Unifying Initial and Loose Semantics of Parameterized Specifications in an Arbitrary Institution

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 and the free functor semantics, using the same formalism. As a consequence we obtain that, when using data constraints 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