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Exploring the Regular Tree Types

  • Peter Morris
  • Thorsten Altenkirch
  • Conor McBride
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3839)

Abstract

In this paper we use the Epigram language to define the universe of regular tree types—closed under empty, unit, sum, product and least fixpoint. We then present a generic decision procedure for Epigram’s in-built equality at each type, taking a complementary approach to that of Benke, Dybjer and Jansson [7]. We also give a generic definition of map, taking our inspiration from Jansson and Jeuring [21]. Finally, we equip the regular universe with the partial derivative which can be interpreted functionally as Huet’s notion of ‘zipper’, as suggested by McBride in [27] and implemented (without the fixpoint case) in Generic Haskell by Hinze, Jeuring and Löh [18]. We aim to show through these examples that generic programming can be ordinary programming in a dependently typed language.

Keywords

Type Theory Functional Programming Type Constructor Functional Programming Language International Summer School 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Peter Morris
    • 1
  • Thorsten Altenkirch
    • 1
  • Conor McBride
    • 1
  1. 1.School of Computer Science and Information TechnologyUniversity of Nottingham 

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