Probabilistic Predicate Transformers

Predicate transformers facilitate reasoning about imperative programs, including those exhibiting demonic non-deterministic choice. Probabilistic predicate transformers extend that facility to programs containing probabilistic choice, so that one can in principle determine not only whether a program is guaranteed to establish a certain result, but also its probability of doing so. We bring together independent work of Claire Jones and Jifeng He, showing how their constructions can be made to correspond; from that link between a predicate-based and a relation-based view of probabilistic execution we are able to propose `probabilistic healthiness conditions', generalising those of Dijkstra for ordinary predicate transformers. The associated calculus seems suitable for exploring further the rigorous derivation of imperative probabilistic programs. Keywords: Probability, predicate transformers, non-determinism, verification, refinement, imperative programming, program derivation, Galois c..