Skip to main content
SpringerLink
Log in

Matching Power

  • Conference paper
  • First Online:
Rewriting Techniques and Applications (RTA 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2051))

Included in the following conference series:

Abstract

In this paper we give a simple and uniform presentation of the rewriting calculus, also called Rho Calculus. In addition to its simplicity, this formulation explicitly allows us to encode complex structures such as lists, sets, and objects. We provide extensive examples of the calculus, and we focus on its ability to represent some object oriented calculi, namely the Lambda Calculus of Objects of Fisher, Honsell, and Mitchell, and the Object Calculus of Abadi and Cardelli. Furthermore, the calculus allows us to get object oriented constructions unreachable in other calculi. In summa, we intend to show that because of its matching ability, the Rho Calculus represents a lingua franca to naturally encode many paradigms of computations. This enlightens the capabilities of the rewriting calculus based language ELAN to be used as a logical as well as powerful semantical framework.

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

Access this chapter

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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. M. Abadi and L. Cardelli. A Theory of Objects. Springer Verlag, 1996.

    Google Scholar 

  2. H. Ait-Kaci, A. Podelski, and G. Smolka. A feature constraint system for logic programming with entailment. Theoretical Computer Science, 122(1-2):263–283, 1994.

    Article  MATH  MathSciNet  Google Scholar 

  3. P. Borovanský, C. Kirchner, H. Kirchner, P.-E. Moreau, and C. Ringeissen. An overview of ELAN. In Proc. of WRLA, volume 15. Electronic Notes in Theoretical Computer Science, 1998.

    Google Scholar 

  4. V. Breazu-Tannen. Combining algebra and higher-order types. In Proc. of LICS, pages 82–90, 1988.

    Google Scholar 

  5. H.-J. Bürckert. Matching — A special case of unification? Journal of Symbolic Computation, 8(5):523–536, 1989.

    Article  MATH  MathSciNet  Google Scholar 

  6. H. Cirstea. Calcul de réécriture: fondements et applications. Thèse de Doctorat d’Université, Université Henri Poincaré-Nancy I, 2000.

    Google Scholar 

  7. H. Cirstea and C. Kirchner. The rewriting calculus — Part I and II. Logic Journal of the Interest Group in Pure and Applied Logics, 9(3):427–498, 2001.

    MathSciNet  Google Scholar 

  8. H. Cirstea, C. Kirchner, and L. Liquori. Matching Power. Technical Report A00-R-363, LORIA, Nancy, 2000.

    Google Scholar 

  9. H. Cirstea, C. Kirchner, and L. Liquori. The Rho Cube. In Proc. of FOSSACS, volume 2030 of LNCS, pages 166–180. Springer-Verlag, 2001.

    Google Scholar 

  10. M. Clavel, S. Eker, P. Lincoln, and J. Meseguer. Principles of Maude. In Proc. of WRLA, volume 4. Electronic Notes in Theoretical Computer Science, 1996.

    Google Scholar 

  11. L. Colson. Une structure de données pour le λ-calcul typé. Private Communication, 1988.

    Google Scholar 

  12. G. Dowek. Third order matching is decidable. Annals of Pure and Applied Logic, 69:135–155, 1994.

    Article  MATH  MathSciNet  Google Scholar 

  13. Hubert Dubois and Hélène Kirchner. Objects, rules and strategies in ELAN., 2000. Submitted.

    Google Scholar 

  14. K. Fisher, F. Honsell, and J. C. Mitchell. A Lambda Calculus of Objects and Method Specialization. Nordic Journal of Computing, 1(1):3–37, 1994.

    MATH  MathSciNet  Google Scholar 

  15. K. Futatsugi and A. Nakagawa. An overview of CAFE specification environment–an algebraic approach for creating, verifying, and maintaining formal specifications over networks. In Proc. of FEM, 1997.

    Google Scholar 

  16. J. Gallier and V. Breazu-Tannen. Polymorphic rewriting conserves algebraic strong normalization and confluence. In Proc. of ICALP, volume 372 of LNCS, pages 137–150. Springer-Verlag, 1989.

    Google Scholar 

  17. P. Di Gianantonio, F. Honsell, and L. Liquori. A Lambda Calculus of Objects with Self-inflicted Extension. In Proc. of OOPSLA, pages 166–178. The ACM Press, 1998.

    Google Scholar 

  18. J. A. Goguen, C. Kirchner, H. Kirchner, A. Mégrelis, J. Meseguer, and T. Winkler. An introduction to OBJ-3. In Proc. of CTRS, volume 308 of LNCS, pages 258–263. Springer-Verlag, 1987.

    Google Scholar 

  19. C. M. Hoffmann and M. J. O’Donnell. Pattern matching in trees. Journal of the ACM, 29(1):68–95, 1982.

    Article  MATH  MathSciNet  Google Scholar 

  20. G. Huet and B. Lang. Proving and applying program transformations expressed with second-order patterns. Acta Informatica, 11:31–55, 1978.

    Article  MATH  MathSciNet  Google Scholar 

  21. J.-M. Hullot. Associative-commutative pattern matching. In Proc. of IJCAI, 1979.

    Google Scholar 

  22. J.P. Jouannaud and M. Okada. Abstract data type systems. Theoretical Computer Science, 173(2):349–391, 1997.

    Article  MATH  MathSciNet  Google Scholar 

  23. C. Kirchner and H. Kirchner. Rewriting, solving, proving. A preliminary version of a book available at http://www.loria.fr/~ckirchne/rsp.ps.gz, 1999.

  24. C. Kirchner, H. Kirchner, and M. Vittek. Designing constraint logic programming languages using computational systems. In Principles and Practice of Constraint Programming. The Newport Papers., chapter 8, pages 131–158. The MIT press, 1995.

    Google Scholar 

  25. J.W. Klop, V. van Oostrom, and F. van Raamsdonk. Combinatory reduction systems: introduction and survey. Theoretical Computer Science, 121:279–308, 1993.

    Article  MATH  MathSciNet  Google Scholar 

  26. Donald E. Knuth, J. Morris, and V. Pratt. Fast pattern matching in strings. SIAM Journal of Computing, 6(2):323–350, 1977.

    Article  MATH  MathSciNet  Google Scholar 

  27. A. Laville. Lazy pattern matching in the ML language. In Proc. FCT & TCS, volume 287 of LNCS, pages 400–419. Springer-Verlag, 1987.

    Google Scholar 

  28. D Miller. A logic programming language with lambda-abstraction, function variables, and simple unification. In Proc. of ELP, volume 475 of LNCS, pages 253–281. Springer-Verlag, 1991.

    Google Scholar 

  29. Tobias Nipkow and Christian Prehofer. Higher-order rewriting and equational reasoning. In W. Bibel and P. Schmitt, editors, Automated Deduction — A Basis for Applications. Volume I: Foundations. Kluwer, 1998.

    Google Scholar 

  30. M. Okada. Strong normalizability for the combined system of the typed λ calculus and an arbitrary convergent term rewrite system. In Proc. of ISSAC, pages 357–363. ACM Press, 1989.

    Google Scholar 

  31. V. Padovani. Decidability of fourth-order matching. Mathematical Structures in Computer Science, 3(10):361–372, 2000.

    Article  MathSciNet  Google Scholar 

  32. G. Peterson and M. E. Stickel. Complete sets of reductions for some equational theories. Journal of the ACM, 28:233–264, 1981.

    Article  MATH  MathSciNet  Google Scholar 

  33. S. Peyton-Jones. The implementation of functional programming languages. Prentice Hall, Inc., 1987.

    Google Scholar 

  34. Équipe Protheo. The Elan Home Page, 2001. http://elan.loria.fr.

  35. A. van Deursen, J. Heering, and P. Klint. Language Prototyping. World Scientific, 1996.

    Google Scholar 

  36. V. van Oostrom. Lambda calculus with patterns. Technical Report IR-228, Vrije Universiteit, November 1990.

    Google Scholar 

  37. P. Viry. Input/Output for ELAN. In Proc. of WRLA, volume 4. Electronic Notes in Theoretical Computer Science, 1996.

    Google Scholar 

  38. E. Visser and Z.e.A. Benaissa. A core language for rewriting. In Proc. of WRLA, volume 15. Electronic Notes in Theoretical Computer Science, 1998.

    Google Scholar 

  39. D. A. Wolfram. The Clausal Theory of Types, volume 21 of Cambridge Tracts in Theoretical Computer Science. Cambridge University Press, 1993.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. LORIA INRIA INPL ENSMN, 54506, Vandoeuvre-lès-Nancy BP 239 Cedex, France

    Horatiu Cirstea, Claude Kirchner & Luigi Liquori

Authors
  1. Horatiu Cirstea
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Claude Kirchner
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Luigi Liquori
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institute of Information Sciences and Electronics, University of Tsukuba, Tsukuba, 305-8573, Japan

    Aart Middeldorp

Rights and permissions

Reprints and permissions

Copyright information

© 2001 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Cirstea, H., Kirchner, C., Liquori, L. (2001). Matching Power. In: Middeldorp, A. (eds) Rewriting Techniques and Applications. RTA 2001. Lecture Notes in Computer Science, vol 2051. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45127-7_8

Download citation

  • DOI: https://doi.org/10.1007/3-540-45127-7_8

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42117-7

  • Online ISBN: 978-3-540-45127-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation