12083 / MINSE and Wolfram

I've unfortunately gotten a little hung up on writing some
Omnimark code for parsing AMS TeX data in preparation for
filtering this to HTML-Math.  Here are a couple of smallish
points in response to Bruce's recent postings.


Regarding ISO 12083 math:

> Unfortunately I don't know 12083, and from what I'd heard, I thought
> its layout was not based on a general "nested expression structure"
> like we're discussing. Can someone who knows it well enough comment
> on this?

I'll post on the AMS server the last copies of the DTD I received a
few years ago.  I can also look for an official posting somewhere, but
when I inquired of Eric van Herwijnen last year about this, I think he
told me I had the latest.  Meanwhile, just note that the parameter entities
declared at the top of the DTD:

<!--  Parameter entities describing the possible contents of formulas.     -->
<!ENTITY % p.trans "bold|italic|sansser|typewrit|smallcap|roman"
                   -- character transformations                            -->
<!ENTITY % m.math "fraction|subform|sup|inf|top|bottom|middle|fence|mark|
   |#PCDATA" -- mathematical formula elements                              -->

give an idea of the "expression" primitives.  These can be nested
(SGML is good as such things), so I would have said that the DTD
enables adequate "nested expression structure".  The DTD is adequate
to express AMS math data, and I think also Elsevier math data (which
is much more extensive than that at AMS).

Regarding MINSE and the Wolfram Proposal:

> Also I should say that I've finally found time to read most of Ping's
> web pages on MINSE, so now I can understand his comparisons with it. I
> have to say that it is an impressive and well-described system. It does
> differ in several important ways from our (Wolfram's) proposal, which
> I'll address mainly when I reply to the letters concerning those
> points; for now I should mention the most important distinction, which
> is that his system is primarily "semantic" and ours is "notational",
> which means (among other things) that the information our systems are
> each trying to represent is quite different.

Although, my feeling is that the difference between the Wolfram
proposal and MINSE is more one of attitude than enforced difference.
This is why I briefly compared MINSE with TeX on the matter of "being
good", because in both systems one has the opportunity of writing
"flat" notation or author-enhanced notation (with macros in TeX,
compounds in MINSE).  This said, I can still agree that

> the information our systems are each trying to represent is quite
> different

may be true when the author of a MINSE document chooses to include
many compounds.

But now this leads to the idea of macros and template-matching as they
will be added to the Wolfram proposal.  I believe macros will be
expanded in the process of creating the expression tree, whereas
template matching will be done on the expression tree.  Does this mean
that the "good" author who distinguishes notations for his/her own
benefit via macros will not be able to use the enhanced notation for
translation purposes?  I'm assuming "yes" at the moment because I'm
thinking that the macros don't appear in the expression tree, but
perhaps I have it wrong.  The MINSE compounds can be thought of as
parsing aids rather than true semantics.  One could claim that MINSE
is still "notational", but it has an enhancement feature (enhancements
to the expression tree) which the Wolfram proposal doesn't have.  No?