Abstract
We present in this paper a narrowing-based proof search method for inductive theorems. It has the specificity to be grounded on deduction modulo and to yield a direct translation from a successful proof search derivation to a proof in the sequent calculus. The method is shown to be sound and refutationally correct in a proof theoretical way.
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References
Baader, F., Nipkow, T.: Term Rewriting and all That. Cambridge University Press (1998)
Barthe, G., Cirstea, H., Kirchner, C., Liquori, L.: Pure Patterns Type Systems. In: Principles of Programming Languages (POPL 2003), ACM, New Orleans (2003)
Berregeb, N., Bouhoula, A., Rusinowitch, M.: SPIKE-AC: A System for Proofs by Induction in Associative-Commutative Theories. In: Ganzinger, H. (ed.) RTA 1996. LNCS, vol. 1103, pp. 428–431. Springer, Heidelberg (1996)
Bouhoula, A., Kounalis, E., Rusinowitch, M.: SPIKE: An Automatic Theorem Prover. In: Voronkov, A. (ed.) LPAR 1992. LNCS, vol. 624, pp. 460–462. Springer, Heidelberg (1992)
Bundy, A., Basin, D., Hutter, D., Ireland, A.: Rippling: Meta-Level Guidance for Mathematical Reasoning. Cambridge University Press (2005)
Comon, H., Nieuwenhuis, R.: Induction=i-axiomatization+first-order consistency. Inf. Comput. 159(1-2), 151–186 (2000)
Deplagne, E.: Système de preuve modulo récurrence. Thèse de doctorat, Université Nancy 1 (November 2002)
Deplagne, E., Kirchner, C.: Induction as deduction modulo. Research report A04-R-468, LORIA (November 2004)
Deplagne, E., Kirchner, C., Kirchner, H., Nguyen, Q.-H.: Proof Search and Proof Check for Equational and Inductive Theorems. In: Baader, F. (ed.) CADE 2003. LNCS (LNAI), vol. 2741, pp. 297–316. Springer, Heidelberg (2003)
Dershowitz, N., Plaisted, D.A.: Rewriting. In: Robinson, A., Voronkov, A. (eds.) Handbook of Automated Reasoning, vol. I, ch. 9, pp. 535–610. Elsevier Science (2001)
Dowek, G.: La part du Calcul. Université de Paris 7, Mémoire d’habilitation (1999)
Dowek, G., Hardin, T., Kirchner, C.: HOL-λσ an intentional first-order expression of higher-order logic. Mathematical Structures in Computer Science 11(1), 21–45 (2001)
Dowek, G., Hardin, T., Kirchner, C.: Theorem proving modulo. Journal of Automated Reasoning 31(1), 33–72 (2003)
Ferreira, M.: Termination of Term Rewriting: Well foundedness, Totality and Transformations. PhD thesis, Utrecht University (1995)
Ganzinger, H., Stuber, J.: Inductive theorem proving by consistency for first-order clauses. In: Rusinowitch, M., Remy, J.-L. (eds.) CTRS 1992. LNCS, vol. 656, pp. 226–241. Springer, Heidelberg (1992); Published in 1993
Girard, J.-Y., Lafont, Y., Taylor, P.: Proofs and Types. Cambridge Tracts in Theoretical Computer Science, vol. 7. Cambridge University Press (1989)
Huet, G.: Constrained Resolution: A Complete Method for Higher Order Logic. PhD thesis, Case Western Reserve University (1972)
Hullot, J.-M.: Canonical Forms and Unification. In: Bibel, W., Kowalski, R. (eds.) Proceedings 5th International Conference on Automated Deduction. LNCS, vol. 87, pp. 318–334. Springer, Heidelberg (1980)
Kapur, D., Zhang, H.: An overview of rewrite rule laboratory (RRL). J. Computer and Mathematics with Applications 29(2), 91–114 (1995)
Kirchner, C., Kirchner, H.: Rewriting, solving, proving. A preliminary version of a book (1999), http://www.loria.fr/~ckirchne/rsp.ps.gz
Kirchner, C., Kirchner, H., Rusinowitch, M.: Deduction with symbolic constraints. Revue d’Intelligence Artificielle 4(3), 9–52 (1990); Special issue on Automatic Deduction
Musser, D.: On proving inductive properties of abstract data types. In: Proceedings, Symposium on Principles of Programming Languages, vol. 7, Association for Computing Machinery (1980)
Nahon, F.: Preuve par induction dans le calcul des séquents modulo. PhD thesis, Université Henri Poincaré - Nancy I, Nancy, France, October 26 (2007)
Nahon, F., Kirchner, C., Kirchner, H., Brauner, P.: Inductive Proof Search Modulo. Annals of Mathematics and Artificial Intelligence 55(1-2), 123–154 (2009)
Steel, G.: Proof by consistency - a literature survey (March 1999)
Wack, B.: Typage et déduction dans le calcul de réécriture. Thèse de doctorat, Université Henri Poincaré - Nancy I, October 7 (2005)
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Kirchner, C., Kirchner, H., Nahon, F. (2013). Narrowing Based Inductive Proof Search. In: Voronkov, A., Weidenbach, C. (eds) Programming Logics. Lecture Notes in Computer Science, vol 7797. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-37651-1_9
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DOI: https://doi.org/10.1007/978-3-642-37651-1_9
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