<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.

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.

There are domain-theoretic computational models in other branches of mathematics including dynamical systems, fractals, measure theory, integration theory, probability theory, and stochastic processes.