====================================================================
Queue
====================================================================

A Queue object is represented as a list ordered by first-in, first-out.
It operates like a line of people, where the "next" person is the one
at the front of the line.

Here we create an queue of integers from a list. Notice that the
order in the list is the order in the queue. ::

   a:Queue INT:= queue [1,2,3,4,5]
      [1,2,3,4,5]

We can remove the top of the queue using dequeue!: ::

   dequeue! a
      1

Notice that the use of dequeue! is destructive (destructive operations
in FriCAS usually end with ! to indicate that the underylying data
structure is changed). ::

   a
      [2,3,4,5]

The extract! operation is another name for the pop! operation and
has the same effect. This operation treats the queue as a BagAggregate: ::

   extract! a
      2

and you can see that it also has destructively modified the queue: ::

   a
      [3,4,5]

Next we use enqueue! to add a new element to the end of the queue: ::

   push!(9,a)
      9

Again, the push! operation is destructive so the queue is changed: ::

   a
      [3,4,5,9]

Another name for enqueue! is insert!, which treats the queue as a 
BagAggregate: ::

   insert!(8,a)
      [3,4,5,9,8]

and it modifies the queue: ::

   a
      [3,4,5,9,8]

The inspect function returns the top of the queue without modification,
viewed as a BagAggregate: ::

   inspect a
      8

The empty? operation returns true only if there are no element on the
queue, otherwise it returns false: ::

   empty? a
      false

The front operation returns the front of the queue without modification: ::

   front a
      3

The back operation returns the back of the queue without modification: ::

   back a
      8

The rotate! operation moves the item at the front of the queue to the
back of the queue::

   rotate! a
      [4,5,9,8,3]

The ``#`` (length) operation:

   #a
       5

The length operation does the same thing: ::

   length a
       5

The less? predicate will compare the queue length to an integer: ::

   less?(a,9)
        true

The more? predicate will compare the queue length to an integer: ::

   more?(a,9)
        false

The size? operation will compare the queue length to an integer: ::

   size?(a,#a)
        true

and since the last computation must alwasy be true we try: ::

   size?(a,9)
        false

The parts function will return  the queue as a list of its elements: ::

   parts a
        [8,9,3,4,5]

If we have a BagAggregate of elements we can use it to construct a queue: ::

   bag([1,2,3,4,5])$Queue(INT)
        [1,2,3,4,5]

The empty function will construct an empty queue of a given type: ::

   b:=empty()$(Queue INT)
        []

and the empty? predicate allows us to find out if a queue is empty: ::

   empty? b
        true

The sample function returns a sample, empty queue: ::

   sample()$Queue(INT)
        []

We can copy a queue and it does not share storage so subsequent
modifications of the original queue will not affect the copy: ::

   c:=copy a
        [4,5,9,8,3]

The eq? function is only true if the lists are the same reference,
so even though c is a copy of a, they are not the same: ::

   eq?(a,c)
        false

However, a clearly shares a reference with itself: ::

   eq?(a,a)
        true

But we can compare a and c for equality: ::

   (a=c)@Boolean
        true

and clearly a is equal to itself: ::

   (a=a)@Boolean
        true

and since a and c are equal, they are clearly NOT not-equal: ::

   a~=c
        false

We can use the any? function to see if a predicate is true for any element: ::

   any?(x+->(x=4),a)
        true

or false for every element: ::

   any?(x+->(x=11),a)
        false

We can use the every? function to check every element satisfies a predicate: ::

   every?(x+->(x=11),a)
        false

We can count the elements that are equal to an argument of this type: ::

   count(4,a)
        1

or we can count against a boolean function: ::

   count(x+->(x>2),a)
        5

You can also map a function over every element, returning a new queue: ::

   map(x+->x+10,a)
        [14,15,19,18,13]

Notice that the orignal queue is unchanged: ::

   a
        [4,5,9,8,3]

You can use map! to map a function over every element and change
the original queue since map! is destructive: ::

   map!(x+->x+10,a)
       [14,15,19,18,13]

Notice that the orignal queue has been changed: ::

   a
       [14,15,19,18,13]

The member function can also get the element of the queue as a list: ::

   members a
       [18,19,13,14,15]

and using member? we can test if the queue holds a given element: ::

   member?(14,a)
       true


See Also:

* )show Stack
* )show ArrayStack
* )show Queue
* )show Dequeue
* )show Heap
* )show BagAggregate