Recursive Program Synthesis from Sketches and Mixed-Quantifier Properties

We present a novel approach to the automatic synthesis of recursive programs from mixed-quantifier first-order logic properties. Our approach uses Skolemization to reduce the mixed-quantifier synthesis problem to a $\forall^*$-synthesis problem, synthesizing witness-generating functions for introduced Skolem symbols alongside the target program. We tackle $\forall^*$-synthesis using a sketching-based, enumerative, counterexample-guided approach. Our algorithm learns syntactic constraints from counterexamples to prune the candidate space and employs a prophylactic pruning technique to avoid enumerating invalid candidates altogether. We evaluate our technique on 42 benchmarks, demonstrating that both counterexample generalization and prophylactic pruning significantly improve performance.