Homotopy type theory (HoTT) can mean several things: it's a new foundation of mathematics that was developed from the start with computer-formalization in mind.

Homotopy type theory (HoTT) can mean several things: it's a new foundation of mathematics that was developed from the start with computer-formalization in mind. But you can also work on HoTT without ever touching a computer. Conversely, there are many ways to do computer-formalization of mathematics, without every doing anything with HoTT.