[Oberon] Numbers - Cat

[Alan Freed]

Hi Doug and others,

> I believe Dr. Wirth was attempting to move in the other direction,
> away from implementation issues and toward a conceptual representation
> of a number.  I deduce this from the fact that the term REAL is used
> rather than float.  A floating point representation of a real number
> is a more accurate description of what computers actually do, however,
> to focus on this aspect diverts ones thinking away from the usual
> task at hand of determining the value of an expression.
>
> I would like to push this avoidence of 'implementation' even farther
> (and perhaps in some far distant future this may happen) by completely
> eliminating the 'size' of a number's representation.  When one uses
> paper and pencil and algebra to solve equations there is no consideration
> of implementation size.  In fact the distinction between real and integer
> is frequently not needed.  The operation of 'quantizing' a number to
> an integer value is sometimes necessary algebraically.  If one is working
> with diaphatine numbers then the whole domain is strictly integer.
> The context of the calculation should be the determining factor.
> But this takes a very high level of abstraction for a machine to
> handle.

This is what I was trying to achieve with Cat, only I did it for integers, 
rationals, reals and complex numbers, their vectors and their matrices.  
It is available for download from the ETH server.

Al

-- 
Alan D. Freed, PhD         email: Alan.D.Freed at grc.nasa.gov
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