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The semantics of Miranda's algebraic types

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Mathematical Foundations of Programming Language Semantics (MFPS 1987)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 298))

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Abstract

Miranda has two interesting features in its typing system: implicit polymorphism (also known as ML-style polymorphism) and algebraic types. Algebraic types create new types from old and can operate on arbitrary types. This paper argues that functions on types, or type constructors, best represent the meaning of algebraic types. Building upon this idea, we develop a denotational semantics for algebraic types. We first define a typed lambda calculus that specifies type constructors. A semantic model of type constructors is then built, using the ideal model as a basis. (The ideal model gives the most natural semantics for Miranda's implicit polymorphism.) The model is shown to be sound with respect to this lambda calculus. Finally, we demonstrate how to use the model to interpret algebraic types, and prove that the translation produces elements in the model.

Partially supported by NSF Grants MCS-8402700, DCR-8603890, and DCR-8511190. The second author is supported by an NSF Graduate Fellowship.

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Author information

Author notes

  1. Jon G. Riecke

    Present address: MIT Laboratory for Computer Science, 545 Technology Square, 02139, Cambridge, MA

Authors and Affiliations

  1. Department of Computer Science, Williams College, 01267, Williamstown, MA

    Kim B. Bruce & Jon G. Riecke

Authors
  1. Kim B. Bruce
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  2. Jon G. Riecke
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Editor information

M. Main A. Melton M. Mislove D. Schmidt

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© 1988 Springer-Verlag Berlin Heidelberg

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Bruce, K.B., Riecke, J.G. (1988). The semantics of Miranda's algebraic types. In: Main, M., Melton, A., Mislove, M., Schmidt, D. (eds) Mathematical Foundations of Programming Language Semantics. MFPS 1987. Lecture Notes in Computer Science, vol 298. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-19020-1_25

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  • DOI: https://doi.org/10.1007/3-540-19020-1_25

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-19020-2

  • Online ISBN: 978-3-540-38920-0

  • eBook Packages: Springer Book Archive

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