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From: jsa@alexandria (Jon S Anthony)
Subject: Re: OO, C++, and something much better!
Date: 1997/02/22
Message-ID: <JSA.97Feb21195346@alexandria>#1/1
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Distribution: world
References: <JSA.97Jan16141937@alexandria>
 <5de62l$f13$1@goanna.cs.rmit.edu.au>
Organization: PSI Public Usenet Link
Newsgroups: 
 comp.lang.c++,comp.lang.smalltalk,comp.lang.eiffel,comp.lang.ada,comp.object
Date: 1997-02-22T00:00:00+00:00
List-Id: <comp.lang.ada>


In article <5eb5jt$kl7$1@goanna.cs.rmit.edu.au> ok@goanna.cs.rmit.edu.au (Richard A. O'Keefe) writes:

> 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.

Yup, that fits exactly.

> 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).

Yes, exactly.  A very standard example would be the usual case of

 Cf = set of continuous functions on R

 ': Cf -> Cf, where f' is the derivative of f


> 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.

Absolutely spot on accurate.

/Jon
-- 
Jon Anthony
Organon Motives, Inc.
Belmont, MA 02178
617.484.3383
jsa@organon.com