Hi,

we know the notion of 1st class object, which, applied to functions
means things like being able to give functions as other
functions'arguments, return functions, aggregate them, using them
literally and so on.

What about partial application and the fact that if you define "f a b",
them "f a" also denotes a function that you can later apply to another
argument? Would you say that this is one of the caracteristics of
functions being 1st class objects, or rather that it is a /consequence/
of that?

Since partial application is very function-specific (as opposed to
concepts like litteral manipulation or function arguments/return
values), I'm reluctant to consider it as a higher order characteristic,
but I'd like other opinions.

--
5th European Lisp Workshop at ECOOP 2008, July 7: http://elw.bknr.net/2008/

Didier Verna, did...@lrde.epita.fr, http://www.lrde.epita.fr/~didier

  f a b = e

is really a shorthand for

  f = \a->\b->e

So you define a function that takes a value a and returns another
function that takes a value b and returns a value (which may or may
not be another function).

So, if you can define functions that return functions, you have the
ability to do partial applications.  So I would say that partial
application is a consequence of first-class functions.  You might not
always have as nice a syntax as the above, though.