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Finite Vector Spaces as Model of Simply-Typed Lambda-Calculi

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Theoretical Aspects of Computing – ICTAC 2014 (ICTAC 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8687))

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Abstract

In this paper we use finite vector spaces (finite dimension, over finite fields) as a non-standard computational model of linear logic. We first define a simple, finite PCF-like lambda-calculus with booleans, and then we discuss two finite models, one based on finite sets and the other on finite vector spaces. The first model is shown to be fully complete with respect to the operational semantics of the language. The second model is not complete, but we develop an algebraic extension of the finite lambda calculus that recovers completeness. The relationship between the two semantics is described, and several examples based on Church numerals are presented.

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Author information

Authors and Affiliations

  1. PPS, UMR 7126, Univ Paris Diderot, Sorbonne Paris Cité, F-75205, Paris, France

    Benoît Valiron

  2. University of Pennsylvania, Philadelphia, US

    Steve Zdancewic

Authors
  1. Benoît Valiron
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  2. Steve Zdancewic
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Editor information

Editors and Affiliations

  1. Institute of Computer Science, Romanian Academy, Blvd. King Carol I no.8, 700505, Iaşi, Romania

    Gabriel Ciobanu

  2. LORIA, Université de Lorraine, Campus Scientifique, BP 239, 54506, Vandœvre-lès-Nancy, France

    Dominique Méry

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Valiron, B., Zdancewic, S. (2014). Finite Vector Spaces as Model of Simply-Typed Lambda-Calculi. In: Ciobanu, G., Méry, D. (eds) Theoretical Aspects of Computing – ICTAC 2014. ICTAC 2014. Lecture Notes in Computer Science, vol 8687. Springer, Cham. https://doi.org/10.1007/978-3-319-10882-7_26

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  • DOI: https://doi.org/10.1007/978-3-319-10882-7_26

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-10881-0

  • Online ISBN: 978-3-319-10882-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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