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How to prove algebraic inductive hypotheses without induction

With applications to the correctness of data type implementation

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5th Conference on Automated Deduction Les Arcs, France, July 8–11, 1980 (CADE 1980)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 87))

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Abstract

This paper proves the correctness of algebraic methods for deciding the equivalence of expressions by applying rewrite rules, and for proving inductive equational hypotheses without using induction; it also shows that the equations true in the initial algebra are just those provable by structural induction. The major results generalize, simplify and rigorize Musser's method for proving inductive hypotheses with the Knuth-Bendix algorithm; our approach uses a very general result, that (under certain conditions) an equation is true iff it is consistent. Finally, we show how these results can be extended to proving the correctness of an implementation of one data abstraction by another.

supported in part by NSF Grant MCS-7816783.

On leave; supported in part by NSF Grant No. MCS-7818918.

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Authors and Affiliations

  1. SRI International, 333 Ravenswood Ave., 94025, Menlo Park, CA

    J. A. Goguen

  2. Computer Science Dept., UCLA, 90024, Los Angeles, CA

    J. A. Goguen

Authors
  1. J. A. Goguen
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Wolfgang Bibel Robert Kowalski

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© 1980 Springer-Verlag Berlin Heidelberg

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Goguen, J.A. (1980). How to prove algebraic inductive hypotheses without induction. In: Bibel, W., Kowalski, R. (eds) 5th Conference on Automated Deduction Les Arcs, France, July 8–11, 1980. CADE 1980. Lecture Notes in Computer Science, vol 87. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-10009-1_27

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  • DOI: https://doi.org/10.1007/3-540-10009-1_27

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  • Print ISBN: 978-3-540-10009-6

  • Online ISBN: 978-3-540-38140-2

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