Re: SGML and Math

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To: Eric van Herwijnen <100043.3201@compuserve.com>
cc: David Cohen <dnc@ebt.com>, Steve Derose <sjd@ebt.com>,
    Paul Ginsparg <ginsparg@xxx.lanl.gov>,
    Michel Goossens <michel.goossens@cern.ch>,
    Dan Grayson <dan@math.uiuc.edu>, Gary Grosso <gpg@arbortext.com>,
    Paul Grosso <pbg@texcel.no>, Frank Harris <fharri@osa.org>,
    Susan Harum <s-harum@uiuc.edu>,
    Melissa Idleman <melissa@wolfram.com>,
    "Patrick D. F. Ion" <ion@math.ams.org>,
    Glenda Jeffrey <jeffrey@lemond.hks.com>,
    Rob de Jeu <ROB.deJEU@wkap.nl>, Scott Johnson <scottj@aip.org>,
    Ralph Johnson <johnson@cs.uiuc.edu>,
    Franck Laloe <laloe@peterpan.ens.fr>, Murray Maloney <murray@sq.com>,
    Patricia Morgan <pam@math.ams.org>,
    Roy Pike <erp@maxwell.ph.kcl.ac.uk>,
    Nico Poppelier <n.poppelier@elsevier.nl>,
    Dave Rodgers <dlr@math.ams.org>, Neil Soiffer <neils@wolfram.com>,
    Joyce Svechota <jms@arbortext.com>, John Turner <johnt@incontext.ca>,
    Fred Veldmeijer <f.veldmeijer@elsevier.nl>,
    Ron Whitney <rfw@ams.org>, Stephen Wolfram <sw@wolfram.com>,
    Ralph Youngen <rey@ams.org>
Subject: Re: SGML and Math 
In-reply-to: Your message of "08 May 1996 09:10:10 EDT."
             <960508131010_100043.3201_JHB103-1@CompuServe.COM> 
Date: Tue, 14 May 1996 17:27:49 -0400
From: "Dave Raggett" <dsr@w3.org>


I thought it might be useful to respond to Evan Owens comments on
the work by the W3C Math group. See:

        http://mish161.cern.ch/sc4wg6/math/dli.htm

The gist of our idea is that math notations are subject to frequent
change as mathematicians ascribe new meanings to symbols for new
areas of math. The presentational schema change much more slowly
and TeX uses a fixed set of some 13 or so.

This argument was made strongly by Eric van Herwijnen and Nico
Poppelier some years ago with the conclusion that SGML Math should
focus on presentational representations.  However, the W3C group
decided that the Web needs to support symbolic evaluation and that
a purely presentational representation is inadequate for both this
and for high quality rendering to speech.

It seems to me that SGML is great as a meta language for conventional
document idioms but a poor match to those of mathematics. This led
the W3C Math group to focus on extensible linear notations based on
augmented operator precedence parsers. Wolfram's own work provides
a strong proof of concept for the utility of this approach.

A metalanguage based on augmented operator precedence and simple
mapping templates seems straightforward, based upon my experimental
work using prolog as a prototyping environment. The next steps for
the W3C group will be to pin down the lexical rules, and to define
the syntax for "Active Math" together with vendors. We will then be
in a position to deploy plugins within a fairly short timescale.

In the short term, this could be done using the existing means to
specify plugins for HTML, but a more flexible approach will be to
define a few new HTML tags for declarations, inline and display
formulae. I expect simple plugins to range from free viewers to
ones with similar power to Wolfram's Notebooks.

Regards,

- -- 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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