Cubical type theory provides a constructive justification of homotopy type theory. A crucial ingredient of cubical type theory is a path lifting operation which is explained computationally by induction on the type involving several non-canonical choices.
Feb 18, 2019
Cubical type theory provides a constructive justification of homotopy type theory and satisfies canonicity: every natural number is convertible to a numeral.
Feb 3, 2022 · Abstract. Cubical type theory provides a constructive justification of homotopy type theory. A crucial ingredient of cubical type theory is ...
Feb 21, 2019 · ▷ We showed homotopy canonicity for cubical type theory without computation rules for composition using a sconing argument. ▷ Having no ...
Cubical type theory provides a constructive justification of homotopy type theory and satisfies canonicity: every natural number is convertible to a numeral ...
Jun 21, 2024 · A version of canonicity where the definitional equalities are replaced with identity types. In the case for the natural numbers type homotopy canonicity states ...
Cubical type theory provides a constructive justification of homotopy type theory and satisfies canonicity: every natural number is convertible to a numeral. A ...
Cubical type theory provides a constructive justification of homotopy type theory. A crucial ingredient of cubical type theory is a path lifting operation ...
Sep 20, 2024 · Cubical type theory is a flavor of dependent type theory in which maps out of an interval primitive is used to define cubical path types.
Aug 16, 2019 · So this does not solve the homotopy canonicity conjecture. • (Unclear if there is a cubical type theory that can be interpreted in standard ...