Recursive Program Synthesis

Input-output examples are a simple and accessible way of describing program behaviour. Program synthesis from input-output examples has the potential of extending the range of computational tasks achievable by end-users who have no programming knowledge, but can articulate their desired computations by describing input-output behaviour. In this paper, we present Escher, a generic and efficient algorithm that interacts with the user via input-output examples, and synthesizes recursive programs implementing intended behaviour. Escher is parameterized by the components (instructions) that can be used in the program, thus providing a generic synthesis algorithm that can be instantiated to suit different domains. To search through the space of programs, Escher adopts a novel search strategy that utilizes special data structures for inferring conditionals and synthesizing recursive procedures. Our experimental evaluation of Escher demonstrates its ability to efficiently synthesize a wide range of programs, manipulating integers, lists, and trees. Moreover, we show that Escher outperforms a state-ofthe-art SAT-based synthesis tool from the literature.