Inductive Theorem Proving by Program Specialisation: Generating proofs for Isabelle using Ecce (Invited talk)
Helko Lehmann, Michaël Leuschel · ePrints Soton (University of Southampton) · 2003
Abstract. In this paper we discuss the similarities between program specialisation and inductive theorem proving, and then show how program specialisation can be used to perform inductive theorem proving. We then study this relationship in more detail for the particular problem of verifying infinite state systems in order to establish a clear link between program specialisation and inductive theorem proving. Indeed, Ecce is a program specialisation system which can be used to automatically generate abstractions for the model checking of infinite state systems. We show that to verify the abstractions generated by Ecce we may employ the proof assistant Isabelle. Thereby Ecce is used to generate the specification, hypotheses and proof script in Isabelle’s theory format. Then, in many cases, Isabelle can automatically execute these proof scripts and thereby verify the soundness of Ecce’s abstraction. In this work we focus on the specification and verification of Petri nets. 1