Re: List functions

[Hans Aberg <haberg-1@telia.com>]

On 1 Dec 2010, at 20:20, Keith Wright wrote:

>> ... in standard syntax would be natural to let (f, g)(x) evaluate
>> to (f(x), g(x)), producing a list of two elements. In Guile, that
>> would be something involving "map". If I try in Haskell, I can let
>> (sin, cos)(2) be the same as
>>   map (g 2) [sin, cos] where g x = \f -> f x
>>    -> [0.909297426825682,-0.416146836547142]
>> But when I try that similar constructs in Guile, I get problems with
>> evaluation.
>
> Works for me
>
> guile> (let ()
>         (define (g x)(lambda (f)(f x)))
>         (map (g 2) (list sin cos)))
>
> (0.909297426825682 -0.416146836547142)
>
> There are other ways to write it, but that
> is the most direct translation of your Haskell
> into Scheme.

I was trying variations like
       (let ()
         (define (g x)(lambda (f)(f x)))
         (map (g 2) '(sin cos)))
Which gives an error:
   In expression (f x):
   Wrong type to apply: sin

I'm not sure when to use quote or list, here. Quote seems to work when  
the list is data, not a list of functions.

>>>> I am writing on a parser that translates normal
>>>> function syntax in to Guile code.
>>>>
>>>> It seems natural to translate (f, g) x into ((f g) x),
>
> If "(f, g) x" is (in normal syntax) supposed to mean:
>
>  apply f to g resulting in a function that is applied to x,
>
> then that is "natural", but whether that is normal
> syntax, I can not say.  I'm liberal on this.
> Normal syntax is whatever you want, but step
> one is to get clear on what you want.
>
> Speaking for myself, I have never before seen that
> syntax with that meaning, so I would hesitatate
> to call it "normal".  But if you define it, you can
> call it what you will.

This normality only has to do with parser grammar implementation. If  
in the evaluation syntax f ..., and the binding syntax corresponding  
in Haskell to \ ... -> f, the two "..." use the same syntax, I can  
eliminate the "\". Then the evaluation syntax
   (f_1, ..., f_k) x
becomes available. I could eliminate it semnatically or set it to what  
is common in math, if not too complicated.

>>>> and () x into (() x), but I'm not sure if the
>>>> lists (f g) and () can be made acting as functions
>>>> this way.
>
> I have not only never seen the "normal syntax" in
> use here, but I have no guess what it is supposed
> to mean.  In Scheme "(() x)" means nothing at all.
> In fact it is so far from meaningful that I can
> not guess how to fix it.

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.