Liquid Tree Automata

Component-based synthesis (CBS) aims to generate loopfree programs from a set of libraries whose methods are annotated with specifications and whose output must satisfy a set of logical constraints, expressed as a query. The effectiveness of a CBS algorithm critically depends on the severity of the constraints imposed by the query. The more exact these constraints are, the sparser the space of feasible solutions. This maxim also applies when we enrich the expressivity of the specifications affixed to library methods. In both cases, search must now contend with constraints that may only hold over a small number of the possible execution paths that can be enumerated by a CBS procedure.

In this paper, we address this challenge by equipping CBS search with the ability to reason about logical similarities among the paths it explores. Our setting considers library methods equipped with refinementtype specifications that enrich ordinary base types with a set of rich logical qualifiers to constrain the set of values accepted by that type.

For efficient representation and enumeration of this space, we introduce a novel tree automata variant called Liquid Tree Automata (LTA) whose construction is driven by the typing rules of a refinement type system. This allows us to leverage subtyping constraints over the refinement types associated with enumerated terms to enable reasoning about similarity among candidate solutions as search proceeds, using this notion of similarity to eagerly merge LTA states. By doing so, we avoid exploration of semantically similar paths, leading to a significantly improved search procedure. We present an implementation of this idea in a tool called Hegel and provide a comprehensive evaluation that demonstrates Hegel's ability to synthesize solutions to complex CBS queries that go well-beyond the capabilities of the existing state-of-the-art.