Reversibility and composition of rewriting in hierarchies
Résumé
In this paper we study how SqPO rewriting of individual objects and hierarchies of objects can be reversed and how the composition of rewrites can be constructed. We introduce the notion of a rule hierarchy , study how such rule hierarchies can be applied to object hierarchies and analyse the conditions under which this application is reversible. We then present a theory for constructing the composition of consecutive hierarchy rewrites. We further illustrate how the reversibility and composition of rewriting can be used to design an audit trail for both individual graphs and graph hierarchies. This provides us a compact way to maintain the history of updates of an object including its multiple versions. The main application of the designed framework is an audit of updates to knowledge represented with hierarchies of graphs. The prototype system for transformations in hierarchies of simple graphs with attributes is implemented as a part of the ReGraph Python library.
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