Semantic constructions for the specification of objects

AbstractHidden algebra is a behavioural algebraic specification formalism for objects. It captures their constructional aspect (concerned with the initialisation and evolution of their states), their observational aspect (concerned with the observable behaviour of such states), and the relationship between these two aspects. When attention is restricted to the observational aspect, final/cofree algebras provide suitable denotations for the specification techniques employed by hidden algebra. However, when the constructional aspect is integrated with the observational one, the possibility of underspecification prevents the existence of such algebras. It is shown here that final/cofree familiesof algebras exist in this case, with each algebra in such a family resolving the nondeterminism arising from underspecification in a particular way. The existence of final/cofree families also yields a canonical way of constructing algebras of structured specifications from algebras of their component specifications