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Leaving the Nest: Nominal Techniques for Variables with Interleaving Scopes

Authors Murdoch J. Gabbay, Dan R. Ghica, Daniela Petrisan

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Murdoch J. Gabbay
Dan R. Ghica
Daniela Petrisan

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Murdoch J. Gabbay, Dan R. Ghica, and Daniela Petrisan. Leaving the Nest: Nominal Techniques for Variables with Interleaving Scopes. In 24th EACSL Annual Conference on Computer Science Logic (CSL 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 41, pp. 374-389, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015) https://doi.org/10.4230/LIPIcs.CSL.2015.374

Abstract

We examine the key syntactic and semantic aspects of a nominal framework allowing scopes of name bindings to be arbitrarily interleaved. Name binding (e.g. delta x.M) is handled by explicit name-creation and name-destruction brackets (e.g. <delta x M x>) which admit interleaving. We define an appropriate notion of alpha-equivalence for such a language and study the syntactic structure required for alpha-equivalence to be a congruence. We develop denotational and categorical semantics for dynamic binding and provide a generalised nominal inductive reasoning principle. We give several standard synthetic examples of working with dynamic sequences (e.g. substitution) and we sketch out some preliminary applications to game semantics and trace semantics.

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Keywords
  • nominal sets
  • scope
  • alpha equivalence
  • dynamic sequences

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