7.1 Pairs

This section describes the simple operations that are available for constructing and manipulating arbitrary graphs constructed from pairs.

procedure: pair? object

Returns #t if object is a pair; otherwise returns #f.

(pair? '(a . b))                        ⇒ #t
(pair? '(a b c))                        ⇒ #t
(pair? '())                             ⇒ #f
(pair? '#(a b))                         ⇒ #f

procedure: cons obj1 obj2

Returns a newly allocated pair whose car is obj1 and whose cdr is obj2. The pair is guaranteed to be different (in the sense of eqv?) from every previously existing object.

(cons 'a '())                           ⇒ (a)
(cons '(a) '(b c d))                    ⇒ ((a) b c d)
(cons "a" '(b c))                       ⇒ ("a" b c)
(cons 'a 3)                             ⇒ (a . 3)
(cons '(a b) 'c)                        ⇒ ((a b) . c)

procedure: xcons obj1 obj2

(SRFI 1) Returns a newly allocated pair whose car is obj2 and whose cdr is obj1.

(xcons '(b c) 'a)                       ⇒ (a b c)

procedure: car pair

Returns the contents of the car field of pair. Note that it is an error to take the car of the empty list.

(car '(a b c))                          ⇒ a
(car '((a) b c d))                      ⇒ (a)
(car '(1 . 2))                          ⇒ 1
(car '())                               error→ Illegal datum

procedure: cdr pair

Returns the contents of the cdr field of pair. Note that it is an error to take the cdr of the empty list.

(cdr '((a) b c d))                      ⇒ (b c d)
(cdr '(1 . 2))                          ⇒ 2
(cdr '())                               error→ Illegal datum

procedure: car+cdr pair

(SRFI 1) The fundamental pair deconstructor:

(lambda (p) (values (car p) (cdr p)))

(receive (a b) (car+cdr (cons 1 2))
  (write-line a)
  (write-line b))
-| 1
-| 2

procedure: set-car! pair object

Stores object in the car field of pair. The value returned by set-car! is unspecified.

(define (f) (list 'not-a-constant-list))
(define (g) '(constant-list))
(set-car! (f) 3)                        ⇒ unspecified
(set-car! (g) 3)                        error→ Illegal datum

procedure: set-cdr! pair object

Stores object in the cdr field of pair. The value returned by set-cdr! is unspecified.

procedure: caar pair

procedure: cadr pair

procedure: cdar pair

procedure: cddr pair

procedure: caaar pair

procedure: caadr pair

procedure: cadar pair

procedure: caddr pair

procedure: cdaar pair

procedure: cdadr pair

procedure: cddar pair

procedure: cdddr pair

procedure: caaaar pair

procedure: caaadr pair

procedure: caadar pair

procedure: caaddr pair

procedure: cadaar pair

procedure: cadadr pair

procedure: caddar pair

procedure: cadddr pair

procedure: cdaaar pair

procedure: cdaadr pair

procedure: cdadar pair

procedure: cdaddr pair

procedure: cddaar pair

procedure: cddadr pair

procedure: cdddar pair

procedure: cddddr pair

These procedures are compositions of car and cdr; for example, caddr could be defined by

(define caddr (lambda (x) (car (cdr (cdr x)))))

procedure: general-car-cdr object path

This procedure is a generalization of car and cdr. Path encodes a particular sequence of car and cdr operations, which general-car-cdr executes on object. Path is an exact non-negative integer that encodes the operations in a bitwise fashion: a zero bit represents a cdr operation, and a one bit represents a car. The bits are executed LSB to MSB, and the most significant one bit, rather than being interpreted as an operation, signals the end of the sequence.⁶

For example, the following are equivalent:

(general-car-cdr object #b1011)
(cdr (car (car object)))

Here is a partial table of path/operation equivalents:

#b10    cdr
#b11    car
#b100   cddr
#b101   cdar
#b110   cadr
#b111   caar
#b1000  cdddr

procedure: tree-copy tree

(SRFI 1) This copies an arbitrary tree constructed from pairs, copying both the car and cdr elements of every pair. This could have been defined by

(define (tree-copy tree)
  (let loop ((tree tree))
    (if (pair? tree)
        (cons (loop (car tree)) (loop (cdr tree)))
        tree)))