Specification of Abstract Data Types

In the last chapter we have introduced algebraic specifications and algebras satisfying the given equations. In general there are many different algebras for each specification SPEC. In this chapter we want to consider a distinguished algebra, the quotient term algebra T _SPEC, which is generated by its operations and satisfies some ground equations E if and only if E is valid in all SPEC-algebras. The last property is called “typical”. In Chapter 3 we will see that these properties “generated” and “typical” are characterizing T_SPEC uniquely up to isomorphism of algebras.