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Iris
Actris
Commits
338adc7d
Commit
338adc7d
authored
4 years ago
by
Robbert Krebbers
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Functional correctness spec of double example.
parent
a50fb42a
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#27611
passed
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theories/logrel/examples/double.v
+84
-56
84 additions, 56 deletions
theories/logrel/examples/double.v
with
84 additions
and
56 deletions
theories/logrel/examples/double.v
+
84
−
56
View file @
338adc7d
From
iris
.
algebra
Require
Import
frac
.
From
iris
.
algebra
Require
Import
frac
auth
excl
updates
.
From
iris
.
heap_lang
.
lib
Require
Export
par
spin_lock
.
From
actris
.
channel
Require
Import
proofmode
.
From
actris
.
logrel
Require
Export
term_typing_judgment
session_types
.
...
...
@@ -19,69 +19,96 @@ Definition prog : val := λ: "c",
)
.
Section
double
.
Context
`{
heapG
Σ
,
chanG
Σ
,
inG
Σ
fracR
,
spawnG
Σ
}
.
Context
`{
!
heapG
Σ
,
!
chanG
Σ
,
!
spawnG
Σ
}
.
Context
`{
!
inG
Σ
(
exclR
unitO
),
inG
Σ
(
prodR
fracR
(
agreeR
(
optionO
valO
)))}
.
Definition
prog_prot
:
iProto
Σ
:=
(
<
?
(
x
:
Z
)
>
MSG
#
x
;
<
?
(
y
:
Z
)
>
MSG
#
y
;
END
)
%
proto
.
Definition
prog_prot
(
P
:
val
→
val
→
iProp
Σ
)
:
iProto
Σ
:=
(
<
?
(
v1
:
val
)
>
MSG
v1
;
<
?
(
v2
:
val
)
>
MSG
v2
{{
P
v1
v2
}}
;
END
)
%
proto
.
Definition
chan_inv
(
c
:
val
)
(
γ
:
gname
)
:
iProp
Σ
:=
(
c
↣
prog_prot
∨
(
own
γ
(
1
/
2
)
%
Qp
∗
c
↣
<
?
(
x
:
Z
)
>
MSG
#
x
;
END
)
∨
(
own
γ
1
%
Qp
∗
c
↣
END
))
%
I
.
Definition
chan_inv
(
γ
γ1
γ2
:
gname
)
(
P
:
val
→
val
→
iProp
Σ
)
(
c
:
val
)
:
iProp
Σ
:=
(
own
γ
(
Excl
())
∗
c
↣
prog_prot
P
∨
(
∃
b
v1
,
own
(
if
b
:
bool
then
γ1
else
γ2
)
(
3
/
4
,
to_agree
(
Some
v1
))
%
Qp
∗
c
↣
<
?
(
v2
:
val
)
>
MSG
v2
{{
P
v1
v2
}};
END
)
∨
(
∃
v1
v2
,
own
γ1
(
1
/
4
,
to_agree
(
Some
v1
))
%
Qp
∗
own
γ2
(
1
/
4
,
to_agree
(
Some
v2
))
%
Qp
))
%
I
.
Lemma
wp_prog
c
:
{{{
▷
c
↣
prog_prot
}}}
Lemma
wp_prog
P
c
:
{{{
▷
c
↣
prog_prot
P
}}}
prog
c
{{{
(
k1
k2
:
Z
)
,
RET
(
#
k
1
,
#
k
2
);
True
}}}
.
{{{
v1
v2
,
RET
(
v
1
,
v
2
);
P
v1
v2
∨
P
v2
v1
}}}
.
Proof
.
iIntros
(
Φ
)
"Hc HΦ"
.
rewrite
/
prog
.
iMod
(
own_alloc
1
%
Qp
)
as
(
γ
)
"[Hcredit1 Hcredit2]"
;
[
done
|]
.
iIntros
(
Φ
)
"Hc HΦ"
.
rewrite
/
prog
.
iMod
(
own_alloc
(
Excl
()))
as
(
γ
)
"Hγ"
;
[
done
|]
.
iMod
(
own_alloc
(
1
,
to_agree
None
)
%
Qp
)
as
(
γ1
)
"Hγ1"
;
[
done
|]
.
iMod
(
own_alloc
(
1
,
to_agree
None
)
%
Qp
)
as
(
γ2
)
"Hγ2"
;
[
done
|]
.
(* Create lock *)
wp_apply
(
newlock_spec
(
chan_inv
c
γ
)
with
"[Hc]"
)
.
{
iLeft
.
iFrame
"Hc"
.
}
iIntros
(
lk
γlk
)
"#Hlock"
.
wp_pures
.
wp_apply
(
newlock_spec
(
chan_inv
γ
γ1
γ2
P
c
)
with
"[Hγ Hc]"
)
.
{
iLeft
.
by
iFrame
.
}
iIntros
(
lk
γlk
)
"#Hlock"
.
wp_pures
.
(* Fork into two threads *)
wp_apply
(
wp_par
(
λ
v
,
∃
k
:
Z
,
⌜
v
=
#
k
⌝
)
%
I
(
λ
v
,
∃
k
:
Z
,
⌜
v
=
#
k
⌝
)
%
I
with
"[Hcredit1] [Hcredit2]"
)
.
wp_apply
(
wp_par
(
λ
v1
,
own
γ1
(
1
/
4
,
to_agree
(
Some
v1
))
%
Qp
∗
own
γ
(
Excl
())
∨
(
∃
v2
,
own
γ1
(
3
/
4
,
to_agree
(
Some
v1
))
%
Qp
∗
own
γ2
(
1
/
2
,
to_agree
(
Some
v2
))
%
Qp
∗
P
v2
v1
))
%
I
(
λ
v2
,
own
γ2
(
1
/
4
,
to_agree
(
Some
v2
))
%
Qp
∗
own
γ
(
Excl
())
∨
(
∃
v1
,
own
γ2
(
3
/
4
,
to_agree
(
Some
v2
))
%
Qp
∗
own
γ1
(
1
/
2
,
to_agree
(
Some
v1
))
%
Qp
∗
P
v1
v2
))
%
I
with
"[Hγ1] [Hγ2]"
)
.
-
(* Acquire lock *)
wp_apply
(
acquire_spec
with
"Hlock"
)
.
iIntros
"[Hlocked Hc]"
.
wp_pures
.
iDestruct
"Hc"
as
"[Hc|[Hc|Hc]]"
.
+
wp_recv
(
x1
)
as
"_"
.
wp_pures
.
wp_apply
(
release_spec
with
"[Hlocked Hcredit1 Hc]"
)
.
{
iFrame
"Hlock Hlocked"
.
iRight
.
iLeft
.
iFrame
"Hcredit1 Hc"
.
}
iIntros
"_"
.
wp_pures
.
eauto
.
+
iDestruct
"Hc"
as
"[Hcredit2 Hc]"
.
wp_recv
(
x1
)
as
"_"
.
wp_pures
.
iCombine
"Hcredit1 Hcredit2"
as
"Hcredit"
.
wp_apply
(
release_spec
with
"[Hlocked Hcredit Hc]"
)
.
{
iFrame
"Hlock Hlocked"
.
iRight
.
iRight
.
iFrame
"Hcredit Hc"
.
}
iIntros
"_"
.
wp_pures
.
eauto
.
+
iDestruct
"Hc"
as
"[Hcredit2 Hc]"
.
by
iDestruct
(
own_valid_2
with
"Hcredit1 Hcredit2"
)
as
%
[]
.
iDestruct
"Hc"
as
"[[Hγ Hc]|[Hc|Hc]]"
.
+
wp_recv
(
v
)
as
"_"
.
wp_pures
.
iMod
(
own_update
_
_
((
3
/
4
⋅
1
/
4
),
to_agree
(
Some
v
))
%
Qp
with
"Hγ1"
)
as
"[Hγ1a Hγ1b]"
;
[
by
apply
cmra_update_exclusive
|]
.
wp_apply
(
release_spec
with
"[$Hlock $Hlocked Hγ1a Hc]"
)
.
{
iRight
.
iLeft
.
iExists
true
,
v
.
iFrame
.
}
iIntros
"_"
.
wp_pures
.
iLeft
.
iFrame
.
+
iDestruct
"Hc"
as
([]
v
)
"[Hγ2 Hc]"
.
{
by
iDestruct
(
own_valid_2
with
"Hγ1 Hγ2"
)
as
%
[]
.
}
wp_recv
(
v'
)
as
"HP"
.
wp_pures
.
iMod
(
own_update
_
_
((
1
/
4
⋅
3
/
4
),
to_agree
(
Some
v'
))
%
Qp
with
"Hγ1"
)
as
"[Hγ1a Hγ1b]"
;
[
by
apply
cmra_update_exclusive
|]
.
rewrite
{
1
}(_
:
3
/
4
=
1
/
4
+
1
/
2
)
%
Qp
;
last
(
by
apply
:
bool_decide_unpack
)
.
iDestruct
"Hγ2"
as
"[Hγ2a Hγ2b]"
.
wp_apply
(
release_spec
with
"[$Hlock $Hlocked Hγ1a Hγ2a Hc]"
)
.
{
do
2
iRight
.
iExists
v'
,
v
.
iFrame
.
}
iIntros
"_"
.
wp_pures
.
iRight
.
iExists
v
.
iFrame
.
+
iDestruct
"Hc"
as
(
v
v'
)
"[Hγ1' _]"
.
by
iDestruct
(
own_valid_2
with
"Hγ1 Hγ1'"
)
as
%
[]
.
-
(* Acquire lock *)
wp_apply
(
acquire_spec
with
"Hlock"
)
.
iIntros
"[Hlocked Hc]"
.
wp_pures
.
iDestruct
"Hc"
as
"[Hc|[Hc|Hc]]"
.
+
wp_recv
(
x1
)
as
"_"
.
wp_pures
.
wp_apply
(
release_spec
with
"[Hlocked Hcredit2 Hc]"
)
.
{
iFrame
"Hlock Hlocked"
.
iRight
.
iLeft
.
iFrame
"Hcredit2 Hc"
.
}
iIntros
"_"
.
wp_pures
.
eauto
.
+
iDestruct
"Hc"
as
"[Hcredit1 Hc]"
.
wp_recv
(
x1
)
as
"Hx1"
.
wp_pures
.
iCombine
"Hcredit1 Hcredit2"
as
"Hcredit"
.
wp_apply
(
release_spec
with
"[Hlocked Hcredit Hc]"
)
.
{
iFrame
"Hlock Hlocked"
.
iRight
.
iRight
.
iFrame
"Hcredit Hc"
.
}
iIntros
"_"
.
wp_pures
.
eauto
.
+
iDestruct
"Hc"
as
"[Hcredit1 Hc]"
.
by
iDestruct
(
own_valid_2
with
"Hcredit1 Hcredit2"
)
as
%
[]
.
-
iIntros
(??
[[
x1
->
]
[
x2
->
]])
"!>"
.
wp_pures
.
by
iApply
"HΦ"
.
iDestruct
"Hc"
as
"[[Hγ Hc]|[Hc|Hc]]"
.
+
wp_recv
(
v
)
as
"_"
.
wp_pures
.
iMod
(
own_update
_
_
((
3
/
4
⋅
1
/
4
),
to_agree
(
Some
v
))
%
Qp
with
"Hγ2"
)
as
"[Hγ2a Hγ2b]"
;
[
by
apply
cmra_update_exclusive
|]
.
wp_apply
(
release_spec
with
"[$Hlock $Hlocked Hγ2a Hc]"
)
.
{
iRight
.
iLeft
.
iExists
false
,
v
.
iFrame
.
}
iIntros
"_"
.
wp_pures
.
iLeft
.
iFrame
.
+
iDestruct
"Hc"
as
([]
v
)
"[Hγ1 Hc]"
;
last
first
.
{
by
iDestruct
(
own_valid_2
with
"Hγ1 Hγ2"
)
as
%
[]
.
}
wp_recv
(
v'
)
as
"HP"
.
wp_pures
.
iMod
(
own_update
_
_
((
1
/
4
⋅
3
/
4
),
to_agree
(
Some
v'
))
%
Qp
with
"Hγ2"
)
as
"[Hγ2a Hγ2b]"
;
[
by
apply
cmra_update_exclusive
|]
.
rewrite
{
1
}(_
:
3
/
4
=
1
/
4
+
1
/
2
)
%
Qp
;
last
(
by
apply
:
bool_decide_unpack
)
.
iDestruct
"Hγ1"
as
"[Hγ1a Hγ1b]"
.
wp_apply
(
release_spec
with
"[$Hlock $Hlocked Hγ1a Hγ2a Hc]"
)
.
{
do
2
iRight
.
iExists
v
,
v'
.
iFrame
.
}
iIntros
"_"
.
wp_pures
.
iRight
.
iExists
v
.
iFrame
.
+
iDestruct
"Hc"
as
(
v
v'
)
"(_ & Hγ2' & _)"
.
by
iDestruct
(
own_valid_2
with
"Hγ2 Hγ2'"
)
as
%
[]
.
-
iIntros
(
v1
v2
)
"[[[H1 Hγ]|H1] [[H2 Hγ']|H2]] !>"
.
+
by
iDestruct
(
own_valid_2
with
"Hγ Hγ'"
)
as
%
[]
.
+
iDestruct
"H2"
as
(
v2'
)
"(_&H1'&HP)"
.
iDestruct
(
own_valid_2
with
"H1 H1'"
)
as
%
[_
[
=->
]
%
agree_op_invL'
]
.
iApply
"HΦ"
;
auto
.
+
iDestruct
"H1"
as
(
v1'
)
"(_&H2'&HP)"
.
iDestruct
(
own_valid_2
with
"H2 H2'"
)
as
%
[_
[
=->
]
%
agree_op_invL'
]
.
iApply
"HΦ"
;
auto
.
+
iDestruct
"H1"
as
(
v1'
)
"[H1 _]"
;
iDestruct
"H2"
as
(
v2'
)
"(_&H2&_)"
.
by
iDestruct
(
own_valid_2
with
"H1 H2"
)
as
%
[]
.
Qed
.
Lemma
prog_typed
:
...
...
@@ -91,11 +118,12 @@ Section double.
iApply
wp_value
.
iSplitL
;
last
by
iApply
env_ltyped_empty
.
iIntros
(
c
)
"Hc"
.
iApply
(
wp_prog
with
"[Hc]"
)
.
iApply
(
wp_prog
(
λ
v1
v2
,
ltty_car
lty_int
v1
∗
ltty_car
lty_int
v2
)
%
I
with
"[Hc]"
)
.
{
iApply
(
iProto_mapsto_le
_
(
lsty_car
(
<
??
>
TY
lty_int
;
<
??
>
TY
lty_int
;
END
))
with
"Hc"
)
.
iIntros
"!> !>"
(
v1
)
.
iMod
1
as
%
[
x1
->
]
.
iExists
x1
.
iIntros
"!>"
(
v2
)
.
iMod
1
as
%
[
x2
->
]
.
iExists
x2
.
auto
.
}
iIntros
"!>"
(
k1
k2
_)
.
iExists
_,
_
.
iSplit
;
first
done
.
eauto
.
iIntros
"!> !>"
(
v1
)
.
iMod
1
as
%
[
x1
->
]
.
iExists
#
x1
.
iIntros
"!>"
(
v2
)
.
iMod
1
as
%
[
x2
->
]
.
iExists
#
x2
.
iSplitL
;
last
done
.
rewrite
/
ltty_car
/=.
auto
.
}
iIntros
"!>"
(
v1
v2
[[[
k1
->
]
[
k2
->
]]|[[
k1
->
]
[
k2
->
]]]);
iExists
_,
_;
iSplit
;
by
eauto
.
Qed
.
End
double
.
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