The rapid advancement of artificial intelligence (AI) is reshaping various sectors, yet the field of design for manufacturing has not fully capitalized on these innovations. This project aims to bridge this gap by developing new design tools that combine AI with traditional design algorithms and principles. A central challenge for design tools in manufacturing is the need to simultaneously nurture the creative ability to conceive novel designs and the analytical prowess to critically evaluate and optimize functionality and production. The goal of this project is to address these challenges and develop novel tools that make it easier for both new and experienced designers to create a wide range of high-quality products. These tools are expected to not only improve product quality and variety, but also enhance sustainable manufacturing. Additionally, the project includes an educational component to make STEM fields more accessible and engaging through design and manufacturing. To unite design precision with creative exploration, this project will develop tools that combine neural abstractions with formal reasoning. Treating computer-aided design (CAD) models as programs that generate geometry, this initiative interprets design as program synthesis, benefiting from formal reasoning and advancements in AI-driven code generation. This approach ensures verifiability and constraint-adherent synthesis, essential for precise engineering analysis. The project will develop a new do