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Abstract  CSP || B is an integration of two well known formal notations: CSP and B. It provides a method for modelling systems with both complex state (described in B machines) and control flow (described as CSP processes). Consistency checking within this approach verifies that a controller process never calls a B operation outside its precondition. Otherwise the behaviour of the operation cannot be predicted. In previous work, this check was carried out by manually decomposing the model before preprocessing the CSP processes to perform a hand-written weakest precondition proof. In this paper, a framework is described that mechanises consistency checking in a theorem prover and removes the need for preprocessing. This work is based on an existing PVS embedding of the CSP traces model, but it is extended by introducing a notion of state so that the interaction between processes and machines can be analysed. Numerous rules have been defined (and proved) which enable consistency checking and decomposition via PVS proof. These rules also formally justify the relaxation of previous constraints on CSP || B architectures, thereby widening the scope of CSP || B modelling. The PVS embedding and rules presented in this paper are not only applicable to CSP || B specifications, but to other combined approaches which use a non-blocking semantics for the state-based operations. [ABSTRACT FROM AUTHOR]

Recent work on combining CSP and B has provided ways of describing systems comprised of components described in both B (to express requirements on state) and CSP (to express interactive and controller behaviour). This approach is driven by the desire to exploit existing tool support for both CSP and B, and by the need for compositional proof techniques. This paper is concerned with the theory underpinning the approach, and proves a number of results for the development and verification of systems described using a combination of CSP and B. In particular, new results are obtained for the use of the hiding operator, which is essential for abstraction. The paper provides theorems which enable results obtained (possibly with tools) on the CSP part of the description to be lifted to the combination. Also, a better understanding of the interaction between CSP controllers and B machines in terms of non-discriminating and open behaviour on channels is introduced, and applied to the deadlock-freedom theorem. The results are illustrated with a toy lift controller running example. [ABSTRACT FROM AUTHOR]