Proving Class Equivalence

We present a sound and complete method for reasoning about contextual equivalence between different implementations of classes in an imperative subset of Java. Our technique successfully deals with public and private methods and fields, imperative fields, inheritance, and invocations of callbacks. To the extent of our knowledge this is the first sound and complete proof method of equivalence between classes for such a subset of Java. Using our technique we were able to prove equivalences in examples with higherorder behavior, where previous methods for functional calculi admit limitations [17, 20]. We were also able to show equivalences between classes that expose part of their state using public fields, hide part of their functionality using private methods, and are extensible by the surrounding context. Other reasoning techniques for classbased languages [2, 10] restrict the way a class communicates with and abstracts functionality from its context. We derive our technique following a methodology similar to our previous work on functional [13] and object-based [12] languages, thus showing that this methodology gives useful results in a diversity of languages.