Logical Relations and Inductive/Coinductive Types

  • Thorsten Altenkirch
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1584)


We investigate a λ calculus with positive inductive and coinductive types , which we call λ μ,ν , using logical relations. We show that parametric theories have the strong categorical properties, that the representable functors and natural transformations have the expected properties. Finally we apply the theory to show that terms of functorial type are almost canonical and that monotone inductive definitions can be reduced to positive in some cases.


Natural Transformation Parametric Theory Logical Relation Extensional Theory Combinatory Logic 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Thorsten Altenkirch
    • 1
  1. 1.Ludwig-Maximilians-UniversitätMünchenGermany

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