It may be more exciting, but the HoTT book has a bad habit of sending people down the homotopy rabbit hole. People with CS backgrounds will probably find it easier to pick up other type theories. (In fact, Church’s “simple type theory” paper may be enough instead of an entire textbook… maybe I’ll update the suggestions.)
Yeah, it could quite easily sidetrack people. But simple type theory, simply wouldn’t do for foundations since you can’t do much mathematics without quantifiers, or dependent types in the case of type theory. Further, IMHO, the univalence axiom is the largest selling point of type theory as foundations. Perhaps a reading guide to the relevant bits of the HoTT book would be useful for people?
Yeah, it could quite easily sidetrack people. But simple type theory, simply wouldn’t do for foundations since you can’t do much mathematics without quantifiers, or dependent types in the case of type theory. Further, IMHO, the univalence axiom is the largest selling point of type theory as foundations. Perhaps a reading guide to the relevant bits of the HoTT book would be useful for people?