OM-services was "[om] Reference vs. Referent: solution to an old problem"

[Richard Fateman]

I have been running a "micro-service" for about 5 years now,
not based on OM or MathML
but on an ad hoc (actually SEVERAL ad hoc) specification:
1. Mathematica syntax/semantics
2. A Common Lisp version, equivalent to the above
3. A looser parser

This server attempts to provide
answers to indefinite integration problems by
table lookup, using a data base mostly from
the CRC table of integrals.. 
http://torte.cs.berkeley.edu:8010/tilu 

There are about 130 queries a day coming in.

Why is this experience relevant?
a. the answers are complex, including clauses such
as "if b^2>4*a*c then ... else ..."
or  even "there are several possible equivalent answers..."

b. The key to describing this was the writing of the
program, and it would be unreasonable, in my opinion,
to write an OM CD on its meaning as a micro-server
independent of its implementation. Indeed, the specification
can be trivially altered by adding another pattern
to its database.  The description IS the database
and the pattern matching algorithm.

Is this unusual in terms of its complexity etc?
Unfortunately for OM, probably not.  Consider
cosine.  What does cos(x) mean for various x?
There are a pile of considerations which alter
the meaning of this, which must be put in the context
of each separate CAS.  Special angle formulas?
Precision? Multiple-angle formulas? ?? Evaluate or
not, etc.
  
If I want to call out to a facility in another
computer algebra system or micro-server, then
I'll learn about that CAS or server, and the
intervention of some OM CD writer is certainly
not appealing.

For what it is worth, there is a beta-test version
of the Macintosh Graphing Calculator, soon to
be released, which uses Tilu as a server.  That
is, there is a button you can push which, instead
of plotting the formula, will send it to tilu and
try to find its integral.  This could have been
a good test for MathML and maybe OM.  Ron Avitzur
and I found MathML to be inadequate. OM would
not have helped, so far as I can tell.

I think that the OM effort must take into account
the reality that CAS systems are NOT defined
axiomatically, but pragmatically.  Imposing an
axiomatic definition on any but the simplest operations
is not going to be an accurate reflection of
what is happening.

If you want to write a new pure axiomatic CAS
or collection of servers, then that is fine.
But it will not be very interesting, beyond
the realm of polynomials over finite fields
or the rationals.

RJF
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