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DOI: 10.4230/LIPIcs.TLCA.2015.180

Dependent Types for Nominal Terms with Atom Substitutions

Authors: Elliot Fairweather, Maribel Fernández, Nora Szasz, and Alvaro Tasistro

Published in: LIPIcs, Volume 38, 13th International Conference on Typed Lambda Calculi and Applications (TLCA 2015)

Abstract

Nominal terms are an extended first-order language for specifying and verifying properties of syntax with binding. Founded upon the semantics of nominal sets, the success of nominal terms with regard to systems of equational reasoning is already well established. This work first extends the untyped language of nominal terms with a notion of non-capturing atom substitution for object-level names and then proposes a dependent type system for this extended language. Both these contributions are intended to serve as a prelude to a future nominal logical framework based upon nominal equational reasoning and thus an extended example is given to demonstrate that this system is capable of encoding various other formal systems of interest.

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Elliot Fairweather, Maribel Fernández, Nora Szasz, and Alvaro Tasistro. Dependent Types for Nominal Terms with Atom Substitutions. In 13th International Conference on Typed Lambda Calculi and Applications (TLCA 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 38, pp. 180-195, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{fairweather_et_al:LIPIcs.TLCA.2015.180,
  author =	{Fairweather, Elliot and Fern\'{a}ndez, Maribel and Szasz, Nora and Tasistro, Alvaro},
  title =	{{Dependent Types for Nominal Terms with Atom Substitutions}},
  booktitle =	{13th International Conference on Typed Lambda Calculi and Applications (TLCA 2015)},
  pages =	{180--195},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-87-3},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{38},
  editor =	{Altenkirch, Thorsten},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TLCA.2015.180},
  URN =		{urn:nbn:de:0030-drops-51636},
  doi =		{10.4230/LIPIcs.TLCA.2015.180},
  annote =	{Keywords: alpha-equivalence, nominal term, substitution, dependent type}
}

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Dependent Types for Nominal Terms with Atom Substitutions

Abstract

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