1 Ecole Nationale Superieure des Telecomunications [Elie.Najm, Abdelkrim.Nimour]@enstfr In a previous work [12] we presented COB, an object calculus which features objects with dynamically changing service offers. We also defined a type system for interfaces and a typing discipline that guarantees that no object may experience an unexpected service request at run-time. In the present paper, we extend our type system such that it describes "infinite state" types. We define equivalence and

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... ng relations over those types based on bisimulation and simulation relations. We also define an algorithm to decide the equivalence or the subtyping relation of two types. The type system is applied to OL, a new calculus that uses the interface "states" in the behavior of the objects. As in COB, in OL there is a distinction between private and public interfaces. A private interface can have at most one client at a time whereas a public interface can be known by more that one client. Private interfaces can thus propose a non-uniform service offer (the set available services may change during the computation). OL extends the results of COB to infinite types: in spite of non-uniform service offers, in a well-typed P. Ciancarini et al. (eds.), Formal Methods for Open Object-Based Distributed Systems