Monads: Easy or Hard?

Executive summary: they are actually both (or neither). It is easy to learn their definition but hard to grasp the consequences. Or we might say they are easy to know and hard to understand (grok). It is vitally important for both teachers and learners to understand and make this distinction.

Background

The plethora of monad tutorials (well-covered elsewhere) has been intimidating Haskell beginners for years. Beginners understandably assume that anything with over thirty wildly different tutorials must be very difficult to learn. Sadly, this attitude is a self-fulfilling prophecy: it is difficult to learn something which intimidates you, independently of its intrinsic difficulty.

Well-meaning members of the Haskell community have sometimes reacted by going to the other extreme, assuring beginners that monads are actually quite easy, and there’s no reason for all the hype. Unfortunately, this can backfire: if someone is really convinced that monads are easy, they are going to be in for a demoralizing shock.

Both attitudes, however, are wrong! The key is to reject the dualistic easy/hard distinction and replace it with something more nuanced.

Profundity

Monads are not hard; they are not easy; so what are they? They are profound. By this I mean that they have very large implications relative to the size of their definition. Here are some examples of other things that are profound in the same sense:

• Board games like checkers, chess, go, and hex. It takes only a few minutes to learn the rules of these games, yet knowing the rules and being a good player are completely different. The simple rules of these games have many nontrivial and nonobvious "emergent" properties—which, of course, is what makes the games so interesting.

• The lambda calculus, and Turing machines. Explaining how these work takes all of 30 minutes. Studying the implications, of course, has spawned multiple fields of active research.

• Algebraic theories like group theory or category theory. Anyone with only a basic mathematical background can be taught the axioms of a group or a category. But, of course, these particular sets of axioms give rise to incredibly rich structure.

Thankfully, monads (as they arise in Haskell) are much less profound than these examples! But I think the analogy is correct. Understanding the definition of monads is simple: a monad is any type m of kind * -> * which supports the operations

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

subject to some laws. But to really grok all the consequences—common example instances and how they are implemented and used; the relationship to Functor, Applicative, and Monoid; the relationship to the alternative definition in terms of join; all the common combinators like sequence, mapM, (>=>), etc.; and, in the end, to get some sort of intuitive sense for what the monad abstraction is really like—all that takes a long time and a lot of hard work!

Implications for pedagogy

So what does this all mean, practically speaking?

If you are learning about monads: take heart! There is a simple, easily accessible foundation from which to get started, namely, the definition of the Monad type class. Study the Monad methods and their types—and come back to this basic foundation whenever you get confused. But also realize that to gain deep understanding will take hard work over a relatively long period of time.

If you are teaching others about monads: encourage those who are intimidated—but don’t go overboard. Keep directing students back to the fundamental definition, but also provide them with many opportunities to engage with examples. (There is something else important here—examples of implementing monads are on a very different level than examples of using them, and in my experience it’s vitally important that students are explicitly taught to think about the two levels and keep them separate—but that’s a subject for another post.)

Postscript

There’s probably nothing here that hasn’t been said by someone somewhere before, and it seems rather obvious now that I have written it, but I really do think this perspective is sometimes missing from the discussion of pedagogy and Haskell. This perspective really crystallized for me as I was teaching an introductory Haskell course last spring.

Of course, this is much in the same vein as my previous post Abstraction, intuition, and the “monad tutorial fallacy”. I still believe what I wrote there, except for one thing: that post makes it seem like it is possible to have a sudden "aha!" moment where one goes from not understanding monads to understanding monads. I now realize this is wrong, just like no one suddenly goes from "not understanding chess" to "understanding chess". The learning process is simply discontinuous; learners often experience big, sudden jumps in comprehension, and it’s easy to interpret these jumps as going from "not understanding" to "understanding". Immediately after making such a jump, it’s easy to believe that one had no prior understanding at all (which is probably not true), and that there’s nothing more to understand (which is certainly not true).

As a final note, I’ve specifically discussed monads here, but of course everything I’ve said applies to many other concepts as well, such as Applicative, continuations, GADTs, iteratees/pipes/conduits, and so on. I’d love for this to spark more explicit, thoughtful discussion of pedagogy in the community, and not just around monads.