Path: utzoo!utgpu!jarvis.csri.toronto.edu!mailrus!ncar!unmvax!deimos.cis.ksu.edu!rutgers!okstate!norman
From: norman@a.cs.okstate.edu (Norman Graham)
Newsgroups: comp.lang.misc
Subject: Re: first class functions (opps)
Message-ID: <4663@okstate.UUCP>
Date: 9 May 89 16:12:38 GMT
References: <451@sdti.SDTI.COM>
Organization: Oklahoma State Univ., Stillwater
Lines: 34

From article <451@sdti.SDTI.COM>, by turner@sdti.SDTI.COM (Prescott K. Turner):
> But isn't it false advertising to claim first-class functions unless you
> can compare functions for equality just like other types?

No. It is false advertising to claim first-class functions if (1) you can
define a magical function-equality algorithm but (2) your language doesn't
allow you to pass functions to a functional abstration of your magical
function-equality algorithm.  Of course, there are many other things that
prevent functions from being first-class, but the requirement that all 
relations be defined for functions is not among them.

In general, values of type 'alpha' (in this case, 'alpha' = 'function') are
first-class citizens of a language when that language does not discriminate
against them in any way.  Reynolds [*] called this the 'Principle of Data
Type Completeness' and in particluar it requires that all values (reguardless
of type) be 
    (1) passable as parameters,
    (2) assignable,
    (3) able to form components of data structures, and
    (4) able to be returned from functions.

Of course, whether any particular function has values of type 'function'
in its domain or codomain is still up to the definition of the function
and has no bearing on the first-classness of values of type 'function'.

[*] J. C. Reynolds, GEDANKEN: a simple typeless language based on the
    principles of completeness and the reference concept, CACM,
    vol. 13 (5), 308-319 (1970).

-- 
Norman Graham                            Oklahoma State University
  Internet:  norman@a.cs.okstate.edu     Computing and Information Sciences
      UUCP:  {cbosgd, rutgers}           219 Mathematical Sciences Building
              !okstate!norman            Stillwater, OK  74078-0599