Combining Textual and Structural Information for Premise Selection in Lean

Abstract: Premise selection is a key bottleneck for scaling theorem proving in large formal libraries. Yet existing language-based methods often treat premises in isolation, ignoring the web of dependencies that connects them. We present a graph-augmented approach that combines dense text embeddings of Lean formalizations with graph neural networks over a heterogeneous dependency graph capturing both state--premise and premise--premise relations. On the LeanDojo Benchmark, our method outperforms the ReProver language-based baseline by over 25% across standard retrieval metrics. These results demonstrate the power of relational information for more effective premise selection.