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Tej Chajed
iris
Commits
cf62a15f
Commit
cf62a15f
authored
Aug 06, 2016
by
Robbert Krebbers
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New test case: counter with explicit CMRA construction.
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7a82a515
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_CoqProject
View file @
cf62a15f
...
...
@@ -110,6 +110,7 @@ tests/proofmode.v
tests/barrier_client.v
tests/list_reverse.v
tests/tree_sum.v
tests/counter.v
proofmode/coq_tactics.v
proofmode/pviewshifts.v
proofmode/environments.v
...
...
tests/counter.v
0 → 100644
View file @
cf62a15f
(* This file contains a formalization of the monotone counter, but with an
explicit contruction of the monoid, as we have also done in the proof mode
paper. A version that uses the authoritative monoid and natural number monoid
under max can be found in `heap_lang/lib/counter.v`. *)
From
iris
.
program_logic
Require
Export
weakestpre
.
From
iris
.
heap_lang
Require
Export
lang
.
From
iris
.
program_logic
Require
Export
hoare
.
From
iris
.
proofmode
Require
Import
invariants
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
read
.
(** The CMRA we need. *)
Inductive
M
:
=
Auth
:
nat
→
M
|
Frag
:
nat
→
M
|
Bot
.
Section
M
.
Arguments
cmra_op
_
!
_
!
_
/.
Arguments
op
_
_
!
_
!
_
/.
Arguments
core
_
_
!
_
/.
Canonical
Structure
M_C
:
cofeT
:
=
leibnizC
M
.
Instance
M_valid
:
Valid
M
:
=
λ
x
,
x
≠
Bot
.
Instance
M_op
:
Op
M
:
=
λ
x
y
,
match
x
,
y
with
|
Auth
n
,
Frag
j
|
Frag
j
,
Auth
n
=>
if
decide
(
j
≤
n
)%
nat
then
Auth
n
else
Bot
|
Frag
i
,
Frag
j
=>
Frag
(
max
i
j
)
|
_
,
_
=>
Bot
end
.
Instance
M_pcore
:
PCore
M
:
=
λ
x
,
Some
match
x
with
Auth
j
|
Frag
j
=>
Frag
j
|
_
=>
Bot
end
.
Instance
M_empty
:
Empty
M
:
=
Frag
0
.
Definition
M_ra_mixin
:
RAMixin
M
.
Proof
.
apply
ra_total_mixin
;
try
solve_proper
||
eauto
.
-
intros
[
n1
|
i1
|]
[
n2
|
i2
|]
[
n3
|
i3
|]
;
repeat
(
simpl
;
case_decide
)
;
f_equal
/=
;
lia
.
-
intros
[
n1
|
i1
|]
[
n2
|
i2
|]
;
repeat
(
simpl
;
case_decide
)
;
f_equal
/=
;
lia
.
-
intros
[
n
|
i
|]
;
repeat
(
simpl
;
case_decide
)
;
f_equal
/=
;
lia
.
-
by
intros
[
n
|
i
|].
-
intros
[
n1
|
i1
|]
y
[[
n2
|
i2
|]
?]
;
exists
(
core
y
)
;
simplify_eq
/=
;
repeat
(
simpl
;
case_decide
)
;
f_equal
/=
;
lia
.
-
intros
[
n1
|
i1
|]
[
n2
|
i2
|]
;
simpl
;
by
try
case_decide
.
Qed
.
Canonical
Structure
M_R
:
cmraT
:
=
discreteR
M
M_ra_mixin
.
Definition
M_ucmra_mixin
:
UCMRAMixin
M
.
Proof
.
split
;
try
(
done
||
apply
_
).
intros
[?|?|]
;
simpl
;
try
case_decide
;
f_equal
/=
;
lia
.
Qed
.
Canonical
Structure
M_UR
:
ucmraT
:
=
discreteUR
M
M_ra_mixin
M_ucmra_mixin
.
Global
Instance
frag_persistent
n
:
Persistent
(
Frag
n
).
Proof
.
by
constructor
.
Qed
.
Lemma
auth_frag_valid
j
n
:
✓
(
Auth
n
⋅
Frag
j
)
→
(
j
≤
n
)%
nat
.
Proof
.
simpl
.
case_decide
.
done
.
by
intros
[].
Qed
.
Lemma
auth_frag_op
(
j
n
:
nat
)
:
(
j
≤
n
)%
nat
→
Auth
n
=
Auth
n
⋅
Frag
j
.
Proof
.
intros
.
by
rewrite
/=
decide_True
.
Qed
.
Lemma
M_update
n
:
Auth
n
~~>
Auth
(
S
n
).
Proof
.
apply
cmra_discrete_update
=>-[
m
|
j
|]
/=
?
;
repeat
case_decide
;
done
||
lia
.
Qed
.
End
M
.
Class
counterG
Σ
:
=
CounterG
{
counter_tokG
:
>
inG
Σ
M_UR
}.
Definition
counterGF
:
gFunctorList
:
=
[
GFunctor
(
constRF
M_UR
)].
Instance
inGF_counterG
`
{
H
:
inGFs
Σ
counterGF
}
:
counterG
Σ
.
Proof
.
destruct
H
.
split
.
apply
:
inGF_inG
.
Qed
.
Section
proof
.
Context
`
{!
heapG
Σ
,
!
counterG
Σ
}.
Implicit
Types
l
:
loc
.
Definition
I
(
γ
:
gname
)
(
l
:
loc
)
:
iProp
Σ
:
=
(
∃
c
:
nat
,
l
↦
#
c
★
own
γ
(
Auth
c
))%
I
.
Definition
C
(
l
:
loc
)
(
n
:
nat
)
:
iProp
Σ
:
=
(
∃
N
γ
,
heapN
⊥
N
∧
heap_ctx
∧
inv
N
(
I
γ
l
)
∧
own
γ
(
Frag
n
))%
I
.
(** The main proofs. *)
Global
Instance
C_persistent
l
n
:
PersistentP
(
C
l
n
).
Proof
.
apply
_
.
Qed
.
Lemma
newcounter_spec
N
:
heapN
⊥
N
→
heap_ctx
⊢
{{
True
}}
newcounter
#()
{{
v
,
∃
l
,
v
=
#
l
∧
C
l
0
}}.
Proof
.
iIntros
(?)
"#Hh !# _ /="
.
rewrite
/
newcounter
.
wp_seq
.
wp_alloc
l
as
"Hl"
.
iVs
(
own_alloc
(
Auth
0
))
as
(
γ
)
"Hγ"
;
first
done
.
rewrite
(
auth_frag_op
0
0
)
//
;
iDestruct
"Hγ"
as
"[Hγ Hγf]"
.
iVs
(
inv_alloc
N
_
(
I
γ
l
)
with
"[Hl Hγ]"
)
as
"#?"
.
{
iIntros
"!>"
.
iExists
0
%
nat
.
by
iFrame
.
}
iVsIntro
.
rewrite
/
C
;
eauto
10
.
Qed
.
Lemma
inc_spec
l
n
:
{{
C
l
n
}}
inc
#
l
{{
v
,
v
=
#()
∧
C
l
(
S
n
)
}}.
Proof
.
iIntros
"!# Hl /="
.
iL
ö
b
as
"IH"
.
wp_rec
.
iDestruct
"Hl"
as
(
N
γ
)
"(% & #Hh & #Hinv & Hγf)"
.
wp_bind
(!
_
)%
E
;
iInv
N
as
(
c
)
"[Hl Hγ]"
"Hclose"
.
wp_load
.
iVs
(
"Hclose"
with
"[Hl Hγ]"
)
;
[
iNext
;
iExists
c
;
by
iFrame
|].
iVsIntro
.
wp_let
.
wp_op
.
wp_bind
(
CAS
_
_
_
).
iInv
N
as
(
c'
)
">[Hl Hγ]"
"Hclose"
.
destruct
(
decide
(
c'
=
c
))
as
[->|].
-
iCombine
"Hγ"
"Hγf"
as
"Hγ"
.
iDestruct
(
own_valid
with
"#Hγ"
)
as
%?%
auth_frag_valid
;
rewrite
-
auth_frag_op
//.
iVs
(
own_update
with
"Hγ"
)
as
"Hγ"
;
first
apply
M_update
.
rewrite
(
auth_frag_op
(
S
n
)
(
S
c
))
;
last
lia
;
iDestruct
"Hγ"
as
"[Hγ Hγf]"
.
wp_cas_suc
.
iVs
(
"Hclose"
with
"[Hl Hγ]"
).
{
iNext
.
iExists
(
S
c
).
rewrite
Nat2Z
.
inj_succ
Z
.
add_1_l
.
by
iFrame
.
}
iVsIntro
.
wp_if
.
iVsIntro
;
rewrite
{
3
}/
C
;
eauto
10
.
-
wp_cas_fail
;
first
(
intros
[=]
;
abstract
omega
).
iVs
(
"Hclose"
with
"[Hl Hγ]"
)
;
[
iNext
;
iExists
c'
;
by
iFrame
|].
iVsIntro
.
wp_if
.
iApply
(
"IH"
with
"[Hγf]"
).
rewrite
{
3
}/
C
;
eauto
10
.
Qed
.
Lemma
read_spec
l
n
:
{{
C
l
n
}}
read
#
l
{{
v
,
∃
m
:
nat
,
■
(
v
=
#
m
∧
n
≤
m
)
∧
C
l
m
}}.
Proof
.
iIntros
"!# Hl /="
.
iDestruct
"Hl"
as
(
N
γ
)
"(% & #Hh & #Hinv & Hγf)"
.
rewrite
/
read
.
wp_let
.
iInv
N
as
(
c
)
"[Hl Hγ]"
"Hclose"
.
wp_load
.
iDestruct
(
own_valid
γ
(
Frag
n
⋅
Auth
c
)
with
"[#]"
)
as
%
?%
auth_frag_valid
.
{
iApply
own_op
.
by
iFrame
.
}
rewrite
(
auth_frag_op
c
c
)
;
last
lia
;
iDestruct
"Hγ"
as
"[Hγ Hγf']"
.
iVs
(
"Hclose"
with
"[Hl Hγ]"
)
;
[
iNext
;
iExists
c
;
by
iFrame
|].
iVsIntro
;
rewrite
/
C
;
eauto
10
with
omega
.
Qed
.
End
proof
.
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