Irrelevance in Type Theory with a Heterogeneous Equality Judgement

  • Andreas Abel
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6604)


Dependently typed programs contain an excessive amount of static terms which are necessary to please the type checker but irrelevant for computation. To obtain reasonable performance of not only the compiled program but also the type checker such static terms need to be erased as early as possible, preferably immediately after type checking. To this end, Pfenning’s type theory with irrelevant quantification, that models a distinction between static and dynamic code, is extended to universes and large eliminations. Novel is a heterogeneously typed implementation of equality which allows the smooth construction of a universal Kripke model that proves normalization, consistency and decidability.


dependent types proof irrelevance heterogeneously typed equality algorithmic equality logical relation universal Kripke model 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Andreas Abel
    • 1
  1. 1.Department of Computer ScienceLudwig-Maximilians-UniversityMunichGermany

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