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This article presents liquid resource types, a technique for automatically verifying the resource consumption of functional programs. Existing resource analysis techniques trade automation for flexibility – automated techniques are restricted to relatively constrained families of resource bounds, while more expressive proof techniques admitting value-dependent bounds rely on handwritten proofs. Liquid resource types combine the best of these approaches, using logical refinements to automatically prove precise bounds on a program’s resource consumption. The type system augments refinement types with potential annotations to conduct an amortized resource analysis. Importantly, users can annotate data structure declarations to indicate how potential is allocated within the type, allowing the system to express bounds with polynomials and exponentials, as well as more precise expressions depending on program values. We prove the soundness of the type system, provide a library of flexible and reusable data structures for conducting resource analysis, and use our prototype implementation to automatically verify resource bounds that previously required a manual proof. 

This article presents resource-guided synthesis, a technique for synthesizing recursive programs that satisfy both a functional specification and a symbolic resource bound. The technique is type-directed and rests upon a novel type system that combines polymorphic refinement types with potential annotations of automatic amortized resource analysis. The type system enables efficient constraint-based type checking and can express precise refinement-based resource bounds. The proof of type soundness shows that synthesized programs are correct by construction. By tightly integrating program exploration and type checking, the synthesizer can leverage the user-provided resource bound to guide the search, eagerly rejecting incomplete programs that consume too many resources. An implementation in the resource-guided synthesizer ReSyn is used to evaluate the technique on a range of recursive data structure manipulations. The experiments show that ReSyn synthesizes programs that are asymptotically more efficient than those generated by a resource-agnostic synthesizer. Moreover, synthesis with ReSyn is faster than a naive combination of synthesis and resource analysis. ReSyn is also able to generate implementations that have a constant resource consumption for fixed input sizes, which can be used to mitigate side-channel attacks.