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Equality saturation is a program optimization technique based on non-destructive rewriting and a form of abstract interpretation called e-class analysis. Existing e-class analyses are pessimistic and therefore typically imprecise when analyzing cyclic programs, such as those in SSA form. We show that a straightforward optimistic variant of e-class analysis can result in unsoundness, due to a subtlety in how e-graphs represent programs. We propose an abstract interpretation algorithm that circumvents this issue and can optimistically analyze e-graphs during equality saturation. This results in a unified algorithm for optimistic analysis and non-destructive rewriting. We implement a prototype abstract interpreter and equality saturation tool for SSA programs. Our tool exhibits precision improvements over pure abstract interpretation (without rewriting) and pessimistic e-class analysis on example programs. Additionally, its performance is comparable to existing abstract interpretation and e-class analysis techniques.
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egg: Fast and extensible equality saturation
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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- Award ID(s):
- 1749570
- PAR ID:
- 10224915
- Date Published:
- Journal Name:
- Proceedings of the ACM on Programming Languages
- Volume:
- 5
- Issue:
- POPL
- ISSN:
- 2475-1421
- Page Range / eLocation ID:
- 1 to 29
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript
- Journal Article:
- https://doi.org/10.1145/3434304
