Henry Spencer wrote on 2000-08-09 20:24 UTC:
> Indeed so; such a notation would have to be extensible... but then, any
> good descriptive markup language already is. Part of the task of getting
> a paper formatted (printed, etc.) would be to review the specific concepts
> used and assign formatting conventions to any that are sufficiently rare
> not to have defaults. A suggested set of such conventions might even be
> part of the usual markup, *accompanying* (not interspersed within!) the
> actual text of the paper.
This has been tried and failed several times. The SGML community has
gained by now quite some experience with proposals for abstract mark-up
for mathematics, and they all turned out to be *way* too complicated and
at the same time *far* too restrictive to be of any practical use. If
you are interested, I can dig out a load of papers on that topic from
the early 1990s. Adding abstract markup to mathematical papers easily
quadruples the amount of work for the author and editor, and considering
that this work is difficult to proof-read and not accessible for anyone
using the printed paper (which is still considered to be the main output
of any publishing system), in practice nobody will be willing to invest
that time. The only potentially practical reason that I have ever heard
for doing abstract markup for mathematical formulae is to allow for
automatic cut&paste to computer algebra software (where the difference
between a superscript index and a superscript exponent does matter for
machine interpretability). Apart from that, what mathematicians want is
direct low-level control over the glyphs and layout in their formulas,
just like they are used to have it with chalk and pencil.
I am rather surprised about your views of mathematical typesetting,
because they sound to me like the state-of-the-hope around 6-10 years
ago (dig out your archive tapes of comp.text.sgml discussions from
then). I thought it is by now fairly widely recognized that the strict
separation between semantics and layout is far from feasible for the
extremely dense structure of mathematical notation (except if you
restrict yourself to very small domains such as high-school calculus for
specific applications such as computer-assisted learning, etc.).
Both MathML and ISO's math DTD follow an approach not too far from TeX,
LaTeX, EQN, etc. which all specify the typography ("superscript") but
not the semantics ("exponentiation") of mathematical notation. Anything
else would require an unjustifiable amount of user training.
Markus
--
Markus G. Kuhn, Computer Laboratory, University of Cambridge, UK
Email: mkuhn at acm.org, WWW: <http://www.cl.cam.ac.uk/~mgk25/>
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