Tony20.hs

module Tony20 (
    Fluffy,
    furry,
    EitherLeft(..),
    EitherRight(..),
    Misty,
    banana,
    unicorn,
    jellybean,
    apple
) where


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


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

-- 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 _ (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 _ (EitherRight (Left a))  = EitherRight (Left a)


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


-- Exercise 7
-- Relative Difficulty: 2
instance Misty [] where
  banana f = concat . furry f
  unicorn x = [x]

-- Exercise 8
-- Relative Difficulty: 2
instance Misty Maybe where
  banana _ Nothing  = Nothing
  banana f (Just x) = f x
  unicorn = Just

-- Exercise 9
-- Relative Difficulty: 6
instance Misty ((->) t) where
  banana f m = \x -> f (m x) x
  unicorn x = \_ -> x

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

-- Exercise 11
-- Relative Difficulty: 6
instance Misty (EitherRight t) where
  banana _ (EitherRight (Left a)) = EitherRight (Left a)
  banana f (EitherRight (Right b)) = f b
  unicorn x = EitherRight (Right x)

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

-- Exercise 13
-- Relative Difficulty: 6
apple :: (Misty m) => m a -> m (a -> b) -> m b
apple = banana . flip furry'

-- Exercise 14
-- Relative Difficulty: 6
moppy :: (Misty m) => [a] -> (a -> m b) -> m [b]
moppy = error "todo"

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

-- Exercise 16
-- Relative Difficulty: 6
-- (bonus: use apple + furry')
banana2 :: (Misty m) => (a -> b -> c) -> m a -> m b -> m c
banana2 = error "todo"

-- 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 = error "todo"

-- 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 = error "todo"

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

-- Exercise 19
-- Relative Difficulty: 9
instance Fluffy (State s) where
  furry = error "todo"

-- Exercise 20
-- Relative Difficulty: 10
instance Misty (State s) where
  banana = error "todo"
  unicorn = error "todo"