Normalization via Rewrite Closures
RtA '99 Proceedings of the 10th International Conference on Rewriting Techniques and Applications
LarrowR2: A Laboratory fro Rapid Term Graph Rewriting
RtA '99 Proceedings of the 10th International Conference on Rewriting Techniques and Applications
Unique normal forms and confluence of rewrite systems: persistence
IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 1
On theorem proving for program checking: historical perspective and recent developments
Proceedings of the 12th international ACM SIGPLAN symposium on Principles and practice of declarative programming
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Implementation of programming language interpreters, proving theorems of the form A=B, and implementation of abstract data types are all problems that can be reduced to the problem of finding a normal form for an expression with respect to a finite set of equation (axiom) schemata The definition of a nonoverlapping s set of axiom schemata is given and the directed congruence closure algorithm is presented; an algorithm that efficiently solves this kind of problem provided the axiom schemata are nonoverlapping. The algorithm is a variation on the congruence closure algorithm? and, like the congruence closure algorithm, it has the advantage of remembering which expressions have already been proved to be equivalent. However, unlike the congruence closure algorithm, which can use only a finite set of axioms, the directed congruence closure algorithm allows a possibly infinite set of axioms generated by a finite set of axiom schemata.