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Connection-Driven Inductive Theorem Proving

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Abstract

We present a method for integrating rippling-based rewriting into matrix-based theorem proving as a means for automating inductive specification proofs. The selection of connections in an inductive matrix proof is guided by symmetries between induction hypothesis and induction conclusion. Unification is extended by decision procedures and a rippling/reverse-rippling heuristic. Conditional substitutions are generated whenever a uniform substitution is impossible. We illustrate the integrated method by discussing several inductive proofs for the integer square root problem as well as the algorithms extracted from these proofs.

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Authors and Affiliations

  1. Department of Computer Science, Cornell-University, Ithaca, NY, 14853-7501, USA

    Christoph Kreitz

  2. Department of Computer Science, Carnegie Mellon University, Pittsburgh, PA, 15213-3891, USA

    Brigitte Pientka

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  1. Christoph Kreitz
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  2. Brigitte Pientka
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Kreitz, C., Pientka, B. Connection-Driven Inductive Theorem Proving. Studia Logica 69, 293–326 (2001). https://doi.org/10.1023/A:1013874024997

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