[om] DefMP elements

[Bill Naylor]

> > I think that the feeling at Bremen was that dissallowing self-reference
> > inside a defining FMP was generally a good thing.  Self-reference and
> > hence recursion is of course quite legal for the evaluating case.
>
> Just a note that this goes against a lot of trends in programming languages
> (and their semantics), and established wisdom in type theory (and thus
> logic), where there are 'too many' semantic objects whose best (and often
> only) definition is recursive.  There is a whole community all of whose
> tools (algebraic and co-algebraic specifications) all use fundamentally
> recursive definitions, even at the concept level.  Not allowing
> self-reference in defining objects just means that lots of very natural
> objects will not be definable within OpenMath, only externally, which can
> get quite tedious.

I think this is a very good point, it would be very dangerous to
exclude mathematical community's at the specification level!

>
> Naive question: is OpenMath only designed to communicate between Computer
> Algebra systems, or is the aim to also include theorem provers and other
> systems that speak 'math' (like PVS, Coq, model-checking software, etc)?
> OpenMath looks very well suited for Maple-Mathematica-MuPad communication,
> but say Maple-Coq communication would appear to be 'out of scope'?  If CA
> communication is the complete scope, then just ignore the above comments as
> they are superfluous.
>

In chapter 1 of the specification it says:

"OpenMath is a standard for representing mathematical objects,
allowing them to be exchanged between computer programs, stored in
databases, or published on the worldwide web.  While the original
designers were mainly developers of computer algebra systems, it is
now attracting interest from other areas of scientific computation and
from many publishers of electronic documents with a significant
mathematical content."

make your own conclusions :-)

Bill

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