From edward.cherlin.sy.67@aya.yale.edu Mon Feb 18 14:25:35 2002 Return-Path: X-Sender: cherlin@pacbell.net X-Apparently-To: lojban@yahoogroups.com Received: (EGP: mail-8_0_2); 18 Feb 2002 22:25:34 -0000 Received: (qmail 75434 invoked from network); 18 Feb 2002 22:25:24 -0000 Received: from unknown (216.115.97.167) by m12.grp.snv.yahoo.com with QMQP; 18 Feb 2002 22:25:24 -0000 Received: from unknown (HELO mta5.snfc21.pbi.net) (206.13.28.241) by mta1.grp.snv.yahoo.com with SMTP; 18 Feb 2002 22:25:24 -0000 Received: from there ([216.102.199.245]) by mta5.snfc21.pbi.net (iPlanet Messaging Server 5.1 (built May 7 2001)) with SMTP id <0GRR005OB2ACE1@mta5.snfc21.pbi.net> for lojban@yahoogroups.com; Mon, 18 Feb 2002 14:25:24 -0800 (PST) Date: Mon, 18 Feb 2002 14:25:23 -0800 Subject: [lojban] Constant-valued functions To: lojban@yahoogroups.com Message-id: <0GRR005OC2ACE1@mta5.snfc21.pbi.net> Organization: Web for Humans MIME-version: 1.0 X-Mailer: KMail [version 1.3.1] Content-type: text/plain; charset=iso-8859-1 Content-transfer-encoding: quoted-printable X-eGroups-From: Edward Cherlin From: Edward Cherlin Reply-To: edward@webforhumans.com X-Yahoo-Group-Post: member; u=31895329 X-Yahoo-Profile: echerlin 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=20 value. In some systems, a constant-valued function could be a niladic=20 function, that is, one with no (0) arguments. Lambda calculus and=20 hence LISP don't provide for this, but APL does. However, 1 is a=20 value in both APL and Lojban, not a function. (Niladic functions in=20 APL are not necessarily constant in value, because they can access=20 global variables, not just arguments.) In set theory, functions are defined as sets of ordered pairs,=20 usually with the first element from the domain set, and no two pairs=20 having the same first element. This does not provide for niladic=20 functions. Another approach allows the argument to be a list. In that=20 case a niladic function is a set containing one ordered pair, namely=20 the empty list first, and the constant value second. This could be=20 written {{},1}. It would be interesting to look for Sapir-Whorf effects of using=20 different function syntax which may or may not support particular=20 classes of functions. >No. Like Jorge, I think that the bridi would be making the (false?) > claim that 1 is a function. [I know that on some stories, numbers > or at least the naturals are indeed defined as functions (though > from what to what, I can't remember), but I don't think that's > pertinent to the current discussion.) That's true for defining the natural numbers in combinatory logic.=20 However, the function that is chosen to represent 1 is not=20 constant-valued. Rather (in one version) it returns one copy of its=20 argument, or does some other processing which can be compounded in=20 some useful arithmetic way with other integers. As you say, not=20 relevant here. >--And. ------------------------------------------------------- --=20 Edward Cherlin edward@webforhumans.com Does your Web site work?