Implementing a priority queue

For our queue implementation, the following invariant holds. If the out list is empty, the in list has to be empty (that is, the entire queue is empty). During the pivot step, the invariant is temporarily violated and then restored:

scala> case class Fifo(out: List[Int], in: List[Int]) { 
     | 
     |   def check(): Boolean = (out, in) match { 
     |     case (Nil, x :: xs) => false 
     |     case _ => true 
     |   } 
     |   require(check, "Invariant Failed - out.em") 
     | } 
defined class Fifo 

Note the use of the require method to make sure the invariant always holds. We use a method called check; this method, in turn, uses pattern matching to check both the lists.

Here's the first clause:

case (Nil, x :: xs) => false 

This clause matches when the out list is empty and the in list is non-empty, that is, it has at least one element. We know this violates our invariant and the object construction...