How to realize LSE narrowing

  • Andreas Werner
  • Alexander Bockmayr
  • Stefan Krischer
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 850)


Narrowing is a complete unification procedure for equational theories defined by canonical term rewriting systems. It is also the operational semantics of various logic and functional programming languages. In [BKW93], we introduced the LSE narrowing strategy which is complete for arbitrary canonical rewriting systems and optimal in the sense that two different LSE narrowing derivations cannot generate the same narrowing substitution. LSE narrowing improves all previously known strategies for arbitrary systems. According to their definition, LSE narrowing steps seem to be very expensive, because a large number of subterms has to be checked for reducibility. In this paper, we first show that many of these subterms are identical. Then we describe how using left-to-right basic occurrences the number of subterms that have to be tested can be reduced drastically. Finally, based on these theoretical results, we develop an efficient implementation of LSE narrowing.


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Copyright information

© Springer-Verlag 1994

Authors and Affiliations

  • Andreas Werner
    • 1
  • Alexander Bockmayr
    • 2
  • Stefan Krischer
    • 3
  1. 1.SFB 314, Univ. KarlsruheKarlsruhe
  2. 2.MPI InformatikSaarbrücken
  3. 3.CRIN & INRIA-LorraineVandœuvre-lès-Nancy

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