Let $$X$$ be a projective variety which is algebraic Lang hyperbolic. We show that Lang's conjecture holds (one direction only): $$X$$ and all its subvarieties are of general type and the canonical divisor $$K_X$$ is ample at smooth points and Kawamata log terminal points of $$X$$ , provided that $$K_X$$ is $$\mathbb {Q}$$ -Cartier, no Calabi-Yau variety is algebraic Lang hyperbolic and a weak abundance conjecture holds.