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Journal of Logic and Computation 1995 5(5):631-668; doi:10.1093/logcom/5.5.631
© 1995 by Oxford University Press
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Original Articles

Automated Mathematical Induction

ADEL BOUHOULA1, EMMANUEL KOUNALIS2 and MICHAËL RUSINOWITCH3

1INRIA Lorraine and CRIN BP101, 54600, Villers-lès-Nancy, France. E-mail: bouhoula{at}loria.fr
2Laboratoire d'Informatique 13S 250 Avenue A. Einstein, 06560 Valbonne, France. E-mail: kounalis{at}unice.fr
3INRIA Lorraine and CRIN BP101, 54600 Villers-lès-Nancy, France. E-mail: rusi{at}loria.fr

Proofs by induction arc important in many computer science and artificial intelligence applications, in particular, in program verification and specification systems. We present a new method to prove (and disprove) automatically inductive properties. Given a set of axioms, a well-suited induction scheme is constructed automatically. We call such an induction scheme a test set. Then, for proving a property, we just instantiate it with terms from the test set and apply pure algebraic simplification 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.

Keywords: Theorem proving; mathematical induction; term rewriting systems


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