This solution is extremely similar to the Haskell one in both structure and technique -- as much of a direct translation as I could manage. I had to roll a couple of tools, but they are elegantly in keeping with functional programming style.

I was really pleased with how this all came together.

use strict; 
use warnings;

# A stream is an array ref, in which the first element is an ordinary
# value, and the second element is a continuation: a sub that yields
# a stream. In other words, a lazy list.

# Takes an ordinary list and turns it into a stream
sub stream_up {
    my ($x, @rest) = @_;
    return [ $x, sub { @rest ? stream_up(@rest) : [] } ];
}

# Yields the first N elements from a stream
sub take {
    my ($N, $x_xs) = @_;
    $N > 0 or return ();
    if (!@$x_xs) { return () }
    my ($x, $xs) = @$x_xs;
    return($x, take($N-1, $xs->()));
}

# merge takes two streams, and returns one
sub merge {
    my ($x_xs, $y_ys) = @_;
    if (!@$x_xs)  { return $y_ys }
    if (!@$y_ys)  { return $x_xs }
    my ($x, $xs) = @$x_xs;
    my ($y, $ys) = @$y_ys;
    if ($x < $y)  { return [$x, sub { merge($xs->(), $y_ys)  } ] }
    if ($x > $y)  { return [$y, sub { merge($x_xs  , $ys->())} ] }
    if ($x == $y) { return [$x, sub { merge($xs->(), $ys->())} ] }
}

# Like map, but applies coderef to stream, returning a stream
sub stream_map {
    my ($coderef, $x_xs) = @_;
    if (!@$x_xs) { return $x_xs }
    my ($x, $xs) = @$x_xs;
    local $_ = $x;
    return [$coderef->($x), sub { stream_map($coderef, $xs->()) }];
}

# genHam takes a stream and returns a stream
sub genHam {
    my ($x_xs) = @_;
    if (!@$x_xs)  { return $x_xs }
    my ($x, $xs) = @$x_xs;
    my $out;
    $out = merge([1, sub {stream_map(sub{$_ * $x}, $out)}], genHam($xs
+->()));
}

print "$_\n" for take 20, genHam stream_up(2,3,5);
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