Representing Nested Inductive Types Using W-Types

  • Michael Abbott
  • Thorsten Altenkirch
  • Neil Ghani
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3142)


We show that strictly positive inductive types, constructed from polynomial functors, constant exponentiation and arbitrarily nested inductive types exist in any Martin-Löf category (extensive locally cartesian closed category with W-types) by exploiting our work on container types. This generalises a result by Dybjer (1997) who showed that non-nested strictly positive inductive types can be represented using W-types. We also provide a detailed analysis of the categorical infrastructure needed to establish the result.


Type Theory Natural Transformation Left Adjoint Elimination Rule Inductive Type 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Michael Abbott
    • 1
  • Thorsten Altenkirch
    • 2
  • Neil Ghani
    • 1
  1. 1.Department of Mathematics and Computer ScienceUniversity of Leicester 
  2. 2.School of Computer Science and Information TechnologyNottingham University 

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