2 @c This is part of the GNU Emacs Lisp Reference Manual.
3 @c Copyright (C) 1990, 1991, 1992, 1993, 1994, 1995, 1998, 1999, 2002, 2003,
4 @c 2004, 2005, 2006 Free Software Foundation, Inc.
5 @c See the file elisp.texi for copying conditions.
6 @setfilename ../info/lists
7 @node Lists, Sequences Arrays Vectors, Strings and Characters, Top
10 @cindex element (of list)
12 A @dfn{list} represents a sequence of zero or more elements (which may
13 be any Lisp objects). The important difference between lists and
14 vectors is that two or more lists can share part of their structure; in
15 addition, you can insert or delete elements in a list without copying
19 * Cons Cells:: How lists are made out of cons cells.
20 * List-related Predicates:: Is this object a list? Comparing two lists.
21 * List Elements:: Extracting the pieces of a list.
22 * Building Lists:: Creating list structure.
23 * List Variables:: Modifying lists stored in variables.
24 * Modifying Lists:: Storing new pieces into an existing list.
25 * Sets And Lists:: A list can represent a finite mathematical set.
26 * Association Lists:: A list can represent a finite relation or mapping.
27 * Rings:: Managing a fixed-size ring of objects.
31 @section Lists and Cons Cells
32 @cindex lists and cons cells
33 @cindex @code{nil} and lists
35 Lists in Lisp are not a primitive data type; they are built up from
36 @dfn{cons cells}. A cons cell is a data object that represents an
37 ordered pair. That is, it has two slots, and each slot @dfn{holds}, or
38 @dfn{refers to}, some Lisp object. One slot is known as the @sc{car},
39 and the other is known as the @sc{cdr}. (These names are traditional;
40 see @ref{Cons Cell Type}.) @sc{cdr} is pronounced ``could-er.''
42 We say that ``the @sc{car} of this cons cell is'' whatever object
43 its @sc{car} slot currently holds, and likewise for the @sc{cdr}.
45 A list is a series of cons cells ``chained together,'' so that each
46 cell refers to the next one. There is one cons cell for each element of
47 the list. By convention, the @sc{car}s of the cons cells hold the
48 elements of the list, and the @sc{cdr}s are used to chain the list: the
49 @sc{cdr} slot of each cons cell refers to the following cons cell. The
50 @sc{cdr} of the last cons cell is @code{nil}. This asymmetry between
51 the @sc{car} and the @sc{cdr} is entirely a matter of convention; at the
52 level of cons cells, the @sc{car} and @sc{cdr} slots have the same
56 Since @code{nil} is the conventional value to put in the @sc{cdr} of
57 the last cons cell in the list, we call that case a @dfn{true list}.
59 In Lisp, we consider the symbol @code{nil} a list as well as a
60 symbol; it is the list with no elements. For convenience, the symbol
61 @code{nil} is considered to have @code{nil} as its @sc{cdr} (and also
62 as its @sc{car}). Therefore, the @sc{cdr} of a true list is always a
67 If the @sc{cdr} of a list's last cons cell is some other value,
68 neither @code{nil} nor another cons cell, we call the structure a
69 @dfn{dotted list}, since its printed representation would use
70 @samp{.}. There is one other possibility: some cons cell's @sc{cdr}
71 could point to one of the previous cons cells in the list. We call
72 that structure a @dfn{circular list}.
74 For some purposes, it does not matter whether a list is true,
75 circular or dotted. If the program doesn't look far enough down the
76 list to see the @sc{cdr} of the final cons cell, it won't care.
77 However, some functions that operate on lists demand true lists and
78 signal errors if given a dotted list. Most functions that try to find
79 the end of a list enter infinite loops if given a circular list.
81 @cindex list structure
82 Because most cons cells are used as part of lists, the phrase
83 @dfn{list structure} has come to mean any structure made out of cons
86 The @sc{cdr} of any nonempty true list @var{l} is a list containing all the
87 elements of @var{l} except the first.
89 @xref{Cons Cell Type}, for the read and print syntax of cons cells and
90 lists, and for ``box and arrow'' illustrations of lists.
92 @node List-related Predicates
93 @section Predicates on Lists
95 The following predicates test whether a Lisp object is an atom,
96 whether it is a cons cell or is a list, or whether it is the
97 distinguished object @code{nil}. (Many of these predicates can be
98 defined in terms of the others, but they are used so often that it is
99 worth having all of them.)
102 This function returns @code{t} if @var{object} is a cons cell, @code{nil}
103 otherwise. @code{nil} is not a cons cell, although it @emph{is} a list.
108 This function returns @code{t} if @var{object} is an atom, @code{nil}
109 otherwise. All objects except cons cells are atoms. The symbol
110 @code{nil} is an atom and is also a list; it is the only Lisp object
114 (atom @var{object}) @equiv{} (not (consp @var{object}))
119 This function returns @code{t} if @var{object} is a cons cell or
120 @code{nil}. Otherwise, it returns @code{nil}.
135 This function is the opposite of @code{listp}: it returns @code{t} if
136 @var{object} is not a list. Otherwise, it returns @code{nil}.
139 (listp @var{object}) @equiv{} (not (nlistp @var{object}))
144 This function returns @code{t} if @var{object} is @code{nil}, and
145 returns @code{nil} otherwise. This function is identical to @code{not},
146 but as a matter of clarity we use @code{null} when @var{object} is
147 considered a list and @code{not} when it is considered a truth value
148 (see @code{not} in @ref{Combining Conditions}).
165 @section Accessing Elements of Lists
166 @cindex list elements
169 This function returns the value referred to by the first slot of the
170 cons cell @var{cons-cell}. Expressed another way, this function
171 returns the @sc{car} of @var{cons-cell}.
173 As a special case, if @var{cons-cell} is @code{nil}, then @code{car}
174 is defined to return @code{nil}; therefore, any list is a valid argument
175 for @code{car}. An error is signaled if the argument is not a cons cell
191 This function returns the value referred to by the second slot of
192 the cons cell @var{cons-cell}. Expressed another way, this function
193 returns the @sc{cdr} of @var{cons-cell}.
195 As a special case, if @var{cons-cell} is @code{nil}, then @code{cdr}
196 is defined to return @code{nil}; therefore, any list is a valid argument
197 for @code{cdr}. An error is signaled if the argument is not a cons cell
212 @defun car-safe object
213 This function lets you take the @sc{car} of a cons cell while avoiding
214 errors for other data types. It returns the @sc{car} of @var{object} if
215 @var{object} is a cons cell, @code{nil} otherwise. This is in contrast
216 to @code{car}, which signals an error if @var{object} is not a list.
220 (car-safe @var{object})
222 (let ((x @var{object}))
230 @defun cdr-safe object
231 This function lets you take the @sc{cdr} of a cons cell while
232 avoiding errors for other data types. It returns the @sc{cdr} of
233 @var{object} if @var{object} is a cons cell, @code{nil} otherwise.
234 This is in contrast to @code{cdr}, which signals an error if
235 @var{object} is not a list.
239 (cdr-safe @var{object})
241 (let ((x @var{object}))
250 This macro is a way of examining the @sc{car} of a list,
251 and taking it off the list, all at once.
253 It operates on the list which is stored in the symbol @var{listname}.
254 It removes this element from the list by setting @var{listname}
255 to the @sc{cdr} of its old value---but it also returns the @sc{car}
256 of that list, which is the element being removed.
269 @anchor{Definition of nth}
270 This function returns the @var{n}th element of @var{list}. Elements
271 are numbered starting with zero, so the @sc{car} of @var{list} is
272 element number zero. If the length of @var{list} is @var{n} or less,
273 the value is @code{nil}.
275 If @var{n} is negative, @code{nth} returns the first element of
291 (nth n x) @equiv{} (car (nthcdr n x))
295 The function @code{elt} is similar, but applies to any kind of sequence.
296 For historical reasons, it takes its arguments in the opposite order.
297 @xref{Sequence Functions}.
301 This function returns the @var{n}th @sc{cdr} of @var{list}. In other
302 words, it skips past the first @var{n} links of @var{list} and returns
305 If @var{n} is zero or negative, @code{nthcdr} returns all of
306 @var{list}. If the length of @var{list} is @var{n} or less,
307 @code{nthcdr} returns @code{nil}.
311 (nthcdr 1 '(1 2 3 4))
315 (nthcdr 10 '(1 2 3 4))
319 (nthcdr -3 '(1 2 3 4))
325 @defun last list &optional n
326 This function returns the last link of @var{list}. The @code{car} of
327 this link is the list's last element. If @var{list} is null,
328 @code{nil} is returned. If @var{n} is non-@code{nil}, the
329 @var{n}th-to-last link is returned instead, or the whole of @var{list}
330 if @var{n} is bigger than @var{list}'s length.
333 @defun safe-length list
334 @anchor{Definition of safe-length}
335 This function returns the length of @var{list}, with no risk of either
336 an error or an infinite loop. It generally returns the number of
337 distinct cons cells in the list. However, for circular lists,
338 the value is just an upper bound; it is often too large.
340 If @var{list} is not @code{nil} or a cons cell, @code{safe-length}
344 The most common way to compute the length of a list, when you are not
345 worried that it may be circular, is with @code{length}. @xref{Sequence
348 @defun caar cons-cell
349 This is the same as @code{(car (car @var{cons-cell}))}.
352 @defun cadr cons-cell
353 This is the same as @code{(car (cdr @var{cons-cell}))}
354 or @code{(nth 1 @var{cons-cell})}.
357 @defun cdar cons-cell
358 This is the same as @code{(cdr (car @var{cons-cell}))}.
361 @defun cddr cons-cell
362 This is the same as @code{(cdr (cdr @var{cons-cell}))}
363 or @code{(nthcdr 2 @var{cons-cell})}.
366 @defun butlast x &optional n
367 This function returns the list @var{x} with the last element,
368 or the last @var{n} elements, removed. If @var{n} is greater
369 than zero it makes a copy of the list so as not to damage the
370 original list. In general, @code{(append (butlast @var{x} @var{n})
371 (last @var{x} @var{n}))} will return a list equal to @var{x}.
374 @defun nbutlast x &optional n
375 This is a version of @code{butlast} that works by destructively
376 modifying the @code{cdr} of the appropriate element, rather than
377 making a copy of the list.
381 @comment node-name, next, previous, up
382 @section Building Cons Cells and Lists
384 @cindex building lists
386 Many functions build lists, as lists reside at the very heart of Lisp.
387 @code{cons} is the fundamental list-building function; however, it is
388 interesting to note that @code{list} is used more times in the source
389 code for Emacs than @code{cons}.
391 @defun cons object1 object2
392 This function is the most basic function for building new list
393 structure. It creates a new cons cell, making @var{object1} the
394 @sc{car}, and @var{object2} the @sc{cdr}. It then returns the new
395 cons cell. The arguments @var{object1} and @var{object2} may be any
396 Lisp objects, but most often @var{object2} is a list.
414 @code{cons} is often used to add a single element to the front of a
415 list. This is called @dfn{consing the element onto the list}.
416 @footnote{There is no strictly equivalent way to add an element to
417 the end of a list. You can use @code{(append @var{listname} (list
418 @var{newelt}))}, which creates a whole new list by copying @var{listname}
419 and adding @var{newelt} to its end. Or you can use @code{(nconc
420 @var{listname} (list @var{newelt}))}, which modifies @var{listname}
421 by following all the @sc{cdr}s and then replacing the terminating
422 @code{nil}. Compare this to adding an element to the beginning of a
423 list with @code{cons}, which neither copies nor modifies the list.}
427 (setq list (cons newelt list))
430 Note that there is no conflict between the variable named @code{list}
431 used in this example and the function named @code{list} described below;
432 any symbol can serve both purposes.
435 @defun list &rest objects
436 This function creates a list with @var{objects} as its elements. The
437 resulting list is always @code{nil}-terminated. If no @var{objects}
438 are given, the empty list is returned.
443 @result{} (1 2 3 4 5)
446 (list 1 2 '(3 4 5) 'foo)
447 @result{} (1 2 (3 4 5) foo)
456 @defun make-list length object
457 This function creates a list of @var{length} elements, in which each
458 element is @var{object}. Compare @code{make-list} with
459 @code{make-string} (@pxref{Creating Strings}).
464 @result{} (pigs pigs pigs)
471 (setq l (make-list 3 '(a b))
472 @result{} ((a b) (a b) (a b))
473 (eq (car l) (cadr l))
479 @defun append &rest sequences
480 @cindex copying lists
481 This function returns a list containing all the elements of
482 @var{sequences}. The @var{sequences} may be lists, vectors,
483 bool-vectors, or strings, but the last one should usually be a list.
484 All arguments except the last one are copied, so none of the arguments
485 is altered. (See @code{nconc} in @ref{Rearrangement}, for a way to join
486 lists with no copying.)
488 More generally, the final argument to @code{append} may be any Lisp
489 object. The final argument is not copied or converted; it becomes the
490 @sc{cdr} of the last cons cell in the new list. If the final argument
491 is itself a list, then its elements become in effect elements of the
492 result list. If the final element is not a list, the result is a
493 dotted list since its final @sc{cdr} is not @code{nil} as required
496 In Emacs 20 and before, the @code{append} function also allowed
497 integers as (non last) arguments. It converted them to strings of
498 digits, making up the decimal print representation of the integer, and
499 then used the strings instead of the original integers. This obsolete
500 usage no longer works. The proper way to convert an integer to a
501 decimal number in this way is with @code{format} (@pxref{Formatting
502 Strings}) or @code{number-to-string} (@pxref{String Conversion}).
505 Here is an example of using @code{append}:
509 (setq trees '(pine oak))
511 (setq more-trees (append '(maple birch) trees))
512 @result{} (maple birch pine oak)
519 @result{} (maple birch pine oak)
522 (eq trees (cdr (cdr more-trees)))
527 You can see how @code{append} works by looking at a box diagram. The
528 variable @code{trees} is set to the list @code{(pine oak)} and then the
529 variable @code{more-trees} is set to the list @code{(maple birch pine
530 oak)}. However, the variable @code{trees} continues to refer to the
537 | --- --- --- --- -> --- --- --- ---
538 --> | | |--> | | |--> | | |--> | | |--> nil
539 --- --- --- --- --- --- --- ---
542 --> maple -->birch --> pine --> oak
546 An empty sequence contributes nothing to the value returned by
547 @code{append}. As a consequence of this, a final @code{nil} argument
548 forces a copy of the previous argument:
556 (setq wood (append trees nil))
570 This once was the usual way to copy a list, before the function
571 @code{copy-sequence} was invented. @xref{Sequences Arrays Vectors}.
573 Here we show the use of vectors and strings as arguments to @code{append}:
577 (append [a b] "cd" nil)
578 @result{} (a b 99 100)
582 With the help of @code{apply} (@pxref{Calling Functions}), we can append
583 all the lists in a list of lists:
587 (apply 'append '((a b c) nil (x y z) nil))
588 @result{} (a b c x y z)
592 If no @var{sequences} are given, @code{nil} is returned:
601 Here are some examples where the final argument is not a list:
607 @result{} (x y . [z])
611 The second example shows that when the final argument is a sequence but
612 not a list, the sequence's elements do not become elements of the
613 resulting list. Instead, the sequence becomes the final @sc{cdr}, like
614 any other non-list final argument.
617 This function creates a new list whose elements are the elements of
618 @var{list}, but in reverse order. The original argument @var{list} is
635 @defun copy-tree tree &optional vecp
636 This function returns a copy of the tree @code{tree}. If @var{tree} is a
637 cons cell, this makes a new cons cell with the same @sc{car} and
638 @sc{cdr}, then recursively copies the @sc{car} and @sc{cdr} in the
641 Normally, when @var{tree} is anything other than a cons cell,
642 @code{copy-tree} simply returns @var{tree}. However, if @var{vecp} is
643 non-@code{nil}, it copies vectors too (and operates recursively on
647 @defun number-sequence from &optional to separation
648 This returns a list of numbers starting with @var{from} and
649 incrementing by @var{separation}, and ending at or just before
650 @var{to}. @var{separation} can be positive or negative and defaults
651 to 1. If @var{to} is @code{nil} or numerically equal to @var{from},
652 the value is the one-element list @code{(@var{from})}. If @var{to} is
653 less than @var{from} with a positive @var{separation}, or greater than
654 @var{from} with a negative @var{separation}, the value is @code{nil}
655 because those arguments specify an empty sequence.
657 If @var{separation} is 0 and @var{to} is neither @code{nil} nor
658 numerically equal to @var{from}, @code{number-sequence} signals an
659 error, since those arguments specify an infinite sequence.
661 All arguments can be integers or floating point numbers. However,
662 floating point arguments can be tricky, because floating point
663 arithmetic is inexact. For instance, depending on the machine, it may
664 quite well happen that @code{(number-sequence 0.4 0.6 0.2)} returns
665 the one element list @code{(0.4)}, whereas
666 @code{(number-sequence 0.4 0.8 0.2)} returns a list with three
667 elements. The @var{n}th element of the list is computed by the exact
668 formula @code{(+ @var{from} (* @var{n} @var{separation}))}. Thus, if
669 one wants to make sure that @var{to} is included in the list, one can
670 pass an expression of this exact type for @var{to}. Alternatively,
671 one can replace @var{to} with a slightly larger value (or a slightly
672 more negative value if @var{separation} is negative).
677 (number-sequence 4 9)
678 @result{} (4 5 6 7 8 9)
679 (number-sequence 9 4 -1)
680 @result{} (9 8 7 6 5 4)
681 (number-sequence 9 4 -2)
685 (number-sequence 8 5)
687 (number-sequence 5 8 -1)
689 (number-sequence 1.5 6 2)
690 @result{} (1.5 3.5 5.5)
695 @section Modifying List Variables
697 These functions, and one macro, provide convenient ways
698 to modify a list which is stored in a variable.
700 @defmac push newelt listname
701 This macro provides an alternative way to write
702 @code{(setq @var{listname} (cons @var{newelt} @var{listname}))}.
714 Two functions modify lists that are the values of variables.
716 @defun add-to-list symbol element &optional append compare-fn
717 This function sets the variable @var{symbol} by consing @var{element}
718 onto the old value, if @var{element} is not already a member of that
719 value. It returns the resulting list, whether updated or not. The
720 value of @var{symbol} had better be a list already before the call.
721 @code{add-to-list} uses @var{compare-fn} to compare @var{element}
722 against existing list members; if @var{compare-fn} is @code{nil}, it
725 Normally, if @var{element} is added, it is added to the front of
726 @var{symbol}, but if the optional argument @var{append} is
727 non-@code{nil}, it is added at the end.
729 The argument @var{symbol} is not implicitly quoted; @code{add-to-list}
730 is an ordinary function, like @code{set} and unlike @code{setq}. Quote
731 the argument yourself if that is what you want.
734 Here's a scenario showing how to use @code{add-to-list}:
740 (add-to-list 'foo 'c) ;; @r{Add @code{c}.}
743 (add-to-list 'foo 'b) ;; @r{No effect.}
746 foo ;; @r{@code{foo} was changed.}
750 An equivalent expression for @code{(add-to-list '@var{var}
751 @var{value})} is this:
754 (or (member @var{value} @var{var})
755 (setq @var{var} (cons @var{value} @var{var})))
758 @defun add-to-ordered-list symbol element &optional order
759 This function sets the variable @var{symbol} by inserting
760 @var{element} into the old value, which must be a list, at the
761 position specified by @var{order}. If @var{element} is already a
762 member of the list, its position in the list is adjusted according
763 to @var{order}. Membership is tested using @code{eq}.
764 This function returns the resulting list, whether updated or not.
766 The @var{order} is typically a number (integer or float), and the
767 elements of the list are sorted in non-decreasing numerical order.
769 @var{order} may also be omitted or @code{nil}. Then the numeric order
770 of @var{element} stays unchanged if it already has one; otherwise,
771 @var{element} has no numeric order. Elements without a numeric list
772 order are placed at the end of the list, in no particular order.
774 Any other value for @var{order} removes the numeric order of @var{element}
775 if it already has one; otherwise, it is equivalent to @code{nil}.
777 The argument @var{symbol} is not implicitly quoted;
778 @code{add-to-ordered-list} is an ordinary function, like @code{set}
779 and unlike @code{setq}. Quote the argument yourself if that is what
782 The ordering information is stored in a hash table on @var{symbol}'s
783 @code{list-order} property.
786 Here's a scenario showing how to use @code{add-to-ordered-list}:
792 (add-to-ordered-list 'foo 'a 1) ;; @r{Add @code{a}.}
795 (add-to-ordered-list 'foo 'c 3) ;; @r{Add @code{c}.}
798 (add-to-ordered-list 'foo 'b 2) ;; @r{Add @code{b}.}
801 (add-to-ordered-list 'foo 'b 4) ;; @r{Move @code{b}.}
804 (add-to-ordered-list 'foo 'd) ;; @r{Append @code{d}.}
807 (add-to-ordered-list 'foo 'e) ;; @r{Add @code{e}}.
808 @result{} (a c b e d)
810 foo ;; @r{@code{foo} was changed.}
811 @result{} (a c b e d)
814 @node Modifying Lists
815 @section Modifying Existing List Structure
816 @cindex destructive list operations
818 You can modify the @sc{car} and @sc{cdr} contents of a cons cell with the
819 primitives @code{setcar} and @code{setcdr}. We call these ``destructive''
820 operations because they change existing list structure.
822 @cindex CL note---@code{rplaca} vs @code{setcar}
826 @b{Common Lisp note:} Common Lisp uses functions @code{rplaca} and
827 @code{rplacd} to alter list structure; they change structure the same
828 way as @code{setcar} and @code{setcdr}, but the Common Lisp functions
829 return the cons cell while @code{setcar} and @code{setcdr} return the
830 new @sc{car} or @sc{cdr}.
834 * Setcar:: Replacing an element in a list.
835 * Setcdr:: Replacing part of the list backbone.
836 This can be used to remove or add elements.
837 * Rearrangement:: Reordering the elements in a list; combining lists.
841 @subsection Altering List Elements with @code{setcar}
843 Changing the @sc{car} of a cons cell is done with @code{setcar}. When
844 used on a list, @code{setcar} replaces one element of a list with a
847 @defun setcar cons object
848 This function stores @var{object} as the new @sc{car} of @var{cons},
849 replacing its previous @sc{car}. In other words, it changes the
850 @sc{car} slot of @var{cons} to refer to @var{object}. It returns the
851 value @var{object}. For example:
869 When a cons cell is part of the shared structure of several lists,
870 storing a new @sc{car} into the cons changes one element of each of
871 these lists. Here is an example:
875 ;; @r{Create two lists that are partly shared.}
878 (setq x2 (cons 'z (cdr x1)))
883 ;; @r{Replace the @sc{car} of a shared link.}
884 (setcar (cdr x1) 'foo)
886 x1 ; @r{Both lists are changed.}
893 ;; @r{Replace the @sc{car} of a link that is not shared.}
896 x1 ; @r{Only one list is changed.}
897 @result{} (baz foo c)
903 Here is a graphical depiction of the shared structure of the two lists
904 in the variables @code{x1} and @code{x2}, showing why replacing @code{b}
909 --- --- --- --- --- ---
910 x1---> | | |----> | | |--> | | |--> nil
911 --- --- --- --- --- ---
925 Here is an alternative form of box diagram, showing the same relationship:
930 -------------- -------------- --------------
931 | car | cdr | | car | cdr | | car | cdr |
932 | a | o------->| b | o------->| c | nil |
934 -------------- | -------------- --------------
946 @subsection Altering the CDR of a List
948 The lowest-level primitive for modifying a @sc{cdr} is @code{setcdr}:
950 @defun setcdr cons object
951 This function stores @var{object} as the new @sc{cdr} of @var{cons},
952 replacing its previous @sc{cdr}. In other words, it changes the
953 @sc{cdr} slot of @var{cons} to refer to @var{object}. It returns the
957 Here is an example of replacing the @sc{cdr} of a list with a
958 different list. All but the first element of the list are removed in
959 favor of a different sequence of elements. The first element is
960 unchanged, because it resides in the @sc{car} of the list, and is not
961 reached via the @sc{cdr}.
978 You can delete elements from the middle of a list by altering the
979 @sc{cdr}s of the cons cells in the list. For example, here we delete
980 the second element, @code{b}, from the list @code{(a b c)}, by changing
981 the @sc{cdr} of the first cons cell:
987 (setcdr x1 (cdr (cdr x1)))
995 Here is the result in box notation:
1001 -------------- | -------------- | --------------
1002 | car | cdr | | | car | cdr | -->| car | cdr |
1003 | a | o----- | b | o-------->| c | nil |
1005 -------------- -------------- --------------
1010 The second cons cell, which previously held the element @code{b}, still
1011 exists and its @sc{car} is still @code{b}, but it no longer forms part
1014 It is equally easy to insert a new element by changing @sc{cdr}s:
1020 (setcdr x1 (cons 'd (cdr x1)))
1027 Here is this result in box notation:
1031 -------------- ------------- -------------
1032 | car | cdr | | car | cdr | | car | cdr |
1033 | a | o | -->| b | o------->| c | nil |
1034 | | | | | | | | | | |
1035 --------- | -- | ------------- -------------
1048 @subsection Functions that Rearrange Lists
1049 @cindex rearrangement of lists
1050 @cindex modification of lists
1052 Here are some functions that rearrange lists ``destructively'' by
1053 modifying the @sc{cdr}s of their component cons cells. We call these
1054 functions ``destructive'' because they chew up the original lists passed
1055 to them as arguments, relinking their cons cells to form a new list that
1056 is the returned value.
1059 See @code{delq}, in @ref{Sets And Lists}, for another function
1060 that modifies cons cells.
1063 The function @code{delq} in the following section is another example
1064 of destructive list manipulation.
1067 @defun nconc &rest lists
1068 @cindex concatenating lists
1069 @cindex joining lists
1070 This function returns a list containing all the elements of @var{lists}.
1071 Unlike @code{append} (@pxref{Building Lists}), the @var{lists} are
1072 @emph{not} copied. Instead, the last @sc{cdr} of each of the
1073 @var{lists} is changed to refer to the following list. The last of the
1074 @var{lists} is not altered. For example:
1083 @result{} (1 2 3 4 5)
1087 @result{} (1 2 3 4 5)
1091 Since the last argument of @code{nconc} is not itself modified, it is
1092 reasonable to use a constant list, such as @code{'(4 5)}, as in the
1093 above example. For the same reason, the last argument need not be a
1103 @result{} (1 2 3 . z)
1107 @result{} (1 2 3 . z)
1111 However, the other arguments (all but the last) must be lists.
1113 A common pitfall is to use a quoted constant list as a non-last
1114 argument to @code{nconc}. If you do this, your program will change
1115 each time you run it! Here is what happens:
1119 (defun add-foo (x) ; @r{We want this function to add}
1120 (nconc '(foo) x)) ; @r{@code{foo} to the front of its arg.}
1124 (symbol-function 'add-foo)
1125 @result{} (lambda (x) (nconc (quote (foo)) x))
1129 (setq xx (add-foo '(1 2))) ; @r{It seems to work.}
1133 (setq xy (add-foo '(3 4))) ; @r{What happened?}
1134 @result{} (foo 1 2 3 4)
1142 (symbol-function 'add-foo)
1143 @result{} (lambda (x) (nconc (quote (foo 1 2 3 4) x)))
1148 @defun nreverse list
1149 @cindex reversing a list
1150 This function reverses the order of the elements of @var{list}.
1151 Unlike @code{reverse}, @code{nreverse} alters its argument by reversing
1152 the @sc{cdr}s in the cons cells forming the list. The cons cell that
1153 used to be the last one in @var{list} becomes the first cons cell of the
1170 ;; @r{The cons cell that was first is now last.}
1176 To avoid confusion, we usually store the result of @code{nreverse}
1177 back in the same variable which held the original list:
1180 (setq x (nreverse x))
1183 Here is the @code{nreverse} of our favorite example, @code{(a b c)},
1184 presented graphically:
1188 @r{Original list head:} @r{Reversed list:}
1189 ------------- ------------- ------------
1190 | car | cdr | | car | cdr | | car | cdr |
1191 | a | nil |<-- | b | o |<-- | c | o |
1192 | | | | | | | | | | | | |
1193 ------------- | --------- | - | -------- | -
1195 ------------- ------------
1200 @defun sort list predicate
1202 @cindex sorting lists
1203 This function sorts @var{list} stably, though destructively, and
1204 returns the sorted list. It compares elements using @var{predicate}. A
1205 stable sort is one in which elements with equal sort keys maintain their
1206 relative order before and after the sort. Stability is important when
1207 successive sorts are used to order elements according to different
1210 The argument @var{predicate} must be a function that accepts two
1211 arguments. It is called with two elements of @var{list}. To get an
1212 increasing order sort, the @var{predicate} should return non-@code{nil} if the
1213 first element is ``less than'' the second, or @code{nil} if not.
1215 The comparison function @var{predicate} must give reliable results for
1216 any given pair of arguments, at least within a single call to
1217 @code{sort}. It must be @dfn{antisymmetric}; that is, if @var{a} is
1218 less than @var{b}, @var{b} must not be less than @var{a}. It must be
1219 @dfn{transitive}---that is, if @var{a} is less than @var{b}, and @var{b}
1220 is less than @var{c}, then @var{a} must be less than @var{c}. If you
1221 use a comparison function which does not meet these requirements, the
1222 result of @code{sort} is unpredictable.
1224 The destructive aspect of @code{sort} is that it rearranges the cons
1225 cells forming @var{list} by changing @sc{cdr}s. A nondestructive sort
1226 function would create new cons cells to store the elements in their
1227 sorted order. If you wish to make a sorted copy without destroying the
1228 original, copy it first with @code{copy-sequence} and then sort.
1230 Sorting does not change the @sc{car}s of the cons cells in @var{list};
1231 the cons cell that originally contained the element @code{a} in
1232 @var{list} still has @code{a} in its @sc{car} after sorting, but it now
1233 appears in a different position in the list due to the change of
1234 @sc{cdr}s. For example:
1238 (setq nums '(1 3 2 6 5 4 0))
1239 @result{} (1 3 2 6 5 4 0)
1243 @result{} (0 1 2 3 4 5 6)
1247 @result{} (1 2 3 4 5 6)
1252 @strong{Warning}: Note that the list in @code{nums} no longer contains
1253 0; this is the same cons cell that it was before, but it is no longer
1254 the first one in the list. Don't assume a variable that formerly held
1255 the argument now holds the entire sorted list! Instead, save the result
1256 of @code{sort} and use that. Most often we store the result back into
1257 the variable that held the original list:
1260 (setq nums (sort nums '<))
1263 @xref{Sorting}, for more functions that perform sorting.
1264 See @code{documentation} in @ref{Accessing Documentation}, for a
1265 useful example of @code{sort}.
1268 @node Sets And Lists
1269 @section Using Lists as Sets
1270 @cindex lists as sets
1273 A list can represent an unordered mathematical set---simply consider a
1274 value an element of a set if it appears in the list, and ignore the
1275 order of the list. To form the union of two sets, use @code{append} (as
1276 long as you don't mind having duplicate elements). You can remove
1277 @code{equal} duplicates using @code{delete-dups}. Other useful
1278 functions for sets include @code{memq} and @code{delq}, and their
1279 @code{equal} versions, @code{member} and @code{delete}.
1281 @cindex CL note---lack @code{union}, @code{intersection}
1283 @b{Common Lisp note:} Common Lisp has functions @code{union} (which
1284 avoids duplicate elements) and @code{intersection} for set operations,
1285 but GNU Emacs Lisp does not have them. You can write them in Lisp if
1289 @defun memq object list
1290 @cindex membership in a list
1291 This function tests to see whether @var{object} is a member of
1292 @var{list}. If it is, @code{memq} returns a list starting with the
1293 first occurrence of @var{object}. Otherwise, it returns @code{nil}.
1294 The letter @samp{q} in @code{memq} says that it uses @code{eq} to
1295 compare @var{object} against the elements of the list. For example:
1299 (memq 'b '(a b c b a))
1303 (memq '(2) '((1) (2))) ; @r{@code{(2)} and @code{(2)} are not @code{eq}.}
1309 @defun delq object list
1310 @cindex deletion of elements
1311 This function destructively removes all elements @code{eq} to
1312 @var{object} from @var{list}. The letter @samp{q} in @code{delq} says
1313 that it uses @code{eq} to compare @var{object} against the elements of
1314 the list, like @code{memq} and @code{remq}.
1317 When @code{delq} deletes elements from the front of the list, it does so
1318 simply by advancing down the list and returning a sublist that starts
1319 after those elements:
1323 (delq 'a '(a b c)) @equiv{} (cdr '(a b c))
1327 When an element to be deleted appears in the middle of the list,
1328 removing it involves changing the @sc{cdr}s (@pxref{Setcdr}).
1332 (setq sample-list '(a b c (4)))
1333 @result{} (a b c (4))
1336 (delq 'a sample-list)
1341 @result{} (a b c (4))
1344 (delq 'c sample-list)
1353 Note that @code{(delq 'c sample-list)} modifies @code{sample-list} to
1354 splice out the third element, but @code{(delq 'a sample-list)} does not
1355 splice anything---it just returns a shorter list. Don't assume that a
1356 variable which formerly held the argument @var{list} now has fewer
1357 elements, or that it still holds the original list! Instead, save the
1358 result of @code{delq} and use that. Most often we store the result back
1359 into the variable that held the original list:
1362 (setq flowers (delq 'rose flowers))
1365 In the following example, the @code{(4)} that @code{delq} attempts to match
1366 and the @code{(4)} in the @code{sample-list} are not @code{eq}:
1370 (delq '(4) sample-list)
1375 @defun remq object list
1376 This function returns a copy of @var{list}, with all elements removed
1377 which are @code{eq} to @var{object}. The letter @samp{q} in @code{remq}
1378 says that it uses @code{eq} to compare @var{object} against the elements
1383 (setq sample-list '(a b c a b c))
1384 @result{} (a b c a b c)
1387 (remq 'a sample-list)
1392 @result{} (a b c a b c)
1396 The function @code{delq} offers a way to perform this operation
1397 destructively. See @ref{Sets And Lists}.
1400 @defun memql object list
1401 The function @code{memql} tests to see whether @var{object} is a member
1402 of @var{list}, comparing members with @var{object} using @code{eql},
1403 so floating point elements are compared by value.
1404 If @var{object} is a member, @code{memql} returns a list starting with
1405 its first occurrence in @var{list}. Otherwise, it returns @code{nil}.
1407 Compare this with @code{memq}:
1411 (memql 1.2 '(1.1 1.2 1.3)) ; @r{@code{1.2} and @code{1.2} are @code{eql}.}
1415 (memq 1.2 '(1.1 1.2 1.3)) ; @r{@code{1.2} and @code{1.2} are not @code{eq}.}
1421 The following three functions are like @code{memq}, @code{delq} and
1422 @code{remq}, but use @code{equal} rather than @code{eq} to compare
1423 elements. @xref{Equality Predicates}.
1425 @defun member object list
1426 The function @code{member} tests to see whether @var{object} is a member
1427 of @var{list}, comparing members with @var{object} using @code{equal}.
1428 If @var{object} is a member, @code{member} returns a list starting with
1429 its first occurrence in @var{list}. Otherwise, it returns @code{nil}.
1431 Compare this with @code{memq}:
1435 (member '(2) '((1) (2))) ; @r{@code{(2)} and @code{(2)} are @code{equal}.}
1439 (memq '(2) '((1) (2))) ; @r{@code{(2)} and @code{(2)} are not @code{eq}.}
1443 ;; @r{Two strings with the same contents are @code{equal}.}
1444 (member "foo" '("foo" "bar"))
1445 @result{} ("foo" "bar")
1450 @defun delete object sequence
1451 If @code{sequence} is a list, this function destructively removes all
1452 elements @code{equal} to @var{object} from @var{sequence}. For lists,
1453 @code{delete} is to @code{delq} as @code{member} is to @code{memq}: it
1454 uses @code{equal} to compare elements with @var{object}, like
1455 @code{member}; when it finds an element that matches, it removes the
1456 element just as @code{delq} would.
1458 If @code{sequence} is a vector or string, @code{delete} returns a copy
1459 of @code{sequence} with all elements @code{equal} to @code{object}
1466 (delete '(2) '((2) (1) (2)))
1470 (delete '(2) [(2) (1) (2)])
1476 @defun remove object sequence
1477 This function is the non-destructive counterpart of @code{delete}. If
1478 returns a copy of @code{sequence}, a list, vector, or string, with
1479 elements @code{equal} to @code{object} removed. For example:
1483 (remove '(2) '((2) (1) (2)))
1487 (remove '(2) [(2) (1) (2)])
1494 @b{Common Lisp note:} The functions @code{member}, @code{delete} and
1495 @code{remove} in GNU Emacs Lisp are derived from Maclisp, not Common
1496 Lisp. The Common Lisp versions do not use @code{equal} to compare
1500 @defun member-ignore-case object list
1501 This function is like @code{member}, except that @var{object} should
1502 be a string and that it ignores differences in letter-case and text
1503 representation: upper-case and lower-case letters are treated as
1504 equal, and unibyte strings are converted to multibyte prior to
1508 @defun delete-dups list
1509 This function destructively removes all @code{equal} duplicates from
1510 @var{list}, stores the result in @var{list} and returns it. Of
1511 several @code{equal} occurrences of an element in @var{list},
1512 @code{delete-dups} keeps the first one.
1515 See also the function @code{add-to-list}, in @ref{List Variables},
1516 for another way to add an element to a list stored in a variable.
1518 @node Association Lists
1519 @section Association Lists
1520 @cindex association list
1523 An @dfn{association list}, or @dfn{alist} for short, records a mapping
1524 from keys to values. It is a list of cons cells called
1525 @dfn{associations}: the @sc{car} of each cons cell is the @dfn{key}, and the
1526 @sc{cdr} is the @dfn{associated value}.@footnote{This usage of ``key''
1527 is not related to the term ``key sequence''; it means a value used to
1528 look up an item in a table. In this case, the table is the alist, and
1529 the alist associations are the items.}
1531 Here is an example of an alist. The key @code{pine} is associated with
1532 the value @code{cones}; the key @code{oak} is associated with
1533 @code{acorns}; and the key @code{maple} is associated with @code{seeds}.
1543 Both the values and the keys in an alist may be any Lisp objects.
1544 For example, in the following alist, the symbol @code{a} is
1545 associated with the number @code{1}, and the string @code{"b"} is
1546 associated with the @emph{list} @code{(2 3)}, which is the @sc{cdr} of
1553 Sometimes it is better to design an alist to store the associated
1554 value in the @sc{car} of the @sc{cdr} of the element. Here is an
1555 example of such an alist:
1558 ((rose red) (lily white) (buttercup yellow))
1562 Here we regard @code{red} as the value associated with @code{rose}. One
1563 advantage of this kind of alist is that you can store other related
1564 information---even a list of other items---in the @sc{cdr} of the
1565 @sc{cdr}. One disadvantage is that you cannot use @code{rassq} (see
1566 below) to find the element containing a given value. When neither of
1567 these considerations is important, the choice is a matter of taste, as
1568 long as you are consistent about it for any given alist.
1570 The same alist shown above could be regarded as having the
1571 associated value in the @sc{cdr} of the element; the value associated
1572 with @code{rose} would be the list @code{(red)}.
1574 Association lists are often used to record information that you might
1575 otherwise keep on a stack, since new associations may be added easily to
1576 the front of the list. When searching an association list for an
1577 association with a given key, the first one found is returned, if there
1580 In Emacs Lisp, it is @emph{not} an error if an element of an
1581 association list is not a cons cell. The alist search functions simply
1582 ignore such elements. Many other versions of Lisp signal errors in such
1585 Note that property lists are similar to association lists in several
1586 respects. A property list behaves like an association list in which
1587 each key can occur only once. @xref{Property Lists}, for a comparison
1588 of property lists and association lists.
1590 @defun assoc key alist
1591 This function returns the first association for @var{key} in
1592 @var{alist}. It compares @var{key} against the alist elements using
1593 @code{equal} (@pxref{Equality Predicates}). It returns @code{nil} if no
1594 association in @var{alist} has a @sc{car} @code{equal} to @var{key}.
1598 (setq trees '((pine . cones) (oak . acorns) (maple . seeds)))
1599 @result{} ((pine . cones) (oak . acorns) (maple . seeds))
1601 @result{} (oak . acorns)
1602 (cdr (assoc 'oak trees))
1604 (assoc 'birch trees)
1608 Here is another example, in which the keys and values are not symbols:
1611 (setq needles-per-cluster
1612 '((2 "Austrian Pine" "Red Pine")
1616 (cdr (assoc 3 needles-per-cluster))
1617 @result{} ("Pitch Pine")
1618 (cdr (assoc 2 needles-per-cluster))
1619 @result{} ("Austrian Pine" "Red Pine")
1623 The function @code{assoc-string} is much like @code{assoc} except
1624 that it ignores certain differences between strings. @xref{Text
1627 @defun rassoc value alist
1628 This function returns the first association with value @var{value} in
1629 @var{alist}. It returns @code{nil} if no association in @var{alist} has
1630 a @sc{cdr} @code{equal} to @var{value}.
1632 @code{rassoc} is like @code{assoc} except that it compares the @sc{cdr} of
1633 each @var{alist} association instead of the @sc{car}. You can think of
1634 this as ``reverse @code{assoc},'' finding the key for a given value.
1637 @defun assq key alist
1638 This function is like @code{assoc} in that it returns the first
1639 association for @var{key} in @var{alist}, but it makes the comparison
1640 using @code{eq} instead of @code{equal}. @code{assq} returns @code{nil}
1641 if no association in @var{alist} has a @sc{car} @code{eq} to @var{key}.
1642 This function is used more often than @code{assoc}, since @code{eq} is
1643 faster than @code{equal} and most alists use symbols as keys.
1644 @xref{Equality Predicates}.
1647 (setq trees '((pine . cones) (oak . acorns) (maple . seeds)))
1648 @result{} ((pine . cones) (oak . acorns) (maple . seeds))
1650 @result{} (pine . cones)
1653 On the other hand, @code{assq} is not usually useful in alists where the
1654 keys may not be symbols:
1658 '(("simple leaves" . oak)
1659 ("compound leaves" . horsechestnut)))
1661 (assq "simple leaves" leaves)
1663 (assoc "simple leaves" leaves)
1664 @result{} ("simple leaves" . oak)
1668 @defun rassq value alist
1669 This function returns the first association with value @var{value} in
1670 @var{alist}. It returns @code{nil} if no association in @var{alist} has
1671 a @sc{cdr} @code{eq} to @var{value}.
1673 @code{rassq} is like @code{assq} except that it compares the @sc{cdr} of
1674 each @var{alist} association instead of the @sc{car}. You can think of
1675 this as ``reverse @code{assq},'' finding the key for a given value.
1680 (setq trees '((pine . cones) (oak . acorns) (maple . seeds)))
1682 (rassq 'acorns trees)
1683 @result{} (oak . acorns)
1684 (rassq 'spores trees)
1688 @code{rassq} cannot search for a value stored in the @sc{car}
1689 of the @sc{cdr} of an element:
1692 (setq colors '((rose red) (lily white) (buttercup yellow)))
1694 (rassq 'white colors)
1698 In this case, the @sc{cdr} of the association @code{(lily white)} is not
1699 the symbol @code{white}, but rather the list @code{(white)}. This
1700 becomes clearer if the association is written in dotted pair notation:
1703 (lily white) @equiv{} (lily . (white))
1707 @defun assoc-default key alist &optional test default
1708 This function searches @var{alist} for a match for @var{key}. For each
1709 element of @var{alist}, it compares the element (if it is an atom) or
1710 the element's @sc{car} (if it is a cons) against @var{key}, by calling
1711 @var{test} with two arguments: the element or its @sc{car}, and
1712 @var{key}. The arguments are passed in that order so that you can get
1713 useful results using @code{string-match} with an alist that contains
1714 regular expressions (@pxref{Regexp Search}). If @var{test} is omitted
1715 or @code{nil}, @code{equal} is used for comparison.
1717 If an alist element matches @var{key} by this criterion,
1718 then @code{assoc-default} returns a value based on this element.
1719 If the element is a cons, then the value is the element's @sc{cdr}.
1720 Otherwise, the return value is @var{default}.
1722 If no alist element matches @var{key}, @code{assoc-default} returns
1726 @defun copy-alist alist
1727 @cindex copying alists
1728 This function returns a two-level deep copy of @var{alist}: it creates a
1729 new copy of each association, so that you can alter the associations of
1730 the new alist without changing the old one.
1734 (setq needles-per-cluster
1735 '((2 . ("Austrian Pine" "Red Pine"))
1736 (3 . ("Pitch Pine"))
1738 (5 . ("White Pine"))))
1740 ((2 "Austrian Pine" "Red Pine")
1744 (setq copy (copy-alist needles-per-cluster))
1746 ((2 "Austrian Pine" "Red Pine")
1750 (eq needles-per-cluster copy)
1752 (equal needles-per-cluster copy)
1754 (eq (car needles-per-cluster) (car copy))
1756 (cdr (car (cdr needles-per-cluster)))
1757 @result{} ("Pitch Pine")
1759 (eq (cdr (car (cdr needles-per-cluster)))
1760 (cdr (car (cdr copy))))
1765 This example shows how @code{copy-alist} makes it possible to change
1766 the associations of one copy without affecting the other:
1770 (setcdr (assq 3 copy) '("Martian Vacuum Pine"))
1771 (cdr (assq 3 needles-per-cluster))
1772 @result{} ("Pitch Pine")
1777 @defun assq-delete-all key alist
1778 This function deletes from @var{alist} all the elements whose @sc{car}
1779 is @code{eq} to @var{key}, much as if you used @code{delq} to delete
1780 each such element one by one. It returns the shortened alist, and
1781 often modifies the original list structure of @var{alist}. For
1782 correct results, use the return value of @code{assq-delete-all} rather
1783 than looking at the saved value of @var{alist}.
1786 (setq alist '((foo 1) (bar 2) (foo 3) (lose 4)))
1787 @result{} ((foo 1) (bar 2) (foo 3) (lose 4))
1788 (assq-delete-all 'foo alist)
1789 @result{} ((bar 2) (lose 4))
1791 @result{} ((foo 1) (bar 2) (lose 4))
1795 @defun rassq-delete-all value alist
1796 This function deletes from @var{alist} all the elements whose @sc{cdr}
1797 is @code{eq} to @var{value}. It returns the shortened alist, and
1798 often modifies the original list structure of @var{alist}.
1799 @code{rassq-delete-all} is like @code{assq-delete-all} except that it
1800 compares the @sc{cdr} of each @var{alist} association instead of the
1805 @section Managing a Fixed-Size Ring of Objects
1807 @cindex ring data structure
1808 This section describes functions for operating on rings. A
1809 @dfn{ring} is a fixed-size data structure that supports insertion,
1810 deletion, rotation, and modulo-indexed reference and traversal.
1812 @defun make-ring size
1813 This returns a new ring capable of holding @var{size} objects.
1814 @var{size} should be an integer.
1817 @defun ring-p object
1818 This returns @code{t} if @var{object} is a ring, @code{nil} otherwise.
1821 @defun ring-size ring
1822 This returns the maximum capacity of the @var{ring}.
1825 @defun ring-length ring
1826 This returns the number of objects that @var{ring} currently contains.
1827 The value will never exceed that returned by @code{ring-size}.
1830 @defun ring-elements ring
1831 This returns a list of the objects in @var{ring}, in order, newest first.
1834 @defun ring-copy ring
1835 This returns a new ring which is a copy of @var{ring}.
1836 The new ring contains the same (@code{eq}) objects as @var{ring}.
1839 @defun ring-empty-p ring
1840 This returns @code{t} if @var{ring} is empty, @code{nil} otherwise.
1843 The newest element in the ring always has index 0. Higher indices
1844 correspond to older elements. Indices are computed modulo the ring
1845 length. Index @minus{}1 corresponds to the oldest element, @minus{}2
1846 to the next-oldest, and so forth.
1848 @defun ring-ref ring index
1849 This returns the object in @var{ring} found at index @var{index}.
1850 @var{index} may be negative or greater than the ring length. If
1851 @var{ring} is empty, @code{ring-ref} signals an error.
1854 @defun ring-insert ring object
1855 This inserts @var{object} into @var{ring}, making it the newest
1856 element, and returns @var{object}.
1858 If the ring is full, insertion removes the oldest element to
1859 make room for the new element.
1862 @defun ring-remove ring &optional index
1863 Remove an object from @var{ring}, and return that object. The
1864 argument @var{index} specifies which item to remove; if it is
1865 @code{nil}, that means to remove the oldest item. If @var{ring} is
1866 empty, @code{ring-remove} signals an error.
1869 @defun ring-insert-at-beginning ring object
1870 This inserts @var{object} into @var{ring}, treating it as the oldest
1871 element. The return value is not significant.
1873 If the ring is full, this function removes the newest element to make
1874 room for the inserted element.
1877 @cindex fifo data structure
1878 If you are careful not to exceed the ring size, you can
1879 use the ring as a first-in-first-out queue. For example:
1882 (let ((fifo (make-ring 5)))
1883 (mapc (lambda (obj) (ring-insert fifo obj))
1885 (list (ring-remove fifo) t
1886 (ring-remove fifo) t
1887 (ring-remove fifo)))
1888 @result{} (0 t one t "two")
1892 arch-tag: 31fb8a4e-4aa8-4a74-a206-aa00451394d4