From mboxrd@z Thu Jan 1 00:00:00 1970 Path: main.gmane.org!not-for-mail From: William Elliot Newsgroups: gmane.emacs.help Subject: Re: Lambda calculus and it relation to LISP Date: Mon, 7 Oct 2002 07:34:00 -0700 Organization: Newsfeeds.com http://www.newsfeeds.com 80,000+ UNCENSORED Newsgroups. Sender: help-gnu-emacs-admin@gnu.org Message-ID: <20021007073339.S95522-100000@agora.rdrop.com> References: <9e8ebeb2.0210041920.2e480123@posting.google.com> <20021006050255.A63895-100000@agora.rdrop.com> <9e8ebeb2.0210062058.5c7ab267@posting.google.com> <20021007025544.G57236-100000@agora.rdrop.com> NNTP-Posting-Host: localhost.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII X-Trace: main.gmane.org 1034001443 13768 127.0.0.1 (7 Oct 2002 14:37:23 GMT) X-Complaints-To: usenet@main.gmane.org NNTP-Posting-Date: Mon, 7 Oct 2002 14:37:23 +0000 (UTC) Return-path: Original-Received: from monty-python.gnu.org ([199.232.76.173]) by main.gmane.org with esmtp (Exim 3.35 #1 (Debian)) id 17yZ0b-0003Zt-00 for ; Mon, 07 Oct 2002 16:37:21 +0200 Original-Received: from localhost ([127.0.0.1] helo=monty-python.gnu.org) by monty-python.gnu.org with esmtp (Exim 4.10) id 17yYzd-0007YC-00; Mon, 07 Oct 2002 10:36:21 -0400 Original-Newsgroups: gnu.emacs.help,comp.lang.lisp,sci.math,sci.logic X-X-Sender: In-Reply-To: Original-NNTP-Posting-Host: 199.26.172.34 Original-X-Trace: corp.newsgroups.com 1034000164 199.26.172.34 (7 Oct 2002 09:16:04 -0500) Original-Lines: 48 X-Comments: This message was posted through Newsfeeds.com X-Comments2: IMPORTANT: Newsfeeds.com does not condone, nor support, spam or any illegal or copyrighted postings. X-Comments3: IMPORTANT: Under NO circumstances will postings containing illegal or copyrighted material through this service be tolerated!! X-Report: Please report illegal or inappropriate use to X-Abuse-Info: Please be sure to forward a copy of ALL headers, INCLUDING the body (DO NOT SEND ATTACHMENTS) Original-Path: shelby.stanford.edu!newsfeed.stanford.edu!cyclone.bc.net!news-out.newsfeeds.com!l2!corp.newsgroups.com!agora.rdrop.com!mars Original-Xref: shelby.stanford.edu gnu.emacs.help:105785 comp.lang.lisp:95869 sci.math:550098 sci.logic:61668 Original-To: help-gnu-emacs@gnu.org Errors-To: help-gnu-emacs-admin@gnu.org X-BeenThere: help-gnu-emacs@gnu.org X-Mailman-Version: 2.0.11 Precedence: bulk List-Help: List-Post: List-Subscribe: , List-Id: Users list for the GNU Emacs text editor List-Unsubscribe: , List-Archive: Xref: main.gmane.org gmane.emacs.help:2331 X-Report-Spam: http://spam.gmane.org/gmane.emacs.help:2331 see@sig.below William Elliot wrote: Using L for lambda with Church's old notion and -> for reduces factorial n > ((lambda (f) ( (lambda (Y) (f (Y Y)) ) (lambda (Y) (f (Y Y)) ))) > (lambda (ff n) (if (< n 1) 1 (* n (ff (- n 1))))) ) ! -> Ln.(Lf.(Ly.f(yy))(Ly.f(yy))) (Lfn.if( What's lambda calculus expressions for -, <, if, = ? _ '-' and '<' are a bit tricky, as is most LC arithmetic using Church _ numerals -- see a textbook that covers LC. It looks like 0; -n0 -> n; -(+n1)1 -> n _ 'if' is usually _ (lambda (test ifTrue ifFalse) (test ifTrue ifFalse)) if -> Lxyz.xyz if true -> Lyz.y -> true if false -> Lyz.z -> false if true NM -> N if false NM -> M _ where the value for TRUE is _ (lambda (ifTrue ifFalse) ifTrue) _ and the value for FALSE is _ (lambda (ifTrue ifFalse) ifFalse) True is Lxy.x False is Lxy.y which is Church numeral 0. Glancing with Google, yicks, the Calculi of Lambda conversion is unreconizable mutant of Alanzo Church's original work. ---- -----= Posted via Newsfeeds.Com, Uncensored Usenet News =----- http://www.newsfeeds.com - The #1 Newsgroup Service in the World! -----== Over 80,000 Newsgroups - 16 Different Servers! =-----