Abstract
This paper provides an overview of an approach to coalgebraic modelling and refinement of state-based software components, summing up some basic results and introducing a discussion on the interplay between behavioural and classical data refinement. The approach builds on coalgebra theory as a suitable tool to capture observational semantics and to base an abstract characterisation of possible behaviour models for components (from partiality to different degrees of non-determinism).

Abstract
Although increasingly popular, software component techniques still lack suitable formal foundations on top of which rigorous methodologies for the description and analysis of software architectures could be built. This paper aims to contribute in this direction: building on previous work by the authors on coalgebraic semantics, it discusses component refinement at three different but interrelated levels: behavioural, syntactic, i.e., relative to component interfaces, and architectural. Software architectures are defined through component aggregation. On the other hand, such aggregations, no matter how large and complex they are, can also be dealt with as components themselves, which paves the way to a discipline of hierarchical design. In this context, a major contribution of this paper is the introduction of a set of rules for architectural refinement.

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In a broad sense, computing is an area of knowledge from which a popular and efSective technology emerged long before a solid, specific, scientific methodology, let alone formal foundations, had been put forward. This might explain some of the weaknesses in the software industv, on the one hand, as well as an excessively technology-oriented view which dominates computer science training at pre-university and even undergraduate teaching, on the other. Modelling, understood as the ability to choose the right abstractions for a problem domain, is consensually recognised as essential for the development of true engineering skills in this area, as it is in all other engineering disciplines. But, how can the basic problemsolving strategy, one gets used to from school physics: understand the problem, build a mathematical model, reason within the model, calculate a solution, be taken (and taught) as the standard way of dealing with software design problems? This paper addresses this question, illustrating and discussing the interplay between modelling and reasoning. © 2007 Woodhead Publishing Limited.