Gradient Descent over Metagrammars for Syntax-Guided Synthesis

Abstract: The performance of a syntax-guided synthesis algorithm is highly dependent on the provision of a good syntactic template, or grammar. Provision of such a template is often left to the user to do manually, though in the absence of such a grammar, state-of-the-art solvers will provide their own default grammar, which is dependent on the signature of the target program to be sythesized. In this work, we speculate this default grammar could be improved upon substantially. We build sets of rules, or metagrammars, for constructing grammars, and perform a gradient descent over these metagrammars aiming to find a metagrammar which solves more benchmarks and on average faster. We show the resulting metagrammar enables CVC4 to solve 26% more benchmarks than the default grammar within a 300s time-out, and that metagrammars learnt from tens of benchmarks generalize to performance on 100s of benchmarks.