Internal type theory

  • Peter Dybjer
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1158)


We introduce categories with families as a new notion of model for a basic framework of dependent types. This notion is close to ordinary syntax and yet has a clean categorical description. We also present categories with families as a generalized algebraic theory. Then we define categories with families formally in Martin-Löf's intensional intuitionistic type theory. Finally, we discuss the coherence problem for these internal categories with families.


Type Theory Dependent Type Proof Assistant Coherence Condition Equality Judgement 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Peter Dybjer
    • 1
  1. 1.Department of Computing ScienceChalmers University of TechnologyGöteborgSweden

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