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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.1

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)))


[1] Note that path is restricted to a machine-dependent range, usually the size of a machine word. On many machines, this means that the maximum length of path will be 30 operations (32 bits, less the sign bit and the “end-of-sequence” bit).