Covariance and Contravariance (Programming)

The teacher introduced the Contravariance Problem when talking about the Liskov Substitution Principle.

Resource

• https://en.wikipedia.org/wiki/Covariance_and_contravariance_(computer_science)

Suppose A and B are types, and I<U> denotes application of a type constructor I with type argument U. Within the type system of a programming language, a typing rule for a type constructor I is:

• covariant if it preserves the ordering of types (≤), which orders types from more specific to more generic: If A ≤ B, then I<A> ≤ I<B>;
• contravariant if it reverses this ordering: If A ≤ B, then I<B> ≤ I<A>;
• bivariant if both of these apply (i.e., if A ≤ B, then I<A> ≡ I<B>);[1]
• variant if covariant, contravariant or bivariant;
• invariant or nonvariant if not variant.