On Sat, Dec 12, 1998 at 07:00:48PM -0500, William F. Hammond wrote:

> : As I understand it, *ML _parses_ (or tries to parse) maths,
>
> No.

Well, what follows in your posting
seems to me precisely an attempt to define a formal language for
(ie to parse) mathematics.

> I would suggest that in a latex-like document preamble one declare,
> with something like "\mathsym" the symbols A, B, C, D either as having
> a type such as "vertex" or else having a type such as "element of an
> additive group".

In other words, you are trying to parse mathematics.

I don't know what "vertex" means,
but there are many meanings that A B could have,
eg A(B) [the value of the function A at B]
or (A)B [the value of the function B at A]
or the composition of two functions B and A
or the composition of A and B,
etc etc

Are you going to require mathematicians to write f(x) [ie with brackets]?
Can they write (x)f if they prefer?

> : The question is, then:
> : is it possible to parse mathematics,
> : and if so, is it wise to try?
>
> Don't readers do it?  You think that it's based on "visual
> intelligence"?

I don't know what "visual intelligence" is.
Yes, a reader parses the mathematical document he is reading,
though the word "parse" must be given a wider meaning than normal,
to include eg graphical arguments which may be perfectly valid,
as eg in categorical diagrams.

However, the point is that the formal system used
depends on the document, and on the subject matter.
There is no "mathematical language" and never will be in my opinion.

> : [It may be impossible,
> : because it may be that mathematicians
> : would refuse to be bound by any particular formal system put forward.]
>
> Ay, there's the rub -- certainly for many.  Note in particular that
> mathematical authors have incentive to provide MathML only if they
> perceive that the *most helpless* of their readers who have browsers
> also have MathML rendering.

It seems to me much easier to design a browser that understands LaTeX,
or DVI, or PDF, than to persuade mathematicians to write in MathML.
Surely the computer should be the slave, not the master.

--
Timothy Murphy
e-mail: [log in to unmask]
tel: +353-1-2842366
s-mail: School of Mathematics, Trinity College, Dublin 2, Ireland