Contravariance vs. Covariance

README.md

• Let C<A> be a higher-kinded type e.g. in List<Animal>, List is C and Animal is A.
• Let S be a subtype of T e.g. in class Cat extends Animal, Cat is S and Animal is T

• See Liskov substitution principle .

• If C<S> is a subtype of C<T>, then C is covaraint on T e.g. List<Cat> is a subtype of List<Animal>
• If C<T> is a subtype of C<S>, then C is contravariant on T e.g. Predicate<Animal> is a subtype of Predicate<Cat>
• If neither C<T> and nor C<S> are subtypes of the other, thenC is invariant on T
• If both C<T> and C<S> are subtypes of each other, then C is phantom variant on T. This is possible in languages which support phantom types like Haskell

In Scala:

• Coavariance is denoted by prefixing the type argument using a + e.g. trait List[+A]
• Contravariance is denoted by prefixing the type argument using a - e.g. trait Predicate[-A]
• Invariance is simply denoted by default without any prefixes e.g. trait Container[A]
• We can have all covariance, contravariance and invariance in a single higher-kinded type e.g. functions are contravariant on the input but covariant on the output i.e. trait Function1[-I, +O]
• Phantom Variance is impossible in Scala since it does not support phantom types.