Newclid: A User-Friendly Replacement for AlphaGeometry

TL;DR

Newclid is a user-friendly, extensible symbolic geometry solver based on AlphaGeometry, featuring improved debugging, visualization, and educational tools, and demonstrating enhanced problem-solving capabilities.

Contribution

It introduces a modular, accessible symbolic solver DDARN with new interfaces, debugging tools, and expanded problem-solving scope, improving upon AlphaGeometry.

Findings

DDARN solves more problems than AlphaGeometry's solver.

Newclid's CLI and debugging tools enhance usability and extendability.

Expanded scope includes metric geometry and theorems like Pythagoras.

Abstract

We introduce a new symbolic solver for geometry, called Newclid, which is based on AlphaGeometry. Newclid contains a symbolic solver called DDARN (derived from DDAR-Newclid), which is a significant refactoring and upgrade of AlphaGeometry's DDAR symbolic solver by being more user-friendly - both for the end user as well as for a programmer wishing to extend the codebase. For the programmer, improvements include a modularized codebase and new debugging and visualization tools. For the user, Newclid contains a new command line interface (CLI) that provides interfaces for agents to guide DDARN. DDARN is flexible with respect to its internal reasoning, which can be steered by agents. Further, we support input from GeoGebra to make Newclid accessible for educational contexts. Further, the scope of problems that Newclid can solve has been expanded to include the ability to have an improved understanding of metric geometry concepts (length, angle) and to use theorems such as the Pythagorean theorem in proofs. Bugs have been fixed, and reproducibility has been improved. Lastly, we re-evaluated the five remaining problems from the original AG-30 dataset that AlphaGeometry was not able to solve and contrasted them with the abilities of DDARN, running in breadth-first-search agentic mode (which corresponds to how DDARN runs by default), finding that DDARN solves an additional problem. We have open-sourced our code under: https://github.com/LMCRC/Newclid