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Re: semantical annotations

To: w3cmatherb@w3.org

Subject: Re: semantical annotations

From: "Robert S. Sutor"<SUTOR@watson.ibm.com>

Date: Sun, 8 Sep 1996 14:40:21 0400

From w3cmatherbrequest@www10.w3.org Sun Sep 8 15: 00:56 1996

MessageID: <8525639F:006541B5.00@watngi05.watson.ibm.com>

XLotusFromDomain: IBM RESEARCH
First, there was a typo in the polynomial in my last example. It
should be X^^3+2*X^^2+2, not X^^^^3+2*X^^^^3+2, in Axiom syntax (with
a corrected exponent).
Within a given type, we would expect all nontype objects to be
represented in HTML math. If you look closely, you'll see that a
type name is really just a function application, where other types
can be arguments. So specifying a type is no more difficult than
giving any other application form. The problem then is just one
of where one puts it as annotation. To continue with the Axiom
example, you would say
x @ T
to indicate that the expression x should be interpreted as having
type T. This is no more difficult that parsing any other infix function
application. Some other syntax in HTML math is acceptable, of course.
[I don't remember if '@' is used.]
If we had something similar, nontypebased systems would be free
to disregard the type and process the expression x. (This could cause
semantic errors, but no fewer than omitting all type information.)
Note that I am not recommending a universal definition of all important
types. I'm just talking syntax for allowing consenting apps and browsers
to transmit the information. Just as not all specialized CAS can handle
finite field extensions, not all will be able to handle types. However I
would expect that most of the big name CAS can agree what
ArbitraryPrecisionInteger is if they see it.
Bob