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Non-linearity as the Metric Completion of Linearity

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Typed Lambda Calculi and Applications (TLCA 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7941))

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Abstract

We summarize some recent results showing how the lambda-calculus may be obtained by considering the metric completion (with respect to a suitable notion of distance) of a space of affine lambda-terms, i.e., lambda-terms in which abstractions bind variables appearing at most once. This formalizes the intuitive idea that multiplicative additive linear logic is “dense” in full linear logic (in fact, a proof-theoretic version of the above-mentioned construction is also possible). We argue that thinking of non-linearity as the “limit” of linearity gives an interesting point of view on well-known properties of the lambda-calculus and its relationship to computational complexity (through lambda-calculi whose normalization is time-bounded).

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Author information

Authors and Affiliations

  1. CNRS, UMR 7030, LIPN, Université Paris 13, Sorbonne Paris Cité, France

    Damiano Mazza

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  1. Damiano Mazza
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Editors and Affiliations

  1. Research Institute for Mathematical Sciences, Kyoto University, Kitashirakawa-Oiwake-cho, Sakyo-ku, 606-8502, Kyoto, Kyoto, Japan

    Masahito Hasegawa

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Mazza, D. (2013). Non-linearity as the Metric Completion of Linearity. In: Hasegawa, M. (eds) Typed Lambda Calculi and Applications. TLCA 2013. Lecture Notes in Computer Science, vol 7941. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38946-7_3

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  • DOI: https://doi.org/10.1007/978-3-642-38946-7_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-38945-0

  • Online ISBN: 978-3-642-38946-7

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