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46fafcf5
Commit
46fafcf5
authored
Feb 10, 2016
by
Robbert Krebbers
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Notation for literals.
parent
e475fff1
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13 additions
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12 deletions
+13
-12
heap_lang/sugar.v
heap_lang/sugar.v
+1
-0
heap_lang/tests.v
heap_lang/tests.v
+12
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heap_lang/sugar.v
View file @
46fafcf5
...
...
@@ -24,6 +24,7 @@ Module notations.
(** Syntax inspired by Coq/Ocaml. Constructions with higher precedence come
first. *)
(* What about Arguments for hoare triples?. *)
Notation
"' l"
:
=
(
Lit
l
)
(
at
level
8
,
format
"' l"
)
:
lang_scope
.
Notation
"! e"
:
=
(
Load
e
%
L
)
(
at
level
10
,
format
"! e"
)
:
lang_scope
.
Notation
"'ref' e"
:
=
(
Alloc
e
%
L
)
(
at
level
30
)
:
lang_scope
.
Notation
"e1 + e2"
:
=
(
BinOp
PlusOp
e1
%
L
e2
%
L
)
...
...
heap_lang/tests.v
View file @
46fafcf5
...
...
@@ -4,20 +4,20 @@ Require Import heap_lang.lifting heap_lang.sugar.
Import
heap_lang
uPred
notations
.
Module
LangTests
.
Definition
add
:
=
(
Lit
21
+
Lit
21
)%
L
.
Goal
∀
σ
,
prim_step
add
σ
(
Lit
42
)
σ
None
.
Definition
add
:
=
(
'
21
+
'
21
)%
L
.
Goal
∀
σ
,
prim_step
add
σ
(
'
42
)
σ
None
.
Proof
.
intros
;
do_step
done
.
Qed
.
Definition
rec_app
:
expr
:
=
(
rec
:
"f"
"x"
:
=
"f"
"x"
)
(
Lit
0
)
.
Definition
rec_app
:
expr
:
=
(
(
rec
:
"f"
"x"
:
=
"f"
"x"
)
'
0
)%
L
.
Goal
∀
σ
,
prim_step
rec_app
σ
rec_app
σ
None
.
Proof
.
intros
.
rewrite
/
rec_app
.
(* FIXME: do_step does not work here *)
by
eapply
(
Ectx_step
_
_
_
_
_
[]),
(
BetaS
_
_
_
_
(
LitV
(
LitNat
0
))).
Qed
.
Definition
lam
:
expr
:
=
λ
:
"x"
,
"x"
+
Lit
21
.
Goal
∀
σ
,
prim_step
(
lam
(
Lit
21
)
)
σ
add
σ
None
.
Definition
lam
:
expr
:
=
λ
:
"x"
,
"x"
+
'
21
.
Goal
∀
σ
,
prim_step
(
lam
'
21
)
%
L
σ
add
σ
None
.
Proof
.
intros
.
rewrite
/
lam
.
(* FIXME: do_step does not work here *)
by
eapply
(
Ectx_step
_
_
_
_
_
[]),
(
BetaS
""
"x"
(
"x"
+
Lit
21
)
_
(
LitV
21
)).
by
eapply
(
Ectx_step
_
_
_
_
_
[]),
(
BetaS
""
"x"
(
"x"
+
'
21
)
_
(
LitV
21
)).
Qed
.
End
LangTests
.
...
...
@@ -27,7 +27,7 @@ Module LiftingTests.
Implicit
Types
Q
:
val
→
iProp
heap_lang
Σ
.
Definition
e
:
expr
:
=
let
:
"x"
:
=
ref
(
Lit
1
)
in
"x"
<-
!
"x"
+
Lit
1
;
!
"x"
.
let
:
"x"
:
=
ref
'
1
in
"x"
<-
!
"x"
+
'
1
;
!
"x"
.
Goal
∀
σ
E
,
ownP
(
Σ
:
=
Σ
)
σ
⊑
wp
E
e
(
λ
v
,
v
=
LitV
2
).
Proof
.
move
=>
σ
E
.
rewrite
/
e
.
...
...
@@ -56,13 +56,13 @@ Module LiftingTests.
Definition
FindPred
(
n2
:
expr
)
:
expr
:
=
rec
:
"pred"
"y"
:
=
let
:
"yp"
:
=
"y"
+
Lit
1
in
let
:
"yp"
:
=
"y"
+
'
1
in
if
"yp"
<
n2
then
"pred"
"yp"
else
"y"
.
Definition
Pred
:
expr
:
=
λ
:
"x"
,
if
"x"
≤
Lit
0
then
Lit
0
else
FindPred
"x"
(
Lit
0
)
.
λ
:
"x"
,
if
"x"
≤
'
0
then
'
0
else
FindPred
"x"
'
0
.
Lemma
FindPred_spec
n1
n2
E
Q
:
(
■
(
n1
<
n2
)
∧
Q
(
LitV
(
pred
n2
)))
⊑
wp
E
(
FindPred
(
Lit
n2
)
(
Lit
n1
)
)
Q
.
(
■
(
n1
<
n2
)
∧
Q
(
LitV
(
pred
n2
)))
⊑
wp
E
(
FindPred
'
n2
'
n1
)
%
L
Q
.
Proof
.
revert
n1
.
apply
l
ö
b_all_1
=>
n1
.
rewrite
(
commutative
uPred_and
(
■
_
)%
I
)
associative
;
apply
const_elim_r
=>?.
...
...
@@ -82,7 +82,7 @@ Module LiftingTests.
by
rewrite
-!
later_intro
-
wp_value'
//
and_elim_r
.
Qed
.
Lemma
Pred_spec
n
E
Q
:
▷
Q
(
LitV
(
pred
n
))
⊑
wp
E
(
Pred
(
Lit
n
))
Q
.
Lemma
Pred_spec
n
E
Q
:
▷
Q
(
LitV
(
pred
n
))
⊑
wp
E
(
Pred
'
n
)%
L
Q
.
Proof
.
rewrite
-
wp_lam
//=.
rewrite
-(
wp_bindi
(
IfCtx
_
_
)).
...
...
@@ -96,7 +96,7 @@ Module LiftingTests.
Qed
.
Goal
∀
E
,
True
⊑
wp
(
Σ
:
=
Σ
)
E
(
let
:
"x"
:
=
Pred
(
Lit
42
)
in
Pred
"x"
)
True
⊑
wp
(
Σ
:
=
Σ
)
E
(
let
:
"x"
:
=
Pred
'
42
in
Pred
"x"
)
(
λ
v
,
v
=
LitV
40
).
Proof
.
intros
E
.
...
...
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