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A Modular Type-Checking Algorithm for Type Theory with Singleton Types and Proof Irrelevance

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Typed Lambda Calculi and Applications (TLCA 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5608))

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Abstract

We define a logical framework with singleton types and one universe of small types. We give the semantics using a PER model; it is used for constructing a normalisation-by-evaluation algorithm. We prove completeness and soundness of the algorithm; and get as a corollary the injectivity of type constructors. Then we give the definition of a correct and complete type-checking algorithm for terms in normal form. We extend the results to proof-irrelevant propositions.

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Author information

Authors and Affiliations

  1. Ludwig-Maximilians-Universität München, Germany

    Andreas Abel

  2. Göteborg University, Sweden

    Thierry Coquand

  3. Universidad Nacional de Córdoba, Argentina

    Miguel Pagano

Authors
  1. Andreas Abel
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  2. Thierry Coquand
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  3. Miguel Pagano
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Editor information

Editors and Affiliations

  1. Laboratoire PPS (CNRS / Paris 7), Case 7014, Université Paris Diderot - Paris 7, 75205, Paris Cedex 13, France

    Pierre-Louis Curien

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Abel, A., Coquand, T., Pagano, M. (2009). A Modular Type-Checking Algorithm for Type Theory with Singleton Types and Proof Irrelevance. In: Curien, PL. (eds) Typed Lambda Calculi and Applications. TLCA 2009. Lecture Notes in Computer Science, vol 5608. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02273-9_3

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  • DOI: https://doi.org/10.1007/978-3-642-02273-9_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02272-2

  • Online ISBN: 978-3-642-02273-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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