This thesis is part of the programme aimed at finding a mathematical theory of well-behaved structural operational semantics. General and basic results shown in 1997 in a seminal paper by Turi and Plotkin are extended in two directions, aiming at greater expressivity of the framework. The so-called bialgebraic framework of Turi and Plotkin is an abstract generalization of the well-known structural operational semantics format GSOS, and provides a theory of operational semantic rules for which bisimulation equivalence is a congruence. The first part of this thesis aims at extending that framework to cover other operational equivalences and preorders (e.g. trace equivalence), known collectively as the van Glabbeek spectrum. To do this, a novel coalgebraic approach to relations on processes is desirable, since the usual approach to coalgebraic bisimulations as spans of coalgebras does not extend easily to other known equivalences on processes. Such an approach, based on fibrations of test

The way that refinement of individual "local" components of a specification relates to development of a "global" system from a specification of requirements is explored. Observational interpretation of specifications and refinements add expressive power and flexibility while bringing in some subtle problems. The results are instantiated in the context of Casl architectural specifications.

Abstract. We study sequential programs that are instruction sequences with direct and indirect jump instructions. The intuition is that indirect jump instructions are jump instructions where the position of the instruction to jump to is the content of some memory cell. We consider several kinds of indirect jump instructions. For each kind, we define the meaning of programs with indirect jump instructions of that kind by means of a translation into programs without indirect jump instructions. For each kind, the intended behaviour of a program with indirect jump instructions of that kind under execution is the behaviour of the translated program under execution on interaction with some memory device.

Abstract. We study sequential programs that are instruction sequences with dynamically instantiated instructions. We define the meaning of such programs in two different ways. In either case, we give a translation by which each program with dynamically instantiated instructions is turned into a program without them that exhibits on execution the same behaviour by interaction with some service. The complexity of the translations differ considerably, whereas the services concerned are equally simple. However, the service concerned in the case of the simpler translation is far more powerful than the service concerned in the other case.

There are two main activities in Component-Based Development: component development, where we build libraried for general use, and component integration, where we assemble an application from existing components. In this work, we analyze how to apply algebraic specificat it s wi7 refinement to component development. So werestriy our research to the use of modules that are descri ed as class expressiy si n a formal speci cat it language, and we present several refinement steps for component development, introducing in each one design decisions and implementation details. This evolution starts from the initial specificat it of a component as an abstract module, and finishes wi/ the final deployment as fully implemented code. The usage of formal tools helps to assure the correctness of each step, and provides the ground to introduce complementary techniques, such as bisimulations, for the process of component integration.

Abstract. We introduce the notion of an ACP process algebra. The models of the axiom system ACP are the origin of this notion. ACP process algebras have to do with processes in which no data are involved. We also introduce the notion of a meadow enriched ACP process algebra, which is a simple generalization of the notion of an ACP process algebra to processes in which data are involved. In meadow enriched ACP process algebras, the mathematical structure for data is a meadow.

Abstract. In this paper, we study the phenomenon that instruction sequences are split into fragments which somehow produce a joint behaviour. In order to bring this phenomenon better into the picture, we formalize a simple mechanism by which several instruction sequence fragments can produce a joint behaviour. We also show that, even in the case of this simple mechanism, it is a non-trivial matter to explain by means of a translation into a single instruction sequence what takes place on execution of a collection of instruction sequence fragments.

Abstract. We formalize a cumulative interest compliant conservation requirement for pure financial products proposed by Wesseling and van den Bergh to make financial issues relating to these products amenable to mathematical analysis. The formalization is given in a timed extension of tuplix calculus and abstracts from the idiosyncrasies of time measurement. We also use the timed tuplix calculus to show how wanted financial behaviours may profit from using pure financial products.

Abstract. Meadow enriched ACP process algebras are essentially enrichments of models of the axiom system ACP that concern processes in which data are involved, the mathematical structure of data being a meadow. For all associative operators from the signature of meadow enriched ACP process algebras, we introduce variable-binding operators as generalizations. These variable-binding operators, which give rise to comprehended terms, have the property that they can always be eliminated. Thus, we obtain a process calculus whose terms can be interpreted in all meadow enriched ACP process algebras. Use of the variable-binding operators that bind variables with a two-valued range can already have a major impact on the size of terms.

Abstract. PGA (ProGram Algebra) is an algebra of programs which concerns programs in their simplest form: sequences of instructions. Molecular dynamics is a simple model of computation developed in the setting of PGA, which bears on the use of dynamic data structures in programming. We consider the programming of an interpreter for a program notation that is close to existing assembly languages using PGA with the primitives of molecular dynamics as basic instructions. It happens that, although primarily meant for explaining programming language features relating to the use of dynamic data structures, the collection of primitives of molecular dynamics in itself is suited to our programming wants.