Egg: A Rust‑Powered Engine for Equality Saturation and Program Synthesis

Equality saturation has emerged as a powerful paradigm for rewrite‑driven compiler optimizations and program synthesis. At its heart lies the e‑graph, a compact data structure that represents a congruence relation over many expressions. The Egg project, released in 2021, brings a fresh perspective to this space by providing a fast, flexible, and extensible e‑graph implementation written in Rust.

From Theory to Practice

E‑graphs were originally conceived in the late 1970s for automated theorem proving. In recent years, researchers have repurposed them for equality saturation, a technique that applies a large set of rewrite rules in parallel to explore the space of equivalent programs. However, existing e‑graph libraries were not tuned for the specific workload characteristics of equality saturation, often requiring ad‑hoc extensions for domain‑specific rewrites.

Egg tackles these shortcomings head‑on. Two key innovations—

  • Rebuilding – an amortized invariant restoration technique that leverages the repetitive nature of equality saturation to achieve asymptotic speedups.
  • E‑class analyses – a general mechanism that integrates domain‑specific analyses directly into the e‑graph, eliminating the need for manual manipulation.

These contributions are detailed in the paper "egg: Fast and Extensible Equality Saturation" (Willsey et al., POPL 2021). The authors report performance gains across three diverse applications, underscoring Egg’s versatility.

"Egg’s performance and flexibility enable state‑of‑the‑art results across diverse domains." – Willsey et al., POPL 2021

The Core Library

Egg’s core library is a high‑performance Rust implementation of e‑graphs. It is available on crates.io and documented on docs.rs. A beginner‑friendly tutorial introduces the fundamentals of e‑graphs and walks through common use cases such as compiler optimization and program synthesis.

use egg::{EGraph, Id, RecExpr, Symbol, Var, Pattern};

// Create an empty e‑graph
let mut egraph = EGraph::default();

// Add an expression: (a * 2) / 2
let expr = RecExpr::from((Symbol("/"), vec![
    RecExpr::from((Symbol("*"), vec![Var(0), Symbol("2")])),
    Symbol("2"),
]));
let id = egraph.add(expr);

// Apply a rewrite rule: (x * 2) / 2 => x
let rule = Pattern::from((Symbol("/"), vec![
    Pattern::from((Symbol("*"), vec![Var(0), Symbol("2")])),
    Symbol("2"),
]));
let rewritten = egraph.apply_rule(&rule);

The example above demonstrates how a simple rewrite rule can be expressed and applied within Egg, showcasing the library’s ease of use.

Egglog: Equality Saturation Meets Datalog

Beyond the core library, Egglog offers an alternative approach to equality saturation based on Datalog. Designed as a language‑centric system, Egglog features incremental execution and composable analyses, making it a compelling tool for researchers exploring the intersection of logic programming and compiler optimizations.

"Egglog’s language‑based design and incremental execution provide a fresh perspective on equality saturation." – Egglog paper (PLDI 2023)

Community and Ecosystem

Egg is part of the broader EGRAPHS Community, which brings together researchers and practitioners interested in e‑graphs and related techniques. The community hosts an annual workshop at PLDI, a monthly seminar, and a Zulip chat for real‑time discussion.

Projects that leverage Egg are showcased on the Awesome E‑graphs list and on GitHub, with citation counts available on Google Scholar. The community’s active engagement ensures that Egg remains at the cutting edge of research and industrial application.

Why It Matters

Equality saturation has the potential to revolutionize compiler construction, automated reasoning, and program synthesis. By providing a robust, high‑performance foundation, Egg lowers the barrier to entry for developers and researchers alike. Its Rust implementation guarantees memory safety without sacrificing speed—a critical combination for production‑grade tooling.

Moreover, Egg’s extensibility means that new rewrite rules, analyses, or domain‑specific optimizations can be integrated with minimal friction, fostering rapid experimentation and innovation.

Source: https://egraphs-good.github.io/