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data Tree a = Node a [Tree a] | Leaf a deriving (Show, Eq)

sample = Node 1 [Node 2 [Leaf 5, Leaf 6], Node 3 [Leaf 7], Node 4 [Leaf 8]]

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reduce f (Leaf x) = x
reduce f (Node x xs) = f x . foldr1 f $ map (reduce f) xs

addTree = reduce (+)
multTree = reduce (*)

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class (Functor w) => Comonad w where
  coreturn :: w a -> a
  cojoin   :: w a -> w (w a)
  (=>>)    ::  w a -> (w a -> b) -> w b 

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instance Functor Tree where
  fmap f (Leaf a) = Leaf $ f a
  fmap f (Node a b) = Node (f a) (map (fmap f) b)
  
instance Comonad Tree where
  coreturn (Leaf a) = a
  coreturn (Node a _) = a
  cojoin l@(Leaf a)   = Leaf l
  cojoin n@(Node a b) = Node n (map cojoin b)
  x =>> f = fmap f $ cojoin x

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sums = sample =>> addTree

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class Monad m where  
    return :: a -> m a  
    (>>=) :: m a -> (a -> m b) -> m b

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data Identity a = Identity a deriving Show

instance Monad Identity where
  return = Identity
  (Identity a) >>= f = f a

m1 = Identity 3

addThree x = return $ x+3
bindExample1 = m1 >>= addThree

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instance Monad Maybe where
  return = Just
  Nothing >>= f = Nothing
  (Just a) >>= f = f a

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instance Monad [] where
  return x = [x]
  xs >>= f = concatMap f xs

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instance Monad ((->) r) where
  return = const
  {-Note:
    (>>=) :: (r -> a) -> (a -> (r -> b)) -> (r -> b)
    f :: (r -> a)
    g :: (a -> (r -> b))
  -}
  f >>= g = \r -> g (f r) r

-- using >>= and lambda functions