-- 1 --
prodsum:: Num a => [a] -> (a,a) 
prodsum [] = (1,0)
prodsum (x:xs) = (x*p,x+s) where (p,s)= prodsum xs

-- 2 --
-- a)
apFunPos :: (a -> a) -> Int -> [a] -> [a] 
apFunPos f p xs = take p xs ++ (f (xs!! p) : drop (p+1) xs)
-- b)
inc :: Num a => a -> Int -> [a] -> [a]  
inc c = apFunPos (+c)

-- 3 --
data Arbol a = G a [Arbol a]			
foldG f g (G r hijos) = f r (g (map (foldG f g) hijos))

sumArb :: Arbol Integer -> Integer   
sumArb = foldG (+) sum

a1 = G 1 [G 2 [G 5 [], G 6 [], G 7 []], 
          G 3 [G 8 [], G 9 []], 
	  G 4 []]

-- 4 --
-- g :: a -> b -> c
-- f :: c -> d
-- h x y = f (g x y)
-- El tipo de h es a -> b -> d
-- Es equivalente a 2) ya que si h x = f . (g x), entonces
-- h x y = (f . (g x)) y = f ((g x) y) = f (g x y)

-- 5 --

ciclica = 1 : map (+3) ciclica

{- ^ denota flecha que sale hacia atrás y ´ donde llega la flecha

   ´1 : map (+3) ^

=>  1 : ´((+3) 1) : map (+3) ^

=>  1 : ´4 : map (+3) ^

=>  1 : 4 : ´((+3) 4) : map (+3) ^

=>  1 : 4 : 7 : map (+3) ^

=>  1 : 4 : 7 : ´((+3) 7) : map (+3) ^

-}