Option is both a functor and a monad?

Question

Is Scala's Option both a monad and a functor?

As I understand it, functor is just a data type that exposes the following API:

Functor:

• wrap (or apply) which takes a primitive and wraps it inside the functor

• map which takes a functor, unwraps it, applies some function and re-wraps it

So Option is a functor. Because I can apply an Option to a primitive giving me Option[T]. I can also map on Option to obtain what's inside the functor and repackage inside Option.

How is monad different? I had thought that a monad also had an apply function and a map function. From this article I gather that a monad also has flatMap? Which is defined as simply map but without repackaging the result inside a monad? (Or is it map without repacking the result inside a functor?!)

Since Option supplies both map and flatMap does that mean that Option is both a functor and a monad?

Answer 1

Short answer: Yes.

Longer answer: Every monad is an applicative functor and every applicative functor is a functor. In Object-Oriented terms: Monad <: Applicative <: Functor.