Refinement-based Construction of Correct Distributed Algorithms

The verification of distributed algorithms is a challenge for formal techniques supported by tools, as model checkers and proof assistants. The difficulties, even for powerful tools, lie in the derivation of proofs of required properties, such as safety and eventuality, for distributed algorithms. Verification by construction can be achieved by using a formal framework in which models are constructed at different levels of abstraction; each level of abstraction is refined by the one below, and this refinement relationships is documented by an abstraction relation namely a gluing invariant. The highest levels of abstraction are used to express the required behavior in terms of the problem domain and the lowest level of abstraction corresponds to an implementation from which an efficient implementation can be derived automatically. We describe a methodology based on the general concept of refinement and used for developing distributed algorithms satisfying a given list of safety and liveness properties. We will show also how formal models can be used for producing distributed programs of a real programming language. The modelling methodology is defined in the Event-B modelling language using the Rodin Formal IDE.