# Matching Logic --- Extended Report

From FSL

**Matching Logic --- Extended Report**- Grigore Rosu and Wolfram Schulte
UIUCDCS-R-2009-3026, January 2009**Technical Report**

*Abstract.*Hoare logics rely on the fact that logic formulae can encode, or specify, program states, including environments, stacks, heaps, path conditions, data constraints, and so on. Such formula encodings tend to lose the structure of the original program state and thus to be complex in practice, making it difficult to relate formal systems and program correctness proofs to the original programming language and program, respectively. Worse, since programs often manipulate mathematical objects such as lists, trees, graphs, etc., one needs to also encode, as logical formulae, the process of identifying these objects in the encoded program state. This paper proposes matching logic, an alternative to Hoare logics in which the state structure plays a crucial role. Program states are represented as algebraic datatypes called (concrete) configurations, and program state specifications are represented as configuration terms with variables and constraints on them, called (configuration) patterns. A pattern specifies those configurations thatmatch it. Patterns can bind variables to their scope, allowing both for pattern abstraction and for expressing loop invariants. Matching logic is tightly connected to rewriting logic semantics (RLS): matching logic formal systems can systematically be obtained from executable RLS of languages. This relationship allows to prove soundness of matching logic formal systems w.r.t. complementary, testable semantics. All notions are exemplified using KernelC, a fragment of C with dynamic memory allocation/deallocation.