We develop an approach to estimate the probability that a program sampled froma large language model is correct. Given a natural language description of a programming problem, our method samples both candidate programs as well as candidate predicates specifying how the program should behave. This allows learninga model that forms a well-calibrated probabilistic prediction of program correctness. Our system also infers the which predicates are useful to explain the behavior of the generated code, and humans preferred these in a human study over rawlanguage model outputs. Our method is simple, easy to implement, and maintainsstate of the art generation accuracy results.