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Inductive proof search modulo

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Abstract

We present an original narrowing-based proof search method for inductive theorems in equational rewrite theories given by a rewrite system \(\mathcal{R}\) and a set E of equalities. It has the specificity to be grounded on deduction modulo and to rely on narrowing to provide both induction variables and instantiation schemas. Whenever the equational rewrite system \((\mathcal{R},E)\) has good properties of termination, sufficient completeness, and when E is constructor and variable preserving, narrowing at defined-innermost positions leads to consider only unifiers which are constructor substitutions. This is especially interesting for associative and associative-commutative theories for which the general proof search system is refined. The method is shown to be sound and refutationally correct and complete. A major feature of our approach is to provide a constructive proof in deduction modulo for each successful instance of the proof search procedure.

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Authors and Affiliations

  1. LORIA and Rectorat Nancy-Metz, Nancy-Metz, France

    Fabrice Nahon

  2. INRIA, Bordeaux, France

    Claude Kirchner & Hélène Kirchner

  3. LORIA and University of Nancy, Nancy, France

    Paul Brauner

Authors
  1. Fabrice Nahon
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  2. Claude Kirchner
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  3. Hélène Kirchner
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  4. Paul Brauner
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Correspondence to Claude Kirchner.

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Nahon, F., Kirchner, C., Kirchner, H. et al. Inductive proof search modulo. Ann Math Artif Intell 55, 123–154 (2009). https://doi.org/10.1007/s10472-009-9154-5

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