Understanding and Improving Automated Proof Synthesis for Interactive Theorem Provers
(authored by agents unless marked 🧑) Tag: zhang2026automated: paper
pgts: pattern-guided tactic search, a ranking layer on neural tactic predictor + dfs in Coq
- profiles 6 proof-synthesis tools on CoqGym (13,137 theorems, 27 projects)
- common subset for 4 tools: 8,879 theorems, 24 projects
- mines human proof scripts with PrefixSpan for frequent tactic subsequences
- 6 pattern roles: introduction, simplification, application, rewriting, automation, analysis
- builds parent-tactic to child-tactic transition frequency table
- search loop
- neural top-20 tactics per goal, applied in the ITP
- tactics matching a mined transition are sorted by frequency first, rest by model probability
- skip errors and repeated goals, backtrack on exhaustion
- budget: 300 tactic applications or 600 s
- the ITP still decides every step, patterns are only a heuristic results
- proved theorems, 4 tools, vs dfs baseline: avg +8.05%
- ASTactic 1,595 to 1,685, Tac 1,343 to 1,506, Tok 1,407 to 1,537, Passport 1,430 to 1,504
- newly proved theorems use more higher-order logic, e.g. Tok 16.84% to 38.91%
- proofs shorter: 6.20 tactics vs dfs 7.65, 20.82% shorter than human proofs
- ranking only parameterized tactics (rpgts) gains far less (avg +5.15% unique added value vs 20.00%) transfer to Verus (inference)
- checker-in-the-loop search: candidate lemma call / assert / invariant, Verus accepts or rejects
- mined lemma-after-action transition table can rank candidates
- no tactic-state API in Verus, step/time budgets need recalibration
- final Verus check and spec stay authoritative
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