From mboxrd@z Thu Jan 1 00:00:00 1970 X-Spam-Checker-Version: SpamAssassin 3.4.4 (2020-01-24) on polar.synack.me X-Spam-Level: X-Spam-Status: No, score=-1.3 required=5.0 tests=BAYES_00,INVALID_MSGID autolearn=no autolearn_force=no version=3.4.4 X-Google-Language: ENGLISH,ASCII-7-bit X-Google-Thread: fac41,b87849933931bc93 X-Google-Attributes: gidfac41,public X-Google-Thread: 109fba,b87849933931bc93 X-Google-Attributes: gid109fba,public X-Google-Thread: 103376,b87849933931bc93 X-Google-Attributes: gid103376,public X-Google-Thread: 1108a1,b87849933931bc93 X-Google-Attributes: gid1108a1,public X-Google-Thread: 114809,b87849933931bc93 X-Google-Attributes: gid114809,public From: jsa@alexandria (Jon S Anthony) Subject: Re: OO, C++, and something much better! Date: 1997/02/17 Message-ID: #1/1 X-Deja-AN: 219479750 Sender: news@organon.com (news) References: <5de62l$f13$1@goanna.cs.rmit.edu.au> Organization: Organon Motives, Inc. Newsgroups: comp.lang.c++,comp.lang.smalltalk,comp.lang.eiffel,comp.lang.ada,comp.object Date: 1997-02-17T00:00:00+00:00 List-Id: In article piercarl@sabi.demon.co.uk (Piercarlo Grandi) writes: > >>> "jsa" == Jon S Anthony writes: > > jsa> Just to be clear: "+" does not stand for some _particular_ function > jsa> in mathematics. > > But it does, and sorry if I used the word "particular" improperly; I > meant by it something "any definite"; My point was simply that there is not one particular interpretation for "+" in mathematics. This is actually obvious and I'm sure you'd agree. > jsa> It varies on context. Specifically, a) what the formal system is > jsa> and b) what interpretation is being given to that system. > > It was also perhaps not clear that by "maths" I meant something like > ``ordinary maths'', a not well defined but hopefully intuitively And? Presumably, by "ordinary maths" here you really mean arithmetic. That is a precisely and rigorously defined system. > perceivable notion; for most any given procedure indicated by "+" > computes *some* mathematical function, even if not necessarily the one > indicated by "+" in most ``ordinary maths'' Presumably you simply mean here that "computer arithmetic" or the specification of arithmetic operations in a programming language definition is not the same as standard arithmetic (even though in many practical cases you can ignore the differences). Well, sure. > (one favourite example is that "+" between 'unsigned' operands in > ``C'' computes the function ``addition module 2^N'' rather than > addition on nonnegative numbers). Why is congruential arithmetic not ordinary? Note that this too has a completely precise and rigorous definition and theory. > by "+" in some branch of maths would tend to be few; one major factor is > that procedures usually compute functions over finite domains/codomains, > which is almost never the case in [``ordinary''] maths, and even in > ``discrete'' maths. What makes you say that?? Certainly any congruence system has this exact aspect. Large chunks of combinatorics deal in finite systems. What about finite groups? And whose to say that in "day to day arithmetic" you aren't dealing with a congruence system whose modulus just happens to be 10^50 or something? > jsa> There are cases where the two will denote identical results. > > Well, this is actually quite impossible as literally written :-); > the results of any particular "+" operation are in the domain of > implementation entities, those of any articular "+" function are in > the domain of mathematical entities. Yes, I see the "smiley", but I'm not sure this distinction is true or of any use. It would seem to imply that any set of "squiggles" on a blackboard or piece of paper are "implementation entities" and have not much to do with the mathematical entities they represent. I don't think so... > What you probably wanted to say is that it can happen that the function > computed by some particular "+" operation is exactly the same as that > meant by some "+" function in ``ordinary'' maths. What I meant was that you can't distinguish the two in any meaningful way even if they are "in some sense different". > jsa> Forget about the notation. That's irrelvant. The real problem is > jsa> that _often_ (not always) the semantics are all wrong in those cases > jsa> where they are "supposed to be the same or at least similar". > > Well, while what I have written expresses a similar sentiment, I would > be so radical in saying that notation is so irrelevant. > > Actually it is irrelevant, but it is not _unimportant_, for programs are > about communicating in textual form, and communicating by suggesting [...etc....] Yeah. OK, I can agree with this. > constantly amazed by the fondness for terminological confusions that > many people display; the major example is "OO", which many people take > literally as being about objects, with dire consequences. Well, here we definitely agree. > Misnomers such as "OO" and notational devices *are* irrelevant, to those > that see them as mere pointers to the concepts they label; but > unfortunately nominalism is rampant. :-( but true... /Jon -- Jon Anthony Organon Motives, Inc. Belmont, MA 02178 617.484.3383 jsa@organon.com