PSI

"PSI is a solver which takes as input a probabilistic program and automatically computes the exact probability density function (PDF) represented by that program. To compute the PDF, PSI uses symbolic inference techniques. It handles probabilistic programs with both discrete and continuous distributions. PSI assumes that loops in the probabilistic program are of finite length. PSI's ability to compute exact PDFs is in contrast to almost all existing techniques which are approximate in nature (these use sampling or variational methods).

The PDF computed by PSI can be used for a variety of queries, including computing the probability of assertions, expectations, performing inference, computing differences, quantifying the loss of precision, and others. Because of this, PSI is a useful platform for encoding applications from various domains that require probabilistic reasoning."

http://psisolver.org/

https://github.com/eth-srl/psi