W3C home > Mailing lists > Public > www-math@w3.org > December 2000

a content question/suggestion

From: Andreas Strotmann <strotman@cs.fsu.edu>
Date: Mon, 18 Dec 2000 12:15:25 -0500 (EST)
To: David Carlisle <davidc@nag.co.uk>
Cc: www-math@w3.org
Message-ID: <Pine.GSO.4.10.10012181156520.7473-100000@xi.cs.fsu.edu>

first of all: good job, as always!

I noticed that you took up my suggestion andnow allow the qualifiers to
appear with any "head" operator. Good!

There's a problem though, that I believe I mentioned when I originally
proposed this change.  You probably discussed it in the group, so I'd like
to know what the results of this discussion were.

The stated goal of content-MathML is to provide the basis of machine-
interpretable math.  I have been arguing that in order for that goal to be
met, it is necessary to define exactly what the behaviour and scope of
bound variables is.  While the current definition implicitly states some
of this, by using the bvar qualifier consistently throughout, there is a
general statement in the spec that says that the qualifiers' meanings
depend on the "head" of the expression they'reappearing in (sorry for
using OpenMath terminology here).

In the case of bvar and its associates (domainofdefinition(?), condition)
that are used in a most consistent manner throughout, it would be a grave
mistake not to exactly specify that *regardless* of the first child of the
enclosing <apply>, these qualifiers have some basic meanings that stay

 - bvar introduces a bound variable
 - that variable's scope is the surrounding apply
 - except for <interval> qualifiers as immediate children of the 
   surrounding apply

and so on.  Without this kind of a definition, you cannot meat the goal,
as should be clear to everyone on this list (especially those who've been
following the OpenMath discussion;-).  In particular, the third item in
the above list is *certain* to be treated differently in different parsers
*unless* there is a clear definition, with potentially catastrophic

I'm willing to come up with a first draft of a corresponding few
paragraphs over thenext few days.

 -  Andreas

"The act of defending any of the cardinal virtues has today 
all the exhilaration of a vice." -
G.K.Chesterton: A Defense of Humilities, The Defendant, 1901 
Received on Monday, 18 December 2000 12:16:02 UTC

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