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ITU  /  Research  /  Technical Reports  /  Technical Reports Archive  /  2008  /  Type Systems for Bigraphs
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    Type Systems for Bigraphs

    TR-2008-110, Authors: Ebbe Elsborg, Thomas T. Hildebrandt and Davide Sangiorgi


    Ebbe Elsborg
    , Thomas T. Hildebrandt, and Davide Sangiorgi

    October 2008

    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 pi-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 pi-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) pi-calculus.


    Technical report TR-2008-110 in IT University Technical Report Series, October 2008.

    Available as PDF.


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