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Modeling languages are a fundamental part of automated software development. MDD, for example, uses UML class diagrams and state machines as languages to define applications. In this paper, we explore how Feature Oriented Software Development (FOSD) uses modern mathematics as a modeling language to express the design and synthesis of programs in software product lines, but demands little mathematical sophistication from its users. Doing so has three practical benefits: (1) it offers a simple and principled mathematical description of how FOSD transforms, derives, and relates program artifacts, (2) it exposes previously unrecognized commuting relationships among tool chains, thereby providing new ways to debug tools, and (3) it reveals new ways to optimize software synthesis.