An e-graph efficiently represents a congruence relation over many expressions. Although they were originally developed in the late 1970s for use in automated theorem provers, a more recent technique known as equality saturation repurposes e-graphs to implement state-of-the-art, rewrite-driven compiler optimizations and program synthesizers. However, e-graphs remain unspecialized for this newer use case. Equality saturation workloads exhibit distinct characteristics and often require ad-hoc e-graph extensions to incorporate transformations beyond purely syntactic rewrites. This work contributes two techniques that make e-graphs fast and extensible, specializing them to equality saturation. A new amortized invariant restoration technique called rebuilding takes advantage of equality saturation's distinct workload, providing asymptotic speedups over current techniques in practice. A general mechanism called e-class analyses integrates domain-specific analyses into the e-graph, reducing the need for ad hoc manipulation. We implemented these techniques in a new open-source library called egg. Our case studies on three previously published applications of equality saturation highlight how egg's performance and flexibility enable state-of-the-art results across diverse domains.

@article{paperbot1142,
  title = {egg: Fast and extensible equality saturation},
  author = {Max Willsey and Chandrakana Nandi and Yisu Remy Wang and Oliver Flatt and Zachary Tatlock and Pavel Panchekha},
  journal = {Proceedings of the ACM on Programming Languages},
  volume = {5},
  number = {POPL},
  year = {2021},
  doi = {10.1145/3434304}
}