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The traditional formulation of the program synthesis problem is to find a program that meets a logical correctness specification. When synthesis is successful, there is a guarantee that the implementation satisfies the specification. Unfortunately, synthesis engines are typically monolithic algorithms, and obscure the correspondence between the specification, implementation and user intent. In contrast, humans often include comments in their code to guide future developers towards the purpose and design of different parts of the codebase. In this paper, we introducesubspecificationsas a mechanism to augment the synthesized implementation with explanatory notes of this form. In this model, the user may ask for explanations of different parts of the implementation; the subspecification generated in response is a logical formula that describes the constraints induced on that subexpression by the global specification and surrounding implementation. We develop algorithms to construct and verify subspecifications and investigate their theoretical properties. We perform an experimental evaluation of the subspecification generation procedure, and measure its effectiveness and running time. Finally, we conduct a user study to determine whether subspecifications are useful: we find that subspecifications greatly aid in understanding the global specification, in identifying alternative implementations, and in debugging faulty implementations. 

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.