Theory of recursive functions and effective computability
Theory of recursive functions and effective computability
Recursive functions of symbolic expressions and their computation by machine, Part I
Communications of the ACM
Transformations and translations from the point of view of generalized finite automata theory
STOC '69 Proceedings of the first annual ACM symposium on Theory of computing
Context-free grammars on trees
STOC '69 Proceedings of the first annual ACM symposium on Theory of computing
Recursive definitions of partial functions and their computations
Proceedings of ACM conference on Proving assertions about programs
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We define a general class of tree-manipulating systems that includes many of the special cases from logic, linguistics, and automata theory. Systems possessing what we call the “Church-Rosser property” are appropriate for evaluation or translation processes: the end result of a complete sequence of applications of the rules does not depend on the order in which the rules were applied. We sketch the theoretical and practical advantages of such flexibility. We derive general sufficient conditions for the Church-Rosser property and apply them to some important tree-manipulating systems. Applications include tree transducers, the McCarthy formalism for recursive computation, and the classical Church-Rosser Theorem for the full lambda-calculus.