((
l
↦
#
0
∗
(
∀
vs
,
P
vs
==
∗
P
(
v
::
vs
)
∗
Q
))
((
l
↦
#
0
∗
(
∀
vs
,
P
vs
=
{
⊤
∖
↑
N
}
=
∗
P
(
v
::
vs
)
∗
Q
))
∨
(
l
↦
#
1
∗
Q
)
∨
(
l
↦
#
1
∗
own
γ
(
Excl
()))
∨
(
l
↦
#
2
∗
own
γ
(
Excl
())))%
I
.
...
...
@@ 79,7 +79,7 @@ Section side_channel.
(
∃
l
,
⌜
v
=
#
l
⌝
∗
(
l
↦
NONEV
∨
(
∃
v'
γ
,
l
↦
SOMEV
v'
∗
is_offer
γ
P
Q
v'
)))%
I
.
End
side_channel
.
Section
stack_works
.
Context
`
{!
heapG
Σ
}
(
N
:
namespace
)
.
Context
`
{!
heapG
Σ
}.
Implicit
Types
l
:
loc
.
...
...
@@ 141,29 +141,19 @@ Section stack_works.
injection
H
;
intros
;
subst
;
auto
.
Qed
.
(* Viewshift based holestack invariant (P). However:
 The resources for the successful and failing pop must be disjoint.
Instead, there should be a normal conjunction between them.
 The updating view shifts have the empty mask.
Open question: How does this relate to a logically atomic spec? *)
Theorem
stack_works
{
channelG0
:
channelG
Σ
}
P
Q
Q'
Q''
Φ
:
(* Wholestack invariant (P). *)
Theorem
stack_works
{
channelG0
:
channelG
Σ
}
N
P
Q
Q'
Q''
Φ
:
(
∀
(
f
₁
f
₂
:
val
),
(
□
((
∀
v
vs
,
P
(
v
::
vs
)
==
∗
Q
v
∗
P
vs
)

∗
(
P
[]
==
∗
Q'
∗
P
[])

∗
(
□
((
(
∀
v
vs
,
P
(
v
::
vs
)
=
{
⊤
∖
↑
N
}
=
∗
Q
v
∗
P
vs
)
∧
(
P
[]
=
{
⊤
∖
↑
N
}
=
∗
Q'
∗
P
[])

∗
WP
f
₁
#()
{{
v
,
(
∃
(
v'
:
val
),
v
≡
SOMEV
v'
∗
Q
v'
)
∨
(
v
≡
NONEV
∗
Q'
)}}))

∗
(
∀
(
v
:
val
),
□
((
∀
vs
,
P
vs
==
∗
P
(
v
::
vs
)
∗
Q''
)

∗
WP
f
₂
v
{{
v
,
Q''
}}))
∧
(
∀
(
v
:
val
),
□
((
∀
vs
,
P
vs
=
{
⊤
∖
↑
N
}
=
∗
P
(
v
::
vs
)
∗
Q''
)

∗
WP
f
₂
v
{{
v
,
Q''
}}))
)

∗
Φ
(
f
₁
,
f
₂
)%
V
)%
I

∗
P
[]

∗
WP
mk_stack
#()
{{
Φ
}}.
Proof
.
iIntros
"HΦ HP"
.
(* assert (exists n : namespace, hidden_eq n (nroot .@ "N")) as H *)
(* by (exists (nroot .@ "N"); unfold hidden_eq; auto). *)
(* destruct H as (N, Neq). *)
(* assert (exists n : namespace, hidden_eq n (nroot .@ "N'")) as H *)
(* by (exists (nroot .@ "N'"); unfold hidden_eq; auto). *)
(* destruct H as (N', N'eq). *)
wp_let
.
wp_let
.
wp_alloc
m
as
"Hm"
.
...
...
@@ 179,8 +169,8 @@ Section stack_works.
iMod
(
inv_alloc
(
N
.@
"stack_inv"
)
_
(
stack_inv
P
#
l
)
with
"[Hl HP]"
)
as
"#Istack"
.
{
iNext
;
iExists
l
,
(
InjLV
#()),
[]
;
iSplit
;
iFrame
;
auto
.
}
wp_let
.
iApply
"HΦ"
.

iIntros
"!# H
succ Hfail
"
.
iApply
"HΦ"
;
iSplit
.

iIntros
"!# H
cont
"
.
iL
ö
b
as
"IH"
.
wp_rec
.
wp_rec
.
...
...
@@ 206,7 +196,10 @@ Section stack_works.
+
subst
.
iDestruct
(
is_stack_empty
with
"Hstack"
)
as
"%"
.
subst
.
iMod
(
"Hfail"
with
"HP"
)
as
"[HQ' HP]"
.
iDestruct
"Hcont"
as
"[_ Hfail]"
.
iDestruct
(
"Hfail"
with
"HP"
)
as
"Hfail"
.
iDestruct
(
fupd_mask_mono
with
"Hfail"
)
as
"Hfail"
;
last
iMod
"Hfail"
as
"[HQ' HP]"
;
first
by
solve_ndisj
.
iMod
(
"Hclose"
with
"[Hl' Hstack HP]"
).
{
iExists
l'
,
(
InjLV
#()),
[]
;
iSplit
;
iFrame
;
auto
.
}
iModIntro
.
...
...
@@ 236,7 +229,10 @@ Section stack_works.
iDestruct
"H"
as
(
ys'
)
"%"
;
subst
.
iDestruct
"Hstack"
as
(
t'
)
"[% Hstack]"
.
injection
H4
;
intros
;
subst
.
iDestruct
(
"Hsucc"
with
"[HP]"
)
as
"> [HQ HP]"
;
auto
.
iDestruct
"Hcont"
as
"[Hsucc _]"
.
iDestruct
(
"Hsucc"
with
"HP"
)
as
"Hsucc"
.
iDestruct
(
fupd_mask_mono
with
"Hsucc"
)
as
"Hsucc"
;
last
iMod
"Hsucc"
as
"[HQ HP]"
;
first
by
solve_ndisj
.
iMod
(
"Hclose"
with
"[Hl'' Hstack HP]"
).
{
iExists
l''
,
t'
,
ys'
;
iSplit
;
iFrame
;
auto
.
}
iModIntro
.
...
...
@@ 248,7 +244,7 @@ Section stack_works.
{
iExists
l''
,
v'
,
ys
;
iSplit
;
iFrame
;
auto
.
}
iModIntro
.
wp_if
.
iApply
(
"IH"
with
"H
succ Hfail
"
).
iApply
(
"IH"
with
"H
cont
"
).
*
iDestruct
"H"
as
(
v'
γ
'
)
"[Hm' Hstages]"
.
wp_load
.
iDestruct
"Hstages"
as
(
v''
l'
)
"[% #Hstages]"
.
...
...
@@ 268,8 +264,15 @@ Section stack_works.
iInv
(
N
.@
"stack_inv"
)
as
"Hstack"
"Hclose2"
.
wp_cas_suc
.
iDestruct
"Hstack"
as
(
l''
v'
xs
)
"[% [Hl'' [Hstack HP]]]"
.
iDestruct
(
"Hmove"
with
"HP"
)
as
"> [HP HQ'']"
.
iDestruct
(
"Hsucc"
with
"HP"
)
as
"> [HQ HP]"
.
iDestruct
(
"Hmove"
with
"HP"
)
as
"Hmove"
.
iDestruct
(
fupd_mask_mono
with
"Hmove"
)
as
"Hmove"
;
last
iMod
"Hmove"
as
"[HP HQ'']"
.
{
apply
ndisj_subseteq_difference
;
try
solve_ndisj
.
}
iDestruct
"Hcont"
as
"[Hsucc _]"
.
iDestruct
(
"Hsucc"
with
"HP"
)
as
"Hsucc"
.
iDestruct
(
fupd_mask_mono
with
"Hsucc"
)
as
"Hsucc"
;
last
(
iMod
"Hsucc"
as
"[HQ HP]"
).
{
apply
ndisj_subseteq_difference
;
try
solve_ndisj
.
}
iMod
(
"Hclose2"
with
"[Hl'' Hstack HP]"
).
{
iExists
l''
,
v'
,
xs
;
iSplit
;
iFrame
;
auto
.
}
iModIntro
.
...
...
@@ 301,7 +304,11 @@ Section stack_works.
**
subst
.
iDestruct
(
is_stack_empty
with
"Hstack"
)
as
"%"
.
subst
.
iMod
(
"Hfail"
with
"HP"
)
as
"[HQ' HP]"
.
iDestruct
"Hcont"
as
"[_ Hfail]"
.
iDestruct
(
"Hfail"
with
"HP"
)
as
"Hfail"
.
iDestruct
(
fupd_mask_mono
with
"Hfail"
)
as
"Hfail"
;
last
iMod
"Hfail"
as
"[HQ' HP]"
;
first
by
solve_ndisj
.
iMod
(
"Hclose"
with
"[Hl' Hstack HP]"
).
{
iExists
l''
,
(
InjLV
#()),
[]
;
iSplit
;
iFrame
;
auto
.
}
iModIntro
.
...
...
@@ 328,7 +335,10 @@ Section stack_works.
iDestruct
(
is_stack_cons
with
"Hstack"
)
as
"[Hstack H]"
.
iDestruct
"H"
as
(
ys'
)
"%"
;
subst
.
iDestruct
"Hstack"
as
(
t'
)
"[% Hstack]"
;
simplify_eq
.
iDestruct
(
"Hsucc"
with
"[HP]"
)
as
"> [HQ HP]"
;
auto
.
iDestruct
"Hcont"
as
"[Hsucc _]"
.
iDestruct
(
"Hsucc"
with
"HP"
)
as
"Hsucc"
.
iDestruct
(
fupd_mask_mono
with
"Hsucc"
)
as
"Hsucc"
;
last
iMod
"Hsucc"
as
"[HQ HP]"
;
first
by
solve_ndisj
.
iMod
(
"Hclose"
with
"[Hl''' Hstack HP]"
).
{
iExists
l'''
,
t'
,
ys'
;
iSplit
;
iFrame
;
auto
.
}
iModIntro
.
...
...
@@ 340,7 +350,7 @@ Section stack_works.
{
iExists
l'''
,
v'''
,
ys
;
iSplit
;
iFrame
;
auto
.
}
iModIntro
.
wp_if
.
iApply
(
"IH"
with
"H
succ Hfail
"
).
iApply
(
"IH"
with
"H
cont
"
).
+
iDestruct
"H"
as
"[Hl' Hγ']"
.
wp_cas_fail
.
iMod
(
"Hclose"
with
"[Hl' Hγ']"
).
...
...
@@ 357,7 +367,10 @@ Section stack_works.
**
subst
.
iDestruct
(
is_stack_empty
with
"Hstack"
)
as
"%"
.
subst
.
iMod
(
"Hfail"
with
"HP"
)
as
"[HQ' HP]"
.
iDestruct
"Hcont"
as
"[_ Hfail]"
.
iDestruct
(
"Hfail"
with
"HP"
)
as
"Hfail"
.
iDestruct
(
fupd_mask_mono
with
"Hfail"
)
as
"Hfail"
;
last
iMod
"Hfail"
as
"[HQ HP]"
;
first
by
solve_ndisj
.
iMod
(
"Hclose"
with
"[Hl' Hstack HP]"
).
{
iExists
l''
,
(
InjLV
#()),
[]
;
iSplit
;
iFrame
;
auto
.
}
iModIntro
.
...
...
@@ 384,7 +397,10 @@ Section stack_works.
iDestruct
(
is_stack_cons
with
"Hstack"
)
as
"[Hstack H]"
.
iDestruct
"H"
as
(
ys'
)
"%"
;
subst
.
iDestruct
"Hstack"
as
(
t'
)
"[% Hstack]"
;
simplify_eq
.
iDestruct
(
"Hsucc"
with
"[HP]"
)
as
"> [HQ HP]"
;
auto
.
iDestruct
"Hcont"
as
"[Hsucc _]"
.
iDestruct
(
"Hsucc"
with
"HP"
)
as
"Hsucc"
.
iDestruct
(
fupd_mask_mono
with
"Hsucc"
)
as
"Hsucc"
;
last
iMod
"Hsucc"
as
"[HQ HP]"
;
first
by
solve_ndisj
.
iMod
(
"Hclose"
with
"[Hl''' Hstack HP]"
).
{
iExists
l'''
,
t'
,
ys'
;
iSplit
;
iFrame
;
auto
.
}
iModIntro
.
...
...
@@ 396,7 +412,7 @@ Section stack_works.
{
iExists
l'''
,
v'''
,
ys
;
iSplit
;
iFrame
;
auto
.
}
iModIntro
.
wp_if
.
iApply
(
"IH"
with
"H
succ Hfail
"
).
iApply
(
"IH"
with
"H
cont
"
).
+
iDestruct
"H"
as
"[Hl' Hγ']"
.
wp_cas_fail
.
...
...
@@ 414,7 +430,10 @@ Section stack_works.
**
subst
.
iDestruct
(
is_stack_empty
with
"Hstack"
)
as
"%"
.
subst
.
iMod
(
"Hfail"
with
"HP"
)
as
"[HQ' HP]"
.
iDestruct
"Hcont"
as
"[_ Hfail]"
.
iDestruct
(
"Hfail"
with
"HP"
)
as
"Hfail"
.
iDestruct
(
fupd_mask_mono
with
"Hfail"
)
as
"Hfail"
;
last
iMod
"Hfail"
as
"[HQ HP]"
;
first
by
solve_ndisj
.
iMod
(
"Hclose"
with
"[Hl' Hstack HP]"
).
{
iExists
l''
,
(
InjLV
#()),
[]
;
iSplit
;
iFrame
;
auto
.
}
iModIntro
.
...
...
@@ 441,7 +460,10 @@ Section stack_works.
iDestruct
(
is_stack_cons
with
"Hstack"
)
as
"[Hstack H]"
.
iDestruct
"H"
as
(
ys'
)
"%"
;
subst
.
iDestruct
"Hstack"
as
(
t'
)
"[% Hstack]"
;
simplify_eq
.
iDestruct
(
"Hsucc"
with
"[HP]"
)
as
"> [HQ HP]"
;
auto
.
iDestruct
"Hcont"
as
"[Hsucc _]"
.
iDestruct
(
"Hsucc"
with
"HP"
)
as
"Hsucc"
.
iDestruct
(
fupd_mask_mono
with
"Hsucc"
)
as
"Hsucc"
;
last
iMod
"Hsucc"
as
"[HQ HP]"
;
first
by
solve_ndisj
.
iMod
(
"Hclose"
with
"[Hl''' Hstack HP]"
).
{
iExists
l'''
,
t'
,
ys'
;
iSplit
;
iFrame
;
auto
.
}
iModIntro
.
...
...
@@ 453,7 +475,7 @@ Section stack_works.
{
iExists
l'''
,
v'''
,
ys
;
iSplit
;
iFrame
;
auto
.
}
iModIntro
.
wp_if
.
iApply
(
"IH"
with
"H
succ Hfail
"
).
iApply
(
"IH"
with
"H
cont
"
).

iIntros
(
v
)
"!# Hpush"
.
iL
ö
b
as
"IH"
.
wp_rec
.
...
...
@@ 465,7 +487,7 @@ Section stack_works.
iInv
(
N
.@
"mailbox_inv"
)
as
"Hmail"
"Hclose"
.
iDestruct
"Hmail"
as
(
m'
)
"[>% Hmail]"
;
simplify_eq
.
iMod
(
own_alloc
(
Excl
()))
as
(
γ
)
"Hγ"
.
done
.
iMod
(
inv_alloc
(
N
.@
"offer_inv"
)
_
(
stages
γ
P
Q''
s
v
)
with
"[Hs Hpush]"
)
as
"#Istages"
.
iMod
(
inv_alloc
(
N
.@
"offer_inv"
)
_
(
stages
N
γ
P
Q''
s
v
)
with
"[Hs Hpush]"
)
as
"#Istages"
.
{
iLeft
;
iFrame
;
auto
.
}
iDestruct
"Hmail"
as
"[H  H]"
.
*
wp_store
.
...
...
@@ 502,7 +524,9 @@ Section stack_works.
iDestruct
"Hstack"
as
(
l''
v''
xs
)
"[>% [Hl'' [Hstack HP]]]"
;
simplify_eq
.
destruct
(
decide
(
v'
=
v''
%
V
)).
++
wp_cas_suc
.
iDestruct
(
"Hpush"
with
"[HP]"
)
as
"> [HP HQ]"
;
auto
.
iDestruct
(
"Hpush"
with
"HP"
)
as
"Hpush"
.
iDestruct
(
fupd_mask_mono
with
"Hpush"
)
as
"Hpush"
;
last
iMod
"Hpush"
as
"[HP HQ]"
;
first
by
solve_ndisj
.
iMod
(
"Hclose"
with
"[Hl'' Hstack HP]"
).
{
iExists
l''
,
(
InjRV
(
v
,
v'
)),
(
v
::
xs
)
;
iSplit
;
iFrame
;
auto
.
iExists
v'
;
iSplit
;
subst
;
auto
.
}
...
...
@@ 564,7 +588,9 @@ Section stack_works.
iDestruct
"Hstack"
as
(
l''
v'''
xs
)
"[>% [Hl'' [Hstack HP]]]"
;
simplify_eq
.
destruct
(
decide
(
v''
=
v'''
%
V
)).
++
wp_cas_suc
.
iDestruct
(
"Hpush"
with
"[HP]"
)
as
"> [HP HQ]"
;
auto
.
iDestruct
(
"Hpush"
with
"HP"
)
as
"Hpush"
.
iDestruct
(
fupd_mask_mono
with
"Hpush"
)
as
"Hpush"
;
last
iMod
"Hpush"
as
"[HP HQ]"
;
first
by
solve_ndisj
.
iMod
(
"Hclose"
with
"[Hl'' Hstack HP]"
).
{
iExists
l''
,
(
InjRV
(
v
,
v''
)),
(
v
::
xs
)
;
iSplit
;
iFrame
;
auto
.
iExists
v''
;
iSplit
;
subst
;
auto
.
}
...
...
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