Refutational theorem proving using term-rewriting systems
Artificial Intelligence
Two applications of equational theories to database theory
Proc. of the first international conference on Rewriting techniques and applications
Rewriting systems on FP expressions to reduce the number of sequences yielded
Science of Computer Programming
Journal of Symbolic Computation
Implementing first-order rewriting with constructor systems (Note)
Theoretical Computer Science
Term-rewriting systems with rule priorities
Theoretical Computer Science - Second Conference on Rewriting Techniques and Applications, Bordeaux, May 1987
Nonoblivious normalization algorithms for nonlinear rewrite systems
Proceedings of the seventeenth international colloquium on Automata, languages and programming
POPL '85 Proceedings of the 12th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Tree-Manipulating Systems and Church-Rosser Theorems
Journal of the ACM (JACM)
Fast Decision Procedures Based on Congruence Closure
Journal of the ACM (JACM)
Variations on the Common Subexpression Problem
Journal of the ACM (JACM)
Journal of the ACM (JACM)
ACM Transactions on Programming Languages and Systems (TOPLAS)
Computing in Systems Described by Equations
Computing in Systems Described by Equations
Smaran: A Congruence-Closure Based System for Equational Computations
RTA '93 Proceedings of the 5th International Conference on Rewriting Techniques and Applications
Proceedings of the 7th International Conference on Automated Deduction
Implementation of an interpreter for abstract equations
POPL '84 Proceedings of the 11th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Complexity of finitely presented algebras
STOC '77 Proceedings of the ninth annual ACM symposium on Theory of computing
Ubiquitous equations, nonoblivious normalization and term =matching problems
Ubiquitous equations, nonoblivious normalization and term =matching problems
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
Remarks on Thatte's transformation of term rewriting systems
Information and Computation
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Implementation of programming language interpreters, proving theorem of the form A=B, implementation of abstract data types, and program optimization 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 equations. In 1980, Chew proposed an elegant congruence closure based simplifier (CCNS) for computing with regular systems, which stores the history of it computations in a compact data structure. In 1990, Verma and Ramakrishnan showed that it can also be used for noetherian systems with no overlaps.In this paper, we develop a general theory of using CCNS for computing normal forms and present several applications. Our results are more powerful and widely applicable than earlier work. We present an independent set of postulates and prove that CCNS can be used for any system that satisfies them. (This proof is based on the notion of strong closure). We then show that CCNS can be used for consistent convergent systems and for various kinds of priority rewrite systems. This is the first time that the applicability of CCNS has been shown for priority systems. Finally, we present a new and simpler translation scheme for converting convergent systems into effectively nonoverlapping convergent priority systems. Such a translation scheme has been proposed earlier, but we show that it is incorrect.Because CCNS requires some strong properties of the given system, our demonstration of its wide applicability is both difficult and surprising. The tension between demands imposed by CCNS and our efforts to satisfy them gives our work much general significance. Our results are partly achieved through the idea of effectively simulating “bad” systems by almost-equivalent “good” ones, partly through our theory that substantially weakens the demands, and partly through the design of a powerful and unifying reduction proof method.