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Automata, Languages and Programming

Volume 3142 of the series Lecture Notes in Computer Science pp 59-71

Representing Nested Inductive Types Using W-Types

  • Michael AbbottAffiliated withCarnegie Mellon UniversityDepartment of Mathematics and Computer Science, University of Leicester
  • , Thorsten AltenkirchAffiliated withCarnegie Mellon UniversitySchool of Computer Science and Information Technology, Nottingham University
  • , Neil GhaniAffiliated withCarnegie Mellon UniversityDepartment of Mathematics and Computer Science, University of Leicester

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Abstract

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.