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Call-by-Value Non-determinism in a Linear Logic Type Discipline

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Logical Foundations of Computer Science (LFCS 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7734))

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Abstract

We consider the call-by-value λ-calculus extended with a may-convergent non-deterministic choice and a must-convergent parallel composition. Inspired by recent works on the relational semantics of linear logic and non-idempotent intersection types, we endow this calculus with a type system based on the so-called Girard’s second translation of intuitionistic logic into linear logic. We prove that a term is typable if and only if it is converging, and that its typing tree carries enough information to give a bound on the length of its lazy call-by-value reduction. Moreover, when the typing tree is minimal, such a bound becomes the exact length of the reduction.

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Author information

Authors and Affiliations

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

    Alejandro Díaz-Caro, Giulio Manzonetto & Michele Pagani

  2. CNRS, UMR 7030, F-93430, Villetaneuse, France

    Giulio Manzonetto & Michele Pagani

Authors
  1. Alejandro Díaz-Caro
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  2. Giulio Manzonetto
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  3. Michele Pagani
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Editor information

Editors and Affiliations

  1. Computer Science, CUNY Graduate Center, 365 Fifth Avenue, 10016, New York, NY, USA

    Sergei Artemov

  2. Department of Mathematics, Cornell University, 545 Malott Hall, 14853, Ithaca, NY, USA

    Anil Nerode

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Díaz-Caro, A., Manzonetto, G., Pagani, M. (2013). Call-by-Value Non-determinism in a Linear Logic Type Discipline. In: Artemov, S., Nerode, A. (eds) Logical Foundations of Computer Science. LFCS 2013. Lecture Notes in Computer Science, vol 7734. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35722-0_12

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  • DOI: https://doi.org/10.1007/978-3-642-35722-0_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-35721-3

  • Online ISBN: 978-3-642-35722-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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