"Temporal media" is information that is directly consumed by a user, and that varies with time. Examples include music, digital sound files, computer animations, and video clips. We are interested in how to represent this information at an abstract level; how to manipulate these representations; how to assign a meaning, or interpretation, to them; and how to reason about such meanings.

To achieve these goals, we define a polymorphic representation of temporal media that allows combining media values in generic ways, independent of the underlying media type. We describe three types of operations on and properties of temporal media: (a) syntactic operations and properties, that depend only on the structural representation of the media, (b) temporal operations and properties, that additionally depend on time, and (c) semantic operations and properties, that depend on the meaning, or interpretation, of the media. The latter development leads to an algebraic theory of polymorphic temporal media that is valid for underlying media types that satisfy specific constraints. The key technical result is an axiomatic semantics that is both sound and complete.