Spark-Prover-X1-7B开源大模型：高效逻辑推理与验证的技术突破

# 安装必要的依赖
# pip install spark-prover

from spark_prover import SparkProverX1

# 初始化模型
model = SparkProverX1.from_pretrained('spark-prover-x1-7b')

# 基本定理证明示例
lean_code = """
import Mathlib.Data.Real.Basic

-- 证明：对于所有实数a，a² ≥ 0
theorem real_square_nonneg (a : ℝ) : a² ≥ 0 :=
  by
    sorry  -- 这里将由模型生成证明
"""

proof = model.generate_proof(lean_code)
print(f"定理: {lean_code}")
print(f"生成的证明: {proof}")

# 精调阶段示例代码
from spark_prover import SparkProverX1, TrainingConfig

# 配置精调参数
config = TrainingConfig(
    learning_rate=1e-5,
    batch_size=8,
    num_epochs=3,
    dataset="lean4-theorem-library",
    save_dir="fine_tuned_model"
)

# 加载预训练模型
model = SparkProverX1.from_pretrained('spark-prover-x1-7b')

# 执行精调
model.fine_tune(config)

# 保存精调后的模型
model.save_pretrained('spark-prover-x1-7b-fine-tuned')

# 数学定理证明示例
lean_code = """
import Mathlib.Data.Real.Basic

-- 证明：对于所有实数a和b，(a + b)² = a² + 2ab + b²
theorem binomial_square (a b : ℝ) : (a + b)² = a² + 2 * a * b + b² :=
  by
    sorry  -- 由模型生成证明
"""

proof = model.generate_proof(lean_code)
print(f"定理: {lean_code}")
print(f"生成的证明: {proof}")

# 代码验证示例
lean_code = """
import Mathlib.Program.Tactics

-- 验证简单排序算法的正确性
@[program]
def bubble_sort (arr : List Nat) : List Nat :=
  match arr with
  | [] => []
  | x :: xs =>
    let sorted_tail := bubble_sort xs
    if x ≤ head sorted_tail then x :: sorted_tail
    else head sorted_tail :: bubble_sort (x :: tail sorted_tail)
  where head [] := 0 | head (y :: _) := y
        tail [] := [] | tail (_ :: ys) := ys

-- 证明排序后的列表是有序的
theorem bubble_sort_sorts (arr : List Nat) : 
    ∀ i j : Nat, i < j → length (bubble_sort arr) → 
    nth_le (bubble_sort arr) i _ ≤ nth_le (bubble_sort arr) j _ :=
  by
    sorry  -- 由模型生成证明
"""

proof = model.generate_proof(lean_code)
print(f"代码验证: {lean_code}")
print(f"生成的证明: {proof}")

# 安装必要的依赖
pip install spark-prover
pip install lean4

# 下载预训练模型
spark-prover download --model spark-prover-x1-7b

# 高级功能示例：批量定理证明
from spark_prover import SparkProverX1

# 初始化模型
model = SparkProverX1.from_pretrained('spark-prover-x1-7b')

# 批量定理证明
theorems = [
    # 定理1: 实数加法交换律
    "theorem add_comm (a b : ℝ) : a + b = b + a := by sorry",
    # 定理2: 实数乘法交换律
    "theorem mul_comm (a b : ℝ) : a * b = b * a := by sorry",
    # 定理3: 实数加法结合律
    "theorem add_assoc (a b c : ℝ) : (a + b) + c = a + (b + c) := by sorry"
]

# 批量生成证明
results = []
for i, theorem in enumerate(theorems):
    lean_code = f"import Mathlib.Data.Real.Basic\n\n{theorem}"
    proof = model.generate_proof(lean_code)
    results.append((i+1, theorem, proof))

# 输出结果
for idx, theorem, proof in results:
    print(f"\n--- 定理 {idx} ---")
    print(f"定理: {theorem}")
    print(f"证明: {proof}")