Domain Theory

Synopsis

Syntax and semantics; denotational semantics; the need for mathematical models. The denotational semantics of a simple programming languages. Partial orders. Information systems: tokens, consistency, entailment, order properties, finite and infinite elements. Domain constructors: lifting, sum, product, function space, powerset; monotonicity and continuity; the solution of domain equations.

Applications of topology to domains. Continuous domains.

Measurement on domains. Domain-theoretic models of topological spaces.

Domain semantics for functional lanaguages.