From xod@sixgirls.org Mon Feb 18 14:35:29 2002 Return-Path: X-Sender: xod@reva.sixgirls.org X-Apparently-To: lojban@yahoogroups.com Received: (EGP: mail-8_0_2); 18 Feb 2002 22:35:29 -0000 Received: (qmail 20571 invoked from network); 18 Feb 2002 22:35:29 -0000 Received: from unknown (216.115.97.171) by m9.grp.snv.yahoo.com with QMQP; 18 Feb 2002 22:35:29 -0000 Received: from unknown (HELO reva.sixgirls.org) (216.27.131.50) by mta3.grp.snv.yahoo.com with SMTP; 18 Feb 2002 22:35:28 -0000 Received: from localhost (localhost [[UNIX: localhost]]) by reva.sixgirls.org (8.11.6+3.4W/8.11.6) with ESMTP id g1IMZRD19167 for ; Mon, 18 Feb 2002 17:35:28 -0500 (EST) Date: Mon, 18 Feb 2002 17:35:27 -0500 (EST) To: lojban@yahoogroups.com Subject: Re: [lojban] Constant-valued functions In-Reply-To: <0GRR005OC2ACE1@mta5.snfc21.pbi.net> Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII From: Invent Yourself X-Yahoo-Group-Post: member; u=1138703 X-Yahoo-Profile: throwing_back_the_apple On Mon, 18 Feb 2002, Edward Cherlin wrote: > Date: Wed, 13 Feb 2002 15:36:27 +0000 > And Rosta wrote: > >Xod: > >#Anyway, whatever is in the 4th place of fancu needs to be > > interpreted as a #function. If I stick "1" in there, it can only > > mean a function that #returns "1" for all arguments, right? > > You have to use "ma'o li pa", which is an expression rather than a > value. This, I can deal with. But, if a number requires typecasting into a function before it can fit into fancu4, how many types of sumti are there? Shouldn't this be made explicit? > In some systems, a constant-valued function could be a niladic > function, that is, one with no (0) arguments. Lambda calculus and > hence LISP don't provide for this, but APL does. However, 1 is a > value in both APL and Lojban, not a function. But ma'o li 1 is a function, isn't it? (Niladic functions in > APL are not necessarily constant in value, because they can access > global variables, not just arguments.) > > In set theory, functions are defined as sets of ordered pairs, > usually with the first element from the domain set, and no two pairs > having the same first element. This does not provide for niladic > functions. What if all the points of D map onto only one point of R? Another approach allows the argument to be a list. In that > case a niladic function is a set containing one ordered pair, namely > the empty list first, and the constant value second. This could be > written {{},1}. > > It would be interesting to look for Sapir-Whorf effects of using > different function syntax which may or may not support particular > classes of functions. The rejection of imaginaries can be viewed as a SW effect. -- The tao that can be tar(1)ed is not the entire Tao. The path that can be specified is not the Full Path.