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)abbrev category QUAGG QueueAggregate
++ Author: Michael Monagan; revised by Manuel Bronstein and Richard Jenks
++ Date Created: August 87 through August 88
++ Date Last Updated: April 1991
++ Description:
++ A queue is a bag where the first item inserted is the first 
++ item extracted.

QueueAggregate(S) : Category == SIG where
  S : Type

  SIG ==> BagAggregate S with

    finiteAggregate

    enqueue_! : (S, %) -> S
      ++ enqueue!(x,q) inserts x into the queue q at the back end.

    dequeue_! : % -> S
      ++ dequeue! s destructively extracts the first (top) element 
      ++ from queue q. The element previously second in the queue becomes 
      ++ the first element. Error: if q is empty.

    rotate_! : % -> %
      ++ rotate! q rotates queue q so that the element at the front of
      ++ the queue goes to the back of the queue.
      ++ Note that rotate! q is equivalent to enqueue!(dequeue!(q)).

    length : % -> NonNegativeInteger
      ++ length(q) returns the number of elements in the queue.
      ++ Note that \axiom{length(q) = #q}.

    front : % -> S
      ++ front(q) returns the element at the front of the queue.
      ++ The queue q is unchanged by this operation.
      ++ Error: if q is empty.

    back : % -> S
      ++ back(q) returns the element at the back of the queue.
      ++ The queue q is unchanged by this operation.
      ++ Error: if q is empty.