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Annual Symposium on Theoretical Aspects of Computer Science

STACS 1984: STACS 84 pp 174–185Cite as

Higher order data structures

Cartesian closure versus λ-calculus

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 166))

Abstract

We discuss connections of typed λ-calculus and cartesian closure and prove equivalence of the theories ‘up to abstraction’. This is a working out of ideas of Scott and Lambeck but in an abstract data type environment. The results serve as a basis for the discussion of higher order specifications. We demonstrate that higher order equations based on λ-calculus are more appropriate if the equivalence of λ-calculus and cartesian closure is to be preserved. We construct higher order theories for higher order specifications. For higher order models we discuss existence of initial models and completeness of higher order theories.

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Author information

Authors and Affiliations

  1. Informatik II, Universität Dortmund, Postfach 50 05 00, D-4600, Dortmund 50, Germany

    Axel Poigné

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  1. Axel Poigné
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M. Fontet K. Mehlhorn

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© 1984 Springer-Verlag Berlin Heidelberg

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Poigné, A. (1984). Higher order data structures. In: Fontet, M., Mehlhorn, K. (eds) STACS 84. STACS 1984. Lecture Notes in Computer Science, vol 166. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-12920-0_16

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  • DOI: https://doi.org/10.1007/3-540-12920-0_16

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-12920-2

  • Online ISBN: 978-3-540-38805-0

  • eBook Packages: Springer Book Archive

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