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General synthetic domain theory — A logical approach (extended abstract)

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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

Synthetic Domain Theory (SDT) is a version of Domain Theory where “all functions are continuous”. In [14, 12] there has been developed a logical and axiomatic version of SDT which is special in the sense that it captures the essence of Domain Theory à la Scott but rules out other important notions of domain.

In this article we will give a logical and axiomatic account of General Synthetic Domain Theory (GSDT) aiming to grasp the structure common to all notions of domain as advocated by various authors. As in [14, 12] the underlying logic is a sufficiently expressive version of constructive type theory. We start with a few basic axioms giving rise to a core theory on top of which we study various notions of predomains as well-complete and replete S-spaces [9], define the appropriate notion of domain and verify the usual induction principles.

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Authors and Affiliations

  1. Institut für Informatik, Ludwig-Maximilians-Universität, Oettingenstr. 67, D-80538, München

    B. Reus

  2. Fachbereich 4 Mathematik, TH Darmstadt, Schlossgartenstr. 7, D-64289, Darmstadt

    Th. Streicher

Authors
  1. B. Reus
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  2. Th. Streicher
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Eugenio Moggi Giuseppe Rosolini

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© 1997 Springer-Verlag Berlin Heidelberg

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Reus, B., Streicher, T. (1997). General synthetic domain theory — A logical approach (extended abstract). 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/BFb0026995

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  • DOI: https://doi.org/10.1007/BFb0026995

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63455-3

  • Online ISBN: 978-3-540-69552-3

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