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.

Development of formal proofs of correctness of programs can increase actual and perceived reliability and facilitate better understanding of program specifications and their underlying assumptions. Tools supporting such development have been available for over 40 years, but have only recently seen wide practical use. Projects based on construction of machine-checked formal proofs are now reaching an unprecedented scale, comparable to large software projects, which leads to new challenges in proof development and maintenance. Despite its increasing importance, the field of proof engineering is seldom considered in its own right; related theories, techniques, and tools span many fields and venues. This survey of the literature presents a holistic understanding of proof engineering for program correctness, covering impact in practice, foundations, proof automation, proof organization, and practical proof development.