Blog post: Playing With a Game (mainly math, some Haskell)

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#1

I thought I’d share this. It’s primarily about a game theory question, but ends up making some mildly interesting use of a probability library Shae Erisson and I wrote together when we used to get together to hack on random stuff on the weekends.

Let me know if people are interested in seeing this kind of haskell-plus content posted here in the future. Also, the library here isn’t on Hackage because there are already more well-known probability monads on Hackage, but this one is nice in a few ways, such as handling left recursion. I’m open to feedback on whether the value is greater than the cost in Hackage namespace and package dilution.

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#2

Yes, please do share when Haskell can serve to make mathematics palpable. We should see more of this in schools. play.haskell.org has greatly lowered the barrier of sprinkling some Haskell into a lesson.

The blog post is maybe not the right place to mention that, but your Distribution monad is the free monad over the functor that provides the basic affine combination:

data Affine prob x = Affine prob x x
type Distribution prob s = Free (Affine prob) s

Hence every monad P that has an algebra structure

affine :: Affine prob (P x) -> P x

should have a monad morphism Distribution prob s -> P s.

Conceptually, by virtue of the infinite tree structure, Distribution is related to the monad used in the LazyPPL library.

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#3

Interesting! Just a question on naming: why is this defined as a “game”, when there is really a single turn and the participants are independent?

#5

I think it’s a fairly standard use of terminology? Simultaneous game - Wikipedia for example.

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