Explore probabilistic programming as a method of Bayesian modeling and inference in this 41-minute conference talk by Sam Staton from the University of Oxford. Delve into fully featured probabilistic programming languages with higher-order functions, soft constraints, and continuous distributions. Learn about "quasi-Borel spaces" as a new foundation for higher-order measure theory and discover a modular inference library derived from this foundation. Examine the integration of logic and learning in complex systems, with insights from recent papers presented at ESOP 2017, LICS 2017, and POPL 2018. Cover topics including synthetic measure theory, random elements, and modular inference algorithms, while gaining a deeper understanding of the opportunities offered by combining formal reasoning and statistical approaches in the field of probabilistic programming.