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examples
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d579dc8d
Commit
d579dc8d
authored
Jun 19, 2019
by
Ralf Jung
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bump Iris for comparison changes
parent
06edc222
Pipeline
#17790
passed with stage
in 17 minutes and 34 seconds
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10 changed files
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190 deletions
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190
opam
opam
+1
1
concurrent_stack1.v
theories/concurrent_stacks/concurrent_stack1.v
+44
41
concurrent_stack2.v
theories/concurrent_stacks/concurrent_stack2.v
+40
38
concurrent_stack3.v
theories/concurrent_stacks/concurrent_stack3.v
+35
30
concurrent_stack4.v
theories/concurrent_stacks/concurrent_stack4.v
+35
30
fg_bag.v
theories/hocap/fg_bag.v
+40
37
stack.v
theories/logatom/elimination_stack/stack.v
+8
4
treiber2.v
theories/logatom/treiber2.v
+3
3
ltyping.v
theories/logrel_heaplang/ltyping.v
+1
4
spanning.v
theories/spanning_tree/spanning.v
+2
2
No files found.
opam
View file @
d579dc8d
...
...
@@ 9,6 +9,6 @@ build: [make "j%{jobs}%"]
install: [make "install"]
remove: ["rm" "rf" "%{lib}%/coq/usercontrib/iris_examples"]
depends: [
"coqiris" { (= "dev.20190618.
2.e039d7c7
")  (= "dev") }
"coqiris" { (= "dev.20190618.
8.72595700
")  (= "dev") }
"coqautosubst" { = "dev.coq86" }
]
theories/concurrent_stacks/concurrent_stack1.v
View file @
d579dc8d
...
...
@@ 36,9 +36,19 @@ Section stacks.
iIntros
"H"
;
iDestruct
"H"
as
(?)
"[Hl Hl']"
;
iSplitL
"Hl"
;
eauto
.
Qed
.
Definition
is_list_pre
(
P
:
val
→
iProp
Σ
)
(
F
:
val

d
>
iProp
Σ
)
:
val

d
>
iProp
Σ
:=
λ
v
,
(
v
≡
NONEV
∨
∃
(
l
:
loc
)
(
h
t
:
val
),
⌜
v
≡
SOMEV
#
l
⌝
∗
l
↦
{}
(
h
,
t
)%
V
∗
P
h
∗
▷
F
t
)%
I
.
Definition
oloc_to_val
(
ol
:
option
loc
)
:
val
:=
match
ol
with

None
=>
NONEV

Some
loc
=>
SOMEV
(#
loc
)
end
.
Local
Instance
oloc_to_val_inj
:
Inj
(=)
(=)
oloc_to_val
.
Proof
.
intros
[][];
simpl
;
congruence
.
Qed
.
Definition
is_list_pre
(
P
:
val
→
iProp
Σ
)
(
F
:
option
loc

d
>
iProp
Σ
)
:
option
loc

d
>
iProp
Σ
:=
λ
v
,
match
v
with

None
=>
True

Some
l
=>
∃
(
h
:
val
)
(
t
:
option
loc
),
l
↦
{}
(
h
,
oloc_to_val
t
)%
V
∗
P
h
∗
▷
F
t
end
%
I
.
Local
Instance
is_list_contr
(
P
:
val
→
iProp
Σ
)
:
Contractive
(
is_list_pre
P
).
Proof
.
...
...
@@ 58,28 +68,22 @@ Section stacks.
rewrite
is_list_eq
.
apply
(
fixpoint_unfold
(
is_list_pre
P
)).
Qed
.
(* TODO: shouldn't have to explicitly return is_list *)
Lemma
is_list_unboxed
(
P
:
val
→
iProp
Σ
)
v
:
is_list
P
v

∗
⌜
val_is_unboxed
v
⌝
∗
is_list
P
v
.
Proof
.
iIntros
"Hstack"
;
iSplit
;
last
done
;
iDestruct
(
is_list_unfold
with
"Hstack"
)
as
"[>Hstack]"
;
last
iDestruct
"Hstack"
as
(
l
h
t
)
"(> & _)"
;
done
.
Qed
.
Lemma
is_list_disj
(
P
:
val
→
iProp
Σ
)
v
:
is_list
P
v

∗
is_list
P
v
∗
(
⌜
v
≡
NONEV
⌝
∨
∃
(
l
:
loc
)
h
t
,
⌜
v
≡
SOMEV
#
l
%
V
⌝
∗
l
↦
{}
(
h
,
t
)%
V
).
Lemma
is_list_dup
(
P
:
val
→
iProp
Σ
)
v
:
is_list
P
v

∗
is_list
P
v
∗
match
v
with

None
=>
True

Some
l
=>
∃
h
t
,
l
↦
{}
(
h
,
oloc_to_val
t
)%
V
end
.
Proof
.
iIntros
"Hstack"
.
iDestruct
(
is_list_unfold
with
"Hstack"
)
as
"[%Hstack]"
;
simplify_eq
.

rewrite
is_list_unfold
;
iSplitR
;
[
iLeft
];
eauto
.

iDestruct
"Hstack"
as
(
l
h
t
)
"(% & Hl & Hlist)
"
.
iDestruct
(
partial_mapsto_duplicable
with
"Hl"
)
as
"[Hl1 Hl2]"
;
simplify_eq
.
rewrite
(
is_list_unfold
_
(
InjRV
_));
iSplitR
"Hl2"
;
iRight
;
iExists
_,
_,
_;
by
iFrame
.
iIntros
"Hstack"
.
iDestruct
(
is_list_unfold
with
"Hstack"
)
as
"Hstack"
.
destruct
v
as
[
l
]
.

iDestruct
"Hstack"
as
(
h
t
)
"(Hl & Hlist)"
.
iDestruct
(
partial_mapsto_duplicable
with
"Hl"
)
as
"[Hl1 Hl2]
"
.
rewrite
(
is_list_unfold
_
(
Some
_));
iSplitR
"Hl2"
;
iExists
_,
_;
by
iFrame
.

rewrite
is_list_unfold
;
iSplitR
;
eauto
.
Qed
.
Definition
stack_inv
P
v
:=
(
∃
l
v'
,
⌜
v
=
#
l
⌝
∗
l
↦
v'
∗
is_list
P
v
'
)%
I
.
(
∃
l
ol'
,
⌜
v
=
#
l
⌝
∗
l
↦
oloc_to_val
ol'
∗
is_list
P
ol
'
)%
I
.
Definition
is_stack
(
P
:
val
→
iProp
Σ
)
v
:=
inv
N
(
stack_inv
P
v
).
...
...
@@ 92,8 +96,8 @@ Section stacks.
wp_lam
.
wp_alloc
ℓ
as
"Hl"
.
iMod
(
inv_alloc
N
⊤
(
stack_inv
P
#
ℓ
)
with
"[Hl]"
)
as
"Hinv"
.
{
iNext
;
iExists
ℓ
,
N
ONEV
;
iFrame
;
by
iSplit
;
last
(
iApply
is_list_unfold
;
iLeft
).
}
{
iNext
;
iExists
ℓ
,
N
one
;
iFrame
;
by
iSplit
;
last
(
iApply
is_list_unfold
).
}
by
iApply
"Hpost"
.
Qed
.
...
...
@@ 109,17 +113,17 @@ Section stacks.
{
iNext
;
iExists
_,
_;
by
iFrame
.
}
iModIntro
.
wp_let
.
wp_alloc
ℓ
'
as
"Hl'"
.
wp_pures
.
wp_bind
(
CAS
_
_
_).
iInv
N
as
(
ℓ
''
v''
)
"(>% & >Hl & Hlist)"
"Hclose"
;
simplify_eq
.
destruct
(
decide
(
v'
=
v''
))
as
[
>
].

iDestruct
(
is_list_unboxed
with
"Hlist"
)
as
"[>% Hlist]"
.
wp_cas_suc
.
destruct
(
decide
(
v'
=
v''
))
as
[>
Hne
].

wp_cas_suc
.
{
destruct
v''
;
left
;
done
.
}
iMod
(
"Hclose"
with
"[HP Hl Hl' Hlist]"
)
as
"_"
.
{
iNext
;
iExists
_,
(
InjRV
#
ℓ
'
);
iFrame
;
iSplit
;
first
done
;
rewrite
(
is_list_unfold
_
(
InjRV
_)).
iRight
;
iExists
_,
_,
_;
iFrame
;
eauto
.
}
{
iNext
;
iExists
_,
(
Some
ℓ
'
);
iFrame
;
iSplit
;
first
done
;
rewrite
(
is_list_unfold
_
(
Some
_)).
iExists
_,
_;
iFrame
;
eauto
.
}
iModIntro
.
wp_if
.
by
iApply
"HΦ"
.

iDestruct
(
is_list_unboxed
with
"Hlist"
)
as
"[>% Hlist]"
.
wp_cas_fail
.

wp_cas_fail
.
{
destruct
v'
,
v''
;
simpl
;
congruence
.
}
{
destruct
v''
;
left
;
done
.
}
iMod
(
"Hclose"
with
"[Hl Hlist]"
)
as
"_"
.
{
iNext
;
iExists
_,
_;
by
iFrame
.
}
iModIntro
.
...
...
@@ 134,37 +138,36 @@ Section stacks.
iL
ö
b
as
"IH"
.
wp_lam
.
wp_bind
(
Load
_).
iInv
N
as
(
ℓ
v'
)
"(>% & Hl & Hlist)"
"Hclose"
;
subst
.
iDestruct
(
is_list_dup
with
"Hlist"
)
as
"[Hlist Hlist2]"
.
wp_load
.
iDestruct
(
is_list_disj
with
"Hlist"
)
as
"[Hlist Hdisj]"
.
iMod
(
"Hclose"
with
"[Hl Hlist]"
)
as
"_"
.
{
iNext
;
iExists
_,
_;
by
iFrame
.
}
iModIntro
.
iDestruct
"Hdisj"
as
"[>  Heq]"
.
destruct
v'
as
[
l
];
last
first
.

wp_match
.
iApply
"HΦ"
;
by
iLeft
.

iDestruct
"Heq"
as
(
l
h
t
)
"[> Hl]"
.
wp_match
.
wp_bind
(
Load
_).

wp_match
.
wp_bind
(
Load
_).
iInv
N
as
(
ℓ
'
v'
)
"(>% & Hl' & Hlist)"
"Hclose"
.
simplify_eq
.
iDestruct
"Hl
"
as
(
q
)
"Hl"
.
iDestruct
"Hl
ist2"
as
(???
)
"Hl"
.
wp_load
.
iMod
(
"Hclose"
with
"[Hl' Hlist]"
)
as
"_"
.
{
iNext
;
iExists
_,
_;
by
iFrame
.
}
iModIntro
.
wp_pures
.
wp_bind
(
CAS
_
_
_).
iInv
N
as
(
ℓ
''
v''
)
"(>% & Hl' & Hlist)"
"Hclose"
.
simplify_eq
.
destruct
(
decide
(
v''
=
InjRV
#
l
))
as
[>
].
destruct
(
decide
(
v''
=
(
Some
l
)
))
as
[>
].
*
rewrite
is_list_unfold
.
iDestruct
"Hlist"
as
"[>%  H]"
;
first
done
.
iDestruct
"H"
as
(
ℓ
'''
h'
t'
)
"(>% & Hl'' & HP & Hlist)"
;
simplify_eq
.
iDestruct
"Hlist"
as
(
h'
t'
)
"(Hl'' & HP & Hlist)"
.
iDestruct
"Hl''"
as
(
q'
)
"Hl''"
.
simpl
.
wp_cas_suc
.
iDestruct
(
mapsto_agree
with
"Hl'' Hl"
)
as
"%"
;
simplify_eq
.
iDestruct
(
mapsto_agree
with
"Hl'' Hl"
)
as
%[=
<
<%
oloc_to_val_inj
]
.
iMod
(
"Hclose"
with
"[Hl' Hlist]"
)
as
"_"
.
{
iNext
;
iExists
ℓ
''
,
_;
by
iFrame
.
}
iModIntro
.
wp_pures
.
iApply
(
"HΦ"
with
"[HP]"
);
iRight
;
iExists
h
;
by
iFrame
.
*
wp_cas_fail
.
iApply
(
"HΦ"
with
"[HP]"
);
iRight
;
iExists
_
;
by
iFrame
.
*
wp_cas_fail
.
{
destruct
v''
;
simpl
;
congruence
.
}
iMod
(
"Hclose"
with
"[Hl' Hlist]"
)
as
"_"
.
{
iNext
;
iExists
ℓ
''
,
_;
by
iFrame
.
}
iModIntro
.
...
...
theories/concurrent_stacks/concurrent_stack2.v
View file @
d579dc8d
...
...
@@ 246,9 +246,19 @@ Section stack_works.
iIntros
"H"
;
iDestruct
"H"
as
(?)
"[Hl Hl']"
;
iSplitL
"Hl"
;
eauto
.
Qed
.
Definition
is_list_pre
(
P
:
val
→
iProp
Σ
)
(
F
:
val

d
>
iProp
Σ
)
:
val

d
>
iProp
Σ
:=
λ
v
,
(
v
≡
NONEV
∨
∃
(
l
:
loc
)
(
h
t
:
val
),
⌜
v
≡
SOMEV
#
l
⌝
∗
l
↦
{}
(
h
,
t
)%
V
∗
P
h
∗
▷
F
t
)%
I
.
Definition
oloc_to_val
(
ol
:
option
loc
)
:
val
:=
match
ol
with

None
=>
NONEV

Some
loc
=>
SOMEV
(#
loc
)
end
.
Local
Instance
oloc_to_val_inj
:
Inj
(=)
(=)
oloc_to_val
.
Proof
.
intros
[][];
simpl
;
congruence
.
Qed
.
Definition
is_list_pre
(
P
:
val
→
iProp
Σ
)
(
F
:
option
loc

d
>
iProp
Σ
)
:
option
loc

d
>
iProp
Σ
:=
λ
v
,
match
v
with

None
=>
True

Some
l
=>
∃
(
h
:
val
)
(
t
:
option
loc
),
l
↦
{}
(
h
,
oloc_to_val
t
)%
V
∗
P
h
∗
▷
F
t
end
%
I
.
Local
Instance
is_list_contr
(
P
:
val
→
iProp
Σ
)
:
Contractive
(
is_list_pre
P
).
Proof
.
...
...
@@ 268,27 +278,21 @@ Section stack_works.
rewrite
is_list_eq
.
apply
(
fixpoint_unfold
(
is_list_pre
P
)).
Qed
.
(* TODO: shouldn't have to explicitly return is_list *)
Lemma
is_list_unboxed
(
P
:
val
→
iProp
Σ
)
v
:
is_list
P
v

∗
⌜
val_is_unboxed
v
⌝
∗
is_list
P
v
.
Proof
.
iIntros
"Hstack"
;
iSplit
;
last
done
;
iDestruct
(
is_list_unfold
with
"Hstack"
)
as
"[>Hstack]"
;
last
iDestruct
"Hstack"
as
(
l
h
t
)
"(> & _)"
;
done
.
Qed
.
Lemma
is_list_disj
(
P
:
val
→
iProp
Σ
)
v
:
is_list
P
v

∗
is_list
P
v
∗
(
⌜
v
≡
NONEV
⌝
∨
∃
(
l
:
loc
)
h
t
,
⌜
v
≡
SOMEV
#
l
%
V
⌝
∗
l
↦
{}
(
h
,
t
)%
V
).
Lemma
is_list_dup
(
P
:
val
→
iProp
Σ
)
v
:
is_list
P
v

∗
is_list
P
v
∗
match
v
with

None
=>
True

Some
l
=>
∃
h
t
,
l
↦
{}
(
h
,
oloc_to_val
t
)%
V
end
.
Proof
.
iIntros
"Hstack"
.
iDestruct
(
is_list_unfold
with
"Hstack"
)
as
"[%Hstack]"
;
simplify_eq
.

rewrite
is_list_unfold
;
iSplitR
;
[
iLeft
];
eauto
.

iDestruct
"Hstack"
as
(
l
h
t
)
"(% & Hl & Hlist)
"
.
iDestruct
(
partial_mapsto_duplicable
with
"Hl"
)
as
"[Hl1 Hl2]"
;
simplify_eq
.
rewrite
(
is_list_unfold
_
(
InjRV
_));
iSplitR
"Hl2"
;
iRight
;
iExists
_,
_,
_;
by
iFrame
.
iIntros
"Hstack"
.
iDestruct
(
is_list_unfold
with
"Hstack"
)
as
"Hstack"
.
destruct
v
as
[
l
]
.

iDestruct
"Hstack"
as
(
h
t
)
"(Hl & Hlist)"
.
iDestruct
(
partial_mapsto_duplicable
with
"Hl"
)
as
"[Hl1 Hl2]
"
.
rewrite
(
is_list_unfold
_
(
Some
_));
iSplitR
"Hl2"
;
iExists
_,
_;
by
iFrame
.

rewrite
is_list_unfold
;
iSplitR
;
eauto
.
Qed
.
Definition
stack_inv
P
l
:=
(
∃
v
,
l
↦
v
∗
is_list
P
v
)%
I
.
Definition
stack_inv
P
l
:=
(
∃
v
,
l
↦
oloc_to_val
v
∗
is_list
P
v
)%
I
.
Definition
is_stack
P
v
:=
(
∃
mailbox
l
,
⌜
v
=
(
mailbox
,
#
l
)%
V
⌝
∗
is_mailbox
Nmailbox
P
mailbox
∗
inv
N
(
stack_inv
P
l
))%
I
.
...
...
@@ 302,7 +306,7 @@ Section stack_works.
wp_apply
mk_mailbox_works
;
first
done
.
iIntros
(
mailbox
)
"#Hmailbox"
.
iMod
(
inv_alloc
N
_
(
stack_inv
P
l
)
with
"[Hl]"
)
as
"#Hinv"
.
{
by
iNext
;
iExists
_;
iFrame
;
rewrite
is_list_unfold
;
iLeft
.
}
{
iNext
;
iExists
None
;
iFrame
.
rewrite
is_list_unfold
.
done
.
}
wp_pures
;
iModIntro
;
iApply
"Hpost"
;
iExists
_,
_;
auto
.
Qed
.
...
...
@@ 325,16 +329,16 @@ Section stack_works.
wp_let
.
wp_alloc
l'
as
"Hl'"
.
wp_pures
.
wp_bind
(
CAS
_
_
_).
iInv
N
as
(
list
)
"(Hl & Hlist)"
"Hclose"
.
destruct
(
decide
(
v''
=
list
))
as
[
>
].
*
iDestruct
(
is_list_unboxed
with
"Hlist"
)
as
"[>% Hlist]"
.
wp_cas_suc
.
*
wp_cas_suc
.
{
destruct
list
;
left
;
done
.
}
iMod
(
"Hclose"
with
"[HP Hl Hl' Hlist]"
)
as
"_"
.
{
iNext
;
iExists
(
S
OMEV
_);
iFrame
.
rewrite
(
is_list_unfold
_
(
InjRV
_)).
iRight
;
iExists
_,
_,
_;
iFrame
;
eauto
.
}
{
iNext
;
iExists
(
S
ome
_);
iFrame
.
rewrite
(
is_list_unfold
_
(
Some
_)).
iExists
_,
_;
iFrame
;
eauto
.
}
iModIntro
.
wp_if
.
by
iApply
"HΦ"
.
*
iDestruct
(
is_list_unboxed
with
"Hlist"
)
as
"[>% Hlist]"
.
wp_cas_fail
.
*
wp_cas_fail
.
{
destruct
list
,
v''
;
simpl
;
congruence
.
}
{
destruct
list
;
left
;
done
.
}
iMod
(
"Hclose"
with
"[Hl Hlist]"
)
as
"_"
.
{
iNext
;
iExists
_;
by
iFrame
.
}
iModIntro
.
...
...
@@ 355,27 +359,25 @@ Section stack_works.

wp_match
.
wp_bind
(
Load
_).
iInv
N
as
(
list
)
"[Hl Hlist]"
"Hclose"
.
wp_load
.
iDestruct
(
is_list_d
isj
with
"Hlist"
)
as
"[Hlist Hdisj
]"
.
iDestruct
(
is_list_d
up
with
"Hlist"
)
as
"[Hlist Hlist2
]"
.
iMod
(
"Hclose"
with
"[Hl Hlist]"
)
as
"_"
.
{
iNext
;
iExists
_;
by
iFrame
.
}
iModIntro
.
iDestruct
"Hdisj"
as
"[>  Heq]"
.
destruct
list
as
[
list
];
last
first
.
*
wp_match
.
iApply
"HΦ"
;
by
iLeft
.
*
iDestruct
"Heq"
as
(
l'
h
t
)
"[> Hl']"
.
wp_match
.
wp_bind
(
Load
_).
*
wp_match
.
wp_bind
(
Load
_).
iInv
N
as
(
v'
)
"[>Hl Hlist]"
"Hclose"
.
iDestruct
"Hl
'"
as
(
q
)
"Hl'"
.
iDestruct
"Hl
ist2"
as
(???
)
"Hl'"
.
wp_load
.
iMod
(
"Hclose"
with
"[Hl Hlist]"
)
as
"_"
.
{
iNext
;
iExists
_;
by
iFrame
.
}
iModIntro
.
wp_let
.
wp_proj
.
wp_bind
(
CAS
_
_
_).
wp_pures
.
iInv
N
as
(
v''
)
"[Hl Hlist]"
"Hclose"
.
destruct
(
decide
(
v''
=
InjRV
#
l'
))
as
[>
].
destruct
(
decide
(
v''
=
Some
list
))
as
[>
].
+
rewrite
is_list_unfold
.
iDestruct
"Hlist"
as
"[>%  H]"
;
first
done
.
iDestruct
"H"
as
(
l''
h'
t'
)
"(>% & Hl'' & HP & Hlist)"
;
simplify_eq
.
iDestruct
"Hlist"
as
(
h'
t'
)
"(Hl'' & HP & Hlist)"
.
iDestruct
"Hl''"
as
(
q'
)
"Hl''"
.
wp_cas_suc
.
iDestruct
(
mapsto_agree
with
"Hl'' Hl'"
)
as
"%"
;
simplify_eq
.
...
...
@@ 383,8 +385,8 @@ Section stack_works.
{
iNext
;
iExists
_;
by
iFrame
.
}
iModIntro
.
wp_pures
.
iApply
(
"HΦ"
with
"[HP]"
);
iRight
;
iExists
h
;
by
iFrame
.
+
wp_cas_fail
.
iApply
(
"HΦ"
with
"[HP]"
);
iRight
;
iExists
_
;
by
iFrame
.
+
wp_cas_fail
.
{
destruct
v''
;
simpl
;
congruence
.
}
iMod
(
"Hclose"
with
"[Hl Hlist]"
)
as
"_"
.
{
iNext
;
iExists
_;
by
iFrame
.
}
iModIntro
.
...
...
theories/concurrent_stacks/concurrent_stack3.v
View file @
d579dc8d
...
...
@@ 44,47 +44,51 @@ Section stack_works.
iApply
(
mapsto_agree
with
"H1 H2"
).
Qed
.
Definition
oloc_to_val
(
ol
:
option
loc
)
:
val
:=
match
ol
with

None
=>
NONEV

Some
loc
=>
SOMEV
(#
loc
)
end
.
Local
Instance
oloc_to_val_inj
:
Inj
(=)
(=)
oloc_to_val
.
Proof
.
intros
[][];
simpl
;
congruence
.
Qed
.
Fixpoint
is_list
xs
v
:
iProp
Σ
:=
(
match
xs
with

[]
=>
⌜
v
=
NONEV
⌝

x
::
xs
=>
∃
l
(
t
:
val
),
⌜
v
=
SOMEV
#
l
%
V
⌝
∗
l
↦
{}
(
x
,
t
)%
V
∗
is_list
xs
t
(
match
xs
,
v
with

[],
None
=>
True

x
::
xs
,
Some
l
=>
∃
t
,
l
↦
{}
(
x
,
oloc_to_val
t
)%
V
∗
is_list
xs
t

_,
_
=>
False
end
)%
I
.
Lemma
is_list_disj
xs
v
:
is_list
xs
v

∗
is_list
xs
v
∗
(
⌜
v
=
NONEV
⌝
∨
∃
l
(
h
t
:
val
),
⌜
v
=
SOMEV
#
l
⌝
∗
l
↦
{}
(
h
,
t
)%
V
).
Lemma
is_list_dup
xs
v
:
is_list
xs
v

∗
is_list
xs
v
∗
match
v
with

None
=>
True

Some
l
=>
∃
h
t
,
l
↦
{}
(
h
,
oloc_to_val
t
)%
V
end
.
Proof
.
destruct
xs
;
auto
.
iIntros
"H"
;
iDestruct
"H"
as
(
l
t
)
"(> &
Hl & Hstack)"
.
destruct
xs
,
v
;
simpl
;
auto
;
first
by
iIntros
"[]"
.
iIntros
"H"
;
iDestruct
"H"
as
(
t
)
"(
Hl & Hstack)"
.
iDestruct
(
partial_mapsto_duplicable
with
"Hl"
)
as
"[Hl1 Hl2]"
.
iSplitR
"Hl2"
;
first
by
(
iExists
_,
_;
iFrame
).
iRight
;
auto
.
Qed
.
Lemma
is_list_unboxed
xs
v
:
is_list
xs
v

∗
⌜
val_is_unboxed
v
⌝
∗
is_list
xs
v
.
Proof
.
iIntros
"Hlist"
;
iDestruct
(
is_list_disj
with
"Hlist"
)
as
"[$ Heq]"
.
iDestruct
"Heq"
as
"[>  H]"
;
first
done
;
by
iDestruct
"H"
as
(?
?
?)
"[> ?]"
.
iSplitR
"Hl2"
;
first
by
(
iExists
_;
iFrame
).
by
iExists
_,
_.
Qed
.
Lemma
is_list_empty
xs
:
is_list
xs
(
InjLV
#())

∗
⌜
xs
=
[]
⌝
.
is_list
xs
None

∗
⌜
xs
=
[]
⌝
.
Proof
.
destruct
xs
;
iIntros
"Hstack"
;
auto
.
iDestruct
"Hstack"
as
(?
?)
"(% & H)"
;
discriminate
.
Qed
.
Lemma
is_list_cons
xs
l
h
t
:
l
↦
{}
(
h
,
t
)%
V

∗
is_list
xs
(
InjRV
#
l
)

∗
is_list
xs
(
Some
l
)

∗
∃
ys
,
⌜
xs
=
h
::
ys
⌝
.
Proof
.
destruct
xs
;
first
by
iIntros
"? %"
.
iIntros
"Hl Hstack"
;
iDestruct
"Hstack"
as
(
l'
t'
)
"(% & Hl' & Hrest)"
;
simplify_eq
.
iIntros
"Hl Hstack"
;
iDestruct
"Hstack"
as
(
t'
)
"(Hl' & Hrest)"
.
iDestruct
(
partial_mapsto_agree
with
"Hl Hl'"
)
as
"%"
;
simplify_eq
;
iExists
_;
auto
.
Qed
.
Definition
stack_inv
P
l
:=
(
∃
v
xs
,
l
↦
v
∗
is_list
xs
v
∗
P
xs
)%
I
.
(
∃
v
xs
,
l
↦
oloc_to_val
v
∗
is_list
xs
v
∗
P
xs
)%
I
.
Definition
is_stack_pred
P
v
:=
(
∃
l
,
⌜
v
=
#
l
⌝
∗
inv
N
(
stack_inv
P
l
))%
I
.
...
...
@@ 96,7 +100,7 @@ Section stack_works.
rewrite

wp_fupd
.
wp_lam
.
wp_alloc
l
as
"Hl"
.
iMod
(
inv_alloc
N
_
(
stack_inv
P
l
)
with
"[Hl HP]"
)
as
"#Hinv"
.
{
by
iNext
;
iExists
_
,
[];
iFrame
.
}
{
iNext
;
iExists
None
,
[];
iFrame
.
}
iModIntro
;
iApply
"HΦ"
;
iExists
_;
auto
.
Qed
.
...
...
@@ 116,16 +120,17 @@ Section stack_works.
iModIntro
.
wp_let
.
wp_alloc
l'
as
"Hl'"
.
wp_pures
.
wp_bind
(
CAS
_
_
_).
iInv
N
as
(
list'
xs
)
"(Hl & Hlist & HP)"
"Hclose"
.
iDestruct
(
is_list_unboxed
with
"Hlist"
)
as
"[>% Hlist]"
.
destruct
(
decide
(
list
=
list'
))
as
[
>
].

wp_cas_suc
.

wp_cas_suc
.
{
destruct
list'
;
left
;
done
.
}
iMod
(
"Hupd"
with
"HP"
)
as
"[HP HΨ]"
.
iMod
(
"Hclose"
with
"[Hl Hl' HP Hlist]"
)
as
"_"
.
{
iNext
;
iExists
(
S
OMEV
_),
(
v
::
xs
);
iFrame
;
iExists
_,
_;
iFrame
;
auto
.
}
{
iNext
;
iExists
(
S
ome
_),
(
v
::
xs
);
iFrame
;
iExists
_;
iFrame
;
auto
.
}
iModIntro
.
wp_if
.
by
iApply
(
"HΦ"
with
"HΨ"
).

wp_cas_fail
.
{
destruct
list
,
list'
;
simpl
;
congruence
.
}
{
destruct
list'
;
left
;
done
.
}
iMod
(
"Hclose"
with
"[Hl HP Hlist]"
).
{
iExists
_,
_;
iFrame
.
}
iModIntro
.
...
...
@@ 146,8 +151,8 @@ Section stack_works.
wp_lam
.
wp_bind
(
Load
_).
iInv
N
as
(
v
xs
)
"(Hl & Hlist & HP)"
"Hclose"
.
wp_load
.
iDestruct
(
is_list_d
isj
with
"Hlist"
)
as
"[Hlist H]"
.
iDestruct
"H"
as
"[>  HSome]"
.
iDestruct
(
is_list_d
up
with
"Hlist"
)
as
"[Hlist H]"
.
destruct
v
as
[
l'
];
last
first
.

iDestruct
(
is_list_empty
with
"Hlist"
)
as
%>.
iDestruct
"Hupd"
as
"[_ Hupdnil]"
.
iMod
(
"Hupdnil"
with
"HP"
)
as
"[HP HΨ]"
.
...
...
@@ 156,7 +161,7 @@ Section stack_works.
iModIntro
.
wp_match
.
iApply
(
"HΦ"
with
"HΨ"
).

iDestruct
"H
Some"
as
(
l'
h
t
)
"[> Hl']
"
.

iDestruct
"H
"
as
(
h
t
)
"Hl'
"
.
iMod
(
"Hclose"
with
"[Hlist Hl HP]"
)
as
"_"
.
{
iNext
;
iExists
_,
_;
iFrame
.
}
iModIntro
.
...
...
@@ 169,13 +174,13 @@ Section stack_works.
iModIntro
.
wp_let
.
wp_proj
.
wp_bind
(
CAS
_
_
_).
wp_pures
.
iInv
N
as
(
v'
xs''
)
"(Hl & Hlist & HP)"
"Hclose"
.
destruct
(
decide
(
v'
=
(
S
OMEV
#
l'
)))
as
[
>
].
destruct
(
decide
(
v'
=
(
S
ome
l'
)))
as
[
>
].
*
wp_cas_suc
.
iDestruct
(
is_list_cons
with
"[Hl'] Hlist"
)
as
(
ys
)
"%"
;
first
by
iExists
_.
simplify_eq
.
iDestruct
"Hupd"
as
"[Hupdcons _]"
.
iMod
(
"Hupdcons"
with
"HP"
)
as
"[HP HΨ]"
.
iDestruct
"Hlist"
as
(
l''
t'
)
"(% & Hl'' & Hlist)"
;
simplify_eq
.
iDestruct
"Hlist"
as
(
t'
)
"(Hl'' & Hlist)"
.
iDestruct
"Hl''"
as
(
q'
)
"Hl''"
.
iDestruct
(
mapsto_agree
with
"Hl' Hl''"
)
as
"%"
;
simplify_eq
.
iMod
(
"Hclose"
with
"[Hlist Hl HP]"
)
as
"_"
.
...
...
@@ 183,7 +188,7 @@ Section stack_works.
iModIntro
.
wp_pures
.
iApply
(
"HΦ"
with
"HΨ"
).
*
wp_cas_fail
.
*
wp_cas_fail
.
{
destruct
v'
;
simpl
;
congruence
.
}
iMod
(
"Hclose"
with
"[Hlist Hl HP]"
)
as
"_"
.
{
iNext
;
iExists
_,
_;
iFrame
.
}
iModIntro
.
...
...
theories/concurrent_stacks/concurrent_stack4.v
View file @
d579dc8d
...
...
@@ 267,47 +267,51 @@ Section proofs.
iApply
(
mapsto_agree
with
"H1 H2"
).
Qed
.
Definition
oloc_to_val
(
ol
:
option
loc
)
:
val
:=
match
ol
with

None
=>
NONEV

Some
loc
=>
SOMEV
(#
loc
)
end
.
Local
Instance
oloc_to_val_inj
:
Inj
(=)
(=)
oloc_to_val
.
Proof
.
intros
[][];
simpl
;
congruence
.
Qed
.
Fixpoint
is_list
xs
v
:
iProp
Σ
:=
(
match
xs
with

[]
=>
⌜
v
=
NONEV
⌝

x
::
xs
=>
∃
l
(
t
:
val
),
⌜
v
=
SOMEV
#
l
%
V
⌝
∗
l
↦
{}
(
x
,
t
)%
V
∗
is_list
xs
t
(
match
xs
,
v
with

[],
None
=>
True

x
::
xs
,
Some
l
=>
∃
t
,
l
↦
{}
(
x
,
oloc_to_val
t
)%
V
∗
is_list
xs
t

_,
_
=>
False
end
)%
I
.
Lemma
is_list_disj
xs
v
:
is_list
xs
v

∗
is_list
xs
v
∗
(
⌜
v
=
NONEV
⌝
∨
∃
l
(
h
t
:
val
),
⌜
v
=
SOMEV
#
l
⌝
∗
l
↦
{}
(
h
,
t
)%
V
).
Lemma
is_list_dup
xs
v
:
is_list
xs
v

∗
is_list
xs
v
∗
match
v
with

None
=>
True

Some
l
=>
∃
h
t
,
l
↦
{}
(
h
,
oloc_to_val
t
)%
V
end
.
Proof
.
destruct
xs
;
auto
.
iIntros
"H"
;
iDestruct
"H"
as
(
l
t
)
"(> &
Hl & Hstack)"
.
destruct
xs
,
v
;
simpl
;
auto
;
first
by
iIntros
"[]"
.
iIntros
"H"
;
iDestruct
"H"
as
(
t
)
"(
Hl & Hstack)"
.
iDestruct
(
partial_mapsto_duplicable
with
"Hl"
)
as
"[Hl1 Hl2]"
.
iSplitR
"Hl2"
;
first
by
(
iExists
_,
_;
iFrame
).
iRight
;
auto
.
Qed
.
Lemma
is_list_unboxed
xs
v
:
is_list
xs
v

∗
⌜
val_is_unboxed
v
⌝
∗
is_list
xs
v
.
Proof
.
iIntros
"Hlist"
;
iDestruct
(
is_list_disj
with
"Hlist"
)
as
"[$ Heq]"
.
iDestruct
"Heq"
as
"[>  H]"
;
first
done
;
by
iDestruct
"H"
as
(?
?
?)
"[> ?]"
.
iSplitR
"Hl2"
;
first
by
(
iExists
_;
iFrame
).
by
iExists
_,
_.
Qed
.
Lemma
is_list_empty
xs
:
is_list
xs
(
InjLV
#())

∗
⌜
xs
=
[]
⌝
.
is_list
xs
None

∗
⌜
xs
=
[]
⌝
.
Proof
.
destruct
xs
;
iIntros
"Hstack"
;
auto
.
iDestruct
"Hstack"
as
(?
?)
"(% & H)"
;
discriminate
.
Qed
.
Lemma
is_list_cons
xs
l
h
t
:
l
↦
{}
(
h
,
t
)%
V

∗
is_list
xs
(
InjRV
#
l
)

∗
is_list
xs
(
Some
l
)

∗
∃
ys
,
⌜
xs
=
h
::
ys
⌝
.
Proof
.
destruct
xs
;
first
by
iIntros
"? %"
.
iIntros
"Hl Hstack"
;
iDestruct
"Hstack"
as
(
l'
t'
)
"(% & Hl' & Hrest)"
;
simplify_eq
.
iIntros
"Hl Hstack"
;
iDestruct
"Hstack"
as
(
t'
)
"(Hl' & Hrest)"
.
iDestruct
(
partial_mapsto_agree
with
"Hl Hl'"
)
as
"%"
;
simplify_eq
;
iExists
_;
auto
.
Qed
.
Definition
stack_inv
P
l
:=
(
∃
v
xs
,
l
↦
v
∗
is_list
xs
v
∗
P
xs
)%
I
.
(
∃
v
xs
,
l
↦
oloc_to_val
v
∗
is_list
xs
v
∗
P
xs
)%
I
.
Definition
is_stack_pred
P
v
:=
(
∃
mailbox
l
,
⌜
v
=
(
mailbox
,
#
l
)%
V
⌝
∗
is_mailbox
P
mailbox
∗
inv
Nstack
(
stack_inv
P
l
))%
I
.
...
...
@@ 321,7 +325,7 @@ Section proofs.
wp_alloc
l
as
"Hl"
.
wp_apply
mk_mailbox_works
;
first
done
.
iIntros
(
v
)
"#Hmailbox"
.
iMod
(
inv_alloc
Nstack
_
(
stack_inv
P
l
)
with
"[Hl HP]"
)
as
"#Hinv"
.
{
by
iNext
;
iExists
_
,
[];
iFrame
.
}
{
by
iNext
;
iExists
None
,
[];
iFrame
.
}
wp_pures
.
iModIntro
;
iApply
"HΦ"
;
iExists
_;
auto
.
Qed
.
...
...
@@ 348,18 +352,19 @@ Section proofs.
iModIntro
.
wp_let
.
wp_alloc
l'
as
"Hl'"
.
wp_pures
.
wp_bind
(
CAS
_
_
_).
iInv
Nstack
as
(
list'
xs
)
"(Hl & Hlist & HP)"
"Hclose"
.
iDestruct
(
is_list_unboxed
with
"Hlist"
)
as
"[>% Hlist]"
.
destruct
(
decide
(
list
=
list'
))
as
[
>
].
*
wp_cas_suc
.
*
wp_cas_suc
.
{
destruct
list'
;
left
;
done
.
}
iMod
(
fupd_intro_mask'
(
⊤
∖
↑
Nstack
)
inner_mask
)
as
"Hupd'"
;
first
solve_ndisj
.
iMod
(
"Hupd"
with
"HP"
)
as
"[HP HΨ]"
.
iMod
"Hupd'"
as
"_"
.
iMod
(
"Hclose"
with
"[Hl Hl' HP Hlist]"
)
as
"_"
.
{
iNext
;
iExists
(
S
OMEV
_),
(
v'
::
xs
);
iFrame
;
iExists
_,
_;
iFrame
;
auto
.
}
{
iNext
;
iExists
(
S
ome
_),
(
v'
::
xs
);
iFrame
;
iExists
_;
iFrame
;
auto
.
}
iModIntro
.
wp_if
.
by
iApply
(
"HΦ"
with
"HΨ"
).
*
wp_cas_fail
.
{
destruct
list
,
list'
;
simpl
;
congruence
.
}
{
destruct
list'
;
left
;
done
.
}
iMod
(
"Hclose"
with
"[Hl HP Hlist]"
).
{
iExists
_,
_;
iFrame
.
}
iModIntro
.
...
...
@@ 399,8 +404,8 @@ Section proofs.

wp_match
.
wp_bind
(
Load
_).
iInv
Nstack
as
(
v
xs
)
"(Hl & Hlist & HP)"
"Hclose"
.
wp_load
.
iDestruct
(
is_list_d
isj
with
"Hlist"
)
as
"[Hlist H]"
.
iDestruct
"H"
as
"[>  HSome]"
.
iDestruct
(
is_list_d
up
with
"Hlist"
)
as
"[Hlist H]"
.
destruct
v
as
[
l'
];
last
first
.
*
iDestruct
(
is_list_empty
with
"Hlist"
)
as
%>.
iMod
(
fupd_intro_mask'
(
⊤
∖
↑
Nstack
)
inner_mask
)
as
"Hupd'"
;
first
solve_ndisj
.
iMod
(
"Hupd"
with
"HP"
)
as
"[HP HΨ]"
.
...
...
@@ 410,7 +415,7 @@ Section proofs.
iModIntro
.
wp_match
.
iApply
(
"HΦ"
with
"HΨ"
).
*
iDestruct
"H
Some"
as
(
l'
h
t
)
"[> Hl']
"
.
*
iDestruct
"H
"
as
(
h
t
)
"Hl'
"
.
iMod
(
"Hclose"
with
"[Hlist Hl HP]"
)
as
"_"
.
{
iNext
;
iExists
_,
_;
iFrame
.
}
iModIntro
.
...
...
@@ 423,7 +428,7 @@ Section proofs.
iModIntro
.
wp_pures
.
wp_bind
(
CAS
_
_
_).
iInv
Nstack
as
(
v'
xs''
)
"(Hl & Hlist & HP)"
"Hclose"
.
destruct
(
decide
(
v'
=
(
S
OMEV
#
l'
)))
as
[
>
].
destruct
(
decide
(
v'
=
(
S
ome
l'
)))
as
[
>
].
+
wp_cas_suc
.
iDestruct
(
is_list_cons
with
"[Hl'] Hlist"
)
as
(
ys
)
"%"
;
first
by
iExists
_.
simplify_eq
.
...
...
@@ 431,7 +436,7 @@ Section proofs.
iDestruct
"Hupd"
as
"[Hupdcons _]"
.
iMod
(
"Hupdcons"
with
"HP"
)
as
"[HP HΨ]"
.
iMod
"Hupd'"
as
"_"
.
iDestruct
"Hlist"
as
(
l''
t'
)
"(% & Hl'' & Hlist)"
;
simplify_eq
.
iDestruct
"Hlist"
as
(
t'
)
"(Hl'' & Hlist)"
.
iDestruct
"Hl''"
as
(
q'
)
"Hl''"
.
iDestruct
(
mapsto_agree
with
"Hl' Hl''"
)
as
"%"
;
simplify_eq
.
iMod
(
"Hclose"
with
"[Hlist Hl HP]"
)
as
"_"
.
...
...
@@ 439,7 +444,7 @@ Section proofs.
iModIntro
.
wp_pures
.
iApply
(
"HΦ"
with
"HΨ"
).
+
wp_cas_fail
.
+
wp_cas_fail
.
{
destruct
v'
;
simpl
;
congruence
.
}
iMod
(
"Hclose"
with
"[Hlist Hl HP]"
)
as
"_"
.
{
iNext
;
iExists
_,
_;
iFrame
.
}
iModIntro
.
...
...
theories/hocap/fg_bag.v
View file @
d579dc8d
...
...
@@ 49,49 +49,51 @@ Section proof.
Lemma
rown_duplicate
l
v
:
rown
l
v

∗
rown
l
v
∗
rown
l
v
.
Proof
.
iDestruct
1
as
(
q
)
"[Hl Hl']"
.
iSplitL
"Hl"
;
iExists
_;
eauto
.
Qed
.
Fixpoint
is_list
(
hd
:
val
)
(
xs
:
list
val
)
:
iProp
Σ
:=
match
xs
with

[]
=>
⌜
hd
=
NONEV
⌝
%
I

x
::
xs
=>
(
∃
(
l
:
loc
)
(
tl
:
val
),
⌜
hd
=
SOMEV
#
l
⌝
∗
rown
l
(
x
,
tl
)
∗
is_list
tl
xs
)%
I
Definition
oloc_to_val
(
ol
:
option
loc
)
:
val
:=
match
ol
with

None
=>
NONEV