Observational Refinement Process

In the algebraic specification of software systems, it is desirable to have freedom in the implementation process, namely for the software reuse. In this paper we will discuss two issues in order to achieve this freedom: we study the observational stepwise refinement process and we propose an alternative formalization of the refinement concept based on the logical translation from the abstract algebraic logic. In the first topic, we go beyond the traditional assumption of maintaining the set of observable sorts during the refinement process by the possibility of changing it between the process steps, i.e., we analise the stepwise refinement with encapsulation and desencapsulation of sorts during the process. In the second topic, we suggest a formalization of the refinement concept where an equation may be mapped into a set of equations, against the refinements based on signature morphisms, where an equation is mapped into another one.