Initial Semantics of Specifications

We study in this chapter initial semantics of equational specifications. In contrast to the former, mainly introductory chapter we will now emphazise the algebraic fundamentals of initial semantics and discuss in more general terms the concepts of quotient term algebras and initiality. These algebraic fundamentals are of great importance since they enable us to develop a theory of data type specification with initial algebra semantics, which not only yields a deeper understanding of initial semantics, but also exhibits results which are of extrordinary help in the practice of specification.