HOL4 is an interactive theorem prover for classical higher-order logic. It provides a platform for formalising mathematics, verifying hardware and software, and developing custom proof tools.
The system follows the LCF approach, with theorems created through a small trusted kernel interface. HOL4 is primarily implemented in Standard ML and supports Poly/ML and Moscow ML.
This is free and open source software.
Key Features
- Uses classical higher-order logic with a typed lambda calculus.
- Small trusted kernel provides a foundation for checked proofs.
- Powerful tactic language for constructing interactive proofs.
- Extensive simplification and rewriting facilities.
- Libraries and theories for formal mathematics and verification.
- Supports hardware and software verification.
- Tools for constructing custom proof procedures.
- Holmake batch compiler for building HOL developments.
- Works with Poly/ML and Moscow ML.
- Includes manuals, online help, and example formal developments.
Website: github.com/HOL-Theorem-Prover/HOL
Support:
Developer: HOL4 Contributors
License: BSD-3-Clause
HOL4 is written in Standard ML. Learn Standard ML with our recommended free books and free tutorials.
Related Software
| Proof Assistants | |
|---|---|
| Rocq Prover | Formal proof management system |
| Isabelle | Generic proof assistant; express mathematical formulas in a formal language |
| Lean | Programming language and theorem prover |
| Agda | Interactive system for writing and checking proofs |
| F* | Functional language for verified programs with dependent refinement types |
| HOL4 | Interactive higher-order logic environment for rigorous theorem development |
| Aya | Dependently typed language for formalisation and certified programming |
| Lambdapi | Logical framework for defining and checking expressive type systems |
| HOL Light | Lightweight higher-order logic system with a small trusted kernel |
| PVS | Specification and verification suite for analysing complex systems |
| LISA | Scala-based platform for formal mathematics and automated reasoning |
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