geproofd

Geproofd is a modular open-source framework designed to support formal reasoning in geometry by integrating a geometric proof engine with practical interfaces for education and research. The project aims to provide a unified approach to constructing, visualizing, and verifying geometric proofs across different geometric theories, including Euclidean, projective, and metric geometry.

Geproofd was conceived in the early 2020s by researchers in formal methods and computational geometry. The name blends geometry with proof deduction, reflecting its goal of turning geometric reasoning into machine-checked proofs. It is positioned as a bridge between geometry libraries and mainstream proof assistants, offering export paths to systems such as Coq and Lean and import paths from existing geometric libraries.

The architecture centers on a core deductive engine, a geometry library, and a tactic-based proof language. The core handles symbolic manipulation of geometric primitives (points, lines, circles) and their relations, supporting axioms from Hilbert or Tarski-style frameworks. The geometry library provides construction tools and transformation rules, while a lightweight tactic language enables users to script proof strategies. Interoperability features allow exporting to standard proof formats and importing external axioms.

Geproofd is used in education to illustrate synthetic reasoning, in research to formalize and verify geometric theorems, and in algorithm verification where geometric properties are integral. The project is maintained with a permissive license and an open contributor model, with ongoing work focused on performance, extended axioms, and richer visualization.