[Haskell-cafe] Mission: To take args from an n-tuple ... generally

[Martin Hofmann]

Dear Community.

I have recently read Joel Koerwer's posting how to evaluate a function
of type (a->a->...->a->a), taking the arguments from a list
(http://haskell.org/pipermail/haskell-cafe/2006-October/018658.html).
Therefore, he introduced a function multApply:

	multApply :: (a->a->...->a->a) -> [a] -> a

I wondered, why not take an n-tuple of arguments s.t.

	multApply' :: (a1->a2->...->an->o) -> (a1,(a2,(...(an,o)...))) -> o

I naively tried to modify Joel's code, but in vain. As far as I can deduce from the error messages, 
GHC fails to fix the accordant types. However, in my understanding the type solely depends on the 
type of the passed function. Or am I wrong? Maybe there is a reason nobody has tried it this way? 

Following the code. First Joel's original multApply and then my attempt to define multApply'. 

------------------------ MultApply.hs ------------------------------
{-# OPTIONS -fglasgow-exts  -fallow-overlapping-instances #-} 

module MultApply where  
 
class MultApply func arg | func -> arg where  
    multApply :: func -> [arg] -> arg  
 
instance MultApply (a->a) a where  
    multApply f (x:xs) = f x  
    multApply f _      = error "MultApply: one too few args"  
 
instance MultApply cascade a => MultApply (a -> cascade) a where  
    multApply f (x:xs) = multApply (f x) xs  
    multApply f _      = error "MultApply: n too few args"  
 
-- some random examples  
oneArg = multApply sqrt [25..]  
twoArg = multApply (+) [1..]  
fiveArg = multApply (\a b c d e -> sqrt ((a+b)^2+(d-e)^2)-5*c) [13..] 



class MultApply' f arg out | f -> arg out where  
    multApply' :: f -> arg -> out
 
instance MultApply' (a->b) a b where  
    multApply' f x = f x  
    multApply' f _      = error "MultApply: one too few args"  
 
instance MultApply' cascade a2 b => MultApply' (a1 -> cascade) (a1,a2) b where  
    multApply' f (x,xs) = multApply' (f x) xs  
    multApply' f _      = error "MultApply: n too few args" 
-------------------End File ------------------------


Hope I didn't stumble in a stupid newbie question. Thanks a lot to everybody who 
could give me some explanation and hints.

Cheers,

Martin