20 Intermediate Haskell Exercises

IntermHaskell.hs

-- https://haskell.fpcomplete.com/user/DanBurton/20-intermediate-exercises
-- Originally from http://blog.tmorris.net/posts/20-intermediate-haskell-exercises/

class Fluffy f where
  furry :: (a -> b) -> f a -> f b

-- Exercise 1
-- Relative Difficulty: 1
instance Fluffy [] where
  furry = fmap

-- Exercise 2
-- Relative Difficulty: 1
instance Fluffy Maybe where
  furry = fmap

-- Exercise 3
-- Relative Difficulty: 5
instance Fluffy ((->) t) where
  furry = (.)

newtype EitherLeft b a = EitherLeft (Either a b)
newtype EitherRight a b = EitherRight (Either a b)

-- Exercise 4
-- Relative Difficulty: 5
instance Fluffy (EitherLeft t) where
  furry f (EitherLeft (Left a)) = EitherLeft . Left . f $ a
  furry f (EitherLeft (Right b)) = EitherLeft . Right $ b
  
-- Exercise 5
-- Relative Difficulty: 5
instance Fluffy (EitherRight t) where
  furry f (EitherRight (Right b)) = EitherRight . Right . f $ b
  furry f (EitherRight (Left a))  = EitherRight . Left $ a

class Misty m where
  banana :: (a -> m b) -> m a -> m b
  unicorn :: a -> m a

-- Exercise 7
-- Relative Difficulty: 2
instance Misty [] where
  banana = concatMap
  unicorn e = [e]

-- Exercise 8
-- Relative Difficulty: 2
instance Misty Maybe where
  banana f (Just a) = f a
  banana f Nothing = Nothing
  unicorn = Just
  
-- Exercise 9
-- Relative Difficulty: 6
instance Misty ((->) t) where
  banana f g t = f (g t) t
  unicorn = const

newtype EitherLeft b a  = EitherLeft (Either a b)
newtype EitherRight a b = EitherRight (Either a b)

-- Exercise 10
-- Relative Difficulty: 6
instance Misty (EitherLeft t) where
  banana f (EitherLeft (Left a))   = f a
  banana f (EitherLeft (Right b))  = EitherLeft . Right $ b
  unicorn = EitherLeft . Left

-- Exercise 11
-- Relative Difficulty: 6
instance Misty (EitherRight t) where
  banana f (EitherRight (Right b)) = f b
  banana f (EitherRight (Left a))  = EitherRight . Left $ a
  
  unicorn = EitherRight . Right
  
class Misty m where
  banana :: (a -> m b) -> m a -> m b
  unicorn :: a -> m a

-- Exercise 6
-- Relative Difficulty: 3
-- (use banana and/or unicorn)
furry' :: (Misty m) => (a -> b) -> m a -> m b
furry' f ma = banana (unicorn . f) ma

-- Exercise 12
-- Relative Difficulty: 3
jellybean :: (Misty m) => m (m a) -> m a
jellybean = banana id

-- Exercise 13
-- Relative Difficulty: 6
apple :: (Misty m) => m a -> m (a -> b) -> m b
apple ma mf = banana (\f -> furry' f ma) mf

-- Exercise 14
-- Relative Difficulty: 6
moppy :: (Misty m) => [a] -> (a -> m b) -> m [b]
moppy [] f     = unicorn []
moppy (x:xs) f = apple (moppy xs f) (furry' (:) (f x))

-- Exercise 15
-- Relative Difficulty: 6
-- (bonus: use moppy)
sausage :: (Misty m) => [m a] -> m [a]
sausage xs = moppy xs id

-- Exercise 16
-- Relative Difficulty: 6
-- (bonus: use apple + furry')
banana2 :: (Misty m) => (a -> b -> c) -> m a -> m b -> m c
banana2 f ma mb = apple mb ((furry' f) ma)

-- Exercise 17
-- Relative Difficulty: 6
-- (bonus: use apple + banana2)
banana3 :: (Misty m) => (a -> b -> c -> d) -> m a -> m b -> m c -> m d
banana3 f ma mb mc = apple mc (banana2 f ma mb)

-- Exercise 18
-- Relative Difficulty: 6
-- (bonus: use apple + banana3)
banana4 :: (Misty m) => (a -> b -> c -> d -> e) -> m a -> m b -> m c -> m d -> m e
banana4 f ma mb mc md = apple md (banana3 f ma mb mc)

class Misty m where
  banana :: (a -> m b) -> m a -> m b
  unicorn :: a -> m a

class Fluffy f where
  furry :: (a -> b) -> f a -> f b


newtype State s a = State {
  state :: (s -> (s, a))
}

-- Exercise 19
-- Relative Difficulty: 9
instance Fluffy (State s) where
  furry f st = State (\s -> let (s', a) = state st s in (s', f a))

-- Exercise 20
-- Relative Difficulty: 10
instance Misty (State s) where
  banana f ma = State (\s -> let (s', a) = state ma s in state (f a) s')
  unicorn a = State (\s -> (s, a))