Functional programming for compiling and decompiling computer-aided design

Desktop-manufacturing techniques like 3D printing are increasingly popular because they reduce the cost and complexity of producing customized objects on demand. Unfortunately, the vibrant communities of early adopters, often referred to as "makers," are not well-served by currently available software pipelines. Users today must compose idiosyncratic sequences of tools which are typically repurposed variants of proprietary software originally designed for expert specialists. This paper proposes fundamental programming-languages techniques to bring improved rigor, reduced complexity, and new functionality to the computer-aided design (CAD) software pipeline for applications like 3D-printing. Compositionality, denotational semantics, compiler correctness, and program synthesis all play key roles in our approach, starting from the perspective that solid geometry is a programming language. Specifically, we define a purely functional language for CAD called LambdaCAD and a polygon surface-mesh intermediate representation. We then define denotational semantics of both languages to 3D solids and a compiler from CAD to mesh accompanied by a proof of semantics preservation. We illustrate the utility of this foundation by developing a novel synthesis algorithm based on evaluation contexts to "reverse compile" difficult-to-edit meshes downloaded from online maker communities back to more-editable CAD programs. All our prototypes have been implemented in OCaml to enable further exploration of functional programming for desktop manufacturing.