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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

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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

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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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

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