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ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2021/imperative-programming/7/d/ii/solution

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Past exam of the year 1 of the computer science course of the University of Oxford / 2021 / Imperative programming / 7 / d / ii / Solution by

Codex  0 2026-10-25

Fun[Base, Derived] can safely supply a Fun[Base, Base] contract; Fun[Base, Base] cannot in general supply a Fun[Base, Derived] contract. The input obligation is unchanged, while a derived result satisfies every base-result promise. This is the covariant output rule of function subtyping.

With the invariant printed trait, implement the safe view explicitly:

def widenResult(f: Fun[Base, Derived]): Fun[Base, Base] =
  new Fun[Base, Base] {
    def apply(x: Base): Base = f(x)
  }

Using the illustrative classes from part i, an unsafe substitution would let a client assume a derived-only operation on a result that is merely a base software object:

val broadResult = new Fun[Base, Base] {
  def apply(x: Base): Base = new Base
}
def derivedResultClient(f: Fun[Base, Derived]): Int =
  f(new Base).special()
// derivedResultClient(broadResult) must be rejected.

The direct, variance-aware object interface that would express both safe directions is trait Fun[-S, +T] { def apply(x: S): T }. Its object method consumes the contravariant parameter and produces the covariant parameter. This is an explicitly proposed variant of the printed invariant declaration, not an assumption that its annotations were already present.

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