Expression Reduction Systems with Patterns

Abstract

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.

First-class patterns

“…Indeed, it would be enough to use a pattern of the form z x y and check equality of x and y afterwards. The restriction to linear patterns is also common when establishing confluence of rewriting systems (Klop, 1980) or of pattern calculi based on rewriting (Forest & Kesner, 2003;Kahl, 2004), but this is related to orthogonality of pairs of rules or cases, while our framework only considers one case at a time.…”