A Type-theoretic Approach to Deadlock-freedom of Asynchronous Systems

Rajagopal Nagarajan, Department of Computing, Imperial College, London
Samson Abramsky, Department of Computer Science, University of Edinburgh
Simon Gay Department of Computer Science, University of London

Proceedings of the Third International Symposium on Theoretical Aspects of Computer Software. (M. Abadi and T.Ito eds.) `

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We present a type-based technique for the verification of deadlock-freedom in asynchronous concurrent systems. Our general appproach is to start with a simple interaction category, in which objects are types containing safety specifications and morphisms are processes. We then use a specification structure to add information to the types so that they specify stronger properties. In this paper the starting point is the category ASProc and the extra type information concerns deadlock-freedom. In the resulting category ASProcD , combining well-typed processes preserves deadlock-freedom. It is also possible to accommodate non-compositional methods within the same framework. The systems we consider are asynchronous, hence issues of divergence become significant; our approach incorporates an elegant treatment of both divergence and successful termination. As an example, we use our methods to verify the deadlock-freedom of an implementation of the alternating-bit protocol.