Tree-Manipulating Systems and Church-Rosser Theorems
Journal of the ACM (JACM)
Computing in Systems Described by Equations
Computing in Systems Described by Equations
Unique normal forms and confluence of rewrite systems: persistence
IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 1
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A term rewriting system is a finite set of axiom schemata of the form A@@@@B where A and B are terms that contain variables. An important question for such systems is whether normal forms are unique (i.e. each term has at most one normal form). For schemata without repeated variables (i.e. no variable is repeated on the left side of an axiom schema), O'Donnell [O'D] has given sufficient conditions for the confluence property (Church-Rosser property), a stronger property than unique normal forms. Klop [Klo] has shown that the confluence property does not necessarily hold in these systems when repeated variables are allowed. This paper shows that normal forms are unique in such systems despite the lack of the confluence property.