Superposition with Structural Induction

Simon Cruanes 1
1 VERIDIS - Modeling and Verification of Distributed Algorithms and Systems
MPII - Max-Planck-Institut für Informatik, Inria Nancy - Grand Est, LORIA - FM - Department of Formal Methods
Abstract : 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.
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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⟩

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