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Open Call-by-Value

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Programming Languages and Systems (APLAS 2016)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 10017))

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Abstract

The elegant theory of the call-by-value lambda-calculus relies on weak evaluation and closed terms, that are natural hypotheses in the study of programming languages. To model proof assistants, however, strong evaluation and open terms are required, and it is well known that the operational semantics of call-by-value becomes problematic in this case. Here we study the intermediate setting—that we call Open Call-by-Value—of weak evaluation with open terms, on top of which Grégoire and Leroy designed the abstract machine of Coq. Various calculi for Open Call-by-Value already exist, each one with its pros and cons. This paper presents a detailed comparative study of the operational semantics of four of them, coming from different areas such as the study of abstract machines, denotational semantics, linear logic proof nets, and sequent calculus. We show that these calculi are all equivalent from a termination point of view, justifying the slogan Open Call-by-Value.

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Acknowledgment

Work partially supported by the A*MIDEX project ANR-11-IDEX-0001-02 funded by the “Investissements d’Avenir” French Government program, managed by the French National Research Agency (ANR), and by ANR projects ANR-12-JS02-006-01 (CoQuaS) and ANR-11-IS02-0002 (Locali).

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Authors and Affiliations

  1. Inria, UMR 7161, LIX, École Polytechnique, Palaiseau, France

    Beniamino Accattoli

  2. Aix Marseille Univ, CNRS, Centrale Marseille, I2M, Marseille, France

    Giulio Guerrieri

Authors
  1. Beniamino Accattoli
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  2. Giulio Guerrieri
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Correspondence to Beniamino Accattoli .

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Editors and Affiliations

  1. Kyoto University , Kyoto, Japan

    Atsushi Igarashi

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Accattoli, B., Guerrieri, G. (2016). Open Call-by-Value. In: Igarashi, A. (eds) Programming Languages and Systems. APLAS 2016. Lecture Notes in Computer Science(), vol 10017. Springer, Cham. https://doi.org/10.1007/978-3-319-47958-3_12

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  • DOI: https://doi.org/10.1007/978-3-319-47958-3_12

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-47957-6

  • Online ISBN: 978-3-319-47958-3

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