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5.4 Building Cons Cells and Lists

Many functions build lists, as lists reside at the very heart of Lisp. cons is the fundamental list-building function; however, it is interesting to note that list is used more times in the source code for Emacs than cons.

— Function: cons object1 object2

This function is the most basic function for building new list structure. It creates a new cons cell, making object1 the car, and object2 the cdr. It then returns the new cons cell. The arguments object1 and object2 may be any Lisp objects, but most often object2 is a list.

          (cons 1 '(2))
               ⇒ (1 2)
          (cons 1 '())
               ⇒ (1)
          (cons 1 2)
               ⇒ (1 . 2)

cons is often used to add a single element to the front of a list. This is called consing the element onto the list. 1 For example:

          (setq list (cons newelt list))

Note that there is no conflict between the variable named list used in this example and the function named list described below; any symbol can serve both purposes.

— Function: list &rest objects

This function creates a list with objects as its elements. The resulting list is always nil-terminated. If no objects are given, the empty list is returned.

          (list 1 2 3 4 5)
               ⇒ (1 2 3 4 5)
          (list 1 2 '(3 4 5) 'foo)
               ⇒ (1 2 (3 4 5) foo)
          (list)
               ⇒ nil
— Function: make-list length object

This function creates a list of length elements, in which each element is object. Compare make-list with make-string (see Creating Strings).

          (make-list 3 'pigs)
               ⇒ (pigs pigs pigs)
          (make-list 0 'pigs)
               ⇒ nil
          (setq l (make-list 3 '(a b)))
               ⇒ ((a b) (a b) (a b))
          (eq (car l) (cadr l))
               ⇒ t
— Function: append &rest sequences

This function returns a list containing all the elements of sequences. The sequences may be lists, vectors, bool-vectors, or strings, but the last one should usually be a list. All arguments except the last one are copied, so none of the arguments is altered. (See nconc in Rearrangement, for a way to join lists with no copying.)

More generally, the final argument to append may be any Lisp object. The final argument is not copied or converted; it becomes the cdr of the last cons cell in the new list. If the final argument is itself a list, then its elements become in effect elements of the result list. If the final element is not a list, the result is a dotted list since its final cdr is not nil as required in a true list.

Here is an example of using append:

     (setq trees '(pine oak))
          ⇒ (pine oak)
     (setq more-trees (append '(maple birch) trees))
          ⇒ (maple birch pine oak)
     
     trees
          ⇒ (pine oak)
     more-trees
          ⇒ (maple birch pine oak)
     (eq trees (cdr (cdr more-trees)))
          ⇒ t

You can see how append works by looking at a box diagram. The variable trees is set to the list (pine oak) and then the variable more-trees is set to the list (maple birch pine oak). However, the variable trees continues to refer to the original list:

     more-trees                trees
     |                           |
     |     --- ---      --- ---   -> --- ---      --- ---
      --> |   |   |--> |   |   |--> |   |   |--> |   |   |--> nil
           --- ---      --- ---      --- ---      --- ---
            |            |            |            |
            |            |            |            |
             --> maple    -->birch     --> pine     --> oak

An empty sequence contributes nothing to the value returned by append. As a consequence of this, a final nil argument forces a copy of the previous argument:

     trees
          ⇒ (pine oak)
     (setq wood (append trees nil))
          ⇒ (pine oak)
     wood
          ⇒ (pine oak)
     (eq wood trees)
          ⇒ nil

This once was the usual way to copy a list, before the function copy-sequence was invented. See Sequences Arrays Vectors.

Here we show the use of vectors and strings as arguments to append:

     (append [a b] "cd" nil)
          ⇒ (a b 99 100)

With the help of apply (see Calling Functions), we can append all the lists in a list of lists:

     (apply 'append '((a b c) nil (x y z) nil))
          ⇒ (a b c x y z)

If no sequences are given, nil is returned:

     (append)
          ⇒ nil

Here are some examples where the final argument is not a list:

     (append '(x y) 'z)
          ⇒ (x y . z)
     (append '(x y) [z])
          ⇒ (x y . [z])

The second example shows that when the final argument is a sequence but not a list, the sequence's elements do not become elements of the resulting list. Instead, the sequence becomes the final cdr, like any other non-list final argument.

— Function: reverse list

This function creates a new list whose elements are the elements of list, but in reverse order. The original argument list is not altered.

          (setq x '(1 2 3 4))
               ⇒ (1 2 3 4)
          (reverse x)
               ⇒ (4 3 2 1)
          x
               ⇒ (1 2 3 4)
— Function: copy-tree tree &optional vecp

This function returns a copy of the tree tree. If tree is a cons cell, this makes a new cons cell with the same car and cdr, then recursively copies the car and cdr in the same way.

Normally, when tree is anything other than a cons cell, copy-tree simply returns tree. However, if vecp is non-nil, it copies vectors too (and operates recursively on their elements).

— Function: number-sequence from &optional to separation

This returns a list of numbers starting with from and incrementing by separation, and ending at or just before to. separation can be positive or negative and defaults to 1. If to is nil or numerically equal to from, the value is the one-element list (from). If to is less than from with a positive separation, or greater than from with a negative separation, the value is nil because those arguments specify an empty sequence.

If separation is 0 and to is neither nil nor numerically equal to from, number-sequence signals an error, since those arguments specify an infinite sequence.

All arguments can be integers or floating point numbers. However, floating point arguments can be tricky, because floating point arithmetic is inexact. For instance, depending on the machine, it may quite well happen that (number-sequence 0.4 0.6 0.2) returns the one element list (0.4), whereas (number-sequence 0.4 0.8 0.2) returns a list with three elements. The nth element of the list is computed by the exact formula (+ from (* n separation)). Thus, if one wants to make sure that to is included in the list, one can pass an expression of this exact type for to. Alternatively, one can replace to with a slightly larger value (or a slightly more negative value if separation is negative).

Some examples:

          (number-sequence 4 9)
               ⇒ (4 5 6 7 8 9)
          (number-sequence 9 4 -1)
               ⇒ (9 8 7 6 5 4)
          (number-sequence 9 4 -2)
               ⇒ (9 7 5)
          (number-sequence 8)
               ⇒ (8)
          (number-sequence 8 5)
               ⇒ nil
          (number-sequence 5 8 -1)
               ⇒ nil
          (number-sequence 1.5 6 2)
               ⇒ (1.5 3.5 5.5)

Footnotes

[1] There is no strictly equivalent way to add an element to the end of a list. You can use (append listname (list newelt)), which creates a whole new list by copying listname and adding newelt to its end. Or you can use (nconc listname (list newelt)), which modifies listname by following all the cdrs and then replacing the terminating nil. Compare this to adding an element to the beginning of a list with cons, which neither copies nor modifies the list.