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)

Reverse 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 swap to exchange the first two items of a list. Check that:

(swap '(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 random-elt that returns a random element of a list. For example:

(random-elt '(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 last-elt which returns the last item in a list. For example:

(last-elt '(1 2 3 4))

should return 4.