Böhm-Like Trees for Term Rewriting Systems

  • Jeroen Ketema
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3091)

Abstract

In this paper we define Böhm-like trees for term rewriting systems (TRSs). The definition is based on the similarities between the Böhm trees, the Lévy-Longo trees, and the Berarducci trees. That is, the similarities between the Böhm-like trees of the λ-calculus. Given a term t a tree partially represents the root-stable part of t as created in each maximal fair reduction of t. In addition to defining Böhm-like trees for TRSs we define a subclass of Böhm-like trees whose members are monotone and continuous.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Barendregt, H.P.: The Lambda Calculus: Its Syntax and Semantics, 2nd edn. Elsevier Science, Amsterdam (1985)MATHGoogle Scholar
  2. 2.
    Lévy, J.J.: An algebraic interpretation of the λβK-calculus and the labelled λ- calculus. In: Böhm, C. (ed.) Lambda-Calculus and Computer Science Theory. LNCS, vol. 37, pp. 147–165. Springer, Heidelberg (1975)CrossRefGoogle Scholar
  3. 3.
    Berarducci, A.: Infinite λ-calculus and non-sensible models. In: Ursini, A., Aglianò, P. (eds.) Logic and Algebra, Marcel Dekker, pp. 339–378. Marcel Dekker, New York (1996)Google Scholar
  4. 4.
    Lévy, J.J.: Réductions correctes et optimales dans le lambda-calcul. PhD thesis, Université de Paris VII (1978)Google Scholar
  5. 5.
    Hyland, M.: A syntactic characterization of the equality in some models for the lambda calculus. Journal of the London Mathematical Society 12(2), 361–370 (1976)MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Wadsworth, C.P.: The relation between computational and denotational properties for Scott’s D∞-models of the lambda-calculus. SIAM Journal on Computing 5, 488–521 (1976)MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Kennaway, J.R., Klop, J.W., Sleep, M., de Vries, F.J.: Infinitary lambda calculus. Theoretical Computer Science 175, 93–125 (1997)MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Blom, S.C.C.: Term Graph Rewriting: syntax and semantics. PhD thesis, Vrije Universiteit Amsterdam (2001)Google Scholar
  9. 9.
    Ariola, Z.M., Blom, S.: Skew confluence and the lambda calculus with letrec. Annals of Pure and Applied Logic 117, 95–168 (2002)MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Boudol, G.: Computational semantics of term rewriting systems. In: Nivat, M., Reynolds, J.C. (eds.) Algebraic methods in semantics, pp. 169–236. Cambridge University Press, Cambridge (1985)Google Scholar
  11. 11.
    Ariola, Z.M.: Relating graph and term rewriting via Böhm models. Applicable Algebra in Engineering, Communication and Computing 7, 401–426 (1996)MATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Kennaway, R., van Oostrom, V., de Vries, F.J.: Meaningless terms in rewriting. The Journal of Functional and Logic Programming 1 (1999)Google Scholar
  13. 13.
    Baader, F., Nipkow, T.: Term Rewriting and All That. Cambridge University Press, Cambridge (1998)Google Scholar
  14. 14.
    Stoltenberg-Hansen, V., Lindström, I., Griffor, E.R.: Mathematical Theory of Domains. Cambridge University Press, Cambridge (1994)MATHGoogle Scholar
  15. 15.
    Klop, J.W., Middeldorp, A.: Sequentiality in orthogonal term rewriting systems. Journal of Symbolic Computation 12, 161–195 (1991)MATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Huet, G., Lévy, J.J.: Computations in orthogonal rewriting systems. In: Lassez, J.L., Plotkin, G. (eds.) Computational Logic, pp. 395–443. MIT Press, Cambridge (1991)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Jeroen Ketema
    • 1
  1. 1.Department of Computer Science Faculty of SciencesVrije Universiteit AmsterdamAmsterdamThe Netherlands

Personalised recommendations