Expression Reduction Systems with Patterns
Résumé
We introduce a new higher-order rewriting formalism, called expression reduction systems with patterns (ERSP), where abstraction is allowed not only on variables but also on nested patterns with metavariables. These patterns are built by combining standard algebraic patterns with choice constructors denoting cases. In other words, the nondeterministic choice between different rewrite rules that is inherent to classical rewriting formalisms can be lifted here to the level of patterns. We show that confluence holds for a reasonable class of systems and terms.