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Simultaneous Critical Pairs and ChurchRosser Property
 Proc. 9th RTA
, 1998
"... . We introduce simultaneous critical pairs, which account for simultaneous overlapping of several rewrite rules. Based on this, we introduce a new CRcriterion widely applicable to arbitrary leftlinear term rewriting systems. Our result extends the wellknown criterion given by Huet (1980), Toyama ..."
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. We introduce simultaneous critical pairs, which account for simultaneous overlapping of several rewrite rules. Based on this, we introduce a new CRcriterion widely applicable to arbitrary leftlinear term rewriting systems. Our result extends the wellknown criterion given by Huet (1980), Toyama (1988), and Oostrom (1997) and incomparable with other wellknown criteria for leftlinear systems. 1 Introduction ChurchRosser (CR for short) property is one of the most important properties of rewrite systems. For (nite) strongly normalising systems, this property is decidable by testing joinability of critical pairs whereas for arbitrary systems, undecidable even if they are weak CR. For this reason, many researchers have been interested in various (decidable) sucient conditions ensuring this property. We refer to these conditions as CRcriteria. To obtain CRcriteria, the criticalpairbased approach is still available as far as leftlinear systems are concerned (Note that nonleft...
A Decidable SecondOrder Semantic Matching in Isabelle
"... We present a complete matching algorithm and an efficient implementation in the theorem prover Isabelle for solving a class of secondorder semantic matching problems, where the equational theory with respect to which the semantic matching is performed has a convergent pattern rewrite system. For a ..."
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We present a complete matching algorithm and an efficient implementation in the theorem prover Isabelle for solving a class of secondorder semantic matching problems, where the equational theory with respect to which the semantic matching is performed has a convergent pattern rewrite system. For a certain class of semantic matching problems this algorithm can even be used as a decision procedure. A number of interesting examples illustrate the application of our approach in the semantic matching of schematic rules in theorem proving and formula manipulation, where the schematic aspects can be presented by defined functions. 1 Introduction The problem of matching and unification modulo a set of equations (i.e. semantic matching and unification) has been extensively studied over the last 10 years, and various algorithms have been discovered. In particular, techniques based on narrowing have been developed and proved complete [7, 14, 25] in solving unification problems associated with c...
prof.dr. C.A. Middelburg CIPDATA LIBRARY TECHNISCHE UNIVERSITEIT EINDHOVEN
"... ter verkrijging van de graad van doctor aan de ..."
Traces of Epimorphism Classes
"... Classes of morphisms that occur as preimages of the class of all epimorphisms, of all extremal epimorphisms, respectively of all retractions under some faithful functor are characterized by suitable closure properties. The corresponding question for regular or strict epimorphisms is presented as an ..."
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Classes of morphisms that occur as preimages of the class of all epimorphisms, of all extremal epimorphisms, respectively of all retractions under some faithful functor are characterized by suitable closure properties. The corresponding question for regular or strict epimorphisms is presented as an open problem. A further application of the methods developed in this context yields a similar characterization of classes of morphisms that are final w.r.t. some faithful functor.