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Towards a Categorical Calculus for Critical-Pair/Completion

  • Karel Stokkermans
Part of the Texts and Monographs in Symbolic Computation book series (TEXTSMONOGR)

Abstract

The ultimate aim of the research reported here is to provide a general framework for algorithms that show the following two characteristics: critical pairs and completion. Here completion means extending a certain set of reductions (given by, e.g., rewrite rules, or polynomials from an ideal) until that set fulfills some completeness property. Critical pairs are used for the selection of elements for which the reduction relation to be completed is not yet confluent. The selection is essentially done by superposing left hand sides of basic reduction rules, and testing whether applying the applicable reduction rules yield the same reducts. If not, one forces confluence by adding a reduction rule between the differing reducts (if possible without violating certain conditions on the reduction relation).

Keywords

Normal Form Reduction Relation Universal Property Reduction Rule Critical Pair 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© Springer-Verlag Wien 1995

Authors and Affiliations

  • Karel Stokkermans

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