Folks,
I recently needed to write a series of codes on lambda calculus in
perl. As MJD has shown Perl 5 can handle lambda calculus but I am
beginning to get tired of whole bunch of 'my $x = shift' needed.
our $ZERO =
sub { my $f = shift;
sub { my $x = shift; $x }};
our $SUCC =
sub { my $n = shift;
sub { my $f = shift;
sub { my $x = shift;
$f->($n->($f)($x)) }}};
our $ADD =
sub{ my $m = shift;
sub { my $n = shift;
sub { my $f = shift;
sub { my $x = shift;
$m->($f)($n->($f)($x)) }}}};
our $MULT =
sub { my $m = shift;
sub { my $n = shift;
sub { my $f = shift;
$m->($n->($f)) }}};
our $POW =
sub { my $m = shift;
sub { my $n = shift;
$n->($m) }};
And I found that these can be made much, much simpler and more
intuitive with Perl 6, even more so than scheme!
our $ZERO = sub($f){ sub($x){ $x }};
our $SUCC = sub($n){ sub($f){ sub($x){ $f.($n.($f)($x)) }}};
our $ADD = sub($m){ sub($n){ sub($f){ sub($x){ $m.($f)($n.($f)
($x)) }}}};
our $MULT = sub($m){ sub($n){ sub($f){ $m.($n.($f)) }}};
our $POW = sub($m){ sub($n){ $n.($m) }};
You can even make it simpler by removing dots but I leave it that way
because it looks more like the original notation that way (i.e.
zero := λf.λx.x).
Runs perfectly fine on Pugs 6.2.8. Add the code below and see it for
yourself.
my $one = $SUCC.($ZERO);
my $two = $SUCC.($one);
my $four = $ADD.($two)($two);
my $eight = $MULT.($two)($four);
my $sixteen = $POW.($four)($two);
for($one, $two, $four, $eight, $sixteen) -> $n {
$n.(sub($i){ 1 + $i})(0).say
};
Maybe we can use this for advocacy.
Dan the Perl 6 User Now
P.S. I am surprised to find Pugs does not include this kind of
sample scripts.
