E-Graph Support Package for DS

An E-Graph (Equality Graph) implementation for the DS deductive system, providing efficient management and manipulation of equivalence classes of terms.

This package implements the egg-style E-Graph data structure with deferred congruence closure, enabling efficient equality reasoning. Inspired by the egg library.

Features

• E-Graph Data Structure: Manage equivalence classes of terms efficiently
• Union-Find: Path-compressed union-find for disjoint set management
• Congruence Closure: Automatic maintenance of congruence relationships
• Deferred Rebuilding: egg-style deferred rebuilding for performance

Installation

Python (pip)

pip install apyds-egg

Requires Python 3.11-3.14.

TypeScript/JavaScript (npm)

npm install atsds-egg

Quick Start

Python Example

import apyds
from apyds_egg import EGraph

# Create an E-Graph
eg = EGraph()

# Add terms to the E-Graph
a = eg.add(apyds.Term("a"))
b = eg.add(apyds.Term("b"))
x = eg.add(apyds.Term("x"))

# Add compound terms
ax = eg.add(apyds.Term("(+ a x)"))
bx = eg.add(apyds.Term("(+ b x)"))

# Initially, (+ a x) and (+ b x) are in different E-classes
assert eg.find(ax) != eg.find(bx)

# Merge a and b
eg.merge(a, b)

# Rebuild to restore congruence
eg.rebuild()

# Now (+ a x) and (+ b x) are in the same E-class
assert eg.find(ax) == eg.find(bx)

TypeScript Example

import { Term } from "atsds";
import { EGraph } from "atsds-egg";

// Create an E-Graph
const eg = new EGraph();

// Add terms to the E-Graph
const a = eg.add(new Term("a"));
const b = eg.add(new Term("b"));
const x = eg.add(new Term("x"));

// Add compound terms
const ax = eg.add(new Term("(+ a x)"));
const bx = eg.add(new Term("(+ b x)"));

// Initially, (+ a x) and (+ b x) are in different E-classes
if (eg.find(ax) === eg.find(bx)) throw new Error("Should be different");

// Merge a and b
eg.merge(a, b);

// Rebuild to restore congruence
eg.rebuild();

// Now (+ a x) and (+ b x) are in the same E-class
if (eg.find(ax) !== eg.find(bx)) throw new Error("Should be same");

Core Concepts

E-Graph

An E-Graph is a data structure that efficiently represents and maintains equivalence classes of terms. It consists of:

• E-Nodes: Nodes representing terms with an operator and children
• E-classes: Equivalence classes of E-Nodes
• Union-Find: Data structure for managing E-class equivalence
• Congruence: Two terms are congruent if they have the same operator and their children are in equivalent E-classes

Congruence Closure

The E-Graph maintains congruence closure automatically. When two E-classes are merged, the E-Graph rebuilds to ensure that congruent terms remain in the same E-class.

Python Example

eg = EGraph()

# Add terms
fa = eg.add(apyds.Term("(f a)"))
fb = eg.add(apyds.Term("(f b)"))

# Merge a and b
a = eg.add(apyds.Term("a"))
b = eg.add(apyds.Term("b"))
eg.merge(a, b)

# Rebuild maintains congruence
eg.rebuild()

# Now (f a) and (f b) are equivalent
assert eg.find(fa) == eg.find(fb)

TypeScript Example

import { Term } from "atsds";
import { EGraph } from "atsds-egg";

const eg = new EGraph();

// Add terms
const fa = eg.add(new Term("(f a)"));
const fb = eg.add(new Term("(f b)"));

// Merge a and b
const a = eg.add(new Term("a"));
const b = eg.add(new Term("b"));
eg.merge(a, b);

// Rebuild maintains congruence
eg.rebuild();

// Now (f a) and (f b) are equivalent
if (eg.find(fa) !== eg.find(fb)) throw new Error("Congruence failed");

API Overview

Python (apyds-egg)

• EGraph(): Create a new E-Graph
• add(term: apyds.Term) -> EClassId: Add a term to the E-Graph
• merge(a: EClassId, b: EClassId) -> EClassId: Merge two E-classes
• rebuild() -> None: Restore congruence closure
• find(eclass: EClassId) -> EClassId: Find canonical E-class representative

TypeScript (atsds-egg)

• new EGraph(): Create a new E-Graph
• add(term: atsds.Term): EClassId: Add a term to the E-Graph
• merge(a: EClassId, b: EClassId): EClassId: Merge two E-classes
• rebuild(): void: Restore congruence closure
• find(eclass: EClassId): EClassId: Find canonical E-class representative

Building from Source

Prerequisites

• Python 3.11-3.14
• Node.js and npm
• apyds and atsds packages

Python Package

cd egg

# Install dependencies
uv sync --extra dev

# Build package
uv build

# Run tests
uv run pytest

# Run with coverage
uv run pytest --cov

TypeScript Package

cd egg

# Install dependencies
npm install

# Build package
npm run build

# Run tests
npm test

License

This project is licensed under the GNU Affero General Public License v3.0 or later (AGPL-3.0-or-later).

Repository

• GitHub: USTC-KnowledgeComputingLab/ds (in /egg directory)
• Python Package: apyds-egg
• npm Package: atsds-egg

Author

Hao Zhang hzhangxyz@outlook.com

Related

This package is a support library for the DS (Deductive System) project. For the main DS library with C++ core and bindings, see the main repository.