on math-specific issues (repost)

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---------------------------------------------------------------- 'over
[020] Nico Poppelier writes:
> I've been asked by people on the
> LaTeX3 development team to express a strong preference for the
> former, and a strong dislike for \over!

I also dislike "over", but for the reason that it directly suggests
positional rendering.  "over" should be the name of a rendering
schemum, not a semantic compound.  The MINSE mathematics context will
use "frac" for fractions (e.g. 3/4 or 'frac(3,4)) and "quot" for
quotients (e.g. (x^2+y+3)/(y-5) or 'quot(x^2+y+3,y-5)).

------------------------------------------------------------ integrals
[028] Ron Whitney writes:
> Dave proposes something on the order of
>   integral from ... to ... of ... \d x
> for an "ordinary" integral.

While this works, i have a little trouble with the notion that
"integral" is just a symbol which gets "operated on" by "from"
and "to".  Integration is an operation in itself; the limits are
attributes to the operation, and the expression is the main
argument of the operation.  I do agree that it is the easiest
to read of the representations i have seen so far, but i think
it's important to separate the namespace of operations and
identifiers.  I've seen "from" and "to" used as identifiers.

[031] Patrick Ion writes:
> Int[l,u,Int[l1,u1,f(x,y), dx],dy]

This notation makes more sense to me.  When doing it this way,
though, there should be no need to write "dx" and "dy", since
the variable of integration is just "x" or "y".

----------------------------------------------- meaning of a subscript
Subscripts have two distinct purposes that i know.

So far i haven't seen any mention of this distinction on the list,
but subscripts are sometimes used as numerical indices -- where they
could themselves be expressions -- and sometimes used as qualifiers,
where their purpose is just to distinguish identifiers.  We need both
to convey the expression accurately.

The MINSE math context makes this distinction with two separate
semantic compounds, 'index and 'qual.  When a "prime" is written,
even though it is a superscript, it isn't an exponent -- it's really
a qualifier.  The same goes for some uses of the asterisk.

------------------------------------------------ labelling expressions
So far i haven't seen much talk of labelling.

We're also going to need a compound which attaches a label to part
of an expression (that might get rendered, for instance, like the
\overbrace or \underbrace from TeX).

We might use a similar compound to produce a compacted expression
with subexpressions shown only as their labels until the user
requests that they be expanded (like AsTeR's subexpression
substitution, or like the alternating link macro added by IBM's

-------------------------------------------------- invisible operators
[089] Bruce Smith writes:
> The rule for deciding which one is inserted is precisely this: an
> invisible function application operator is inserted if and only if
> its left operand would be an identifier or a scripted identifier,
> and the token to its right is a left bracket operator (such as a
> left parentheses).

Correct me if i am wrong, but simply checking for identifiers doesn't
seem to be enough.  I tried such a scheme too, and it worked fine
until i realized that this would disallow the use of operations on
functions, such as in the case of a function composition operator
(f 'compose g)(x) or functions of functions, as in f(g)(x).  

So in MINSE, this problem is solved by requiring an explicit
multiplication operator.  This also alleviates the ambiguity between
multiple-character operands and multiplication of single-character
operands.  Function application is parsed by looking for an element
before a parenthesized element (in effect, treating the
left-parenthesis as though it were an infix operator).

----------------------------------------------------------- references

[020] http://lists.w3.org/Archives/Public/w3c-math-erb/msg00020.html
[028] http://lists.w3.org/Archives/Public/w3c-math-erb/msg00028.html
[031] http://lists.w3.org/Archives/Public/w3c-math-erb/msg00031.html
[089] http://lists.w3.org/Archives/Public/w3c-math-erb/msg00089.html