Program logic for higher-order probabilistic programs in Isabelle/HOL

The verification framework PPV (Probabilistic Program Verification) verifies functional probabilistic programs supporting higher-order functions, continuous distributions, and conditional inference. PPV is based on the theory of quasi-Borel spaces which is introduced to give a semantics of higher-order probabilistic programming languages with continuous distributions. In this paper, we formalize a theory of quasi-Borel spaces and a core part of PPV in Isabelle/HOL. We first construct a probability monad on quasi-Borel spaces based on the Giry monad in the Isabelle/HOL library. Our formalization of PPV is extended so that integrability of functions can be discussed formally. Finally, we prove integrability and convergence of the Monte Carlo approximation in our mechanized PPV. •We formalize quasi-Borel spaces in Isabelle/HOL.•We formalize the probability monad on the category of quasi-Borel spaces.•We formalize the system PPV in Isabelle/HOL.•We verify the Monte Carlo approximation in our mechanized PPV.