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Exploring the Regular Tree Types

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Types for Proofs and Programs (TYPES 2004)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3839))

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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.

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Authors and Affiliations

  1. School of Computer Science and Information Technology, University of Nottingham,  

    Peter Morris, Thorsten Altenkirch & Conor McBride

Authors
  1. Peter Morris
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  2. Thorsten Altenkirch
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  3. Conor McBride
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Editor information

Editors and Affiliations

  1. LRI, Univ Paris-Sud, CNRS, Orsay F-91405, INRIA Futurs, ProVal, F-91893, Orsay

    Jean-Christophe Filliâtre

  2. INRIA Saclay - Île-de-France, ProVal - Orsay 91893 and LRI, Univ Paris-Sud, CNRS - Orsay 91405LRI, Université Paris Sud and INRIA Futurs, Bât. 490, Université Paris Sud, F-91405, Orsay Cedex, France

    Christine Paulin-Mohring

  3. INRIA-Futurs at, LIX, École Polytechnique, Palaiseau, France

    Benjamin Werner

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Morris, P., Altenkirch, T., McBride, C. (2006). Exploring the Regular Tree Types. In: Filliâtre, JC., Paulin-Mohring, C., Werner, B. (eds) Types for Proofs and Programs. TYPES 2004. Lecture Notes in Computer Science, vol 3839. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11617990_16

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  • DOI: https://doi.org/10.1007/11617990_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-31428-8

  • Online ISBN: 978-3-540-31429-5

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