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.
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© 2014 Springer International Publishing Switzerland
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Keimel, K., Lawson, J. (2014). Continuous and Completely Distributive Lattices. In: Grätzer, G., Wehrung, F. (eds) Lattice Theory: Special Topics and Applications. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-06413-0_1
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DOI: https://doi.org/10.1007/978-3-319-06413-0_1
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