Unifying initial and loose semantics of parameterized specifications in an arbitrary institution

Abstract

In this paper we are going to present a theory of parameterized abstract datatypes as the model-theoretic level of parameterized specifications. We will show that parameterized abstract datatypes allow us to model the main approaches to the semantics of parameterized specifications, the loose approach (e.g. [GB90]) and the free functor semantics (e.g. [TWW82, EM85]), using the same formalism. As a consequence we obtain that, when using data constraints [Rei86, GB90, OSC89, EM90] in a specification language, this language is able to cope with both the loose and the free functor semantics at the same time. To be independent of a specific logic this theory is developed in the context of an arbitrary institution.