Abstract
Higraphs, a kind of hierarchical graph, underlie a number of sophisticated diagrammatic formalisms, including Statecharts. Naturally arising from hierarchy in higraphs is an abstraction operation known as zooming out, which is of profound importance to reasoning about higraph-based systems. We motivate how, in general, the use of zooming in reasoning requires sophisticated extensions to the basic notion of higraph and a careful definition of higraph dynamics (i.e. semantics), which we contribute. Our main results characterise zooming by means of a universal property and establish a precise relationship between the dynamics of a higraph and that of its zoom-out.
Both authors wish to acknowledge the support of a British Council grant and of AIST Japan. John Power also acknowledges the support of EPSRC grant no. M566333, and Konstantinos Tourlas the support of EPSRC grant no. GR/N12480.
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Power, J., Tourlas, K. (2003). Abstraction in Reasoning about Higraph-Based Systems. In: Gordon, A.D. (eds) Foundations of Software Science and Computation Structures. FoSSaCS 2003. Lecture Notes in Computer Science, vol 2620. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36576-1_25
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DOI: https://doi.org/10.1007/3-540-36576-1_25
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