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Iris
Iris
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3b3a0a1a
Commit
3b3a0a1a
authored
Feb 08, 2016
by
Robbert Krebbers
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Improve notations for heap_lang.
parent
095fde7e
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2 changed files
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51 deletions
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-51
heap_lang/sugar.v
heap_lang/sugar.v
+31
-36
heap_lang/tests.v
heap_lang/tests.v
+9
-15
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heap_lang/sugar.v
View file @
3b3a0a1a
Require
Export
heap_lang
.
heap_lang
heap_lang
.
lifting
.
Import
uPred
.
Import
heap_lang
.
Import
uPred
heap_lang
.
(** Define some syntactic sugar. LitTrue and LitFalse are defined in heap_lang.v. *)
Definition
Lam
(
e
:
{
bind
expr
})
:
=
Rec
e
.[
ren
(+
1
)].
...
...
@@ -17,42 +16,38 @@ Definition LamV (e : {bind expr}) := RecV e.[ren(+1)].
Definition
LetCtx
(
e2
:
{
bind
expr
})
:
=
AppRCtx
(
LamV
e2
).
Definition
SeqCtx
(
e2
:
expr
)
:
=
LetCtx
(
e2
.[
ren
(+
1
)]).
Delimit
Scope
lang_scope
with
L
.
Bind
Scope
lang_scope
with
expr
.
Arguments
wp
{
_
_
}
_
_
%
L
_
.
(* TODO: The levels are all random. Also maybe we should not
make 'new' a keyword. What about Arguments for hoare triples?. *)
(* The colons indicate binders. "let" is not consistent here though,
thing are only bound in the "in". *)
Notation
"'rec::' e"
:
=
(
Rec
e
)
(
at
level
100
)
:
lang_scope
.
Notation
"'λ:' e"
:
=
(
Lam
e
)
(
at
level
100
)
:
lang_scope
.
Notation
"'let:' e1 'in' e2"
:
=
(
Let
e1
e2
)
(
at
level
70
)
:
lang_scope
.
Notation
"e1 ';' e2"
:
=
(
Seq
e1
e2
)
(
at
level
70
)
:
lang_scope
.
Notation
"'if' e1 'then' e2 'else' e3"
:
=
(
If
e1
e2
e3
)
:
lang_scope
.
Module
notations
.
Delimit
Scope
lang_scope
with
L
.
Bind
Scope
lang_scope
with
expr
.
Arguments
wp
{
_
_
}
_
_
%
L
_
.
Notation
"#0"
:
=
(
Var
0
)
(
at
level
0
)
:
lang_scope
.
Notation
"#1"
:
=
(
Var
1
)
(
at
level
0
)
:
lang_scope
.
Notation
"#2"
:
=
(
Var
2
)
(
at
level
0
)
:
lang_scope
.
Notation
"#3"
:
=
(
Var
3
)
(
at
level
0
)
:
lang_scope
.
Notation
"#4"
:
=
(
Var
4
)
(
at
level
0
)
:
lang_scope
.
Notation
"#5"
:
=
(
Var
5
)
(
at
level
0
)
:
lang_scope
.
Notation
"#6"
:
=
(
Var
6
)
(
at
level
0
)
:
lang_scope
.
Notation
"#7"
:
=
(
Var
7
)
(
at
level
0
)
:
lang_scope
.
Notation
"#8"
:
=
(
Var
8
)
(
at
level
0
)
:
lang_scope
.
Notation
"#9"
:
=
(
Var
9
)
(
at
level
0
)
:
lang_scope
.
Coercion
LitNat
:
nat
>->
expr
.
Coercion
LitNatV
:
nat
>->
val
.
Coercion
Loc
:
loc
>->
expr
.
Coercion
LocV
:
loc
>->
val
.
Coercion
App
:
expr
>->
Funclass
.
Notation
"'★' e"
:
=
(
Load
e
)
(
at
level
30
)
:
lang_scope
.
Notation
"e1 '<-' e2"
:
=
(
Store
e1
e2
)
(
at
level
60
)
:
lang_scope
.
Notation
"'new' e"
:
=
(
Alloc
e
)
(
at
level
60
)
:
lang_scope
.
Notation
"e1 '+' e2"
:
=
(
Plus
e1
e2
)
:
lang_scope
.
Notation
"e1 '≤' e2"
:
=
(
Le
e1
e2
)
:
lang_scope
.
Notation
"e1 '<' e2"
:
=
(
Lt
e1
e2
)
:
lang_scope
.
Coercion
LitNat
:
nat
>->
expr
.
Coercion
LitNatV
:
nat
>->
val
.
Coercion
Loc
:
loc
>->
expr
.
Coercion
LocV
:
loc
>->
val
.
Coercion
App
:
expr
>->
Funclass
.
(** Syntax inspired by Coq/Ocaml. Constructions with higher precedence come
first. *)
(* What about Arguments for hoare triples?. *)
(* The colons indicate binders. "let" is not consistent here though,
thing are only bound in the "in". *)
Notation
"# n"
:
=
(
Var
n
)
(
at
level
1
,
format
"# n"
)
:
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"
:
=
(
Plus
e1
%
L
e2
%
L
)
(
at
level
50
,
left
associativity
)
:
lang_scope
.
Notation
"e1 ≤ e2"
:
=
(
Le
e1
%
L
e2
%
L
)
(
at
level
70
)
:
lang_scope
.
Notation
"e1 < e2"
:
=
(
Lt
e1
%
L
e2
%
L
)
(
at
level
70
)
:
lang_scope
.
(* The unicode ← is already part of the notation "_ ← _; _" for bind. *)
Notation
"e1 <- e2"
:
=
(
Store
e1
%
L
e2
%
L
)
(
at
level
80
)
:
lang_scope
.
Notation
"e1 ; e2"
:
=
(
Seq
e1
%
L
e2
%
L
)
(
at
level
100
)
:
lang_scope
.
Notation
"'let:' e1 'in' e2"
:
=
(
Let
e1
%
L
e2
%
L
)
(
at
level
102
)
:
lang_scope
.
Notation
"'λ:' e"
:
=
(
Lam
e
%
L
)
(
at
level
102
)
:
lang_scope
.
Notation
"'rec::' e"
:
=
(
Rec
e
%
L
)
(
at
level
102
)
:
lang_scope
.
Notation
"'if' e1 'then' e2 'else' e3"
:
=
(
If
e1
%
L
e2
%
L
e3
%
L
)
(
at
level
200
,
e1
,
e2
,
e3
at
level
200
,
only
parsing
)
:
lang_scope
.
End
notations
.
Section
suger
.
Context
{
Σ
:
iFunctor
}.
...
...
heap_lang/tests.v
View file @
3b3a0a1a
(** This file is essentially a bunch of testcases. *)
Require
Import
program_logic
.
upred
.
Require
Import
heap_lang
.
lifting
heap_lang
.
sugar
.
Import
heap_lang
.
Import
uPred
.
Import
heap_lang
uPred
notations
.
Module
LangTests
.
Definition
add
:
=
(
21
+
21
)%
L
.
...
...
@@ -24,7 +23,7 @@ Module LiftingTests.
Implicit
Types
Q
:
val
→
iProp
heap_lang
Σ
.
(* FIXME: Fix levels so that we do not need the parenthesis here. *)
Definition
e
:
expr
:
=
let
:
new
1
in
(
#
0
<-
★
#
0
+
1
;
★
#
0
)%
L
.
Definition
e
:
expr
:
=
(
let
:
ref
1
in
#
0
<-
!
#
0
+
1
;
!
#
0
)%
L
.
Goal
∀
σ
E
,
(
ownP
σ
:
iProp
heap_lang
Σ
)
⊑
(
wp
E
e
(
λ
v
,
■
(
v
=
2
))).
Proof
.
move
=>
σ
E
.
rewrite
/
e
.
...
...
@@ -56,15 +55,12 @@ Module LiftingTests.
(* TODO: once asimpl preserves notation, we don't need
FindPred' anymore. *)
(* FIXME: fix notation so that we do not need parenthesis or %L *)
Definition
FindPred'
n1
Sn1
n2
f
:
expr
:
=
if
Sn1
<
n2
then
f
Sn1
else
n1
.
Definition
FindPred
n2
:
expr
:
=
rec
::
(
let
:
(#
1
+
1
)
in
FindPred'
#
2
#
0
n2
.[
ren
(+
3
)]
#
1
)%
L
.
Definition
Pred
:
expr
:
=
λ
:
(
if
#
0
≤
0
then
0
else
FindPred
(#
0
)
0
)%
L
.
Definition
FindPred'
n1
Sn1
n2
f
:
expr
:
=
if
Sn1
<
n2
then
f
Sn1
else
n1
.
Definition
FindPred
n2
:
expr
:
=
rec
::
(
let
:
#
1
+
1
in
FindPred'
#
2
#
0
n2
.[
ren
(+
3
)]
#
1
)%
L
.
Definition
Pred
:
expr
:
=
λ
:
(
if
#
0
≤
0
then
0
else
FindPred
#
0
0
)%
L
.
Lemma
FindPred_spec
n1
n2
E
Q
:
(
■
(
n1
<
n2
)
∧
Q
(
pred
n2
))
⊑
...
...
@@ -112,9 +108,7 @@ Module LiftingTests.
Qed
.
Goal
∀
E
,
True
⊑
wp
(
Σ
:
=
Σ
)
E
(* FIXME why do we need %L here? *)
(
let
:
Pred
42
in
Pred
#
0
)%
L
(
λ
v
,
■
(
v
=
40
)).
True
⊑
wp
(
Σ
:
=
Σ
)
E
(
let
:
Pred
42
in
Pred
#
0
)
(
λ
v
,
■
(
v
=
40
)).
Proof
.
intros
E
.
rewrite
-
wp_let
.
rewrite
-
Pred_spec
-!
later_intro
.
asimpl
.
(* TODO RJ: Can we somehow make it so that Pred gets folded again? *)
...
...
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