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Many problem domains, including program synthesis and rewrite-based optimization, require searching astronomically large spaces of programs. Existing approaches often rely on building specialized data structures—version-space algebras, finite tree automata, or e-graphs—to compactly represent such spaces. At their core, all these data structures exploit independence of subterms; as a result, they cannot efficiently represent more complex program spaces, where the choices of subterms are entangled. We introduceequality-constrained tree automata(ECTAs), a new data structure, designed to compactly represent large spaces of programs with entangled subterms. We present efficient algorithms for extracting programs from ECTAs, implemented in a performant Haskell library, ecta. Using the ecta library, we construct Hectare, a type-driven program synthesizer for Haskell. Hectare significantly outperforms a state-of-the-art synthesizer Hoogle+—providing an average speedup of 8×—despite its implementation being an order of magnitude smaller. 

Programmers are told "depend on interfaces, not implementations." But, given a program, is it possible even to assess objectively whether such advice has been followed? Programmers frequently talk in ways like this about dependence, but the very term, like many used in software engineering, has hitherto eluded precise definition. In this work, we resolve a variety of confusions about dependence, and present a formal definition unifying multiple varieties of software dependence, grounded in Halpern and Pearl's theory of actual causation. This definition is parameterized by the formal system characterizing the property of interest, and by constraints on "reasonable changes" to the program. By picking different choices of formal system, one can specialize our definition to characterize several notions of dependence, including build, correctness, and performance dependences. Overall, our work provides a path to making conversations about software dependence fully objective, and might serve as a basis for future work that automatically checks forms of dependence that were previously too abstract or high-level to be candidates for tools.