[om] Re: OM-services

[Andrew Solomon]

Ok, so here's how I see it.
The original email I sent was mixing together several issues:

1. Whether it is possible to specify the behaviour of a mathematical service "formally"
   (in fact I suggested how, using OM CDs ... but let's not get into that just yet);
2. Whether the specification should be part of an OpenMath CD;
3. Whether the specification should be part of the OpenMath effort.

For the moment it would probably be best to leave aside issues 2 and 3.

What was my goal in asking (1)? It was this networked mathematical dream 
where a computer algebra system (or other program) which is missing some functionality 
can call out to some index of mathematical services and find a service on the net
which will do the job required. And all of this, automatically.

The point Richard seems to be making is that there are some situations
(would it be fair to say, quite a lot of analysis?)
where an algorithm's behaviour doesn't have a nice compact description
but will just "do its best" to get some kind of answer. On the other hand
(well, in algebra anyway) I think there are quite a few functions which 
can be neatly and almost canonically specified (e.g polynomial factorization and gcd,
groebner basis, knuth bendix, todd coxeter...) even though the methods used 
can vary widely. 

The question which remains (and I'm beginning to think it doesn't have a fixed absolute answer)
is whether it is possible to specify the functionality of a service closely enough that
the specification can be understood by another program which can decide if it will do 
the calculation it desires. Perhaps where this is heading is that we are defining a class
of services which can be specified in a machine readable format.

Thoughts?

Andrew


-- 
PIMS/MITACS/CECM                       http://www.cecm.sfu.ca
Simon Fraser University
Personal homepage:                     http://www.illywhacker.net

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