Question

Possible Duplicate:
Why is such a function definition not allowed in haskell?

I would like to create a function flist that takes a function f as argument and returns another function whose argument will be a list but behaves exactly same as f.

For example:

let f x1 x2 x3 = x1+ x2 + x3

I want this behaviour

(flist f) [x1,x2,x3] = x1+x2+x3

When the list is not of length 3 it may behave in any way. flist should take care of any function (not only functions with 3 argument, i.e. if g x1 x2 x3 x4 = x1+x2+x3*x4, then (flist g) [x1,x2,x3,x4] = x1+x2+x3*x4 ).

I tried this,

flist f [] = f
flist f (x:xs) = flist (f x) xs

But it is not working. How do I achieve this? Can I use data types to do this?

Answer 1

With type families, you can get pretty far—but it surely is not for the faint of heart:

{-# LANGUAGE FlexibleContexts  #-}
{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE TypeFamilies      #-}

class FList a where
  type Point a
  flist :: a -> [Point a] -> Point a

instance FList (a -> a) where
  type Point (a -> a) = a
  flist f [x] = f x

instance (FList (a -> b), a ~ Point (a -> b)) => FList (a -> (a -> b)) where
  type Point (a -> (a -> b)) = Point (a -> b)
  flist f (x : xs) = flist (f x) xs

For your example, we get:

> let f x y z = x + y + z
> flist f [2, 3, 5]
10