[Oberon] Numbers

[Douglas G. Danforth]

Frank van Riet wrote:
> 
> Hi Patrik, Paul, Greg
> 
> Thanks very much for your comments.
...
> If you have a look at my original submission you'll note that I did 
> raise this issue, as well as a simple solution. Simply don't allow 
> interoperability between signed and unsigned variables. This makes the 
> impact on the compiler negligable.  This has the additional benefit of 
> forcing to programmer to think about the range of the variables.

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.

Do you really want to 'program' or do you want to 'specify' and
'solve'.  Ultimately, the later approach would be my choice.

-Doug