---
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.

```python
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:

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