See here: Stan: A Probabilistic Programming Language. Journal of Statistical Software. (Bob Carpenter, Andrew Gelman, Matthew D. Hoffman, Daniel Lee, Ben Goodrich, Michael Betancourt, Marcus Brubaker, Jiqiang Guo, Peter Li, Allen Riddell)

And here: Stan is Turing Complete. So what? (Bob Carpenter)

And, the pre-stan version: Fully Bayesian computing. (Jouni Kerman and Andrew Gelman)

Apparently there was some question about whether Stan is a “probabilistic programming language,” so I want to make it clear that it is. In the comment thread, we should be able to resolve any questions on this.