Efficient strong sequentiality using replacement restrictions

  • Salvador Lucas
Contributed Papers
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1338)


Huet and Lévy defined the (orthogonal) strongly sequential term rewriting systems, for which index reduction, i.e., reduction of redexes placed at special positions called (strong) indices, is optimal and normalizing. Despite the fact that Huet and Lévy give an algorithm to compute indices for the general case, there are many proposals to define subclasses of strongly sequential rewrite systems for which this can be done more efficiently. In this paper, we show that sometimes it is possible to enlarge such classes by only introducing fixed replacement restrictions, without forcing any sensible modification of the corresponding index reduction strategy.


functional programming neededness replacement restrictions term rewriting 


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  1. 1.
    S. Antoy and A. Middeldorp. A Sequential Reduction Strategy. Theoretical Computer Science 165:75–95, 1996.Google Scholar
  2. 2.
    G. Huet and J.J. Lévy. Computations in orthogonal term rewriting systems. In Computational logic: essays in honour of J. Alan Robinson, MIT Press, 1991.Google Scholar
  3. 3.
    J.W. Klop. Term Rewriting Systems. In Handbook of Logic in Computer Science, volume 3, pages 1–116. Oxford University Press, 1992.Google Scholar
  4. 4.
    J.W. Klop and A. Middeldorp. Sequentiality in Orthogonal Term Rewriting Systems. Journal of Symbolic Computation 12:161–195, 1991.Google Scholar
  5. 5.
    S. Lucas. Context-sensitive computations in functional and functional logic programs. Journal of Functional and Logic Programming, 1997, to appear.Google Scholar
  6. 6.
    S. Lucas. Needed Reductions with Context-Sensitive Rewriting. In Proc. of ALP'97, LNCS to appear.Google Scholar
  7. 7.
    S. Lucas. Termination of Context-Sensitive Rewriting by Rewriting. In Proc. of ICALP'96, LNCS 1099:122–133, Springer-Verlag, 1996.Google Scholar
  8. 8.
    M.J. O'Donnell. Equational Logic as a Programming Language. The MIT Press, 1985.Google Scholar
  9. 9.
    R.C. Sekar, S. Pawagi and I.V. Ramakrishnan. Transforming Strongly Sequential Rewrite Systems with Constructors for Efficient Parallel Execution. In Proc. of RTA'89, LNCS 355:404–418, 1989.Google Scholar
  10. 10.
    Y. Toyama, S. Smetsers, M.C.J.D. van Eekelen and R. Plasmeijer. The Functional Strategy and Transitive Term Rewriting Systems. Term Graph Rewriting — Theory and Practice, pages 117–129, John Wiley & sons, 1993.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Salvador Lucas
    • 1
  1. 1.Departamento de Sistemas Informáticos y ComputaciónUniversidad Politécnica de ValenciaValenciaSpain

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