At 15:08 -0500 1998/12/02, William F. Hammond wrote:
>: 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.

I do not think that MathML itself will have that capacity, so one needs to
add OpenMath and perhaps some other such movements: It's *ML, SGML stuff,
but not only SGML itself, which somebody remarked is just a framework for
markup type of languages.

>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.

This is what I mean too: Computer programs have some capacity to understand
what the expressions means, but the piece that each computer program
understands differ from what the other computer programs understand. For
example, a computer algebra program understands some algebraic aspect of a
formula, a typesetting or WWW browser understands how to produce renderings.

But the mathematician understand how to integrate all those aspects.
Therefore, the ideal manuscript should contain that information, not just
one aspect. The importance if this aspect will increase when the reuse of
the information in the manuscripts increase: For example, a reader might
want to be able to copy a formula and paste it into a computer algebra
program.

The problem with the SGML stuff is that it restricts the syntax, so it is
difficult to combine different meanings in a single syntax, the way it is
done in mathematics.

>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.

You need more than that: You need the ability to parse expressions. TeX
does not have that capacity. It means that there is no way for the program
to verify that the input syntax is correct.

Otherwise, I think that the observation is correct that one cannot hope for
a single syntax to cover all the possible uses: So one needs being able to
create syntactic environments, which may vary with the context or intention
of the author. I think this is how humans read and create manuscripts, and
therefore am authoring language must support it.

>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.

The idea is that the author at any point should only provide as exactly
possible what corresponds to his or her intent. The rest should be provided
by a style, or graphical fine-tuning info.

  Hans Aberg
                  * Email: Hans Aberg <mailto:[log in to unmask]>
                  * Home Page: <http://www.matematik.su.se/~haberg/>
                  * AMS member listing: <http://www.ams.org/cml/>