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Developing the Algebraic Hierarchy with Type Classes in Coq

  • Bas Spitters
  • Eelis van der Weegen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6172)

Abstract

We present a new formalization of the algebraic hierarchy in Coq, exploiting its new type class mechanism to make practical a solution formerly thought infeasible. Our approach addresses both traditional challenges as well as new ones resulting from our ambition to build upon this development a library of constructive analysis in which abstraction penalties inhibiting efficient computation are reduced to a bare minimum. To support mathematically sound abstract interfaces for ℕ, ℤ, and ℚ, our formalization includes portions of category theory and multisorted universal algebra.

Keywords

Type Class Category Theory Equational Theory Universal Algebra Constructive Analysis 
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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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Bas Spitters
    • 1
  • Eelis van der Weegen
    • 1
  1. 1.Radboud University Nijmegen 

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