From mboxrd@z Thu Jan 1 00:00:00 1970 Return-Path: X-Original-To: caml-list@yquem.inria.fr Delivered-To: caml-list@yquem.inria.fr Received: from concorde.inria.fr (concorde.inria.fr [192.93.2.39]) by yquem.inria.fr (Postfix) with ESMTP id 8CE76BCA2 for ; Thu, 18 Aug 2005 19:51:39 +0200 (CEST) Received: from ash25e.internode.on.net (ash25e.internode.on.net [203.16.214.182]) by concorde.inria.fr (8.13.0/8.13.0) with ESMTP id j7IHpbvG004294 for ; Thu, 18 Aug 2005 19:51:38 +0200 Received: from rosella (ppp14-151.lns2.syd7.internode.on.net [59.167.14.151]) by ash25e.internode.on.net (8.12.9/8.12.6) with ESMTP id j7IHpGU8017750; Fri, 19 Aug 2005 03:21:32 +0930 (CST) (envelope-from skaller@users.sourceforge.net) Subject: Re: [Caml-list] Snd question From: skaller To: Andrej Bauer Cc: caml-list@yquem.inria.fr In-Reply-To: <430444BC.9090903@andrej.com> References: <161F0D30A699A84A8B7435B62BCE33B30360E19F@APS-MSG-01.southpacific.corp.microsoft.com> <200508161734.38909.jon@ffconsultancy.com> <20050816181604.GA21719@furbychan.cocan.org> <200508162242.50803.jon@ffconsultancy.com> <1124261702.6858.21.camel@localhost.localdomain> <430444BC.9090903@andrej.com> Content-Type: multipart/signed; micalg=pgp-sha1; protocol="application/pgp-signature"; boundary="=-LKyJwEe34akX7A7I51Ym" Date: Fri, 19 Aug 2005 03:51:15 +1000 Message-Id: <1124387475.8402.32.camel@localhost.localdomain> Mime-Version: 1.0 X-Mailer: Evolution 2.2.1.1 X-Miltered: at concorde with ID 4304CAA9.000 by Joe's j-chkmail (http://j-chkmail.ensmp.fr)! X-Spam: no; 0.00; caml-list:01 andrej:01 functor:01 recursion:01 ...:98 ...:98 wrote:01 sourceforge:01 sourceforge:01 polynomial:02 polynomial:02 types:02 types:02 languages:03 thu:05 X-Attachments: type="application/pgp-signature" name="signature.asc" 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 --=-LKyJwEe34akX7A7I51Ym Content-Type: text/plain Content-Transfer-Encoding: quoted-printable On Thu, 2005-08-18 at 10:20 +0200, Andrej Bauer wrote: > Contrary to what skaller says, no inductive types are allowed in a > polynomial functor.=20 This isn't contrary to what I said: I didn't say inductive types were allowed, I said the polynomial could be built *using* induction.=20 EG: 1 is a list, if L is a list then T * L is a list. It follows T is a list, T * T is a list .. etc, and so a list is given by the polynomial 1 + T + T * T + T * T * T + ... I accept this may not be the most general definition. You said later: "Such types are well understood and have accompanying induction and recursion principles from which various operations (map, fold, etc.) can be built systematically." and I wonder why no production languages actually do that... --=20 John Skaller --=-LKyJwEe34akX7A7I51Ym Content-Type: application/pgp-signature; name=signature.asc Content-Description: This is a digitally signed message part -----BEGIN PGP SIGNATURE----- Version: GnuPG v1.2.5 (GNU/Linux) iD8DBQBDBMqSsRp8/9aGVGsRAoIJAJ42uZNgoIaqTdWqPaAWY+Xi0vCZ5ACdFoVu 0zo3TJiRZyG3zxnbPz9XdEY= =QOHB -----END PGP SIGNATURE----- --=-LKyJwEe34akX7A7I51Ym--