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Linearity in the Non-deterministic Call-by-Value Setting

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Logic, Language, Information and Computation (WoLLIC 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7456))

Abstract

We consider the non-deterministic extension of the call-by-value lambda calculus, which corresponds to the additive fragment of the linear-algebraic lambda-calculus. We define a fine-grained type system, capturing the right linearity present in such formalisms. After proving the subject reduction and the strong normalisation properties, we propose a translation of this calculus into the System F with pairs, which corresponds to a non linear fragment of linear logic. The translation provides a deeper understanding of the linearity in our setting.

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Author information

Authors and Affiliations

  1. Université Paris 13, Sorbonne Paris Cité, LIPN, F-93430, Villetaneuse, France

    Alejandro Díaz-Caro

  2. FOCUS (INRIA) – Università di Bologna, Italy

    Barbara Petit

Authors
  1. Alejandro Díaz-Caro
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  2. Barbara Petit
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Oxford, Wolfson Building, Parks Road, OX1 3QD, Oxford, UK

    Luke Ong

  2. Centro de Informática, Universidade Federal de Pernambuco, Av. jornalista Anibal Fernandes, s/n, 50740-560, Recife, PE, Brazil

    Ruy de Queiroz

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Díaz-Caro, A., Petit, B. (2012). Linearity in the Non-deterministic Call-by-Value Setting. In: Ong, L., de Queiroz, R. (eds) Logic, Language, Information and Computation. WoLLIC 2012. Lecture Notes in Computer Science, vol 7456. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32621-9_16

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  • DOI: https://doi.org/10.1007/978-3-642-32621-9_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-32620-2

  • Online ISBN: 978-3-642-32621-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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