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 nez-perce.inria.fr (nez-perce.inria.fr [192.93.2.78]) by yquem.inria.fr (Postfix) with ESMTP id B4E1DBBBB for ; Fri, 31 Mar 2006 23:01:29 +0200 (CEST) Received: from pauillac.inria.fr (pauillac.inria.fr [128.93.11.35]) by nez-perce.inria.fr (8.13.0/8.13.0) with ESMTP id k2VL1SNp004659 for ; Fri, 31 Mar 2006 23:01:29 +0200 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 XAA31098 for ; Fri, 31 Mar 2006 23:01:28 +0200 (MET DST) Received: from mail.physik.uni-muenchen.de (mail.physik.uni-muenchen.de [192.54.42.129]) by concorde.inria.fr (8.13.0/8.13.0) with ESMTP id k2VL1RY6025347 (version=TLSv1/SSLv3 cipher=DHE-RSA-AES256-SHA bits=256 verify=FAIL) for ; Fri, 31 Mar 2006 23:01:28 +0200 Received: from localhost (unknown [127.0.0.1]) by mail.physik.uni-muenchen.de (Postfix) with ESMTP id 88F232000F; Fri, 31 Mar 2006 23:01:27 +0200 (CEST) Received: from mail.physik.uni-muenchen.de ([127.0.0.1]) by localhost (mail.physik.uni-muenchen.de [127.0.0.1]) (amavisd-new, port 10024) with LMTP id 28072-01-2; Fri, 31 Mar 2006 23:01:27 +0200 (CEST) Received: from mailhost.cip.physik.uni-muenchen.de (kaiser.cip.physik.uni-muenchen.de [141.84.136.1]) by mail.physik.uni-muenchen.de (Postfix) with ESMTP id 6F1082000B; Fri, 31 Mar 2006 23:01:27 +0200 (CEST) Received: from aso.cip.physik.uni-muenchen.de (eiger.cip.physik.uni-muenchen.de [141.84.136.54]) by mailhost.cip.physik.uni-muenchen.de (Postfix) with ESMTP id 2A4FC26E89; Fri, 31 Mar 2006 23:01:27 +0200 (CEST) Received: by aso.cip.physik.uni-muenchen.de (Postfix, from userid 3092) id CC83BC8671; Fri, 31 Mar 2006 23:01:26 +0200 (CEST) Received: from localhost (localhost [127.0.0.1]) by aso.cip.physik.uni-muenchen.de (Postfix) with ESMTP id C5AF3D06B6; Fri, 31 Mar 2006 23:01:26 +0200 (CEST) Date: Fri, 31 Mar 2006 23:01:26 +0200 (CEST) From: Thomas Fischbacher To: yoann padioleau Cc: Oliver Bandel , caml-list@inria.fr Subject: Re: [Caml-list] Lambda-Term (f x) (x f) translated to Ocaml? In-Reply-To: <24000351.1143506695382.JavaMail.www@wwinf1608> Message-ID: References: <24000351.1143506695382.JavaMail.www@wwinf1608> X-BOFH: Daemons did it MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII X-Virus-Scanned: amavisd-new at physik.uni-muenchen.de X-Miltered: at nez-perce with ID 442D98A8.000 by Joe's j-chkmail (http://j-chkmail.ensmp.fr)! X-Miltered: at concorde with ID 442D98A7.001 by Joe's j-chkmail (http://j-chkmail.ensmp.fr)! X-Spam: no; 0.00; translated:01 ocaml:01 lambda:01 combinator:01 lambda:01 rec:01 val:01 cip:98 cip:98 caml-list:01 calculus:01 calculus:01 debian:02 physik:02 physik:02 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 > I guess that this is not a lambda term that can be typed. > There are many of them. A famous one is the Y combinator. > The _typed_ lambda calculus does not allow all the lambda terms > of the (normal) lambda calculus. # let rec y f = f (y f);; val y : ('a -> 'a) -> 'a = -- regards, tf@cip.physik.uni-muenchen.de (o_ Thomas Fischbacher - http://www.cip.physik.uni-muenchen.de/~tf //\ (lambda (n) ((lambda (p q r) (p p q r)) (lambda (g x y) V_/_ (if (= x 0) y (g g (- x 1) (* x y)))) n 1)) (Debian GNU)