Salvador Lucas
José Meseguer
ABSTRACT
Types (or sorts) are pervasive in computer science and in rewritingbased programming languages, which often support subtypes (subsorts) and subtype polymorphism. Programs in these languages can be modeled as order-sorted term rewriting systems (OS-TRSs). Often, termination of such programs heavily depends on sort information. But few techniques are currently available for proving termination of OS-TRSs; and they often fail for interesting OS-TRSs. In this paper we generalize the dependency pairs approach to prove termination of OS-TRSs. Preliminary experiments suggest that this technique can succeed where existing ones fail, yielding easier and simpler termination proofs
- B. Alarcón, R. Gutiérrez, and S. Lucas. Context-Sensitive Dependency Pairs. In N. Garg and S. Arun-Kumar, editors Proc. of the 26th Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS'06, LNCS 4337:297--308, Springer-Verlag, Berlin, 2006.]] Google Scholar
Digital Library
- B. Alarcón, R. Gutiérrez, and S. Lucas. Improving the Context-Sensitive Dependency Graph. Electronic Notes in Theoretical Computer Science, 188:91--103, 2007.]] Google ScholarDigital Library
- T. Aoto. Solution to the Problem of Zantema on a Persistent Property of Term Rewriting Systems. Journal of Functional and Logic Programming, 2001(11):1--20, 2001.]]Google Scholar
- T. Aoto and T. Yamada. Dependency Pairs for Simply Typed Term Rewriting. In J. Giesl, editor, Proc. of the 16th International Conference on Rewriting Techniques and Applications, RTA'05, LNCS 3467:120--134, Springer-Verlag, Berlin, 2005.]] Google ScholarDigital Library
- T. Arts and J. Giesl. Termination of Term Rewriting Using Dependency Pairs Theoretical Computer Science, 236:133--178, 2000.]] Google ScholarDigital Library
- P. Borovanský, C. Kirchner, H. Kirchner, and P.-E. Moreau. ELAN from a rewriting logic point of view. Theoretical Computer Science, 285:155--185, 2002.]] Google ScholarDigital Library
- M. Clavel, F. Durán, S. Eker, P. Lincoln, N. Martí-Oliet, J. Meseguer, and C. Talcott. All About Maude ¿ A High-Performance Logical Framework. Lecture Notes in Computer Science 4350, 2007.]] Google ScholarDigital Library
- N. Dershowitz. Orderings for term rewriting systems. Theoretical Computer Science, 17(3):279--301, 1982.]]Google ScholarCross Ref
- N. Dershowitz. Termination by Abstraction. In B. Demoen and V. Lifschitz, editors, Proc. of 20th International Conference on Logic Programming, ICLP'04, LNCS 3132:1--18, Springer-Verlag, Berlin, 2004.]]Google Scholar
- F. Durán, S. Lucas, C. Marché, J. Meseguer, and X. Urbain. Proving Termination of Membership Equational Programs. In P. Sestoft and N. Heintze, editors, Proc. of ACM SIGPLAN 2004 Symposium PEPM'04, pages 147--158. ACM Press, 2004.]] Google ScholarDigital Library
- F. Durán, S. Lucas, and J. Meseguer. MTT: The Maude Termination Tool. In A. Armando, P. Baumgartner, and G. Dowek, editors, Proc. of the Fourth International Joint Conference on Automated Reasoning, IJCAR'08, LNAI to appear, Springer-Verlag, Berlin, 2008. Available at http://www.lcc.uma.es/~duran/MTT.]]Google Scholar
- F. Durán, S. Lucas, J. Meseguer, C. Marché, and X. Urbain. Proving Operational Termination of Membership Equational Programs. Higher-Order and Symbolic Computation, 21(1-2):59--88, 2008.]] Google ScholarDigital Library
- J. Endrullis, J. Waldmann, and H. Zantema. Matrix Interpretations for Proving Termination of Term Rewriting. Journal of Automated Reasoning 40(2-3):195--220, 2008.]] Google ScholarDigital Library
- K. Futatsugi and R. Diaconescu. CafeOBJ Report. World Scientific, AMAST Series, 1998.]]Google Scholar
- J. Giesl, T. Arts, and E. Ohlebusch. Modular Termination Proofs for Rewriting Using Dependency Pairs. Journal of Symbolic Computation, 34(1):21--58, 2002.]] Google ScholarDigital Library
- J. Giesl and D. Kapur. Dependency Pairs for Equational Rewriting. In A. Middeldorp, editor, Proc of the 12th International Conference on Rewriting Techniques and Applications, RTA'01, LNCS 2051:93--107, Springer Verlag, Berlin, 2001.]] Google ScholarDigital Library
- J. Giesl, S. Swiderski, P. Schneider-Kamp, and R. Thiemann. Automated Termination Analysis for Haskell: From Term Rewriting to Programming Languages. In F. Pfenning, editor, Proc of the 18th International Conference on Rewriting Techniques and Applications, RTA'06, LNCS 4098:297--312, Springer Verlag, Berlin, 2006.]] Google ScholarDigital Library
- J. Giesl, P. Schneider-Kamp, and R. Thiemann. APROVE 1.2: Automatic Termination Proofs in the Dependency Pair Framework. In U. Furbach and N. Shankar, editors, Proc. of Third International Joint Conference on Automated Reasoning, IJCAR'06, LNAI 4130:281--286, Springer-Verlag, Berlin, 2006. Available at http://www-i2.informatik.rwth-aachen.de/AProVE.]] Google ScholarDigital Library
- J. Giesl, R. Thiemann, and P. Schneider-Kamp. The Dependency Pair Framework: Combining Techniques for Automated Termination Proofs. In F. Baader and A. Voronkov, editors, Proc. of XI International Conference on Logic for Programming Artificial Intelligence and Reasoning, LPAR'04, volume 3452 of Lecture Notes in Artificial Intelligence, pages 301--331, Montevideo, Uruguay, 2004. Springer-Verlag.]]Google Scholar
- J. Giesl, R. Thiemann, P. Schneider-Kamp, and S. Falke. Mechanizing and Improving Dependency Pairs. Journal of Automatic Reasoning, 37(3):155--203, 2006.]] Google ScholarDigital Library
- I. Gnaedig. Termination of Order-sorted Rewriting. In H. Kirchner and G. Levi, editors, Proc. of the 3th International Conference on Algebraic and Logic Programming, ALP'92, LNCS 632:37--52, Springer-Verlag, Berlin, 1992.]] Google ScholarDigital Library
- J. Goguen, J.-P. Jouannaud, and J. Meseguer. Operational Semantics for Order-Sorted Algebra. In Proc. of Automata, Languages and Programming, 12th Colloquium, ICALP'85, LNCS 194:221--23, Springer-Verlag, Berlin, 1985.]] Google ScholarDigital Library
- J. Goguen and J. Meseguer. Order-sorted algebra I: Equational deduction for multiple inheritance, overloading, exceptions and partial operations. Theoretical Computer Science, 105:217--273, 1992.]] Google ScholarDigital Library
- J.A. Goguen, T. Winkler, J. Meseguer, K. Futatsugi, and J.-P. Jouannaud. Introducing OBJ. In Software Engineering with OBJ: algebraic specification in action, Kluwer, 2000.]]Google ScholarCross Ref
- N. Hirokawa and A. Middeldorp. Dependency Pairs Revisited. In V. van Oostrom, editor, Proc. of 15th International Conference on Rewriting Techniques and Applications, RTA'04, LNCS 3091:249--268, Springer-Verlag, 2004.]]Google Scholar
- N. Hirokawa and A. Middeldorp. Automating the Dependency Pair Method. Information and Computation, 199:172--199, 2005.]]Google ScholarDigital Library
- N. Hirokawa and A. Middeldorp. Tyrolean termination tool: Techniques and features. Information and Computation, 205:474--511, 2007.]] Google ScholarDigital Library
- P. Hudak, S. Peyton-Jones, and P. Wadler. Report on the Functional Programming Language Haskell: a non'strict, purely functional language. SIGPLAN Notices, 27:1--164, 1992.]] Google ScholarDigital Library
- S. Kamin and J.-J. Lévy. Two generalizations of the recursive path ordering. University of Illinois at Urbana-Champaign. Unpublished manuscript, 1980.]]Google Scholar
- C. Kirchner, H. Kirchner, and J. Meseguer. Operational Semantics of OBJ3 In T. Lepistö and A. Salomaa, editors, Proc. of 15th Intl. Coll. on Automata, Languages and Programming, ICALP'88, LNCS 317:287--301, Springer-Verlag, Berlin, 1988.]] Google ScholarDigital Library
- K. Kusakari, M. Nakamura, and Y. Toyama. Argument Filtering Transformation. In G. Nadathur, editor, Proc. of International Conference on Principles and Practice of Declarative Programming, PPDP'99, LNCS 1702:47--61, Springer-Verlag, 1999.]] Google ScholarDigital Library
- K. Kusakari and M. Sakai. Enhancing dependency pair method using strong computability in simply-typed term rewriting. Applicable Algebra in Engineering, Communication and Computing 18:407--431, 2007.]]Google ScholarDigital Library
- S. Lucas. MU-TERM: A Tool for Proving Termination of Context-Sensitive Rewriting In V. van Oostrom, editor, Proc. of 15th International Conference on Rewriting Techniques and Applications, RTA'04, LNCS 3091:200--209, Springer-Verlag, Berlin, 2004. Available at http://zenon.dsic.upv.es/muterm.]]Google Scholar
- S. Lucas. Termination of on-demand rewriting and termination of OBJ programs. In Proc. of 3rd International Conference on Principles and Practice of Declarative Programming, PPDP'01, pages 82--93, ACM Press, 2001.]] Google ScholarDigital Library
- S. Lucas and J. Meseguer. Operational Termination of Membership Equational Programs: the Order-Sorted Way. In G. Rosu, editor, Proc. of the 7th International Workshop on Rewriting Logic and its Applications, WRLA'08, Electronic Notes in Theoretical Computer Science, to appear, 2008.]] Google ScholarDigital Library
- C. Marché and X. Urbain. Modular and incremental proofs of ACtermination. Journal of Symbolic Computation, 38(1):873--897, 2004.]]Google ScholarCross Ref
- J. Meseguer. Membership algebra as a logical framework for equational specification. In F. Parisi-Presicce, editor, Proc. of WADT'97, volume 1376 of Lecture Notes in Computer Science, LNCS 1376:18--61, Springer-Verlag, 1998.]] Google ScholarDigital Library
- U. Nilsson and J. Maluszynski. Logic, Programming and Prolog (2nd. ed.) John Wiley & Sons, 1995]] Google ScholarDigital Library
- E. Ohlebusch. Advanced Topics in Term Rewriting. Springer-Verlag, Berlin, 2002.]] Google ScholarDigital Library
- P.C. Ölveczky and O. Lysne. Order-Sorted Termination: The Unsorted Way. In M. Hanus and M. Rodríguez-Artalejo, editors, Proc. of the 5th International Conference on Algebraic and Logic Programming, ALP'96, LNCS 1139:92--106, Springer-Verlag, Berlin, 1996.]] Google ScholarDigital Library
- P. Schneider-Kamp, J. Giesl, A. Serebrenik, and R. Thiemann. Automated Termination Analysis for Logic Programs by Term Rewriting. In R. K. Shyamasundar, editor, Proc. of the 16th International Symposium on Logic-Based Program Synthesis and Transformation, LOPSTR '06, LNCS 4407:177--193, Springer-Verlag, Berlin, 2007.]] Google ScholarDigital Library
- TeReSe, editor, Term Rewriting Systems, Cambridge University Press, 2003.]]Google Scholar
- H. Zantema. Termination of term rewriting: interpretation and type elimination. Journal of Symbolic Computation, 17:23--50, 1994.]] Google ScholarDigital Library
Index Terms
- Order-sorted dependency pairs
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