---
license: bsd-3-clause
tags:
  - theorem-proving
  - formal-methods
  - hol4
  - higher-order-logic
  - standard-ml
task_categories:
  - text-generation
  - feature-extraction
language:
  - en
size_categories:
  - 10K<n<100K
---

# HOL4

A structured dataset of theorems and definitions from **HOL4**, a mature theorem prover for higher-order logic.

## Source

- **Repository:** https://github.com/HOL-Theorem-Prover/HOL
- **License:** BSD-3-Clause

## Statistics

| Property | Value |
|----------|-------|
| **Total Entries** | 63,341 |
| **Theorems** | 50,840 |
| **Definitions** | 12,501 |
| **Script Files** | 1,334 |

### Top Libraries

| Library | Count |
|---------|-------|
| real | 5,491 |
| examples/algebra | 3,618 |
| algebra | 3,147 |
| pred_set | 2,723 |
| examples/lambda | 2,633 |
| probability | 2,193 |

## Schema

| Column | Type | Description |
|--------|------|-------------|
| `fact` | string | Theorem statement or definition body |
| `type` | string | "theorem" or "definition" |
| `library` | string | HOL4 library/example directory |
| `imports` | list[string] | SML open statements |
| `filename` | string | Source Script.sml file |
| `symbolic_name` | string | Theorem/definition name |

## About HOL4

HOL4 is an interactive theorem prover for classical higher-order logic. Key areas:
- Real analysis and topology
- Probability theory
- Algebra (groups, rings, fields)
- Formal languages and automata
- Hardware verification
- Program verification

## Creator

Charles Norton ([phanerozoic](https://huggingface.co/phanerozoic))