.. $Id: logic_tricks.txt 66 2008-02-23 02:55:45Z mtnyogi $
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restindex
    crumb: Logic Tricks
    page-description:
        How to accomplish different logic operations with rules.
    /description
    format: rest
    encoding: utf8
    output-encoding: utf8
    include: yes
/restindex

===================================
Logic Tricks
===================================

This describes how to accomplish different logic operations with rules.

X OR Y
===========

For example: check for text_x($arg) OR test_y($arg).

Create a separate subgoal for the OR case, let's call it ``or_goal``.  Then use
a separate rule for each OR clause::

    or_goal_test_x:
        use or_goal($arg)
        when
            test_x($arg)

    or_goal_test_y:
        use or_goal($arg)
        when
            test_y($arg)

Then you'd use ``or_goal($arg)`` where you wanted the *OR* clause.

This can go on for any number of OR-ed clauses by just adding more rules for
``or_goal``.

IF X THEN Y
=============

For example: if test_x($arg) then test_y($arg).

What this means is that test_y($arg) must be true if test_x($arg) is true.
But if test_x($arg) is not true, then test_y($arg) doesn't matter and ``if
test_x($arg) then test_y($arg)`` is true.

Create a new subgoal, let's call it ``if_x_then_y``.  Use two rules::

    if_x_then_y_if:
        use if_x_then_y($arg)
        when
            test_x($arg)            # if this fails, the next rule will be used
            special.claim_goal()    # don't use any other rules for if_x_then_y
            test_y($arg)            # if this fails, the next rule will not be used, so if_x_then_y will fail.

    if_x_then_y_else:
        use if_x_then_y($_)         # this rule is only used if test_x($arg) fails

NOT X
==========================

For example: not test_x($arg)

You have to be careful about *not* logic because it can mean different things.
In this example, if we try ``not test_x($arg)`` and ``$arg`` is unbound what
should happen?  Should it generate all of the different values for ``$arg``
for which ``test_x($arg)`` fails?  This generally isn't very practical!

The other interpretation is that there is **no** possible binding for ``$arg``
that makes ``test_x($arg)`` true.  In this example, ``not test_x($arg)`` would
then be false, because there is some ``$arg`` value that makes ``test_x($arg)``
true.

This second interpretation can be implemented by creating a new subgoal, let's
say ``not_test_x`` and using a pair of rules::

    not_test_x_fail:
        use not_test_x($arg)
        when
            test_x($arg)            # if there is any way for test_x($arg) to be true
            special.claim_goal()    # don't use any other rules for not_test_x
            check False             # and cause this rule to fail, which causes the not_test_x goal to fail

    not_test_x_success:
        use not_test_x($_)          # this rule only runs if test_x($arg) fails, above

EXISTS X SUCH THAT Y
===============================================================

For example: there exists a ``$x`` from ``generate_x($x)``, where
``test_y($x)`` is true.

This doesn't require a new subgoal.  You can just use the following two
clauses in place of the ``exists`` test::

    generate_x($x)
    test_y($x)          # if this fails, it will backtrack and try the next value from generate_x($x)

FOR ALL X, Y
===============================================================

For example: for all $x from generate_x($x), test_y($x) is true

Rethink this as a combination of two negatives on ``exists``, above: there
does *not* ``exist`` an ``$x`` from ``generate_x($x)`` where ``test_y($x)`` is
*not* true.  Then combine the ``not`` trick with the ``exists`` trick.
This needs a new subgoal, we'll call it ``for_all_x``::

    for_all_x_failure:
        use for_all_x()
        when
            generate_x($x)          # these two lines are the exists trick
            not_test_y($x)
            special.claim_goal()    # don't use any other rules for for_all_x
            check False             # and cause this rule to fail, which causes the for_all_x goal to fail

    for_all_x_success:
        use for_all_x()             # we only make it here if all generated $x values have test_y($x) true

Then you also need to create rules for the ``not_test_y`` goal using the
``not`` trick, above::

    not_test_y_fail:
        use not_test_y($x)
        when
            test_y($x)              # if there is any way for test_y($x) to be true
            special.claim_goal()    # don't use any other rules for not_test_y
            check False             # and cause this rule to fail, which causes the not_test_y goal to fail

    not_test_y_success:
        use not_test_y($_)          # this rule only runs if test_y($x) fails, above

