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Iris
Fairis
Commits
757807b0
Commit
757807b0
authored
Jul 03, 2016
by
Robbert Krebbers
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Correctness of monotone counter.
parent
a17e5b6e
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heap_lang/lib/counter.v
heap_lang/lib/counter.v
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_CoqProject
View file @
757807b0
...
...
@@ -94,6 +94,7 @@ heap_lang/lib/spawn.v
heap_lang/lib/par.v
heap_lang/lib/assert.v
heap_lang/lib/lock.v
heap_lang/lib/counter.v
heap_lang/lib/barrier/barrier.v
heap_lang/lib/barrier/specification.v
heap_lang/lib/barrier/protocol.v
...
...
heap_lang/lib/counter.v
0 → 100644
View file @
757807b0
(
*
Monotone
counter
,
but
using
an
explicit
CMRA
instead
of
auth
*
)
From
iris
.
program_logic
Require
Export
global_functor
.
From
iris
.
program_logic
Require
Import
auth
.
From
iris
.
proofmode
Require
Import
invariants
ghost_ownership
coq_tactics
.
From
iris
.
heap_lang
Require
Import
proofmode
notation
.
Import
uPred
.
Definition
newcounter
:
val
:=
λ
:
<>
,
ref
#
0.
Definition
inc
:
val
:=
rec:
"inc"
"l"
:=
let:
"n"
:=
!
'
"l"
in
if:
CAS
'
"l"
'
"n"
(#
1
+
'
"n"
)
then
#()
else
'
"inc"
'
"l"
.
Definition
read
:
val
:=
λ
:
"l"
,
!
'
"l"
.
Global
Opaque
newcounter
inc
get
.
(
**
The
CMRA
we
need
.
*
)
Class
counterG
Σ
:=
CounterG
{
counter_tokG
:>
authG
heap_lang
Σ
mnatUR
}
.
Definition
counterGF
:
gFunctorList
:=
[
authGF
mnatUR
].
Instance
inGF_counterG
`
{
H
:
inGFs
heap_lang
Σ
counterGF
}
:
counterG
Σ
.
Proof
.
destruct
H
;
split
;
apply
_.
Qed
.
Section
proof
.
Context
{
Σ
:
gFunctors
}
`
{!
heapG
Σ
,
!
counterG
Σ
}
.
Context
(
heapN
:
namespace
).
Local
Notation
iProp
:=
(
iPropG
heap_lang
Σ
).
Definition
counter_inv
(
l
:
loc
)
(
n
:
mnat
)
:
iProp
:=
(
l
↦
#
n
)
%
I
.
Definition
counter
(
l
:
loc
)
(
n
:
nat
)
:
iProp
:=
(
∃
N
γ
,
heapN
⊥
N
∧
heap_ctx
heapN
∧
auth_ctx
γ
N
(
counter_inv
l
)
∧
auth_own
γ
(
n
:
mnat
))
%
I
.
(
**
The
main
proofs
.
*
)
Global
Instance
counter_persistent
l
n
:
PersistentP
(
counter
l
n
).
Proof
.
apply
_.
Qed
.
Lemma
newcounter_spec
N
(
R
:
iProp
)
Φ
:
heapN
⊥
N
→
heap_ctx
heapN
★
(
∀
l
,
counter
l
0
-
★
Φ
#
l
)
⊢
WP
newcounter
#()
{{
Φ
}}
.
Proof
.
iIntros
{?}
"[#Hh HΦ]"
.
rewrite
/
newcounter
.
wp_seq
.
wp_alloc
l
as
"Hl"
.
iPvs
(
auth_alloc
(
counter_inv
l
)
N
_
(
O
:
mnat
)
with
"[Hl]"
)
as
{
γ
}
"[#? Hγ]"
;
try
by
auto
.
iPvsIntro
.
iApply
"HΦ"
.
rewrite
/
counter
;
eauto
10.
Qed
.
Lemma
inc_spec
l
j
(
Φ
:
val
→
iProp
)
:
counter
l
j
★
(
counter
l
(
S
j
)
-
★
Φ
#())
⊢
WP
inc
#
l
{{
Φ
}}
.
Proof
.
iIntros
"[Hl HΦ]"
.
iL
ö
b
as
"IH"
.
wp_rec
.
iDestruct
"Hl"
as
{
N
γ
}
"(% & #? & #Hγ & Hγf)"
.
wp_focus
(
!
_
)
%
E
;
iApply
(
auth_fsa
(
counter_inv
l
)
(
wp_fsa
_
)
_
N
);
auto
.
iIntros
"{$Hγ $Hγf}"
;
iIntros
{
j
'
}
"[% Hl] /="
;
rewrite
{
2
}/
counter_inv
.
wp_load
;
iPvsIntro
;
iExists
j
;
iSplit
;
[
done
|
iIntros
"{$Hl} Hγf"
].
wp_let
;
wp_op
.
wp_focus
(
CAS
_
_
_
);
iApply
(
auth_fsa
(
counter_inv
l
)
(
wp_fsa
_
)
_
N
);
auto
.
iIntros
"{$Hγ $Hγf}"
;
iIntros
{
j
''
}
"[% Hl] /="
;
rewrite
{
2
}/
counter_inv
.
destruct
(
decide
(
j
`max
`
j
''
=
j
`max
`
j
'
))
as
[
Hj
|
Hj
].
-
wp_cas_suc
;
first
(
by
do
3
f_equal
);
iPvsIntro
.
iExists
(
1
+
j
`max
`
j
'
)
%
nat
;
iSplit
.
{
iPureIntro
.
apply
mnat_local_update
.
abstract
lia
.
}
rewrite
{
2
}/
counter_inv
!
mnat_op_max
(
Nat
.
max_l
(
S
_
));
last
abstract
lia
.
rewrite
Nat2Z
.
inj_succ
-
Z
.
add_1_l
.
iIntros
"{$Hl} Hγf"
.
wp_if
.
iPvsIntro
;
iApply
"HΦ"
;
iExists
N
,
γ
;
repeat
iSplit
;
eauto
.
iApply
(
auth_own_mono
with
"Hγf"
).
apply
mnat_included
.
abstract
lia
.
-
wp_cas_fail
;
first
(
rewrite
!
mnat_op_max
;
by
intros
[
=
?%
Nat2Z
.
inj
]).
iPvsIntro
.
iExists
j
;
iSplit
;
[
done
|
iIntros
"{$Hl} Hγf"
].
wp_if
.
iApply
(
"IH"
with
"[Hγf] HΦ"
).
rewrite
{
3
}/
counter
;
eauto
10.
Qed
.
Lemma
read_spec
l
j
(
Φ
:
val
→
iProp
)
:
counter
l
j
★
(
∀
i
,
■
(
j
≤
i
)
%
nat
→
counter
l
i
-
★
Φ
#
i
)
⊢
WP
read
#
l
{{
Φ
}}
.
Proof
.
iIntros
"[Hc HΦ]"
.
iDestruct
"Hc"
as
{
N
γ
}
"(% & #? & #Hγ & Hγf)"
.
rewrite
/
read
.
wp_let
.
iApply
(
auth_fsa
(
counter_inv
l
)
(
wp_fsa
_
)
_
N
);
auto
.
iIntros
"{$Hγ $Hγf}"
;
iIntros
{
j
'
}
"[% Hl] /="
.
wp_load
;
iPvsIntro
;
iExists
(
j
`max
`
j
'
);
iSplit
.
{
iPureIntro
;
apply
mnat_local_update
;
abstract
lia
.
}
rewrite
!
mnat_op_max
-
Nat
.
max_assoc
Nat
.
max_idempotent
;
iIntros
"{$Hl} Hγf"
.
iApply
(
"HΦ"
with
"[%]"
);
first
abstract
lia
;
rewrite
/
counter
;
eauto
10.
Qed
.
End
proof
.
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