Probabilities are extensively used in Computer Science. Algorithms use probabilistic choices for improving efficiency or even for tackling problems that are unsolvable with deterministic computing. Recently, (Functional) Probabilistic Programming has been introduced for applications in Machine Learning and Artificial Intelligence. Probabilistic programs are used to describe statistical models and for developing probabilistic data analysis.

In Probabilistic Programming Languages, inference algorithms are often delegated to compilers including optimizations. This program transformations are error prone, yet they should not change the probabilistic models. Hence the need for formal methods to avoid bugs. Developing formal semantics for probabilistic computing is challenging but crucial in order to systematize the analysis and certification of probabilistic programs.

In this talk, I will first introduce functional probabilistic programing and the related problems. Then, I will present recent works in semantics of probabilistic computing, based on approximation of programs according to their use of resources.