In computer science and mathematical logic, a proof assistant or interactive theorem prover is a software tool to assist with the development of formal proofs by human-machine collaboration. This involves some sort of interactive proof editor, or other interface, with which a human can guide the search for proofs, the details of which are stored in, and some steps provided by, a computer.
This type of software provides a formal language to write mathematical definitions, executable algorithms and theorems together with an environment for semi-interactive development of machine-checked proofs.
These software tools aid the development of formal proofs by man-machine collaboration. They offer a formal language where mathematical definitions, executable algorithms and theorems co-exist, and an interactive environment keeping the current status of the proof, and updating it according to commands (usually called tactics) issued by the user.
Here’s our verdict captured in a legendary LinuxLinks-style ratings chart. They are all free and open source software.
Let’s explore the 5 proof assistants. For each title we have compiled its own portal page, a full description with an in-depth analysis of its features, a screenshot of the software in action together with links to relevant resources.
| Proof Assistants | |
|---|---|
| Coq | Formal proof management system |
| Isabelle | Generic proof assistant; express mathematical formulas in a formal language |
| Agda | Interactive system for writing and checking proofs |
| Lean | Programming language and theorem prover |
| Matita | Experimental, interactive theorem prover |
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