Searching Entangled Program Spaces
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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 these programs. To find a compact representation, existing data structures exploit independence of subterms; they blow up when the choices of subterms are entangled. We introduce equality-constrained tree automata (ECTAs), a generalization of the three aforementioned data structures that can efficiently represent large spaces of programs with entangled subterms. We present efficient algorithms for extracting programs from ECTAs, implemented in a performant Haskell library, . Using 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 8x – despite its implementation being an order of magnitude smaller.
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