Using Vampire with Support for Algebraic Datatypes in Type Soundness Proofs

Abstract

In our ongoing project VeriTaS, we aim at automating soundness proofs for type sys- tems of domain-specific languages. In the past, we successfully used previous Vampire versions for automatically discharging many intermediate proof obligations arising within standard soundness proofs for small type systems. With older Vampire versions, encoding the individual proof problems required manual encoding of algebraic datatypes via the theory of finite term algebras. One of the new Vampire versions now supports the direct specification of algebraic datatypes and integrates reasoning about term algebras into the internally used superposition calculus.In this work, we investigate how many proof problems that typically arise within type soundness proofs different Vampire 4.1 versions can prove. Our test set consists of proof problems from a progress proof of a type system for a subset of SQL. We compare running Vampire 4.1 with our own encodings of algebraic datatypes (in untyped as well as in typed first-order logic) to running Vampire 4.1 with support for algebraic datatypes, which uses SMTLIB as input format. We observe that with our own encodings, Vampire 4.1 still proves more of our input problems. We discuss the differences between our own encoding of algebraic datatypes and the ones used within Vampire 4.1 with support for algebraic datatypes.