#!/usr/bin/perl -w

# A non-recursive left fold (foldl), taken from Language::Functional
sub foldl(&$$) {
  my($f, $z, $xs) = @_;
  map { $z = $f->($z, $_) } @{$xs};
  return $z;
}

# Recursive foldl
sub foldl_rec {
  my($f, $z, $xs) = @_;
  my($head, @tail) = @$xs;
  $head ? foldl_rec($f, $f->($z,$head), \@tail) : $z;
}

# "Fold" is the universal list traversal function. Also known as
# "reduce" (see List::Util) and "accumulate" (C++ STL).  Any function
# you write that munges lists (map, grep, etc.) can be rewritten in
# terms of a fold.  It essentially takes a list and replaces each "cons"
# constructor with a function.  Stated another way, if you have a list
# @a = (1, 2, 3, 4), fold will replace the commas with another function
# of your choosing.  Let's say you want the sum of the elements in @a.
# Replace the commas with a '+' sign, (1 + 2 + 3 + 4).  Easy isn't it?
# You might write it as...

$s = foldl(sub{ $_[0] + $_[1] }, 0, [1..4]);
print "sum = $s\n";  # 10

# ...in addition to providing the function and the list, you supply an
# initial value to start out with.  In the case of $sum above, we use
# 0.  If you want the product of the elements in the list you can change
# to...

$p = foldl(sub{ $_[0] * $_[1] }, 1, [1..4]);
print "product = $p\n";  # 24

# The "left" portion comes into play because we start at the left end of
# the list and work towards the right.  The actual sum that is
# calculated is (((((0+1)+2)+3)+4).  It only makes a difference when the
# function used isn't associative.  Subtraction is an example...


$l = foldl(sub{ $_[0] - $_[1] }, 0, [1..4]);
print "left fold subtraction = $l\n";  # ((((0-1)-2)-3)-4) == -10

# Recursive foldr
sub foldr_rec {
    my($f, $z, $xs) = @_;
    my($head, @tail) = @$xs;
    $head ? $f->($head,foldr_rec($f, $z, \@tail)) : $z;
}

$r = foldr_rec(sub{ $_[0] - $_[1] }, 0, [1..4]);
print "right fold subtraction = $r\n";  # (1-(2-(3-(4-0)))) == -2

# The dual of "fold" is the universal list creation function, "unfold".
# See more unfold in action...
#
#    http://use.perl.org/~Greg%20Buchholz/journal/26747