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Discrete Normalization and Standardization in Deterministic Residual Structures

  • Term Rewriting
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Algebraic and Logic Programming (ALP 1996)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1139))

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Abstract

We prove a version of the Standardization Theorem and the Discrete Normalization Theorem in stable Deterministic Residual Structures, Abstract Reduction Systems with axiomatized notions of residual, which model orthogonal rewrite systems. The latter theorem gives a strategy for construction of reductions Lévy-equivalent (or permutation-equivalent) to a given, finite or infinite, regular (or semi-linear) reduction, based on the neededness concept of Huet and Lévy. This and other results of this paper add to the understanding of Lévy-equivalence of reductions, and consequently, Lévy's reduction space. We demonstrate how elements of this space can be used to give denotational semantics to known functional languages in an abstract manner.

This work was supported by the Engineering and Physical Sciences Research Council of Great Britain under grant GR/H 41300

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Authors and Affiliations

  1. School of Information Systems, UEA, NR4 7TJ, Norwich, England

    Zurab Khasidashvili & John Glauert

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  1. Zurab Khasidashvili
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  2. John Glauert
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Michael Hanus Mario Rodríguez-Artalejo

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© 1996 Springer-Verlag Berlin Heidelberg

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Khasidashvili, Z., Glauert, J. (1996). Discrete Normalization and Standardization in Deterministic Residual Structures. In: Hanus, M., Rodríguez-Artalejo, M. (eds) Algebraic and Logic Programming. ALP 1996. Lecture Notes in Computer Science, vol 1139. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61735-3_9

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  • DOI: https://doi.org/10.1007/3-540-61735-3_9

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