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9331a371
Commit
9331a371
authored
Jan 19, 2016
by
Robbert Krebbers
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Introduce notion of reducible, as in the appendix.
parent
ae972c48
Changes
4
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4 changed files
with
12 additions
and
7 deletions
+12
-7
iris/hoare_lifting.v
iris/hoare_lifting.v
+4
-4
iris/language.v
iris/language.v
+5
-0
iris/lifting.v
iris/lifting.v
+2
-2
iris/weakestpre.v
iris/weakestpre.v
+1
-1
No files found.
iris/hoare_lifting.v
View file @
9331a371
...
...
@@ -15,7 +15,7 @@ Import uPred.
Lemma
ht_lift_step
E1
E2
(
φ
:
iexpr
Σ
→
istate
Σ
→
option
(
iexpr
Σ
)
→
Prop
)
P
P'
Q1
Q2
R
e1
σ
1
:
E1
⊆
E2
→
to_val
e1
=
None
→
(
∃
e2
σ
2
ef
,
prim_step
e1
σ
1 e2
σ
2
ef
)
→
reducible
e1
σ
1
→
(
∀
e2
σ
2
ef
,
prim_step
e1
σ
1 e2
σ
2
ef
→
φ
e2
σ
2
ef
)
→
(
P
>{
E2
,
E1
}>
(
ownP
σ
1
★
▷
P'
)
∧
∀
e2
σ
2
ef
,
(
■
φ
e2
σ
2
ef
★
ownP
σ
2
★
P'
)
>{
E1
,
E2
}>
(
Q1
e2
σ
2
ef
★
Q2
e2
σ
2
ef
)
∧
...
...
@@ -45,7 +45,7 @@ Qed.
Lemma
ht_lift_atomic
E
(
φ
:
iexpr
Σ
→
istate
Σ
→
option
(
iexpr
Σ
)
→
Prop
)
P
e1
σ
1
:
atomic
e1
→
(
∃
e2
σ
2
ef
,
prim_step
e1
σ
1 e2
σ
2
ef
)
→
reducible
e1
σ
1
→
(
∀
e2
σ
2
ef
,
prim_step
e1
σ
1 e2
σ
2
ef
→
φ
e2
σ
2
ef
)
→
(
∀
e2
σ
2
ef
,
{{
■
φ
e2
σ
2
ef
★
P
}}
ef
?@
coPset_all
{{
λ
_
,
True
}})
⊑
{{
ownP
σ
1
★
▷
P
}}
e1
@
E
{{
λ
v
,
∃
σ
2
ef
,
ownP
σ
2
★
■
φ
(
of_val
v
)
σ
2
ef
}}.
...
...
@@ -71,7 +71,7 @@ Proof.
Qed
.
Lemma
ht_lift_pure_step
E
(
φ
:
iexpr
Σ
→
option
(
iexpr
Σ
)
→
Prop
)
P
P'
Q
e1
:
to_val
e1
=
None
→
(
∀
σ
1
,
∃
e2
σ
2
ef
,
prim_step
e1
σ
1 e2
σ
2
ef
)
→
(
∀
σ
1
,
reducible
e1
σ
1
)
→
(
∀
σ
1 e2
σ
2
ef
,
prim_step
e1
σ
1 e2
σ
2
ef
→
σ
1
=
σ
2
∧
φ
e2
ef
)
→
(
∀
e2
ef
,
{{
■
φ
e2
ef
★
P
}}
e2
@
E
{{
Q
}}
∧
...
...
@@ -97,7 +97,7 @@ Qed.
Lemma
ht_lift_pure_determistic_step
E
(
φ
:
iexpr
Σ
→
option
(
iexpr
Σ
)
→
Prop
)
P
P'
Q
e1
e2
ef
:
to_val
e1
=
None
→
(
∀
σ
1
,
prim_step
e1
σ
1 e2
σ
1
ef
)
→
(
∀
σ
1
,
reducible
e1
σ
1
)
→
(
∀
σ
1 e2
'
σ
2
ef'
,
prim_step
e1
σ
1 e2
'
σ
2
ef'
→
σ
1
=
σ
2
∧
e2
=
e2'
∧
ef
=
ef'
)
→
({{
P
}}
e2
@
E
{{
Q
}}
∧
{{
P'
}}
ef
?@
coPset_all
{{
λ
_
,
True
}})
⊑
{{
▷
(
P
★
P'
)
}}
e1
@
E
{{
Q
}}.
...
...
iris/language.v
View file @
9331a371
...
...
@@ -18,6 +18,11 @@ Class Language (E V St : Type) := {
Section
language
.
Context
`
{
Language
E
V
St
}.
Definition
reducible
(
e
:
E
)
(
σ
:
St
)
:
=
∃
e'
σ
'
ef
,
prim_step
e
σ
e'
σ
'
ef
.
Lemma
reducible_not_val
e
σ
:
reducible
e
σ
→
to_val
e
=
None
.
Proof
.
intros
(?&?&?&?)
;
eauto
using
values_stuck
.
Qed
.
Lemma
atomic_of_val
v
:
¬
atomic
(
of_val
v
).
Proof
.
by
intros
Hat
;
apply
atomic_not_value
in
Hat
;
rewrite
to_of_val
in
Hat
.
...
...
iris/lifting.v
View file @
9331a371
...
...
@@ -16,7 +16,7 @@ Transparent uPred_holds.
Lemma
wp_lift_step
E1
E2
(
φ
:
iexpr
Σ
→
istate
Σ
→
option
(
iexpr
Σ
)
→
Prop
)
Q
e1
σ
1
:
E1
⊆
E2
→
to_val
e1
=
None
→
(
∃
e2
σ
2
ef
,
prim_step
e1
σ
1 e2
σ
2
ef
)
→
reducible
e1
σ
1
→
(
∀
e2
σ
2
ef
,
prim_step
e1
σ
1 e2
σ
2
ef
→
φ
e2
σ
2
ef
)
→
pvs
E2
E1
(
ownP
σ
1
★
▷
∀
e2
σ
2
ef
,
(
■
φ
e2
σ
2
ef
∧
ownP
σ
2
)
-
★
pvs
E1
E2
(
wp
E2
e2
Q
★
default
True
ef
(
flip
(
wp
coPset_all
)
(
λ
_
,
True
))))
...
...
@@ -37,7 +37,7 @@ Proof.
Qed
.
Lemma
wp_lift_pure_step
E
(
φ
:
iexpr
Σ
→
option
(
iexpr
Σ
)
→
Prop
)
Q
e1
:
to_val
e1
=
None
→
(
∀
σ
1
,
∃
e2
σ
2
ef
,
prim_step
e1
σ
1 e2
σ
2
ef
)
→
(
∀
σ
1
,
reducible
e1
σ
1
)
→
(
∀
σ
1 e2
σ
2
ef
,
prim_step
e1
σ
1 e2
σ
2
ef
→
σ
1
=
σ
2
∧
φ
e2
ef
)
→
(
▷
∀
e2
ef
,
■
φ
e2
ef
→
wp
E
e2
Q
★
default
True
ef
(
flip
(
wp
coPset_all
)
(
λ
_
,
True
)))
...
...
iris/weakestpre.v
View file @
9331a371
...
...
@@ -9,7 +9,7 @@ Local Hint Extern 10 (✓{_} _) =>
Record
wp_go
{
Σ
}
(
E
:
coPset
)
(
Q
Qfork
:
iexpr
Σ
→
nat
→
res'
Σ
→
Prop
)
(
k
:
nat
)
(
rf
:
res'
Σ
)
(
e1
:
iexpr
Σ
)
(
σ
1
:
istate
Σ
)
:
=
{
wf_safe
:
∃
e2
σ
2
ef
,
prim_step
e1
σ
1 e2
σ
2
ef
;
wf_safe
:
reducible
e1
σ
1
;
wp_step
e2
σ
2
ef
:
prim_step
e1
σ
1 e2
σ
2
ef
→
∃
r2
r2'
,
...
...
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