Proof search and proof check for equational and inductive theorems

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 2741, Issue , 2003, Pages 297-316

  Deplagne, Eric ^a   Kirchner, Claude ^a   Kirchner, Hélène ^a   Nguyen, Quang Huy ^a  

^a LORIA   (France)

Author keywords

Automated theorem proving; Computation; Deduction; Induction; Proof assistant; Proof terms; Rewrite rules

Indexed keywords

AUTOMATIC GUIDED VEHICLES; AUTOMATION; CALCULATIONS; ARTIFICIAL INTELLIGENCE; AUTOMATIC PROGRAMMING; CONSTRAINT THEORY; RESEARCH;

AUTOMATED THEOREM PROVING; DEDUCTION; INDUCTION; PROOF ASSISTANT; PROOF TERMS; REWRITE RULES; EQUATIONAL THEOREMS; INDUCTIVE THEOREMS; PROOF CHECKING; PROOF SEARCH;

THEOREM PROVING;

EID: 7044249054     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-540-45085-6_26     Document Type: Conference Paper

References (40)

1. W. Ahrendt, B. Beckert, R. Hähnle, W. Menzel, W. Reil, G. Schellhorn, and P. Schmitt. Integrating automated and interactive theorem proving. In W. Bibel and P. Schmitt, editors, Automated - A Basis for Applications, volume 1. Kluwer Academic Publishers, 1998.
2. M. Abadi, L. Cardelli, P.-L. Curien, and J.-J. Lévy. Explicit substitutions. In ACM, editor, Conf. Rec. 17th Symp. POPL, pages 31-46, 1990.
3. A. W. Appel and A. P. Felty. A semantic model of types and machine instructions for proof-carrying code. In Proc. of 27th POPL, pages 243-253, January 2000.
4. A. W. Appel. Foundational proof-carrying code. In Proc. 16th LICS, pages 247-258, June 2001.
5. H. Barendregt and E. Barendsen. Autarkic computations in formal proofs. Journal of Automated Reasoning, 28(3):321-336, April 2002.
6. M. Bezem, D. Hendriks, and H. de Nivelle. Automated proof construction in type theory using resolution. Journal of Automated Reasoning, 29(3-4):253-275, 2002.
7. P. Borovansky, C. Kirchner, H. Kirchner, and P.-E. Moreau. ELAN from a rewriting logic point of view. Theoretical Computer Science, (285):155-185, July 2002.
8. A. Bouhoula, E. Kounalis, and M. Rusinowitch. Spike: An automatic theorem prover. In Proceedings of the 1st International Conference on Logic Programming and Automated Reasoning, St. Petersburg (Russia), volume 624 of Lecture Notes in Artificial Intelligence, pages 460-462, July 1992.
9. S. Boutin. Using reflection to build efficient and certified decision procedures. In M. Abadi and T. Ito, editors, Proc. TACS’97, volume 1281 of Lecture Notes in Computer Science, pages 515-529, 1997.
10. R. Boulton, K. Slind, A. Bundy, and M. Gordon. An interface between clam and HOL. In J. Grundy and M. Newey, editors, Proc. of the 11th Int. Conf. TPHOL, volume 1479 of Lecture Notes in Computer Science, pages 87-104, 1998.
11. T. Coquand and G. Huet. The Calculus of Constructions. Information and Computation, 76, 1988.
12. P.-L. Curien, T. Hardin, and J.-J. Lévy. Confluence properties of weak and strong calculi of explicit substitutions. Journal of the ACM, 43(2):362-397, March 1996.
13. A. Church. A formulation of the simple theory of types. Journal of Symbolic Logic, 5:56-68, 1940.
14. H. Cirstea. Calcul de réécriture: fondements et applications. Thèse de Doctorat d’Université, Université Henri Poincaré - Nancy 1, October 2000.
15. H. Cirstea and C. Kirchner. The rewriting calculus-Part I and II. Logic Journal of the Interest Group in Pure and Applied Logics, 9(3):427-498, May 2001.
16. E. Deplagne. Système de preuve modulo récurrence. Thèse de doctorat, Université Nancy 1, November 2002.
17. G. Dowek, T. Hardin, and C. Kirchner. HOL-λσ an intentional first-order expression of higher-order logic. Mathematical Structures in Computer Science, 11(1):21-45, 2001.
18. G. Dowek, T. Hardin, and C. Kirchner. Theorem proving modulo. Journal of Automated Reasoning, 2003. To appear. See also ftp://ftp.inria.fr/INRIA/publication/RR/RR-3400.ps.gz.
19. E. Deplagne and C. Kirchner. Induction as deduction modulo. research report, Loria, 2003. in preparation.
20. G. Dowek. La part du Calcul. 1999. Mémoire d’habilitation, Universit´e de Paris 7.
21. J. Goubault-Larrecq. Well-founded recursive relations. In Proc. 15th Int. Workshop Computer Science Logic (CSL’2001), LNCS 2142, pages 484-497. Springer, Paris, France, 2001.
22. J. Harrison. Metatheory and reflection in theorem proving: A survey and critique. Technical Report CRC-053, SRI Cambridge, UK, 1995. Available at http://www.cl.cam.ac.uk/users/jrh/papers/reflect.dvi.gz+. HT 98.
23. J. Harrison and L. Théry. A sceptic’s approach to combining hoal and mapple. In Journal of Automated Reasoning, volume 21, pages 279-294, 1998.
24. J. Hurd. Integrating gandalf and HOL. In Y. Bertot, G. Dowek, A. Hirschowitz, C. Paulin, and L. Thery, editors, Proc. of TPHOLs’99, volume 1690 of Lecture Notes in Computer Science, pages 311-321, 1999.
25. J.-P. Jouannaud and H. Kirchner. Completion of a set of rules modulo a set of equations. SIAM Journal of Computing, 15(4):1155-1194, 1986.
26. J. Joyce and C. Seger. The HOL-Voss system: Model-checking inside a general-purpose theorem-prover. Lecture Notes in Computer Science, 780:185-198, 1994.
27. H. Kirchner and P.-E. Moreau. Promoting rewriting to a programming language: A compiler for non-deterministic rewrite programs in associativecommutative theories. Journal of Functional Programming, 11(2):207-251, 2001. Report LORIA A01-R- 007.
28. D. Kapur and H. Zhang. An overview of rewrite rule laboratory (rrl). J. Computer and Mathematics with Applications, 29(2):91-114, 1995.
29. F. Leclerc. Termination proof of term rewriting systems with the multiset path ordering: A complete development in the system coq. In Proc. 2nd Int. Conf. on Typed Lambda Calculi and Applications (TLCA-95), LNCS 902, pages 312-327. Springer, Edinburgh, UK, 1995.
30. G. C. Necula. Proof-carrying code. In Proc. of 24th POPL, pages 106-119, January 1997.
31. Q.-H. Nguyen. Calcul de réécriture et automatisation du raisonnement dans les assistants de preuve. Thèse de Doctorat d’Université, Université Henri Poincaré - Nancy 1, Octobre 2002.
32. Q.-H. Nguyen. A constructive decision procedure for equalities modulo AC. In C. Ringeissen, C. Tinelli, R. Treinen, and R. Verma, editors, Proc. of 18th UNIF, pages 59-63, 2002.
33. Q.-H. Nguyen, C. Kirchner, and H. Kirchner. External rewriting for skeptical proof assistants. Journal of Automated Reasoning, 29(3-4):309-336, 2002.
34. G. Necula and P. Lee. Efficient representation and validation of logical proofs. In Proc. LICS’98, pages 93-104, June 1998.
35. L. Paulson. A Generic Tableau Prover and its Integration with Isabelle. Journal of Universal Computer Science, 5(3):73-87, March 1999.
36. C. Paulin-Mohring. Inductive definitions in the system Coq: Rules and properties. In M. Bezem and J. F. Groote, editors, Proc. of the 1st Int. Conf. TLCA, volume 664 of Lecture Notes in Computer Science, pages 328-345, Berlin, 1993.
37. G. Peterson and M. E. Stickel. Complete sets of reductions for some equational theories. Journal of the ACM, 28:233-264, 1981.
38. F. Pfenning and C. Schürmann. System description: Twelf - a meta-logical framework for deductive systems. In H. Ganzinger, editor, Proc. of CADE 16, volume 1632 of Lecture Notes in Computer Science, July 1999.
39. J. Rushby. Integrated formal verification: Using model checking with automated abstraction, invariant generation, and theorem proving. In D. Dams, R. Gerth, S. Leue, and M. Massinek, editors, Theoretical and Practical Aspects of SPIN Model Checking, volume 1680 of Lecture Notes in Computer Science, pages 311-321, 1999.
40. A. Stump and D. L. Dill. Faster proof checking in the Edinburgh Logical Framework. In Proc. of CADE 18, volume 2392 of Lecture Notes in Computer Science, pages 391-406, 2002.