Pierre Boulet's Public Library

This reasoning points to a general principle in type system design: it is safe to assume that a type T is a subtype of a type U if you can substitute a value of type T wherever a value of type U is required. This is called the Liskov Substitution Principle. The principle holds if T supports the same operations as U and all of T's operations require less and provide more than the corresponding operations in U.

Sometimes covariance and contravariance are mixed in the same type. A prominent example is Scala's function traits.  For instance, whenever you write the function type A => B, Scala expands this to Function1[A, B]. The definition of Function1 in the standard library uses both covariance and contravariance: the Function1 trait is contravariant in the function argument type S and covariant in the result type T, as shown in Listing 19.8. This satisfies the Liskov substitution principle, because arguments are something that's required, whereas results are something that's provided.

  

  

    trait Function1[-S, +T] {       def apply(x: S): T     } 

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Listing 19.8 - Covariance and contravariance of Function1s.