In math, we call it "variance" - as in invariance, contravariance, and covariance. They each refer to the character of a given functor between categories. A functor is covariant if a -> b maps to Fa -> Fb, contravariant if a -> b maps to Fb -> Fa, and invariant (otherwise known as exponential) if (a -> b) and (b -> a) map to Fa -> Fb.
Every example of variant functors follow these laws. It helps to say that every higher-kinded type which admits a type parameter (i.e. List, Array, Option, etc) can be seen as an instance of a Functor (in fact, in haskell, they are instances of the Functor Typeclass).
Variance is a statement about the functionality of containers given a pre-existing relationship between types they contain. In Math, keeping with the example set, the functor \pi_n : hTop* -> Grp is canonically covariant, while P: Set -> Set: s -> P(s), the powerset functor, is canonically contravariant.
In keeping with the Scala tradition, Option and List, which you can check obey the functor laws. For more info, see Scalaz or Cats.
In math, we call it "variance" - as in invariance, contravariance, and covariance. They each refer to the character of a given functor between categories. A functor is covariant if a -> b maps to Fa -> Fb, contravariant if a -> b maps to Fb -> Fa, and invariant (otherwise known as exponential) if (a -> b) and (b -> a) map to Fa -> Fb.
Every example of variant functors follow these laws. It helps to say that every higher-kinded type which admits a type parameter (i.e. List, Array, Option, etc) can be seen as an instance of a Functor (in fact, in haskell, they are instances of the Functor Typeclass).
Variance is a statement about the functionality of containers given a pre-existing relationship between types they contain. In Math, keeping with the example set, the functor \pi_n : hTop* -> Grp is canonically covariant, while P: Set -> Set: s -> P(s), the powerset functor, is canonically contravariant.
In keeping with the Scala tradition, Option and List, which you can check obey the functor laws. For more info, see Scalaz or Cats.