Streams, Stream Transformers and Domain Representations

We present a general theory for the computation of stream transformers of the form F : (R! B)! (T ! A), where time T and R, and data A and B, are discrete or continuous. We show how methods for representing topological algebras by algebraic domains can be applied to transformations of continuous streams. A stream transformer is continuous in the compact-open topology on continuous streams if and only if it has a continuous lifting to a standard algebraic domain representation of such streams. We also examine the important problem of representing discontinuous streams, such as signals T ! A, where time T is continuous and data A is discrete.