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Abstract: Compact closed categories provide a foundational formalism for a variety ofimportant domains, including quantum computation. These categories have anatural visualisation as a form of graphs. We present a formalism forequational reasoning about such graphs and develop this into a generic proofsystem with a fixed logical kernel for equational reasoning about compactclosed categories. Automating this reasoning process is motivated by the slowand error prone nature of manual graph manipulation. A salient feature of oursystem is that it provides a formal and declarative account of derived resultsthat can include `ellipses-style notation. We illustrate the framework byinstantiating it for a graphical language of quantum computation and show howthis can be used to perform symbolic computation.



Author: Lucas Dixon, Ross Duncan

Source: https://arxiv.org/







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