The Universe of Discourse

A short bibliography of probability monads
Several people helpfully wrote to me to provide references to earlier work on probability distribution monads. Here is a summary:

• Material related to Martin Erwig and Steve Kollmansberger's probability library:
  • Probabilistic Functional Programming in Haskell, their 2006 paper
  • the package, described in the paper, and specifically its probability distribution monad
  • Some commentary on this library, by someone who doesn't put their name on their blog.

• Some stuff from Dan Piponi's blog:
  • "Monads, Vector Spaces and Quantum Mechanics, part I"
  • and part II

• Eric Kidd's blog: "What would a programming language look like if Bayes’ rule were as simple as an if statement?"

I did not imagine that my idea was a new one. I arrived at it by thinking about List as a representation of non-deterministic computation. But if you think of it that way, the natural interpretation is that every list element represents an equally likely outcome, and so annotating the list elements with probabilities is the obvious next step. So the existence of the Erwig library was not a big surprise.

A little more surprising though, were the references in the Erwig paper. Specifically, the idea dates back to at least 1981; Erwig cites a paper that describes the probability monad in a pure-mathematics context.

Nobody responded to my taunting complaint about Haskell's failure to provide support a good monad of sets. It may be that this is because they all agree with me. (For example, the documentation of the Erwig package says "Unfortunately we cannot use a more efficient data structure because the key type must be of class Ord, but the Monad class does not allow constraints for result types.") But a number of years ago I said that the C++ macro processor blows goat dick. I would not have put it so strongly had I not naïvely believed that this was a universally-held opinion. But no, plenty of hapless C++ programmers wrote me indignant messages defending their macro system. So my being right is no guarantee that language partisans will not dispute with me, and the Haskell community's failure to do so in this case reflects well on them, I think.

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