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From: ok@goanna.cs.rmit.edu.au (Richard A. O'Keefe)
Subject: Re: OO, C++, and something much better!
Date: 1997/02/18
Message-ID: <5eb5jt$kl7$1@goanna.cs.rmit.edu.au>#1/1
X-Deja-AN: 219926959
References: <JSA.97Jan16141937@alexandria>
 <5de62l$f13$1@goanna.cs.rmit.edu.au> 	<32FB8B51.1759@concentric.net>
 <vwjsp316ai1.fsf@saturn.dcs.aber.ac.uk> 	<3302DB3E.F70@concentric.net>
 <yf3ybcsm5ce.fsf@sabi.demon.co.uk> 	<33054E63.C2A@concentric.net>
 <JSA.97Feb16135327@alexandria>
Organization: Comp Sci, RMIT, Melbourne, Australia
Newsgroups: 
 comp.lang.c++,comp.lang.smalltalk,comp.lang.eiffel,comp.lang.ada,comp.object
NNTP-Posting-User: ok
Date: 1997-02-18T00:00:00+00:00
List-Id: <comp.lang.ada>


In article <33054E63.C2A@concentric.net> Alan Lovejoy <alovejoy@concentric.net> writes:
> Is there a useful semantic distinction between "function" and "operator" 
> in math?  If so, what is it?

jsa@alexandria (Jon S Anthony) writes:
>Generally speaking, the terms "operator" and "operation" are used to
>refer to functions which map an "n-order" set to the "base" or
>"1-order" set.

Ahem.  This is a case where APL terminology is actually quite
close to mathematics.  In APL, an operator is a higher-order operation
that takes a function as an argument and delivers another function.

In mathematics, one talks about "differential operators" and "integral
operators" and they are something that takes a function and delivers
a related function (e.g. the derivative).  Anyone who has done any
signal processing will remember the "E" (time lag) operator and the
"Delta" (difference) operator.

Here's the abstract of a subject at another university (so as not to
advertise):

	Math XXXX: Functional Analysis
	Linear metric and topological spaces, duality, weak topology,
	spaces of functions, generalised derivatives and distributions,
	Sobolev spaces, linear operators, compact operators, elements
	of spectral theory, and operator calculus.

This use of the word "operator" 
 - is pretty much standard in mathematics
 - refers to a *semantic* property rather than a *syntactic* one
 - refers to a property that "+" does not have in any major programming
   language.

-- 
limits on the scope of cooperation are often due to the inability
to recognise the identity or the acts of the other playes.  --R.Axelrod
Richard A. O'Keefe; http://www.cs.rmit.edu.au/%7Eok; RMIT Comp.Sci.