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A Type-Checking Algorithm for Martin-Löf Type Theory with Subtyping Based on Normalisation by Evaluation

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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 present a core Martin-Löf type theory with subtyping; it has a cumulative hierarchy of universes and the contravariant rule for subtyping between dependent product types. We extend to this calculus the normalisation by evaluation technique defined for a variant of MLTT without subtyping. This normalisation function makes the subtyping relation and type-checking decidable. To our knowledge, this is the first time that the normalisation by evaluation technique has been considered in the context of subtypes, which introduce some subtleties in the proof of correctness of NbE; an important result to prove correctness and completeness of type-checking.

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Author information

Authors and Affiliations

  1. Universidad Nacional de Córdoba, Argentina

    Daniel Fridlender & Miguel Pagano

Authors
  1. Daniel Fridlender
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  2. Miguel Pagano
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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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Fridlender, D., Pagano, M. (2013). A Type-Checking Algorithm for Martin-Löf Type Theory with Subtyping Based on Normalisation by Evaluation. 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_12

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  • DOI: https://doi.org/10.1007/978-3-642-38946-7_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-38945-0

  • Online ISBN: 978-3-642-38946-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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