From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/174 Path: news.gmane.org!not-for-mail From: Robin Cockett Newsgroups: gmane.science.mathematics.categories Subject: Re: Functions in programming Date: Tue, 17 Mar 2009 17:06:38 -0600 Message-ID: Reply-To: Robin Cockett NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1237382522 4419 80.91.229.12 (18 Mar 2009 13:22:02 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 18 Mar 2009 13:22:02 +0000 (UTC) To: categories@mta.ca Original-X-From: categories@mta.ca Wed Mar 18 14:23:19 2009 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from mailserv.mta.ca ([138.73.1.1]) by lo.gmane.org with esmtp (Exim 4.50) id 1LjvjH-0006pU-LT for gsmc-categories@m.gmane.org; Wed, 18 Mar 2009 14:22:43 +0100 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1Ljv4y-0004Lh-Rs for categories-list@mta.ca; Wed, 18 Mar 2009 09:41:04 -0300 Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:174 Archived-At: Vaughan Pratt wrote: > The categories mailing list is a good one for this sort of discussion ... So here is some (gentle) push-back for Vaughan ... BTW thank you everyone for pointing out that /everything/ I said was wrong/right! There really are underlying serious pedagogical and practical issue behind this ... typified by the comment. > Thorsten Altenkirch wrote: > > There really shouldn't be a difference between the functions in > > Mathematics and in Computer Science, especially functional programming. > The fact that nothing is quite what it "should be" in what has become the/a leading functional language is bothersome on the one hand for students struggling to develop a (unified) mathematical view and, simultaneously exciting for researchers who now have to find out which (!?!@!) category one is actually working in ... the fact that the answer is not an entirely simple (I do like Vaughan's "nuanced"!) is cause simultaneously for (pedagogical) concern and (researcher) delight. This reflects a general tension between semantics and implementation and the tussle over which is to be the cart and which is to be the horse. As it happens (I recall) one of the motivations behind Haskell was to produce a /lazy/ functional language and so a significant focus was actually on the implementation side ... perhaps at some semantical cost? Vaughan comments: > There should be differences within Mathematics and within Computer > Science, and therefore between them. I confess -- in this context -- what springs (uncalled) to mind is the (modified) comment of Chairman Mao: Computer Science is the continuation of Mathematics by other means! ... and sometimes the balance between what /should/ be done and what /can/ be done is pushed too far. At what stage this becomes a "bug" -- as Thorsten bluntly puts it -- definitely should be up for debate. And there is no doubt in my mind that in making this judgment the clarity of the underlying (categorical) semantics adds an important perspective .... and even should be prescriptive. Semantics does have some "real" effects: the semantics that a programmer has in mind and what is actually implemented by a language/API can be rather different ... and this can become particularly subtle as languages become more abstract (and peculiar) and are built on top of each other. Through these gaps can lie some very unexpected behaviors! Vaughan comments: > 2. One should not assume that mathematics has the answer to every > practical problem. Oft quoted John Arbuthnot commented (some time ago!): "There are very few things which we know, which are not capable of being reduced to a Mathematical Reasoning; and when they cannot it's a sign our knowledge of them is very small and confused; and when a Mathematical Reasoning can be had it's as great a folly to make use of any other, as to grope for a thing in the dark, when you have a Candle standing by you." It really is hard to say more :-) ... but maybe "candle" should be replaced "compact florescent light bulb"? -robin