Skip to content
GitLab
Projects
Groups
Snippets
Help
Loading...
Help
What's new
10
Help
Support
Community forum
Keyboard shortcuts
?
Submit feedback
Contribute to GitLab
Sign in / Register
Toggle navigation
Open sidebar
Iris
Iris
Commits
12d7f42c
Commit
12d7f42c
authored
Feb 24, 2016
by
Ralf Jung
Browse files
Options
Browse Files
Download
Email Patches
Plain Diff
seal STS ownership
parent
18f2e6b0
Pipeline
#120
failed with stage
Changes
1
Pipelines
1
Hide whitespace changes
Inline
Side-by-side
Showing
1 changed file
with
50 additions
and
21 deletions
+50
-21
program_logic/sts.v
program_logic/sts.v
+50
-21
No files found.
program_logic/sts.v
View file @
12d7f42c
...
...
@@ -13,18 +13,35 @@ Instance inGF_stsG sts `{inGF Λ Σ (stsGF sts)}
`
{
Inhabited
(
sts
.
state
sts
)}
:
stsG
Λ
Σ
sts
.
Proof
.
split
;
try
apply
_
.
apply
:
inGF_inG
.
Qed
.
Section
definitions
.
Context
`
{
i
:
stsG
Λ
Σ
sts
}
(
γ
:
gname
).
Import
sts
.
Definition
sts_inv
(
φ
:
state
sts
→
iPropG
Λ
Σ
)
:
iPropG
Λ
Σ
:
=
(
∃
s
,
own
γ
(
sts_auth
s
∅
)
★
φ
s
)%
I
.
Definition
sts_ownS
(
S
:
states
sts
)
(
T
:
tokens
sts
)
:
iPropG
Λ
Σ
:
=
own
γ
(
sts_frag
S
T
).
Definition
sts_own
(
s
:
state
sts
)
(
T
:
tokens
sts
)
:
iPropG
Λ
Σ
:
=
own
γ
(
sts_frag_up
s
T
).
Definition
sts_ctx
(
N
:
namespace
)
(
φ
:
state
sts
→
iPropG
Λ
Σ
)
:
iPropG
Λ
Σ
:
=
inv
N
(
sts_inv
φ
).
End
definitions
.
Definition
sts_ownS_def
`
{
i
:
stsG
Λ
Σ
sts
}
(
γ
:
gname
)
(
S
:
sts
.
states
sts
)
(
T
:
sts
.
tokens
sts
)
:
iPropG
Λ
Σ
:
=
own
γ
(
sts_frag
S
T
).
Definition
sts_own_def
`
{
i
:
stsG
Λ
Σ
sts
}
(
γ
:
gname
)
(
s
:
sts
.
state
sts
)
(
T
:
sts
.
tokens
sts
)
:
iPropG
Λ
Σ
:
=
own
γ
(
sts_frag_up
s
T
).
(* Perform sealing. *)
Module
Type
StsOwnSig
.
Parameter
sts_ownS
:
∀
`
{
i
:
stsG
Λ
Σ
sts
}
(
γ
:
gname
)
(
S
:
sts
.
states
sts
)
(
T
:
sts
.
tokens
sts
),
iPropG
Λ
Σ
.
Parameter
sts_own
:
∀
`
{
i
:
stsG
Λ
Σ
sts
}
(
γ
:
gname
)
(
s
:
sts
.
state
sts
)
(
T
:
sts
.
tokens
sts
),
iPropG
Λ
Σ
.
Axiom
sts_ownS_def
:
@
sts_ownS
=
@
sts_ownS_def
.
Axiom
sts_own_def
:
@
sts_own
=
@
sts_own_def
.
End
StsOwnSig
.
Module
Export
StsOwn
:
StsOwnSig
.
Definition
sts_ownS
:
=
@
sts_ownS_def
.
Definition
sts_own
:
=
@
sts_own_def
.
Definition
sts_ownS_def
:
=
Logic
.
eq_refl
(@
sts_ownS_def
).
Definition
sts_own_def
:
=
Logic
.
eq_refl
(@
sts_own_def
).
End
StsOwn
.
Definition
sts_inv
`
{
i
:
stsG
Λ
Σ
sts
}
(
γ
:
gname
)
(
φ
:
sts
.
state
sts
→
iPropG
Λ
Σ
)
:
iPropG
Λ
Σ
:
=
(
∃
s
,
own
γ
(
sts_auth
s
∅
)
★
φ
s
)%
I
.
Definition
sts_ctx
`
{
i
:
stsG
Λ
Σ
sts
}
(
γ
:
gname
)
(
N
:
namespace
)
(
φ
:
sts
.
state
sts
→
iPropG
Λ
Σ
)
:
iPropG
Λ
Σ
:
=
inv
N
(
sts_inv
γ
φ
).
Instance
:
Params
(@
sts_inv
)
5
.
Instance
:
Params
(@
sts_ownS
)
5
.
Instance
:
Params
(@
sts_own
)
6
.
...
...
@@ -46,9 +63,11 @@ Section sts.
Proper
(
pointwise_relation
_
(
≡
)
==>
(
≡
))
(
sts_inv
γ
).
Proof
.
by
intros
φ
1
φ
2
H
φ
;
rewrite
/
sts_inv
;
setoid_rewrite
H
φ
.
Qed
.
Global
Instance
sts_ownS_proper
γ
:
Proper
((
≡
)
==>
(
≡
)
==>
(
≡
))
(
sts_ownS
γ
).
Proof
.
intros
S1
S2
HS
T1
T2
HT
.
by
rewrite
/
sts_ownS
HS
HT
.
Qed
.
Proof
.
intros
S1
S2
HS
T1
T2
HT
.
by
rewrite
!
sts_ownS_def
/
Top
.
sts_ownS_def
HS
HT
.
Qed
.
Global
Instance
sts_own_proper
γ
s
:
Proper
((
≡
)
==>
(
≡
))
(
sts_own
γ
s
).
Proof
.
intros
T1
T2
HT
.
by
rewrite
/
sts_own
HT
.
Qed
.
Proof
.
intros
T1
T2
HT
.
by
rewrite
!
sts_own_def
/
Top
.
sts_own
_def
HT
.
Qed
.
Global
Instance
sts_ctx_ne
n
γ
N
:
Proper
(
pointwise_relation
_
(
dist
n
)
==>
dist
n
)
(
sts_ctx
γ
N
).
Proof
.
by
intros
φ
1
φ
2
H
φ
;
rewrite
/
sts_ctx
H
φ
.
Qed
.
...
...
@@ -61,17 +80,24 @@ Section sts.
Lemma
sts_ownS_weaken
E
γ
S1
S2
T1
T2
:
T2
⊆
T1
→
S1
⊆
S2
→
sts
.
closed
S2
T2
→
sts_ownS
γ
S1
T1
⊑
(|={
E
}=>
sts_ownS
γ
S2
T2
).
Proof
.
intros
?
?
?.
by
apply
own_update
,
sts_update_frag
.
Qed
.
Proof
.
intros
?
?
?.
rewrite
sts_ownS_def
.
by
apply
own_update
,
sts_update_frag
.
Qed
.
Lemma
sts_own_weaken
E
γ
s
S
T1
T2
:
T2
⊆
T1
→
s
∈
S
→
sts
.
closed
S
T2
→
sts_own
γ
s
T1
⊑
(|={
E
}=>
sts_ownS
γ
S
T2
).
Proof
.
intros
???.
by
apply
own_update
,
sts_update_frag_up
.
Qed
.
Proof
.
intros
???.
rewrite
sts_ownS_def
sts_own_def
.
by
apply
own_update
,
sts_update_frag_up
.
Qed
.
Lemma
sts_ownS_op
γ
S1
S2
T1
T2
:
T1
∩
T2
⊆
∅
→
sts
.
closed
S1
T1
→
sts
.
closed
S2
T2
→
sts_ownS
γ
(
S1
∩
S2
)
(
T1
∪
T2
)
≡
(
sts_ownS
γ
S1
T1
★
sts_ownS
γ
S2
T2
)%
I
.
Proof
.
intros
.
by
rewrite
/
sts_ownS
-
own_op
sts_op_frag
.
Qed
.
Proof
.
intros
.
by
rewrite
sts_ownS_def
/
Top
.
sts_ownS_def
-
own_op
sts_op_frag
.
Qed
.
Lemma
sts_alloc
E
N
s
:
nclose
N
⊆
E
→
...
...
@@ -85,7 +111,7 @@ Section sts.
rewrite
sep_exist_l
.
apply
exist_elim
=>
γ
.
rewrite
-(
exist_intro
γ
).
trans
(
▷
sts_inv
γ
φ
★
sts_own
γ
s
(
⊤
∖
sts
.
tok
s
))%
I
.
{
rewrite
/
sts_inv
-(
exist_intro
s
)
later_sep
.
ecancel
[
▷
φ
_
]%
I
.
ecancel
[
▷
φ
_
]%
I
.
rewrite
sts_own_def
.
by
rewrite
-
later_intro
-
own_op
sts_op_auth_frag_up
;
last
set_solver
.
}
rewrite
(
inv_alloc
N
)
/
sts_ctx
pvs_frame_r
.
by
rewrite
always_and_sep_l
.
...
...
@@ -95,7 +121,7 @@ Section sts.
(
▷
sts_inv
γ
φ
★
sts_ownS
γ
S
T
)
⊑
(|={
E
}=>
∃
s
,
■
(
s
∈
S
)
★
▷
φ
s
★
own
γ
(
sts_auth
s
T
)).
Proof
.
rewrite
/
sts_inv
/
sts_ownS
later_exist
sep_exist_r
.
apply
exist_elim
=>
s
.
rewrite
/
sts_inv
sts_ownS
_def
later_exist
sep_exist_r
.
apply
exist_elim
=>
s
.
rewrite
later_sep
pvs_timeless
!
pvs_frame_r
.
apply
pvs_mono
.
rewrite
-(
exist_intro
s
).
rewrite
[(
_
★
▷φ
_
)%
I
]
comm
-!
assoc
-
own_op
-[(
▷φ
_
★
_
)%
I
]
comm
.
...
...
@@ -112,7 +138,7 @@ Section sts.
sts
.
steps
(
s
,
T
)
(
s'
,
T'
)
→
(
▷
φ
s'
★
own
γ
(
sts_auth
s
T
))
⊑
(|={
E
}=>
▷
sts_inv
γ
φ
★
sts_own
γ
s'
T'
).
Proof
.
intros
Hstep
.
rewrite
/
sts_inv
/
sts_own
-(
exist_intro
s'
)
later_sep
.
intros
Hstep
.
rewrite
/
sts_inv
sts_own
_def
-(
exist_intro
s'
)
later_sep
.
(* TODO it would be really nice to use cancel here *)
rewrite
[(
_
★
▷
φ
_
)%
I
]
comm
-
assoc
.
rewrite
-
pvs_frame_l
.
apply
sep_mono_r
.
rewrite
-
later_intro
.
...
...
@@ -162,5 +188,8 @@ Section sts.
■
(
sts
.
steps
(
s
,
T
)
(
s'
,
T'
))
★
▷
φ
s'
★
(
sts_own
γ
s'
T'
-
★
Ψ
x
)))
→
P
⊑
fsa
E
Ψ
.
Proof
.
apply
sts_fsaS
.
Qed
.
Proof
.
rewrite
sts_own_def
.
intros
.
eapply
sts_fsaS
;
try
done
;
[].
by
rewrite
sts_ownS_def
sts_own_def
.
Qed
.
End
sts
.
Write
Preview
Markdown
is supported
0%
Try again
or
attach a new file
.
Attach a file
Cancel
You are about to add
0
people
to the discussion. Proceed with caution.
Finish editing this message first!
Cancel
Please
register
or
sign in
to comment