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Summary: We consider lists, the most important compound data type in Lisp.
One of Scheme's great strengths is that it includes a powerful data
structure, the list, as a built-in data type. In contrast to Scheme's
unstructured data types, such as symbols and numbers, lists are
structures that contain other values as elements. A list
is an ordered collection of values. In Scheme, lists can
be heterogeneous, in that they may contain different kinds
As we will see throughout the semester, lists provide an elegant and easy-to-use mechanism for organizing collections of information.
In order to work with lists, you need to know how to create lists, update lists (or at least create new lists based on other lists), and extract values from lists.
The easiest way to create a list is to invoke a procedure named
list. This procedure takes all of its arguments, however
many of them there may be, and packs them into a list. Just as the
+ sums its arguments and returns the
result, so the
list procedure collects its arguments and
returns the resulting list:
> (list 38 72 'apple -1/3 'sample) (38 72 apple -1/3 sample) > (define a 2) > (define b 3) > (list a b) (2 3) > (list 'a a 'b b) (a 2 b 3)
list is a convenient way to build lists,
list operation is, itself, composed of other, more
primitive, operations. Behind the scenes,
cons once for each element of
the completed list, to hook that element onto the previously created list.
We have to start somewhere. As you might guess, the simplest list is the empty list, that contains no elements at all. Any other list is constructed by attaching some value, called the car of the new list, to a previously constructed list, which is called the cdr of the new list.
Scheme's name for the empty list is a pair of parentheses with nothing
(). When we refer to the empty list in a Scheme
program, we have to put an apostrophe before the left parenthesis, so that
Scheme won't mistake the parentheses for a procedure call:
> '() ()
Since this conventional name for the empty list is not very readable, our
implementation of Scheme also provides a built-in name,
for the empty list. We follow this usage and recommend it.
> null ()
If, for some reason, the implementation of Scheme that you're using does
null, you can always define it yourself.
(define null '())
constructor procedure for non-empty lists is called
cons. It takes two arguments
and returns a list that is just like the second argument, except that
the first argument has been added at the beginning, as a new first
element. By repeated applications of
cons, we can build up a list of
> (define singleton (cons 'sample null)) > singleton (sample) > (define doubleton (cons 'another-element singleton)) > doubleton (another-element sample) > (define tripleton (cons 'yet-another-element doubleton)) > tripleton (yet-another-element another-element sample) > (cons 'senior (cons 'third-year (cons 'second-year (cons 'freshling null)))) (senior third-year second-year freshling)
cons procedure never returns an empty list, since it
always adds an element at the beginning of another list.
Although we have defined
cons in such a way that it expects
a list as its second parameter, it is possible to use a value other than
a list as the second parameter. When you do so, you build something that
is a bit like a list, but also a bit different. Most Scheme environments
indicate the difference by putting a period before the final value.
> (cons 'a (cons 'b null)) (a b) > (cons 'a (cons 'b 'null)) (a b . null)
If you are trying to create a list and you see the period, you have probably done something wrong, so you'll need to think about your algorithm.
Warning! This section discusses a technique that we do not recommend using. We include it because it reveals a lot about the workings of Scheme.
As you may have noted from the discussion of atoms, there is another way to create lists. You can
For example, the value of the expression
'(38 72 apple -1/3 sample)
is a five-element list consisting of two numbers, a symbol, another number, and finally another symbol. Note that the apostrophe blocks the evaluation of the whole list, so that it is not necessary to quote separately the symbols that occur as elements of the list.
In a list literal like this one, the apostrophe must be present so
that Scheme does not misinterpret the left parenthesis as the beginning of
a procedure call. Sometimes that apostrophe is all that distinguishes two
different, correctly formed expressions. For instance,
(+ 5 3) is a procedure call that has the value 8,
'(+ 5 3) is a list literal denoting a list
of three elements, the symbol
+ and the numbers 5 and 3.
> > (+ 5 3) 8 > '(+ 5 3) (+ 5 3)
While list literals seem like a convenient way to create lists, experience shows that they can also lead to problems. We recommend that you generally avoid using list literals.
It is possible, and indeed common, for a list to be an element of another list. For instance, the expression
(list 'alpha 'beta (list 'gamma-1 'gamma-2) 'delta)
creates a four-element list: Its first element is the symbol
alpha, its second is the symbol
beta, its third
is a two-element list comprising the symbols
gamma-2, and its fourth is the symbol
It is possible for all of the elements of a list to be lists. It is possible for a list that is an element of another list to have lists as its elements, and so on -- lists can be embedded within lists to any desired level of nesting. This idea is subtler and more powerful than it may initially seem to be.
To recover elements from a list, one commonly uses the built-in Scheme
car, which takes one argument (a non-empty
list) and returns its first element, and
cdr, which takes
one argument (a non-empty list), and returns a list just like the one
it was given, except that the first element has been removed. In a
cdr are the inverses of
cons; if you think of a non-empty list as having been assembled
by a call to the
you back the first argument to
gives you back the second one.
> (car (cons 'apple (cons 'orange null))) apple > (cdr (cons 'apple (cons 'orange null))) (orange)
If you want the second rather than the first element of a list, you
cdr to extract it:
> (define sample (cons 'apple (cons 'orange null))) > (car (cdr sample)) orange
The idea is that the procedure call
computes a list just like
sample except that the symbol
apple is gone, and then
car gives you the
first element of that computed list. Similarly,
(car (cdr (cdr
longer-list))) is the third element of
and so on.
Many implementations of Scheme provide these variants, using names like
cadr (for the car of the cdr) and
cddr for the
(cdr of the cdir).
Just as Scheme provides many built-in procedures that perform simple operations on numbers, there are several built-in procedures that operate on lists. Here are four that are very frequently used:
length procedure takes
one argument, which must be a list, and computes the number of elements
in the list. (An element that happens to be itself a list nevertheless
contributes 1 to the total that
length computes, regardless
of how many elements it happens to contain.)
reverse procedure takes
a list and returns a new list containing the same elements, but in the
> (reverse '(a b c)) (c b a)
append procedure takes any number
of arguments, each of which is a list, and returns a new list formed by
stringing together all of the elements of the argument lists, in order,
to form one long list.
list-ref procedure takes two arguments, the first of which
is a list and the second a non-negative integer less than the length of the
list. It recovers an element from the list by skipping over the number of
initial elements specified by the second argument (applying
that many times) and extracting the next element (by invoking
(list-ref sample 0) is the same as
(list-ref sample 1) is the same as
(car (cdr sample)), and so on.
I usually create these pages
on the fly, which means that I rarely
proofread them and they may contain bad grammar and incorrect details.
It also means that I tend to update them regularly (see the history for
more details). Feel free to contact me with any suggestions for changes.
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