AlphaGeometry DSL Guide: Google Geometry DSL, defs.txt Actions, and Predicates

This article focuses only on AlphaGeometry DSL itself. It does not cover model training, search strategy, or paper results. The goal is to treat the DSL as an engineering-facing protocol document and answer four questions: How problem input is encoded How actions are defined in defs.txt How geometric relations are mapped into predicates How numerical construction and symbolic reasoning are connected If you want to reproduce AlphaGeometry, build a geometry data generator, or design a compatibility layer for a custom solver, understanding the DSL protocol is a prerequisite. 1. Role of the DSL AlphaGeometry DSL is a domain-specific language for geometric construction and relation expression. It mainly serves 3 purposes: Express initial geometric premises Express executable construction actions Express target geometric goals to be verified Its output is not a final proof text, but a set of geometric relations consumable by a reasoning engine. From an implementation perspective, the DSL is