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Automated mathematical induction

Adel Bouhoula 1 Emmanuel Kounalis Michaël Rusinowitch 1
1 EURECA - Proof, Symbolic Computation and Logic
UHP - Université Henri Poincaré - Nancy 1, CRIN - Centre de Recherche en Informatique de Nancy, INRIA Lorraine
Abstract : Proofs by induction are important in many computer science and artifical intelligence applications, in particular, in program verification and specification systems. We present a new method to prove (and disprove) automatically inductives properties. Given a set of axioms, a well-suited induction scheme is constructed automatically. We call such and induction scheme a test set. Then, for proving a property, we just instantiate it with terms from the test set and apply pure algebraic simplifications to the result. This method needs no completion and explicit induction. However it retains their positive features, namely, the completeness of the former and the robustness of the latter. It has been implemented in the theorem-prover SPIKE.
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https://hal.inria.fr/inria-00074894
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Submitted on : Wednesday, May 24, 2006 - 4:49:28 PM
Last modification on : Friday, February 4, 2022 - 3:25:31 AM
Long-term archiving on: : Tuesday, April 12, 2011 - 3:58:50 PM

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Adel Bouhoula, Emmanuel Kounalis, Michaël Rusinowitch. Automated mathematical induction. [Research Report] RR-1663, INRIA. 1992. ⟨inria-00074894⟩

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