Skip to main content
SpringerLink
Log in
Book cover

International Symposium on Functional and Logic Programming

FLOPS 2008: Functional and Logic Programming pp 113–129Cite as

Termination of Narrowing in Left-Linear Constructor Systems

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 4989))

Abstract

Narrowing extends rewriting with logic capabilities by allowing logic variables in terms and replacing matching with unification. Narrowing has been widely used in different contexts, ranging from theorem proving to language design. Surprisingly, the termination of narrowing has been mostly overlooked. In this paper, we present a new approach for analyzing the termination of narrowing in left-linear constructor systems|a widely accepted class of systems|that allows us to reuse existing methods in the literature on termination of rewriting.

This work has been partially supported by the EU (FEDER) and the Spanish MEC under grants TIN2005-09207-C03-02 and Acción Integrada HA2006-0008.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Albert, E., Vidal, G.: The Narrowing-Driven Approach to Functional Logic Program Specialization. New Generation Computing 20(1), 3–26 (2002)

    MathSciNet  MATH  Google Scholar 

  2. Alpuente, M., Falaschi, M., Ramis, M.J., Vidal, G.: Narrowing Approximations as an Optimization for Equational Logic Programs. In: Penjam, J., Bruynooghe, M. (eds.) PLILP 1993. LNCS, vol. 714, pp. 391–409. Springer, Heidelberg (1993)

    Google Scholar 

  3. Antoy, S.: Optimal non-deterministic functional logic computations. In: Hanus, M., Heering, J., Meinke, K. (eds.) ALP 1997 and HOA 1997. LNCS, vol. 1298, pp. 16–30. Springer, Heidelberg (1997)

    Chapter  Google Scholar 

  4. Antoy, S., Ariola, Z.: Narrowing the Narrowing Space. In: Hartel, P.H., Kuchen, H. (eds.) PLILP 1997. LNCS, vol. 1292, pp. 1–15. Springer, Heidelberg (1997)

    Chapter  Google Scholar 

  5. Antoy, S., Echahed, R., Hanus, M.: A Needed Narrowing Strategy. Journal of the ACM 47(4), 776–822 (2000)

    Article  MathSciNet  Google Scholar 

  6. Antoy, S., Hanus, M.: Overlapping Rules and Logic Variables in Functional Logic Programs. In: Etalle, S., Truszczyński, M. (eds.) ICLP 2006. LNCS, vol. 4079, pp. 87–101. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  7. Arroyo, G., Ramos, J.G., Silva, J., Vidal, G.: Improving Offline Narrowing-Driven Partial Evaluation using Size-Change Graphs. In: Puebla, G. (ed.) LOPSTR 2006. LNCS, vol. 4407, pp. 60–76. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  8. Arts, T., Giesl, J.: Termination of Term Rewriting Using Dependency Pairs. Theoretical Computer Science 236(1-2), 133–178 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  9. Baader, F., Nipkow, T.: Term Rewriting and All That. Cambridge University Press, Cambridge (1998)

    Google Scholar 

  10. 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 

  11. Christian, J.: Some Termination Criteria for Narrowing and E-narrowing. In: Kapur, D. (ed.) CADE 1992. LNCS, vol. 607, pp. 582–588. Springer, Heidelberg (1992)

    Google Scholar 

  12. de Dios-Castro, J., López-Fraguas, F.: Extra Variables Can Be Eliminated from Functional Logic Programs. In: Proc. of the 6th Spanish Conf. on Programming and Languages (PROLE 2006), ENTCS, vol. 188, pp. 3–19. (2007)

    Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  14. Dershowitz, N., Sivakumar, G.: Goal-Directed Equation Solving. In: Proc. of 7th National Conf. on Artificial Intelligence, pp. 166–170. Morgan Kaufmann, San Francisco (1988)

    Google Scholar 

  15. Hanus, M. (ed.): Curry: An Integrated Functional Logic Language, http://www.informatik.uni-kiel.de/~mh/curry/

  16. Escobar, S., Meadows, C., Meseguer, J.: A Rewriting-Based Inference System for the NRL Protocol Analyzer and its Meta-Logical Properties. Theoretical Computer Science 367(1-2), 162–202 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  17. Escobar, S., Meseguer, J.: Symbolic Model Checking of Infinite-State Systems Using Narrowing. In: Baader, F. (ed.) RTA 2007. LNCS, vol. 4533, pp. 153–168. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  18. Giesl, J., Middeldorp, A.: Eliminating Dummy Elimination. In: McAllester, D. (ed.) CADE 2000. LNCS, vol. 1831, pp. 309–323. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  19. Giesl, J., Schneider-Kamp, P., Thiemann, R.: AProVE 1. In: Furbach, U., Shankar, N. (eds.) IJCAR 2006. LNCS (LNAI), vol. 4130, pp. 281–286. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  20. Giesl, J., Thiemann, R., Schneider-Kamp, P., Falke, S.: Mechanizing and Improving Dependency Pairs. Journal of Automated Reasoning 37(3), 155–203 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  21. Hanus, M.: The Integration of Functions into Logic Programming: From Theory to Practice. Journal of Logic Programming 19&20, 583–628 (1994)

    Article  MathSciNet  Google Scholar 

  22. Hölldobler, S. (ed.): Foundations of Equational Logic Programming. LNCS, vol. 353. Springer, Heidelberg (1989)

    MATH  Google Scholar 

  23. Hullot, J.M.: Canonical Forms and Unification. In: Bibel, W. (ed.) CADE 1980. LNCS, vol. 87, pp. 318–334. Springer, Heidelberg (1980)

    Google Scholar 

  24. Jones, N.D., Gomard, C.K., Sestoft, P.: Partial Evaluation and Automatic Program Generation. Prentice-Hall, Englewood Cliffs (1993)

    MATH  Google Scholar 

  25. Klop, J.W.: Term Rewriting Systems: A Tutorial. Bulletin of the European Association for Theoretical Computer Science 32, 143–183 (1987)

    MATH  Google Scholar 

  26. Kusakari, K., Nakamura, M., Toyama, Y.: Argument Filtering Transformation. In: Nadathur, G. (ed.) PPDP 1999. LNCS, vol. 1702, pp. 48–62. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  27. López-Fraguas, F., Sánchez-Hernández, J.: TOY: A Multiparadigm Declarative System. In: Narendran, P., Rusinowitch, M. (eds.) RTA 1999. LNCS, vol. 1631, pp. 244–247. Springer, Heidelberg (1999)

    Google Scholar 

  28. Meseguer, J., Thati, P.: Symbolic Reachability Analysis Using Narrowing and its Application to Verification of Cryptographic Protocols. Electronic Notes in Theoretical Computer Science 117, 153–182 (2005)

    Article  Google Scholar 

  29. Moreno-Navarro, J.J., Kuchen, H., Loogen, R., Rodriguez-Artalejo, M.: Lazy Narrowing in a Graph Machine. In: Kirchner, H., Wechler, W. (eds.) ALP 1990. LNCS, vol. 463, pp. 298–317. Springer, Heidelberg (1990)

    Google Scholar 

  30. Nishida, N., Miura, K.: Dependency Graph Method for Proving Termination of Narrowing. In: Proc. of WST 2006, pp. 12–16 (2006)

    Google Scholar 

  31. Nishida, N., Sakai, M., Sakabe, T.: Narrowing-Based Simulation of Term Rewriting Systems with Extra Variables. ENTCS, 86(3) (2003)

    Google Scholar 

  32. Ramos, J.G., Silva, J., Vidal, G.: Fast Narrowing-Driven Partial Evaluation for Inductively Sequential Systems. In: Proc. of the 10th ACM SIGPLAN Int’l Conf. on Functional Programming (ICFP 2005), pp. 228–239. ACM Press, New York (2005)

    Chapter  Google Scholar 

  33. Schneider-Kamp, P., Giesl, J., Serebrenik, A., Thiemann, R.: Automated Termination Analysis for Logic Programs by Term Rewriting. In: Puebla, G. (ed.) LOPSTR 2006. LNCS, vol. 4407, pp. 177–193. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  34. Sheard, T.: Type-Level Computation Using Narrowing in Ωmega. In: In Proc. of PLPV 2006. ENTCS, vol. 174, pp. 105–128 (2007)

    Google Scholar 

  35. Slagle, J.R.: Automated Theorem-Proving for Theories with Simplifiers, Commutativity and Associativity. Journal of the ACM 21(4), 622–642 (1974)

    Article  MathSciNet  MATH  Google Scholar 

  36. Vidal, G.: Termination of Narrowing in Left-Linear Constructor Systems. Technical report, DSIC, Technical University of Valencia (2007), http://www.dsic.upv.es/~gvidal/german/papers.html#tnt

Download references

Author information

Authors and Affiliations

  1. Technical University of Valencia, Spain

    Germán Vidal

Authors
  1. Germán Vidal
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Jacques Garrigue Manuel V. Hermenegildo

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Vidal, G. (2008). Termination of Narrowing in Left-Linear Constructor Systems. In: Garrigue, J., Hermenegildo, M.V. (eds) Functional and Logic Programming. FLOPS 2008. Lecture Notes in Computer Science, vol 4989. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78969-7_10

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-78969-7_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-78968-0

  • Online ISBN: 978-3-540-78969-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation