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-- 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))
-- Exercise 5
nats :: Stream Integer
nats = streamFromSeed (+1) 0
-- The number of times an integer can be evenly divided by 2.
evenDiv2 :: Integer -> Integer
evenDiv2 n = toInteger $ length $ takeWhile even $ iterate (`quot` 2) n
ruler :: Stream Integer
ruler = streamMap evenDiv2 $ streamFromSeed (+1) 1
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