Abstract

Abstract
We constructed a tool, called VooDooM, which converts datatypes in VDM-SL into SQL relational data models. The conversion involves transformation of algebraic types to maps and products, and pointer introduction. The conversion is specified as a theory of refinement by calculation. The implementation technology is strategic term rewriting in Haskell, as supported by the Strafunski bundle. Due to these choices of theory and technology, the road from theory to practise is straightforward.

Abstract
Genericity is a topic which is not sufficiently developed in state-based systems modelling, mainly due to a myriad of approaches and behaviour models which lack unification. This paper adopts coalgebra theory to propose a generic notion of a state-based software component, and an associated calculus, by quantifying over behavioural models specified as strong monads. This leads to the pointfree, calculational reasoning style which is typical of the so-called Bird-Meertens school. ©2003 Published by Elsevier Science B. V.

Abstract
A partial component is a process which fails or dies at some stage, thus exhibiting a finite, more ephemeral behaviour than expected. Partiality-which is the rule rather than exception in formal modelling-can be treated mathematically via totalization techniques. In the case of partial functions, totalization involves error values and exceptions. In the context of a coalgebraic approach to component semantics, this paper argues that the behavioural counterpart to such functional techniques should extend behaviour with try-again cycles preventing from component collapse, thus extending totalization or transposition from the algebraic to the coalgebraic context. We show that a refinement relationship holds between original and totalized components which is reasoned about in a coalgebraic approach to component refinement expressed in the pointfree binary relation calculus. As part of the pragmatic aims of this research, we also address the factorization of every such totalized coalgebra into two coalgebraic components-the original one and an added front-end-which cooperate in a client-server style.

Abstract
A transition system can be presented either as a binary relation or as a coalgebra for the powerset functor, each representation being obtained from the other by transposition. More generally, a coalgebra for a functor F generalises transition systems in the sense that a shape for transitions is determined by F, typically encoding a signature of methods and observers. This paper explores such a duality to frame in purely relational terms coalgebraic refinement, showing that relational (data) refinement of transition relations, in its two variants, downward and upward (functional) simulations, is equivalent to coalgebraic refinement based on backward and forward morphisms, respectively. Going deeper, it is also shown that downward simulation provides a complete relational rule to prove coalgebraic refinement. With such a single rule the paper defines a pre-ordered calculus for refinement of coalgebras, with bisimilarity as the induced equivalence. The calculus is monotonic with respect to the main relational operators and arbitrary relator F, therefore providing a framework for structural reasoning about refinement.

Abstract
The algebra of programming (AoP) is a discipline for programming from specifications using relation algebra. Specification vagueness and nondeterminism are captured by relations. (Final) implementations are functions. Probabilistic functions are half way between relations and functions: they express the propensity, or likelihood of ambiguous, multiple outputs. This paper puts forward a basis for a linear algebra of programming (LAoP) extending standard AoP towards probabilistic functions. Because of the quantitative essence of these functions, the allegory of binary relations which supports the AoP has to be extended. We show that, if one restricts to discrete probability spaces, categories of matrices provide adequate support for the extension, while preserving the pointfree reasoning style typical of the AoP.