Behaviour-Refinement of Coalgebraic Specifications with Coinductive Correctness Proofs

A notion of reenement is deened in the context of coalgebraic spec-iication of classes in object-oriented languages. It tells us when objects in a \concrete" class behave exactly like (or: simulate) objects in an \abstract" class. The deenition of reenement involves certain selection functions between procedure-inputs and attribute-outputs, which gives this notion considerable exibility. The coalgebraic approach allows us to use coinductive proof methods in establishing reenements (via (bi)simulations). This is illustrated in several examples.