Pairs (MIT/GNU Scheme 10.1.4)

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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.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)))

#### 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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