Programming language semantics based on pure rewrite rules suers from the gap between the rewriting strategy implemented in rewriting engines and the intended evaluation strategy. This paper shows how programmable rewriting strategies can be used to implement interpreters for programming languages based on rewrite rules. The advantage of this approach is that reduction rules are rst class entities that can be reused in dierent strategies, even in other kinds of program transformations such as optimizers. The approach is illustrated with several interpreters for the lambda calculus based on implicit and explicit (parallel) substitution, dierent strategies including normalization, eager evaluation, lazy evaluation, and lazy evaluation with updates. An extension with pattern matching and choice shows that such interpreters can easily be extended.

In this paper we present a functional language supporting first-class rules and generic traversal. This is achieved by generalizing the pattern matching constructs of standard functional languages. The case construct that ties rules together and prevents their reuse, is replaced by separate, firstclass, pattern matching rules and a choice combinator that deals with pattern match failure. Generic traversal is achieved through application pattern matching in which a constructor application is generically divided into a prefix and a su#x, thus giving generic access to the subterms of a constructor term. Many highly generic term traversals can be defined in a type-safe way using this feature.