Skip to content
Projects
Groups
Snippets
Help
Loading...
Help
Support
Keyboard shortcuts
?
Submit feedback
Contribute to GitLab
Sign in / Register
Toggle navigation
E
examples
Project overview
Project overview
Details
Activity
Releases
Repository
Repository
Files
Commits
Branches
Tags
Contributors
Graph
Compare
Issues
1
Issues
1
List
Boards
Labels
Milestones
Merge Requests
3
Merge Requests
3
CI / CD
CI / CD
Pipelines
Jobs
Schedules
Analytics
Analytics
CI / CD
Repository
Value Stream
Wiki
Wiki
Snippets
Snippets
Members
Members
Collapse sidebar
Close sidebar
Activity
Graph
Create a new issue
Jobs
Commits
Issue Boards
Open sidebar
Iris
examples
Commits
30b963ae
Commit
30b963ae
authored
Mar 07, 2018
by
Ralf Jung
Browse files
Options
Browse Files
Download
Email Patches
Plain Diff
update concurrent_stack4
parent
8cd27e65
Pipeline
#7534
passed with stage
in 6 minutes and 20 seconds
Changes
1
Pipelines
15
Hide whitespace changes
Inline
Sidebyside
Showing
1 changed file
with
64 additions
and
38 deletions
+64
38
theories/concurrent_stacks/concurrent_stack4.v
theories/concurrent_stacks/concurrent_stack4.v
+64
38
No files found.
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 helping, (weak)
viewshift spec. *)
(** Stack
3: Helping,
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
.
}
...
...
Write
Preview
Markdown
is supported
0%
Try again
or
attach a new file
Attach a file
Cancel
You are about to add
0
people
to the discussion. Proceed with caution.
Finish editing this message first!
Cancel
Please
register
or
sign in
to comment