Behavioral Subtyping is Equivalent to Modular Reasoning for Object-oriented Programs

Behavioral subtyping is an established idea that enables modular reasoning about behavioral properties of object-oriented programs. It requires that syntactic subtypes are behavioral refinements. It validates reasoning about a dynamically-dispatched method call, say E .m(), using the specification associated with the static type of the receiver expression E . For languages with references and mutable objects the idea of behavioral subtyping has not been rigorously formalized as such and the standard informal notion has inadequacies. This paper formalizes behavioral subtyping and introduces a new formalization of modular reasoning, called supertype abstraction. A Java-like sequential language is considered, with classes and interfaces, recursive types, first-class exceptions and handlers, and dynamically allocated mutable heap objects; the semantics is designed to serve as foundation for the Java Modeling Language (JML), a widely used specification language. Behavioral subtyping is characterized as sound and semantically complete for reasoning with supertype abstraction.