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Church-Rosser Property

A reduction system is said to posses the Church-Rosser property if, for all x and y such that x<->_*y, there exists a z such that x->_*z and y->_*z.

A reduction system is Church-Rosser iff it is confluent.

See also

Church-Rosser Theorem, Confluent, Critical Pair, Finitely Terminating, Knuth-Bendix Completion Algorithm, Reduction Order

This entry contributed by Alex Sakharov (author's link)

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References

Baader, F. and Nipkow, T. Term Rewriting and All That. Cambridge, England: Cambridge University Press, 1999.Wolfram, S. A New Kind of Science. Champaign, IL: Wolfram Media, pp. 507 and 1036-1037, 2002.

Referenced on Wolfram|Alpha

Church-Rosser Property

Cite this as:

Sakharov, Alex. "Church-Rosser Property." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/Church-RosserProperty.html

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