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Domains in a realizability framework

  • Roberto M. Amadio
CAAP Colloquium On Trees In Algebra And Programming
Part of the Lecture Notes in Computer Science book series (LNCS, volume 493)

Abstract

We aim to relate and develop various approaches to a theory of domains in a realizability framework.

In the first part we develop the theory in an arbitrary partial cartesian closed category and, as a particular instance, in the category of partial equivalence relations (per) over an arbitrary partial combinatory algebra (pca). In this way one obtains the category of separated pers that may be regarded as a universe of partially ordered sets and monotone maps with strong closure properties.

Pursuing the analogy with domain theory one tries to build a category of directed complete partial orders and continuous maps. We consider two main approaches: one based on Kleene's pca of numbers and partial recursive functions and the other based on Scott's D λ-model.

Contents: 0. Introduction, 1. Dominance and Intrinsic Preorder, 2. Separated Partial Equivalence Relations (Σper), 3. N-completeness, 4. Σ-connection and Extensionality, 5. D-completeness and Uniformity, 6. Conclusion.

Keywords

Full Subcategory Terminal Object Realizability Framework Admissible Family Partial Recursive Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Roberto M. Amadio
    • 1
  1. 1.Labo. Informatique, Ecole Normale SupérieureParis

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