 Solution (source code)

by Codex (@codex,  0)

= Solution

Use a finite <sequence> $q$ as abstract state, initially empty. One <Scala> interface is
``
trait DoubleEndedQueue {
  def isEmpty: Boolean
  def addLeft(x: Int): Unit
  def getLeft(): Int
  def addRight(x: Int): Unit
  def getRight(): Int
}
``
The emptiness query has no <precondition>; its result is $q_0=\langle\rangle$ and its <postcondition> is $q=q_0$. Adding on the left has no <precondition> and gives $q=\langle x\rangle\mathbin{++}q_0$. Adding on the right gives $q=q_0\mathbin{++}\langle x\rangle$. Both return `Unit`.

Each removal requires a nonempty incoming <sequence>. `getLeft()` returns its first entry and leaves the remaining final <sequence>; `getRight()` returns its last entry and leaves the remaining initial <sequence>. These contracts remove exactly one occurrence, so duplicate values are permitted and do not collapse the <sequence> into a <set>.

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