module Aula9 where

f x y = x ^ y

-- quadrados = fmap (\x -> x^2) [1, 2..10 ]
-- quadrados = (\x -> x^2) `fmap` [1, 2..10 ]
quadrados = (\x -> x^2) <$> [1, 2..10 ]

(#) :: Integral b => b -> b -> b
x # y = (x*y)^(y+x)
infixr 0 #

g x y z w = 0

h :: Integer -> Integer
h x = 2

i :: Integer -> Integer
i y = y+1

j :: Integer -> Integer
j z = z^z

(?) :: (a -> b) -> (b -> c) -> (a -> c)
-- f ? g = g . f
(f ? g) x = g (f x)
infixr 9 ?

instance Semigroup Integer
  where
    x <> y = x - y

class Grupo a
  where
    op :: a -> a -> a
    inv :: a -> a
    neutro :: a

    pot :: Integral b => a -> b -> a
    pot x 0 = neutro
    pot x n = (pot x (n-1)) `op` x

instance Grupo Integer
  where
    op x y = x + y
    inv x = -x
    neutro = 0

instance Grupo Float
  where
    op x y = x*y
    inv x = 1.0/x
    neutro = 1.0

instance Monoid Integer
  where
    mempty = 0