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International Conference on Mathematics of Program Construction

MPC 2002: Mathematics of Program Construction pp 148–174Cite as

Type-Indexed Data Types

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2386))

Abstract

A polytypic function is a function that can be instantiated on many data types to obtain data type specific functionality. Examples of polytypic functions are the functions that can be derived in Haskell, such as show, read, and ‘==’. More advanced examples are functions for digital searching, pattern matching, unification, rewriting, and structure editing. For each of these problems, we not only have to define polytypic functionality, but also a type-indexed data type: a data type that is constructed in a generic way from an argument data type. For example, in the case of digital searching we have to define a search tree type by induction on the structure of the type of search keys. This paper shows how to define type-indexed data types, discusses several examples of type-indexed data types, and shows how to specialize type-indexed data types. The approach has been implemented in Generic Haskell, a generic programming extension of the functional language Haskell.

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Author information

Authors and Affiliations

  1. Institut für Informatik III, Universität Bonn, Römerstraße 164, 53117, Bonn, Germany

    Ralf Hinze

  2. Institute of Information and Computing Sciences, Utrecht University, P.O.Box 80.089, 3508 TB, Utrecht, The Netherlands

    Ralf Hinze, Johan Jeuring & Andres Löh

  3. Open University, Heerlen, The Netherlands

    Johan Jeuring

Authors
  1. Ralf Hinze
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  2. Johan Jeuring
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  3. Andres Löh
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Editor information

Editors and Affiliations

  1. Computing Laboratory, University of Kent at Canterbury, CT2 7NF, Canterbury, Kent, UK

    Eerke A. Boiten

  2. Institut für Informatik, Universität Augsburg, Universitätsstr. 14, 86135, Augsburg, Germany

    Bernhard Möller

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© 2002 Springer-Verlag Berlin Heidelberg

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Hinze, R., Jeuring, J., Löh, A. (2002). Type-Indexed Data Types. In: Boiten, E.A., Möller, B. (eds) Mathematics of Program Construction. MPC 2002. Lecture Notes in Computer Science, vol 2386. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45442-X_10

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  • DOI: https://doi.org/10.1007/3-540-45442-X_10

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43857-1

  • Online ISBN: 978-3-540-45442-7

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