Two applications of equational theories to database theory
Proc. of the first international conference on Rewriting techniques and applications
PETRIREVE: proving Petri net properties with rewriting systems
Proc. of the first international conference on Rewriting techniques and applications
Report on the Larch shared language
Science of Computer Programming
Rewriting systems on FP expressions to reduce the number of sequences yielded
Science of Computer Programming
Artificial Intelligence
POPL '85 Proceedings of the 12th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Computer experiments with the REVE term rewriting system generator
POPL '83 Proceedings of the 10th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
On proving inductive properties of abstract data types
POPL '80 Proceedings of the 7th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
How to Prove Algebraic Inductive Hypotheses Without Induction
Proceedings of the 5th Conference on Automated Deduction
Abstract Data Type Specification in the Affirm System
IEEE Transactions on Software Engineering
Debugging Larch Shared Language Specifications
IEEE Transactions on Software Engineering
Formal methods: state of the art and future directions
ACM Computing Surveys (CSUR) - Special ACM 50th-anniversary issue: strategic directions in computing research
A general framework to build contextual cover set
Journal of Symbolic Computation - Calculemus-99: integrating computation and deduction
Heuristics for completion in automatic proofs by structural induction
Nordic Journal of Computing
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Rewriting techniques have been used to reason about a variety of topics related to programming languages, e.g., abstract data types, Petri Nets, FP programs, and data bases. They have also been used in the implementation and definition of a variety of programming languages.At the 1980 POPL Conference, David Musser proposed a new method of proving inductive properties of abstract data types. Since that time, this method, which came to be called inductionless induction, has attracted considerable attention. Numerous applications and improvements have been proposed and several implementations described. However, little or no work has appeared that questions the basic utility of the idea.The thesis of this paper is that while induction using equational term-rewriting holds great promise, inductionless induction does not. More specifically, we argue that for reasoning about abstract data types traditional inductive methods are usually superior.