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 ABF64BB9C for ; Fri, 20 Jan 2006 01:49:55 +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 k0K0ntkc014028 for ; Fri, 20 Jan 2006 01:49:55 +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 BAA16355 for ; Fri, 20 Jan 2006 01:49:54 +0100 (MET) Received: from singularity.stwing.upenn.edu (YAVIN.STWING.upenn.edu [165.123.132.64]) by concorde.inria.fr (8.13.0/8.13.0) with ESMTP id k0K0nrHu014022 (version=TLSv1/SSLv3 cipher=DHE-RSA-AES256-SHA bits=256 verify=FAIL) for ; Fri, 20 Jan 2006 01:49:54 +0100 Received: from localhost (localhost [127.0.0.1]) by singularity.stwing.upenn.edu (Postfix) with ESMTP id 0B3131403 for ; Thu, 19 Jan 2006 19:49:53 -0500 (EST) Received: from singularity.stwing.upenn.edu ([127.0.0.1]) by localhost (yavin.stwing.upenn.edu [127.0.0.1]) (amavisd-new, port 10024) with ESMTP id 00254-05 for ; Thu, 19 Jan 2006 19:49:52 -0500 (EST) Received: from coruscant.stwing.upenn.edu (coruscant.stwing.upenn.edu [165.123.132.62]) by singularity.stwing.upenn.edu (Postfix) with ESMTP id C5F671388 for ; Thu, 19 Jan 2006 19:49:52 -0500 (EST) Received: by coruscant.stwing.upenn.edu (Postfix, from userid 5302) id 79F25E51E; Thu, 19 Jan 2006 19:49:52 -0500 (EST) Date: Thu, 19 Jan 2006 19:49:50 -0500 From: William Lovas To: caml-list@inria.fr Subject: Re: [Caml-list] Coinductive semantics Message-ID: <20060120004948.GA2490@coruscant.stwing.upenn.edu> Mail-Followup-To: caml-list@inria.fr References: <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> <1137594157.8943.106.camel@rosella> Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Disposition: inline In-Reply-To: <1137594157.8943.106.camel@rosella> User-Agent: Mutt/1.5.6i X-Virus-Scanned: amavisd-new at stwing.upenn.edu X-Miltered: at concorde with ID 43D033B3.000 by Joe's j-chkmail (http://j-chkmail.ensmp.fr)! X-Miltered: at concorde with ID 43D033B1.000 by Joe's j-chkmail (http://j-chkmail.ensmp.fr)! X-Spam: no; 0.00; lovas:01 wlovas:01 stwing:01 upenn:01 caml-list:01 coinductive:01 semantics:01 hendrik:01 tews:01 o'caml:01 lacks:01 o'caml's:01 datatypes:01 recursive:01 polymorphism: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 Thu, Jan 19, 2006 at 01:22:37AM +1100, skaller wrote: > On Wed, 2006-01-18 at 13:58 +0100, Hendrik Tews wrote: > > 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? A thought: products and sums are duals, classically, but not intuitionistically. Since O'Caml lacks classical control constructs like callcc, there's no redundancy having both products and sums: neither is representable solely using the other. Also, O'Caml's datatypes are much more than just sums: they also include recursive types, polymorphism, pattern matching, and a degree of abstraction. cheers, William