A function accepting every Base can safely be used where only Derived inputs will be supplied. The reverse direction is unsafe. A Derived argument is already a valid Base argument; restricting the possible callers introduces no new obligation for the function. This is the contravariant input rule of function subtyping.
The printed trait has generic type invariance, so Scala does not directly permit either parameter-changing assignment. The safe behavior can be exposed using an explicit adapter without changing that trait:
def restrictInput(f: Fun[Base, Base]): Fun[Derived, Base] =
  new Fun[Derived, Base] {
    def apply(x: Derived): Base = f(x)
  }
For the unsafe direction, take illustrative classes in which a derived software object has an extra operation:
class Base
class Derived extends Base { def special(): Int = 1 }
val narrow = new Fun[Derived, Base] {
  def apply(x: Derived): Base = { x.special(); x }
}
def broadClient(f: Fun[Base, Base]): Base = f(new Base)
// broadClient(narrow) must be rejected.
If that substitution were accepted, the client could pass an ordinary base software object to code that calls special, which that software object does not support. The rejected call is intentional counterexample code, not a promised compilable application. Variance annotations are needed to make sound direct conversions part of the generic trait's declared subtyping relation.[ref]

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