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Syntax for Free: Representing Syntax with Binding Using Parametricity

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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 show that, in a parametric model of polymorphism, the type ∀ α. ((α→α) →α) →(α→α→α) →α is isomorphic to closed de Bruijn terms. That is, the type of closed higher-order abstract syntax terms is isomorphic to a concrete representation. To demonstrate the proof we have constructed a model of parametric polymorphism inside the Coq proof assistant. The proof of the theorem requires parametricity over Kripke relations. We also investigate some variants of this representation.

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Author information

Authors and Affiliations

  1. School of Informatics, University of Edinburgh, UK

    Robert Atkey

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  1. Robert Atkey
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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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Atkey, R. (2009). Syntax for Free: Representing Syntax with Binding Using Parametricity. 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_5

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  • DOI: https://doi.org/10.1007/978-3-642-02273-9_5

  • 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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