Re: semantics

Bob writes:

> I think people sometimes overestimate just how much semantic
> information is necessary. Whatever its commercial success, AXIOM
> has at least proved that type information can go a long way in 
> converting a general expression into a fully analyzed one. So stating
> that a polynomial expression has a particular type of coefficients
> will significantly aid those apps that can handle a bit of semantics.

I'll interpret your remarks in this paragraph and from the phone
conversation Monday to mean that you expect, at least to begin with,
these helpful type-theoretic aids to be generated by software which
handles the expression before presentation and not so much by author
data entry.  So for the paragraphs of an AMS journal article I posted
a few weeks ago, one might expect no semantical aids, but for a
calculus text done with Scientific Word one might expect many.

With both the Wolfram and MINSE proposals I have been concerned about
the need to name objects which one doesn't quite want to name.  We
have seen this in MINSE with the .idx operators, and I'm thinking that
the WP might require a similar thing insofar as designation of
type-theoretic information might have to be done via macros.  Neil and
Steve have mentioned use of contructs similar to Mathematica's
InterpretationBox.  Is is easy to describe how that will fit into
the Wolfram Proposal?  I'm imagining that that is what I want in terms
of on-the-fly semantics which doesn't require new notational vocabulary
for designation of objects.  The situations I'm contrasting are:

1. i .idx j  where .idx is an indexer of i:N->N
2. i _&Interpretation{lambda y(x_y):N->N} j

The first uses new vocabulary, the second doesn't.