10 Monads

10.1 Overview

../code/Class2.hs

data Tree e = Empty | Branch e (Tree e) (Tree e)
 deriving (Show, Eq)

instance Functor Tree where
  -- fmap :: (a -> b) -> Tree a -> Tree b
  fmap f Empty          = Empty
  fmap f (Branch x l r) = Branch (f x) (fmap f l) (fmap f r)


instance Monad Tree where
  -- return :: a -> Tree a
  return x = Branch x Empty Empty

  -- bind :: Tree a -> (a -> Tree b) -> Tree b
  Empty >>= k = Empty
  (Branch x l r) >>= k = let l' = l >>= k
                             r' = r >>= k
                          in case k x of
                             Empty -> Empty
                             Branch z _ _ -> Branch z l' r'
















-- Ignore this
-- Avert your eyes
instance Applicative Tree where
  pure x = Branch x Empty Empty
  (<*>) = undefined