Equivalence Hypergraphs: DPO Rewriting for Monoidal E-Graphs
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.
Keywords
Cite
@article{arxiv.2406.15882,
title = {Equivalence Hypergraphs: DPO Rewriting for Monoidal E-Graphs},
author = {Aleksei Tiurin and Chris Barrett and Dan R. Ghica and Nick Hu},
journal= {arXiv preprint arXiv:2406.15882},
year = {2025}
}