Subject: [lojban] Constant-valued functions

From: Edward Cherlin <[email-masked]>
Date: Mon, 18 Feb 2002 14:25:23 -0800

Date: Wed, 13 Feb 2002 15:36:27 +0000
And Rosta <[email-masked]> 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.

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. (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. 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.

>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. 
However, the function that is chosen to represent 1 is not 
constant-valued. Rather (in one version) it returns one copy of its 
argument, or does some other processing which can be compounded in 
some useful arithmetic way with other integers. As you say, not 
relevant here.

>--And.

-------------------------------------------------------

-- 
Edward Cherlin
[email-masked]
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