Open Graphs and Computational Reasoning

Details Open Graphs and Computational Reasoning Open Graphs and Computational Reasoning

2010-07-22

arxiv.org/abs/1007.3794v1

EPTCS 26, 2010, pp. 169-180

Computer Science

Logic in Computer Science

In Proceedings DCM 2010, arXiv:1006.1937

Scientific paper

10.4204/EPTCS.26.16

We present a form of algebraic reasoning for computational objects which are expressed as graphs. Edges describe the flow of data between primitive operations which are represented by vertices. These graphs have an interface made of half-edges (edges which are drawn with an unconnected end) and enjoy rich compositional principles by connecting graphs along these half-edges. In particular, this allows equations and rewrite rules to be specified between graphs. Particular computational models can then be encoded as an axiomatic set of such rules. Further rules can be derived graphically and rewriting can be used to simulate the dynamics of a computational system, e.g. evaluating a program on an input. Examples of models which can be formalised in this way include traditional electronic circuits as well as recent categorical accounts of quantum information.

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