Stream Ring Theory

A stream is an ever expanding and contracting list of objects. Stream functions consume objects from an incoming stream and produce objects for an outgoing stream. The presented stream algebra enables the composition of functional structures that respect the axioms and entailed theorems of algebraic ring theory. The algebra can be used to write expressions that are computationally equivalent to any Turing machine and as such, can be leveraged as the theoretical foundation for all stream-based processing languages and systems.