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Synthesis is the problem of obtaining programs from relational specifications. We present grammar-modular (GM) synthesis, an algorithm for synthesis from tree-structured relational specifications. GM synthesis makes synthesis applicable to previously intractable relational specifications by decomposing them into smaller subproblems, which can be tackled in isolation by off-the-shelf synthesis procedures. The program fragments thus generated are subsequently composed to form a program satisfying the overall specification. We also generalize our technique to tree languages of relational specifications. Here, we synthesize a single program capable satisfying any (tree-shaped) relation belonging to the language; the synthesized program is syntax-directed by the structure of the relation. We evaluate our work by applying GM synthesis to document layout: given the semantics of a layout language, we synthesize tailored constraint solvers capable of laying out languages of documents. Our experiments show that GM synthesis is sufficiently complete to successfully generate solvers for non-trivial data visualizations, and that our synthesized solvers are between 39- to 200-times faster than general-purpose constraint solvers.

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