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examples
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0247cec5
Commit
0247cec5
authored
Jul 06, 2018
by
Ralf Jung
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concurrent stacks: also unify concurrent bag (per-element) specs for stacks 1 and 2
parent
68473b43
Pipeline
#10766
passed with stage
in 9 minutes and 5 seconds
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5
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5 changed files
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58 additions
and
22 deletions
+58
-22
theories/concurrent_stacks/concurrent_stack1.v
theories/concurrent_stacks/concurrent_stack1.v
+16
-6
theories/concurrent_stacks/concurrent_stack2.v
theories/concurrent_stacks/concurrent_stack2.v
+11
-1
theories/concurrent_stacks/concurrent_stack3.v
theories/concurrent_stacks/concurrent_stack3.v
+9
-8
theories/concurrent_stacks/concurrent_stack4.v
theories/concurrent_stacks/concurrent_stack4.v
+9
-7
theories/concurrent_stacks/spec.v
theories/concurrent_stacks/spec.v
+13
-0
No files found.
theories/concurrent_stacks/concurrent_stack1.v
View file @
0247cec5
...
...
@@ -5,6 +5,9 @@ From iris.program_logic Require Export weakestpre hoare.
From
iris
.
heap_lang
Require
Export
lang
.
From
iris
.
algebra
Require
Import
agree
list
.
From
iris
.
heap_lang
Require
Import
assert
proofmode
notation
.
From
iris_examples
.
concurrent_stacks
Require
Import
spec
.
Set
Default
Proof
Using
"Type"
.
(** Stack 1: No helping, bag spec. *)
...
...
@@ -14,10 +17,10 @@ Definition mk_stack : val :=
let
:
"r"
:
=
ref
NONEV
in
(
rec
:
"pop"
"n"
:
=
match
:
!
"r"
with
NONE
=>
#-
1
NONE
=>
NONE
|
SOME
"hd"
=>
if
:
CAS
"r"
(
SOME
"hd"
)
(
Snd
!
"hd"
)
then
Fst
!
"hd"
then
SOME
(
Fst
!
"hd"
)
else
"pop"
"n"
end
,
rec
:
"push"
"n"
:
=
...
...
@@ -81,8 +84,8 @@ Section stacks.
(* Per-element invariant (i.e., bag spec). *)
Theorem
stack_works
P
Φ
:
(
∀
(
f
₁
f
₂
:
val
),
(
∀
(
v
:
val
),
□
WP
f
₁
#()
{{
v
,
P
v
∨
v
≡
#-
1
}})
▷
(
∀
(
f
₁
f
₂
:
val
),
(
□
WP
f
₁
#()
{{
v
,
(
∃
v'
,
v
≡
SOMEV
v'
∗
P
v'
)
∨
v
≡
NONEV
}})
-
∗
(
∀
(
v
:
val
),
□
(
P
v
-
∗
WP
f
₂
v
{{
v
,
True
}}))
-
∗
Φ
(
f
₁
,
f
₂
)%
V
)%
I
-
∗
WP
mk_stack
#()
{{
Φ
}}.
...
...
@@ -98,7 +101,7 @@ Section stacks.
wp_let
.
iModIntro
.
iApply
"HΦ"
.
-
iIntros
(
v
)
"!#"
.
-
iIntros
"!#"
.
iL
ö
b
as
"IH"
.
wp_rec
.
wp_bind
(!
#
l
)%
E
.
...
...
@@ -129,7 +132,7 @@ Section stacks.
wp_if
.
wp_load
.
wp_proj
.
iLeft
;
auto
.
e
auto
.
*
simpl
in
Hne
.
wp_cas_fail
.
iMod
(
"Hclose"
with
"[Hl'' Hstack]"
).
{
iExists
v''
;
iFrame
;
auto
.
}
...
...
@@ -172,3 +175,10 @@ Section stacks.
done
.
Qed
.
End
stacks
.
Program
Definition
is_concurrent_bag
`
{!
heapG
Σ
}
:
concurrent_bag
Σ
:
=
{|
spec
.
mk_bag
:
=
mk_stack
|}.
Next
Obligation
.
iIntros
(???
P
Φ
)
"_ HΦ"
.
iApply
stack_works
.
iNext
.
iIntros
(
f
₁
f
₂
)
"Hpop Hpush"
.
iApply
"HΦ"
.
iFrame
.
Qed
.
theories/concurrent_stacks/concurrent_stack2.v
View file @
0247cec5
...
...
@@ -3,6 +3,9 @@ stricter CAS requirements yet. *)
From
iris
.
program_logic
Require
Export
weakestpre
hoare
.
From
iris
.
heap_lang
Require
Export
lang
proofmode
notation
.
From
iris
.
algebra
Require
Import
excl
.
From
iris_examples
.
concurrent_stacks
Require
Import
spec
.
Set
Default
Proof
Using
"Type"
.
(** Stack 2: With helping, bag spec. *)
...
...
@@ -268,7 +271,7 @@ Section stack_works.
(* Per-element invariant (i.e., bag spec). *)
Theorem
stack_works
{
channelG0
:
channelG
Σ
}
P
Φ
:
(
∀
(
f
₁
f
₂
:
val
),
▷
(
∀
(
f
₁
f
₂
:
val
),
(
□
WP
f
₁
#()
{{
v
,
(
∃
(
v'
:
val
),
v
≡
SOMEV
v'
∗
P
v'
)
∨
v
≡
NONEV
}})
-
∗
(
∀
(
v
:
val
),
□
(
P
v
-
∗
WP
f
₂
v
{{
v
,
True
}}))
-
∗
Φ
(
f
₁
,
f
₂
)%
V
)%
I
...
...
@@ -405,3 +408,10 @@ Section stack_works.
done
.
Qed
.
End
stack_works
.
Program
Definition
is_concurrent_bag
`
{!
heapG
Σ
,
!
channelG
Σ
}
:
concurrent_bag
Σ
:
=
{|
spec
.
mk_bag
:
=
mk_stack
|}.
Next
Obligation
.
iIntros
(????
P
Φ
)
"_ HΦ"
.
iApply
stack_works
.
iNext
.
iIntros
(
f
₁
f
₂
)
"Hpop Hpush"
.
iApply
"HΦ"
.
iFrame
.
Qed
.
theories/concurrent_stacks/concurrent_stack3.v
View file @
0247cec5
From
iris
.
program_logic
Require
Export
weakestpre
hoare
.
From
iris
.
heap_lang
Require
Export
lang
proofmode
notation
.
From
iris
.
algebra
Require
Import
excl
.
Set
Default
Proof
Using
"Type"
.
From
iris_examples
.
concurrent_stacks
Require
Import
spec
.
Set
Default
Proof
Using
"Type"
.
(** Stack 3: No helping, view-shift spec. *)
Definition
mk_stack
:
val
:
=
...
...
@@ -213,11 +214,11 @@ Section stack_works.
wp_if
.
iApply
(
"IH"
with
"Hpush"
).
Qed
.
Program
Definition
is_concurrent_stack
:
concurrent_stack
Σ
:
=
{|
spec
.
mk_stack
:
=
mk_stack
|}.
Next
Obligation
.
iIntros
(?????
Φ
)
"HP HΦ"
.
iApply
(
stack_works
with
"[HΦ] HP"
).
iNext
.
iIntros
(
f
₁
f
₂
)
"Hpop Hpush"
.
iApply
"HΦ"
.
iFrame
.
Qed
.
End
stack_works
.
Program
Definition
is_concurrent_stack
`
{!
heapG
Σ
}
:
concurrent_stack
Σ
:
=
{|
spec
.
mk_stack
:
=
mk_stack
|}.
Next
Obligation
.
iIntros
(???????
Φ
)
"HP HΦ"
.
iApply
(
stack_works
with
"[HΦ] HP"
).
iNext
.
iIntros
(
f
₁
f
₂
)
"Hpop Hpush"
.
iApply
"HΦ"
.
iFrame
.
Qed
.
theories/concurrent_stacks/concurrent_stack4.v
View file @
0247cec5
...
...
@@ -6,6 +6,8 @@ From iris.algebra Require Import excl.
From
iris_examples
.
concurrent_stacks
Require
Import
spec
.
Set
Default
Proof
Using
"Type"
.
(** Stack 3: Helping, view-shift spec. *)
Definition
mk_offer
:
val
:
=
...
...
@@ -620,11 +622,11 @@ Section stack_works.
wp_cas_fail
.
by
iDestruct
(
own_valid_2
with
"Hγ Hγ'"
)
as
%?.
Qed
.
Program
Definition
is_concurrent_stack
`
{!
channelG
Σ
}
:
concurrent_stack
Σ
:
=
{|
spec
.
mk_stack
:
=
mk_stack
|}.
Next
Obligation
.
iIntros
(??????
Φ
)
"HP HΦ"
.
iApply
(
stack_works
with
"[HΦ] HP"
).
iNext
.
iIntros
(
f
₁
f
₂
)
"#[Hpop Hpush]"
.
iApply
"HΦ"
.
iFrame
"#"
.
Qed
.
End
stack_works
.
Program
Definition
is_concurrent_stack
`
{!
heapG
Σ
,
!
channelG
Σ
}
:
concurrent_stack
Σ
:
=
{|
spec
.
mk_stack
:
=
mk_stack
|}.
Next
Obligation
.
iIntros
(????????
Φ
)
"HP HΦ"
.
iApply
(
stack_works
with
"[HΦ] HP"
).
iNext
.
iIntros
(
f
₁
f
₂
)
"#[Hpop Hpush]"
.
iApply
"HΦ"
.
iFrame
"#"
.
Qed
.
theories/concurrent_stacks/spec.v
View file @
0247cec5
...
...
@@ -2,6 +2,19 @@ From stdpp Require Import namespaces.
From
iris
.
program_logic
Require
Export
weakestpre
.
From
iris
.
heap_lang
Require
Export
proofmode
notation
.
(** General (HoCAP-style) spec for a concurrent bag ("per-elemt spec") *)
Record
concurrent_bag
{
Σ
}
`
{!
heapG
Σ
}
:
=
ConcurrentBag
{
mk_bag
:
val
;
mk_bag_spec
(
N
:
namespace
)
(
P
:
val
→
iProp
Σ
)
:
{{{
True
}}}
mk_bag
#()
{{{
(
f
₁
f
₂
:
val
),
RET
(
f
₁
,
f
₂
)
;
(
□
WP
f
₁
#()
{{
v
,
(
∃
(
v'
:
val
),
v
≡
SOMEV
v'
∗
P
v'
)
∨
v
≡
NONEV
}})
∗
(
∀
(
v
:
val
),
□
(
P
v
-
∗
WP
f
₂
v
{{
v
,
True
}}))
}}}
}.
Arguments
concurrent_bag
_
{
_
}.
(** General (HoCAP-style) spec for a concurrent stack *)
Record
concurrent_stack
{
Σ
}
`
{!
heapG
Σ
}
:
=
ConcurrentStack
{
...
...
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