Obligatory Monad Post

I'm taking a break from blogging for a while, but before I go, here is a (now cliché) blog post on monads.

There are far more precise, formal descriptions out there; however, I'll give a practical but imprecise description of monads that I believe makes them easier to think about:

A monad is a datatype¹ that allows us to: represent computations² that have some structured³ result, and chain such computations together⁴

1. The datatype defines two operations, which (in Haskell parlance) are called bind (»=) and return. return places a value in the monad, and bind is used to pass this monadic value to another function. Implementations of these operations must satisfy certain laws.
2. Some expression to be evaluated.
3. The result has some additional context. For example, that context could be that the computation may fail (Haskell’s Maybe monad), or that it is non-deterministic (List), or that some interaction with the outside-world occurs (IO).
4. Sequential composition. We can combine monadic values by passing them between functions that operate on them (using the bind operator)

Here’s an example in Haskell:

-- Placing a value inside the context of the Maybe monad, using 'return'
x :: Maybe Int 
x = return 3
 
-- Let's define a function to operate on x
-- It takes in a non-monadic value and produces a monadic value
f :: Int -> Maybe String 
f a = return $ show a
 
-- Lets apply function f to value 'inside' x using the bind operator
applyFtoX :: Maybe String 
applyFtoX = x >>= f

As a bonus, here’s an example in Scala making use of the Writer monad from the Scalaz library. The Writer monad is useful for computations that accumulate some additional output alongside the result (e.g. logging).

I hope this has been useful 🙂