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Pierre Roux
Iris
Commits
9a3439f5
Commit
9a3439f5
authored
5 years ago
by
Robbert Krebbers
Browse files
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Make use of `excl_auth` camera.
parent
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2 changed files
theories/base_logic/lib/boxes.v
+13
-13
13 additions, 13 deletions
theories/base_logic/lib/boxes.v
theories/program_logic/ownp.v
+12
-14
12 additions, 14 deletions
theories/program_logic/ownp.v
with
25 additions
and
27 deletions
theories/base_logic/lib/boxes.v
+
13
−
13
View file @
9a3439f5
From
iris
.
proofmode
Require
Import
tactics
.
From
iris
.
proofmode
Require
Import
tactics
.
From
iris
.
algebra
Require
Import
excl
auth
gmap
agree
.
From
iris
.
algebra
Require
Import
excl
_
auth
gmap
agree
.
From
iris
.
base_logic
.
lib
Require
Export
invariants
.
From
iris
.
base_logic
.
lib
Require
Export
invariants
.
Set
Default
Proof
Using
"Type"
.
Set
Default
Proof
Using
"Type"
.
Import
uPred
.
Import
uPred
.
...
@@ -7,10 +7,10 @@ Import uPred.
...
@@ -7,10 +7,10 @@ Import uPred.
(** The CMRAs we need. *)
(** The CMRAs we need. *)
Class
boxG
Σ
:=
Class
boxG
Σ
:=
boxG_inG
:>
inG
Σ
(
prodR
boxG_inG
:>
inG
Σ
(
prodR
(
authR
(
optionUR
(
excl
R
boolO
)
))
(
excl_auth
R
boolO
)
(
optionR
(
agreeR
(
laterO
(
iPrePropO
Σ
)))))
.
(
optionR
(
agreeR
(
laterO
(
iPrePropO
Σ
)))))
.
Definition
boxΣ
:
gFunctors
:=
#
[
GFunctor
(
authR
(
optionUR
(
excl
R
boolO
))
*
Definition
boxΣ
:
gFunctors
:=
#
[
GFunctor
(
excl_auth
R
boolO
*
optionRF
(
agreeRF
(
▶
∙
))
)
]
.
optionRF
(
agreeRF
(
▶
∙
))
)
]
.
Instance
subG_boxΣ
Σ
:
subG
boxΣ
Σ
→
boxG
Σ
.
Instance
subG_boxΣ
Σ
:
subG
boxΣ
Σ
→
boxG
Σ
.
...
@@ -21,14 +21,14 @@ Section box_defs.
...
@@ -21,14 +21,14 @@ Section box_defs.
Definition
slice_name
:=
gname
.
Definition
slice_name
:=
gname
.
Definition
box_own_auth
(
γ
:
slice_name
)
(
a
:
auth
(
option
(
excl
bool
))
)
:
iProp
Σ
:=
Definition
box_own_auth
(
γ
:
slice_name
)
(
a
:
excl_authR
bool
O
)
:
iProp
Σ
:=
own
γ
(
a
,
None
)
.
own
γ
(
a
,
None
)
.
Definition
box_own_prop
(
γ
:
slice_name
)
(
P
:
iProp
Σ
)
:
iProp
Σ
:=
Definition
box_own_prop
(
γ
:
slice_name
)
(
P
:
iProp
Σ
)
:
iProp
Σ
:=
own
γ
(
ε
,
Some
(
to_agree
(
Next
(
iProp_unfold
P
))))
.
own
γ
(
ε
,
Some
(
to_agree
(
Next
(
iProp_unfold
P
))))
.
Definition
slice_inv
(
γ
:
slice_name
)
(
P
:
iProp
Σ
)
:
iProp
Σ
:=
Definition
slice_inv
(
γ
:
slice_name
)
(
P
:
iProp
Σ
)
:
iProp
Σ
:=
(
∃
b
,
box_own_auth
γ
(
●
Excl'
b
)
∗
if
b
then
P
else
True
)
%
I
.
(
∃
b
,
box_own_auth
γ
(
●
E
b
)
∗
if
b
then
P
else
True
)
%
I
.
Definition
slice
(
γ
:
slice_name
)
(
P
:
iProp
Σ
)
:
iProp
Σ
:=
Definition
slice
(
γ
:
slice_name
)
(
P
:
iProp
Σ
)
:
iProp
Σ
:=
(
box_own_prop
γ
P
∗
inv
N
(
slice_inv
γ
P
))
%
I
.
(
box_own_prop
γ
P
∗
inv
N
(
slice_inv
γ
P
))
%
I
.
...
@@ -36,7 +36,7 @@ Section box_defs.
...
@@ -36,7 +36,7 @@ Section box_defs.
Definition
box
(
f
:
gmap
slice_name
bool
)
(
P
:
iProp
Σ
)
:
iProp
Σ
:=
Definition
box
(
f
:
gmap
slice_name
bool
)
(
P
:
iProp
Σ
)
:
iProp
Σ
:=
(
∃
Φ
:
slice_name
→
iProp
Σ
,
(
∃
Φ
:
slice_name
→
iProp
Σ
,
▷
(
P
≡
[
∗
map
]
γ
↦
_
∈
f
,
Φ
γ
)
∗
▷
(
P
≡
[
∗
map
]
γ
↦
_
∈
f
,
Φ
γ
)
∗
[
∗
map
]
γ
↦
b
∈
f
,
box_own_auth
γ
(
◯
Excl'
b
)
∗
box_own_prop
γ
(
Φ
γ
)
∗
[
∗
map
]
γ
↦
b
∈
f
,
box_own_auth
γ
(
◯
E
b
)
∗
box_own_prop
γ
(
Φ
γ
)
∗
inv
N
(
slice_inv
γ
(
Φ
γ
)))
%
I
.
inv
N
(
slice_inv
γ
(
Φ
γ
)))
%
I
.
End
box_defs
.
End
box_defs
.
...
@@ -75,18 +75,18 @@ Global Instance box_proper f : Proper ((≡) ==> (≡)) (box N f).
...
@@ -75,18 +75,18 @@ Global Instance box_proper f : Proper ((≡) ==> (≡)) (box N f).
Proof
.
apply
ne_proper
,
_
.
Qed
.
Proof
.
apply
ne_proper
,
_
.
Qed
.
Lemma
box_own_auth_agree
γ
b1
b2
:
Lemma
box_own_auth_agree
γ
b1
b2
:
box_own_auth
γ
(
●
Excl'
b1
)
∗
box_own_auth
γ
(
◯
Excl'
b2
)
⊢
⌜
b1
=
b2
⌝.
box_own_auth
γ
(
●
E
b1
)
∗
box_own_auth
γ
(
◯
E
b2
)
⊢
⌜
b1
=
b2
⌝.
Proof
.
Proof
.
rewrite
/
box_own_prop
-
own_op
own_valid
prod_validI
/=
and_elim_l
.
rewrite
/
box_own_prop
-
own_op
own_valid
prod_validI
/=
and_elim_l
.
by
iDestruct
1
as
%
[[[]
[
=
]
%
leibniz_equiv
]
?]
%
auth_both_valid
.
by
iDestruct
1
as
%
?
%
excl_auth_agreeL
.
Qed
.
Qed
.
Lemma
box_own_auth_update
γ
b1
b2
b3
:
Lemma
box_own_auth_update
γ
b1
b2
b3
:
box_own_auth
γ
(
●
Excl'
b1
)
∗
box_own_auth
γ
(
◯
Excl'
b2
)
box_own_auth
γ
(
●
E
b1
)
∗
box_own_auth
γ
(
◯
E
b2
)
==∗
box_own_auth
γ
(
●
Excl'
b3
)
∗
box_own_auth
γ
(
◯
Excl'
b3
)
.
==∗
box_own_auth
γ
(
●
E
b3
)
∗
box_own_auth
γ
(
◯
E
b3
)
.
Proof
.
Proof
.
rewrite
/
box_own_auth
-!
own_op
.
apply
own_update
,
prod_update
;
last
done
.
rewrite
/
box_own_auth
-!
own_op
.
apply
own_update
,
prod_update
;
last
done
.
by
apply
auth_update
,
option_local_update
,
exclusive_local
_update
.
apply
excl_auth
_update
.
Qed
.
Qed
.
Lemma
box_own_agree
γ
Q1
Q2
:
Lemma
box_own_agree
γ
Q1
Q2
:
...
@@ -108,7 +108,7 @@ Lemma slice_insert_empty E q f Q P :
...
@@ -108,7 +108,7 @@ Lemma slice_insert_empty E q f Q P :
slice
N
γ
Q
∗
▷
?q
box
N
(
<
[
γ
:=
false
]
>
f
)
(
Q
∗
P
)
.
slice
N
γ
Q
∗
▷
?q
box
N
(
<
[
γ
:=
false
]
>
f
)
(
Q
∗
P
)
.
Proof
.
Proof
.
iDestruct
1
as
(
Φ
)
"[#HeqP Hf]"
.
iDestruct
1
as
(
Φ
)
"[#HeqP Hf]"
.
iMod
(
own_alloc_cofinite
(
●
Excl'
false
⋅
◯
Excl'
false
,
iMod
(
own_alloc_cofinite
(
●
E
false
⋅
◯
E
false
,
Some
(
to_agree
(
Next
(
iProp_unfold
Q
))))
(
dom
_
f
))
Some
(
to_agree
(
Next
(
iProp_unfold
Q
))))
(
dom
_
f
))
as
(
γ
)
"[Hdom Hγ]"
;
first
by
(
split
;
[
apply
auth_both_valid
|])
.
as
(
γ
)
"[Hdom Hγ]"
;
first
by
(
split
;
[
apply
auth_both_valid
|])
.
rewrite
pair_split
.
iDestruct
"Hγ"
as
"[[Hγ Hγ'] #HγQ]"
.
rewrite
pair_split
.
iDestruct
"Hγ"
as
"[[Hγ Hγ'] #HγQ]"
.
...
@@ -225,7 +225,7 @@ Lemma box_empty E f P :
...
@@ -225,7 +225,7 @@ Lemma box_empty E f P :
Proof
.
Proof
.
iDestruct
1
as
(
Φ
)
"[#HeqP Hf]"
.
iDestruct
1
as
(
Φ
)
"[#HeqP Hf]"
.
iAssert
(([
∗
map
]
γ
↦
b
∈
f
,
▷
Φ
γ
)
∗
iAssert
(([
∗
map
]
γ
↦
b
∈
f
,
▷
Φ
γ
)
∗
[
∗
map
]
γ
↦
b
∈
f
,
box_own_auth
γ
(
◯
Excl'
false
)
∗
box_own_prop
γ
(
Φ
γ
)
∗
[
∗
map
]
γ
↦
b
∈
f
,
box_own_auth
γ
(
◯
E
false
)
∗
box_own_prop
γ
(
Φ
γ
)
∗
inv
N
(
slice_inv
γ
(
Φ
γ
)))
%
I
with
"[> Hf]"
as
"[HΦ ?]"
.
inv
N
(
slice_inv
γ
(
Φ
γ
)))
%
I
with
"[> Hf]"
as
"[HΦ ?]"
.
{
rewrite
-
big_sepM_sep
-
big_sepM_fupd
.
iApply
(
@
big_sepM_impl
with
"[$Hf]"
)
.
{
rewrite
-
big_sepM_sep
-
big_sepM_fupd
.
iApply
(
@
big_sepM_impl
with
"[$Hf]"
)
.
iIntros
"!#"
(
γ
b
?)
"(Hγ' & #HγΦ & #Hinv)"
.
iIntros
"!#"
(
γ
b
?)
"(Hγ' & #HγΦ & #Hinv)"
.
...
...
This diff is collapsed.
Click to expand it.
theories/program_logic/ownp.v
+
12
−
14
View file @
9a3439f5
From
iris
.
proofmode
Require
Import
tactics
classes
.
From
iris
.
proofmode
Require
Import
tactics
classes
.
From
iris
.
algebra
Require
Import
excl
auth
.
From
iris
.
algebra
Require
Import
excl
_
auth
.
From
iris
.
program_logic
Require
Export
weakestpre
.
From
iris
.
program_logic
Require
Export
weakestpre
.
From
iris
.
program_logic
Require
Import
lifting
adequacy
.
From
iris
.
program_logic
Require
Import
lifting
adequacy
.
From
iris
.
program_logic
Require
ectx_language
.
From
iris
.
program_logic
Require
ectx_language
.
...
@@ -16,24 +16,24 @@ union.
...
@@ -16,24 +16,24 @@ union.
Class
ownPG
(
Λ
:
language
)
(
Σ
:
gFunctors
)
:=
OwnPG
{
Class
ownPG
(
Λ
:
language
)
(
Σ
:
gFunctors
)
:=
OwnPG
{
ownP_invG
:
invG
Σ
;
ownP_invG
:
invG
Σ
;
ownP_inG
:>
inG
Σ
(
authR
(
optionUR
(
excl
R
(
stateO
Λ
))
))
;
ownP_inG
:>
inG
Σ
(
excl_auth
R
(
stateO
Λ
));
ownP_name
:
gname
;
ownP_name
:
gname
;
}
.
}
.
Instance
ownPG_irisG
`{
!
ownPG
Λ
Σ
}
:
irisG
Λ
Σ
:=
{
Instance
ownPG_irisG
`{
!
ownPG
Λ
Σ
}
:
irisG
Λ
Σ
:=
{
iris_invG
:=
ownP_invG
;
iris_invG
:=
ownP_invG
;
state_interp
σ
κs
_
:=
own
ownP_name
(
●
(
Excl'
σ
)
)
%
I
;
state_interp
σ
κs
_
:=
own
ownP_name
(
●
E
σ
)
%
I
;
fork_post
_
:=
True
%
I
;
fork_post
_
:=
True
%
I
;
}
.
}
.
Global
Opaque
iris_invG
.
Global
Opaque
iris_invG
.
Definition
ownPΣ
(
Λ
:
language
)
:
gFunctors
:=
Definition
ownPΣ
(
Λ
:
language
)
:
gFunctors
:=
#
[
invΣ
;
#
[
invΣ
;
GFunctor
(
authR
(
optionUR
(
excl
R
(
stateO
Λ
))
))
]
.
GFunctor
(
excl_auth
R
(
stateO
Λ
))]
.
Class
ownPPreG
(
Λ
:
language
)
(
Σ
:
gFunctors
)
:
Set
:=
IrisPreG
{
Class
ownPPreG
(
Λ
:
language
)
(
Σ
:
gFunctors
)
:
Set
:=
IrisPreG
{
ownPPre_invG
:>
invPreG
Σ
;
ownPPre_invG
:>
invPreG
Σ
;
ownPPre_state_inG
:>
inG
Σ
(
authR
(
optionUR
(
excl
R
(
stateO
Λ
))
))
ownPPre_state_inG
:>
inG
Σ
(
excl_auth
R
(
stateO
Λ
))
}
.
}
.
Instance
subG_ownPΣ
{
Λ
Σ
}
:
subG
(
ownPΣ
Λ
)
Σ
→
ownPPreG
Λ
Σ
.
Instance
subG_ownPΣ
{
Λ
Σ
}
:
subG
(
ownPΣ
Λ
)
Σ
→
ownPPreG
Λ
Σ
.
...
@@ -41,8 +41,7 @@ Proof. solve_inG. Qed.
...
@@ -41,8 +41,7 @@ Proof. solve_inG. Qed.
(** Ownership *)
(** Ownership *)
Definition
ownP
`{
!
ownPG
Λ
Σ
}
(
σ
:
state
Λ
)
:
iProp
Σ
:=
Definition
ownP
`{
!
ownPG
Λ
Σ
}
(
σ
:
state
Λ
)
:
iProp
Σ
:=
own
ownP_name
(
◯
(
Excl'
σ
))
.
own
ownP_name
(
◯
E
σ
)
.
Typeclasses
Opaque
ownP
.
Typeclasses
Opaque
ownP
.
Instance
:
Params
(
@
ownP
)
3
:=
{}
.
Instance
:
Params
(
@
ownP
)
3
:=
{}
.
...
@@ -53,9 +52,9 @@ Theorem ownP_adequacy Σ `{!ownPPreG Λ Σ} s e σ φ :
...
@@ -53,9 +52,9 @@ Theorem ownP_adequacy Σ `{!ownPPreG Λ Σ} s e σ φ :
Proof
.
Proof
.
intros
Hwp
.
apply
(
wp_adequacy
Σ
_)
.
intros
Hwp
.
apply
(
wp_adequacy
Σ
_)
.
iIntros
(?
κs
)
.
iIntros
(?
κs
)
.
iMod
(
own_alloc
(
●
(
Excl'
σ
)
⋅
◯
(
Excl'
σ
))
)
as
(
γσ
)
"[Hσ Hσf]"
;
iMod
(
own_alloc
(
●
E
σ
⋅
◯
E
σ
))
as
(
γσ
)
"[Hσ Hσf]"
;
first
by
apply
auth_bo
th_valid
.
first
by
apply
excl_au
th_valid
.
iModIntro
.
iExists
(
λ
σ
κs
,
own
γσ
(
●
(
Excl'
σ
))
)
%
I
,
(
λ
_,
True
%
I
)
.
iModIntro
.
iExists
(
λ
σ
κs
,
own
γσ
(
●
E
σ
))
%
I
,
(
λ
_,
True
%
I
)
.
iFrame
"Hσ"
.
iFrame
"Hσ"
.
iApply
(
Hwp
(
OwnPG
_
_
_
_
γσ
))
.
rewrite
/
ownP
.
iFrame
.
iApply
(
Hwp
(
OwnPG
_
_
_
_
γσ
))
.
rewrite
/
ownP
.
iFrame
.
Qed
.
Qed
.
...
@@ -69,9 +68,9 @@ Theorem ownP_invariance Σ `{!ownPPreG Λ Σ} s e σ1 t2 σ2 φ :
...
@@ -69,9 +68,9 @@ Theorem ownP_invariance Σ `{!ownPPreG Λ Σ} s e σ1 t2 σ2 φ :
Proof
.
Proof
.
intros
Hwp
Hsteps
.
eapply
(
wp_invariance
Σ
Λ
s
e
σ1
t2
σ2
_)=>
//.
intros
Hwp
Hsteps
.
eapply
(
wp_invariance
Σ
Λ
s
e
σ1
t2
σ2
_)=>
//.
iIntros
(?
κs
)
.
iIntros
(?
κs
)
.
iMod
(
own_alloc
(
●
(
Excl'
σ1
)
⋅
◯
(
Excl'
σ1
))
)
as
(
γσ
)
"[Hσ Hσf]"
;
iMod
(
own_alloc
(
●
E
σ1
⋅
◯
E
σ1
))
as
(
γσ
)
"[Hσ Hσf]"
;
first
by
apply
auth_both_valid
.
first
by
apply
auth_both_valid
.
iExists
(
λ
σ
κs'
_,
own
γσ
(
●
(
Excl'
σ
))
)
%
I
,
(
λ
_,
True
%
I
)
.
iExists
(
λ
σ
κs'
_,
own
γσ
(
●
E
σ
))
%
I
,
(
λ
_,
True
%
I
)
.
iFrame
"Hσ"
.
iFrame
"Hσ"
.
iMod
(
Hwp
(
OwnPG
_
_
_
_
γσ
)
with
"[Hσf]"
)
as
"[$ H]"
;
iMod
(
Hwp
(
OwnPG
_
_
_
_
γσ
)
with
"[Hσf]"
)
as
"[$ H]"
;
first
by
rewrite
/
ownP
;
iFrame
.
first
by
rewrite
/
ownP
;
iFrame
.
...
@@ -118,8 +117,7 @@ Section lifting.
...
@@ -118,8 +117,7 @@ Section lifting.
iModIntro
;
iSplit
;
[
by
destruct
s
|];
iNext
;
iIntros
(
e2
σ2
efs
Hstep
)
.
iModIntro
;
iSplit
;
[
by
destruct
s
|];
iNext
;
iIntros
(
e2
σ2
efs
Hstep
)
.
iDestruct
"Hσκs"
as
"Hσ"
.
rewrite
/
ownP
.
iDestruct
"Hσκs"
as
"Hσ"
.
rewrite
/
ownP
.
iMod
(
own_update_2
with
"Hσ Hσf"
)
as
"[Hσ Hσf]"
.
iMod
(
own_update_2
with
"Hσ Hσf"
)
as
"[Hσ Hσf]"
.
{
apply
auth_update
.
apply
option_local_update
.
{
apply
excl_auth_update
.
}
by
apply
(
exclusive_local_update
_
(
Excl
σ2
))
.
}
iFrame
"Hσ"
.
iApply
(
"H"
with
"[]"
);
eauto
with
iFrame
.
iFrame
"Hσ"
.
iApply
(
"H"
with
"[]"
);
eauto
with
iFrame
.
Qed
.
Qed
.
...
...
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