Canonicity and homotopy canonicity for cubical type theory

Cubical type theory provides a constructive justification of homotopy theory. A crucial ingredient cubical is path lifting operation which explained computationally by induction on the involving several non-canonical choices. We present in this article two canonicity results, both proved sconing argument: result, every natural number equal to numeral, even if we take away equations defining structure, and uses these way. Both proofs are done internally presheaf model.