Automating Type Soundness Proofs via Decision Procedures and Guided Reductions

Operational models of fragments of the Java Virtual Machine and the .NET Common Language Runtime have been the focus of considerable study in recent years, and of particular interest have been specifications and machine-checked proofs of type soundness. In this paper we aim to increase the level of automation used when checking type soundness for these formalizations. We present a semi-automated technique for reducing a range of type soundness problems to a form that can be automatically checked using a decidable first-order theory. Deciding problems within this fragment is exponential in theory but is often efficient in practice, and the time required for proof checking can be controlled by further hints from the user. We have applied this technique to two case studies, both of which are type soundness properties for subsets of the .NET Common Language Runtime. These case studies have in turn aided us in our informal analysis of that system.