Confluent Reductions: Abstract Properties and Applications to Term Rewriting Systems

This paper gives new results, and presents old ones m a umfied formahsm, concerning ChurchRosser theorems for rewrmng systems Abstract confluence propentes, depending solely on axioms for a binary relatton called reduction, are first presented Results of Newman and others are presented m a unified formahsm The systemattc use of a powerful mductmn pnnciple permRs the generahzauon of results of Sethl on reduction modulo eqmvalence. Simphficatton systems operating on terms of a first-order logic are then considered. Results by Rosen and Knuth and Bendix are extended to give several new crtteria for confluence of these systems It ts then shown how these criteria yield new methods for the mechanizaUon of equattonal theories