Re: List functions

[Hans Aberg]

On 1 Dec 2010, at 22:34, Keith Wright wrote:

> > One can set the constants to functions that evaluate
> > to themselves.  One use would be expressions like
> > (1 + f)(x). The () just shows up in the context above.
>
> I didn't really follow that, but in seems that
> you want to be able to apply a list of functions
> to a single argument, and get a list of the
> results of applying each function separately
> to the same argument.
>
> guile>
> (define (fmap fs x)
>  (if (null? fs)
>      '()
>      (cons (apply (car fs) (list x))
>             (fmap (cdr fs) x) )))
>
> guile> (fmap (list sin cos) 2)
> (0.909297426825682 -0.416146836547142)

If I extend your function to one of pairs and non-pairs as well, then  
() becomes naturally a constant:
(define (fmap fs x)
  (if (null? fs)
    '()
    (if (not (pair? fs))
      (apply fs (list x))
      (cons (fmap (car fs) x)
            (fmap (cdr fs) x)))))

Then
  (fmap sqrt 2)
    --> 1.4142135623731
  (fmap (list sin cos) 2)
    --> (0.909297426825682 -0.416146836547142)
  (fmap (cons sin cos) 2)
    --> (0.909297426825682 . -0.416146836547142)

But also
  (fmap (list) 2)
    --> ()

So this acts essentially as an extension of the evaluator, if all  
expressions (f x1 ...) are replaced by (fmap f x1 ...).