Abstract
We propose a novel and uniform approach to type systems for (process) calculi, which roughly pushes the challenge of designing type systems and proving properties about them to the meta-model of bigraphs. Concretely, we propose to define type systems for the term language for bigraphs, which is based on a fixed set of elementary bigraphs and operators on these. An essential elementary bigraph is an ion, to which a control can be attached modelling its kind (its ordered number of channels and whether it is a guard), e.g. an input prefix of π-calculus. A model of a calculus is then a set of controls and a set of reaction rules, collectively a bigraphical reactive system (BRS). Possible advantages of developing bigraphical type systems include: a deeper understanding of a type system itself and its properties; transfer of the type systems to the concrete family of calculi that the BRS models; and the possibility of modularly adapting the type systems to extensions of the BRS (with new controls). As proof of concept we present a model of a π-calculus, develop an i/o-type system with subtyping on this model, prove crucial properties (including subject reduction) for this type system, and transfer these properties to the (typed) π-calculus.
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This work was funded in part by the Danish Research Agency (grants no.: 2059-03-0031 and 274-06-0415) and the ITU (the LaCoMoCo/BPL and CosmoBiz projects).
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Elsborg, E., Hildebrandt, T.T., Sangiorgi, D. (2009). Type Systems for Bigraphs . In: Kaklamanis, C., Nielson, F. (eds) Trustworthy Global Computing. TGC 2008. Lecture Notes in Computer Science, vol 5474. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00945-7_8
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DOI: https://doi.org/10.1007/978-3-642-00945-7_8
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