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%                                                                           %
% File:            arithmet.dtr                                             %
% Purpose:         simple arithmetic operations                             %
% Author:          Gerald Gazdar, 24 March 1989                             %
% Email:           geraldg@cogs.sussex.ac.uk                                %
% Version:         1.01                                                     %
%      Copyright (c) University of Sussex 1989.  All rights reserved.       %
%                                                                           %
% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % %

Epsilon:<> == ''.

Error:  <> == '** ILL-FORMED INPUT **'.

% Add:      <a ... a b ... b> = c ... c.
%            ------- -------    -------
%               A   +   B     =    C

Add:    <> == Epsilon
        <a> == c
        <b> == c
        <a a> == c <a>
        <a b> == c <b>
        <b b> == c <b>
        <b a> == Error.

% Multiply: <a ... a b ... b> = c ... c.
%            ------- -------    -------
%               A   x   B     =    C

Multiply:
        <> == Epsilon
        <x a> == <x>
        <a b> == <x b>
        <x b> == Add:<b>
        <a a> == <x> <a>
        <b a> == Error.

% Square:   <a ... a>    = c ... c.
%            -------       -------
%               A   x A  =    C

Square:
        <> == Epsilon
        <b> == Error
        <y b> == Error
        <a> == Add:<a> <y> 
        <y a> == Add:<a> Add:<a> <y>.

% Exercises:
%
% (i) define Difference, such that
%
% Difference:<a> = c.
% Difference:<a b> = .
% Difference:<a a b> = c.
% Difference:<a b b> = c.
% Difference:<a a b b> = .
% Difference:<a b b b> = c c.
% Difference:<a a a a b> = c c c.
% etc.
%
% (ii) define Factorial, such that
%
% Factorial:<a> = c.
% Factorial:<a a> = c c.
% Factorial:<a a a> = c c c c c c.
% Factorial:<a a a a> = c c c c c c c c c c c c c c c c c c c c c c c c.
% etc.
%
% (iii) define Power, such that
%
% Power:<a b> = c.
% Power:<a b b> = c.
% Power:<a a b> = c c.
% Power:<a a b b> = c c c c.
% Power:<a a b b b> = c c c c c c c c.
% Power:<a a a b b> = c c c c c c c c c.
% Power:<a a b b b b> = c c c c c c c c c c c c c c.
% Power:<a a a a b b> = c c c c c c c c c c c c c c.
% etc.

# show  <a>
        <a a>
        <a a a>
        <a a a a>
        <b>
        <a b>
        <a a b>
        <a b b>
        <a a b b>
        <a a a b b>
        <a a b b b>
        <a a a b b b>
        <a a b b b b>
        <a a a a b b>
        <a a b a a a>.

# hide Epsilon Error.

% 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 $