# Experiment 5-2: Code Tools for Logic / 实验 5-2：用代码生成工具提升逻辑思考能力

> Companion lab for *AI Agents in Depth*, Chapter 5 — Knights & Knaves as CSP with `python-constraint`; pure reasoning vs code-assisted vs offline solver.  
> 《深入理解 AI Agent》第 5 章配套：骑士与无赖谜题转 CSP，对比纯思考 / 代码辅助 / 离线约束求解。

← [Chapter 5 index / 返回第 5 章目录](../README.md)

## Formal manuscript result (canonical)

The canonical run uses the pinned revision of
`K-and-K/perturbed-knights-and-knaves`, stratified across six perturbations and
2–8 people (84 paired tasks). Every code trajectory invoked
`python-constraint`, but observed accuracy was 39.3% for code assistance versus
75.0% for pure reasoning (p=2.27e-7 in the opposite direction). The campaign is
complete; the manuscript's >90% and significant-improvement hypothesis was not
observed. Evidence: [`validation/real_ark_doubao_flash_hf84_20260730.json`](validation/real_ark_doubao_flash_hf84_20260730.json).

正式活动固定 K&K 数据集版本，按六类扰动与 2–8 人规模分层抽取 84 道配对题。代码臂
每题都调用了 `python-constraint`，但实测准确率为 39.3%，低于纯思考的 75.0%
（p=2.27e-7，方向与预期相反）。因此下文离线求解器 100% 的表格只能证明确定性 CSP
机制正确，不能替代真实 LLM 对照或正文的 >90% 验收结论。

---

## English

### Overview

This lab evaluates whether an Agent can use **constraint-solving** code to support logical thinking. The same LLM gets a Code Interpreter preloaded with `python-constraint`, and turns Knights & Knaves (K&K) puzzles into formal **constraint satisfaction problems (CSP)**—variables (each islander is knight or knave), constraints (“knights tell truth, knaves lie”), then a solver search.

On a set of 12 K&K puzzles (2–5 people, each with a unique truth assignment), three modes are compared:

- **Pure thinking (`pure`)**: natural-language chain-of-thought only; answer directly.
- **Code-assisted (`code`)**: use `run_python` to write a constraint model and call the solver, then answer from the result.
- **Constraint solver (`solver`)**: **offline baseline**—solve structured statements with `python-constraint` only, no API/network. Deterministic; theoretically 100% correct; validates “translate puzzle → constraints → solve” (see real results below).

### Core idea: why code helps

The key modeling rule for K&K is one **biconditional (equivalence)** per resident X:

```
X is knight (True)  <=>  X's statement is true
```

i.e. `X == (semantic truth of that statement)`. Hand this to a deterministic solver that **enumerates** all Boolean assignments and logic cannot “slip”; pure thinking often fails on multi-person, counting (“exactly two knights”), or self-referential (“A and B are the same type”) puzzles when propagating truth values by hand.

### Files

| File | Role |
| --- | --- |
| `demo.py` | Main: pure / code / solver comparison; accuracy table |
| `csp_solver.py` | Offline CSP solver: structured statement DSL + `python-constraint` (shared by demo solver mode and `build_puzzles` checks) |
| `sandbox.py` | Minimal Code Interpreter: subprocess sandbox for model-generated Python (python-constraint preinstalled) |
| `puzzles.json` | 12 puzzles: stems + structured statements + unique solutions (LLM sees stems only) |
| `build_puzzles.py` | Generate/validate puzzles: solve with `python-constraint`, assert unique solution; export curated or random sets |
| `requirements.txt` | Dependencies (openai + python-constraint) |
| `env.example` | Env var sample |
| `last_run.json` | Full per-problem record after each run (including model-generated code) for review |

### Quick start

```bash
# From the repository root: use the shared Chapter 5 environment
uv sync --locked --python 3.12 --extra ch5

# Activate it before changing directories:
# macOS/Linux:
source .venv/bin/activate
# Windows PowerShell: .\.venv\Scripts\Activate.ps1
# Windows cmd: .venv\Scripts\activate.bat

# pip fallback when uv is not installed:
# python -m pip install -e ".[ch5]"

cd chapter5/code-for-logic

# Single-project compatibility path, still supported during migration:
# python -m pip install -r requirements.txt
```

#### 1) Offline solver baseline (no API key; recommended first)

```bash
python demo.py --mode solver          # offline solve all 12 with python-constraint
python demo.py --mode solver --min-people 4   # only puzzles with >=4 people
```

Fully offline and deterministic; demonstrates “puzzle → constraints → solve” at 100% accuracy.

#### 2) LLM comparison (needs `OPENAI_API_KEY` or `OPENROUTER_API_KEY`)

```bash
cp env.example .env        # then edit .env with OPENAI_API_KEY
# or: export OPENAI_API_KEY=your-openai-api-key

python demo.py             # default both: pure vs code, all 12
python demo.py --mode pure # pure baseline only
python demo.py --limit 4   # first 4 only (cheap smoke)
python demo.py --max-people 3        # only puzzles with <=3 people
python demo.py --model gpt-4o-mini   # model (default gpt-4o-mini)
python demo.py --puzzles my.json --output run.json   # custom data / output path
```

**OpenRouter fallback**: if `OPENAI_API_KEY` is unset but `OPENROUTER_API_KEY` is set, traffic goes through OpenRouter (`gpt-*` → `openai/*`). Default `gpt-4o-mini` works on direct OpenAI; OpenRouter is preferred when you switch `--model` to gpt-5.x models that need org verification and `OPENROUTER_API_KEY` is set.

Full flags: `python demo.py --help` (Chinese help text).

#### 3) Build / expand the puzzle set

```bash
python build_puzzles.py                     # export built-in 12 curated puzzles (default)
python build_puzzles.py --generate 20 --min-people 3 --max-people 5 --seed 7
python build_puzzles.py --generate 20 --output my.json
```

The random generator solves each candidate with `python-constraint` and keeps only unique-solution puzzles.

`sandbox.py` / `csp_solver.py` can also be run alone for self-tests:
`python sandbox.py`, `python csp_solver.py` each solve a minimal puzzle with python-constraint.

### Real results (1): offline solver (`--mode solver`, no API)

Actual output of `python demo.py --mode solver` (12 curated puzzles, offline, deterministic):

```
== 约束求解(solver，离线) ==
  [solver] kk01 (2人) ✓  解数=1  预测={'A': 'knight', 'B': 'knave'}
  [solver] kk05 (3人) ✓  解数=1  预测={'A': 'knave', 'B': 'knave', 'C': 'knight'}
  [solver] kk11 (5人) ✓  解数=1  预测={'A': 'knight', 'B': 'knight', 'C': 'knave', 'D': 'knave', 'E': 'knight'}
  ...（其余题略）
------------------------------------------------------------
准确率            100.0%
============================================================
约束求解   准确率: 100.0%  (12/12)
```

This path translates each structured statement into `python-constraint` and enumerates—12/12 correct. It proves determinism of “puzzle → constraints → solve”; if the LLM translates correctly, it gets the same 100%. Random puzzles from `build_puzzles.py --generate` also solve 100% and match the unique solutions recorded at generation time.

### Real results (2): LLM comparison (gpt-4o-mini, 12 puzzles)

```
准确率对比表
============================================================
题号      人数    纯思考       代码辅助
------------------------------------------------------------
kk01    2     ✓         ✓
kk02    2     ✓         ✓
kk03    2     ✓         ✓
kk04    3     ✓         ✓
kk05    3     ✗         ✓
kk06    3     ✗         ✓
kk07    3     ✗         ✓
kk08    4     ✗         ✓
kk09    4     ✗         ✓
kk10    4     ✓         ✓
kk11    5     ✗         ✓
kk12    5     ✓         ✓
------------------------------------------------------------
准确率             50.0%    100.0%
============================================================
纯思考    准确率:  50.0%  (6/12)
代码辅助   准确率: 100.0%  (12/12)
提升(代码辅助 - 纯思考): +50.0 个百分点
```

> A weaker `gpt-4o-mini` is used on purpose: pure thinking got **6/12 (50%)**, with errors concentrated on ≥3 people and counting/self-reference (kk05–kk09, kk11)—exactly where mental truth propagation fails; code-assisted maps each sentence to biconditionals and lets `python-constraint` enumerate for **12/12** and **+50 percentage points**. Correctness no longer depends on the model’s own reasoning strength. There is some run-to-run noise on individual items, but “pure ≪ code-assisted” is stable.

> **Model ↔ harness tradeoff**: stronger models need thinner harnesses; weaker models need more (e.g. offload logic to code/solvers). With weak `gpt-4o-mini` the contrast is visible; with strong reasoners like `gpt-5.6-luna`, pure thinking can also full-solve and code gains can go to 0. Code-assisted (and offline solver) turn correctness into something **deterministic and model-strength-independent**.

#### Example constraint code (model-generated, kk11, 5 people + count)

Stem: A says “B is a knight”; B says “C is a knave”; C says “D is a knight”; D says “E is a knave”;
E says “at least two of us five are knights”.

```python
from constraint import Problem

p = Problem()
for name in ['A', 'B', 'C', 'D', 'E']:
    p.addVariable(name, [True, False])   # True=knight (truth), False=knave (lie)

# Each sentence: X == (truth value of the claim)
p.addConstraint(lambda a, b: a == (b == True), ['A', 'B'])          # A:"B is knight"
p.addConstraint(lambda b, c: b == (c == False), ['B', 'C'])        # B:"C is knave"
p.addConstraint(lambda c, d: c == (d == True), ['C', 'D'])         # C:"D is knight"
p.addConstraint(lambda d, e: d == (e == False), ['D', 'E'])        # D:"E is knave"
p.addConstraint(lambda a, b, c, d, e: e == ((a + b + c + d + e) >= 2),
                ['A', 'B', 'C', 'D', 'E'])                          # E:"at least two knights"

for s in p.getSolutions():
    print({k: ('knight' if v else 'knave') for k, v in s.items()})
# Output: {'A': 'knight', 'B': 'knight', 'C': 'knave', 'D': 'knave', 'E': 'knight'}
```

The solver enumerates \(2^5=32\) assignments and returns the unique solution—the kind of chain pure thinking most often gets wrong.

### Notes

- **Cost**: default `gpt-4o-mini` (weaker model for contrast); 12 puzzles × two modes is cheap; override with `MODEL` / `--model`.
- **API key**: `OPENAI_API_KEY` or `OPENROUTER_API_KEY` from env / `.env`; `MODEL` to switch models.
- **Sandbox**: `sandbox.py` uses subprocess + timeout—teaching minimal sandbox; production should use containers/gVisor etc.
- **Puzzle reliability**: `build_puzzles.py` solves each puzzle (curated or random) with `python-constraint` and asserts unique solution before writing; extend via `CURATED` or `--generate`.

---

## 中文

### 概述

本实验评估 Agent 通过**约束求解**代码来辅助逻辑思考的能力：为同一个 LLM 配备一个预装
`python-constraint` 的 Code Interpreter，让它把「骑士与无赖」(Knights & Knaves) 逻辑谜题
转化为形式化的**约束满足问题(CSP)**——识别变量(每个岛民是骑士还是无赖)、定义约束
(“骑士说真话、无赖说假话”)，再调用求解器搜索满足所有约束的解。

我们用一组 12 道 K&K 谜题(2~5 人，均带唯一真值解)对比三种模式：

- **纯思考(pure)**：LLM 只用自然语言链式推理，直接给答案；
- **代码辅助(code)**：LLM 用 `run_python` 工具写约束模型并调求解器，再据结果作答；
- **约束求解(solver)**：**离线基线**，直接用 `python-constraint` 求解结构化陈述，
  不需要任何 API/网络——它是确定性求解器路径本身，理论上 100% 正确，用来验证
  「把谜题翻译成约束程序并求解」这一核心论点(见下方真实运行结果)。

### 核心思想：为什么代码辅助更强

K&K 谜题的关键建模规则只有一条——对每位居民 X 加一条**双条件(等价)约束**：

```
X 是骑士(True)  <=>  X 说的那句话为真
```

即 `X == (该陈述的语义真值)`。把它交给确定性求解器**穷举**所有布尔组合，逻辑上不会出错；
而纯思考在多人、含计数(“恰好两个骑士”)或自指(“我和 B 同类”)的谜题上，很容易在心算
真值传播时出错。

### 文件说明

| 文件 | 作用 |
| --- | --- |
| `demo.py` | 主程序：跑 纯思考/代码辅助/约束求解 的对照实验，打印准确率对比表 |
| `csp_solver.py` | 离线约束求解器：结构化陈述 DSL + `python-constraint` 求解(供 demo 的 solver 模式与 build_puzzles 校验共用) |
| `sandbox.py` | 极简 Code Interpreter：子进程沙箱执行模型生成的 Python(预装 python-constraint) |
| `puzzles.json` | 12 道谜题的题面 + 结构化陈述 + 唯一真值解(给 LLM 的只有题面) |
| `build_puzzles.py` | 生成/校验谜题：用 `python-constraint` 求解并断言每题“解唯一”，可导出精选题或随机生成 |
| `requirements.txt` | 依赖(openai + python-constraint) |
| `env.example` | 环境变量样例 |
| `last_run.json` | 每次运行后自动保存的逐题完整记录(含模型生成的代码)，便于复盘 |

### 快速开始

```bash
# 在仓库根目录使用统一的第 5 章环境
uv sync --locked --python 3.12 --extra ch5

# 切换目录前先激活环境：
# macOS/Linux：
source .venv/bin/activate
# Windows PowerShell：.\.venv\Scripts\Activate.ps1
# Windows cmd：.venv\Scripts\activate.bat

# 未安装 uv 时可用 pip 兜底：
# python -m pip install -e ".[ch5]"

cd chapter5/code-for-logic

# 迁移期间仍支持单项目兼容路径：
# python -m pip install -r requirements.txt
```

#### 1) 离线约束求解基线（不需要 API Key，推荐先跑）

```bash
python demo.py --mode solver          # 用 python-constraint 离线求解全部 12 题
python demo.py --mode solver --min-people 4   # 只跑 >=4 人的难题
```

这条路径完全离线、确定性，直接演示「谜题→约束程序→求解」的核心论点，准确率 100%。

#### 2) LLM 对照实验（需要 OPENAI_API_KEY 或 OPENROUTER_API_KEY）

```bash
cp env.example .env        # 然后编辑 .env 填入 OPENAI_API_KEY
# 或直接 export OPENAI_API_KEY=your-openai-api-key

python demo.py             # 默认 both：纯思考 vs 代码辅助，全部 12 题
python demo.py --mode pure # 只跑纯思考基线
python demo.py --limit 4   # 只跑前 4 题(省钱冒烟测试)
python demo.py --max-people 3        # 只跑 <=3 人的谜题(按难度筛选)
python demo.py --model gpt-4o-mini   # 指定模型(默认 gpt-4o-mini)
python demo.py --puzzles my.json --output run.json   # 换数据集/输出路径
```

**通用 OpenRouter 兜底**：未配置 `OPENAI_API_KEY` 时，只要设置了 `OPENROUTER_API_KEY`
即自动改走 OpenRouter（`gpt-*` → `openai/*`）。默认模型 `gpt-4o-mini` 是普通 gpt id，可
直连 OpenAI；仅当把 `--model` 换成 `gpt-5.x` 这类需组织实名认证的模型、且设置了
`OPENROUTER_API_KEY` 时，才会优先走 OpenRouter。

完整参数见 `python demo.py --help`（中文说明）。

#### 3) 生成/扩充谜题数据集

```bash
python build_puzzles.py                     # 导出内置 12 道精选题(默认)
python build_puzzles.py --generate 20 --min-people 3 --max-people 5 --seed 7
python build_puzzles.py --generate 20 --output my.json
```

随机生成器会用 `python-constraint` 求解每个候选谜题，只保留「解唯一」的题目。

`sandbox.py` / `csp_solver.py` 也可单独运行做自测：
`python sandbox.py`、`python csp_solver.py` 都会用 python-constraint 求解一道最简谜题。

### 真实运行结果（一）：离线约束求解基线（`--mode solver`，无需 API）

`python demo.py --mode solver` 的真实输出（12 道精选题，完全离线、确定性）：

```
== 约束求解(solver，离线) ==
  [solver] kk01 (2人) ✓  解数=1  预测={'A': 'knight', 'B': 'knave'}
  [solver] kk05 (3人) ✓  解数=1  预测={'A': 'knave', 'B': 'knave', 'C': 'knight'}
  [solver] kk11 (5人) ✓  解数=1  预测={'A': 'knight', 'B': 'knight', 'C': 'knave', 'D': 'knave', 'E': 'knight'}
  ...（其余题略）
------------------------------------------------------------
准确率            100.0%
============================================================
约束求解   准确率: 100.0%  (12/12)
```

这条路径把每题的结构化陈述翻译成 `python-constraint` 约束并穷举求解，12/12 全对——
它直接证明了「谜题→约束程序→求解」的确定性；LLM 只要把谜题正确翻译成同样的约束，
就能拿到同样 100% 的结果（下节）。随机生成的谜题（`build_puzzles.py --generate`）经
solver 复核同样 100% 解出且与生成时的唯一解一致。

### 真实运行结果（二）：LLM 对照实验（gpt-4o-mini，12 题）

```
准确率对比表
============================================================
题号      人数    纯思考       代码辅助
------------------------------------------------------------
kk01    2     ✓         ✓
kk02    2     ✓         ✓
kk03    2     ✓         ✓
kk04    3     ✓         ✓
kk05    3     ✗         ✓
kk06    3     ✗         ✓
kk07    3     ✗         ✓
kk08    4     ✗         ✓
kk09    4     ✗         ✓
kk10    4     ✓         ✓
kk11    5     ✗         ✓
kk12    5     ✓         ✓
------------------------------------------------------------
准确率             50.0%    100.0%
============================================================
纯思考    准确率:  50.0%  (6/12)
代码辅助   准确率: 100.0%  (12/12)
提升(代码辅助 - 纯思考): +50.0 个百分点
```

> 说明：这里刻意选用能力较弱的 `gpt-4o-mini` 来暴露对照——纯思考只做对了 **6/12
> (50%)**，且错误集中在 3 人及以上、含计数/自指的谜题上（kk05~kk09、kk11），正是心算
> 真值传播最容易出错的题型；而代码辅助把每句话翻译成双条件约束、交给 `python-constraint`
> 穷举求解，**12/12 全对**，一举把准确率拉满，净提升 **+50 个百分点**。这正是本实验想
> 说明的核心：把逻辑外包给确定性求解器，正确性不再依赖模型自己的推理强弱。`gpt-4o-mini`
> 有一定随机性，多次运行个别题目可能有小幅波动，但“纯思考明显低于代码辅助”的整体格局稳定。

> **模型与脚手架（harness）是此消彼长的关系**：模型足够强时，脚手架可以更薄——模型自己
> 就能算对；模型不够强时，就需要在脚手架里做更多事（如把逻辑交给代码/求解器）来兜住
> 正确性。本实验刻意用较弱的 `gpt-4o-mini`，正是为了让这一对照可见——换成 `gpt-5.6-luna`
> 这类强推理模型，纯思考也能全解，代码增益会收敛为 0。换句话说，代码辅助（乃至离线
> solver）真正的价值，是把正确性变成**确定性、与模型强弱无关**：对更弱的模型或更大/更难
> 的谜题，纯思考会随人数增加而掉分，而“翻译成约束程序 + 求解器穷举”的路径始终稳定给出正确解。

#### 一道谜题的约束建模代码（模型自动生成，kk11，5 人链式+计数）

题面：A 说“B 是骑士”；B 说“C 是无赖”；C 说“D 是骑士”；D 说“E 是无赖”；
E 说“我们五人当中至少有两个骑士”。

```python
from constraint import Problem

p = Problem()
for name in ['A', 'B', 'C', 'D', 'E']:
    p.addVariable(name, [True, False])   # True=骑士(说真话), False=无赖(说假话)

# 每句话都写成「X == (那句话的真值)」的双条件约束
p.addConstraint(lambda a, b: a == (b == True), ['A', 'B'])          # A:"B 是骑士"
p.addConstraint(lambda b, c: b == (c == False), ['B', 'C'])        # B:"C 是无赖"
p.addConstraint(lambda c, d: c == (d == True), ['C', 'D'])         # C:"D 是骑士"
p.addConstraint(lambda d, e: d == (e == False), ['D', 'E'])        # D:"E 是无赖"
p.addConstraint(lambda a, b, c, d, e: e == ((a + b + c + d + e) >= 2),
                ['A', 'B', 'C', 'D', 'E'])                          # E:"至少两个骑士"

for s in p.getSolutions():
    print({k: ('knight' if v else 'knave') for k, v in s.items()})
# 输出: {'A': 'knight', 'B': 'knight', 'C': 'knave', 'D': 'knave', 'E': 'knight'}
```

求解器直接穷举 2^5=32 种组合，返回满足全部约束的唯一解——这正是纯思考在链式真值
传播中最容易算错的题型。

### 注意事项

- **成本**：默认 `gpt-4o-mini`（刻意选用较弱模型以显现对照，见上文），跑完 12 题两种模式的开销很小；用 `MODEL`/`--model` 可换更便宜或更强的模型。
- **API Key**：从环境变量或 `.env` 读 `OPENAI_API_KEY`（或 `OPENROUTER_API_KEY` 兜底）；用 `MODEL` 可换模型。
- **沙箱**：`sandbox.py` 用子进程 + 超时执行代码，属教学用极简沙箱；生产环境应换成
  容器/gVisor 等更强隔离。
- **谜题可靠性**：`build_puzzles.py` 用 `python-constraint` 求解每题(内置精选题或随机生成)，
  断言“解唯一”后才写出，确保真值解无歧义；想自己加题就改 `CURATED` 或用 `--generate`。

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## Notes / 说明

- Run `--mode solver` first for a free offline baseline. / 建议先跑 `--mode solver` 离线基线。
- Commands, code, paths, and env vars are identical in both language sections. / 命令、代码、路径与环境变量在中英文两侧保持一致。