# Types

## Queue

</>

A queue is an ordered collection of elements. It is similar to a list, but unlike a list elements can be added to or removed from either the front or the back in a performant fashion.

The internal representation may be different for two queues with the same elements in the same order if the queues were constructed in different ways. This is the price paid for a queue’s fast access at both the front and the back.

Because of unpredictable internal representation the equality operator `==` may return surprising results, and the `is_equal` and `is_logically_equal` functions are the recommended way to test queues for equality.

``pub opaque type Queue(element)``

# Functions

## from_list

</>
``pub fn from_list(list: List(a)) -> Queue(a)``

Converts a list of elements into a queue of the same elements in the same order. The head element in the list becomes the front element in the queue.

This function runs in constant time.

# Examples

``````> [1, 2, 3] |> from_list |> length
3
``````

## is_empty

</>
``pub fn is_empty(queue: Queue(a)) -> Bool``

Determines whether or not the queue is empty.

This function runs in constant time.

## Examples

``````> [] |> from_list |> is_empty
True

>  |> from_list |> is_empty
False

> [1, 2] |> from_list |> is_empty
False
``````

## is_equal

</>
``pub fn is_equal(a: Queue(a), to b: Queue(a)) -> Bool``

Checks whether two queues have the same elements in the same order.

This function is useful as the internal representation may be different for two queues with the same elements in the same order depending on how they were constructed, so the equality operator `==` may return surprising results.

This function runs in linear time.

## is_logically_equal

</>
``````pub fn is_logically_equal(a: Queue(a), to b: Queue(a), checking element_is_equal: fn(
a,
a,
) -> Bool) -> Bool``````

Checks whether two queues have equal elements in the same order, where the equality of elements is determined by a given equality checking function.

This function is useful as the internal representation may be different for two queues with the same elements in the same order depending on how they were constructed, so the equality operator `==` may return surprising results.

This function runs in linear time multiplied by the time taken by the element equality checking function.

## length

</>
``pub fn length(queue: Queue(a)) -> Int``

Counts the number of elements in a given queue.

This function has to traverse the queue to determine the number of elements, so it runs in linear time.

## Examples

``````> length(from_list([]))
0

> length(from_list())
1

> length(from_list([1, 2]))
2
``````

## new

</>
``pub fn new() -> Queue(a)``

Creates a fresh queue that contains no values.

## pop_back

</>
``````pub fn pop_back(from queue: Queue(a)) -> Result(
#(a, Queue(a)),
Nil,
)``````

Gets the last element from the queue, returning the element and a new queue without that element.

This function typically runs in constant time, but will occasionally run in linear time.

# Examples

``````> queue.new()
> |> queue.push_back(0)
> |> queue.push_back(1)
> |> queue.pop_back()
Ok(#(1, queue.push_front(queue.new(), 0)))

> queue.new()
> |> queue.push_front(0)
> |> queue.pop_back()
Ok(#(0, queue.new()))

> queue.new()
> |> queue.pop_back()
Error(Nil)
``````

## pop_front

</>
``````pub fn pop_front(from queue: Queue(a)) -> Result(
#(a, Queue(a)),
Nil,
)``````

Gets the first element from the queue, returning the element and a new queue without that element.

This function typically runs in constant time, but will occasionally run in linear time.

# Examples

``````> queue.new()
> |> queue.push_front(1)
> |> queue.push_front(0)
> |> queue.pop_front()
Ok(#(0, queue.push_back(queue.new(), 1)))

> queue.new()
> |> queue.push_back(0)
> |> queue.pop_front()
Ok(#(0, queue.new()))

> queue.new()
> |> queue.pop_back()
Error(Nil)
``````

## push_back

</>
``pub fn push_back(onto queue: Queue(a), this item: a) -> Queue(a)``

Pushes an element onto the back of the queue.

# Examples

``````> [1, 2] |> from_list |> push_back(3) |> to_list
[1, 2, 3]
``````

## push_front

</>
``pub fn push_front(onto queue: Queue(a), this item: a) -> Queue(a)``

Pushes an element onto the front of the queue.

# Examples

``````> [0, 0] |> from_list |> push_front(1) |> to_list
[1, 0, 0]
``````

## reverse

</>
``pub fn reverse(queue: Queue(a)) -> Queue(a)``

Creates a new queue from a given queue containing the same elements, but in the opposite order.

This function runs in constant time.

## Examples

``````> [] |> from_list |> reverse |> to_list
[]

>  |> from_list |> reverse |> to_list


> [1, 2] |> from_list |> reverse |> to_list
[2, 1]
``````

## to_list

</>
``pub fn to_list(queue: Queue(a)) -> List(a)``

Converts a queue of elements into a list of the same elements in the same order. The front element in the queue becomes the head element in the list.

This function runs in linear time.

# Examples

``````> new() |> push_back(1) |> push_back(2) |> to_list
[1, 2]
``````