A Model of Countable Nondeterminism in Guarded Type Theory

  • Aleš Bizjak
  • Lars Birkedal
  • Marino Miculan
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8560)


We show how to construct a logical relation for countable nondeterminism in a guarded type theory, corresponding to the internal logic of the topos Sh ω 1 of sheaves over ω 1. In contrast to earlier work on abstract step-indexed models, we not only construct the logical relations in the guarded type theory, but also give an internal proof of the adequacy of the model with respect to standard contextual equivalence. To state and prove adequacy of the logical relation, we introduce a new propositional modality. In connection with this modality we show why it is necessary to work in the logic of bf Shω 1.


Type Theory Operational Semantic Logical Relation Internal Logic Impossible World 
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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Aleš Bizjak
    • 1
  • Lars Birkedal
    • 1
  • Marino Miculan
    • 2
  1. 1.Aarhus UniversityAarhusDenmark
  2. 2.University of UdineUdineItaly

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