From mboxrd@z Thu Jan 1 00:00:00 1970 Path: main.gmane.org!not-for-mail From: "Charles Matthews" Newsgroups: gmane.emacs.help Subject: Re: Lambda calculus and it relation to LISP Date: Sat, 5 Oct 2002 08:58:57 +0100 Organization: ntl Cablemodem News Service Sender: help-gnu-emacs-admin@gnu.org Message-ID: References: <9e8ebeb2.0210041920.2e480123@posting.google.com> NNTP-Posting-Host: localhost.gmane.org X-Trace: main.gmane.org 1033804921 18092 127.0.0.1 (5 Oct 2002 08:02:01 GMT) X-Complaints-To: usenet@main.gmane.org NNTP-Posting-Date: Sat, 5 Oct 2002 08:02:01 +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 17xjst-0004hg-00 for ; Sat, 05 Oct 2002 10:02:00 +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 17xjs4-00042m-00; Sat, 05 Oct 2002 04:01:08 -0400 Original-Path: shelby.stanford.edu!newsfeed.stanford.edu!news-spur1.maxwell.syr.edu!news.maxwell.syr.edu!newsfeed.icl.net!newsfeed.fjserv.net!proxad.net!proxad.net!newspeer1-gui.server.ntli.net!ntli.net!newsfep2-gui.POSTED!53ab2750!not-for-mail Original-Newsgroups: gnu.emacs.help,comp.lang.lisp,sci.math,sci.logic Original-Lines: 41 X-Priority: 3 X-MSMail-Priority: Normal X-Newsreader: Microsoft Outlook Express 6.00.2600.0000 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2600.0000 Original-NNTP-Posting-Host: 80.4.0.2 Original-X-Complaints-To: abuse@ntlworld.com Original-X-Trace: newsfep2-gui 1033804724 80.4.0.2 (Sat, 05 Oct 2002 08:58:44 BST) Original-NNTP-Posting-Date: Sat, 05 Oct 2002 08:58:44 BST Original-Xref: shelby.stanford.edu gnu.emacs.help:105740 comp.lang.lisp:95612 sci.math:549523 sci.logic:61522 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:2286 X-Report-Spam: http://spam.gmane.org/gmane.emacs.help:2286 "gnuist" wrote > I read the following quote in a book on emacs and similar > things in a book on lisp. > > "The lambda calculus is a mathematical formalism > having to do with the way functions instantiate > their arguments. To some extent it is the theoretical > basis for Lisp and plenty of other computer languages." > > I am interested in a little concrete elaboration > of this statement by any mathematicians, logicians > or practitioners/users of lisp and lisp in emacs. There are a few obstacles in understanding what is going on here. For example: - the lambda calculus may be a 'mathematical formalism', but it is not one mathematicians usually have a feeling for, unless they have cause to use it in some way: what it is really is a very basic piece of syntax for computer science; - the underlying programming theory of lambda calculus is functional programming, so on the whole it might be more accurate to call lambda calculus a mechanism for expressing accurately the substitution of one function in another, rather than instantiation (an operational rather than a mathematical difference); - you can call LISP a functional programming language if you want - not everybody would so want; - the untyped lambda calculus written in the usual compressed way abbreviates heavily, and going a couple of steps back to a more tree-like representation of combinators is much more perspicuous. So, this connection can be made ... but joining it all up required a fair amount of background. Charles