From mboxrd@z Thu Jan 1 00:00:00 1970 Received: from mail4-relais-sop.national.inria.fr (mail4-relais-sop.national.inria.fr [192.134.164.105]) by walapai.inria.fr (8.13.6/8.13.6) with ESMTP id p1ILYIpB016921 for ; Fri, 18 Feb 2011 22:34:18 +0100 X-IronPort-Anti-Spam-Filtered: true X-IronPort-Anti-Spam-Result: AvcDALF0Xk1iizXUgGdsb2JhbACmPgEBCwsKBRMDIbschV4EhQuKQA X-IronPort-AV: E=Sophos;i="4.62,189,1297033200"; d="scan'208";a="88298047" Received: from nm19-vm0.bullet.mail.ac4.yahoo.com ([98.139.53.212]) by mail4-smtp-sop.national.inria.fr with SMTP; 18 Feb 2011 22:34:12 +0100 Received: from [98.139.52.189] by nm19.bullet.mail.ac4.yahoo.com with NNFMP; 18 Feb 2011 21:34:11 -0000 Received: from [98.139.52.166] by tm2.bullet.mail.ac4.yahoo.com with NNFMP; 18 Feb 2011 21:34:11 -0000 Received: from [127.0.0.1] by omp1049.mail.ac4.yahoo.com with NNFMP; 18 Feb 2011 21:34:11 -0000 X-Yahoo-Newman-Id: 782661.90926.bm@omp1049.mail.ac4.yahoo.com Received: (qmail 62150 invoked from network); 18 Feb 2011 21:34:11 -0000 Received: from 172.16.1.34 (norm@76.204.179.198 with plain) by smtp105.sbc.mail.ac4.yahoo.com with SMTP; 18 Feb 2011 13:34:11 -0800 PST X-Yahoo-SMTP: 6wM9MhqswBCJxy9jDcYebttHhXX021oP4RUg3aXahuvJwcSQLA-- X-YMail-OSG: XKII7yEVM1lJU4KivUy_U1zgS9Xzr.UaOlEc3BxqTi.KSVd uzkkb8Au2U_sJx0cbjjLScwvCfNd.ZbCeJnK2Z6CkjWXPK0YW00bFJHj6GkY UfNF_vdneswZzGzXxsrvT_.DMLDjhoBtQO7Cj9.wWXuzmWbJdPMDaPg5p4GS 42nXTs_zwrzxYEU.5bwrYnIwPJbV7ZlvH2Efk_xWgPMUSajvRpVv2LrfXsMM 0T.e1IQh1Uwhwm4LQS_T9wMfxfZYifOAyLHCMmgmGqrb94jHS4LXA6VIq71q EF99ds0ataZMKoqEbwgLCfyrjfgmn7pH0gO_eTr74a5uV0Ve2L22YkqGuORY LRIAvotGsXFEWmZCoww5atT6Kzq.sDNZz8Aa5lTIPn1FS X-Yahoo-Newman-Property: ymail-3 References: <81B704C0-2971-47D8-BB9E-3F259016AB92@x9c.fr> <6C3CFF1F-DD4B-4BE3-BF3E-C78DCFE6200D@math.nagoya-u.ac.jp> In-Reply-To: <6C3CFF1F-DD4B-4BE3-BF3E-C78DCFE6200D@math.nagoya-u.ac.jp> Mime-Version: 1.0 (Apple Message framework v1082) Content-Type: text/plain; charset=windows-1252 Message-Id: <3861C31E-5FB0-48D7-921E-D7DF593811F5@cap-lore.com> From: Norman Hardy Date: Fri, 18 Feb 2011 13:34:02 -0800 To: caml-list users X-Mailer: Apple Mail (2.1082) Content-Transfer-Encoding: 8bit X-MIME-Autoconverted: from quoted-printable to 8bit by walapai.inria.fr id p1ILYIpB016921 Subject: Re: [Caml-list] Definition of module synonyms I think that OCaml lacks recursive functors but my page at: http://cap-lore.com/MathPhys/Algebras/ocaml/ builds the quaternions from the reals thus: module Quaternion = G(G(Reals));; G is a functor which does the 19th century “Cayley–Dickson construction” ( http://en.wikipedia.org/wiki/Cayley-Dickson_construction ) and other candidate division algebras as well. In Scheme I could loop building higher algebras until division failed. It was only slightly clunkier in OCaml, but in other ways better in OCaml.