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22.1 Pairs

Pairs are used to combine two Scheme objects into one compound object. Hence the name: A pair stores a pair of objects.

The data type pair is extremely important in Scheme, just like in any other Lisp dialect. The reason is that pairs are not only used to make two values available as one object, but that pairs are used for constructing lists of values. Because lists are so important in Scheme, they are described in a section of their own (see Lists).

Pairs can literally get entered in source code or at the REPL, in the so-called dotted list syntax. This syntax consists of an opening parentheses, the first element of the pair, a dot, the second element and a closing parentheses. The following example shows how a pair consisting of the two numbers 1 and 2, and a pair containing the symbols foo and bar can be entered. It is very important to write the whitespace before and after the dot, because otherwise the Scheme parser would not be able to figure out where to split the tokens.

(1 . 2)
(foo . bar)

But beware, if you want to try out these examples, you have to quote the expressions. More information about quotation is available in the section (REFFIXME). The correct way to try these examples is as follows.

'(1 . 2)
(1 . 2)
'(foo . bar)
(foo . bar)

A new pair is made by calling the procedure cons with two arguments. Then the argument values are stored into a newly allocated pair, and the pair is returned. The name cons stands for "construct". Use the procedure pair? to test whether a given Scheme object is a pair or not.

cons x y Scheme Procedure
scm_cons (x, y) C Function
Return a newly allocated pair whose car is x and whose cdr is y. The pair is guaranteed to be different (in the sense of eq?) from every previously existing object.

pair? x Scheme Procedure
scm_pair_p (x) C Function
Return #t if x is a pair; otherwise return #f.

The two parts of a pair are traditionally called car and cdr. They can be retrieved with procedures of the same name (car and cdr), and can be modified with the procedures set-car! and set-cdr!. Since a very common operation in Scheme programs is to access the car of a pair, or the car of the cdr of a pair, etc., the procedures called caar, cadr and so on are also predefined.

car pair Scheme Procedure
cdr pair Scheme Procedure
Return the car or the cdr of pair, respectively.

caar pair Scheme Procedure
cadr pair ... Scheme Procedure
cdddar pair Scheme Procedure
cddddr pair Scheme Procedure
These procedures are compositions of car and cdr, where for example caddr could be defined by
(define caddr (lambda (x) (car (cdr (cdr x)))))

set-car! pair value Scheme Procedure
scm_set_car_x (pair, value) C Function
Stores value in the car field of pair. The value returned by set-car! is unspecified.

set-cdr! pair value Scheme Procedure
scm_set_cdr_x (pair, value) C Function
Stores value in the cdr field of pair. The value returned by set-cdr! is unspecified.