DreamProver: AI Framework Evolves Transferable Lemma Libraries for Theorem Proving

DreamProver has been unveiled by researchers as an agentic framework that employs a wake-sleep program induction paradigm to identify reusable lemmas for formal theorem proving. Traditional methods either depend on static lemma libraries, which restrict flexibility, or generate highly specific intermediate lemmas for particular theorems, lacking broader applicability. DreamProver fills this void with its iterative two-stage approach. During the wake phase, it seeks to prove theorems from a training set using the existing lemma library while suggesting new candidate lemmas. In the sleep phase, it abstracts, refines, and consolidates these candidates to enhance and streamline the library. This alternating process allows DreamProver to develop a compact collection of high-level, transferable lemmas, significantly boosting performance in formal theorem proving tasks, as shown by experimental results.