{
  "schema_version": 1,
  "id": "evt-2023-copra",
  "slug": "copra-in-context-formal-proof-agent",
  "title": {
    "en": "COPRA turns a general LLM into a stateful formal proof-search agent",
    "zh-CN": "COPRA 将通用大模型转化为有状态的形式证明搜索 Agent"
  },
  "dates": {
    "event": "2023-10-06",
    "first_public_claim": "2023-10-06",
    "paper_release": "2023-10-06",
    "artifact_release": null,
    "independently_verified": null,
    "added_to_chronicle": "2026-09-10",
    "last_updated": "2026-09-10"
  },
  "event_types": [
    "system",
    "formalization",
    "proof"
  ],
  "significance": {
    "tier": "H2",
    "rationale": {
      "en": "COPRA was an early explicit agentic theorem-proving design in which a general-purpose LLM repeatedly acted inside Lean or Coq, consumed proof-assistant feedback and backtracked through a maintained search state rather than answering in one shot.",
      "zh-CN": "COPRA 是较早明确采用 Agent 结构的定理证明系统之一：通用大模型反复在 Lean 或 Coq 中行动，读取证明助手反馈并维护可回溯的搜索状态，而不是一次性生成答案。"
    }
  },
  "mathematical_novelty": {
    "type": "benchmark_result"
  },
  "interfaces": [
    "formal",
    "symbolic",
    "hybrid"
  ],
  "claim": {
    "en": "COPRA used GPT-4 in a stateful backtracking loop with proof-environment feedback and retrieval, outperforming few-shot GPT-4 and reporting competitive results against finetuned provers on Lean miniF2F while also operating on Coq tasks.",
    "zh-CN": "COPRA 将 GPT-4 置于带证明环境反馈、检索和回溯机制的有状态循环中；论文报告其明显优于 few-shot GPT-4，并在 Lean miniF2F 上与微调证明器竞争，同时还能处理 Coq 任务。"
  },
  "summary": {
    "en": "At each step the agent proposed a tactic, executed it in the proof assistant, incorporated errors or new goals into the next prompt and maintained a search history for backtracking. The architecture showed how a frontier general model could be wrapped in a proof-oriented agent harness without task-specific finetuning.",
    "zh-CN": "Agent 在每一步提出战术、在证明助手中执行，将错误或新的目标写回下一轮提示，并维护搜索历史以支持回溯。该架构展示了无需针对任务专门微调，也能把前沿通用模型封装为证明导向 Agent。"
  },
  "why_it_matters": {
    "en": "COPRA made the proof assistant an interactive environment for an LLM agent, anticipating the generate-execute-observe-revise loop that later became central to formal mathematical agents.",
    "zh-CN": "COPRA 把证明助手变成 LLM Agent 的交互环境，提前体现了后来形式数学 Agent 中核心的“生成—执行—观察—修订”循环。"
  },
  "ai_role": {
    "level": "ai_primary_human_verified",
    "description": {
      "en": "GPT-4 proposed tactics and navigated the proof search, while Lean or Coq checked each accepted proof action mechanically.",
      "zh-CN": "GPT-4 提出战术并推进证明搜索，Lean 或 Coq 对每个被接受的证明动作进行机械检查。"
    }
  },
  "human_contribution": {
    "description": {
      "en": "Researchers designed the agent state, retrieval, backtracking and prompting protocol, selected benchmarks and built the interfaces to the proof assistants.",
      "zh-CN": "研究者设计 Agent 状态、检索、回溯与提示协议，选择基准并构建与证明助手之间的接口。"
    }
  },
  "systems": [
    "copra",
    "gpt-4",
    "lean",
    "coq"
  ],
  "organizations": [
    "university-of-texas-at-austin"
  ],
  "people": [
    "amitayush-thakur",
    "george-tsoukalas",
    "yeming-wen",
    "jimmy-xin",
    "swarat-chaudhuri"
  ],
  "problems": [
    "minif2f",
    "compcert"
  ],
  "methods": [
    "agentic-proof-search",
    "in-context-learning",
    "backtracking",
    "retrieval",
    "proof-assistant-feedback"
  ],
  "verification": {
    "evidence_level": "E3",
    "status": "paper_released",
    "formal_assurance": "artifact_available",
    "history": [
      {
        "date": "2023-10-06",
        "status": "paper_released",
        "evidence_level": "E2",
        "note": {
          "en": "The authors released the paper describing the agent and its Lean and Coq evaluations.",
          "zh-CN": "作者公开论文，说明 Agent 设计以及 Lean 与 Coq 评测。"
        }
      },
      {
        "date": "2023-10-06",
        "status": "paper_released",
        "evidence_level": "E3",
        "note": {
          "en": "Code and experiment infrastructure were made available in the public COPRA repository.",
          "zh-CN": "代码与实验基础设施通过公开 COPRA 仓库提供。"
        }
      }
    ]
  },
  "sources": [
    {
      "id": "arxiv-copra-2310.04353",
      "tier": "S1",
      "type": "paper",
      "title": "An In-Context Learning Agent for Formal Theorem-Proving",
      "url": "https://arxiv.org/abs/2310.04353",
      "primary": true,
      "published_date": "2023-10-06",
      "accessed_at": "2026-09-10"
    },
    {
      "id": "github-trishullab-copra",
      "tier": "S1",
      "type": "repository",
      "title": "COPRA repository",
      "url": "https://github.com/trishullab/copra",
      "primary": true,
      "published_date": null,
      "accessed_at": "2026-09-10"
    }
  ],
  "artifacts": [
    {
      "id": "copra-repository",
      "kind": "code",
      "title": "COPRA formal theorem-proving agent",
      "url": "https://github.com/trishullab/copra"
    }
  ],
  "relationships": {
    "predecessors": [
      "evt-2020-gpt-f",
      "evt-2021-minif2f"
    ],
    "successors": [
      "evt-2024-deepseek-prover-v1-5",
      "evt-2026-alphaproof-nexus"
    ],
    "related": [
      "evt-2023-leandojo"
    ]
  },
  "timeline": {
    "featured": true,
    "significance": "primary"
  },
  "tags": [
    "agent",
    "theorem-proving",
    "lean",
    "coq",
    "gpt-4",
    "proof-feedback",
    "backtracking"
  ],
  "editorial": {
    "created_at": "2026-09-10",
    "last_reviewed": "2026-09-11",
    "reviewers": [
      "Charlie-Wang-03"
    ]
  },
  "corrections": []
}