-- 1 
eliminAlgunos :: Integral a => [a] -> [a]   
eliminAlgunos ys = aux [] ys

aux :: Integral a => [a] -> [a] -> [a]  
aux [] []= []
aux [] (x:xs) 
  = if ((x `mod` 2)==0) then (x: aux [x] xs) else (x: aux [] xs)
aux [z] [] = []
aux [z] (x:xs) 
  | (x `mod` 2)==0 = x: aux [x] xs
  | (x `mod` 2)==1 = if (z<x) then (x: aux [z] xs) else  (aux [z] xs)


-- 2 
-- f1 :: Eq a => a -> [a] -> [a]
f1 a xs = takeWhile (/= a) xs ++ [a]

--f2 :: (a->c)->(b->d)-> (a,b)->(c,d)
f2 g  h (x,y) = (g x, h y)

-- f3 :: Ord a => b -> (a -> c) -> [a] -> [c] 
f3 g h (x:xs) = [ h y | y<-xs, x<=y]



--3
r1 b= iterate g b
     where  g x= 1/2 * (x+b/x)

r2 b= zs
     where zs = b:map g zs
	   g x= 1/2 * (x+b/x)


--5
data ConCad a 	=   Nil | Unit a | Cad (ConCad a) (ConCad a)

instance (Eq a) => Eq (ConCad  a) where
  l1==l2  =  lista l1 == lista l2

lista Nil = []
lista(Unit x) = [x]
lista (Cad l1 l2) = lista l1 ++ lista l2


primero l
    | l==Nil = error " lista vacia" 
    | otherwise = head (lista l)

primero' l 
    | xs == [] = error " lista vacia"
    | otherwise = head xs
    where xs = lista l

primero'' Nil = []
primero'' (Unit x) = x
primero'' (Cad xs ys) 
   | xs==Nil = primero'' ys
   | otherwise = primero'' xs

numElementos = length.lista 

k0= Nil
k1= Cad Nil (Unit 'p') 
k2= Unit 'p'
k3= Cad (Unit 'p') (Cad  (Unit 'r') (Unit 's'))
k4= Cad (Cad (Unit 'p') (Unit 'r')) (Unit 's')
k5= Cad (Unit 'p') (Unit 'r')
k6= Cad (Unit 'r') (Unit 'p')