Structured Co-spans: An Algebra of Interaction Protocols

Abstract

Software is becoming an integral part of a range of products and services performing vital functions in all sectors of economic and social activity. In such softwareintensive systems, software applications are required to interact, in a seamless way, with other software components, devices, sensors, even humans. The complexity involved in building the software components that will be deployed in such systems in not so much on the "size" of their code but on the number and intricacy on the interactions in which they will be involved, what in [6] we have called social complexity.From an algebraic point of view, social complexity raises new challenges with respect to the more established physiological complexity, i.e. the fact that a complex whole can be understood as a composition of its parts. The basic difference is that it does not make sense to see software-intensive systems as being compositions, in an algebraic sense, of simpler components. There is not a notion of whole to which the parts contribute but, rather, a number of autonomous entities that interact with each other through external connectors. This is why it is so important to put the notion of interaction at the centre of research in software-intensive system modelling, and to support methods and languages that separate interaction concerns from computational ones. In the past, we developed Abstract. We extend the theory of (co-)spans as a means of providing an algebraic approach to complex interactions as they arise in software-intensive systems. In order to make interconnections independent of the nature of components involved, interaction protocols are formalised not in terms of morphisms (i.e. part-of relationships) but a generalised notion of (co-)span in which the arms are structured morphisms -the head (the glue of the protocol) and the hands (the interfaces of the protocol) belong to different categories, the category of glues being coordinated over that of the interfaces. The proposed generalization sheds some additional light into adjunctions in bicategories, namely on the factorisation of left adjoint 2-sided enrichments.

The Sensoria Reference Modelling Language

“…SRML is supported by an Eclipse-based editor (available from www.cs.le.ac.uk/srml) that is part of the Sensoria Development Environment (SDE). A mathematical semantics is available for all aspects of the approach as partially illustrated in the paper (see [4,6,31,32,33,34] for a more comprehensive account).…”

“…We present the language primitives that SRML offers for modelling business services and activities, and discuss the methodological approach that SRML supports, which includes the use of the UMC model-checker (developed at CNR-ISTI) for qualitative analysis and of the Markovian process algebra PEPA (developed at the University of Edinburgh) for quantitative analysis of timing properties. Only some elements of the mathematical semantics that we developed for the approach are provided in this chapter; full details can be found in [4,6,32,33,34].…”

What Do Semantics Matter When the Meat Is Overcooked?

“…Select one of the services that maximises the level of satisfaction offered by the corresponding contract. We are now going to define each of these steps in more detail, though most of the technical aspects need to be consulted in [5] and [13,14]. Consider a business configuration BC=〈 SF,B,C 〉 and let R be a requires-interface of a business activity a such that trigger(R) holds in SF.…”

“…The semantics of the actual reconfiguration operated during a resolution step was given based on algebraic, graph-based techniques [13,14]. The notion of configuration and module were formalised in terms of graphs and their labelling with different kinds of components, connectors, specifications and specification morphisms.…”

Specifying and Composing Interaction Protocols for Service-Oriented System Modelling

“…Another important aspect of our model is an algebraic semantics that accounts for interaction protocols as structured co-spans, the full mathematical characterisation of which can be found in [8]. In the paper, we illustrated how this semantics provides a model for the composition of interaction protocols, connectors and wires, which is required for service discovery and binding.…”