PZ: A Z-based Formalism for Modeling Probabilistic Behavior

Probabilistic techniques in computer programs are becoming more and more widely used. Therefore, there is a big interest in the formal specification, verification, and development of probabilistic programs. In our work-in-progress project, we are attempting to make a constructive framework for developing probabilistic programs formally. The main contribution of this paper is to introduce an intermediate artifact of our work, a Z-based formalism called PZ, by which one can build set theoretical models of probabilistic programs. We propose to use a constructive set theory, called CZ set theory, to interpret the specifications written in PZ. Since CZ has an interpretation in Martin-Löf’s theory of types, this idea enables us to derive probabilistic programs from correctness proofs of their PZ specifications. Keywords—formal specification, formal program development, probabilistic programs, CZ set theory, type theory.