Title is literally true. This may not be the best place to learn about these concepts for the first time, because I’m going to focus on knocking down the misconceptions about them.
Then again, it may not be the worst place, for the same reason.
I had promised myself I would not add to the pile of functor or monad “tutorials”, but I’ve been worn down. I gave up when I saw a reddit comment complaining about how Functor was “too hard to understand”, which made me sad, because the correct response to the Functor interface is, “That’s it?”. And while Monad is legitimately a bit more interesting and complex, the correct response to that is not that different.
I am aware of the notorious effect that people “get” monads and then post their own idiosyncratic takes on them. In my defense, this isn’t something I write just after my “ah ha!” moment, I’ve understood them in Haskell’s context for many years now, and actually… this isn’t even about that “ah ha!” moment at all. This is only about what they are. Even if you completely understand everything I write in this post, the real “ah ha!” where you realize just how useful the libraries built up around the monad interface are, the first time you search for a type on Hoogle where you’re like this should exist and it turns out it does in fact exist already, that’s still in your future. In fact I’m quite deliberately not trying to convey that feeling in the interests of getting at simply what the monad interface is. Which isn’t, strictly speaking, a pre-requisite to that experience, but it does help.