Well-definedness of Streams by Transformation and Termination (original) (raw)

A Tool Proving Well-Definedness of Streams Using Termination Tools

Lecture Notes in Computer Science, 2009

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.

Well-definedness of Streams by 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 TRS in such a way that termination of the resulting TRS implies that the stream specification admits a unique solution. As a consequence, proving such well-definedness of several interesting stream specifications can be done fully automatically using present powerful tools for proving TRS termination.

mu-term: A Tool for Proving Termination of Context-Sensitive Rewriting

Rewriting Techniques and Applications, 2004

Restrictions of rewriting can eventually achieve termination by pruning all infinite rewrite sequences issued from every term. Contextsensitive rewriting (CSR) is an example of such a restriction. In CSR, the replacements in some arguments of the function symbols are permanently forbidden. This paper describes mu-term, a tool which can be used to automatically prove termination of CSR. The tool implements the generation of the appropriate orderings for proving termination of CSR by means of polynomial interpretations over the rational numbers. In fact, mu-term is the first termination tool which generates term orderings based on such polynomial interpretations. These orderings can also be used, in a number of different ways, for proving termination of ordinary rewriting. Proofs of termination of CSR are also possible via existing transformations to TRSs (without any replacement restriction) which are also implemented in mu-term.

Proving termination of rewriting automatically

In this paper we give an introduction to term rewriting and termi-nation. Moreover, we sketch some developments in proving termination of rewriting automatically, in particular in using satisfiability for finding suitable interpretations.

An overview of term rewriting systems

African Journal of Mathematics and Computer Science Research, 2012

It is well-known that termination of finite term of rewriting systems is generally undecidable. Notwithstanding, a remarkable result is that, rewriting systems are Turing complete. A number of methods have been developed to establish termination for certain term of rewriting systems, particularly occurring in practical situations. In this paper, we present an overview of the existing methods used for termination proofs. We also outline areas of applications of term rewriting systems along with recent developments in regard to automated termination proofs.

Termination of term rewriting: interpretation and type elimination

Journal of Symbolic Computation, 1994

We investigate proving termination of term rewriting systems by interpretation of terms in a well-founded monotone algebra. The well-known polynomial interpretations can be considered as a particular case in this framework. A classi cation of types of termination, including simple termination, is proposed based on properties in the semantic level. A transformation on term rewriting systems eliminating distributive rules is introduced. Using this distribution elimination a new termination proof of the system SUBST of Hardin and Laville (1986) is given. This system describes explicit substitution incalculus. Another tool for proving termination is based on introduction and removal of type restrictions. A property of many-sorted term rewriting systems is called persistent if it is not a ected by removing the corresponding typing restriction. Persistence turns out to be a generalization of direct sum modularity, but is more powerful for both proving con uence and termination. Termination is proved to be persistent for the class of term rewriting systems for which not both duplicating rules and collapsing rules occur, generalizing a similar result of Rusinowitch for modularity. This result has nice applications, in particular in undecidability proofs.

A path ordering for proving termination of term rewriting systems

Mathematical Foundations of …, 1985

A new partial ordering scheme for proving uniform termination of term rewriting systems is presented. The basic idea is that two terms are compared by comparing the paths through them. It is shown that the ordering is a well-founded simplification ordering and also a ...

Size-Change Termination for Term Rewriting

Lecture Notes in Computer Science, 2003

, a new size-change principle was proposed to verify termination of functional programs automatically. We extend this principle in order to prove termination and innermost termination of arbitrary term rewrite systems (TRSs). Moreover, we compare this approach with existing techniques for termination analysis of TRSs (such as recursive path orderings or dependency pairs). It turns out that the size-change principle on its own fails for many examples that can be handled by standard techniques for rewriting, but there are also TRSs where it succeeds whereas existing rewriting techniques fail. In order to benefit from their respective advantages, we show how to combine the size-change principle with classical orderings and with dependency pairs. In this way, we obtain a new approach for automated termination proofs of TRSs which is more powerful than previous approaches.

Total Termination of Term Rewriting is Undecidable

Journal of Symbolic Computation - JSC, 1995

Usually termination of term rewriting systems (TRS's) is proved bymeans of a monotonic well-founded order. If this order is total on groundterms, the TRS is called totally terminating. In this paper we prove thattotal termination is an undecidable property of finite term rewriting systems.The proof is given by means of Post's Correspondence Problem.1 IntroductionTermination of term rewriting systems (TRS's) is an important property. Oftentermination proofs are given by defining an order ...