On the role of category theory in the area of algebraic specifications

Abstract

The paper summarizes the main concepts and paradigms of category theory and explores some of their applications to the area of algebraic specifications. In detail we discuss different approaches to an abstract theory of specification logics. Further we present a uniform framework for developing particular specification logics. We make use of 'classifying categories', to present categories of algebras as functor categories and to obtain necessary basic results for particular specification logics in a uniform manner. The specification logics considered are: equational logic for total algebras, conditional equational logic for partial algebras, and rewrite logic for concurrent systems.