[om] Reference vs. Referent: solution to an old problem

[Manfred Riem]

Hi Paul,

> I think your cynic here... of course such generic things as
> "eval" or "simplify" or... are too short general.
>
> But, also, of course, that "operators" CD would have to
> mention the domains which, in your example would not be
> supported, period.
>
> Such a CD could NEVER rely on the on-purpose-simplistically-designed
> language a Computer algebra system can eat. This is a shell language
> that has a lot of contexts in and this context is precisely the delicate
> task of such a thing !!

I take your point here is to say that either a CAS should be cleaner
in its output so that we exactly know what it outputs, or that you should
limit yourself in using the CAS only for properly, totally defined
functions (which could use other functions not well so defined inside
the CAS), right?

> > Any time two CAS differ in their capabilities, you will have to choose
for
> > the standard the least capable.  Otherwise you must distinguish between
them,
> > and once you do that, you have no standard.

Not really the case. In a proper design of an distributed system it is
feasible
that the capabilities differ, and distinguishing between them is possible.
See for more information, either Linda tuple spaces, TSpaces (IBM)
or JavaSpaces (Sun). If you use totally defined functions it is not even
really hard.

The hardest part is for the mathematician, computer scientist, etceteras to
use the systems to their full effectiveness. They need to know which engine
supports what. Which means they determine how a given calculation runs and
where.

Back to the CDs, the CDs define what you would want a CAS to implement, but
it
is still quite acceptable to only implement a part of a CD. The CAS engine
will
export only the functions (OMS-ses) that it supports.

This is of course under the assumption that it does an EVAL on the
arguments.
Other stuff could be done with the engine also, but it should not be part
of the OpenMath CD stuff, because it is used to steer the engine itself
(like quitting it, resetting, adding functions, etceteras).

> > Imagine a CAS that only knows about polynomials.  How do you standardize
> > its response to a question that requires rational, algebraic,
logarithmic,
> > exponential, trigonometric, etc. functions.

A very simple solution would be to refuse to do the operation, in that way
only if a proper set of arguments is supplied to a function it will perform
the function call.

Regards,

Manfred.


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