## Manipulating lists

We've already seen the function list that constructs a list out of several items. Here are some more functions for working with lists.

### Returning the first element of a list: first

The function first returns the first element of a list:

`> (first '(23 34 45))23`

There are similar functions second, third, and so on up to tenth for getting later items in a list.

### Returning all but the first element of a list: rest

The function rest takes a list and returns the list minus the first element:

`> (rest '(23 34 45))(34 45)`

Note that first and rest were traditionally called car and cdr; you can also use these alternative names.

### Returning the nth element of a list: nth

The function nth takes a number and a list and returns the nth element of the list, counting the first element as zero:

`> (nth 1 '(23 34 45))34`

Note that usually Lisp counts things starting from zero; the functions first and second are exceptions to this, so:

(nth 0 lst) is equivalent to (first lst)

and (nth 1 lst) is equivalent to (second lst).

### Finding the length of a list: length

The function length returns the length of a list; for example:

```> (length '(1 2 3))
3```

### Constructing lists: cons

The function cons takes two parameters - an object and a list - and returns a new list with the object added to the front of the list. For example:

```> (cons 1 '(2 3 4 5 6))
(1 2 3 4 5 6)```

Note that the first object can itself be a list:

`> (cons '(0 1) '(2 3 4 5 6))((0 1) 2 3 4 5 6)`

If the second parameter is not a list cons creates a dotted pair:

`> (cons 'a 'b)(a . b)`

### Joining lists: append

The function append takes any number of lists, and joins them all together into a single list. For example:

```> (append '(1 3 5 7) '(2 4 6 8))
(1 3 5 7 2 4 6 8)```

### Reversing a list: reverse

The function reverse takes a list and reverses it:

```> (reverse '(1 2 3 4))
(4 3 2 1)```

### Combining the list functions

Using these functions for manipulating lists, we can define a new function to perform just about any operation on lists that we need.

For example, let's define a function insert that inserts an item between the first and second items in a list. So:

`> (insert 2 '(1 3 4 5 6))`

should give:

`(1 2 3 4 5 6)`

We can do it as follows:

```(defun insert (item lst)
(cons (first lst)
(cons item
(rest lst))))```

### Exercises

#### 1. Swap the first two items in a list

Write a function swp to swap the first two items of a list. Check that:

`(swp '(9 8 7 6))`

gives:

`(8 9 7 6)`

#### 2. Duplicate the first item in a list

Write a function dup to duplicate the first item in a list, Check that:

`(dup '(0 1 2 3))`

gives:

`(0 0 1 2 3)`

#### 3. Return a random item from a list

Write a function rel that returns a random element of a list. For example:

`(rel '(11 22 33 44))`

would randomly return one of the four numbers. Hint: use nth and random.

#### 4. Return the last item in a list

Write a function las which returns the last item in a list. For example:

`(las '(1 2 3 4))`

should return 4.

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