Well-definedness of Streams by Transformation and Termination

Abstract

Streams are infinite sequences over a given data type. A stream specificationis a set of equations intended to define a stream. We propose a transformationfrom such a stream specification to a term rewriting system (TRS) in such a waythat termination of the resulting TRS implies that the stream specification iswell-defined, that is, admits a unique solution. As a consequence, provingwell-definedness of several interesting stream specifications can be done fullyautomatically using present powerful tools for proving TRS termination. Inorder to increase the power of this approach, we investigate transformationsthat preserve semantics and well-definedness. We give examples for which theabove mentioned technique applies for the ransformed specification while itfails for the original one