{ "schema_version": 1, "id": "evt-2018-tactictoe", "slug": "tactictoe-hol4-tactic-learning", "title": { "en": "TacticToe learns tactic-level proof search from human HOL4 proofs", "zh-CN": "TacticToe 从人工 HOL4 证明中学习 tactic 级证明搜索" }, "dates": { "event": "2017-05-04", "first_public_claim": "2017-05-04", "paper_release": "2017-05-04", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-15", "last_updated": "2026-09-15" }, "event_types": [ "system" ], "significance": { "tier": "H2", "rationale": { "en": "TacticToe was an important early proof-assistant-native learning system that used recorded human HOL4 proofs to guide tactic-level proof search directly inside a mature interactive theorem prover. The initial LPAR-21 publication combined learned tactic and premise selection with modified A* search; an expanded 2018 study developed the same system further with Monte Carlo tree search. Together the work established a line later continued by reinforcement-learning systems such as TacticZero.", "zh-CN": "TacticToe 是较早具有代表性的证明助手原生学习系统之一，利用既有人工 HOL4 证明，在成熟交互式定理证明器内部直接引导 tactic 级证明搜索。LPAR-21 的初始版本将学习式 tactic / premise selection 与改进 A* 搜索结合，2018 年扩展研究又进一步以蒙特卡洛树搜索发展同一系统；这一路线后来由 TacticZero 等强化学习系统继续推进。" } }, "mathematical_novelty": { "type": "tooling_only" }, "interfaces": [ "formal", "symbolic" ], "claim": { "en": "Thibault Gauthier, Cezary Kaliszyk and Josef Urban introduced TacticToe in the LPAR-21 proceedings published on 4 May 2017. The system learned tactic and premise choices from previous HOL4 proofs and used modified A* search to explore tactic-level proof paths, re-proving 39% of 7,902 HOL4 theorems within five seconds in the reported evaluation. A later expanded study published in 2018 replaced the search with Monte Carlo tree search and reported stronger results on the HOL4 standard library.", "zh-CN": "Thibault Gauthier、Cezary Kaliszyk 与 Josef Urban 在 2017 年 5 月 4 日发布的 LPAR-21 proceedings 中提出 TacticToe。系统从既有 HOL4 证明中学习 tactic 与前提选择，并使用改进 A* 搜索探索 tactic 级证明路径；论文报告在五秒限制下重新证明了 7,902 个 HOL4 定理中的 39%。2018 年发布的扩展研究进一步把搜索机制发展为蒙特卡洛树搜索，并在 HOL4 标准库上报告了更强结果。" }, "summary": { "en": "TacticToe records tactic-level proof information from HOL4, learns which proof actions are promising in a new goal state, and searches over complete tactic sequences directly in higher-order logic rather than translating every problem to first-order logic. The 2017 system used a modified A*-style search with tactic prediction and small-scale hammering; the later expanded implementation developed the search machinery further and remains available in the HOL4 repository.", "zh-CN": "TacticToe 从 HOL4 中记录 tactic 级证明信息，学习在新目标状态下哪些证明动作更有希望，并直接在高阶逻辑环境中搜索完整 tactic 序列，而不是把每个问题都翻译到一阶逻辑。2017 年系统采用改进 A* 风格搜索并结合 tactic prediction 与小规模 hammering；后续扩展实现进一步发展搜索机制，相关代码至今仍可在 HOL4 仓库中检查。" }, "why_it_matters": { "en": "The work demonstrated that machine learning could guide proof-assistant-native tactic search rather than only premise filtering for an external automated prover. This combination of learned action prediction, search and kernel-checked proof construction became a recurring design pattern in later neural interactive theorem proving.", "zh-CN": "该工作展示了机器学习可以直接引导证明助手原生的 tactic 搜索，而不仅仅为外部自动证明器筛选前提。“学习式动作预测 + 搜索 + 内核检查证明”的组合后来成为神经交互式定理证明中反复出现的设计范式。" }, "ai_role": { "level": "ai_primary_human_verified", "description": { "en": "Learned predictors ranked tactics and supporting premises while the search algorithm explored proof paths; successful proof scripts were constructed and checked inside HOL4.", "zh-CN": "学习式预测器负责排序 tactics 与支持前提，搜索算法负责探索证明路径；成功的证明脚本最终在 HOL4 内构造并接受检查。" } }, "human_contribution": { "description": { "en": "Researchers designed the proof-trace recording, learned predictors, tactic-level search procedure, HOL4 integration and evaluation protocol, while the learning signal came from existing human-written HOL4 proofs.", "zh-CN": "研究者设计证明轨迹记录、学习式预测器、tactic 级搜索机制、HOL4 集成与评测协议；学习信号来自既有人工编写的 HOL4 证明。" } }, "systems": [ "tactictoe", "hol4" ], "organizations": [], "people": [ "thibault-gauthier", "cezary-kaliszyk", "josef-urban", "ramana-kumar", "michael-norrish" ], "problems": [ "hol4-theorem-proving" ], "methods": [ "tactic-prediction", "premise-selection", "a-star-search", "monte-carlo-tree-search", "proof-search" ], "verification": { "evidence_level": "E3", "status": "paper_released", "formal_assurance": "machine_checked", "history": [ { "date": "2017-05-04", "status": "paper_released", "evidence_level": "E2", "note": { "en": "The LPAR-21 proceedings establish the initial public TacticToe system, its learned tactic-level proof search and the reported HOL4 evaluation. Machine checking refers to proof scripts accepted by HOL4 and does not imply independent reproduction of the reported success rate.", "zh-CN": "LPAR-21 proceedings 确认了首次公开的 TacticToe 系统、其学习式 tactic 级证明搜索以及论文报告的 HOL4 评测。machine_checked 仅指证明脚本通过 HOL4 检查，并不表示论文报告的成功率已获得独立复现。" } }, { "date": "2018-04-02", "status": "paper_released", "evidence_level": "E2", "note": { "en": "The expanded 2018 research record documents the later Monte Carlo tree-search version and stronger HOL4 standard-library evaluation without changing the identity of the underlying TacticToe milestone.", "zh-CN": "2018 年扩展研究记录描述了后续蒙特卡洛树搜索版本及更强的 HOL4 标准库评测，但并未构成另一个独立的 TacticToe 历史事件。" } }, { "date": "2026-09-15", "status": "paper_released", "evidence_level": "E3", "note": { "en": "The maintained public HOL4 repository contains the TacticToe implementation, recording workflow, evaluation support and usage instructions. E3 denotes inspectable artifacts rather than independent verification of every experimental claim.", "zh-CN": "持续维护的 HOL4 公开仓库包含 TacticToe 实现、证明记录流程、评测支持与使用说明。E3 表示存在可直接检查的 artifacts，而非对全部实验结论的独立验证。" } } ] }, "sources": [ { "id": "easychair-tactictoe-lpar2017", "tier": "S1", "type": "paper", "title": "TacticToe: Learning to Reason with HOL4 Tactics — LPAR-21", "url": "https://easychair.org/publications/paper/WsM", "primary": true, "published_date": "2017-05-04", "accessed_at": "2026-09-15" }, { "id": "arxiv-tactictoe-1804.00596", "tier": "S1", "type": "paper", "title": "TacticToe: Learning to Prove with Tactics", "url": "https://arxiv.org/abs/1804.00596", "primary": true, "published_date": "2018-04-02", "accessed_at": "2026-09-15" }, { "id": "github-hol4-tactictoe", "tier": "S1", "type": "repository", "title": "HOL4 TacticToe implementation", "url": "https://github.com/HOL-Theorem-Prover/HOL/tree/develop/src/tactictoe", "primary": true, "published_date": null, "accessed_at": "2026-09-15" } ], "artifacts": [ { "id": "tactictoe-hol4-code", "kind": "code", "title": "TacticToe implementation in the HOL4 repository", "url": "https://github.com/HOL-Theorem-Prover/HOL/tree/develop/src/tactictoe" } ], "relationships": { "predecessors": [], "successors": [ "evt-2021-tacticzero" ], "related": [ "evt-2018-rl-theorem-proving" ] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "tactictoe", "hol4", "theorem-proving", "tactic-learning", "premise-selection", "proof-search", "machine-learning" ], "editorial": { "created_at": "2026-09-15", "last_reviewed": "2026-09-15", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [ { "date": "2026-09-15", "summary": { "en": "Corrected the canonical event date from 2018-04-02 to 2017-05-04 after locating the LPAR-21 proceedings publication of the initial TacticToe system, and revised the record to distinguish the 2017 A*-guided version from the expanded 2018 Monte Carlo tree-search study while preserving the stable Event ID.", "zh-CN": "在确认 LPAR-21 proceedings 已于 2017-05-04 公开初始 TacticToe 系统后，将 canonical event date 从 2018-04-02 纠正为 2017-05-04，并区分 2017 年 A* 引导版本与 2018 年蒙特卡洛树搜索扩展研究，同时保留稳定 Event ID。" }, "source_ids": [ "easychair-tactictoe-lpar2017", "arxiv-tactictoe-1804.00596" ] } ] }