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Monads

Introduction

Monads are a useful construct for allowing one to chain operations together.

Examples

Some examples of Monads can be seen below:

Reading data from the console

-- do-notation
do
  putStrLn "Enter your name"
  name <- getLine
  putStrLn ("Hello " ++ name)

-- bind notation, messier but better for understanding
putStrLn "Enter your name"
>>= (\_ -> getLine)
>>= (\name -> putStrLn ("Hello " ++ name))

Implementation

The operation that defines a Monad is the >>= operator (also called the bind operator) which has the following type definition:

(>>=) :: Monad m => m a -> (a -> m b) -> m b

Which means >>= takes in an item of type Monad as the first parameter and a function as the second parameter.

The result of Monad m gets mapped to parameter a in the lambda function, which can then be used to produce a new Monad (or pass it to more >>= calls)

Let's define the following recursive data type:

data Turtles a = Last a | Turtle (Turtles a)

To make this an instance of a Monad we need to define the bind (>>=) and return functions.

instance Monad Turtles where
  -- base case
  return a = Last a

  -- when we get a Last type, pass its internal (a primitive) into k
  Last a >>= k = k a

  -- for a Turtle type, pass its internal value (a Last or Turtle) into k
  Turtle a >>= k = Turtle (a >>= k)

For more information, this StackOverflow post provides a great description.