this paper, we focus on methods of fault tolerance, and investigate the differences between hardware fault tolerance and software fault tolerance. 1.2 Fault, Error and Failure

Traditional programming calculi focus on transforming a specification into a program. With the advent of such recent paradigms as white box reuse, component-based software development, and reengineering, and with the continued predominance of software maintenance, less and less software engineering activity nowadays deals with straightforward development. More and more, software products are derived by incrementing, composing, merging, or otherwise modifying existing components. In this paper we present a calculus that models these paradigms. Keywords Formal specifications, Programming calculi, Program construction, Software merging, Software incrementation, Software modification. 1 Program Adaptation: An Emerging Paradigm Traditional programming paradigms revolve around mapping a single requirements specification into a program. As less and less software is developed from scratch, and more and more is developed from existing software artifacts, this traditional paradigm is growing l...

Traditional programming calculi focus on transforming a specification into a program. With the advent of such recent paradigms as white box reuse, component based software development, and reengineering, and with the continued predominance of software maintenance, less and less software engineering activity nowadays deals with straightforward development. More and more, software products are derived by combining, merging, or adapting existing components. In this paper we present a calculus that models several aspects of these paradigms.

Behavioral specifications of objects, modules, and data types can be defined by relations, which can in turn be represented by axiomatic systems. These axiomatic systems define the relation at hand by induction on the complexity of the invocation history of the object; their semantics can be defined by fixpoint theory. In this paper we discuss how the fixpoint semantics of such specifications can be used as a basis for proving the correctness of an implementation against axiomatic specifications.