Island Bigraph4 - Elementary Bigraphs

xholonWorkbook.xml

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Xholon
------
Title: Island Bigraph4 - Elementary Bigraphs
Description: 
Url: http://www.primordion.com/Xholon/gwt/
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My Notes
--------
July 30, 2019
Elementary Bigraphs

References
----------
(1) Milner's Bigraph book (p. 29+)
- elementary node-free bigraphs
- elementary placings
- elementary linkings


(2) Type Systems for Bigraphs, by Ebbe Elsborg, Thomas T. Hildebrandt, and Davide Sangiorgi, 2008
Abstract We propose a novel and uniform approach to type systems for (pro-
cess) 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 con-
trols 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 prop-
erties (including subject reduction) for this type system, and transfer these
properties to the (typed) π-calculus.

All bigraphs are obtained by combining elementary bigraphs via the operators of categorical tensor
product and composition. An essential elementary bigraph is an ion, to which a con-
trol 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.


]]></Notes> 

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    <RootBG roleName="1">
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  </Bigraph>
  <Bigraph roleName="0.b"><Attribute_String><![CDATA[
B = (VB,EB,PB,ctrlB,prntB,linkB) : 〈m,X〉 → 〈n,Y〉,
m=2, X=∅, n=2, Y={},
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m=0, X=∅, n=1, Y={},
VB = {0},
EB = ∅,
ctrlB = {(0,RootBG)}
  ]]></Attribute_String><BigraphParser/></Bigraph>
  
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  <Bigraph roleName="2">
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