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Static Analysis of Modularity of β-Reduction in the Hyperbalanced λ-Calculus

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Rewriting Techniques and Applications (RTA 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2378))

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Abstract

We investigate the degree of parallelism (or modularity) in the hyperbalanced λ-calculus, λH, a subcalculus of λ-calculus containing all simply typable terms (up to a restricted η-expansion). In technical terms, we study the family relation on redexes in λH, and the contribution relation on redex-families, and show that the latter is a forest (as a partial order). This means that hyperbalanced λ-terms allow for maximal possible parallelism in computation. To prove our results, we use and further refine, for the case of hyperbalanced terms, some well known results concerning paths, which allow for static analysis of many fundamental properties of β-reduction.

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Author information

Authors and Affiliations

  1. School of Information Systems, University of East Anglia, Norwich, NR4 7TJ, England

    Richard Kennaway

  2. Department of Mathematics and Computer Science, Bar-Ilan University, Ramat-Gan, 52900, Israel

    Zurab Khasidashvili

  3. Dipartimento di Informatica, Università di Roma “La Sapienza”, Via Salaria 113, 00198, Roma, Italy

    Adolfo Piperno

Authors
  1. Richard Kennaway
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  2. Zurab Khasidashvili
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  3. Adolfo Piperno
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Editor information

Editors and Affiliations

  1. LIFL Bâtiment M3, Université de Lille 1, Cité Scientifique, 59655, Villeneuve d’Ascq cedex, France

    Sophie Tison

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© 2002 Springer-Verlag Berlin Heidelberg

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Kennaway, R., Khasidashvili, Z., Piperno, A. (2002). Static Analysis of Modularity of β-Reduction in the Hyperbalanced λ-Calculus. In: Tison, S. (eds) Rewriting Techniques and Applications. RTA 2002. Lecture Notes in Computer Science, vol 2378. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45610-4_5

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  • DOI: https://doi.org/10.1007/3-540-45610-4_5

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43916-5

  • Online ISBN: 978-3-540-45610-0

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