Rewriting induction (Reddy, 1990) is an automated proof method for inductive theorems of term rewriting systems. Reasoning by the rewriting induction is based on the noetherian induction on some reduction order and the original rewriting induction is not capable of proving theorems which are not orientable by that reduction order. To deal with such theorems, Bouhoula (1995) as well as Dershowit...

Programming in the large require the use of formal speci cation languages for describing program requirements and a method to test (automatically) such requirements. These methods can also be applied in other areas like complex system modeling. In this thesis we study the theoretical kernel of a formal speci cation language, named Calculus of Re nements (COR), based on the use of monotonic incl...

We address the problem of an efficient rewriting strategy for general term rewriting systems. Several strategies have been proposed over the last two decades for rewriting, the most efficient of all being the natural rewriting strategy [9]. All the strategies so far, including natural rewriting, assume that the given term rewriting system is a left-linear constructor system. Although these rest...

A simple method is proposed for testing equivalence in a restricted domain of two given term rewriting systems. By using the Church-Rosser property and the teachability of term rewriting systems, the method allows us to prove equivalence of these systems without the explicit use of induction; this proof usually requires some kind of induction. The method proposed is a general extension of induc...

We study approximate, that is contained and containing, rewritings of queries using views. We consider conjunctive queries with arithmetic comparisons (CQACs), which capture the full expressive power of SQL select-project-join queries. For contained rewritings, we present a sound and complete algorithm for constructing, for CQAC queries and views, a maximally-contained rewriting (MCR) whose all...

A property is called persistent if for any manysorted term rewriting system , has the property if and only if term rewriting system , which results from by omitting its sort information, has the property . In this paper, we show that termination is persistent for right-linear overlay term rewriting systems and we give the example as application of this result. Furthermore we obtain that termina...

Outermost-needed rewriting/narrowing is a sound and complete optimal demand-driven strategy for the class of inductively sequential constructor systems. Its parallel extension, known as weakly, deals with non-inductively sequential constructor systems. Recently, refinements of (weakly) outermost-needed rewriting and narrowing have been obtained. These new strategies are called natural rewriting...

String diagrams are a powerful and intuitive graphical syntax, originating in theoretical physics later formalised the context of symmetric monoidal categories. In recent years, they have found application modelling various computational structures, fields as diverse Computer Science, Physics, Control Theory, Linguistics, Biology. several these proposals, transformations systems modelled rewrit...

This paper places concurrent rewriting in the perspective of supporting the development and use of computational systems. We brieey recall the usefulness of computational systems (i.e. a rewriting theory with strategies) as a logical framework. We then show that the right implementation model for concurrent rewriting allows us to give a meaning to the concurrent rewrite of overlapping redexes. ...