@article{Lucas-Dixon:2009yq,
  abstract = "Compact closed categories provide a foundational formalism for a variety of important domains, including quantum computation. These categories have a natural visualisation as a form of graphs. We present a formalism for equational reasoning about such graphs and develop this into a generic proof system with a fixed logical kernel for equational reasoning about compact closed categories. Automating this reasoning process is motivated by the slow and error prone nature of manual graph manipulation. A salient feature of our system is that it provides a formal and declarative account of derived results that can include `ellipses'-style notation. We illustrate the framework by instantiating it for a graphical language of quantum computation and show how this can be used to perform symbolic computation.",
  author = "Lucas Dixon and Ross Duncan",
  doi = "10.1007/s10472-009-9141-x",
  journal = "Annals of Mathematics and Artificial Intelligence",
  keywords = "categorical quantum mechanics; compact closed categories; rewriting; graphical calculi",
  note = "preprint available at http://arxiv.org/abs/0902.0514",
  title = "Graphical Reasoning in Compact Closed Categories for Quantum Computation",
  year = "2009",
}