Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content
SpringerLink
Log in

Unravelings and ultra-properties

  • Term Rewriting
  • Conference paper
  • First Online:
Algebraic and Logic Programming (ALP 1996)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1139))

Included in the following conference series:

Abstract

Conditional rewriting is universally recognized as being much more complicated than unconditional rewriting. In this paper we study how much of conditional rewriting can be automatically inferred from the simpler theory of unconditional rewriting. We introduce a new tool, called unraveling, to automatically translate a conditional term rewriting system (CTRS) into a term rewriting system (TRS). An unraveling enables to infer properties of a CTRS by studying the corresponding ultra-properties using the corresponding TRS. We show how to rediscover properties like decreasingness, and to give nice proofs of some existing results on CTRSs. Moreover, we show how unravelings provide a valuable tool to study modularity of CTRSs, automatically giving a multitude of new results.

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. J.A. Bergstra and J.W. Klop. Conditional rewrite rules: Confluence and termination. Journal of Computer and System Sciences, 32(3):323–362, 1986.

    Google Scholar 

  2. N. Dershowitz. Hierarchical termination. In Proceedings 4th International Workshop on Conditional and Typed Rewriting Systems, volume 968 of LNCS, Springer-Verlag, 1995.

    Google Scholar 

  3. N. Dershowitz and J.-P. Jouannaud. Rewrite systems. In J. van Leeuwen, editor, Handbook of Theoretical Computer Science, vol. B, ch. 6, pp. 243–320. Elsevier, 1990.

    Google Scholar 

  4. N. Dershowitz and M. Okada. A rationale for conditional equational programming. Theoretical Computer Science, 75:111–138, 1990.

    Google Scholar 

  5. N. Dershowitz, M. Okada, and G. Sivakumar. Canonical conditional rewrite systems. In Proceedings of the 9th CADE, volume 310 of LNCS, pages 538–549. Springer-Verlag, 1988.

    Google Scholar 

  6. E. Giovannetti and C. Moiso. Notes on the elimination of conditions. In Proceedings 1st International Workshop on Conditional and Typed Rewriting Systems, volume 308 of LNCS, pages 91–97. Springer-Verlag, 1988.

    Google Scholar 

  7. B. Gramlich. Relating innermost, weak, uniform and modular termination of term rewriting systems. In Proc. LPAR, vol. 624 of LNAI, pages 285–296. Springer-Verlag, 1992.

    Google Scholar 

  8. B. Gramlich. Sufficient conditions for modular termination of conditional term rewriting systems. In Third International Workshop on Conditional Term Rewriting Systems, volume 656 of LNCS, pages 128–142. Springer-Verlag, 1993.

    Google Scholar 

  9. B. Gramlich. Generalized sufficient conditions for modular termination of rewriting. Applicable Algebra in Engineering, Communication and Computing, 5:131–158, 1994.

    Google Scholar 

  10. B. Gramlich. On modularity of termination and confluence properties of conditional rewrite systems. In 4th Int. Conf. on Algebraic and Logic Programming, volume 850 of LNCS, pages 186–203. Springer-Verlag, 1994.

    Google Scholar 

  11. C. Hintermeier. How to transform canonical decreasing CTRSs into equivalent canonical TRSs. In Proceedings 4th International Workshop on Conditional and Typed Rewriting Systems, volume 968 of LNCS, pages 186–205. Springer-Verlag, 1995.

    Google Scholar 

  12. J.-P. Jouannaud and B. Waldmann. Reductive conditional term rewrite systems. In 3rd IFIP Working Conference on Formal Description of Programming Concepts, pages 223–244, Ebberup, Denmark, 1986.

    Google Scholar 

  13. S. Kaplan. Conditional rewrite rules. Theoretical Computer Science, 33(2):175–193, 1984.

    Google Scholar 

  14. S. Kaplan. Simplifying conditional term rewriting systems. JSC, 4(3):295–334, 1987.

    Google Scholar 

  15. J.W. Klop. Term rewriting systems. In S. Abramsky, Dov M. Gabbay, and T.S.E. Maibaum, editors, Handbook of Logic in Computer Science, volume 2, chapter 1, pages 1–116. Clarendon Press, Oxford, 1992.

    Google Scholar 

  16. M. Kurihara and A. Ohuchi. Modularity of simple termination of term rewriting systems. Journal of IPS Japan, 31(5):633–642, 1990.

    Google Scholar 

  17. M. Marchiori. Bubbles in modularity. Technical Report 5, Dept. of Pure and Applied Mathematics, University of Padova, 1995. Submitted to TCS.

    Google Scholar 

  18. M. Marchiori. Unravelings and ultra-properties. Technical Report 8, Dept. of Pure and Applied Mathematics, University of Padova, 1995.

    Google Scholar 

  19. M. Marchiori. On the modularity of normal forms in rewriting. J. of Symbolic Computation, 1996. In press. Also available as Tech. Rep. CS-R9433, CWI, Amsterdam, 1994.

    Google Scholar 

  20. A. Middeldorp. A sufficient condition for the termination of the direct sum of term rewriting systems. In Proc. 4th IEEE LICS, pages 396–401, 1989.

    Google Scholar 

  21. A. Middeldorp. Modular properties of conditional term rewriting systems. Information and Computation, 104(1):110–158, 1993.

    Google Scholar 

  22. A. Middeldorp and E. Hamoen. Completeness results for basic narrowing. Applicable Algebra in Engineering, Communication and Computing, 5:213–253, 1994.

    Google Scholar 

  23. E. Ohlebusch. Combinations of simplifying conditional term rewriting systems. In Proceedings 3rd International Workshop on Conditional and Typed Rewriting Systems, volume 656 of LNCS, pages 113–127. Springer-Verlag, 1993.

    Google Scholar 

  24. E. Ohlebusch. On the modularity of termination of term rewriting systems. Theoretical Computer Science, 136(2):333–360, 1994.

    Google Scholar 

  25. E. Ohlebusch. Modular properties of composable term rewriting systems. Journal of Symbolic Computation, 20(1):1–41, 1995.

    Google Scholar 

  26. K. Rao. Completeness of hierarchical combinations of term rewriting systems. In Proc. 13th FST&TCS, volume 761 of LNCS, pages 125–139. Springer-Verlag, 1993.

    Google Scholar 

  27. K. Rao. Simple termination of hierarchical combinations of term rewriting systems. In Proc. TACS, volume 789 of LNCS, pages 203–223. Springer-Verlag, 1994.

    Google Scholar 

  28. K.-C. Raoult and J. Vuillemin. Operational and semantic equivalence between recursive programs. Journal of the ACM, 27(4):772–796, 1980.

    Google Scholar 

  29. M. Rusinowitch. On termination of the direct sum of term rewriting systems. Information Processing Letters, 26:65–70, 1987.

    Google Scholar 

  30. M. Schmidt-Schauß. Unification in a combination of arbitrary disjoint equational theories. Journal of Symbolic Computation, 8(1,2):51–99, 1989.

    Google Scholar 

  31. M. Schmidt-Schauß, M. Marchiori, and S.E. Panitz. Modular termination of r-consistent and left-linear term rewriting systems. TCS, 149(2):361–374, 1995.

    Google Scholar 

  32. R.M. Verma. Unique normal forms and confluence of rewrite systems: Persistence. In Proc. 14th IJCAI, volume 1, pages 362–368, 1995.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Pure and Applied Mathematics, University of Padova, Via Belzoni 7, 35131, Padova, Italy

    Massimo Marchiori

Authors
  1. Massimo Marchiori
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Michael Hanus Mario Rodríguez-Artalejo

Rights and permissions

Reprints and permissions

Copyright information

© 1996 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Marchiori, M. (1996). Unravelings and ultra-properties. In: Hanus, M., Rodríguez-Artalejo, M. (eds) Algebraic and Logic Programming. ALP 1996. Lecture Notes in Computer Science, vol 1139. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61735-3_7

Download citation

  • DOI: https://doi.org/10.1007/3-540-61735-3_7

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-61735-8

  • Online ISBN: 978-3-540-70672-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation