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International Conference on Theorem Proving in Higher Order Logics

TPHOLs 2008: Theorem Proving in Higher Order Logics pp 278–293Cite as

First-Class Type Classes

  • Conference paper

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 5170)

Abstract

Type Classes have met a large success in Haskell and Isabelle, as a solution for sharing notations by overloading and for specifying with abstract structures by quantification on contexts. However, both systems are limited by second-class implementations of these constructs, and these limitations are only overcomed by ad-hoc extensions to the respective systems. We propose an embedding of type classes into a dependent type theory that is first-class and supports some of the most popular extensions right away. The implementation is correspondingly cheap, general and integrates well inside the system, as we have experimented in Coq. We show how it can be used to help structured programming and proving by way of examples.

Keywords

  • Type Theory
  • Type Class
  • Dependent Type
  • Proof Assistant
  • Proof Search

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Author information

Authors and Affiliations

  1. Univ. Paris Sud, CNRS,Laboratoire LRI, UMR 8623,Orsay, F-91405 INRIA Saclay, ProVal, Parc Orsay Université, F-91893, France

    Matthieu Sozeau

  2. University of Nottingham, UK

    Nicolas Oury

Authors
  1. Matthieu Sozeau
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  2. Nicolas Oury
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Editor information

Editors and Affiliations

  1. Department of Electrical and Computer Engineering, Concordia University, 1455 de Maisonneuve Blvd. W, H3G 1M8, Montreal, Quebec, Canada

    Otmane Ait Mohamed

  2. National Institute of Aerospace, 100 Exploration Way, VA 23666, Hampton, USA

    César Muñoz

  3. Dept. of Electrical & Computer Engineering, Concordia University, 1455 de Maisonette W, H3G 1M8, Montreal, Quebec, Canada

    Sofiène Tahar

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Sozeau, M., Oury, N. (2008). First-Class Type Classes. In: Mohamed, O.A., Muñoz, C., Tahar, S. (eds) Theorem Proving in Higher Order Logics. TPHOLs 2008. Lecture Notes in Computer Science, vol 5170. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-71067-7_23

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  • DOI: https://doi.org/10.1007/978-3-540-71067-7_23

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-71065-3

  • Online ISBN: 978-3-540-71067-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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