Datasets:

englund
/

quantum-lean-hard-vvuq-dataset

license: mit
task_categories:
  - text-generation
  - text2text-generation
language:
  - en
tags:
  - lean
  - formal-verification
  - mathematics
  - physics
  - theorem-proving
  - code-repair
size_categories:
  - n<1K
configs:
  - config_name: default
    data_files:
      - split: train
        path: data/train-00000-of-00001.parquet
      - split: validation
        path: data/validation-00000-of-00001.parquet
      - split: test
        path: data/test-00000-of-00001.parquet

Quantum Lean Hard VVUQ Dataset

Overview

This dataset contains challenging Lean 4 verification and repair problems designed to test advanced reasoning capabilities and demonstrate the effectiveness of Physics World Models (PWMs) in formal verification.

Problem Categories

Type Theory: 3 problems (coercion, dependent types, universes)
Tactic Sequences: 3 problems (wrong tactics, incorrect ordering)
Proof Strategies: 3 problems (wrong high-level approaches)
Advanced Type Theory: 1 problems (higher-order reasoning)
Baseline: 1 problems (simple for comparison)

Difficulty Distribution

Easy: 1 problems
Hard: 4 problems
Expert: 6 problems

PWM Knowledge Levels

W1 (Basic): 1 problems
W2 (Intermediate): 3 problems
W3 (Advanced): 7 problems

Expected Performance

Method A (LLM only): Should struggle with hard/expert problems
Method E (LLM + W3): Should handle most problems successfully
Clear gradient: Performance should improve from A→B→C→D→E

Dataset Structure

Each example contains:

id: Unique problem identifier
category: Problem category (type_theory, tactic_sequence, proof_strategy, etc.)
difficulty: Difficulty level (easy, hard, expert)
corrupted_code: Lean code with intentional errors
repair_target: Correct version of the code
error_info: Detailed error information
domain_knowledge_required: List of concepts needed to solve
pwm_level: Required Physics World Model knowledge level

Usage

This dataset is designed for NeurIPS experiments demonstrating PWM effectiveness in formal verification tasks.

from datasets import load_dataset

# Load the dataset
dataset = load_dataset("englund/quantum-lean-hard-vvuq-dataset")

# Access train split
train_data = dataset["train"]

# Example usage
for example in train_data:
    print(f"Problem: {example['id']}")
    print(f"Corrupted: {example['corrupted_code']}")
    print(f"Target: {example['repair_target']}")
    print(f"Difficulty: {example['difficulty']}")

Requirements

Lean 4 with Mathlib
Enhanced diagnostics: set_option diagnostics true
Actual compilation verification (RequirementLEAN)

Citation

If you use this dataset, please cite:

@dataset{englund2025quantum,
  title={Quantum Lean Hard VVUQ Dataset},
  author={Englund, Dirk},
  year={2025},
  url={https://huggingface.co/datasets/englund/quantum-lean-hard-vvuq-dataset}
}