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1. Resource-Guided Program Synthesis

   Knoth, Tristan; Wang, Di; Polikarpova, Nadia; Hoffmann, Jan (January 2019, 40th Conference on Programming Language Design and Implementation (PLDI'19))

   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. 

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2. A Decidable Logic for Tree Data-Structures with Measurements

   https://doi.org/10.1007/978-3-030-11245-5_15  

   Qiu, Xiaokang; Wang, Yanjun (January 2019, 20th International Conference on Verification, Model Checking, and Abstract Interpretation)

   We present DRYADdec, a decidable logic that allows reasoning about tree data-structures with measurements. This logic supports user-defined recursive measure functions based on Max or Sum, and recursive predicates based on these measure functions, such as AVL trees or red-black trees. We prove that the logic’s satisfiability is decidable. The crux of the decidability proof is a small model property which allows us to reduce the satisfiability of DRYADdec to quantifier-free linear arithmetic theory which can be solved efficiently using SMT solvers. We also show that DRYADdec can encode a variety of verification and synthesis problems, including natural proof verification conditions for functional correctness of recursive tree-manipulating programs, legality conditions for fusing tree traversals, synthesis conditions for conditional linear-integer arithmetic functions. We developed the decision procedure and successfully solved 220+ DRYADdec formulae raised from these application scenarios, including verifying functional correctness of programs manipulating AVL trees, red-black trees and treaps, checking the fusibility of height-based mutually recursive tree traversals, and counterexample-guided synthesis from linear integer arithmetic specifications. To our knowledge, DRYADdec is the first decidable logic that can solve such a wide variety of problems requiring flexible combination of measure-related, data-related and shape-related properties for trees. 

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3. Bootstrapping Library-Based Synthesis

   https://doi.org/10.1007/978-3-031-22308-2_13  

   Huang, Kangjing; Qiu, Xiaokang (December 2022, Lecture notes in computer science)

   Singh, Gagandeep; Urban, Caterina (Ed.)

   Constraint-based program synthesis techniques have been widely used in numerous settings. However, synthesizing programs that use libraries remains a major challenge. To handle complex or black-box libraries, the state of the art is to provide carefully crafted mocks or models to the synthesizer, requiring extra manual work. We address this challenge by proposing TOSHOKAN, a new synthesis framework as an alternative approach in which library-using programs can be generated without any user-provided artifacts at the cost of moderate performance overhead. The framework extends the classic counterexample-guided synthesis framework with a bootstrapping, log-based library model. The model collects input-output samples from running failed candidate programs on witness inputs. We prove that the framework is sound when a sound, bounded verifier is available, and also complete if the underlying synthesizer and verifier promise to produce minimal outputs. We implement and incorporate the framework to JSKETCH, a Java sketching tool. Experiments show that TOSHOKAN can successfully synthesize programs that use a variety of libraries, ranging from mathematical functions to data structures. Comparing to state-of-the-art synthesis algorithms which use mocks or models, TOSHOKAN reduces up to 159 lines of code of required manual inputs, at the cost of less than 40s of performance overheads. 

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4. Trace-Guided Inductive Synthesis of Recursive Functional Programs

   https://doi.org/10.1145/3591255  

   Yuan, Yongwei; Radhakrishna, Arjun; Samanta, Roopsha (June 2023, Proceedings of the ACM on Programming Languages)

   We propose a novel trace-guided approach to tackle the challenges of ambiguity and generalization in synthesis of recursive functional programs from input-output examples. Our approach augments the search space of programs with recursion traces consisting of recursive subcalls of the programs. Our method is based on a new version space algebra (VSA) for succinct representation and efficient manipulation of pairs of recursion traces and programs that are consistent with each other. We have implemented this approach in a tool called SyRup and evaluated it on benchmarks from prior work. Our evaluation demonstrates that SyRup not only requires fewer examples to achieve a certain success rate than existing synthesizers, but is also less sensitive to the quality of the examples. 

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5. Metric Program Synthesis

   John Feser; Isil Dillig; Armando Solar-Lezama (January 2022, POPL 2022)

   We present a new domain-agnostic synthesis technique for generating programs from input-output examples. Our method, called metric program synthesis, relaxes the well-known observational equivalence idea (used widely in bottom-up enumerative synthesis) into a weaker notion of observational similarity, with the goal of reducing the search space that the synthesizer needs to explore. Our method clusters programs into equivalence classes based on a distance metric and constructs a version space that compactly represents ""approximately correct"" programs. Then, given a ""close enough"" program sampled from this version space, our approach uses a distance-guided repair algorithm to find a program that exactly matches the given input-output examples. We have implemented our proposed metric program synthesis technique in a tool called SyMetric and evaluate it in three different domains considered in prior work. Our evaluation shows that SyMetric outperforms other domain-agnostic synthesizers that use observational equivalence and that it achieves results competitive with domain-specific synthesizers that are either designed for or trained on those domains. 

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