Computational category-theoretic rewriting

Abstract

We demonstrate how category theory provides specifications that can efficiently be implemented via imperative algorithms and apply this to the field of graph transformation. By examples, we show how this paradigm of software development makes it easy to quickly write correct and performant code. We provide a modern implementation of graph rewriting techniques at the level of abstraction of finitely-presented $C$-sets and clarify the connections between $C$-sets and the typed graphs supported in existing rewriting software. We emphasize that our open-source library is extensible: by taking new categorical constructions (such as slice categories, structured cospans, and distributed graphs) and relating their limits and colimits to those of their underlying categories, users inherit efficient algorithms for pushout complements and (final) pullback complements. This allows one to perform double-, single-, and sesqui-pushout rewriting over a broad class of data structures. Graph transformation researchers, scientists, and engineers can then use this library to computationally manipulate rewriting systems and apply them to their domains of interest.