Superposition with Structural Induction

Simon Cruanes (1, 2)

1 VERIDIS - Modeling and Verification of Distributed Algorithms and Systems
2 MOSEL - Proof-oriented development of computer-based systems

Superposition-based provers have been successfully used to discharge proof obligations stemming from proof assistants. However, many such obligations require induction to be proved. We present a new extension of typed superposition that can perform structural induction. Several inductive goals can be attempted within a single saturation loop, by leveraging AVATAR [1]. Lemmas obtained by generalization or theory exploration can be introduced during search, used, and proved, all in the same search space. We describe an implementation and present some promising results.

Domaines: Logique en informatique [cs.LO]; Théorie et langage formel [cs.FL]

Simon Cruanes. Superposition with Structural Induction. Clare Dixon; Marcelo Finger. Frontiers of Combining Systems, Springer, pp.172-188, 2017, 11th International Symposium on Frontiers of Combining Systems - FroCoS 2017, Brasília, Brazil, September 27-29, 2017, Proceedings, 978-3-319-66166-7. ⟨10.1007/978-3-319-66167-4_10⟩. ⟨hal-02062459⟩