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When Do Datatypes Commute?

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Category Theory and Computer Science (CTCS 1997)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1290))

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Abstract

Polytypic programs are programs that are parameterised by type constructors (like List), unlike polymorphic programs which are parameterised by types (like Int). In this paper we formulate precisely the polytypic programming problem of “commuting” two datatypes. The precise formulation involves a notion of higher order naturality. We demonstrate via a number of examples the relevance and interest of the problem, and we show that all “regular datatypes" (tree-like datatypes that one can define in a functional programming language) do indeed commute according to our specification. The framework we use is the theory of allegories, a combination of category theory with the pointfree relation calculus.

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Authors and Affiliations

  1. Department of Mathematics and Computing Science, Eindhoven University of Technology, The Netherlands

    Paul Hoogendijk & Roland Backhouse

Authors
  1. Paul Hoogendijk
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  2. Roland Backhouse
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Eugenio Moggi Giuseppe Rosolini

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© 1997 Springer-Verlag Berlin Heidelberg

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Hoogendijk, P., Backhouse, R. (1997). When Do Datatypes Commute?. In: Moggi, E., Rosolini, G. (eds) Category Theory and Computer Science. CTCS 1997. Lecture Notes in Computer Science, vol 1290. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0026992

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  • DOI: https://doi.org/10.1007/BFb0026992

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63455-3

  • Online ISBN: 978-3-540-69552-3

  • eBook Packages: Springer Book Archive

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