Automated Reasoning for Probabilistic Sequential Programs with Theorem Proving

Semantics for nondeterministic probabilistic sequential pro- grams has been well studied in the past decades. In a variety of semantic models, how nondeterministic choice interacts with probabilistic choice is the most significant difference. In He, Morgan, and McIver’s relational model, probabilistic choice refines nondeterministic choice. This model is general because of its predicative-style semantics in Hoare and He’s Unifying Theories of Programming, and suitable for automated reasoning because of its algebraic feature. Previously, we gave probabilistic semantics to the RoboChart notation based on this model, and also formalised the proof that the semantic embedding is a homomorphism, and revealed interesting details. In this paper, we present our mechanisation of the proof in Isabelle/UTP enabling automated reasoning for probabilistic sequential programs including a subset of the RoboChart language. With mechanisation, we even reveal more interesting questions, hidden in the original model. We demonstrate several examples, including an ex- ample to illustrate the interaction between nondeterministic choice and probabilistic choice, and a RoboChart model for randomisation based on binary probabilistic choice.