XML & Math

Paul Prescod wrote:

>Someone from Waterloo Maple came through today to speak about "Making
>the Internet Safe For Math." He mentioned that the OpenMath process was
>going painfully slowly but that he had better hopes for HTML Math. He said
>that there are currently two proposals under development:
>1) a semantic one based on the unfinished OpenMath effort headed up by
>INRIA, based on "SGML".
>2) a math typesetting oriented one based on an extensive survey of math
>literature headed up by Wolfram Research, based on XML.
>I do not know if the former uses any SGML features that are not available in
>XML.  Most likely it is "based on SGML" because OpenMath had described
>an SGML representation of the OpenMath expressions. I expect it would
>be moved over to XML when it gets back to the W3C unless it depends on
>ShortRefs or something.
>This guy believed that the HTML Math standard would be finished this year
>because the participants are really chomping at the bit for a standard after
>the disappointment (in multiple senses) of HTML Math and the delays of the
>OpenMath group. It is very believable that there will be implementations soon
>after it is a standard.

>These fixed-tagset applications are going to really propel XML into the
>limelight even if full implementations w/ stylesheet take some time. On the
>other hand, we might want to talk to this HTML-Math group about if it
>would be possible to put rendering in stylesheets, to allow the semantic
>model to evolve independent of the software.

The following are some excerpts from the (draft) minutes of the W3C maths
 at MIT on March 10-11.

The Wolfram Proposal
Neil Soiffer and Bruce Smith then presented some highlights of the
"Wolfram Proposal"  (WP) first floated in May 1996, and revised on a
couple of occasions thereafter.  It is rather comprehensive, and is
accompanied by some prototype software --- an operator precedence
parser (OPP) to support a suggested input style for math, implemented
in Mathematica and now being ported to Java.  In addition a first
attempt of an interface from such a parser to Robert Miner's WebEQ as
a display engine has been shown.

Neil Soiffer offered a graphical representation  which showed a
central blob for an XML representation of the math's structure (after
all this seems to be the way the Web is going), arrows out to the
various renderings desired (Display, Audio, OpenMath, specific
Computer Algebra Systems), and input mediated by an OPP filter from
the user input source.

The WP XML representation is based on an expression structure with
structure schema that correspond to visual display schema as far as
possible.  The expression structure is augmented with schemas [schemata] for
encoding type information about leaf nodes, and several purely logical
structure schemas.


The INRIA Proposal
The INRIA proposal was authored by Stephen Buswell, Stéphane Dalmas,
Stan Devitt, Angel Diaz, Marc Gaetano, Robert Sutor, Terry van Belle,
and Stephen Watt, and released as a TeX document Thursday 6, 1997.  It
should more properly be called "An HTML-Native Math
proposal" though IP had been adopted as a shorthand by the

All authors present helped in the exposition of the main points of
their proposal. It results from an international and diverse
collaboration.  The basis is intended to be securely within
international standards like SGML.  Here though there is an emphasis
on the semantic aspects.  The IP proposes the fully SGML form of
OpenMath as a syntax for expressing the semantics.  For the expression
of the formulas the IP envisages an XML compliant mark-up language.

The proposal's parts may be seen as
Content Tags -- such as for cos and sin
 - a question being for how much of HTML
Presentation tags
 - to be about like those of Neil
Scope and operators
 - to be done roughly suggested in the IP
OpenMath elements
 - Semantics is assumed to be specified in this form, rather than OpenMath
being one option among several for this. OpenMath has both SGML and
Lisp-like forms.
ISO Entity sets
 - of which there are about 20 published to be collected.

For input the IP expects the user to type the full XML expression
syntax, with the argument that it is simple enough for simple formulas
and that the insistence on explicit use of braces for grouping ensures
correct input.


Following these presentations the WG began by setting down points of
consensus. The HTML-Math WG agreed that:

There should be an XML compliant standard for "full-form" expression
for math formulas

Some small amount of pre-processing may be acceptable to achieve
this full form

Pre-processing shall not restrict the expressiveness of the input
and should be "idempotent"

The full form's syntax will be acceptable as input within the tags
which mark math

Some kind of macro facility based on at least template replacement
is foreseen in a final proposal
, but is not part of the WG's first proposal

The presentation tagging will be derived from modification of the
description of a powerful scheme provided by the WP.  A subcommittee
of NS (chair), SW, RM, BS, SDv, SDl and RW will report back by April 1
with a detailed proposal.

There will be some content tagging.  An initial proposal of some
basic content tags  suitable for K-12 use will be returned by the
subcommittee chaired by SB and including AD, PI, SW, SDv and BS by April 1


(end of excerpts from the minutes)

>"we might want to talk to this HTML-Math group"

This seems a good idea. The co-chairs of the group are
Robert Miner (rminer@geom.umn.edu) and Patrick Ion (ion@math.ams.org).


Stephen Buswell
Stilo Technology