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cpdt
Commits
63785816
Commit
63785816
authored
Oct 06, 2011
by
Adam Chlipala
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Hide some more Subset code in template
parent
e660789e
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src/Subset.v
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63785816
...
@@ -484,6 +484,8 @@ let rec eq_nat_dec' n m0 =
...
@@ -484,6 +484,8 @@ let rec eq_nat_dec' n m0 =
We
can
build
%
``
%
#
"#smart#"
#
%
''
%
versions
of
the
usual
boolean
operators
and
put
them
to
good
use
in
certified
programming
.
For
instance
,
here
is
a
[
sumbool
]
version
of
boolean
%
``
%
#
"#or.#"
#
%
''
%
*
)
We
can
build
%
``
%
#
"#smart#"
#
%
''
%
versions
of
the
usual
boolean
operators
and
put
them
to
good
use
in
certified
programming
.
For
instance
,
here
is
a
[
sumbool
]
version
of
boolean
%
``
%
#
"#or.#"
#
%
''
%
*
)
(
*
EX
:
Write
a
function
that
decides
if
an
element
belongs
to
a
list
.
*
)
(
*
begin
thide
*
)
(
*
begin
thide
*
)
Notation
"x || y"
:=
(
if
x
then
Yes
else
Reduce
y
)
.
Notation
"x || y"
:=
(
if
x
then
Yes
else
Reduce
y
)
.
...
@@ -638,12 +640,16 @@ Notation "x <- e1 ; e2" := (match e1 with
...
@@ -638,12 +640,16 @@ Notation "x <- e1 ; e2" := (match e1 with
This
notation
is
very
helpful
for
composing
richly
typed
procedures
.
For
instance
,
here
is
a
very
simple
implementation
of
a
function
to
take
the
predecessors
of
two
naturals
at
once
.
*
)
This
notation
is
very
helpful
for
composing
richly
typed
procedures
.
For
instance
,
here
is
a
very
simple
implementation
of
a
function
to
take
the
predecessors
of
two
naturals
at
once
.
*
)
(
*
EX
:
Write
a
function
that
tries
to
compute
predecessors
of
two
[
nat
]
s
at
once
.
*
)
(
*
begin
thide
*
)
Definition
doublePred
:
forall
n1
n2
:
nat
,
{{
p
|
n1
=
S
(
fst
p
)
/
\
n2
=
S
(
snd
p
)
}}.
Definition
doublePred
:
forall
n1
n2
:
nat
,
{{
p
|
n1
=
S
(
fst
p
)
/
\
n2
=
S
(
snd
p
)
}}.
refine
(
fun
n1
n2
=>
refine
(
fun
n1
n2
=>
m1
<-
pred_strong7
n1
;
m1
<-
pred_strong7
n1
;
m2
<-
pred_strong7
n2
;
m2
<-
pred_strong7
n2
;
[
|
(
m1
,
m2
)
|
])
;
tauto
.
[
|
(
m1
,
m2
)
|
])
;
tauto
.
Defined
.
Defined
.
(
*
end
thide
*
)
(
**
We
can
build
a
[
sumor
]
version
of
the
%
``
%
#
"#bind#"
#
%
''
%
notation
and
use
it
to
write
a
similarly
straightforward
version
of
this
function
.
*
)
(
**
We
can
build
a
[
sumor
]
version
of
the
%
``
%
#
"#bind#"
#
%
''
%
notation
and
use
it
to
write
a
similarly
straightforward
version
of
this
function
.
*
)
...
@@ -657,6 +663,9 @@ Notation "x <-- e1 ; e2" := (match e1 with
...
@@ -657,6 +663,9 @@ Notation "x <-- e1 ; e2" := (match e1 with
(
**
printing
*
$
\
times
$
*
)
(
**
printing
*
$
\
times
$
*
)
(
*
EX
:
Write
a
more
expressively
typed
version
of
the
last
exercise
.
*
)
(
*
begin
thide
*
)
Definition
doublePred
'
:
forall
n1
n2
:
nat
,
Definition
doublePred
'
:
forall
n1
n2
:
nat
,
{
p
:
nat
*
nat
|
n1
=
S
(
fst
p
)
/
\
n2
=
S
(
snd
p
)
}
{
p
:
nat
*
nat
|
n1
=
S
(
fst
p
)
/
\
n2
=
S
(
snd
p
)
}
+
{
n1
=
0
\
/
n2
=
0
}.
+
{
n1
=
0
\
/
n2
=
0
}.
...
@@ -665,6 +674,7 @@ Definition doublePred' : forall n1 n2 : nat,
...
@@ -665,6 +674,7 @@ Definition doublePred' : forall n1 n2 : nat,
m2
<--
pred_strong8
n2
;
m2
<--
pred_strong8
n2
;
[
||
(
m1
,
m2
)
||
])
;
tauto
.
[
||
(
m1
,
m2
)
||
])
;
tauto
.
Defined
.
Defined
.
(
*
end
thide
*
)
(
**
*
A
Type
-
Checking
Example
*
)
(
**
*
A
Type
-
Checking
Example
*
)
...
...
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