The diagrammatic specification and automatic generation of geometry subroutines

Programming has advanced a great deal since the appearance of the stored-program architecture. Through the successive generations of machine codes, assembly languages, high-level languages, and object-oriented languages, the drive has been toward program descriptions that express more meaning in a shorter space. This trend continues today with domain-specific languages. However, conventional languages rely on a textual formalism (commands, statements, lines of code) to capture the programmer's intent, which, regardless of its level of abstraction, imposes inevitable overheads. Before successful programming activities can take place, the syntax has to be mastered, names and keywords memorized, the library routines mastered, etc. Existing visual programming languages avoid some of these overheads, but do not release the programmer from the task of specifying the program logic, which consumes the main portion of programming time and also is the major source of difficult bugs.

Our work aims to minimize the demands a formalism imposes on the programmer of geometric subroutines other than what is inherent in the problem itself. Our approach frees the programmer from syntactic constraints and generates logically correct programs automatically from program descriptions in the form of diagrams. To write a program, the programmer simply draws a few diagrams to depict the problem context and specifies all the necessary parameters through menu operations.

Diagrams are succinct, easy to learn, and intuitive to use. They are much easier to modify than code, and they help the user visualize and analyze the problem, in addition to providing information to the computer. Furthermore, diagrams describe a situation rather than a task and thus are reusable for different tasks—in general, a single diagram can generate many programs. For these reasons, we have chosen diagrams as the main specification mechanism.

In addition, we leverage the power of automatic inference to reason about diagrams and generic components—the building blocks of our programs—and discover the logic for assembling these components into correct programs. To facilitate inference, symbolic facts encode entities present in the diagrams, their spatial relationships, and the preconditions and effects of reusable components. We have developed a reference implementation and tested it on a number of real-world examples to demonstrate the feasibility and efficacy of our approach.