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arXiv · 2406.15882

Equivalence Hypergraphs: DPO Rewriting for Monoidal E-Graphs

Aleksei Tiurin·Chris Barrett·Dan R. Ghica·Nick Hu
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Abstract

The technique of \emph{equality saturation}, which equips graphs with an equivalence relation, has proven effective for program optimisation. We give a categorical semantics to these structures, called \emph{e-graphs}, in terms of Cartesian categories enriched over the category of semilattices. This approach generalises to monoidal categories, which opens the door to new applications of e-graph techniques, from algebraic to monoidal theories. Finally, we present a sound and complete combinatorial representation of morphisms in such a category, based on a generalisation of hypergraphs which we call \emph{e-hypergraphs}. They have the usual advantage that many of their structural equations are absorbed into a general notion of isomorphism. This new principled approach to e-graphs enables double-pushout (DPO) rewriting for these structures, which constitutes the main contribution of this paper.

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Aleksei Tiurin, Chris Barrett, Dan R. Ghica, Nick Hu. 2024-06-22. Equivalence Hypergraphs: DPO Rewriting for Monoidal E-Graphs. https://arxiv.org/abs/2406.15882

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