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William Mansky
Iris
Commits
6646e43c
Commit
6646e43c
authored
9 years ago
by
Robbert Krebbers
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Notations for LitTrue and LitFalse.
parent
eba4ac6e
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2 changed files
heap_lang/heap_lang.v
+6
-4
6 additions, 4 deletions
heap_lang/heap_lang.v
heap_lang/lifting.v
+10
-11
10 additions, 11 deletions
heap_lang/lifting.v
with
16 additions
and
15 deletions
heap_lang/heap_lang.v
+
6
−
4
View file @
6646e43c
...
...
@@ -7,6 +7,8 @@ Definition loc := positive. (* Really, any countable type. *)
Inductive
base_lit
:
Set
:=
|
LitNat
(
n
:
nat
)
|
LitBool
(
b
:
bool
)
|
LitUnit
.
Notation
LitTrue
:=
(
LitBool
true
)
.
Notation
LitFalse
:=
(
LitBool
false
)
.
Inductive
un_op
:
Set
:=
|
NegOp
.
Inductive
bin_op
:
Set
:=
...
...
@@ -177,9 +179,9 @@ Inductive head_step : expr -> state -> expr -> state -> option expr -> Prop :=
bin_op_eval
op
l1
l2
=
Some
l'
→
head_step
(
BinOp
op
(
Lit
l1
)
(
Lit
l2
))
σ
(
Lit
l'
)
σ
None
|
IfTrueS
e1
e2
σ
:
head_step
(
If
(
Lit
(
Lit
Bool
t
rue
)
)
e1
e2
)
σ
e1
σ
None
head_step
(
If
(
Lit
Lit
T
rue
)
e1
e2
)
σ
e1
σ
None
|
IfFalseS
e1
e2
σ
:
head_step
(
If
(
Lit
(
Lit
Bool
f
alse
)
)
e1
e2
)
σ
e2
σ
None
head_step
(
If
(
Lit
Lit
F
alse
)
e1
e2
)
σ
e2
σ
None
|
FstS
e1
v1
e2
v2
σ
:
to_val
e1
=
Some
v1
→
to_val
e2
=
Some
v2
→
head_step
(
Fst
(
Pair
e1
e2
))
σ
e1
σ
None
...
...
@@ -206,11 +208,11 @@ Inductive head_step : expr -> state -> expr -> state -> option expr -> Prop :=
|
CasFailS
l
e1
v1
e2
v2
vl
σ
:
to_val
e1
=
Some
v1
→
to_val
e2
=
Some
v2
→
σ
!!
l
=
Some
vl
→
vl
≠
v1
→
head_step
(
Cas
(
Loc
l
)
e1
e2
)
σ
(
Lit
(
Lit
Bool
f
alse
)
)
σ
None
head_step
(
Cas
(
Loc
l
)
e1
e2
)
σ
(
Lit
Lit
F
alse
)
σ
None
|
CasSucS
l
e1
v1
e2
v2
σ
:
to_val
e1
=
Some
v1
→
to_val
e2
=
Some
v2
→
σ
!!
l
=
Some
v1
→
head_step
(
Cas
(
Loc
l
)
e1
e2
)
σ
(
Lit
(
Lit
Bool
t
rue
)
)
(
<
[
l
:=
v2
]
>
σ
)
None
.
head_step
(
Cas
(
Loc
l
)
e1
e2
)
σ
(
Lit
Lit
T
rue
)
(
<
[
l
:=
v2
]
>
σ
)
None
.
(** Atomic expressions *)
Definition
atomic
(
e
:
expr
)
:
Prop
:=
...
...
This diff is collapsed.
Click to expand it.
heap_lang/lifting.v
+
10
−
11
View file @
6646e43c
...
...
@@ -56,23 +56,24 @@ Qed.
Lemma
wp_cas_fail_pst
E
σ
l
e1
v1
e2
v2
v'
Q
:
to_val
e1
=
Some
v1
→
to_val
e2
=
Some
v2
→
σ
!!
l
=
Some
v'
→
v'
≠
v1
→
(
ownP
σ
★
▷
(
ownP
σ
-★
Q
$
LitV
$
Lit
Bool
f
alse
))
⊑
wp
E
(
Cas
(
Loc
l
)
e1
e2
)
Q
.
(
ownP
σ
★
▷
(
ownP
σ
-★
Q
(
LitV
Lit
F
alse
))
)
⊑
wp
E
(
Cas
(
Loc
l
)
e1
e2
)
Q
.
Proof
.
intros
.
rewrite
-
(
wp_lift_atomic_det_step
σ
(
LitV
$
Lit
Bool
f
alse
)
σ
None
)
?right_id
//
;
last
by
intros
;
inv_step
;
eauto
.
intros
.
rewrite
-
(
wp_lift_atomic_det_step
σ
(
LitV
Lit
F
alse
)
σ
None
)
?right_id
//
;
last
by
intros
;
inv_step
;
eauto
.
Qed
.
Lemma
wp_cas_suc_pst
E
σ
l
e1
v1
e2
v2
Q
:
to_val
e1
=
Some
v1
→
to_val
e2
=
Some
v2
→
σ
!!
l
=
Some
v1
→
(
ownP
σ
★
▷
(
ownP
(
<
[
l
:=
v2
]
>
σ
)
-★
Q
$
LitV
$
LitBool
true
))
⊑
wp
E
(
Cas
(
Loc
l
)
e1
e2
)
Q
.
(
ownP
σ
★
▷
(
ownP
(
<
[
l
:=
v2
]
>
σ
)
-★
Q
(
LitV
LitTrue
)))
⊑
wp
E
(
Cas
(
Loc
l
)
e1
e2
)
Q
.
Proof
.
intros
.
rewrite
-
(
wp_lift_atomic_det_step
σ
(
LitV
$
Lit
Bool
t
rue
)
(
<
[
l
:=
v2
]
>
σ
)
None
)
intros
.
rewrite
-
(
wp_lift_atomic_det_step
σ
(
LitV
Lit
T
rue
)
(
<
[
l
:=
v2
]
>
σ
)
None
)
?right_id
//
;
last
by
intros
;
inv_step
;
eauto
.
Qed
.
(** Base axioms for core primitives of the language: Stateless reductions *)
Lemma
wp_fork
E
e
:
▷
wp
(
Σ
:=
Σ
)
coPset_all
e
(
λ
_,
True
)
⊑
wp
E
(
Fork
e
)
(
λ
v
,
■
(
v
=
LitV
$
LitUnit
))
.
▷
wp
(
Σ
:=
Σ
)
coPset_all
e
(
λ
_,
True
)
⊑
wp
E
(
Fork
e
)
(
λ
v
,
■
(
v
=
LitV
LitUnit
))
.
Proof
.
rewrite
-
(
wp_lift_pure_det_step
(
Fork
e
)
(
Lit
LitUnit
)
(
Some
e
))
//=
;
last
by
intros
;
inv_step
;
eauto
.
...
...
@@ -107,15 +108,13 @@ Proof.
by
rewrite
-
wp_value'
.
Qed
.
Lemma
wp_if_true
E
e1
e2
Q
:
▷
wp
E
e1
Q
⊑
wp
E
(
If
(
Lit
$
LitBool
true
)
e1
e2
)
Q
.
Lemma
wp_if_true
E
e1
e2
Q
:
▷
wp
E
e1
Q
⊑
wp
E
(
If
(
Lit
LitTrue
)
e1
e2
)
Q
.
Proof
.
rewrite
-
(
wp_lift_pure_det_step
(
If
_
_
_)
e1
None
)
?right_id
//
;
last
by
intros
;
inv_step
;
eauto
.
Qed
.
Lemma
wp_if_false
E
e1
e2
Q
:
▷
wp
E
e2
Q
⊑
wp
E
(
If
(
Lit
$
LitBool
false
)
e1
e2
)
Q
.
Lemma
wp_if_false
E
e1
e2
Q
:
▷
wp
E
e2
Q
⊑
wp
E
(
If
(
Lit
LitFalse
)
e1
e2
)
Q
.
Proof
.
rewrite
-
(
wp_lift_pure_det_step
(
If
_
_
_)
e2
None
)
?right_id
//
;
last
by
intros
;
inv_step
;
eauto
.
...
...
@@ -123,7 +122,7 @@ Qed.
Lemma
wp_fst
E
e1
v1
e2
v2
Q
:
to_val
e1
=
Some
v1
→
to_val
e2
=
Some
v2
→
▷
Q
v1
⊑
wp
E
(
Fst
(
Pair
e1
e2
))
Q
.
▷
Q
v1
⊑
wp
E
(
Fst
(
Pair
e1
e2
))
Q
.
Proof
.
intros
.
rewrite
-
(
wp_lift_pure_det_step
(
Fst
_)
e1
None
)
?right_id
//
;
last
by
intros
;
inv_step
;
eauto
.
...
...
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