[om] DefMP elements

[Bill Naylor]

> >
> >>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:
> >>
> >>"NumericalValue
> >>
> >>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
> >>not?
> >>
> >>
> >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

In fact "NumericalValue" is a symbol:
http://www.openmath.org/cocoon/openmath/cd/sts.html#NumericalValue
so I guess an application which 'understood' the sts CD should have some
idea about what a 'Numerical Value' was.

> 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.

I notice that in the OpenMath2 specification there is a discussion on STS
signatures, there is no mention on the issue of multiple signatures for an
element. I guess that this could be performed by simply having more than
one 'Signature' element with the same 'name' attribute. However if this is
the resolution of this problem, it definitly should be stated in the
specification, and examples displaying this should also be given.

Bill
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