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Termination by Abstraction

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Logic Programming (ICLP 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3132))

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Abstract

Abstraction can be used very effectively to decompose and simplify termination arguments. If a symbolic computation is nonterminating, then there is an infinite computation with a top redex, such that all redexes are immortal, but all children of redexes are mortal. This suggests applying weakly-monotonic well-founded relations in abstraction-based termination methods, expressed here within an abstract framework for term-based proofs. Lexicographic combinations of orderings may be used to match up with multiple levels of abstraction.

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References

  1. Arts, T., Giesl, J.: Termination of term rewriting using dependency pairs. Theoretical Computer Science 236, 133–178 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  2. Arts, T., Zantema, H.: Termination of logic programs using semantic unification. In: Proietti, M. (ed.) LOPSTR 1995. LNCS, vol. 1048, pp. 219–233. Springer, Heidelberg (1996)

    Google Scholar 

  3. Bachmair, L., Dershowitz, N.: Commutation, transformation, and termination. In: Siekmann, J.H. (ed.) CADE 1986. LNCS, vol. 230, pp. 5–20. Springer, Heidelberg (1986)

    Google Scholar 

  4. Bellegarde, F., Lescanne, P.: Termination by completion. Applied Algebra on Engineering, Communication and Computer Science 1(2), 79–96 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  5. Borralleras, C., Ferreira, M., Rubio, A.: Complete monotonic semantic path orderings. In: McAllester, D. (ed.) CADE 2000. LNCS, vol. 1831, pp. 346–364. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  6. Chabin, J., Réty, P.: Narrowing directed by a graph of terms. In: Book, R.V. (ed.) RTA 1991. LNCS, vol. 488, pp. 112–123. Springer, Heidelberg (1991)

    Google Scholar 

  7. Codish, M., Genaim, S., Bruynooghe, M., Gallagher, J., Vanhoof, W.: One loop at a time. In: 6th International Workshop on Termination, WST 2003 (June 2003)

    Google Scholar 

  8. Codish, M., Taboch, C.: A semantic basis for the termination analysis of logic programs. J. Logic Programming 41(1), 103–123 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  9. Cousot, P.M., Cousot, R.: Abstract interpretation: A unified lattice model for static analysis of programs by construction or approximation of fixpoints. In: Conference Record of the Fourth Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, Los Angeles, California, pp. 238–252. ACM Press, New York (1977)

    Chapter  Google Scholar 

  10. De Schreye, D., Decorte, S.: Termination of logic programs: The neverending story. J. Logic Programming 19/20, 199–260 (1993)

    Google Scholar 

  11. Dershowitz, N.: Termination of linear rewriting systems. In: Even, S., Kariv, O. (eds.) ICALP 1981. LNCS, vol. 115, pp. 448–458. Springer, Heidelberg (1981)

    Google Scholar 

  12. Dershowitz, N.: Orderings for term-rewriting systems. Theoretical Computer Science 17(3), 279–301 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  13. Dershowitz, N.: Termination of rewriting. J. Symbolic Computation 3(1&2), 69–115 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  14. Dershowitz, N., Hoot, C.: Natural termination. Theoretical Computer Science 142(2), 179–207 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  15. Dershowitz, N., Jouannaud, J.-P.: Rewrite systems. In: van Leeuwen, J. (ed.) Handbook of Theoretical Computer Science. Formal Methods and Semantics, vol. B, ch. 6, pp. 243–320. North-Holland, Amsterdam (1990)

    Google Scholar 

  16. Dershowitz, N., Lindenstrauss, N., Sagiv, Y., Serebrenik, A.: A general framework for automatic termination analysis of logic programs. Applicable Algebra in Engineering, Communication and Computing 12(1/2), 117–156 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  17. Dershowitz, N., Manna, Z.: Proving termination with multiset orderings. Communications of the ACM 22(8), 465–476 (1979)

    Article  MATH  MathSciNet  Google Scholar 

  18. Dershowitz, N., Okada, M., Sivakumar, G.: Confluence of conditional rewrite systems. In: Kaplan, S., Jouannaud, J.-P. (eds.) CTRS 1987. LNCS, vol. 308, pp. 31–44. Springer, Heidelberg (1988)

    Google Scholar 

  19. Dershowitz, N., Plaisted, D.A.: Equational programming. In: Hayes, J.E., Michie, D., Richards, J. (eds.) Machine Intelligence 11: The logic and acquisition of knowledge, ch. 2, pp. 21–56. Oxford Press, Oxford (1988)

    Google Scholar 

  20. 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, Amsterdam (2001)

    Chapter  Google Scholar 

  21. Dershowitz, N., Sivakumar, G.: Goal-directed equation solving. In: Proceedings of the Seventh National Conference on Artificial Intelligence, St. Paul, MN, August 1988, pp. 166–170. AAAI, Menlo Park (1988)

    Google Scholar 

  22. Floyd, R.W.: Assigning meanings to programs. In: Proceedings of Symposia in Applied Mathematics, Providence, RI. Mathematical Aspects of Computer Science, vol. XIX, pp. 19–32. American Mathematical Society, Providence (1967)

    Google Scholar 

  23. Geser, A.: An improved general path order. Applicable Algebra in Engineering, Communication, and Computing 7(6), 469–511 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  24. Geupel, O.: Overlap closures and termination of term rewriting systems. Report MIP-8922, Universität Passau, Passau, West Germany (July 1989)

    Google Scholar 

  25. Giesl, J., Kapur, D.: Dependency pairs for equational rewriting. In: Middeldorp, A. (ed.) RTA 2001. LNCS, vol. 2051, pp. 93–107. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  26. Gries, D.: Is sometime ever better than alway? ACM Transactions on Programming Languages and Systems 1(2), 258–265 (1979)

    Article  MATH  Google Scholar 

  27. Hanus, M.: The integration of functions into logic programming: From theory to practice. J. Logic Programming 19&20, 583–628 (1994)

    Article  MathSciNet  Google Scholar 

  28. Hullot, J.-M.: Canonical forms and unification. In: Bibel, W. (ed.) CADE 1980. LNCS, vol. 87, pp. 318–334. Springer, Heidelberg (1980)

    Google Scholar 

  29. Kamin, S., Lévy, J.-J.: Two generalizations of the recursive path ordering, February 1980. Unpublished note, Department of Computer Science, University of Illinois, Urbana, IL. Available at http://www.ens-lyon.fr / LIP / REWRITING / OLD PUBLICATIONS ON TERMINATION / KAMIN LEVY (viewed June 2004)

    Google Scholar 

  30. Katz, S.M., Manna, Z.: A closer look at termination. Acta Informatica 5(4), 333–352 (1975)

    Article  MATH  MathSciNet  Google Scholar 

  31. Kirby, L., Paris, J.: Accessible independence results for Peano arithmetic. Bulletin London Mathematical Society 14, 285–293 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  32. Lankford, D.S.: On proving term rewriting systems are Noetherian. Memo MTP-3, Mathematics Department, Louisiana Tech. University, Ruston, LA (May 1979) (revised October 1979)

    Google Scholar 

  33. Lee, C.S., Jones, N.D., Ben-Amram, A.M.: The size-change principle for program termination. In: Conference Record of the Twenty-Eighth Symposium on Principles of Programming Languages, London, UK, January 2001, vol. 36(3), pp. 81–92 (2001); ACM SIGPLAN Notices

    Google Scholar 

  34. Manna, Z.: Mathematical Theory of Computation. McGraw-Hill, New York (1974)

    MATH  Google Scholar 

  35. Middeldorp, A.: Personal communication (June 2003)

    Google Scholar 

  36. Ohlebusch, E., Claves, C., Marché, C.: TALP: A tool for the termination analysis of logic programs. In: Narendran, P., Rusinowitch, M. (eds.) RTA 1999. LNCS, vol. 1631, pp. 270–273. Springer, Heidelberg (1999)

    Google Scholar 

  37. Plaisted, D.A.: Semantic confluence tests and completion methods. Information and Control 65(2/3), 182–215 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  38. Sagiv, Y.: A termination test for logic programs. In: Logic Programming: Proceedings of the 1991 International Symposium, San Diego, CA, October 1991, pp. 518–532. MIT Press, Cambridge (1991)

    Google Scholar 

  39. Serebrenik, A.: Termination Analysis of Logic Programs. PhD thesis, Katholieke Universiteit Leuven, Leuven, Belgium (July 2003)

    Google Scholar 

  40. Sintzoff, M.: Calculating properties of programs by valuations on specific models. In: Proceedings of the ACM Conference on Proving Assertions About Programs, January 1972, vol. 7(1), pp. 203–207 (1972)

    Google Scholar 

  41. Tait, W.W.: Intensional interpretations of functionals of finite type I. Journalof Symbolic Logic 32(2), 198–212 (1967)

    Article  MATH  MathSciNet  Google Scholar 

  42. Terese. In: Bezem, M., Klop, J.W., de Vrijer, R. (eds.) Term Rewriting Systems, Cambridge University Press, Cambridge (2002)

    Google Scholar 

  43. Turing, A.M.: Checking a large routine. In: Report of a Conference on High Speed Automatic Calculating Machines, Cambridge, England, pp. 67–69 (1949), University Mathematics Laboratory

    Google Scholar 

  44. Vershaetse, K., De Schreye, D.: Deriving termination proofs for logic programs, using abstract procedures. In: Furukawa, K. (ed.) Proceeedings of the Eighth International Conference on Logic Programming, Cambridge, MA, pp. 301–315. The MIT Press, Cambridge (1991)

    Google Scholar 

  45. Wegbreit, B.: Property extraction in well-founded property sets. IEEE Transactions on Software Engineering SE-1(3), 270–285 (1975)

    MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. School of Computer Science, Tel-Aviv University, Ramat Aviv, Tel-Aviv, 69978, Israel

    Nachum Dershowitz

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  1. Nachum Dershowitz
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Editors and Affiliations

  1. Katholieke Universiteit Leuven, Belgium

    Bart Demoen

  2. Department of Computer Sciences, University of Texas at Austin, USA

    Vladimir Lifschitz

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Dershowitz, N. (2004). Termination by Abstraction. In: Demoen, B., Lifschitz, V. (eds) Logic Programming. ICLP 2004. Lecture Notes in Computer Science, vol 3132. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-27775-0_1

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  • DOI: https://doi.org/10.1007/978-3-540-27775-0_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-22671-0

  • Online ISBN: 978-3-540-27775-0

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