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PreprintarXiv licencearXiv

How to prove equations using diagrams: A categorical and operational semantics for e-graphs

  • Evan Patterson
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Abstract

E-graphs are a powerful algorithmic technique for automated equational reasoning but have resisted a conceptual understanding independent of issues of presentation and implementation. We propose an operational semantics for e-graphs based on the fundamental category-theoretic concepts of diagrams, limits, and initial functors. We illustrate the formalism through numerous example calculations and establish its soundness and completeness. Technical prerequisites are kept to a minimum in the main text; less standard elements of the mathematical theory are developed in two appendices.

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Cite

BibTeXRIS
BibTeX
@misc{patterson2026prove,
  title = {{How to prove equations using diagrams: A categorical and operational semantics for e-graphs}},
  author = {Evan Patterson},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.05924},
  eprint = {2611.05924},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.05924},
}
RIS
TY  - UNPB
TI  - How to prove equations using diagrams: A categorical and operational semantics for e-graphs
AU  - Evan Patterson
PY  - 2026
DA  - 2026/11/04
PB  - arXiv
DO  - 10.48550/arxiv.2611.05924
UR  - https://arxiv.org/abs/2611.05924
AB  - E-graphs are a powerful algorithmic technique for automated equational reasoning but have resisted a conceptual understanding independent of issues of presentation and implementation. We propose an operational semantics for e-graphs based on the fundamental category-theoretic concepts of diagrams, limits, and initial functors. We illustrate the formalism through numerous example calculations and establish its soundness and completeness. Technical prerequisites are kept to a minimum in the main text; less standard elements of the mathematical theory are developed in two appendices.
ER  -