L2S: A Framework for Synthesizing the Most Probable Program under a Specification

Abstract

In many scenarios, we need to find the most likely program that meets a specification under a local context, where the local context can be an incomplete program, a partial specification, natural language description, and so on. We call such a problem program estimation. In this article, we propose a framework, LingLong Synthesis Framework (L2S), to address this problem. Compared with existing work, our work is novel in the following aspects. (1) We propose a theory of expansion rules to describe how to decompose a program into choices. (2) We propose an approach based on abstract interpretation to efficiently prune off the program sub-space that does not satisfy the specification. (3) We prove that the probability of a program is the product of the probabilities of choosing expansion rules, regardless of the choosing order. (4) We reduce the program estimation problem to a pathfinding problem, enabling existing pathfinding algorithms to solve this problem. L2S has been applied to program generation and program repair. In this article, we report our instantiation of this framework for synthesizing conditional expressions (L2S-Cond) and repairing conditional statements (L2S-Hanabi). The experiments on L2S-Cond show that each option enabled by L2S, including the expansion rules, the pruning technique, and the use of different pathfinding algorithms, plays a major role in the performance of the approach. The default configuration of L2S-Cond correctly predicts nearly 60% of the conditional expressions in the top 5 candidates. Moreover, we evaluate L2S-Hanabi on 272 bugs from two real-world Java defects benchmarks, namely Defects4J and Bugs.jar. L2S-Hanabi correctly fixes 32 bugs with a high precision of 84%. In terms of repairing conditional statement bugs, L2S-Hanabi significantly outperforms all existing approaches in both precision and recall.