Probabilistic Modeling in Haskell

I translated the probabilistic modeling example from F# to Haskell. I ran into the restricted monad problem, because Support implemented as a Set requires the type class Ord. Perhaps, this problem is a step up from F#: if one uses a set with a type that doesn't implement Comparable, the error only appears at run-time in F#! 

I don't think this sample as translated does justice to Haskell. I ought to look at the Haskell implementation in the original paper by Ramsey and Pfeffer. In addition, the blog randomhacks.net has a whole series about probabilistic monads in Haskell, culminating in a paper (PDF). There also a functional pearl about probabilistic functional programming in Haskell.

Implementing Probabilistic Modeling Using Monads in F# and Scala

For my induction into Scala, I wanted to translate the probabilistic monad of Chapter 9 of Expert F# (Introducing Language-Oriented Programming). The idea, based on the paper Stochastic Lambda Calculus and Monads of Probability Distributions, is to define a probability monad to compute over distributions of a domain instead of the domain itself. We limit ourselves to distributions over discrete domains characterized by three functions:

1. sampling


2. support
   (i.e. a set of values where all elements outside the set have zero chance of being sampled)


3. expectation of a function over the distribution
   (e.g. the probability of selecting element A by evaluating the function f(x) = 1 if x equals A and 0 otherwise)

Contrast the F# implementation with the Scala implementation. The Scala implementation closely follows the F# one, except for one major frustration: the type inference is not as powerful in Scala, as all function arguments must be declared.

Perhaps, I am missing a few tricks because I am new to Scala. If anyone has any suggestions for improving the Scala implementation, please share.

Cross-posted to the Scala wiki.