## Concept:

# Immutable list

## Headline

A form of list without basic operations for mutation

## Description

An immutable list is a data structure for lists (ordered sequences) of elements of a common type. An immutable list can be manipulated in a basic sense like this:

- Observations
- Determine whether the list is
*null*(i.e., empty). - Retrieve the
*head*of the list, if it exists (i.e., the first element of the list) - Retrieve the
*tail*of the list, if it exists (i.e., the rest or all but the head of the list).

- Determine whether the list is
- Construction
- Construct a
*nil*list (i.e., the empty list). - Construct a
*cons*list (i.e., a non-empty list from given head and tail).

- Construct a

- Adding an element in ways other than by using
*cons*. - Removing an element in ways other than by using
*tail*.

## Illustration

### Immutable lists in Haskell

Here are some lists with an increasing number of elements:

```
[]
[1]
[1,2]
[1,2,3]
```

We showed convenience notation for list construction. Fundamentally, lists
are constructed from two constructor functions: *nil* (square brackets) and *cons* (colon). Let us construct the same lists with the fundamental constructors:

```
[]
1:[]
1:(2:[])
1:(2:(3:[]))
```

These are the functions to retrieve the head and the tail of a list:

```
head :: [a] -> a
tail :: [a] -> [a]
```

(In reality, these functions have more general types, but let's simplify things here.)

Here are some applications of *head* and *tail*:

```
> head [1,2]
1
> tail [1,2]
[2]
```

Here is how we test a list to be empty:

```
null :: [a] -> Bool
```

For instance:

```
> null []
True
> null [1,2]
False
```

Further operations on lists can be expressed in terms of the operations described so far. Let us define an operation *snoc* for adding an element at the end of a list. (*snoc* is inverse of *cons* in that cons adds an element at the start of a list.) Here is the function definition:

```
snoc :: [a] -> a -> [a]
snoc [] x = [x]
snoc (x:xs) y = x : snoc xs y
```

Here is an illustrative function application:

```
> snoc [1,2] 3
[1,2,3]
```

The function definition for *snoc* is representative for functions on lists in that we leverage pattern matching with two cases: one for the empty list, another one for nonempty lists. Further, we leverage recursion: the function *snoc* is defined in terms of itself; the first equation is the base case for recursion.

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