Capturing constrained constructor patterns in matching logic

Reachability logic for rewrite theories consists of a specification of system states that are given by constrained constructor patterns, a transition relation that is given by a rewrite theory, and reachability properties expressed as pairs of state specifications. Matching logic has been recently proposed as a unifying foundation for programming languages, specification and verification. It is known that reachability properties can be naturally expressed in matching logic. In this paper, we show that constrained constructor patterns can be faithfully specified as a matching logic theory. As a result, we obtain a full encoding of reachability logic for rewrite theories as matching logic theories, by combining the two encodings. We also show that the main properties of constrained constructor patterns can be specified and proved within matching logic, using the existing proof system.