Matching logic explained

Matching logic was recently proposed as a unifying logic for specifying and reasoning about static structure and dynamic behavior of programs. In matching logic, patterns and specifications are used to uniformly represent mathematical domains (such as numbers and Boolean values), datatypes, and transition systems, whose properties can be reasoned about using one fixed matching logic proof system. In this paper we give a tutorial to matching logic. We use a suite of examples to explain the basic concepts of matching logic and show how to capture many important mathematical domains, datatypes, and transition systems using patterns and specifications. We put special emphasis on the general principles of induction and coinduction in matching logic and show how to do inductive and coinductive reasoning about datatypes and codatatypes. To encourage the development of the future tools for matching logic, we propose and use throughout the paper a human-readable formal syntax to write specifications in a modular and compact way. Keywords— matching logic, program logics, (co)inductive data types, dependent types, specification of transition systems, (co)monad specification