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by Henrik Linnestad, Olav Lysne, Christian Prehofer
http://www4.in.tum.de/publ/papers/fsttcs_prehofer_1996_Publication.pdf
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Abstract:
Abstract. We investigate an integration of the rst-order method of proof by consistency (PBC), also known as term rewriting induction, into theorem proving in higher-order speci cations. PBC may beseenaswell-founded induction over an ordering whichcontains the rewrite relation, and in this paper we extend this method to the higher-order rewrite relation due to Nipkow. This yields a proof procedure which has several advantages over conventional induction. First, it is less control demanding � second, it is more exible in the sense that it does not instantiate variables precisely with every constructor, but instantiates according to the rewrite rules. We showhowanumber of technical problems can be solved in order for this integration to work, and point out some desirable re nements that involve challenging problems. 1
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