Monad

The Monad type-class inherits from Applicative (from GHC 7.10 onward; see the Monad as applicative section for more on this):

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

The return function looks just like the pure function of the Applicative type-class (it lifts a value to Monad).

The bind operator (>>=) combines a Monad (m a) with a function (a -> m b), which we'll call a monadic function. The monadic function acts on type a of the first monad and returns a new monad of type (m b).

Let's make our Maybe' type a Monad:

import Control.Monad
import Control.Applicative

data Maybe' a = Just' a | Nothing'
  deriving (Show)

instance Functor Maybe' where
–- ...

instance Applicative Maybe' where
–- ...

instance Monad Maybe' where
  return x = Just' x
  Nothing'  >>= _   = Nothing'
  (Just' x) >>= f   = (f x)

The bind operator for Maybe' says:

• Given Nothing', ignore the monadic function and simply return...