=head1 NAME

AI::Prolog::Introduction - The what and the why of logic programming.

=head1 REVISION

 $Id: Introduction.pod,v 1.2 2005/02/20 18:27:55 ovid Exp $

=head1 RATIONALE

You can skip this if you already know logic programming.

Note that most of this was pulled from my write-up about logic programming in
Perl at L<http://www.perlmonks.org/?node_id=424075>.

In Perl, generally you can append one list to another with this:

 my @Z = (@X, @Y);

However, that's telling the language what to do.  As sentient beings, we can
look at that and infer more information.  Given C<@Z> and C<@X>, we could infer
C<@Y>.  Given just C<@Z>, we could infer all combinations of C<@X> and C<@Y>
that can be combined to form C<@Z>.

Perl cannot do that.  In logic programming, however, by defining what
C<append()> looks like, we get all of that other information.

In Prolog, it looks like this:

 append([], X, X).
 append([W|X],Y,[W|Z]) :- append(X,Y,Z).

(There's actually often something called a "cut" after the first definition,
but we'll keep this simple.)

What the above code says is "appending an empty list to a non-empty list yields
the non-empty list." This is a boundary condition. Logic programs frequently
require a careful analysis of boundary conditions to avoid infinite loops
(similar to how recursive functions in Perl generally should have a terminating
condition defined in them.)

The second line is where the bulk of the work gets done. In Prolog, to identify
the head (first element) of a list and its tail (all elements except the
first), we use the syntax [head|tail]. Since ":-" is read as "if" in Prolog,
what this says if we want to concatenate (a,b,c) and (d,e,f):

=over 4

=item * Given a list with a head of W and a tail of X:

 @list1 = qw/a b c/; (qw/a/ is W, the head, and qw/b c/ is X, the tail)

=item * If it's appended to list Y:

 @Y = qw/d e f/;

=item * We get a list with a head of W and a tail of Z:

 @list2 = qw/a b c d e f/;

=item * Only if X appended to Y forms Z:

 X is qw/b c/. Y is qw/d e f/. Z is qw/b c d e f/.

=back

But how do we know if X appended to Y forms Z? Well, it's recursive. You see,
the head of X is 'b' and it's tail is 'c'. Let's follow the transformations:

 append([a,b,c],[d,e,f],[a,b,c,d,e,f])
  if append([b,c],[d,e,f],[b,c,d,e,f])
  if append([c],[d,e,f],[c,d,e,f])
  if append([],[d,e,f],[d,e,f])

As you can see, the last line matches our boundary condition, so the program
can determine what the concatenation is.

Now that may seem confusing at first, but so was the Schwartzian transform when
many of us encountered it. After a while, it becomes natural. Sit down and work
it out and you'll see what's going one.

So what does this give us? Well, we can now append lists X and Y to form Z:

 append([a], [b,c,d], Z).

Given Y and Z, we can infer X.

 append(X, [b,c,d], [a,b,c,d]).

And finally, given Z, we can infer all X and Y that combine to form Z.

 append(X,Y,[a,b,c,d]).

Note that you get all of that from one definition of how to append two lists.
You also don't have to tell the program how to do it. It just figures it out
for you.

Translating all of this into C<AI::Prolog> looks like this:

 use AI::Prolog;
 use Data::Dumper;

 my $prolog = AI::Prolog->new(append_prog());
 $prolog->query("append(X,Y,[a,b,c,d])");
 while (my $result = $prolog->results) {
     print Dumper($result->X); # array references
     print Dumper($result->Y);
 }

 sub append_prog {
     return <<'    END_PROLOG';
     append([], X, X).
     append([W|X],Y,[W|Z]) :- append(X,Y,Z).
     END_PROLOG
 }

=head1 SEE ALSO

W-Prolog:  L<http://goanna.cs.rmit.edu.au/~winikoff/wp/>

X-Prolog:  L<http://www.iro.umontreal.ca/~vaucher/XProlog/>

Roman BartE<225>k's online guide to programming Prolog:
L<http://kti.ms.mff.cuni.cz/~bartak/prolog/index.html>

=head1 AUTHOR

Curtis "Ovid" Poe, E<lt>moc tod oohay ta eop_divo_sitrucE<gt>

Reverse the name to email me.

This work is based on W-Prolog, http://goanna.cs.rmit.edu.au/~winikoff/wp/,
by Dr. Michael Winikoff.  Many thanks to Dr. Winikoff for granting me
permission to port this.

=head1 COPYRIGHT AND LICENSE

Copyright 2005 by Curtis "Ovid" Poe

This library is free software; you can redistribute it and/or modify
it under the same terms as Perl itself. 

=cut