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Free dynamics and algebraic semantics

  • Section B Computation Theory in Category
  • Conference paper
  • First Online:
Fundamentals of Computation Theory (FCT 1977)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 56))

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Abstract

Adámek has recently given general criteria for the construction of a free X-dynamics. We specialize this result to the case in which the free dynamics is over the initial object, noting that the result, μ0:A X → A is an isomorphism. This result not only specializes to the theory of minimal fixed points, but provides a new method of constructing solutions to Scott's domain equations which does not require coincidence of limits and colimits. Finally, we show how free dynamics allow us to construct semantics for programming schemes.

This research was supported in part by NSF Grant No. DCR 72-03733 A01, and was conducted while the author was on 1976–77 sabbatical at the University of Edinburgh. Discussions with Rod Burstall, Robin Milner, John Reynolds and, especially, Gordon Plotkin were most helpful.

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References

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Authors and Affiliations

  1. Computer and Information Science, University of Massachusetts at Amherst, 01003, MA, USA

    Michael A. Arbib

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  1. Michael A. Arbib
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Marek Karpiński

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© 1977 Springer-Verlag Berlin Heidelberg

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Arbib, M.A. (1977). Free dynamics and algebraic semantics. In: Karpiński, M. (eds) Fundamentals of Computation Theory. FCT 1977. Lecture Notes in Computer Science, vol 56. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-08442-8_88

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  • DOI: https://doi.org/10.1007/3-540-08442-8_88

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08442-6

  • Online ISBN: 978-3-540-37084-0

  • eBook Packages: Springer Book Archive

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