Mechanizing Matching Logic In Coq

Abstract

Matching logic is a formalism for specifying, and reasoning about, mathematical structures, using patterns and pattern matching. Growing in popularity, it has been used to define many logical systems such as separation logic with recursive definitions and linear temporal logic. In addition, it serves as the logical foundation of the K semantic framework, which was used to build practical verifiers for a number of real-world languages. Despite being a fundamental formal system accommodating substantial theories, matching logic lacks a general-purpose, machine-checked formalization. Hence, we formalize matching logic using the Coq proof assistant. Specifically, we create a new representation of matching logic that uses a locally nameless encoding, and we formalize the syntax, semantics, and proof system of this representation in the Coq proof assistant. Crucially, we prove the soundness of the formalized proof system and provide a means to carry out interactive matching logic reasoning in Coq. We believe this work provides a previously unexplored avenue for reasoning about matching logic, its models, and the proof system.

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“…Matching logic is a formalism, useful to specify logical systems and their properties, that has at its hearth a notion of patterns and pattern matching. In Bereczky et al (2022) it is presented a mechanization in Coq of a version of this meta-language, including its syntax, its notion of semantics, formal system and verified soundness results. In particular, its syntax defines a language of patterns, whose semantics is defined in terms of the set of elements (from a given model) that match against this pattern.…”