Operators.hs

import Control.Monad
import Control.Applicative

-- Application operators        LHS      |   RHS     |  RESULT
($)   ::                    (a ->   b)  ->    a     ->   b
(<$>) :: Functor f     =>   (a ->   b)  ->  f a     -> f b
(<*>) :: Applicative f => f (a ->   b)  ->  f a     -> f b
(=<<) :: Monad m       =>   (a -> m b)  ->  m a     -> m b

      (5+)             $         5     ==        10

      (5+)            <$>   Just 5     ==   Just 10
      (5+)            <$>   Nothing    ==   Nothing


Just  (5+)            <*>   Just 5     ==   Just 10
Just  (5+)            <*>   Nothing    ==   Nothing
Nothing               <*>   Just 5     ==   Nothing

(+) <$> Just 5        <*>   Just 5     ==   Just 10
(+) <$> Just 5        <*>   Nothing    ==   Nothing
(+) <$> Nothing       <*>   Just 5     ==   Nothing

(\x -> Just (x + 5))  =<<   Just 5     ==   Just 10
(\x -> Just (x + 5))  =<<   Nothing    ==   Nothing
(\x -> Nothing)       =<<   Just 5     ==   Nothing

-- Composition operators             LHS      |       RHS     |       RESULT
(.)        ::                    (b ->   c)  ->   (a ->   b) ->   (a ->   c)
fmap.fmap  :: Functor     f =>   (b ->   c)  -> f (a ->   b) -> f (a ->   c)
liftA2 (.) :: Applicative f => f (b ->   c)  -> f (a ->   b) -> f (a ->   c)
(<=<)      :: Monad m       =>   (b -> m c)  ->   (a -> m b) ->   (a -> m c)