Coalgebraic Semantics and Observational Equivalences of an Imperative Class-based OO-Language

Fickle is a class-based object oriented imperative language, which extends Java with object re-classification. In this paper, we introduce a natural observational equivalence on Fickle programs. This is a contextual equivalence on main methods with respect to a given sequence of class definitions, i.e. a program. To study it, we use the formal computational model for OO-programming based on coalgebras, which has recently emerged, whereby objects are taken to be equal when the actions of methods on them yield the same observations and equivalent next states. However, in order to deal with imperative features, we need to extend the original approach of H.Reichel and B.Jacobs in various ways. In particular, we introduce a coalgebraic description of objects (states of a class), which induces a coinductive behavioural equivalence on programs. For simplicity, we focus on Fickle objects whose methods do not take more than one object parameter as argument. Completeness results as well as problematic issues arising from binary methods are also discussed.