[om] critique of the notion of phrasebook

Andreas Strotmann strotman at cs.fsu.edu
Sat Jun 23 22:44:25 CEST 2001

You're welcome, Andrew.

Another aspect that was part of the notion of a phrasebook was that it was
application / system specific. I'm just looking at the 95 ISSAC Objectives
poster which I found on my parents' attic -- this aspect was clearly there
even then. This has two consequences; one - only that part of OpenMath
that is of interest to the application / system needs to be part of any
given phrasebook (i.e. no phrasebook is expected to cover all of
OpenMath); two - each application/ system phrasebook would take care of
the ideosynchracies of the system.

On the other hand, the term phrasebook also conveys an idea of common
structure among phrasebooks for different applications and systems.  A
good categorial semantics would induce a skeleton import and export
routine that would only need to be refined for the idiosynchratic
components (non-compositional components ;-) of the system.

This commonality is not a theoretical prediction, I've realized the
(basically) same structure of import/export functionality in Prolog, LISP,
and C/Java based systems.  More often than not, this is made all the
easier because such systems tend to have a common notion of a term
structure, or prefix tree, or what have you, and this can be utilized for
the backbone.

Note the "compositionality" requirement above.  A well-designed system
would only have a very small and finite number of distinct *classes* of
objects (or should this be classes of classes of objects?).  Realistic
systems will also have a few distinct classes, but many special cases.
Special cases, however, do not pose a problem with providing a skeleton
"interpret"/"represent" pair of functions, as any LISP programmer will
tell you.  Just provide hooks for recognizers and translators.

Thus, I do not believe that it is true that we have an infinite number of
distinct classes to deal with -- at least not if OpenMath is well designed
and if it is hooked into reasonably well designed systems. The
compositionality requirement for OpenMath was meant to ensure that.

 -- Andreas

"The act of defending any of the cardinal virtues has today
all the exhilaration of a vice." -
G.K.Chesterton: A Defense of Humilities, The Defendant, 1901

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