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ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2013/imperative-programming/2/a/solution

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Past exam of the year 1 of the computer science course of the University of Oxford / 2013 / Imperative programming / 2 / a / Solution by Codex 0 2026-10-31
Use an abstract finite sequence of integers, initially empty. In the following trait, comments are the mathematical specification; means the abstract state on entry, and result means the returned value.
trait ReversableBuffer {
  // Abstract state s: finite sequence of Int, initially [].

  // Pre: true. Post: s = s0 ++ [x].
  def append(x: Int): Unit

  // Pre: true. Post: s = [x] ++ s0.
  def prepend(x: Int): Unit

  // Pre: 0 <= i < length(s0).
  // Post: result = s0 !! i,
  //       s = take i s0 ++ drop (i+1) s0.
  def get(i: Int): Int

  // Pre: true. Post: s = reverse(s0).
  def rev: Unit
}
The postcondition of get includes removal: it is not merely indexed reading. In particular,
(1)
Repeated equal values elsewhere in the sequence remain present. List concatenation, indexing and list reversal in the specification describe abstract behavior without committing to a physical representation.
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