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Tej Chajed
iris
Commits
23de2030
Commit
23de2030
authored
Jan 30, 2016
by
Ralf Jung
Browse files
move sugar to separate file, and prove some more rules for it
parent
d8ad2335
Changes
4
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_CoqProject
View file @
23de2030
...
...
@@ -65,4 +65,5 @@ iris/tests.v
barrier/heap_lang.v
barrier/parameter.v
barrier/lifting.v
barrier/sugar.v
barrier/tests.v
barrier/heap_lang.v
View file @
23de2030
...
...
@@ -38,10 +38,9 @@ Instance Rename_expr : Rename expr. derive. Defined.
Instance
Subst_expr
:
Subst
expr
.
derive
.
Defined
.
Instance
SubstLemmas_expr
:
SubstLemmas
expr
.
derive
.
Qed
.
Definition
Lam
(
e
:
{
bind
expr
})
:
=
Rec
e
.[
ren
(+
1
)].
Definition
Let
(
e1
:
expr
)
(
e2
:
{
bind
expr
})
:
=
App
(
Lam
e2
)
e1
.
Definition
Seq
(
e1
e2
:
expr
)
:
=
Let
e1
e2
.[
ren
(+
1
)].
Definition
If
(
e0
e1
e2
:
expr
)
:
=
Case
e0
e1
.[
ren
(+
1
)]
e2
.[
ren
(+
1
)].
(* This sugar is used by primitive reduction riles (<=, CAS) and hence defined here. *)
Definition
LitTrue
:
=
InjL
LitUnit
.
Definition
LitFalse
:
=
InjR
LitUnit
.
Inductive
value
:
=
|
RecV
(
e
:
{
bind
2
of
expr
})
...
...
@@ -53,11 +52,7 @@ Inductive value :=
|
LocV
(
l
:
loc
)
.
Definition
LamV
(
e
:
{
bind
expr
})
:
=
RecV
e
.[
ren
(+
1
)].
Definition
LitTrue
:
=
InjL
LitUnit
.
Definition
LitTrueV
:
=
InjLV
LitUnitV
.
Definition
LitFalse
:
=
InjR
LitUnit
.
Definition
LitFalseV
:
=
InjRV
LitUnitV
.
Fixpoint
v2e
(
v
:
value
)
:
expr
:
=
...
...
@@ -192,9 +187,6 @@ Fixpoint comp_ctx (Ko : ectx) (Ki : ectx) :=
|
CasRCtx
v0
v1
K2
=>
CasRCtx
v0
v1
(
comp_ctx
K2
Ki
)
end
.
Definition
LetCtx
(
K1
:
ectx
)
(
e2
:
{
bind
expr
})
:
=
AppRCtx
(
LamV
e2
)
K1
.
Definition
SeqCtx
(
K1
:
ectx
)
(
e2
:
expr
)
:
=
LetCtx
K1
(
e2
.[
ren
(+
1
)]).
Lemma
fill_empty
e
:
fill
EmptyCtx
e
=
e
.
Proof
.
...
...
barrier/lifting.v
View file @
23de2030
...
...
@@ -220,16 +220,6 @@ Proof.
apply
const_elim_l
=>->.
done
.
Qed
.
Lemma
wp_lam
E
ef
e
v
Q
:
e2v
e
=
Some
v
→
▷
wp
(
Σ
:
=
Σ
)
E
ef
.[
e
/]
Q
⊑
wp
(
Σ
:
=
Σ
)
E
(
App
(
Lam
ef
)
e
)
Q
.
Proof
.
intros
Hv
.
rewrite
-
wp_rec
;
last
eassumption
.
(* RJ: This pulls in functional extensionality. If that bothers us, we have
to talk to the Autosubst guys. *)
by
asimpl
.
Qed
.
Lemma
wp_plus
n1
n2
E
Q
:
▷
Q
(
LitNatV
(
n1
+
n2
))
⊑
wp
(
Σ
:
=
Σ
)
E
(
Plus
(
LitNat
n1
)
(
LitNat
n2
))
Q
.
Proof
.
...
...
@@ -329,13 +319,6 @@ Qed.
(** Some derived stateless axioms *)
Lemma
wp_let
e1
e2
E
Q
:
wp
(
Σ
:
=
Σ
)
E
e1
(
λ
v
,
▷
wp
(
Σ
:
=
Σ
)
E
(
e2
.[
v2e
v
/])
Q
)
⊑
wp
(
Σ
:
=
Σ
)
E
(
Let
e1
e2
)
Q
.
Proof
.
rewrite
-(
wp_bind
(
LetCtx
EmptyCtx
e2
)).
apply
wp_mono
=>
v
.
rewrite
-
wp_lam
//.
by
rewrite
v2v
.
Qed
.
Lemma
wp_le
n1
n2
E
P
Q
:
(
n1
≤
n2
→
P
⊑
▷
Q
LitTrueV
)
→
(
n1
>
n2
→
P
⊑
▷
Q
LitFalseV
)
→
...
...
barrier/tests.v
View file @
23de2030
(** This file is essentially a bunch of testcases. *)
Require
Import
modures
.
logic
.
Require
Import
barrier
.
lifting
.
Require
Import
barrier
.
lifting
barrier
.
sugar
.
Import
uPred
.
Module
LangTests
.
...
...
@@ -62,7 +62,6 @@ Module LiftingTests.
Import
Nat
.
Definition
Lt
e1
e2
:
=
Le
(
Plus
e1
$
LitNat
1
)
e2
.
Definition
FindPred'
n1
Sn1
n2
f
:
=
If
(
Lt
Sn1
n2
)
(
App
f
Sn1
)
n1
.
...
...
@@ -87,10 +86,12 @@ Module LiftingTests.
rewrite
-(
wp_let
_
(
FindPred'
(
LitNat
n1
)
(
Var
0
)
(
LitNat
n2
)
(
FindPred
$
LitNat
n2
))).
rewrite
-
wp_plus
.
asimpl
.
rewrite
-(
wp_bind
(
CaseCtx
EmptyCtx
_
_
)).
rewrite
-(
wp_bind
(
LeLCtx
EmptyCtx
_
)).
rewrite
-
wp_plus
-!
later_intro
.
simpl
.
apply
wp_le
;
intros
Hn12
.
-
rewrite
-
wp_case_inl
//.
rewrite
-!
later_intro
.
simpl
.
apply
wp_lt
;
intros
Hn12
.
-
(* TODO RJ: It would be better if we could use wp_if_true here
(and below). But we cannot, because the substitutions in there
got already unfolded. *)
rewrite
-
wp_case_inl
//.
rewrite
-!
later_intro
.
asimpl
.
rewrite
(
forall_elim
(
S
n1
)).
eapply
impl_elim
;
first
by
eapply
and_elim_l
.
apply
and_intro
.
...
...
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