Verifying Probabilistic Correctness in Isabelle with pGCL

This paper presents a formalisation of pGCL in Isabelle/HOL. Using a shallow embedding, we demonstrate close integration with existing automation support. We demonstrate the facility with which the model can be extended to incorporate existing results, including those of the L4.verified project. We motivate the applicability of the formalism to the mechanical verification of probabilistic security properties, including the effectiveness of side-channel countermeasures in real systems.