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On Explicit Substitution with Names

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Abstract

This paper recounts the origins of the λx family of calculi of explicit substitution with proper variable names, including the original result of preservation of strong β-normalization based on the use of synthetic reductions for garbage collection. We then discuss the properties of a variant of the calculus which is also confluent for “open” terms (with meta-variables), and verify that a version with garbage collection preserves strong β-normalization (as is the state of the art), and we summarize the relationship with other efforts on using names and garbage collection rules in explicit substitution.

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Authors and Affiliations

  1. IBM Thomas J. Watson Research Center, P. O. Box 704, Yorktown Heights, NY, 10598, USA

    Kristoffer H. Rose

  2. Eindhoven University of Technology, P. O. Box 513, 5600 MB, Eindhoven, The Netherlands

    Roel Bloo

  3. INRIA Grenoble Rhône-Alpes/LIG, 655, Av. de l’Europe, Montbonnot, 38334, Saint-Ismier Cedex, France

    Frédéric Lang

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  1. Kristoffer H. Rose
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  2. Roel Bloo
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  3. Frédéric Lang
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Correspondence to Kristoffer H. Rose.

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Rose, K.H., Bloo, R. & Lang, F. On Explicit Substitution with Names. J Autom Reasoning 49, 275–300 (2012). https://doi.org/10.1007/s10817-011-9222-5

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