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- """
- 实验:用 LLM + Dataset 构造 Lambda 演算原语(本地模拟版)
- 通过 subprocess 调用 claude CLI 逐个执行 LDS 测试。
- 每个测试将 dataset (few-shot examples) + 新输入组成 prompt,
- 然后让 LLM 输出结果,对比期望值。
- 使用方式:
- python run_experiment.py
- """
- import subprocess
- import json
- import sys
- import time
- from dataclasses import dataclass, field
- @dataclass
- class ExperimentResult:
- name: str
- tests: list[dict] = field(default_factory=list)
- def add(self, input_val: str, expected: str, actual: str):
- # 宽松匹配:去空格、去引号、大小写
- def normalize(s):
- return s.strip().strip("'\"").strip().lower()
- passed = normalize(actual) == normalize(expected)
- self.tests.append({
- "input": input_val,
- "expected": expected,
- "actual": actual,
- "passed": passed,
- })
- @property
- def passed_count(self):
- return sum(1 for t in self.tests if t["passed"])
- @property
- def total_count(self):
- return len(self.tests)
- def summary(self) -> str:
- lines = [
- f"\n{'='*60}",
- f"实验: {self.name}",
- f"通过: {self.passed_count}/{self.total_count}",
- f"{'='*60}",
- ]
- for t in self.tests:
- status = "✓" if t["passed"] else "✗"
- lines.append(
- f" {status} input={t['input']!r:40s} "
- f"expected={t['expected']!r:12s} actual={t['actual']!r}"
- )
- return "\n".join(lines)
- def call_llm(prompt: str, max_retries: int = 2) -> str:
- """调用 claude CLI 执行 LDS prompt"""
- for attempt in range(max_retries + 1):
- try:
- result = subprocess.run(
- ["claude", "-p", prompt, "--model", "sonnet"],
- capture_output=True,
- text=True,
- timeout=30,
- )
- if result.returncode == 0:
- return result.stdout.strip()
- else:
- if attempt < max_retries:
- time.sleep(1)
- continue
- return f"ERROR: {result.stderr.strip()}"
- except subprocess.TimeoutExpired:
- if attempt < max_retries:
- continue
- return "ERROR: timeout"
- except FileNotFoundError:
- return "ERROR: claude CLI not found"
- return "ERROR: max retries exceeded"
- def build_prompt(description: str, examples: list[tuple[str, str]], test_input: str) -> str:
- """构造 LDS prompt: system instruction + dataset + test input"""
- lines = [
- "You are a precise function executor. Given the examples below, "
- "learn the pattern and apply it to the new input. "
- "Output ONLY the result, nothing else. No explanation, no quotes, no extra text.",
- "",
- f"Function: {description}",
- "",
- "Examples:",
- ]
- for inp, out in examples:
- lines.append(f" Input: {inp}")
- lines.append(f" Output: {out}")
- lines.append("")
- lines.append(f"Input: {test_input}")
- lines.append("Output:")
- return "\n".join(lines)
- # ============================================================
- # 实验定义
- # ============================================================
- def experiment_succ() -> ExperimentResult:
- """实验 1: SUCC 后继函数 ≡ λn.λf.λx. f(n f x)"""
- result = ExperimentResult("SUCC (后继函数)")
- dataset = [
- ("0", "1"), ("1", "2"), ("2", "3"),
- ("5", "6"), ("9", "10"), ("13", "14"), ("99", "100"),
- ]
- tests = [3, 4, 7, 10, 15, 42, 127, 255]
- for n in tests:
- prompt = build_prompt(
- "Given a number n, output n+1 (the successor).",
- dataset, str(n)
- )
- actual = call_llm(prompt)
- result.add(str(n), str(n + 1), actual)
- return result
- def experiment_booleans() -> ExperimentResult:
- """实验 2: TRUE/FALSE ≡ λa.λb.a / λa.λb.b"""
- result = ExperimentResult("TRUE/FALSE (Church 布尔值)")
- true_dataset = [
- ("A='apple', B='banana'", "apple"),
- ("A='red', B='blue'", "red"),
- ("A='1', B='0'", "1"),
- ("A='yes', B='no'", "yes"),
- ("A='cat', B='dog'", "cat"),
- ]
- false_dataset = [
- ("A='apple', B='banana'", "banana"),
- ("A='red', B='blue'", "blue"),
- ("A='1', B='0'", "0"),
- ("A='yes', B='no'", "no"),
- ("A='cat', B='dog'", "dog"),
- ]
- test_pairs = [("sun", "moon"), ("hello", "world"), ("42", "0"), ("alpha", "omega")]
- for a, b in test_pairs:
- inp = f"A='{a}', B='{b}'"
- # TRUE
- prompt_t = build_prompt("Given two options A and B, always select A (the first one).", true_dataset, inp)
- actual_t = call_llm(prompt_t)
- result.add(f"TRUE({a},{b})", a, actual_t)
- # FALSE
- prompt_f = build_prompt("Given two options A and B, always select B (the second one).", false_dataset, inp)
- actual_f = call_llm(prompt_f)
- result.add(f"FALSE({a},{b})", b, actual_f)
- return result
- def experiment_logic() -> ExperimentResult:
- """实验 3: AND/OR/NOT"""
- result = ExperimentResult("AND/OR/NOT (逻辑运算)")
- and_ds = [("TRUE, TRUE", "TRUE"), ("TRUE, FALSE", "FALSE"),
- ("FALSE, TRUE", "FALSE"), ("FALSE, FALSE", "FALSE")]
- or_ds = [("TRUE, TRUE", "TRUE"), ("TRUE, FALSE", "TRUE"),
- ("FALSE, TRUE", "TRUE"), ("FALSE, FALSE", "FALSE")]
- not_ds = [("TRUE", "FALSE"), ("FALSE", "TRUE")]
- # AND
- for inp, exp in and_ds:
- prompt = build_prompt("Logical AND of two boolean values.", and_ds, inp)
- actual = call_llm(prompt)
- result.add(f"AND({inp})", exp, actual)
- # OR
- for inp, exp in or_ds:
- prompt = build_prompt("Logical OR of two boolean values.", or_ds, inp)
- actual = call_llm(prompt)
- result.add(f"OR({inp})", exp, actual)
- # NOT
- for inp, exp in not_ds:
- prompt = build_prompt("Logical NOT of a boolean value.", not_ds, inp)
- actual = call_llm(prompt)
- result.add(f"NOT({inp})", exp, actual)
- return result
- def experiment_if() -> ExperimentResult:
- """实验 4: IF-THEN-ELSE ≡ λcond.λthen.λelse. cond then else"""
- result = ExperimentResult("IF-THEN-ELSE (条件分支)")
- dataset = [
- ("condition=TRUE, then='yes', else='no'", "yes"),
- ("condition=FALSE, then='yes', else='no'", "no"),
- ("condition=TRUE, then='42', else='0'", "42"),
- ("condition=FALSE, then='42', else='0'", "0"),
- ("condition=TRUE, then='go', else='stop'", "go"),
- ("condition=FALSE, then='go', else='stop'", "stop"),
- ]
- tests = [
- ("condition=TRUE, then='accept', else='reject'", "accept"),
- ("condition=FALSE, then='accept', else='reject'", "reject"),
- ("condition=TRUE, then='100', else='-1'", "100"),
- ("condition=FALSE, then='100', else='-1'", "-1"),
- ("condition=TRUE, then='open', else='close'", "open"),
- ("condition=FALSE, then='open', else='close'", "close"),
- ]
- for inp, exp in tests:
- prompt = build_prompt(
- "IF-THEN-ELSE: If condition is TRUE, output the THEN value. If FALSE, output the ELSE value.",
- dataset, inp
- )
- actual = call_llm(prompt)
- result.add(inp, exp, actual)
- return result
- def experiment_pairs() -> ExperimentResult:
- """实验 5: PAIR/FST/SND"""
- result = ExperimentResult("PAIR/FST/SND (有序对)")
- pair_ds = [
- ("a=3, b=7", "(3, 7)"),
- ("a=hello, b=world", "(hello, world)"),
- ("a=0, b=1", "(0, 1)"),
- ]
- fst_ds = [
- ("(3, 7)", "3"), ("(hello, world)", "hello"),
- ("(0, 1)", "0"), ("(42, 99)", "42"),
- ]
- snd_ds = [
- ("(3, 7)", "7"), ("(hello, world)", "world"),
- ("(0, 1)", "1"), ("(42, 99)", "99"),
- ]
- # PAIR
- for inp, exp in [("a=10, b=20", "(10, 20)"), ("a=foo, b=bar", "(foo, bar)")]:
- prompt = build_prompt("Construct a pair from a and b.", pair_ds, inp)
- actual = call_llm(prompt)
- result.add(f"PAIR({inp})", exp, actual)
- # FST
- for inp, exp in [("(5, 8)", "5"), ("(alpha, beta)", "alpha"), ("(100, 200)", "100")]:
- prompt = build_prompt("Extract the first element of a pair.", fst_ds, inp)
- actual = call_llm(prompt)
- result.add(f"FST({inp})", exp, actual)
- # SND
- for inp, exp in [("(5, 8)", "8"), ("(alpha, beta)", "beta"), ("(100, 200)", "200")]:
- prompt = build_prompt("Extract the second element of a pair.", snd_ds, inp)
- actual = call_llm(prompt)
- result.add(f"SND({inp})", exp, actual)
- return result
- def experiment_composition() -> ExperimentResult:
- """实验 6: 函数组合 DOUBLE ∘ SUCC ≡ (g ∘ f)(x) = g(f(x))"""
- result = ExperimentResult("DOUBLE ∘ SUCC (函数组合)")
- succ_ds = [("0", "1"), ("1", "2"), ("2", "3"), ("5", "6"), ("9", "10")]
- double_ds = [("0", "0"), ("1", "2"), ("2", "4"), ("3", "6"), ("5", "10"), ("10", "20")]
- for n in [0, 1, 3, 5, 7, 10]:
- # Step 1: SUCC(n)
- p1 = build_prompt("Given a number n, output n+1.", succ_ds, str(n))
- succ_result = call_llm(p1)
- # Step 2: DOUBLE(SUCC(n))
- p2 = build_prompt("Given a number n, output 2*n.", double_ds, succ_result)
- double_result = call_llm(p2)
- expected = str(2 * (n + 1))
- result.add(f"DOUBLE(SUCC({n}))", expected, double_result)
- return result
- def experiment_factorial() -> ExperimentResult:
- """实验 7: FACTORIAL —— 递归通过 CoT 展开,等价于 Y 组合子"""
- result = ExperimentResult("FACTORIAL (递归/Y 组合子)")
- dataset = [
- ("0", "0! = 1\nResult: 1"),
- ("1", "1! = 1 × 0! = 1 × 1 = 1\nResult: 1"),
- ("3", "3! = 3 × 2!\n2! = 2 × 1!\n1! = 1 × 0!\n0! = 1\nSo: 1 × 1 × 2 × 3 = 6\nResult: 6"),
- ("5", "5! = 5 × 4!\n4! = 4 × 3!\n3! = 3 × 2!\n2! = 2 × 1!\n1! = 1 × 0!\n0! = 1\nSo: 1 × 1 × 2 × 3 × 4 × 5 = 120\nResult: 120"),
- ]
- import math
- for n in [2, 4, 6, 7, 8, 10]:
- prompt = build_prompt(
- "Compute n! (factorial) step by step. Show recursive expansion. End with 'Result: <number>'.",
- dataset, str(n)
- )
- actual_raw = call_llm(prompt)
- # 提取 Result 行
- actual = actual_raw
- for line in reversed(actual_raw.split("\n")):
- if "Result:" in line:
- actual = line.split("Result:")[-1].strip()
- break
- expected = str(math.factorial(n))
- result.add(f"{n}!", expected, actual)
- return result
- def experiment_church_numerals() -> ExperimentResult:
- """实验 8: Church 数 c_n ≡ λf.λx. f^n(x)"""
- result = ExperimentResult("CHURCH 数 (f^n(x))")
- dataset = [
- ("n=0, f='add1', x='0'", "0"),
- ("n=1, f='add1', x='0'", "1"),
- ("n=2, f='add1', x='0'", "2"),
- ("n=3, f='add1', x='0'", "3"),
- ("n=0, f='double', x='1'", "1"),
- ("n=1, f='double', x='1'", "2"),
- ("n=2, f='double', x='1'", "4"),
- ("n=3, f='double', x='1'", "8"),
- ("n=4, f='double', x='1'", "16"),
- ]
- # add1 tests
- for n in [4, 5, 7, 10]:
- prompt = build_prompt(
- "Apply function f to value x exactly n times. "
- "add1 adds 1 each time. double multiplies by 2 each time.",
- dataset, f"n={n}, f='add1', x='0'"
- )
- actual = call_llm(prompt)
- result.add(f"add1^{n}(0)", str(n), actual)
- # double tests: double^n(1) = 2^n
- for n in [5, 6, 7, 8]:
- prompt = build_prompt(
- "Apply function f to value x exactly n times. "
- "add1 adds 1 each time. double multiplies by 2 each time.",
- dataset, f"n={n}, f='double', x='1'"
- )
- actual = call_llm(prompt)
- result.add(f"double^{n}(1)", str(2**n), actual)
- return result
- # ============================================================
- # 主程序
- # ============================================================
- def main():
- print("=" * 60)
- print("LDS ≡ Lambda Calculus 实验验证")
- print("模式: 本地 Claude CLI 模拟")
- print("=" * 60)
- # 检查 claude CLI
- try:
- r = subprocess.run(["claude", "--version"], capture_output=True, text=True, timeout=5)
- print(f"Claude CLI: {r.stdout.strip()}")
- except Exception as e:
- print(f"错误: 无法找到 claude CLI: {e}")
- sys.exit(1)
- experiments = [
- ("1. 后继函数 SUCC", experiment_succ),
- ("2. Church 布尔值 TRUE/FALSE", experiment_booleans),
- ("3. 逻辑运算 AND/OR/NOT", experiment_logic),
- ("4. 条件分支 IF-THEN-ELSE", experiment_if),
- ("5. 有序对 PAIR/FST/SND", experiment_pairs),
- ("6. 函数组合 DOUBLE∘SUCC", experiment_composition),
- ("7. 递归/阶乘 (Y 组合子)", experiment_factorial),
- ("8. Church 数 f^n(x)", experiment_church_numerals),
- ]
- all_results = []
- for name, fn in experiments:
- print(f"\n>>> 运行实验 {name}...")
- r = fn()
- all_results.append(r)
- print(r.summary())
- # 汇总
- total = sum(r.total_count for r in all_results)
- passed = sum(r.passed_count for r in all_results)
- print("\n" + "=" * 60)
- print("汇总结果")
- print("=" * 60)
- for r in all_results:
- rate = r.passed_count / r.total_count * 100 if r.total_count else 0
- bar = "█" * int(rate / 5) + "░" * (20 - int(rate / 5))
- print(f" {r.name:40s} {r.passed_count:2d}/{r.total_count:2d} {bar} {rate:.0f}%")
- print(f"\n {'总计':40s} {passed:2d}/{total:2d} {passed/total*100:.1f}%")
- print("=" * 60)
- # 保存 JSON
- output = {
- "model": "claude-sonnet (via CLI)",
- "timestamp": time.strftime("%Y-%m-%d %H:%M:%S"),
- "experiments": [
- {
- "name": r.name,
- "passed": r.passed_count,
- "total": r.total_count,
- "tests": r.tests,
- }
- for r in all_results
- ],
- "total_passed": passed,
- "total_tests": total,
- }
- with open("experiment_results.json", "w", encoding="utf-8") as f:
- json.dump(output, f, ensure_ascii=False, indent=2)
- print("\n结果已保存到 experiment_results.json")
- if __name__ == "__main__":
- main()
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