Path: utzoo!mnetor!uunet!mcrware!jejones
From: jejones@mcrware.UUCP (James Jones)
Newsgroups: comp.lang.misc
Subject: Re: History of := (was: == vs =)
Message-ID: <600@mcrware.UUCP>
Date: 28 Jan 88 08:47:49 GMT
References: <2337@haddock.ISC.COM> <51300003@uxe.cso.uiuc.edu> <715@PT.CS.CMU.EDU>
Organization: Microware Systems Corp., Des Moines, Ia.
Lines: 39
Summary: my life as an undergraduate
	 (and how I saw functions defined)

In article <715@PT.CS.CMU.EDU>, cef@H.GP.CS.CMU.EDU (Charles Fineman) writes:
> 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}

I'm not sure whether it reflects on my, uh, alma mater, but I must admit
to never having seen ":=" used this way.  I've seen Russell & Whitehead's

	x = y Df

They used dots rather than parentheses for grouping in *PM*, in the
fashion, I think, of Peano.  Could that be where this whole mess came up?

There was also x =df y for infix purists. :=)  However, what I would almost
always see is either the straight equals sign

"Let a(x) = etc."

or the Bourbakioid

"define a : Z+ -> P(Z+) [there's no script font on most terminals, so I
can't use script capital P for "the power set of..."] by

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

(where some texts, particularly number theoretical ones, would just say
(x, y) for gcd (not lcm; I'm sure the original poster meant gcd)).  Maybe
I didn't hang out with the right crowd. :=)  Let's all just have a good
guffaw, recognize that human factors (other than wear and tear on typing
fingers) had nothing to do with the choice of syntax for C (I scrupulously
avoid the word "design" in this context), and hope that language designers
will do better next time.

	James Jones