Mutative covariant containers are unsound.

For example, and using no language in particular,

interface Pet;
class Cat extends Pet { meow(); }
class Dog extends Pet { woof(); }

class Box[T] {
  value: T;
}

var dog: Box[Dog] = new Box(new Dog);
var pet: Box[Pet] = dog;
pet.value = new Cat;
dog.woof();  // uh oh!

Is there an analogous unsoundness with contravariant types?

My intuition is no. Loosely, the above unsoundness comes from the fact that a Box[T] "contains" a reference to a T, but a contravariant type like Predicate[T] does not "contain" anything at all.

However, I can't find much on the subjet.