From mboxrd@z Thu Jan 1 00:00:00 1970 Return-Path: Received: from concorde.inria.fr (concorde.inria.fr [192.93.2.39]) by yquem.inria.fr (Postfix) with ESMTP id B043BBB9C for ; Wed, 18 Jan 2006 15:22:44 +0100 (CET) Received: from pauillac.inria.fr (pauillac.inria.fr [128.93.11.35]) by concorde.inria.fr (8.13.0/8.13.0) with ESMTP id k0IEMiM5013444 for ; Wed, 18 Jan 2006 15:22:44 +0100 Received: from nez-perce.inria.fr (nez-perce.inria.fr [192.93.2.78]) by pauillac.inria.fr (8.7.6/8.7.3) with ESMTP id PAA17103 for ; Wed, 18 Jan 2006 15:22:43 +0100 (MET) Received: from smtp3.adl2.internode.on.net (smtp3.adl2.internode.on.net [203.16.214.203]) by nez-perce.inria.fr (8.13.0/8.13.0) with ESMTP id k0IEMf0u019079 for ; Wed, 18 Jan 2006 15:22:42 +0100 Received: from rosella (ppp33-253.lns1.syd6.internode.on.net [59.167.33.253]) by smtp3.adl2.internode.on.net (8.13.5/8.13.5) with ESMTP id k0IEMcWx088235; Thu, 19 Jan 2006 00:52:39 +1030 (CST) (envelope-from skaller@users.sourceforge.net) Subject: Re: [Caml-list] Coinductive semantics From: skaller To: Hendrik Tews Cc: caml-list@inria.fr In-Reply-To: References: <43BD6418.4090407@barettadeit.com> <43BE6CAB.2030503@andrej.com> <43C3963D.5030601@tsc.uc3m.es> <1136981974.8962.100.camel@rosella> <43C51C33.2000206@andrej.com> <1137031853.3681.138.camel@rosella> <43C661AF.2080404@andrej.com> <1137102848.3681.268.camel@rosella> <1137163342.3681.533.camel@rosella> Content-Type: text/plain Date: Thu, 19 Jan 2006 01:22:37 +1100 Message-Id: <1137594157.8943.106.camel@rosella> Mime-Version: 1.0 X-Mailer: Evolution 2.4.1 Content-Transfer-Encoding: 7bit X-Miltered: at concorde with ID 43CE4F34.000 by Joe's j-chkmail (http://j-chkmail.ensmp.fr)! X-Miltered: at nez-perce with ID 43CE4F31.000 by Joe's j-chkmail (http://j-chkmail.ensmp.fr)! X-Spam: no; 0.00; caml-list:01 coinductive:01 semantics:01 hendrik:01 tews:01 ocaml:01 contrast:01 wrote:01 sourceforge:01 sourceforge:01 writes:01 theorem:01 theorem:01 simpler:01 precisely:01 X-Spam-Checker-Version: SpamAssassin 3.0.3 (2005-04-27) on yquem.inria.fr X-Spam-Level: X-Spam-Status: No, score=0.0 required=5.0 tests=none autolearn=disabled version=3.0.3 On Wed, 2006-01-18 at 13:58 +0100, Hendrik Tews wrote: > skaller writes: > > > Nobody is interested in final coalgebras in Set^op. > > Why not? This is really the key point of misunderstanding > I think. I'm not disputing your claim, I'm asking why not? > Perhaps they should be? > > Coalgebras in Set^op are for all intents and purposes identical > to algebras in Set. If you want to study them, study them as > algebras in Set. You will see nothing new if you look at these > objects as coalgebras in Set^op. That's what duality means. > > Looking at an object through a mirror you see precisely what you > can see looking at the object itself. Perhaps my analysis is naive. But consider a simpler case of products and sums. They're dual concepts, are they not? In Ocaml we have representations of both, each can be used with reasonable utility -- there is a degree of symmetry, associated with the duality. It feels good! Contrast to C, which has products, but the union construction isn't a sum. And the many other 'popular' languages with this weakness. Sometimes it seems looking in the mirror is good. It's what we want. We don't want something new! > > Go out, read the papers on > > the Co-Birkhoff theorem! > > That's a pretty big ask of someone who isn't a > category theorist isn't it? Most mathematicians > can't understand category theory .. and I'm just > an ordinary programmer :) > > Well, you could try. I guess, that already the introductions > contain enough information for what you are interested in: the > duality of the Birkhoff and the Co-Birkhoff theorem. In any case, > if you don't even try, your speculations about the contents of > these papers remain wild guesses. I often do try.. but seemed like a good idea to read Adameck first: http://www.tac.mta.ca/tac/volumes/14/8/14-08abs.html Still this is quite heavy going for me. Incidentally .. if you look in Wikipedia for 'coalgebra' you may be a bit disappointed. http://en.wikipedia.org/wiki/Coalgebra -- John Skaller Felix, successor to C++: http://felix.sf.net