% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % %
%                                                                           %
% File:            creeping.dtr                                             %
% Purpose:         capture integer similarity with a creeping Gray code     %
% Author:          Gerald Gazdar, August 1994                               %
% Email:           geraldg@cogs.sussex.ac.uk                                %
% Address:         COGS, Sussex University, Brighton BN1 9QH, UK            %
% Related files:   graycode.dtr                                             %
% Version:         1.0                                                      %
%                                                                           %
%      Copyright (c) University of Sussex 1994.  All rights reserved.       %
%                                                                           %
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% Gray codes are a (family of) number representations that have the
% interesting (and possibly useful) property that N and N+1 will always
% differ by exactly one bit.

% Creeping Gray codes are elegant and intuitive -- but verbose.  Whilst only
% five bits are required to represent 0-9, fifty bits are required to
% represent 0-99.  Their use in default inheritance networks is thus
% probably best restricted to fairly gross scalar distinctions (e.g.,
% those found in a tone system).

Zero:
    <> == 0
    <gray code> == "<gray4>" "<gray3>" "<gray2>" "<gray1>" "<gray0>" .

One:
    <> == Zero
    <gray0> == 1.

Two:
    <> == One
    <gray1> == 1.

Three:
    <> == Two
    <gray2> == 1.

Four:
    <> == Three
    <gray3> == 1.

Five:
    <> == Four
    <gray4> == 1.

Six:
    <> == Five
    <gray0> == 0.

Seven:
    <> == Six
    <gray1> == 0.

Eight:
    <> == Seven
    <gray2> == 0.

Nine:
    <> == Eight
    <gray3> == 0.

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% Some example theorems:
%
%   Zero:  <gray code> = 0 0 0 0 0.
%   One:   <gray code> = 0 0 0 0 1.
%   Two:   <gray code> = 0 0 0 1 1.
%   Three: <gray code> = 0 0 1 1 1.
%   Four:  <gray code> = 0 1 1 1 1.
%   Five:  <gray code> = 1 1 1 1 1.
%   Six:   <gray code> = 1 1 1 1 0.
%   Seven: <gray code> = 1 1 1 0 0.
%   Eight: <gray code> = 1 1 0 0 0.
%   Nine:  <gray code> = 1 0 0 0 0.
%
% Note how the sequence of 1s creeps in at one end of the representation
% and exits at the other end.

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# show <gray code>.

% The next line is the Revision Control System Id: do not delete it.
% $Id: archive.dtr,v 1.1 1997/04/09 20:40:33 root Exp $