Synthesis through Unification

Abstract: Given a specification and a set of candidate programs (program space), the program synthesis problem is to find a candidate program that satisfies the specification. We present the synthesis through unification (STUN) approach, which is an extension of the counter-example guided inductive synthesis (CEGIS) approach. In CEGIS, the synthesizer maintains a subset S of inputs and a candidate program Prog that is correct for S. The synthesizer repeatedly checks if there exists a counter-example input c such that the execution of Prog is incorrect on c. If so, the synthesizer enlarges S to include c, and picks a program from the program space that is correct for the new set S. The STUN approach extends CEGIS with the idea that given a program Prog that is correct for a subset of inputs, the synthesizer can try to find a program Prog' that is correct for the rest of the inputs. If Prog and Prog' can be unified into a program in the program space, then a solution has been found. We present a generic synthesis procedure based on the STUN approach and specialize it for three different domains by providing the appropriate unification operators. We implemented these specializations in prototype tools, and we show that our tools often per- forms significantly better on standard benchmarks than a tool based on a pure CEGIS approach.