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.