Message-ID:  <199812130000.TAA29345@hilbert.math.albany.edu>
Reply-To: Mailing list for the LaTeX3 project
              <LATEX-L@URZ.UNI-HEIDELBERG.DE>
Date:         Sat, 12 Dec 1998 19:00:48 -0500
From: "William F. Hammond" <hammond@CSC.ALBANY.EDU>
Sender: Mailing list for the LaTeX3 project
              <LATEX-L@URZ.UNI-HEIDELBERG.DE>
To: Multiple recipients of list LATEX-L
              <LATEX-L@URZ.UNI-HEIDELBERG.DE>
Subject:      Re: portable LaTeX
Status: R

Timothy Murphy writes:

: On Sat, Dec 12, 1998 at 06:05:25PM +0100, Chris Rowley wrote:
:
: There is a fundamental question about MathML/XML/OpenMath vs TeX/LaTeX
: which does not seem to me to have been answered here.
:
: As I understand it, *ML _parses_ (or tries to parse) maths,

No.

: while Knuth in his wisdom decided this was impractical.
: For example, if I write $AB = CD$
: this might refer to variables AB,CD (perhaps line segments)
: or it might refer to products of 4 variables A,B,C,D;

I would suggest that in a latex-like document preamble one declare,
with something like "\mathsym" the symbols A, B, C, D either as having
a type such as "vertex" or else having a type such as "element of an
additive group".

In either case to obtain recognition of the typed symbols, one should
in the body use $A B = C D$ if either "AB" or "CD" is a symbol as
declared by another \mathsym.  Absent a mathsym declaration the string
"AB" in a math zone would be equivalent, by tradition, to "A B".

Although I argue that "A B" by default should stand for function
composition of A and B when it makes sense, it does not make sense,
absent symbol declarations, to assume that A and B are functions that
can be composed.  The next choice, absent other guidance, is to assume
an arithmetic context with juxtaposition standing for multiplication.

(But note that I need none of this, other than symbol separation if I
don't process math zones specially, to get the representations that I
put up in my last posting to latex-l under the subject "notational
examples".)

: Would I perhaps have to put in an \invisibletimes between A and B?

I hope not.

: The question is, then:
: is it possible to parse mathematics,
: and if so, is it wise to try?

Don't readers do it?  You think that it's based on "visual
intelligence"?

: [It may be impossible,
: because it may be that mathematicians
: would refuse to be bound by any particular formal system put forward.]

Ay, there's the rub -- certainly for many.  Note in particular that
mathematical authors have incentive to provide MathML only if they
perceive that the *most helpless* of their readers who have browsers
also have MathML rendering.

It would be helpful if some of the W3C MathML working group (whose
emissary usually listens here) would ponder a format for a flexible
author-specified type system and provide us with testbed code for
generating MathML based on it.

                                   -- Bill