Continuous and completely distributive lattices

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