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RE: Goals verses syntax in MathML

From: Stan Devitt <jsdevitt@maplesoft.com>
Date: Thu, 7 May 1998 09:59:37 -0400
Message-ID: <DFBA4AED6924D111959A0060975EA7B4511A64@romulus.maplesoft.on.ca>
To: "'mathas@maths.usyd.edu.au'" <mathas@maths.usyd.edu.au>, www-math@w3.org, mailing@maths.usyd.edu.au, list@maths.usyd.edu.au
Dear Andrew:

In your note "Goals verses syntax in MathML"
you raise several points which I understand roughly as:

	1.  A desire for simple hand-editable formulae
	2.  Concern over the size of resuling encoding.
		3.  A desire to get by with something closer to
	a simple extension to HTML including
	font changes such as triggered by <EM>, perhaps 
	introducing shortcuts such as ^ for superscripts, etc.

Let me attempt to address each of these.  My remarks
are from my personal point of view and do not necessarily
represent the position of the working group.  Other members of the group
will no doubt speak up when necessary.

(1) Initial attempts in the MathML working group to deal with an input
syntax seriously considered all the issues you raise.  Some of the
alternatives considered and rejected for (1) included:

	- TeX / LaTeX
	- ISO-12083 and extensions
	- simple linearizations of formulae such as 
		(x + y)^2 / z;
	- Programming language syntaxes such as for FORTAN, C, 
		Maple or Mathematica
	- Inventing a new "simple input language."
	- internal formats of existing Math Editors.

To be be acceptable,  (remember we were seeking to provide the
infrastructure for the next generation of publishing tools) a solution
needed to support professional quality publication (as rich as TeX) and
archival of machine readable mathematical data for purposes of automatic
searching and computation.  The latter was based on the mathematical
meaning of the expressions, not their appearance. 

Anything less than the above, and effectively we are reduced to using
pictures of formulae and that we already have.  The pictures are not
really editable.  Nor is it possible to 
reliably deduce semantics.

None of the considered syntaxes came even close.  Programming input
languages had one narrow semantic interpretation and were generally weak
on presentation.  Any presentation encoding less than TeX did not
provide the kind of professional quality presentation needed by
publishers.  At the same time, TeX was fully presentation based and did
not provide any mechanism for capturing semantics. For example did
$D^2\,y$ represent a double application of a differential operator to
the function y or was it a simple monomial?  

As an interim position on simple input syntax, perhaps
the only position consistent with ensuring that adequate information
could actually archived on Web pages, we have been translating to and
from MathML from many of the above formats.  Each of the companies
involved has found this fairly easy to do and it has meant that everyone
can work with the simple input syntaxes and tools they are already
comfortable with.  

Developing yet another syntax for mathematical expressions
is never to be taken lightly, and that is why we are moving
with extreme caution.  Should it emphasise semantics or appearance?
Should it be based on syntax familiar to a large number of users or
should it be new?  If the author wrote someting in a particular style,
did they do so to achieve a certain visual effect, or did they want to
specify particular semantics?  Can we provide the infrastructure
for the author to "say what they mean?" (They can still choose not to.)

It seems clear that no one "simple" input syntax meets all needs, and
even though any particular user may not be interested in all aspects of
math representation at this time, growth of electronic publishing cannot
occur without
the infrastructure, and that very growth may have the same user
clamoring for different information just a few months from now.  

(2)  On the issue of band width, while the notation
is verbose, it also compresses extremely well.  This
issue of transmission is common to a wide range of 
emerging applications including such things as CML,
a chemical markup language, and XML in general.  It
was a conscious decision to focus on a proper specification
and factor out this issue.

(3) During the development of MathML we looked long and
hard at simple extensions to HTML.  In particular, interim
reports based in part on ISO-12083 and the use of
SGML conventions to provide short-cuts were developed
and rejected.

With regard to compatibility with HTML, etc. there is 
currently an enormous amount of activity in W3C
dealing with the integration of XML (of which MathML is an sample
application) into the HTML environment.  This
includes work on Cascading Style Sheets which
have enormous potential as a mechanism for setting
default attribute values (fonts?) etc. in the manner
you have proposed.  The role of the style sheet mechanism must be
clarified but it is potentially ideal for setting (or overriding)
default presentation and semantic information.

I hope my explanation helps, and by all means feel free to ask for
further clarification.

Stan Devitt, Ph.D.
Senior Math developer
Waterloo Maple Inc.

> -----Original Message-----
> From:	mathas@maths.usyd.edu.au [SMTP:mathas@maths.usyd.edu.au]
> Sent:	Wednesday, May 06, 1998 11:57 PM
> To:	www-math@w3.org; mailing@maths.usyd.edu.au;
> list@maths.usyd.edu.au
> Subject:	Goals verses syntax in MathML
> Dear All:
> I have just been reading about the proposed MathML solution to
> displaying mathematics on the web. I would like to echo the
> comments of others that the proposed solution is absurdly
> complicated.
	[Stan Devitt]  ... stuff deleted .
Received on Thursday, 7 May 1998 10:03:45 UTC

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