Abstract
Term rewriting systems employed for the specification of abstract data types and for very high level programming languages based on rewrite rules are often required to have properties, such as confluence, termination, and sufficient-completeness, which are undecidable. Rather than attempting, as it is usually done, to check these properties in a system a posteriori, i.e. after the rules have been designed, we propose two strategies for addressing this problem a priori, i.e. during the design phase of rules. We propose the concepts of under- and over-specification, determine sufficient and/or necessary conditions to avoid them, show how to obtain these conditions in a constructive way, and relate them to a number of desirable properties which have appeared in the literature. Our approach is based on the completeness and parsimony properties of sets of tuples of terms and on a recursive mechanism which extends primitive recursion from natural numbers to abstract data types. We prove a number of results, illustrate their application to the design of rewriting systems by means of examples, and discuss the power and the limitations of our approach.
This material is based upon work supported by the National Science Foundation Grant No. CCR-8908565.
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Antoy, S. (1991). Design strategies for rewrite rules. In: Kaplan, S., Okada, M. (eds) Conditional and Typed Rewriting Systems. CTRS 1990. Lecture Notes in Computer Science, vol 516. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-54317-1_102
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DOI: https://doi.org/10.1007/3-540-54317-1_102
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