Writing Larch interface language specifications
ACM Transactions on Programming Languages and Systems (TOPLAS)
Simplification Orderings: History Of Results
Fundamenta Informaticae
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This thesis presents new results in the use of term rewriting systems for automatic theorem proving. The design and implementation of REVE 2, a computer program that incorporates these results, is described. In addition, an introduction to the basic theory, procedures, and algorithms of term rewriting is provided, in a manner suitable for non-specialists. A principal application of rewriting systems is reasoning about the equational and inductive theories associated with a finite set of axioms. In this context, the Knuth-Bendix completion procedure is typically used in the hope of constructing a confluent and termination rewriting system from the axioms. Knuth-Bendix in automatic proofs of equational and inductive theorems have been: 1) the need for user interaction, and 2) the lack of available state-of-the art implementations. REVE 2 reduces the need for user interaction in two ways. First, it uses automatic orderings whose implementations automatically compute all of the possible valid extensions to the ordering that allow an unorderable equation to be ordered. Second, it uses a robust, task-based, failure-resistant Knuth-Bendix design that incorporates a fine-grained scheme for automatic equation postponement. From the beginning, it has been a fundamental design goal to make REVE 2 a well-documented, highly-modular, easily-modified program, based on sound principles of software engineering. The user interface to REVE 2 has been designed for ease of use by both novice and expert.