[om] DefMP elements

Andreas Strotmann Strotmann at rrz.uni-koeln.de
Thu Dec 11 17:20:44 CET 2003

Professor James Davenport wrote:

>On Wed, 10 Dec 2003, Bill Naylor wrote:
>>Excuse me for appearing a bit ignorant here. The signature for sin in STS
>>is defined as sin: NumericalValue -> NumericalValue, where NumericalValue
>>is defined as:
>>Denotes an OpenMath object that is to be thought of as something that
>>represents a numerical value, or a numerical value."
>>this seems very circular to me, where do we define a 'numerical value'? I
>>mean integers are clearly numerical values, so are reals. Almost as
>>clearly complex numbers are numerical values. What about Quaternions? I
>>would have thought so? What is it that makes them numerical and matrices
>We don't, and this is a weakness of a system like STS. Now that the Pisa 
>meeting has approved multiple signatures, we could tidy this up a little. 
>I had thought of NumericalValue as being substes of C or Z/(n).
Technically, "NumericalValue" is a variable, which means that these 
signatures are for human consumption, not for computer systems. From a 
purely technical point of view, there is nothing in the STS signature 
that tells a computer program that sin(A), A a matrix, is not allowed.  
The reference to STS signatures thus doesn't help in this issue at all.

However, notice that you just pointed out, James, that here is yet 
another case in the joint OpenMath/MathML history where premature 
insistence on uniqueness (or some other arbitrary restriction) has had 
to be relaxed.  I know that it's bad taste to say so -- but there were 
many who questioned the decision to allow only a single signature even 
before that decision was made, including myself.  There was no need to 
wait years to fix the problem -- it had been entirely possible at that 
point not to make it in the first place.

Please, *pretty please*, let us not make the same mistakes again, and 
again, and again(*).

 -- Andreas

(*) See also the parallel discussion on the proposed (overly) 
restrictive reading of a symbol's "role" that I argued against in Bremen.
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