Covariance & Contravariance

• Covariant if it preserves the ordering of types (≤), which orders types from more specific to more generic;
• Contravariant if it reverses this ordering;
• Bivariant if both of these apply (i.e., both I<A> ≤ I<B> and I<B> ≤ I<A> at the same time);
• Invariant or Nonvariant if neither of these applies.

In C# interfaces, in represents contravariance, and out represents covariance.

For example in C#, if Cat is a subtype of Animal, then:

IEnumerable<Cat> is a subtype of IEnumerable<Animal>. The subtyping is preserved because IEnumerable<T> is covariant on T.

Action<Animal> is a subtype of Action<Cat>. The subtyping is reversed because Action<T> is contravariant on T.

Neither IList<Cat> nor IList<Animal> is a subtype of the other, because IList<T> is invariant on T.

Further Reading

• Wikipedia on Covariance and Contravariance
• MS Docs on Covariance and Contravariance