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Explicit cyclic substitutions

  • Type Systems and Graph Rewriting
  • Conference paper
  • First Online:
Conditional Term Rewriting Systems (CTRS 1992)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 656))

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Abstract

In this paper we consider rewrite systems that describe the λ-calculus enriched with recursive and non-recursive local definitions by generalizing the lsexplicit substitutions’ used by Abadi, Cardelli, Curien, and Lévy [1] to describe sharing in λ-terms. This leads to ‘explicit cyclic substitutions’ that can describe the mutual sharing of local recursive definitions. We demonstrate how this may be used to describe standard binding constructions (let and letrec)—directly using substitution and fixed point induction as well as using ‘small-step’ rewriting semantics where substitution is interleaved with the mechanics of the following β-reductions.

With this we hope to contribute to the synthesis of denotational and operational specifications of sharing and recursion.

Supported by the Danish Research Council (SNF) under project DART.

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Authors and Affiliations

  1. DIKU, University of Copenhagen, Universitetsparken 1, 2100, København Ø, Denmark

    Kristoffer Høgsbro Rose

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  1. Kristoffer Høgsbro Rose
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Michaël Rusinowitch Jean-Luc Rémy

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© 1993 Springer-Verlag Berlin Heidelberg

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Rose, K.H. (1993). Explicit cyclic substitutions. In: Rusinowitch, M., Rémy, JL. (eds) Conditional Term Rewriting Systems. CTRS 1992. Lecture Notes in Computer Science, vol 656. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56393-8_3

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  • DOI: https://doi.org/10.1007/3-540-56393-8_3

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-56393-8

  • Online ISBN: 978-3-540-47549-1

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