Towards Normalization by Evaluation for the βη-Calculus of Constructions

  • Andreas Abel
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6009)


We consider the Calculus of Constructions with typed beta-eta equality and an algorithm which computes long normal forms. The normalization algorithm evaluates terms into a semantic domain, and reifies the values back to terms in normal form. To show termination, we interpret types as partial equivalence relations between values and type constructors as operators on PERs. This models also yields consistency of the beta-eta-Calculus of Constructions. The model construction can be carried out directly in impredicative type theory, enabling a formalization in Coq.


Normal Form Type Theory Proof Assistant Type Constructor Strong Normalization 
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

  • Andreas Abel
    • 1
  1. 1.Project PI.R2, INRIA Rocquencourt and PPS, Paris 

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