Specification of Rewriting Strategies

User-definable strategies for the application of rewrite rules provide a means to construct transformation systems that apply rewrite rules in a controlled way. This paper describes a strategy language and its interpretation. The language is used to control the rewriting of terms using labeled rewrite rules. Rule labels are atomic strategies. Compound strategies are formed by means of sequential composition, nondeterministic choice, left choice, fixed point recursion, and two primitives for expressing term traversal. Several complex strategies such as bottom-up and top-down applica-tion and (parallel) innermost and (parallel) outermost reduction can be defined in terms of these primitives. The paper contains two case studies of the application of strategies.