Kristopher Micinski

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Five Minute Monad Madness!!!

Authored: September 22, 2012

Purely functional programming gives us a certain sense of mathematical completeness. Programming with functions gives us a very high level of expressiveness, along with an enhanced view of safety. When you don’t have any state underlying you, you can program in a much more compositional style: you don’t have to worry about as much context. However, it’s not immediately obvious how you can encode stateful operations within purely functional languages. This starts to become a problem when we start to interface our functional languages with the “real world,” which typically involves stateful objects (the infamous “fire missiles” example: once you fire the missiles, they’re gone, you can’t fire them again, and you can’t reset the state of the world).

Initially, the way to deal with this was to basically say: “hey, okay, so state exists, but we’re just not going to use very much of it in our code, and we’ll probably be okay forgetting about it most of the time.” (This was the approach taken by ML, for example, and while some ML uses a good number of references, much does not — or at least presents a purely functional interface to the impure code.) However, the question of how to reconcile the seemingly stateful world with our purely functional upbringings started nagging on the community more and more. A variety of solutions were posited to the community (for example, “Linear Types Can Change the World!”), but none seemed to catch on until…

Monads. It’s a complicated sounding word, expressing a simple-ish concept. Eventually, monads were settled upon by the purely functional (Haskell) community as the way you did stateful feeling things inside a purely functional framework. In reality, you can do much more, as the definition of monads is high level and really doesn’t specify all that much: you can chain things together, need some identities, and some composition laws hold. (I remember the quote “to say something about a category is really to say very little at all…” from somewhere, does anyone remember?)

If you haven’t read the second sentence of every monad tutorial ever “monads come from a category theory.” This is such a canned sentence, it’s almost infamous among the purely functional web community. I feel like I could walk into bars with my suave not-quite-shaven look, order an old fashioned, walk up a cool looking group of people, and say “yeah, you know, monads come from category theory.” To me, this line basically conveys:

I have no idea what category theory is. It sounds really hard, I did a Google image search on it, and I found all these huge Pi symbols with arrows going to them and stuff. But it seems like everyone suddenly gets monads are by saying they come from category theory, it hasn’t helped me yet, but I would be remiss not to mention this in my tutorial, because I totally read a few pages of Mac Lane’s book before bed every night, right after having a cup of my fancy red wine and posting some snarky remarks about left adjoints, primitive recursive functions, and catamorphisms on #haskell.

You can even buy the T-shirt!

It seems like nobody truly gets monads until they write a monad tutorial. In fact, given by the number of monad tutorials on the web, I must only conclude that this is the best monad tutorial in history:

Step one: write a monad tutorial.

So I’m telling you to do that! That’s right! But I’ve got a few rules for you!

  • Make your tutorial five minutes or less.

  • Do whatever you see fit to get the main point of monads across to your audience. (Don’t take your clothes off and flip them inside out, unless you’re going to describe monads by proxy of the Cont monad and continuations.)

  • Don’t use any slides, unless they contain animations. Basically, you can use a whiteboard, and if you don’t want to show your snazzy khaki pants and sweater vest waving your hands across a slightly hazy whiteboard (just erased from your trying to figure out what the hell homotopy type theory is all about), I can forgive you for instead making an animation.

  • (If you really want to use slides to show formulas and pictures things, you can, but I feel like having a bunch of bullet points and speech really kills the mood. But hey, prove me wrong.)

I want to make a small meta comment: I’m not writing this because I’m implying that I have a great five minute monad speech: I don’t! I’m writing this because I think it will be very hard to get across the main point of monads in a very short interval, and I think that most of the tutorials out there on the web are instances of people half understanding the main point, writing up a bunch of stuff, and putting it on their blog. (But hey, that’s probably me right now, too, so you can’t feel too bad.)

Some points:

  • I don’t think monads are the hard part about learning monads! I think it’s that using monads forces you to really grapple with higher order behavior in a very direct way. Monads can be used to create very elaborate higher order control structures, and figuring these out really gives you a run for your money.

  • I say that monads let you chain things together and hide stuff off to the side. Obviously that’s a vast trivialization and not quite right, but that’s why I’m not saying I have a good five minute monad speech yet.

  • I heard a very good quote about monads from Mike Hicks: “Monads are just an API…”

  • By the way, when you finish your five minute monad madness tutorial, please send me a link to it! I would like to post it here! My email address is the obvious one for the name that’s not my first.

  • Eventually I have the idea to get a session at an FP workshop where people can give these…

Love the lambda!

– Kris Micinski

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