Lamda Calculus in Perl(5|6)

And here is lambda calculus in perl -- perl5 and perl6

Here is perl5.

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 see if it works.

sub num2int{
    my $n = shift;
    $n->(sub{ 1 + shift })(0);
}
my $one     = $SUCC->($ZERO);
my $two     = $SUCC->($one);
my $four    = $ADD->($two)($two);
my $eight   = $MULT->($two)($four);
my $sixteen = $POW->($eight)($two);
for my $n ($one, $two, $four, $eight, $sixteen){
    print num2int($n), "\n";
}

Looking good? Not good enough in front of perl6!

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) }};

Beautiful, isn't it?

And here is how to run it.

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
};

This is a consice example. If you are looking for a "full-fledged" example with Y-combinator, check MJD'sfamous example (no perl6 implementation, though).

Dan the Lambdacamel

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