In a component-based software development, components are considered as black boxes. They are only described by their interfaces expressing their visible behaviors. They must be connected in an appropriate way, through required and provided interfaces. To guarantee interoperability of components, we must consider each connection of a required interface with another provided interface. In the best cases, a provided interface -- after some renaming -- constitutes an implementation of the required interface. In the general cases, to construct a working system out of components, adapters have to be defined. They connect the required operations and attributes to the required ones. The interoperability between a required interface and provided interfaces through an adapter is guaranteed by the use of the B formal method with its underlying concept of refinement, and its powerful tool support, the B prover.