2000 character limit reached
Relating homotopy equivalences to conservativity in dependendent type theories with propositional computation (2303.05623v2)
Published 9 Mar 2023 in math.LO, cs.LO, and math.CT
Abstract: We prove a conservativity result for extensional type theories over propositional ones, i.e. dependent type theories with propositional computation rules, using insights from homotopy type theory. The argument exploits a notion of canonical homotopy equivalence between contexts, and uses the notion of a category with attributes to phrase the semantics of theories of dependent types. Informally, our main result asserts that, for judgements essentially concerning h-sets, reasoning with extensional or propositional type theories is equivalent.