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domain theory A branch of mathematics introduced by Dana Scott in 1970 as a mathematical theory of programming languages, and for nearly a quarter of a century developed almost exclusively in connection with denotational semantics in computer science. In denotational semantics of programming languages, the meaning of a program is taken to be an element of a domain. A domain is a mathematical structure consisting of a set of values (or "points") and an ordering relation, <= on those values. Domain theory is the study of such structures. ("<=" is written in LaTeX as subseteq) Different domains correspond to the different types of object with which a program deals. In a language containing functions, we might have a domain X -> Y which is the set of functions from domain X to domain Y with the ordering f <= g iff for all x in X, f x <= g x. In the pure lambda-calculus all objects are functions or application>s of functions to other functions. To represent the application>s of functions to other functions. To represent the
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