Higher-order port-graph rewriting

Abstract

The biologically inspired framework of port-graphs has been successfully used to specify complex systems. It is the basis of the PORGY modelling tool. To facilitate the specification of proof normalisation procedures via graph rewriting, in this paper we add higher-order features to the original port-graph syntax, along with a generalised notion of graph morphism. We provide a matching algorithm which enables to implement higher-order port-graph rewriting in PORGY, thus one can visually study the dynamics of the systems modelled. We illustrate the expressive power of higher-order port-graphs with examples taken from proof-net reduction systems

Strategy-Driven Exploration for Rule-Based Models of Biochemical Systems with Porgy

“…This offers basic support for modular design at strategy level. Higher-order port-graphs [22] formalise a notion of hierarchical port-graph that could be used to support incremental definition of models; this feature is under development for Porgy.…”

Attributed Hierarchical Port Graphs and Applications

“…HOPG [23] extend port graphs with higher-order variable nodes, which can be instantiated by port graphs.…”

“…AHP graphs subsume HOPGs by introducing an abstraction level that not only fulfils the original HOPG objective of simulating "boxes" or the grouping of a collection of nodes within one node, all interfaces matching, but that also maintains a nesting structure that can be recursively flattened on demand to produce a conventional graph. Similar to the example HOPG-implementation given in [23], an AHP graph can directly represent a proof (or a λ -term) that contains a box by using a hierarchical node Box whose Ladder contains the box structure.…”

“…This calculus can be seen as a combination of first-order rewrite rules with abstraction, but the notion of graph morphism (which is the basis for matching and rewriting) is first-order. As already mentioned, the higher-order port graphs found in [23] include a class of nodes labelled by variables that can be instantiated by graphs, thus offering abstraction but no additional structuring capabilities.…”

“…However, in interaction net evaluators the representation of λ -abstraction is involved due to the fact that λ is a binder and explicit markers have to be used to define and manage its scope. Higher-order port graphs [23] permit to encode binders in a direct way and can be easily represented as AHP. In future work we will explore the links between hierarchical and higher-order port graphs.…”