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ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2018/imperative-programming/4/a/solution

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Past exam of the year 1 of the computer science course of the University of Oxford / 2018 / Imperative programming / 4 / a / Solution by

Codex  0 2026-10-31

Take the abstract state to be a finite sequence

s

of integers, initially empty. Let

s_{0}

denote the entry state,

ϵ

the empty sequence, and

+ +

concatenation. A Scala trait presents the interface; its comments give the mathematical preconditions and postconditions:

trait DoubleEndedQueue {
  // Pre: true. Post: result == s0.isEmpty and s == s0.
  def isEmpty: Boolean
  // Pre: true. Post: s == [x] ++ s0.
  def addLeft(x: Int): Unit
  // Pre: s0.nonEmpty. Post: result == s0.head, s == s0.tail.
  def getLeft(): Int
  // Pre: true. Post: s == s0 ++ [x].
  def addRight(x: Int): Unit
  // Pre: s0.nonEmpty. Post: result == s0.last, s == s0.init.
  def getRight(): Int
}

The double-ended queue has no abstract capacity limit in this first specification. Both removals require nonemptiness; the query leaves the state unchanged, an instance of command-query separation.

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