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Information Retrieval in a Coq Proof Library Using Type Isomorphisms

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Types for Proofs and Programs (TYPES 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1956))

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Abstract

We propose a method to search for a lemma in a Coq proof library by using the lemma type as a key. The method is based on the concept of type isomorphism developed within the functional programming framework. We introduce a theory which is a generalization of the axiomatization for the simply typed γ-calculus (associated with Closed Cartesian Categories) to an Extended Calculus of Constructions with a more Extensional conversion rule. We show a soundness theorem for this theory but we notice that it is not contextual and requires “ad hoc” contextual rules. Thus, we see how we must adapt this theory for Coq and we define an approximation of the contextual part of this theory, which is implemented in a decision procedure.

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Author information

Authors and Affiliations

  1. INRIA-Rocquencourt, domaine de Voluceau, B.P. 105, 78153, Le Chesnay Cedex, France

    David Delahaye

Authors
  1. David Delahaye
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Editor information

Editors and Affiliations

  1. Department of Computing Science, Chalmers University of Technology and University of Göteborg, 41296, Göteborg, Sweden

    Thierry Coquand , Peter Dybjer , Bengt Nordström  & Jan Smith , ,  & 

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Delahaye, D. (2000). Information Retrieval in a Coq Proof Library Using Type Isomorphisms. In: Coquand, T., Dybjer, P., Nordström, B., Smith, J. (eds) Types for Proofs and Programs. TYPES 1999. Lecture Notes in Computer Science, vol 1956. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44557-9_8

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  • DOI: https://doi.org/10.1007/3-540-44557-9_8

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41517-6

  • Online ISBN: 978-3-540-44557-9

  • eBook Packages: Springer Book Archive

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