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license: mit
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# 📜 ProofWalaDataset

The **ProofWalaDataset** is a multilingual dataset of formal theorem proving traces collected from multiple interactive theorem prover (ITP) ecosystems. It provides a structured view of proof steps, goals, hypotheses, and theorem names from diverse mathematical and program verification libraries.

This dataset is intended for researchers and practitioners working on:
- **Automated theorem proving**
- **Formal code generation**
- **Machine learning for logic**
- **Proof step prediction**
- **Multi-language transfer in formal systems**

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## 📂 Dataset Structure

The dataset is organized into the following ITP families:

- `lean/`
- `coq/`
- `GeoCoq/`
- `math-comp/`
- `multilingual/` (cross-formal-language hybrid)

Each family includes standard splits:  
**`train/`**, **`test/`**, and **`eval/`**, each containing multiple JSON files.  
Each JSON file contains a top-level key: `"training_data"` with a list of proof records.

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## 🔍 Each record contains

| Field                         | Description |
|------------------------------|-------------|
| `proof_id`                   | Unique identifier for the proof trace |
| `goal_description`           | Optional natural language description of the proof |
| `start_goals`                | List of starting goals (each with `goal` and `hypotheses`) |
| `end_goals`                  | Final goals after applying proof steps |
| `proof_steps`                | List of applied proof tactics (`inv`, `rewrite`, etc.) |
| `simplified_goals`          | Simplified representations of goals (if any) |
| `all_useful_defns_theorems` | Set of useful definitions or theorems (static analysis) |
| `addition_state_info`        | Optional additional metadata about the proof context |
| `file_path`                  | Source file where the proof appears |
| `project_id`                 | The ITP project or repository path (e.g., CompCert) |
| `theorem_name`              | Name of the theorem being proved |

For convenience, structured fields such as `start_goals[*].goal`, `start_goals[*].hypotheses`, `end_goals[*].goal`, and `end_goals[*].hypotheses` are exposed directly through the Croissant [metadata](https://huggingface.co/datasets/amitayusht/ProofWalaDataset/raw/main/croissant.json).

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## 🧠 Use Cases

- Pretraining and finetuning **LLMs for formal verification**
- Evaluating **proof search** strategies
- Building **cross-language proof translators**
- Fine-grained **proof tactic prediction**

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## 📊 Format

- Data format: **JSON**
- Schema described via **Croissant metadata** (`croissant.json`)
- Fully validated using [mlcroissant](https://github.com/mlcommons/croissant)

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