Type Systems for Bigraphs

  • Authors:
  • Ebbe Elsborg;Thomas T. Hildebrandt;Davide Sangiorgi

  • Affiliations:
  • IT University of Copenhagen (ITU),;IT University of Copenhagen (ITU),;Università di Bologna,

  • Venue:
  • Trustworthy Global Computing
  • Year:
  • 2009

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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 *** -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 *** -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) *** -calculus.