Comparing free algebras in Topological and Classical Domain Theory

  • Authors:
  • Ingo Battenfeld

  • Affiliations:
  • Fakultät für Informatik, Technische Universität Dortmund, Lehrstuhl 10, 44221Dortmund, Germany

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2010

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Abstract

We compare how computational effects are modelled in Classical Domain Theory and Topological Domain Theory. Both of these theories provide powerful toolkits for denotational semantics: Classical Domain Theory having been introduced by Scott, and well established and developed since; Topological Domain Theory being a generalization in which topologies more general than the Scott-topology are admitted. Computational effects can be modelled using free algebra constructions, according to Plotkin and Power, and we show that for a wide range of computational effects, including all the classical powerdomains, this free algebra construction coincides in Classical and Topological Domain Theory, when restricted to countably-based continuous domains.