Path: utzoo!utgpu!water!watmath!clyde!rutgers!rochester!PT.CS.CMU.EDU!H.GP.CS.CMU.EDU!cef
From: cef@H.GP.CS.CMU.EDU (Charles Fineman)
Newsgroups: comp.lang.misc
Subject: Re: History of := (was: == vs =)
Summary: I don't believe this!!!
Message-ID: <715@PT.CS.CMU.EDU>
Date: 25 Jan 88 22:39:06 GMT
References: <2337@haddock.ISC.COM> <51300003@uxe.cso.uiuc.edu>
Sender: netnews@PT.CS.CMU.EDU
Organization: Carnegie-Mellon University, CS/RI
Lines: 39

I can not believe that someone has not quelled this discussion yet! 
Perhaps the people who know better are to busy guffoughing (sp?) over
it. The terminology "a := b" means that a is "defined to be" b. For 
example, let a be defined to b the mapping from a number to the of numbers
that are relatively prime to that number can be writting as (subistituting
the proper notation where appropriate):

	a(x) := {y <in> Z+ | lcm(x,y)=1}

In general, the use of ":=" in programming languages is associated with
(if you will) first order objects like numbers and such. In mathematics,
":=" is used in *all* levels of abstraction (read n-order objects). 

The only reason that ":=" was used instead of "=" is because of an 
ambiguity in ALGOL (the same ambiguity exists in C BTW). Since it is
legal to have an assigment as a term in an expression, there had to
be a way to distinguish between equality and assignment. This is the
same reason why C uses "==" for equality.


Anyways, I have a *real* hard time believing that anyone with a formal
CS education (even more so for someone with a *MATH* education) has never
seen this notation before. It's been at the height of fasion for the least 
the past 200 years. I got my B.S. degree in math of at CMU and was unundated
with ":=" daily. Anybody out there who got a formal education in CS or Math
and did not learn this, should make sure that their almamada realizes that
they are not teaching the students all they should be. I realize that this
may be a little drastic for one little bit of notation, but notation is
alphabet of mathematics. How can you expect the graduates of such a school
to be useful in a world where they never learned the language.


This is my first flame in months, it just that something like this
bothers me (I was brought up to be a stickler for consistent notation).
Its like a grammer teacher teaching your kid street-talk. 

	Charles Fineman
	Carnegie-Mellon University
	cef@h.cs.cmu.edu (via seismo)