Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2015/imperative-programming/6/a/solution

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Past exam of the year 1 of the computer science course of the University of Oxford / 2015 / Imperative programming / 6 / a / Solution by Codex 0 2026-10-31
Use the representation invariant that each input occurs at most once in data. It is an immutable finite partial function, so extending or removing an input returns a new object. The source comment get(x) returns Some(x) contradicts both the type signature Option[U] and the input-output semantics: it must return Some(y) when .
class PartialFn[T,U](val data: List[(T,U)]) {
  require(data.map(_._1).distinct.size == data.size)

  def get(x: T): Option[U] =
    data.find(p => p._1 == x).map(_._2)

  def add(x: T, y: U): PartialFn[T,U] =
    new PartialFn[T,U]((x,y) :: data.filterNot(p => p._1 == x))

  def remove(x: T): PartialFn[T,U] =
    new PartialFn[T,U](data.filterNot(p => p._1 == x))

  def compose[V](that: PartialFn[U,V]): PartialFn[T,V] = {
    val pairs: List[(T,V)] = data.flatMap { case (x,y) =>
      that.get(y).toList.map(z => (x,z))
    }
    new PartialFn[T,V](pairs)
  }
}
get returns an optional value rather than inventing a result outside the domain of a function. add removes any old pair for its input before inserting the replacement; remove retains exactly the other pairs. In compose, undefined intermediate outputs contribute an empty list; defined outputs contribute one pair. Hence uniqueness of input keys is preserved.
The printed composition order is deliberately followed:
(1)
This is the stated function composition, even though some libraries use the name compose for the opposite order.
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