Pairs (MIT/GNU Scheme 12.0.90)

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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.

standard 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

standard 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)

SRFI 1 procedure: xcons obj1 obj2 ¶

  Returns a newly allocated pair whose car is obj2 and whose cdr is obj1.

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

standard 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

standard 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

SRFI 1 procedure: car+cdr pair ¶

  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

standard 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

standard procedure: set-cdr! pair object ¶

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

standard procedure: caar pair ¶
standard procedure: cadr pair ¶
standard procedure: cdar pair ¶
standard procedure: cddr pair ¶
standard procedure: caaar pair ¶
standard procedure: caadr pair ¶
standard procedure: cadar pair ¶
standard procedure: caddr pair ¶
standard procedure: cdaar pair ¶
standard procedure: cdadr pair ¶
standard procedure: cddar pair ¶
standard procedure: cdddr pair ¶
standard procedure: caaaar pair ¶
standard procedure: caaadr pair ¶
standard procedure: caadar pair ¶
standard procedure: caaddr pair ¶
standard procedure: cadaar pair ¶
standard procedure: cadadr pair ¶
standard procedure: caddar pair ¶
standard procedure: cadddr pair ¶
standard procedure: cdaaar pair ¶
standard procedure: cdaadr pair ¶
standard procedure: cdadar pair ¶
standard procedure: cdaddr pair ¶
standard procedure: cddaar pair ¶
standard procedure: cddadr pair ¶
standard procedure: cdddar pair ¶
standard 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

SRFI 1 procedure: tree-copy tree ¶

  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)))

#### Footnotes

##### (6)

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).

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