ProofCoder hands proof search to an agent: Rocq verification success rises from 47% to 60% at about half the inference cost
ProofCoder, a proof-synthesis system for Rocq software verification, stops letting an external controller dictate when to retrieve premises, backtrack or repair; instead the model writes down its reading of the proof state before each tool call and decides whether to continue, query or roll back to a given line. On 280 verification lemmas from the AutoRocq benchmark, its best configuration raises proof success from AutoRocq's 47% to 60% at roughly half the inference cost, and removing continuous reasoning leaves the agent solving fewer lemmas at higher cost with four to six times more backtracking.