=NAME Yet Another S<Perl 6> Operator: Reduce Operators - Part II

=VERSION

  Maintainer: Adriano Ferreira <ferreira@cpan.org>
  Date: 28 Dec 2007
  Last Modified: 28 Dec 2007
  Number: 17
  Version: 1

  Status: Draft

=head1 Body

In L< a previous article | reduce1.html >, we introduced
the reduction operators (like C<'[*]'> and C<'[~]'>)
which produced list operators from infix operators
(like C<'*'> and C<'~'>). 

There is a variant of the reduction operator
that operates over its list argument producing
all intermediate results along with the final result
of the ordinary reduction.

  [\+] 1..5   # (1, 3, 6, 10, 15)

which is equivalent to

  ([+] 1), 
  ([+] 1, 2), 
  ([+] 1, 2, 3),
  ([+] 1, 2, 3, 4),
  ([+] 1, 2, 3, 4, 5)

The above decomposition illustrates that the visual
picture of a triangle in the reduce operator (eg, C<'[\+]'>) is 
not accidental.

The triangular reduction lazily generates its resulting
list, so that it can be applied to infinite lists.

  [\*] 1..*   # (1, 2, 6, 24, ...)

As many other S<Perl 6> operators, this one has a functional
flavor which may estimulate some Haskellish solutions
to some problems. A (rather contrived) application example
is to implement a C<mkpath> function (similar to the one
provided by the S<Perl 5> module 
L< C<File::Path> | http://search.cpan.org/perldoc?File::Path >)
with a C<mkdir> builtin.

=begin code

  sub mkpath (Str $path) {

    # split 'a/b/c' into ( 'a/', 'b/', 'c' )
    my @segments = $path.split( /<!after '\/'>/ );

    for =[\~] @segments {
      # path exists as dir or create it
      .:d || .mkdir;
    }    
  }

=end code

This will create the directories C<'a/'>, C<'a/b/'>, and 
C<'a/b/c'> if they do not exist yet.

=SEEALSO

L< Reduce Operators - Part I | reduce1.html >

$Revision$

=begin comment

Keywords:
  Perl
  Perl 6
  operators
  reduce operator
  reduction operator
  meta-operator

=end comment