The notion of abstract rewriting system is the simplest mathematical formalization of what is a rewriting system. It doesn’t presuppose anything on the nature of the syntactical objects which are rewritten, thus the word “abstract”.
An abstract rewriting system is given by a set and a binary relation on , ie. a subset of the cartesian product .
So this is a concept with an attitude: While an abstract re-writing system is just a relation, calling this relation an abstract rewriting system indicates that one is interested in studying the behaviour of chains of related elements (thought of as successive stages of rewriting ), for instance to see if they are confluent.
Wikipedia, Abstract rewriting system
Wikipedia, Confluence_(abstract_rewriting)
Last revised on November 25, 2022 at 06:03:34. See the history of this page for a list of all contributions to it.