-- Exercise 1

fib :: Integer -> Integer
fib 0 = 0
fib 1 = 1
fib n = (fib (n-1)) + (fib (n-2))

fibs1 :: [Integer]
fibs1 = map fib [0..]

-- Exercise 2

fibs2 :: [Integer]
fibs2 = map fst $ iterate (\l -> ( snd l , snd l + fst l )) (0,1)

-- Exercise 3

data Stream a = Cons a (Stream a)

streamToList :: Stream a -> [a]
streamToList (Cons a s) = a : streamToList s

instance Show a => Show (Stream a) where
	show s = show $ take 20 $ streamToList s

-- Exercise 4

streamRepeat :: a -> Stream a
streamRepeat e = Cons e (streamRepeat e)

streamMap :: (a -> b) -> Stream a -> Stream b
streamMap f (Cons a as) = Cons (f a) (streamMap f as)

streamFromSeed :: (a -> a) -> a -> Stream a
streamFromSeed f s = Cons s (streamFromSeed f (f s))