Our attempt to give semantics to a core, functional probabilistic programming language uses computable distributions. The semantics uses largely standard techniques from denotational semantics. One nice property of computable distributions is that they are completely characterized by a sampling algorithm. Hence, it is possible to faithfully implement (in a Turing-complete language) a semantics based on computable distributions as a sampling library. We are interested in the pros and cons of using computable distributions as opposed to measure theory in giving semantics to probabilistic programming languages.
This is joint work with Greg Morrisett.