A Solver‐Aided Hierarchical Language for LLM‐Driven CAD Design

Abstract Parametric CAD systems use domain‐specific languages (DSLs) to represent geometry as programs, enabling both flexible modeling and structured editing. With the rise of large language models (LLMs), there is growing interest in generating such programs from natural language. This raises a key question: what kind of DSL best supports both CAD generation and editing, whether performed by a human or an AI? In this work, we introduce AIDL, a hierarchical, solver‐aided DSL designed to align with the strengths of LLMs while remaining interpretable and editable by humans. AIDL enables high‐level reasoning by breaking problems into abstract components and structural relationships, while offloading low‐level geometric reasoning to a constraint solver. We evaluate AIDL in a 2D text‐to‐CAD setting using a zero‐shot prompt‐based interface and compare it to OpenSCAD, a widely used CAD DSL that appears in LLM training data. AIDL produces results that are visually competitive and significantly easier to edit. Our findings suggest that language design is a powerful complement to model training and prompt engineering for building collaborative AI–human tools in CAD. Code is available at https://github.com/deGravity/aidl .