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Continuous and Completely Distributive Lattices

In: Lattice Theory: Special Topics and Applications

Author

Listed:
  • Klaus Keimel

    (University of Manitoba, Department of Mathematics)

  • Jimmie Lawson

    (University of Caen, Department of Mathematics)

Abstract

The study of continuous lattices was initiated by Dana Scott in the late 1960s in order to build mathematical models for certain constructs in theoretical computer science ([638] in LTF), and computational notions and motivations have continued to play a key role in the theory. Early successes included construction of a denotational semantics for certain programming languages where programs were semantically interpreted as functions between appropriate input and output domains (see, e.g., [271]) and construction of a specific domain of computation that provided a model for the untyped lambda calculus (see, [639] in LTF), no concrete model of the untyped lambda calculus having hitherto been given.

Suggested Citation

  • Klaus Keimel & Jimmie Lawson, 2014. "Continuous and Completely Distributive Lattices," Springer Books, in: George Grätzer & Friedrich Wehrung (ed.), Lattice Theory: Special Topics and Applications, edition 127, chapter 0, pages 5-53, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-06413-0_1
    DOI: 10.1007/978-3-319-06413-0_1
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