Linking theories of probabilistic programming

Formal methods advocate the critical role played by the algebraic approach in specification and implementation of programs. Traditionally, a top-down approach (with denotational model as its origin) links the algebra of programs with the denotational representation by establishment of the soundness and completeness of the algebra against the given model, while a bottom-up approach (a journey started from operational model) introduces a variety of bisimulations to establish the equivalence relation among programs. This paper follows up a new way presented in [1] to handle probabilistic programming. Our approach takes an algebra of probabilistic programs as its foundation, and then generates both denotational model and transition system, and explores the consistency among three types of representations.