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 BC684BB81 for ; Fri, 13 Jan 2006 11:39:35 +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 k0DAdZwt020329 for ; Fri, 13 Jan 2006 11:39:35 +0100 Received: from concorde.inria.fr (concorde.inria.fr [192.93.2.39]) by pauillac.inria.fr (8.7.6/8.7.3) with ESMTP id LAA02156 for ; Fri, 13 Jan 2006 11:39:34 +0100 (MET) Received: from haka.fmf.uni-lj.si (haka.fmf.uni-lj.si [193.2.67.18]) by concorde.inria.fr (8.13.0/8.13.0) with ESMTP id k0DAdXkU020324 (version=TLSv1/SSLv3 cipher=AES256-SHA bits=256 verify=NO) for ; Fri, 13 Jan 2006 11:39:34 +0100 Received: from theo.dagstuhl.de ([192.76.146.31] helo=[192.168.11.178]) by haka.fmf.uni-lj.si with esmtpa (Exim 4.50) id 1ExML8-0007Xy-RB; Fri, 13 Jan 2006 11:39:32 +0100 Message-ID: <43C7838F.1090306@andrej.com> Date: Fri, 13 Jan 2006 11:40:15 +0100 From: Andrej Bauer Reply-To: Andrej.Bauer@andrej.com User-Agent: Debian Thunderbird 1.0.7 (X11/20051017) X-Accept-Language: en-us, en MIME-Version: 1.0 To: skaller Cc: caml-list@inria.fr 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> In-Reply-To: <1137102848.3681.268.camel@rosella> Content-Type: text/plain; charset=ISO-8859-2 Content-Transfer-Encoding: 7bit X-SA-Exim-Connect-IP: 192.76.146.31 X-SA-Exim-Mail-From: Andrej.Bauer@andrej.com Subject: Re: [Caml-list] Coinductive semantics X-SA-Exim-Version: 4.2 (built Thu, 03 Mar 2005 10:44:12 +0100) X-SA-Exim-Scanned: Yes (on haka.fmf.uni-lj.si) X-Miltered: at concorde with ID 43C78367.000 by Joe's j-chkmail (http://j-chkmail.ensmp.fr)! X-Miltered: at concorde with ID 43C78365.000 by Joe's j-chkmail (http://j-chkmail.ensmp.fr)! X-Spam: no; 0.00; andrej:01 andrej:01 caml-list:01 coinductive:01 semantics:01 model:01 model:01 corresponds:01 trivial:01 lambda:01 computation:01 precisely:01 calculus:02 suggesting:02 seems:03 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 Your main observation seems to be this: algebras in a category C are dual to coalgebras in the opposite category C^op. Leaving further insults aside, let me explain why this observation does not help much. In order to have a category C which is a useful model of computation, the category C must have certain properties (such as being cartesian closed so that we can interpret lambda calculus in it). Also, one cannot use _two_ categories C and D and model some features in C, others in D, and hope to get a coherent picture which tells how the features interact with each other. Whenever C is useful for modelling programming languages, C^op is useless. While it is true that whatever you prove about algebras in C corresponds to something about coalgebras in C^op, this tells you absolutely nothing about coalgebras in C. Since C is what we care about, we then need to study coalgebras in C separately. The symmetries that you want are not there, provably. Believe me, what you are suggesting is trivial and researchers know precisely to what amount it works. Andrej