Explore a conference talk on formalizing a probabilistic programming language using the Coq proof assistant. Delve into the use of intrinsically-typed syntax and dependent types for semantic values in this formalization effort. Learn about the application of Coq's features to simplify notation in concrete examples and enable equational reasoning for probabilistic programs. Discover how this work contributes to ongoing formal verification experiments in security proofs and artificial intelligence, supporting the diverse features of probabilistic programming.