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.

重写理论的可达性逻辑由约束构造器模式给出的系统状态规范、重写理论给出的转换关系和表示为状态规范对的可达性属性组成。匹配逻辑最近被提议作为编程语言、规范和验证的统一基础。众所周知，可达性属性可以自然地用匹配逻辑表示。在本文中，我们展示了受约束的构造函数模式可以忠实地指定为匹配逻辑理论。结果，我们通过结合两种编码，获得了重写理论的可达性逻辑的完整编码作为匹配逻辑理论。