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A Set-Theoretic Framework for Component Composition

Moschoyiannis S., Shields M.W.

Fundamenta Informaticae

2004

Vol. 59, nr 4

373--396

Modern software systems become increasingly complex as they are expected to support a large variety of different functions. We need to create more software in a shorter time, and without compromising the quality of the software. In order to build such systems efficiently, a compositional approach is required. This entails some formal technique for analysis and reasoning on local component properties as well as on properties of the composite. In this paper, we present a mathematical framework for the composition of software components, at a semantic modelling level. We describe a mathematical concept of a component and identify properties that ensure its potential behaviour can be captured. Based on that, we give a formal definition of composition and examine its effect on the individual components. We argue that properties of the individual components can, under certain conditions, be preserved in the composite. The proposed framework can be used for guiding the composition of components as it advocates formal reasoning about the composite before the actual composition takes place.

An acceptance vector semantics for path programs

Shields M.W.

Fundamenta Informaticae

1999

Vol. 40, Nr 2,3

285-316

In this paper, we consider two formal semantics for path programs. The first is a version of the net semantics introduced in [8] and further described in [7], and the second is an extension of the vector semantics of [15]. The extension involves the idea of tagging vectors with sets of sets of action names as with acceptance sets [3, 5] or refusal sets [1, 6] as used in the semantics of certain process algebras. The net semantics of [8, 7] associates a path program with an isomorphism class of labelled, marked nets - two such nets being isomorphic if they have identical pictorial representations and consequently describe the same system. A behaviour of such a class is an isomorphism class of cycle-free labeled nets showing the (partial) order in which conditions have held and events have occurred. We review these basic ideas and then present a version of the [7] semantics. We next present an acceptance vector semantics for path programs. An acceptance vector consists of a collection of sequences, one for each component path, describing the sequence of actions associated with the path in question during some period of activity, together with a set of actions which are available to continue the behaviour represented by the collection. Finally, we show that the two semantics are related in the sense that every net based behaviour may be transformed into an accceptance vector.