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Orthogonal higher-order rewrite systems are confluent

  • Tobias Nipkow
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 664)

Abstract

The results about higher-order critical pairs and the confluence of OHRSs provide a firm foundation for the further study of higher-order rewrite systems. It should now be interesting to lift more results and techniques both from term-rewriting and λ-calculus to the level of HRSs. For example termination proof techniques are much studied for TRSs and are urgently needed for HRSs; similarly the extension of our result to weakly orthogonal HRSs or even to Huet's “parallel closed” systems is highly desirable. Conversely, a large body of λ-calculus reduction theory has been lifted to CRSs [10] already and should be easy to carry over to HRSs.

Finally there is the need to extend the notion of an HRS to more general left-hand sides. For example the eta-rule for the case-construct on disjoint unions [15] case(U,λx.F(inl(x)),λy.G(inr(y))) F(U) is outside our framework, whichever way it is oriented.

Keywords

Normal Form Induction Hypothesis Logic Program Free Variable Critical Pair 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Tobias Nipkow
    • 1
  1. 1.Institut für InformatikTechnische Universität MünchenMünchen 2Germany

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