Computer Science Technical Reports Computer Science 9-3-2006 Behavioral Subtyping, Specification Inheritance, and Modular Reasoning Gary T. Leavens Iowa State University David A. Naumann Iowa State University Follow this and additional works at: http://lib.dr.iastate.edu/cs_techreports Part of the Software Engineering Commons Recommended Citation Leavens, Gary T. and Naumann, David A., "Behavioral Subtyping, Specification Inheritance, and Modular Reasoning" (2006). Computer Science Technical Reports. 269. http://lib.dr.iastate.edu/cs_techreports/269 This Article is brought to you for free and open access by the Computer Science at Iowa State University Digital Repository. It has been accepted for inclusion in Computer Science Technical Reports by an authorized administrator of Iowa State University Digital Repository. For more information, please contact
[email protected]. Behavioral Subtyping, Specification Inheritance, and Modular Reasoning Abstract 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, the standard informal notion has inadequacies, and exact definitions are not obvious. This paper formalizes behavioral subtyping and supertype abstraction for a Java-like sequential language with classes, interfaces, exceptions, mutable heap objects, references, and recursive types. Behavioral subtyping is proved sound and semantically complete for reasoning with supertype abstraction. Specification inheritance, as used in the specification language JML, is formalized and proved to entail behavioral subtyping.