Subject: Re: [lojban] Constant-valued functions

From: Invent Yourself <[email-masked]>
Date: Mon, 18 Feb 2002 17:35:27 -0500 (EST)

On Mon, 18 Feb 2002, Edward Cherlin wrote:

> 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.

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.