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)


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.


Type Class Category Theory Equational Theory Universal Algebra Constructive Analysis 
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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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