ion for Concurrent Programs Ashutosh Gupta, Corneliu Popeea, and Andrey Rybalchenko Technische Universität München Abstract. Verification based on abstraction refinement is a successful technique for checking program properties. Conventional abstraction refinement schemes increase precision of the abstraction monotonically, and therefore cannot recover from overly precise refinement decisions. ...

Pop-refinement is an approach to stepwise refinement, carried out inside an interactive theorem prover by constructing a monotonically decreasing sequence of predicates over deeply embedded target programs. The sequence starts with a predicate that characterizes the possible implementations, and ends with a predicate that characterizes a unique program in explicit syntactic form. Compared to ex...

We develop algebraic semantics of refinement modal logic using duality theory. Refinement modal logic has quantifiers that are interpreted using a refinement relation. A refinement relation is like a bisimulation, except that from the three relational requirements only ‘atoms’ and ‘back’ have to be satisfied. We study the dual notion of refinement on algebras and present algebraic semantics of ...

We present a generalisation of data refinement in Z, called IO-refinement, that allows changes in input and output parameters of operations. Several informal motivations for the desirability of such a refinement relation are given, followed by a formal derivation that demonstrates its theoretical soundness. It is proved that IO-refinement indeed generalizes data refinement. Several theorems are...

We automatically verify Back’s atomicity refinement law and a classical data refinement law for action systems. Our novel approach mechanises a refinement calculus based on Kleene algebras in an off the shelf resolution and paramodulation theorem prover and a counterexample checker with heuristics for hypothesis learning. The proofs are supported by a toolkit of meaningful refinement laws that ...

While refinement is at the heart of the B Method so far no automatic refinement checker has been developed for it. In this paper we present a refinement checking algorithm and implementation for B. It is based on using an operational semantics of B, obtained in practice by the ProB animator. The refinement checker has been integrated into ProB toolset and we present various case studies and emp...