Rigorous Software Development -spring 2013

/*@ public normal_behavior @ requires !isEmpty(); @ ensures \old(queue).has(\result) && @ queue.equals(\old(queue).remove(\result)) && @ (\forall Comparable o; queue.has(o); @ \result.compareTo(o) <= 0); @ modifies queue; @*/ public Comparable removeFirst() { Comparable first = elems[0]; Comparable last = elems[--numElems]; int pos = 0; int child = 1; while (child < numElems) { if (child + 1 < numElems && elems[child].compareTo(elems[child+1]) < 0) { child++; } if (elems[child].compareTo(last) < 0) break; elems[pos] = elems[child]; pos = child; child = 2*pos; } elems[pos] = last; //@ set ghostQueue = ghostQueue.remove(first); return first; }