The Cycle Contraction Mapping Theorem

This report lays the foundation for a theory of total correctness for programs not based upon termination. The Cycle Contraction Mapping Theorem is both an extension of Wadge''s cycle sum theorem for Kahn data flow and a generalisation of Banach''s contraction mapping theorem to a class of quasi metric spaces definable using the symmetric Partial Metric distance function. This work provides considerable evidence that it is possible after all to construct a metric theory for Scott style partial order domains.