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A recursion planning analysis of inductive completion

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Abstract

We use the AI proof planning techniques ofrecursion analysis andrippling as tools to analyze so-calledinductionless induction proof techniques. Recursion analysis chooses induction schemas and variables and rippling controls rewriting in explicit induction proofs. They provide a basis for explaining the success and failure of inductionless induction, both in deduction of critical pairs and in their simplification. Furthermore, these explicit induction techniques motivate and provide insight into advancements in inductive completion algorithms and suggest directions for further improvements. Our study includes an experimental comparison of Clam, an explicit induction theorem prover, with an implementation of Huet and Hullot's inductionless induction.

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References

  1. R. Aubin, Some generalization heuristics in proofs by induction,Actes du Colloque Construction: Amelioration et Verification des Programmes INRIA (1975).

  2. L. Bachmair, Proofs by consistency in equational theories,Proc. LICS (1988).

  3. R. Barnett, An implementation and evaluation of inductive completion, MSc Thesis, University of Edinburgh (1990).

  4. D. Basin and T. Walsh, Difference matching, in:Proc. 11th Int. Conf. on Automated Deduction (CADE-11), Saratoga Springs, New York, June 1992 (Springer) pp. 295–309.

  5. S. Biundo, B. Hummel, D. Hutter and C. Walther, The Karlsruhe induction theorem proving system, in:8th Int. Conf. on Automated Deduction, Oxford, UK (1986).

  6. R. Boyer and J. Moore,A Computational Logic, ACM Monograph Series (Academic Press, 1979).

  7. A. Bundy, F. van Harmelen, J. Hesketh, A. Smaill and A. Stevens, A rational reconstruction and extension of recursion analysis, DAI Research Paper No. 419, University of Edinburgh (1989).

  8. A. Bundy, A. Stevens, F. van Harmelen, A. Ireland and A. Smaill, Rippling: A heuristic for guiding inductive proofs, Research Paper No. 567, Department of Artificial Intelligence, Edinburgh (1991). To appear in Artificial Intelligence.

    Google Scholar 

  9. R.M. Burstall and J. Darlington, A transformation system for developing recursive programs, J. Assoc. Comput. Mach. 24(1977)44–67.

    Google Scholar 

  10. N. Dershowitz, Applications of the Knuth-Bendix completion procedure,Proc. Seminaire d'Informatique Theorique (1982).

  11. L. Fribourg, A strong restriction of the inductive completion procedure,Proc. ICALP 13 (1986), LNCS 226 (Springer).

  12. R. Göbel, A specialized Knuth-Bendix algorithm for inductive proofs,Proc. Combinatorial Algorithms in Algebraic Structures (1985).

  13. B. Gramlich, Inductive theorem proving using refined unfailing completion techniques, SEKI Report SR-89-14.

  14. F. van Harmelen, The Clam proof planner, Technical Report No. 4, Department of Artificial Intelligence, University of Edinburgh (1989).

  15. G. Huet and J.-M. Hullot, Proofs by induction in equational theories with constructors, INRIA (1982).

  16. J.-P. Jouannaud and E. Kornalis, Automatic proofs by induction in equational theories without constructors,Proc. LICS (1986).

  17. W. Küchlin, Inductive completion by ground proof transformation, Technical Report No. 87-08, Department of Computer and Information Sciences, University of Delaware (1987).

  18. D.R. Musser, On proving inductive properties of abstract data types, in:ACM Symp. on Principles of Programming Languages, Las Vegas (1980) pp. 1154–1162.

  19. U. Reddy, Term rewriting induction,Proc. CADE 10 (1990), LNAI 449 (Springer).

  20. A. Stevens, A rational reconstruction of Boyer and Moore's technique for constructing induction formulas,Proc. ECAI-88, Research Paper No. 360, Department of Artificial Intelligence, University of Edinburgh.

  21. H. Zhang, D. Kapur and M. Krishnamoorthy, A mechanizable induction principle for equational specifications,Proc. CADE 9 (1988), LNCS 310 (Springer).

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Authors and Affiliations

  1. ICL Cavendish Road, SG1 3DS, Stevenage, Herts, UK

    Richard Barnett

  2. Max-Planck-Institut, Im Stadtwald, 6600, Saarbrücken, Germany

    David Basin

  3. University of Edinburgh, 80 South Bridge, EH1 1HN, Edinburgh, Scotland, UK

    Jane Hesketh

Authors
  1. Richard Barnett
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  2. David Basin
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  3. Jane Hesketh
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Barnett, R., Basin, D. & Hesketh, J. A recursion planning analysis of inductive completion. Ann Math Artif Intell 8, 363–381 (1993). https://doi.org/10.1007/BF01530798

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