Initial algebra semantics in matching logic

Xiaohong Chen and Dorel Lucanu and Grigore Rosu
Technical Report July 2020
PDF BIB Matching Logic

Abstract. Matching logic is a unifying foundational logic for defining formal programming language semantics, which adopts a minimalist design with few primitive constructs that are enough to express all properties within a variety of logical systems, including FOL, separation logic, (dependent) type systems, modal mu-logic, and more. In this paper, we consider initial algebra semantics and show how to capture it by matching logic specifications. Formally, given an algebraic specification E that defines a set of sorts (of data) and a set of operations whose behaviors are defined by a set of equational axioms, we define a corresponding matching logic specification, denoted INITIALALGEBRA(E), whose models are exactly the initial algebras of E. Thus, we reduce initial E-algebra semantics to the matching logic specifications INITIALALGEBRA(E), and reduce extrinsic initial E-algebra reasoning, which includes inductive reasoning, to generic, intrinsic matching logic reasoning.