Re: User definable operators

Charles Fiterman <cef@geodesic.com>:
>In math it's name and conquer so people need to build their own symbols
>easily and use them easily.


As an APL programmer, I have some comments on this specific "symbolistic"
view of operators.


* APL was devised as a substitute for standard mathematical notation.
    "MN" has quite a bunch of inconsistencies and quirks. APL offers
    a more systematic way to write mathmatics. Unlike Charles Fiterman
    suggested, the power of APL comes often from _dropping_ special
    symbols like large sigma and deriving their functionality from more
    fundamental concepts (addition and "reduction": "+/"). Very often, this
    leads to generalized notations: Where MN stops when it runs out of
    special symbols Large Sigma and Large Pi, APL really takes off after
    +/ and */ because the "reduction" is available (which is what Heaviside
    would have called an "operator").


* APL is, uhm, "famous" for its graphical character set.
    In the end, it died because such peculiar notations didn't
    communicate well enough with new people.


* One of the recent APL dialects, J, is straight ASCII. J-ers usually
    don't miss the distinct APL symbol kit after getting used to something that
    might look like line noise from time to time. It's certainly a small
    price for being able mail a program around which does not work in
    terms of just Silly Scalars.


Definite classic references on APL vs. Mathematical Notation are contained
in IBM Systems Journal v30 n4 (1990 or 91).


Martin Neitzel
--

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