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Rodolphe Lepigre
Iris
Commits
8bf6270c
Commit
8bf6270c
authored
Apr 19, 2016
by
Robbert Krebbers
Browse files
Misc clean up.
parent
3466bb6e
Changes
3
Hide whitespace changes
Inline
Sidebyside
program_logic/hoare.v
View file @
8bf6270c
...
...
@@ 107,18 +107,15 @@ Proof. setoid_rewrite (comm _ _ R); apply ht_frame_l. Qed.
Lemma
ht_frame_step_l
E
E1
E2
P
R1
R2
R3
e
Φ
:
to_val
e
=
None
→
E
⊥
E1
→
E2
⊆
E1
→
((
R1
={
E1
,
E2
}=>
▷
R2
)
∧
(
R2
={
E2
,
E1
}=>
R3
)
∧
{{
P
}}
e
@
E
{{
Φ
}})
⊢
{{
R1
★
P
}}
e
@
(
E
∪
E1
)
{{
λ
v
,
R3
★
Φ
v
}}.
⊢
{{
R1
★
P
}}
e
@
E
∪
E1
{{
λ
v
,
R3
★
Φ
v
}}.
Proof
.
iIntros
{???}
"[#Hvs1 [#Hvs2 #Hwp]] ! [HR HP]"
.
iApply
(
wp_frame_step_l
E
E1
E2
)
;
try
done
.
iSplitL
"HR"
.

(* TODO: Is there a way to do "apply Hvs1 in Hr"? *)
iPvs
"Hvs1"
"HR"
;
first
by
set_solver
.
(* TODO: iApply pvs_intro? *)
rewrite

pvs_intro
.
iNext
.
iPvs
"Hvs2"
"Hvs1"
;
first
by
set_solver
.
rewrite

pvs_intro
.
done
.

iApply
"Hwp"
.
done
.
iSplitL
"HR"
;
[
by
iApply
"Hwp"
].
iPvs
"Hvs1"
"HR"
;
first
by
set_solver
.
iPvsIntro
.
iNext
.
iPvs
"Hvs2"
"Hvs1"
;
first
by
set_solver
.
by
iPvsIntro
.
Qed
.
Lemma
ht_frame_step_r
E
E1
E2
P
R1
R2
R3
e
Φ
:
...
...
@@ 128,8 +125,7 @@ Lemma ht_frame_step_r E E1 E2 P R1 R2 R3 e Φ :
Proof
.
iIntros
{???}
"[#Hvs1 [#Hvs2 #Hwp]]"
.
setoid_rewrite
(
comm
_
_
R3
).
iApply
ht_frame_step_l
;
try
eassumption
.
iSplit
;
last
iSplit
;
iIntros
"!"
;
done
.
iApply
ht_frame_step_l
;
try
eassumption
.
repeat
iSplit
;
by
iIntros
"!"
.
Qed
.
Lemma
ht_frame_step_l'
E
P
R
e
Φ
:
...
...
program_logic/weakestpre.v
View file @
8bf6270c
...
...
@@ 198,33 +198,37 @@ Proof.
Qed
.
Lemma
wp_frame_step_r
E
E1
E2
e
Φ
R
:
to_val
e
=
None
→
E
⊥
E1
→
E2
⊆
E1
→
(
WP
e
@
E
{{
Φ
}}
★
={
E1
,
E2
}=>
▷
={
E2
,
E1
}=>
R
)
⊢
WP
e
@
(
E
∪
E1
)
{{
v
,
Φ
v
★
R
}}.
(
WP
e
@
E
{{
Φ
}}
★
={
E1
,
E2
}=>
▷
={
E2
,
E1
}=>
R
)
⊢
WP
e
@
E
∪
E1
{{
v
,
Φ
v
★
R
}}.
Proof
.
rewrite
wp_eq
pvs_eq
=>
He
??.
uPred
.
unseal
;
split
;
intros
n
r'
Hvalid
(
r
&
rR
&
Hr
&
Hwp
&
HR
)
;
cofe_subst
.
constructor
;
[
done
]=>
rf
k
Ef
σ
1
??
Hws1
.
destruct
Hwp
as
[
n
r
e
?
Hgo
]
;
[
by
rewrite
to_of_val
in
He
].
(* "execute" HR *)
edestruct
(
HR
(
r
⋅
rf
)
(
S
k
)
(
E
∪
Ef
)
σ
1
)
as
[
s
[
Hvs
Hws2
]]
;
[
omega

set_solver

].
{
eapply
wsat_change
,
Hws1
;
first
by
set_solver
+.
rewrite
assoc
[
rR
⋅
_
]
comm
.
done
.
}
clear
Hws1
HR
.
destruct
(
HR
(
r
⋅
rf
)
(
S
k
)
(
E
∪
Ef
)
σ
1
)
as
(
s
&
Hvs
&
Hws2
)
;
auto
.
{
eapply
wsat_proper
,
Hws1
;
first
by
set_solver
+.
by
rewrite
assoc
[
rR
⋅
_
]
comm
.
}
clear
Hws1
HR
.
(* Take a step *)
destruct
(
Hgo
(
s
⋅
rf
)
k
(
E2
∪
Ef
)
σ
1
)
as
[
Hsafe
Hstep
]
;
[
done

set_solver

].
{
eapply
wsat_change
,
Hws2
;
first
by
set_solver
+.
rewrite
!
assoc
[
s
⋅
_
]
comm
.
done
.
}
clear
Hgo
.
destruct
(
Hgo
(
s
⋅
rf
)
k
(
E2
∪
Ef
)
σ
1
)
as
[
Hsafe
Hstep
]
;
auto
.
{
eapply
wsat_proper
,
Hws2
;
first
by
set_solver
+.
by
rewrite
!
assoc
[
s
⋅
_
]
comm
.
}
clear
Hgo
.
split
;
[
done

intros
e2
σ
2
ef
?].
destruct
(
Hstep
e2
σ
2
ef
)
as
(
r2
&
r2'
&
Hws3
&?&?)
;
auto
.
clear
Hws2
.
(* Execute 2nd part of the view shift *)
edestruct
(
Hvs
(
r2
⋅
r2'
⋅
rf
)
k
(
E
∪
Ef
)
σ
2
)
as
[
t
[
HR
Hws4
]]
;
[
omega

set_solver

].
{
eapply
wsat_change
,
Hws3
;
first
by
set_solver
+.
rewrite
!
assoc
[
_
⋅
s
]
comm
!
assoc
.
done
.
}
clear
Hvs
Hws3
.
destruct
(
Hvs
(
r2
⋅
r2'
⋅
rf
)
k
(
E
∪
Ef
)
σ
2
)
as
(
t
&
HR
&
Hws4
)
;
auto
.
{
eapply
wsat_proper
,
Hws3
;
first
by
set_solver
+.
by
rewrite
!
assoc
[
_
⋅
s
]
comm
!
assoc
.
}
clear
Hvs
Hws3
.
(* Execute the rest of e *)
exists
(
r2
⋅
t
),
r2'
.
split_and
?
;
auto
.

eapply
wsat_
change
,
Hws4
;
first
by
set_solver
+.
rewrite
!
assoc
[
_
⋅
t
]
comm
.
done
.

rewrite

uPred_sep_eq
.
move
:
(
wp_frame_r
)
.
rewrite
wp_eq
=>
Hframe
.

eapply
wsat_
proper
,
Hws4
;
first
by
set_solver
+.
by
rewrite
!
assoc
[
_
⋅
t
]
comm
.

rewrite

uPred_sep_eq
.
move
:
wp_frame_r
.
rewrite
wp_eq
=>
Hframe
.
apply
Hframe
;
first
by
auto
.
uPred
.
unseal
;
exists
r2
,
t
;
split_and
?
;
auto
.
move
:
(
wp_mask_frame_mono
)
.
rewrite
wp_eq
=>
Hmask
.
move
:
wp_mask_frame_mono
.
rewrite
wp_eq
=>
Hmask
.
eapply
(
Hmask
E
)
;
by
auto
.
Qed
.
Lemma
wp_bind
`
{
LanguageCtx
Λ
K
}
E
e
Φ
:
...
...
program_logic/wsat.v
View file @
8bf6270c
...
...
@@ 42,11 +42,11 @@ Proof.
Qed
.
Global
Instance
wsat_ne
n
:
Proper
(
dist
n
==>
iff
)
(@
wsat
Λ
Σ
n
E
σ
)

1
.
Proof
.
by
intros
E
σ
w1
w2
Hw
;
split
;
apply
wsat_ne'
.
Qed
.
Global
Instance
wsat_proper
n
:
Proper
((
≡
)
==>
iff
)
(@
wsat
Λ
Σ
n
E
σ
)

1
.
Global
Instance
wsat_proper
'
n
:
Proper
((
≡
)
==>
iff
)
(@
wsat
Λ
Σ
n
E
σ
)

1
.
Proof
.
by
intros
E
σ
w1
w2
Hw
;
apply
wsat_ne
,
equiv_dist
.
Qed
.
Lemma
wsat_
change
n
E1
E2
σ
r1
r2
:
Lemma
wsat_
proper
n
E1
E2
σ
r1
r2
:
E1
=
E2
→
r1
≡
r2
→
wsat
n
E1
σ
r1
→
wsat
n
E2
σ
r2
.
Proof
.
move
=>>>.
done
.
Qed
.
Proof
.
by
move
=>>>.
Qed
.
Lemma
wsat_le
n
n'
E
σ
r
:
wsat
n
E
σ
r
→
n'
≤
n
→
wsat
n'
E
σ
r
.
Proof
.
destruct
n
as
[
n
],
n'
as
[
n'
]
;
simpl
;
try
by
(
auto
with
lia
).
...
...
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