Continuous and Completely Distributive Lattices

Klaus Keimel and Jimmie Lawson
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Klaus Keimel: University of Manitoba, Department of Mathematics
Jimmie Lawson: University of Caen, Department of Mathematics

Chapter Chapter 1 in Lattice Theory: Special Topics and Applications, 2014, pp 5-53 from Springer

Abstract: 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.

Keywords: Distributive Lattice; Complete Lattice; Continuous Lattice; Compact Element; Domain Equation (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/978-3-319-06413-0_1

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