A Tool Proving Well-Definedness of Streams Using Termination Tools

Abstract

Abstract.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.

Stream Productivity by Outermost Termination

“…In [9] a related approach is described, while an implementation of that technique is described in [8]. However, there the result is on well-definedness of stream specifications, which is a slightly weaker notion than productivity.…”

Well-definedness of Streams by Transformation and Termination

“…This paper is an extension of the RTA conference paper [19] and the corresponding tool description [18]. Compared to these papers • some definitions have been slightly modified in order to cover a more general setting, • the process of unfolding and other transformations preserving the semantics have been worked out in detail in Section 3 and Section 8, while in [19] only some of the ideas were sketched by examples, • more examples are given, in particular specifying the paper folding stream and the Kolakoski stream.…”

“…This paper is an extension of the RTA conference paper [19] and the corresponding tool description [18]. Compared to these papers • some definitions have been slightly modified in order to cover a more general setting,…”