Re: SGML Math Workshop/ a suggestion

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To: "Richard J. Fateman" <fateman@cs.berkeley.edu>
cc: dli-math@ncsa.uiuc.edu, s-harum@uiuc.edu
Subject: Re: SGML Math Workshop/ a suggestion 
In-reply-to: Your message of "Mon, 20 May 1996 09:13:05 EDT."
             <199605201613.JAA27194@peoplesparc.CS.Berkeley.EDU> 
Date: Mon, 20 May 1996 12:46:20 -0400
From: "Dave Raggett" <dsr@w3.org>


> con: semantic approach.
> 
>   It is pretty much inevitable that the notation given by
> any predetermined collection will be inadequate, since authors
> are not restricted a priori to notation that can be mapped into 
> existing Mathematica (etc.) semantics.
> 
> An extension language is therefore necessary.
> 
> If you are unwilling to allow people to define new formats based
> on new operators "on the fly" then a semantic encoding would be
> impossible to live with.

This is very much the direction that I have been investigating
with the W3C Math group which has the goal of developing a
solution for HTML.  I have been experimenting with the Prolog
language as a rapid prototyping tool, but believe that the
goals can be realized using simple algorithms that don't rely
on backtracking.

Unfortunately, most of the people at the SGML Math workshop
failed to follow my presentation, heretical as it was in
advocating moving from SGML to more flexible notations, based
upon augmented operator precedence plus mapping rules.

The general idea is to define the parser declaratively, referenced
by a URL, and used dynamically to parse an input string representing
a given math expression. The result is mapped to an extensible
semantic form and a rendering tree based on a small set of
schema (TeX has about 13 of these). It seems to be practical
to define linear notations based on how people say math e.g.
over the phone.

We are also investigating a middle ground based on ideas from
Wolfram and my work on HTML 3.0. This would keep some SGML
markup but allow limited use of operator precedence and several
new entities for special characters like the differential `d'.

- -- Dave Raggett <dsr@w3.org> tel: +1 (617) 258 5741 fax: +1 (617) 258 5999
   World Wide Web Consortium, 545 Technology Square, Cambridge, MA 02139
   url = http://www.w3.org/People/Raggett

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