Stream Productivity by Outermost Termination

Streams are infinite sequences over a given data type. A stream specification is a set of equations intended to define a stream. A core property is productivity: unfolding the equations produces the intended stream in the limit. In this paper we show that productivity is equivalent to termination with respect to the balanced outermost strategy of a TRS obtained by adding an additional rule. For specifications not involving branching symbols balancedness is obtained for free, by which tools for proving outermost termination can be used to prove productivity fully automatically

Well-definedness of Streams by Transformation and Termination

Streams are infinite sequences over a given data type. A stream specification is a set of equations intended to define a stream. We propose a transformation from such a stream specification to a term rewriting system (TRS) in such a way that termination of the resulting TRS implies that the stream specification is well-defined, that is, admits a unique solution. As a consequence, proving well-definedness of several interesting stream specifications can be done fully automatically using present powerful tools for proving TRS termination. In order to increase the power of this approach, we investigate transformations that preserve semantics and well-definedness. We give examples for which the above mentioned technique applies for the ransformed specification while it fails for the original one

Behavioral Rewrite Systems and Behavioral Productivity

Abstract. This paper introduces behavioral rewrite systems, where rewriting is used to evaluate experiments, and behavioral productivity, which says that each experiment can be fully evaluated, and investigates some of their properties. First, it is shown that, in the case of (infinite) streams, behavioral productivity generalizes and may bring to a more basic rewriting setting the existing notion of stream productivity defined in the context of infinite rewriting and lazy strategies; some arguments are given that in some cases one may prefer the behavioral approach. Second, a behavioral productivity criterion is given, which reduces the problem to conventional term rewrite system termination, so that one can use off-the-shelf termination tools and techniques for checking behavioral productivity in general, not only for streams. Finally, behavioral productivity is shown to be equivalent to a proof-theoretic (rather than model-theoretic) notion of behavioral well-specifiedness, and its difficulty in the arithmetic hierarchy is shown to be Π 0 2 -complete. All new concepts are exemplified over streams, infinite binary trees, and processes

A tool proving well-definedness of streams using termination tools

A stream specification is a set of equations intended to define a stream, that is, an infinite sequence over a given data type. In [5] a transformation from such a stream specification to a TRS is defined in such a way that termination of the resulting TRS implies that the stream specification admits a unique solution. In this tool description we present how proving such well-definedness of several interesting boolean stream specifications can be done fully automatically using present powerful tools for proving TRS termination

A tool proving well-definedness of streams using termination tools

A stream specification is a set of equations intended to define a stream, that is, an infinite sequence over a given data type. In [5] a transformation from such a stream specification to a TRS is defined in such a way that termination of the resulting TRS implies that the stream specification admits a unique solution. In this tool description we present how proving such well-definedness of several interesting boolean stream specifications can be done fully automatically using present powerful tools for proving TRS termination