2007/5/23, Vincent Aravantinos <vincent.aravantinos@yahoo.fr>:
> On Wed, 23 May 2007, Loup Vaillant wrote :
>
> > (...)
>
> >> * Anonymous functions are still beyond most of them.
> >
> > That sounds surprising, for anonymous function are no different
> > from named ones:
> >
> > 5;; (* a value *)
> > fun x -> x+1;; (* another value, which happens to be a function *)
>
> Those are typically the comments of a "used-to-functional-
> programming" guy.
> It certainly doesn't match what a beginner would think (no beginner
> will call a
> function a "value").

You are quite right. My point was to find a way to tell the beginners.
A way to stress upon the fact that functions are values like any other
(in Ocaml, at the very least).

I see some difficulties, thought :

First, the syntax:
b = fun x -> x+1;; (* b defined as a functionnal value *)
b x = x+1;; (* b defined as a mere function *)

Second, imperative languages, where b can only be defined as a mere
function. Many courses begin with an imperative language.

Third, high school, where the only functions we dare name as such are
of type number -> number. Derivation and composition, for instance,
are named "operations", not functions. As if they have anything
special (usefulness excepted). Finally, each function has a name in
high shool mathematics.


> Or do you really think that seeing functions as first-class object is
> the natural way ?
> IMHO this is not the case, and therefore not the case of a beginner.

I agree. I just hope it can become A natural way.

> To my eyes, there are (I mean, "in human mind" or at least in an
> ocaml beginner's mind)
> values AND functions. A function turns into a value (in the mind of
> the programmer)
> only when it is used by a higher order function.

I think there are some other uses, too : data structures can contain
closures for instance. A lazily evaluated value is a function (a
closure).


> > Did your students used map and fold-like functions much? These almost
> > require anonymous functions.
>
> Indeed, using map and fold puts the focus on the fact that functions
> _can_ be values.
> Thus their importance in a pedagogical context.

Not only : most loops in a list or an array can be expressed as a
combination of map and fold (and filter, and...). Using these
significantly reduce the amount of code.

> Maybe all this is just a matter of belief...

I am quite a zeelot of abstraction. :)

Regards,
Loup