Enhancing dependency pair method using strong computability in simply-typed term rewriting

Applicable Algebra in Engineering, Communications and Computing

Volumn 18, Issue 5, 2007, Pages 407-431

  Kusakari, Keiichirou ^a   Sakai, Masahiko ^a  

^a NAGOYA UNIVERSITY   (Japan)

Author keywords

Dependency pair; Plain function passing; Simply typed term rewriting system; Strong computability; Termination

Indexed keywords

COMPUTABILITY AND DECIDABILITY; COMPUTATIONAL METHODS; FUNCTIONAL ANALYSIS; PROBLEM SOLVING; RECURSIVE FUNCTIONS;

DEPENDENCY PAIR; PLAIN FUNCTION PASSING; RECURSIVE STRUCTURE; SIMPLY TYPED TERM REWRITING SYSTEMS; STRONG COMPUTABILITY;

SYSTEMS ANALYSIS;

EID: 34848844698     PISSN: 09381279     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00200-007-0046-9     Document Type: Article

References (39)

1. Anderson, H., Khoo, S.C.: Affine-based size-change termination. In: Proceedings of the 1st Asign Symposium. On Programming Languages and Systems, LNCS 2895 (APLAS2003), pp. 122-140 (2003)
2. Aoto, T., Yamada, T.: Dependency pairs for simply typed term rewriting. In: Proceedings of the 16th International Conference On Rewriting Techniques and Applications, LNCS 3467 (RTA2005), pp. 120-134 (2005)
3. Arts T. and Giesl J. (2000). Termination of term rewriting using dependency pairs. Theor. Comput. Sci. 236: 133-178
4. Blanqui, F.: Termination and confluence of higher-order rewrite systems. In: Proceedings of the 11th International Conference On Rewriting Techniques and Applications, LNCS 1833 (RTA2000), pp. 47-61 (2000)
5. Blanqui, F.: Higher-order dependency pairs. In: Proceedings of the 8th International Workshop on Termination (WST06), pp. 22-26 (2006)
6. Dershowitz N. (1982). Orderings for term-rewriting systems. Theor. Comput. Sci 17(3): 279-301
7. Dershowitz, N.: Termination dependencies. In: Proceedings of the 6th International Workshop on Termination (WST03), pp. 27-30 (2003)
8. Giesl J., Arts T. and Ohlebusch E. (2002). Modular termination proofs for rewriting using dependency pairs. J. Sym. Comput. 34(1): 21-58
9. Giesl, J., Thiemann, R., Schneider-Kamp, P., Falke, S.: Improving dependency pairs. In: Proceedings of the 10th International Conference on Logic for Programming, Artificial Intelligence and Reasoning, LNAI 2850 (LPAR2003), pp. 165-179 (2003)
10. Giesl, J., Thiemann, R., Schneider-Kamp, P., Falke, S.: Automated termination proofs with AProVE. In: Proceedings of the 15th International Conference On Rewriting Techniques and Applications, LNCS 3091 (RTA2004), pp. 210-220 (2004)
11. Giesl, J., Thiemann, R., Schneider-Kamp, P.: The dependency pair framework: combining techniques for automated termination proofs. In: Proceedings of the 11th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning, LNCS 3452 (LPAR2004), pp. 301-331 (2005)
12. Giesl, J., Thiemann, R., Schneider-Kamp, P.: Proving and disproving termination of higher-order functions. In: Proceedings the 5th International. Workshop on Frontiers of Combining Systems LNAI 3717 (FroCoS'05), pp. 216-231 (2005)
13. Girard, J.-Y.: Interprétation fonctionnelle et élimination des coupures de l'arithmétique d'ordre supérieur. Ph.D. thesis, University of Paris VII (1972)
14. Goguen, J.A.: Higher-order functions considered unnecessary for higher-order programming. In: Truner, D.A. (ed.) Research Topics in Functional Programming. Addison-Wesley Longman Publishing, Reading, pp. 309-351 (1990)
15. Hindley J.R. and Seldin J.P. (1986). Introduction to Combinators and λ-Calculus. Cambridge University Press, Cambridge
16. Hirokawa, N., Middeldorp, A.: Dependency pairs revisited. In: Proceedings of the 15th International Conference On Rewriting Techniques and Applications, LNCS 3091 (RTA04), pp. 249-268 (2004)
17. Jouannaud, J.-P., Rubio, A.: The higher-order recursive path ordering. In: Proceedings of 14th Annual IEEE Symposium on Logic in Computer Science, IEEE Comp. Sci. Press, New York, pp. 402-411
18. Kennaway R., Klop J.W., Sleep M.R. and Vries F.J. (1996). Comparing curried and uncurried rewriting. J. Sym. Comput. 21(1): 15-39
19. Kusakari, K., Nakamura, M., Toyama, Y.: Argument filtering transformation. In: Proceedings of International Conference On Principles and Practice of Declarative Programming, LNCS 1702 (PPDP'99), pp. 47-61 (1999)
20. Kusakari, K.: On proving termination of term rewriting systems with higher-order variables. In: IPSJ Transactions on Programming, vol. 42, no.SIG 7 (PRO 11), pp. 35-45 (2001)
21. Kusakari K. (2004). Higher-order path orders based on computability. IEICE Trans. Inform. Syst. E E87-D(2): 352-359
22. Kusakari K., Sakai M. and Sakabe T. (2005). Primitive inductive theorems bridge implicit induction methods and inductive theorems in higher-order rewriting. IEICE Trans. Inform. Syst. E E88-D(12): 2715-2726
23. Kusakari K. and Chiba Y. (2007). A higher-order Knuth-Bendix procedure and its applications. IEICE Trans. Inform. Syst. E E90-D(4): 707-715
24. Lee, C.S., Jones, N.D., Ben-Amram, A.M.: The size-change principle for program termination. In: Proceedings of the 28th ACM Symposium. On Principles of Programming Languages (POPL2001), pp. 81-92 (2001)
25. Marché C. and Urbain X. (2004). Modular and incremental proofs of AC-termination. J. Sym. Comput. 38: 873-897
26. Middeldorp, A.: Approximating dependency graphs using tree automata techniques. In: Proceedings of the International Joint Conference on Automated Reasoning, LNAI 2083 (IJCAR01), pp. 593-610 (2001)
27. Van Raamsdonk, F.: On termination of higher-order rewriting. In: Proceedings of 12th International Conference On Rewriting Techniques and Applications, LNCS 2051 (RTA2001), pp. 261-275 (2001)
28. Reynolds J. (1998). Definitional interpreters for higher-order programming languages. Higher Order Computation 11(4): 363-397(1998) Reprinted from the Proceedings of the 25th ACM National Conference (1972)
29. Sakai M., Watanabe Y. and Sakabe T. (2001). Dependency pair method for proving termination of higher-order rewrite systems. IEICE Trans. Inform. Syst. E E84-D(8): 1025-1032
30. Sakai M. and Kusakari K. (2005). On dependency pair method for proving termination of higher-order rewrite systems. IEICE Trans. Inform. Syst. E E88-D(3): 583-593
31. Sakurai T., Kusakari K., Sakai M., Sakabe T. and Nishida N. (2007). Usable rules and labeling product-typed terms for dependency pair method in simply-typed term rewriting systems. IEICE Trans. Inform. Syst. J J90-D(4): 978-989
32. Sakurai, T., Kusakari, K., Nishida, N., Sakai, M., Sakabe, T.: Proving sufficient completeness of functional programs based on recursive structure analysis and strong computability. In: Proceedings of the Forum on Information Technology 2005 (FIT2005), Information Technology Letters, LA-001, pp. 1-4, 2005 (in Japanese)
33. Tait T.T. (1967). Intensional interpretation of functionals of finite type. J. Symbolic Logic 32: 198-212
34. Terese: Term Rewriting Systems. Cambridge Tracts in Theoretical Computer Science, vol. 55. Cambridge University Press, Cambridge (2003)
35. Thiemann, R., Giesl, J., Schneider-Kamp, P.: Improved modular termination proofs using dependency pairs. In: Proceedings of the 2nd International Joint Conference on Automated Reasoning, LNAI 3097 (IJCAR2004), pp. 75-90 (2004)
36. Thiemann R. and Giesl J. (2005). The size-change principle and dependency pairs for termination of term rewriting. Appl. Algebra Eng. Commun. Comput. 16(4): 229-270
37. Toyama, Y.: Termination of S-expression rewriting systems: lexicographic path ordering for higher-order terms. In: Proceedings of the 15th International Conference On Rewriting Techniques and Applications, LNCS 3091 (RTA2004), pp. 40-54 (2004)
38. Ullman, Jeffrey D.: Elements of ML Programming. Prentice Hall, Englewood cliffs (1997)
39. Urbain X. (2004). Modular & incremental automated termination proofs. J. Automated Reason. 32(4): 315-355