Covariance can be thought of as a mechanism for overriding functions. Assume there is a (base) function

    f: X -> Y

We want to override it by providing a new mapping from U to V:

    f: U -> V

This mechanism is said to be covariant if the new function guarantees that

    If u <: x then v=f(u) <: y=f(x)

This means that for each more specific input u in U the function returns more specific (not more general) output v in V.