Hans Aberg:

: At 11:16 -0500 1998/12/02, William F. Hammond wrote:
: >: I think it is well-known by now, that all these mass-consumer movements,
: >: which the *ML currently represents, usually lacks crucial quality.
: >: Eventually such quality might built in, of course.
: >
: >Only because very few elitist mathematicians have been involved (up to
: >now).
: >
: >: But until then, there will be a need for TeX/LaTeX.
: >
: >And beyond then, as well!
:
: I think that when at the point when the various *ML movements have moved so
: far that they have the capacity of generating a manuscript with all the
: information that a mathematician want, then one would still need a NL
: (notational language) with capacity of accepting less corny syntaxes than
: the SGML stuff.

When Hans says "SGML stuff", I assume that he is referring specifically
to MathML, a W3C recommendation.

: But then there is no point in using TeX/LaTeX as everything that can be
: done in those languages can be done more conveniently and accurately in
: this NL.

The point of my drafty draft on notation

  http://www.albany.edu/~hammond/gellmu/notation [please read and comment]

is that the legacy of 200 years of typeset mathematical notation is
not as ambiguous as some imagine.  The main ingredient that is missing
is the ability of computer programs to understand what the notation
means.  On the other hand, mathematicians usually do understand.

Why?  My point is that (1) a mathematician reads the accompanying text
which explains the meaning of symbols and (2) a mathematician understands
how to parse complicated expressions.

So one needs to formalize tex math zones under a regime of mathexpr's,
something analogous to regexp's, and then formalize a protocol for
parsing standard tex math zones.

The only new information that a tex-like document then needs for this
to work is a formal type declaration in a context-specific family of
types.  That is, for authoring, a single declaration for each variable
in the document preamble.  Math zones may still be more or less
traditional.

Even so, good technical typists have been parsing handwritten professor
notation for years without understanding content.  Analogously there
is, I believe, a logic to the parsing of math zones that can be made
robotic within reason if author's take a little care.

Many authors will balk at providing type information, which, in the
end, will be mainly of use for "smart documents".  In that case one
would want to fall back to the analogue of good technical typing.

Comment: for authoring I don't think that one should assume
MathML to be the only output format.  Other things may come along,
and authors will not want to repair old documents.

I won't be too eager to generate MathML until I see that my audience
has it.

Authors who do not wish to declare symbols will still be included.

                                   -- Bill