Wellfounded Trees and Dependent Polynomial Functors

  • Nicola Gambino
  • Martin Hyland
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3085)


We set out to study the consequences of the assumption of types of wellfounded trees in dependent type theories. We do so by investigating the categorical notion of wellfounded tree introduced in [16]. Our main result shows that wellfounded trees allow us to define initial algebras for a wide class of endofunctors on locally cartesian closed categories.


Type Theory Natural Transformation Monoidal Category Left Adjoint Forgetful Functor 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Nicola Gambino
    • 1
  • Martin Hyland
    • 1
  1. 1.Department of Pure Mathematics and Mathematical StatisticsUniversity of Cambridge 

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