egg: Fast and Extensible Equality Saturation
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by
Max Willsey, Chandrakana Nandi, Yisu Remy Wang, Oliver Flatt, Zachary Tatlock, Pavel Panchekha
2020
Abstract
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.
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