What is a monad?

Question

Having briefly looked at Haskell recently, what would be a brief, succinct, practical explanation as to what a monad essentially is?

I have found most expla

Answer 1

I will try to explain Monad in the context of Haskell.

In functional programming, function composition is important. It allows our program to consist of small, easy-to-read functions.

Let's say we have two functions: g :: Int -> String and f :: String -> Bool.

We can do (f . g) x, which is just the same as f (g x), where x is an Int value.

When doing composition/applying the result of one function to another, having the types match up is important. In the above case, the type of the result returned by g must be the same as the type accepted by f.

But sometimes values are in contexts, and this makes it a bit less easy to line up types. (Having values in contexts is very useful. For example, the Maybe Int type represents an Int value that may not be there, the IO String type represents a String value that is there as a result of performing some side effects.)

Let's say we now have g1 :: Int -> Maybe String and f1 :: String -> Maybe Bool. g1 and f1 are very similar to g and f respectively.

We can't do (f1 . g1) x or f1 (g1 x), where x is an Int value. The type of the result returned by g1 is not what f1 expects.

We could compose f and g with the . operator, but now we can't compose f1 and g1 with .. The problem is that we can't straightforwardly pass a value in a context to a function that expects a value that is not in a context.

Wouldn't it be nice if we introduce an operator to compose g1 and f1, such that we can write (f1 OPERATOR g1) x? g1 returns a value in a context. The value will be taken out of context and applied to f1. And yes, we have such an operator. It's <=<.

We also have the >>= operator that does for us the exact same thing, though in a slightly different syntax.

We write: g1 x >>= f1. g1 x is a Maybe Int value. The >>= operator helps take that Int value out of the "perhaps-not-there" context, and apply it to f1. The result of f1, which is a Maybe Bool, will be the result of the entire >>= operation.

And finally, why is Monad useful? Because Monad is the type class that defines the >>= operator, very much the same as the Eq type class that defines the == and /= operators.

To conclude, the Monad type class defines the >>= operator that allows us to pass values in a context (we call these monadic values) to functions that don't expect values in a context. The context will be taken care of.

If there is one thing to remember here, it is that Monads allow function composition that involves values in contexts.