An extension of an automated termination method of recursive functions

International Journal of Foundations of Computer Science

Volumn 13, Issue 3, 2002, Pages 361-386

  Kamareddine, Fairouz ^a   Monin, Francois ^b  

^a HERIOT WATT UNIVERSITY   (United Kingdom)

^b CAMPUS DE BEAULIEU   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 26844539996     PISSN: 01290541     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0129054102001163     Document Type: Conference Paper

References (30)

1. T. Arts and J. Giesl. Automatically proving termination where simplification orderings fail. In Proceedings of Theory and Practice of Software Development TAPSOFT'97, volume 1214 of Lecture Notes in Computer Science, 1997. Springer-Verlag.
2. A. Bouhoula and M. Rusinowitch. Implicit induction in conditional theories. Journal of Automated Reasoning, 14(2):189-235, 1995.
3. R. S. Boyer and J S. Moore. A computational logic handbook. Academic Press, 1988.
4. A. Ben Cherifa and P. Lescanne. Termination of rewriting systems by polynomial interpretations and its implementation. Science of Computer Programming, 9(2):137-159, 1987.
5. Dershowitz. Orderings for term-rewriting systems. Theoretical Computer Science, 17(3):279-301, 1982.
6. J. Giesl. Automated termination proofs with measures functions. In Proceedings of the 19th annual german conference on artificial intelligence, volume 981 of Lecture Notes in Artificial Intelligence, pages 149-160, 1995. Springer-Verlag.
7. J. Giesl. Generating polynomial orderings for termination proofs. In Proceedings of the 6th International Conference on Rewriting Techniques and Application, volume 914 of Lecture Notes in Computer Science, 1995. Springer-Verlag.
8. J. Giesl. Termination analysis for functional programs using term orderings. In Proceedings of the Second International Static Analysis Symposium, volume 983 of Lecture Notes in Computer Science, pages 154-171, Glasgow, 1995. Springer-Verlag.
9. G. Huet and J. M. Hullot. Proofs by induction in equational theories with constructors. Journal of Computer and System Sciences, 25(2):239-266, 1982.
10. F. Kamareddine and F. Monin. On formalised proofs of termination of recursive functions. In G. Nadathur, editor, Proceedings of the International Conference on Principles and Practice of Declarative Programming, volume 1702 of Lecture Notes in Computer Science, pages 29-46, 1999. Springer-Verlag.
11. F. Kamareddine and F. Monin. On Automating Inductive and Non-inductive Ter mination Methods. In P.S. Thiagarajan and R. Yap, editors, Proceedings of the Asian Computing Science Conference, volume 1742 of Lecture Notes in Computer Science, pages 177-189, 1999. Springer-Verlag.
12. F. Kamareddine and F. Monin. On the simplification of formal proofs with abstracted propositions in an automated system for program synthesis. Technical report, Heriot-Watt University, 2000.
13. D. Kapur, P. Narendran, and H. Zhang. Automatic inductionless induction using test sets. Journal of Symbolic Computation, 11(1-20:83-111, 1991.
14. D. E. Knuth and P. B. Bendix. Simple word problems in universal algebras. In J. Leech, editor, Computational problems in abstract algebra, pages 263-297. Pergamon Press, 1970.
15. T. Kolbe. Challenge problems for automated termination proofs of term rewriting systems. Technical report, Technische Hochshule Darmstadt, Alexanderstr 10, 64283 Darmstadt, Germany, 1996.
16. J. L. Krivine. Lambda-calculus, Types and Models. Computers and Their Applications. Ellis Horwood, 1993.
17. J. L. Krivine and M. Parigot. Programming with proofs. J. Inf. Process Cybern, 26(3): 149-167, 1990.
18. D. Leivant. Typing and computational properties of lambda expression. Theoretical Computer Science, 44:51-68, 1986.
19. P. Manoury. A user's friendly syntax to define recursive functions as typed lambdaterms. In Proceedings of Type for Proofs and Programs TYPES'94, volume 996 of Lecture Note in Computer Science, 1994. Springer-Verlag.
20. P. Manoury and M. Simonot. Des preuves de totalite de fonctions comme synthese de programmes. PhD thesis, University Paris 7, 1992.
21. P. Manoury and M. Simonot. Automatizing termination proofs of recursively defined functions. Theoretical Computer Science, 135(2):319-343, 1994.
22. F. Monin and M. Simonot. An ordinal measure based procedure for termination of functions. Theoretical Computer Science, 254:63-94, 2001.
23. D. R. Musser. On proving inductive properties of abstract data types. In Proceedings 7th ACM symposium on principles of Programming Languages, ACM, pages 154-162, 1980.
24. F. Nielson and H. R. Nielson. operational semantics of termination types. Nordic Journal of Computing, 3(2):144-187, 1996.
25. M. Parigot. Recursive programming with proofs. Theoretical Computer Science, 94(2):335-356, 1992.
26. C. Sangler. Termination of algorithms over non-freely generated data types. In Proceedings of International Conference on Automated Deduction, volume 1104 of Lecture Notes in Artificial Intelligence, pages 121-136, 1996. Springer-Verlag.
27. J. Steinbach. Generating polynomial orderings. Information Processing Letters, 49, 1994.
28. J. Steinbach. Simplification orderings: history of results. Fundamenta Informaticae, 24:47-87, 1995.
29. J. J. Thiel. Stop losing sleep over incomplete data type specifications. In Proceedings 11th ACM symposium on principles of programming languages, pages 76-82, 1984.
30. C. Walther. On proving the termination of algorithms by machine. Artificial Intelligence, 71(1):101-157, 1994.