2 @c This is part of the GNU Emacs Lisp Reference Manual.
3 @c Copyright (C) 1990, 1991, 1992, 1993, 1994, 1995, 1998, 1999,
5 @c Free Software Foundation, Inc.
6 @c See the file elisp.texi for copying conditions.
7 @setfilename ../info/lists
8 @node Lists, Sequences Arrays Vectors, Strings and Characters, Top
11 @cindex element (of list)
13 A @dfn{list} represents a sequence of zero or more elements (which may
14 be any Lisp objects). The important difference between lists and
15 vectors is that two or more lists can share part of their structure; in
16 addition, you can insert or delete elements in a list without copying
20 * Cons Cells:: How lists are made out of cons cells.
21 * List-related Predicates:: Is this object a list? Comparing two lists.
22 * List Elements:: Extracting the pieces of a list.
23 * Building Lists:: Creating list structure.
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 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}))
251 This macro is a way of examining the @sc{car} of a list,
252 and taking it off the list, all at once.
254 It operates on the list which is stored in the symbol @var{listname}.
255 It removes this element from the list by setting @var{listname}
256 to the @sc{cdr} of its old value---but it also returns the @sc{car}
257 of that list, which is the element being removed.
270 @anchor{Definition of nth}
271 This function returns the @var{n}th element of @var{list}. Elements
272 are numbered starting with zero, so the @sc{car} of @var{list} is
273 element number zero. If the length of @var{list} is @var{n} or less,
274 the value is @code{nil}.
276 If @var{n} is negative, @code{nth} returns the first element of
292 (nth n x) @equiv{} (car (nthcdr n x))
296 The function @code{elt} is similar, but applies to any kind of sequence.
297 For historical reasons, it takes its arguments in the opposite order.
298 @xref{Sequence Functions}.
302 This function returns the @var{n}th @sc{cdr} of @var{list}. In other
303 words, it skips past the first @var{n} links of @var{list} and returns
306 If @var{n} is zero or negative, @code{nthcdr} returns all of
307 @var{list}. If the length of @var{list} is @var{n} or less,
308 @code{nthcdr} returns @code{nil}.
312 (nthcdr 1 '(1 2 3 4))
316 (nthcdr 10 '(1 2 3 4))
320 (nthcdr -3 '(1 2 3 4))
326 @defun last list &optional n
327 This function returns the last link of @var{list}. The @code{car} of
328 this link is the list's last element. If @var{list} is null,
329 @code{nil} is returned. If @var{n} is non-@code{nil}, the
330 @var{n}th-to-last link is returned instead, or the whole of @var{list}
331 if @var{n} is bigger than @var{list}'s length.
334 @defun safe-length list
335 @anchor{Definition of safe-length}
336 This function returns the length of @var{list}, with no risk of either
337 an error or an infinite loop. It generally returns the number of
338 distinct cons cells in the list. However, for circular lists,
339 the value is just an upper bound; it is often too large.
341 If @var{list} is not @code{nil} or a cons cell, @code{safe-length}
345 The most common way to compute the length of a list, when you are not
346 worried that it may be circular, is with @code{length}. @xref{Sequence
349 @defun caar cons-cell
350 This is the same as @code{(car (car @var{cons-cell}))}.
353 @defun cadr cons-cell
354 This is the same as @code{(car (cdr @var{cons-cell}))}
355 or @code{(nth 1 @var{cons-cell})}.
358 @defun cdar cons-cell
359 This is the same as @code{(cdr (car @var{cons-cell}))}.
362 @defun cddr cons-cell
363 This is the same as @code{(cdr (cdr @var{cons-cell}))}
364 or @code{(nthcdr 2 @var{cons-cell})}.
367 @defun butlast x &optional n
368 This function returns the list @var{x} with the last element,
369 or the last @var{n} elements, removed. If @var{n} is greater
370 than zero it makes a copy of the list so as not to damage the
371 original list. In general, @code{(append (butlast @var{x} @var{n})
372 (last @var{x} @var{n}))} will return a list equal to @var{x}.
375 @defun nbutlast x &optional n
376 This is a version of @code{butlast} that works by destructively
377 modifying the @code{cdr} of the appropriate element, rather than
378 making a copy of the list.
382 @comment node-name, next, previous, up
383 @section Building Cons Cells and Lists
385 @cindex building lists
387 Many functions build lists, as lists reside at the very heart of Lisp.
388 @code{cons} is the fundamental list-building function; however, it is
389 interesting to note that @code{list} is used more times in the source
390 code for Emacs than @code{cons}.
392 @defun cons object1 object2
393 This function is the most basic function for building new list
394 structure. It creates a new cons cell, making @var{object1} the
395 @sc{car}, and @var{object2} the @sc{cdr}. It then returns the new
396 cons cell. The arguments @var{object1} and @var{object2} may be any
397 Lisp objects, but most often @var{object2} is a list.
415 @code{cons} is often used to add a single element to the front of a
416 list. This is called @dfn{consing the element onto the list}.
417 @footnote{There is no strictly equivalent way to add an element to
418 the end of a list. You can use @code{(append @var{listname} (list
419 @var{newelt}))}, which creates a whole new list by copying @var{listname}
420 and adding @var{newelt} to its end. Or you can use @code{(nconc
421 @var{listname} (list @var{newelt}))}, which modifies @var{listname}
422 by following all the @sc{cdr}s and then replacing the terminating
423 @code{nil}. Compare this to adding an element to the beginning of a
424 list with @code{cons}, which neither copies nor modifies the list.}
428 (setq list (cons newelt list))
431 Note that there is no conflict between the variable named @code{list}
432 used in this example and the function named @code{list} described below;
433 any symbol can serve both purposes.
437 @defmac push newelt listname
438 This macro provides an alternative way to write
439 @code{(setq @var{listname} (cons @var{newelt} @var{listname}))}.
451 @defun list &rest objects
452 This function creates a list with @var{objects} as its elements. The
453 resulting list is always @code{nil}-terminated. If no @var{objects}
454 are given, the empty list is returned.
459 @result{} (1 2 3 4 5)
462 (list 1 2 '(3 4 5) 'foo)
463 @result{} (1 2 (3 4 5) foo)
472 @defun make-list length object
473 This function creates a list of @var{length} elements, in which each
474 element is @var{object}. Compare @code{make-list} with
475 @code{make-string} (@pxref{Creating Strings}).
480 @result{} (pigs pigs pigs)
487 (setq l (make-list 3 '(a b))
488 @result{} ((a b) (a b) (a b))
489 (eq (car l) (cadr l))
495 @defun append &rest sequences
496 @cindex copying lists
497 This function returns a list containing all the elements of
498 @var{sequences}. The @var{sequences} may be lists, vectors,
499 bool-vectors, or strings, but the last one should usually be a list.
500 All arguments except the last one are copied, so none of the arguments
501 is altered. (See @code{nconc} in @ref{Rearrangement}, for a way to join
502 lists with no copying.)
504 More generally, the final argument to @code{append} may be any Lisp
505 object. The final argument is not copied or converted; it becomes the
506 @sc{cdr} of the last cons cell in the new list. If the final argument
507 is itself a list, then its elements become in effect elements of the
508 result list. If the final element is not a list, the result is a
509 dotted list since its final @sc{cdr} is not @code{nil} as required
512 In Emacs 20 and before, the @code{append} function also allowed
513 integers as (non last) arguments. It converted them to strings of
514 digits, making up the decimal print representation of the integer, and
515 then used the strings instead of the original integers. This obsolete
516 usage no longer works. The proper way to convert an integer to a
517 decimal number in this way is with @code{format} (@pxref{Formatting
518 Strings}) or @code{number-to-string} (@pxref{String Conversion}).
521 Here is an example of using @code{append}:
525 (setq trees '(pine oak))
527 (setq more-trees (append '(maple birch) trees))
528 @result{} (maple birch pine oak)
535 @result{} (maple birch pine oak)
538 (eq trees (cdr (cdr more-trees)))
543 You can see how @code{append} works by looking at a box diagram. The
544 variable @code{trees} is set to the list @code{(pine oak)} and then the
545 variable @code{more-trees} is set to the list @code{(maple birch pine
546 oak)}. However, the variable @code{trees} continues to refer to the
553 | --- --- --- --- -> --- --- --- ---
554 --> | | |--> | | |--> | | |--> | | |--> nil
555 --- --- --- --- --- --- --- ---
558 --> maple -->birch --> pine --> oak
562 An empty sequence contributes nothing to the value returned by
563 @code{append}. As a consequence of this, a final @code{nil} argument
564 forces a copy of the previous argument:
572 (setq wood (append trees nil))
586 This once was the usual way to copy a list, before the function
587 @code{copy-sequence} was invented. @xref{Sequences Arrays Vectors}.
589 Here we show the use of vectors and strings as arguments to @code{append}:
593 (append [a b] "cd" nil)
594 @result{} (a b 99 100)
598 With the help of @code{apply} (@pxref{Calling Functions}), we can append
599 all the lists in a list of lists:
603 (apply 'append '((a b c) nil (x y z) nil))
604 @result{} (a b c x y z)
608 If no @var{sequences} are given, @code{nil} is returned:
617 Here are some examples where the final argument is not a list:
623 @result{} (x y . [z])
627 The second example shows that when the final argument is a sequence but
628 not a list, the sequence's elements do not become elements of the
629 resulting list. Instead, the sequence becomes the final @sc{cdr}, like
630 any other non-list final argument.
633 This function creates a new list whose elements are the elements of
634 @var{list}, but in reverse order. The original argument @var{list} is
651 @defun copy-tree tree &optional vecp
652 This function returns a copy of the tree @code{tree}. If @var{tree} is a
653 cons cell, this makes a new cons cell with the same @sc{car} and
654 @sc{cdr}, then recursively copies the @sc{car} and @sc{cdr} in the
657 Normally, when @var{tree} is anything other than a cons cell,
658 @code{copy-tree} simply returns @var{tree}. However, if @var{vecp} is
659 non-@code{nil}, it copies vectors too (and operates recursively on
663 @defun number-sequence from &optional to separation
664 This returns a list of numbers starting with @var{from} and
665 incrementing by @var{separation}, and ending at or just before
666 @var{to}. @var{separation} can be positive or negative and defaults
667 to 1. If @var{to} is @code{nil} or numerically equal to @var{from},
668 the value is the one-element list @code{(@var{from})}. If @var{to} is
669 less than @var{from} with a positive @var{separation}, or greater than
670 @var{from} with a negative @var{separation}, the value is @code{nil}
671 because those arguments specify an empty sequence.
673 If @var{separation} is 0 and @var{to} is neither @code{nil} nor
674 numerically equal to @var{from}, @code{number-sequence} signals an
675 error, since those arguments specify an infinite sequence.
677 All arguments can be integers or floating point numbers. However,
678 floating point arguments can be tricky, because floating point
679 arithmetic is inexact. For instance, depending on the machine, it may
680 quite well happen that @code{(number-sequence 0.4 0.6 0.2)} returns
681 the one element list @code{(0.4)}, whereas
682 @code{(number-sequence 0.4 0.8 0.2)} returns a list with three
683 elements. The @var{n}th element of the list is computed by the exact
684 formula @code{(+ @var{from} (* @var{n} @var{separation}))}. Thus, if
685 one wants to make sure that @var{to} is included in the list, one can
686 pass an expression of this exact type for @var{to}. Alternatively,
687 one can replace @var{to} with a slightly larger value (or a slightly
688 more negative value if @var{separation} is negative).
693 (number-sequence 4 9)
694 @result{} (4 5 6 7 8 9)
695 (number-sequence 9 4 -1)
696 @result{} (9 8 7 6 5 4)
697 (number-sequence 9 4 -2)
701 (number-sequence 8 5)
703 (number-sequence 5 8 -1)
705 (number-sequence 1.5 6 2)
706 @result{} (1.5 3.5 5.5)
710 @node Modifying Lists
711 @section Modifying Existing List Structure
712 @cindex destructive list operations
714 You can modify the @sc{car} and @sc{cdr} contents of a cons cell with the
715 primitives @code{setcar} and @code{setcdr}. We call these ``destructive''
716 operations because they change existing list structure.
718 @cindex CL note---@code{rplaca} vs @code{setcar}
722 @b{Common Lisp note:} Common Lisp uses functions @code{rplaca} and
723 @code{rplacd} to alter list structure; they change structure the same
724 way as @code{setcar} and @code{setcdr}, but the Common Lisp functions
725 return the cons cell while @code{setcar} and @code{setcdr} return the
726 new @sc{car} or @sc{cdr}.
730 * Setcar:: Replacing an element in a list.
731 * Setcdr:: Replacing part of the list backbone.
732 This can be used to remove or add elements.
733 * Rearrangement:: Reordering the elements in a list; combining lists.
737 @subsection Altering List Elements with @code{setcar}
739 Changing the @sc{car} of a cons cell is done with @code{setcar}. When
740 used on a list, @code{setcar} replaces one element of a list with a
743 @defun setcar cons object
744 This function stores @var{object} as the new @sc{car} of @var{cons},
745 replacing its previous @sc{car}. In other words, it changes the
746 @sc{car} slot of @var{cons} to refer to @var{object}. It returns the
747 value @var{object}. For example:
765 When a cons cell is part of the shared structure of several lists,
766 storing a new @sc{car} into the cons changes one element of each of
767 these lists. Here is an example:
771 ;; @r{Create two lists that are partly shared.}
774 (setq x2 (cons 'z (cdr x1)))
779 ;; @r{Replace the @sc{car} of a shared link.}
780 (setcar (cdr x1) 'foo)
782 x1 ; @r{Both lists are changed.}
789 ;; @r{Replace the @sc{car} of a link that is not shared.}
792 x1 ; @r{Only one list is changed.}
793 @result{} (baz foo c)
799 Here is a graphical depiction of the shared structure of the two lists
800 in the variables @code{x1} and @code{x2}, showing why replacing @code{b}
805 --- --- --- --- --- ---
806 x1---> | | |----> | | |--> | | |--> nil
807 --- --- --- --- --- ---
821 Here is an alternative form of box diagram, showing the same relationship:
826 -------------- -------------- --------------
827 | car | cdr | | car | cdr | | car | cdr |
828 | a | o------->| b | o------->| c | nil |
830 -------------- | -------------- --------------
842 @subsection Altering the CDR of a List
844 The lowest-level primitive for modifying a @sc{cdr} is @code{setcdr}:
846 @defun setcdr cons object
847 This function stores @var{object} as the new @sc{cdr} of @var{cons},
848 replacing its previous @sc{cdr}. In other words, it changes the
849 @sc{cdr} slot of @var{cons} to refer to @var{object}. It returns the
853 Here is an example of replacing the @sc{cdr} of a list with a
854 different list. All but the first element of the list are removed in
855 favor of a different sequence of elements. The first element is
856 unchanged, because it resides in the @sc{car} of the list, and is not
857 reached via the @sc{cdr}.
874 You can delete elements from the middle of a list by altering the
875 @sc{cdr}s of the cons cells in the list. For example, here we delete
876 the second element, @code{b}, from the list @code{(a b c)}, by changing
877 the @sc{cdr} of the first cons cell:
883 (setcdr x1 (cdr (cdr x1)))
891 Here is the result in box notation:
897 -------------- | -------------- | --------------
898 | car | cdr | | | car | cdr | -->| car | cdr |
899 | a | o----- | b | o-------->| c | nil |
901 -------------- -------------- --------------
906 The second cons cell, which previously held the element @code{b}, still
907 exists and its @sc{car} is still @code{b}, but it no longer forms part
910 It is equally easy to insert a new element by changing @sc{cdr}s:
916 (setcdr x1 (cons 'd (cdr x1)))
923 Here is this result in box notation:
927 -------------- ------------- -------------
928 | car | cdr | | car | cdr | | car | cdr |
929 | a | o | -->| b | o------->| c | nil |
930 | | | | | | | | | | |
931 --------- | -- | ------------- -------------
944 @subsection Functions that Rearrange Lists
945 @cindex rearrangement of lists
946 @cindex modification of lists
948 Here are some functions that rearrange lists ``destructively'' by
949 modifying the @sc{cdr}s of their component cons cells. We call these
950 functions ``destructive'' because they chew up the original lists passed
951 to them as arguments, relinking their cons cells to form a new list that
952 is the returned value.
955 See @code{delq}, in @ref{Sets And Lists}, for another function
956 that modifies cons cells.
959 The function @code{delq} in the following section is another example
960 of destructive list manipulation.
963 @defun nconc &rest lists
964 @cindex concatenating lists
965 @cindex joining lists
966 This function returns a list containing all the elements of @var{lists}.
967 Unlike @code{append} (@pxref{Building Lists}), the @var{lists} are
968 @emph{not} copied. Instead, the last @sc{cdr} of each of the
969 @var{lists} is changed to refer to the following list. The last of the
970 @var{lists} is not altered. For example:
979 @result{} (1 2 3 4 5)
983 @result{} (1 2 3 4 5)
987 Since the last argument of @code{nconc} is not itself modified, it is
988 reasonable to use a constant list, such as @code{'(4 5)}, as in the
989 above example. For the same reason, the last argument need not be a
999 @result{} (1 2 3 . z)
1003 @result{} (1 2 3 . z)
1007 However, the other arguments (all but the last) must be lists.
1009 A common pitfall is to use a quoted constant list as a non-last
1010 argument to @code{nconc}. If you do this, your program will change
1011 each time you run it! Here is what happens:
1015 (defun add-foo (x) ; @r{We want this function to add}
1016 (nconc '(foo) x)) ; @r{@code{foo} to the front of its arg.}
1020 (symbol-function 'add-foo)
1021 @result{} (lambda (x) (nconc (quote (foo)) x))
1025 (setq xx (add-foo '(1 2))) ; @r{It seems to work.}
1029 (setq xy (add-foo '(3 4))) ; @r{What happened?}
1030 @result{} (foo 1 2 3 4)
1038 (symbol-function 'add-foo)
1039 @result{} (lambda (x) (nconc (quote (foo 1 2 3 4) x)))
1044 @defun nreverse list
1045 @cindex reversing a list
1046 This function reverses the order of the elements of @var{list}.
1047 Unlike @code{reverse}, @code{nreverse} alters its argument by reversing
1048 the @sc{cdr}s in the cons cells forming the list. The cons cell that
1049 used to be the last one in @var{list} becomes the first cons cell of the
1066 ;; @r{The cons cell that was first is now last.}
1072 To avoid confusion, we usually store the result of @code{nreverse}
1073 back in the same variable which held the original list:
1076 (setq x (nreverse x))
1079 Here is the @code{nreverse} of our favorite example, @code{(a b c)},
1080 presented graphically:
1084 @r{Original list head:} @r{Reversed list:}
1085 ------------- ------------- ------------
1086 | car | cdr | | car | cdr | | car | cdr |
1087 | a | nil |<-- | b | o |<-- | c | o |
1088 | | | | | | | | | | | | |
1089 ------------- | --------- | - | -------- | -
1091 ------------- ------------
1096 @defun sort list predicate
1098 @cindex sorting lists
1099 This function sorts @var{list} stably, though destructively, and
1100 returns the sorted list. It compares elements using @var{predicate}. A
1101 stable sort is one in which elements with equal sort keys maintain their
1102 relative order before and after the sort. Stability is important when
1103 successive sorts are used to order elements according to different
1106 The argument @var{predicate} must be a function that accepts two
1107 arguments. It is called with two elements of @var{list}. To get an
1108 increasing order sort, the @var{predicate} should return non-@code{nil} if the
1109 first element is ``less than'' the second, or @code{nil} if not.
1111 The comparison function @var{predicate} must give reliable results for
1112 any given pair of arguments, at least within a single call to
1113 @code{sort}. It must be @dfn{antisymmetric}; that is, if @var{a} is
1114 less than @var{b}, @var{b} must not be less than @var{a}. It must be
1115 @dfn{transitive}---that is, if @var{a} is less than @var{b}, and @var{b}
1116 is less than @var{c}, then @var{a} must be less than @var{c}. If you
1117 use a comparison function which does not meet these requirements, the
1118 result of @code{sort} is unpredictable.
1120 The destructive aspect of @code{sort} is that it rearranges the cons
1121 cells forming @var{list} by changing @sc{cdr}s. A nondestructive sort
1122 function would create new cons cells to store the elements in their
1123 sorted order. If you wish to make a sorted copy without destroying the
1124 original, copy it first with @code{copy-sequence} and then sort.
1126 Sorting does not change the @sc{car}s of the cons cells in @var{list};
1127 the cons cell that originally contained the element @code{a} in
1128 @var{list} still has @code{a} in its @sc{car} after sorting, but it now
1129 appears in a different position in the list due to the change of
1130 @sc{cdr}s. For example:
1134 (setq nums '(1 3 2 6 5 4 0))
1135 @result{} (1 3 2 6 5 4 0)
1139 @result{} (0 1 2 3 4 5 6)
1143 @result{} (1 2 3 4 5 6)
1148 @strong{Warning}: Note that the list in @code{nums} no longer contains
1149 0; this is the same cons cell that it was before, but it is no longer
1150 the first one in the list. Don't assume a variable that formerly held
1151 the argument now holds the entire sorted list! Instead, save the result
1152 of @code{sort} and use that. Most often we store the result back into
1153 the variable that held the original list:
1156 (setq nums (sort nums '<))
1159 @xref{Sorting}, for more functions that perform sorting.
1160 See @code{documentation} in @ref{Accessing Documentation}, for a
1161 useful example of @code{sort}.
1164 @node Sets And Lists
1165 @section Using Lists as Sets
1166 @cindex lists as sets
1169 A list can represent an unordered mathematical set---simply consider a
1170 value an element of a set if it appears in the list, and ignore the
1171 order of the list. To form the union of two sets, use @code{append} (as
1172 long as you don't mind having duplicate elements). You can remove
1173 @code{equal} duplicates using @code{delete-dups}. Other useful
1174 functions for sets include @code{memq} and @code{delq}, and their
1175 @code{equal} versions, @code{member} and @code{delete}.
1177 @cindex CL note---lack @code{union}, @code{intersection}
1179 @b{Common Lisp note:} Common Lisp has functions @code{union} (which
1180 avoids duplicate elements) and @code{intersection} for set operations,
1181 but GNU Emacs Lisp does not have them. You can write them in Lisp if
1185 @defun memq object list
1186 @cindex membership in a list
1187 This function tests to see whether @var{object} is a member of
1188 @var{list}. If it is, @code{memq} returns a list starting with the
1189 first occurrence of @var{object}. Otherwise, it returns @code{nil}.
1190 The letter @samp{q} in @code{memq} says that it uses @code{eq} to
1191 compare @var{object} against the elements of the list. For example:
1195 (memq 'b '(a b c b a))
1199 (memq '(2) '((1) (2))) ; @r{@code{(2)} and @code{(2)} are not @code{eq}.}
1205 @defun delq object list
1206 @cindex deletion of elements
1207 This function destructively removes all elements @code{eq} to
1208 @var{object} from @var{list}. The letter @samp{q} in @code{delq} says
1209 that it uses @code{eq} to compare @var{object} against the elements of
1210 the list, like @code{memq} and @code{remq}.
1213 When @code{delq} deletes elements from the front of the list, it does so
1214 simply by advancing down the list and returning a sublist that starts
1215 after those elements:
1219 (delq 'a '(a b c)) @equiv{} (cdr '(a b c))
1223 When an element to be deleted appears in the middle of the list,
1224 removing it involves changing the @sc{cdr}s (@pxref{Setcdr}).
1228 (setq sample-list '(a b c (4)))
1229 @result{} (a b c (4))
1232 (delq 'a sample-list)
1237 @result{} (a b c (4))
1240 (delq 'c sample-list)
1249 Note that @code{(delq 'c sample-list)} modifies @code{sample-list} to
1250 splice out the third element, but @code{(delq 'a sample-list)} does not
1251 splice anything---it just returns a shorter list. Don't assume that a
1252 variable which formerly held the argument @var{list} now has fewer
1253 elements, or that it still holds the original list! Instead, save the
1254 result of @code{delq} and use that. Most often we store the result back
1255 into the variable that held the original list:
1258 (setq flowers (delq 'rose flowers))
1261 In the following example, the @code{(4)} that @code{delq} attempts to match
1262 and the @code{(4)} in the @code{sample-list} are not @code{eq}:
1266 (delq '(4) sample-list)
1271 @defun remq object list
1272 This function returns a copy of @var{list}, with all elements removed
1273 which are @code{eq} to @var{object}. The letter @samp{q} in @code{remq}
1274 says that it uses @code{eq} to compare @var{object} against the elements
1279 (setq sample-list '(a b c a b c))
1280 @result{} (a b c a b c)
1283 (remq 'a sample-list)
1288 @result{} (a b c a b c)
1292 The function @code{delq} offers a way to perform this operation
1293 destructively. See @ref{Sets And Lists}.
1296 The following three functions are like @code{memq}, @code{delq} and
1297 @code{remq}, but use @code{equal} rather than @code{eq} to compare
1298 elements. @xref{Equality Predicates}.
1300 @defun member object list
1301 The function @code{member} tests to see whether @var{object} is a member
1302 of @var{list}, comparing members with @var{object} using @code{equal}.
1303 If @var{object} is a member, @code{member} returns a list starting with
1304 its first occurrence in @var{list}. Otherwise, it returns @code{nil}.
1306 Compare this with @code{memq}:
1310 (member '(2) '((1) (2))) ; @r{@code{(2)} and @code{(2)} are @code{equal}.}
1314 (memq '(2) '((1) (2))) ; @r{@code{(2)} and @code{(2)} are not @code{eq}.}
1318 ;; @r{Two strings with the same contents are @code{equal}.}
1319 (member "foo" '("foo" "bar"))
1320 @result{} ("foo" "bar")
1325 @defun delete object sequence
1326 If @code{sequence} is a list, this function destructively removes all
1327 elements @code{equal} to @var{object} from @var{sequence}. For lists,
1328 @code{delete} is to @code{delq} as @code{member} is to @code{memq}: it
1329 uses @code{equal} to compare elements with @var{object}, like
1330 @code{member}; when it finds an element that matches, it removes the
1331 element just as @code{delq} would.
1333 If @code{sequence} is a vector or string, @code{delete} returns a copy
1334 of @code{sequence} with all elements @code{equal} to @code{object}
1341 (delete '(2) '((2) (1) (2)))
1345 (delete '(2) [(2) (1) (2)])
1351 @defun remove object sequence
1352 This function is the non-destructive counterpart of @code{delete}. If
1353 returns a copy of @code{sequence}, a list, vector, or string, with
1354 elements @code{equal} to @code{object} removed. For example:
1358 (remove '(2) '((2) (1) (2)))
1362 (remove '(2) [(2) (1) (2)])
1369 @b{Common Lisp note:} The functions @code{member}, @code{delete} and
1370 @code{remove} in GNU Emacs Lisp are derived from Maclisp, not Common
1371 Lisp. The Common Lisp versions do not use @code{equal} to compare
1375 @defun member-ignore-case object list
1376 This function is like @code{member}, except that @var{object} should
1377 be a string and that it ignores differences in letter-case and text
1378 representation: upper-case and lower-case letters are treated as
1379 equal, and unibyte strings are converted to multibyte prior to
1383 @defun delete-dups list
1384 This function destructively removes all @code{equal} duplicates from
1385 @var{list}, stores the result in @var{list} and returns it. Of
1386 several @code{equal} occurrences of an element in @var{list},
1387 @code{delete-dups} keeps the first one.
1390 See also the function @code{add-to-list}, in @ref{Setting Variables},
1391 for another way to add an element to a list stored in a variable.
1393 @node Association Lists
1394 @section Association Lists
1395 @cindex association list
1398 An @dfn{association list}, or @dfn{alist} for short, records a mapping
1399 from keys to values. It is a list of cons cells called
1400 @dfn{associations}: the @sc{car} of each cons cell is the @dfn{key}, and the
1401 @sc{cdr} is the @dfn{associated value}.@footnote{This usage of ``key''
1402 is not related to the term ``key sequence''; it means a value used to
1403 look up an item in a table. In this case, the table is the alist, and
1404 the alist associations are the items.}
1406 Here is an example of an alist. The key @code{pine} is associated with
1407 the value @code{cones}; the key @code{oak} is associated with
1408 @code{acorns}; and the key @code{maple} is associated with @code{seeds}.
1418 The associated values in an alist may be any Lisp objects; so may the
1419 keys. For example, in the following alist, the symbol @code{a} is
1420 associated with the number @code{1}, and the string @code{"b"} is
1421 associated with the @emph{list} @code{(2 3)}, which is the @sc{cdr} of
1428 Sometimes it is better to design an alist to store the associated
1429 value in the @sc{car} of the @sc{cdr} of the element. Here is an
1430 example of such an alist:
1433 ((rose red) (lily white) (buttercup yellow))
1437 Here we regard @code{red} as the value associated with @code{rose}. One
1438 advantage of this kind of alist is that you can store other related
1439 information---even a list of other items---in the @sc{cdr} of the
1440 @sc{cdr}. One disadvantage is that you cannot use @code{rassq} (see
1441 below) to find the element containing a given value. When neither of
1442 these considerations is important, the choice is a matter of taste, as
1443 long as you are consistent about it for any given alist.
1445 Note that the same alist shown above could be regarded as having the
1446 associated value in the @sc{cdr} of the element; the value associated
1447 with @code{rose} would be the list @code{(red)}.
1449 Association lists are often used to record information that you might
1450 otherwise keep on a stack, since new associations may be added easily to
1451 the front of the list. When searching an association list for an
1452 association with a given key, the first one found is returned, if there
1455 In Emacs Lisp, it is @emph{not} an error if an element of an
1456 association list is not a cons cell. The alist search functions simply
1457 ignore such elements. Many other versions of Lisp signal errors in such
1460 Note that property lists are similar to association lists in several
1461 respects. A property list behaves like an association list in which
1462 each key can occur only once. @xref{Property Lists}, for a comparison
1463 of property lists and association lists.
1465 @defun assoc key alist
1466 This function returns the first association for @var{key} in
1467 @var{alist}. It compares @var{key} against the alist elements using
1468 @code{equal} (@pxref{Equality Predicates}). It returns @code{nil} if no
1469 association in @var{alist} has a @sc{car} @code{equal} to @var{key}.
1473 (setq trees '((pine . cones) (oak . acorns) (maple . seeds)))
1474 @result{} ((pine . cones) (oak . acorns) (maple . seeds))
1476 @result{} (oak . acorns)
1477 (cdr (assoc 'oak trees))
1479 (assoc 'birch trees)
1483 Here is another example, in which the keys and values are not symbols:
1486 (setq needles-per-cluster
1487 '((2 "Austrian Pine" "Red Pine")
1491 (cdr (assoc 3 needles-per-cluster))
1492 @result{} ("Pitch Pine")
1493 (cdr (assoc 2 needles-per-cluster))
1494 @result{} ("Austrian Pine" "Red Pine")
1498 The function @code{assoc-string} is much like @code{assoc} except
1499 that it ignores certain differences between strings. @xref{Text
1502 @defun rassoc value alist
1503 This function returns the first association with value @var{value} in
1504 @var{alist}. It returns @code{nil} if no association in @var{alist} has
1505 a @sc{cdr} @code{equal} to @var{value}.
1507 @code{rassoc} is like @code{assoc} except that it compares the @sc{cdr} of
1508 each @var{alist} association instead of the @sc{car}. You can think of
1509 this as ``reverse @code{assoc}'', finding the key for a given value.
1512 @defun assq key alist
1513 This function is like @code{assoc} in that it returns the first
1514 association for @var{key} in @var{alist}, but it makes the comparison
1515 using @code{eq} instead of @code{equal}. @code{assq} returns @code{nil}
1516 if no association in @var{alist} has a @sc{car} @code{eq} to @var{key}.
1517 This function is used more often than @code{assoc}, since @code{eq} is
1518 faster than @code{equal} and most alists use symbols as keys.
1519 @xref{Equality Predicates}.
1522 (setq trees '((pine . cones) (oak . acorns) (maple . seeds)))
1523 @result{} ((pine . cones) (oak . acorns) (maple . seeds))
1525 @result{} (pine . cones)
1528 On the other hand, @code{assq} is not usually useful in alists where the
1529 keys may not be symbols:
1533 '(("simple leaves" . oak)
1534 ("compound leaves" . horsechestnut)))
1536 (assq "simple leaves" leaves)
1538 (assoc "simple leaves" leaves)
1539 @result{} ("simple leaves" . oak)
1543 @defun rassq value alist
1544 This function returns the first association with value @var{value} in
1545 @var{alist}. It returns @code{nil} if no association in @var{alist} has
1546 a @sc{cdr} @code{eq} to @var{value}.
1548 @code{rassq} is like @code{assq} except that it compares the @sc{cdr} of
1549 each @var{alist} association instead of the @sc{car}. You can think of
1550 this as ``reverse @code{assq}'', finding the key for a given value.
1555 (setq trees '((pine . cones) (oak . acorns) (maple . seeds)))
1557 (rassq 'acorns trees)
1558 @result{} (oak . acorns)
1559 (rassq 'spores trees)
1563 Note that @code{rassq} cannot search for a value stored in the @sc{car}
1564 of the @sc{cdr} of an element:
1567 (setq colors '((rose red) (lily white) (buttercup yellow)))
1569 (rassq 'white colors)
1573 In this case, the @sc{cdr} of the association @code{(lily white)} is not
1574 the symbol @code{white}, but rather the list @code{(white)}. This
1575 becomes clearer if the association is written in dotted pair notation:
1578 (lily white) @equiv{} (lily . (white))
1582 @defun assoc-default key alist &optional test default
1583 This function searches @var{alist} for a match for @var{key}. For each
1584 element of @var{alist}, it compares the element (if it is an atom) or
1585 the element's @sc{car} (if it is a cons) against @var{key}, by calling
1586 @var{test} with two arguments: the element or its @sc{car}, and
1587 @var{key}. The arguments are passed in that order so that you can get
1588 useful results using @code{string-match} with an alist that contains
1589 regular expressions (@pxref{Regexp Search}). If @var{test} is omitted
1590 or @code{nil}, @code{equal} is used for comparison.
1592 If an alist element matches @var{key} by this criterion,
1593 then @code{assoc-default} returns a value based on this element.
1594 If the element is a cons, then the value is the element's @sc{cdr}.
1595 Otherwise, the return value is @var{default}.
1597 If no alist element matches @var{key}, @code{assoc-default} returns
1601 @defun copy-alist alist
1602 @cindex copying alists
1603 This function returns a two-level deep copy of @var{alist}: it creates a
1604 new copy of each association, so that you can alter the associations of
1605 the new alist without changing the old one.
1609 (setq needles-per-cluster
1610 '((2 . ("Austrian Pine" "Red Pine"))
1611 (3 . ("Pitch Pine"))
1613 (5 . ("White Pine"))))
1615 ((2 "Austrian Pine" "Red Pine")
1619 (setq copy (copy-alist needles-per-cluster))
1621 ((2 "Austrian Pine" "Red Pine")
1625 (eq needles-per-cluster copy)
1627 (equal needles-per-cluster copy)
1629 (eq (car needles-per-cluster) (car copy))
1631 (cdr (car (cdr needles-per-cluster)))
1632 @result{} ("Pitch Pine")
1634 (eq (cdr (car (cdr needles-per-cluster)))
1635 (cdr (car (cdr copy))))
1640 This example shows how @code{copy-alist} makes it possible to change
1641 the associations of one copy without affecting the other:
1645 (setcdr (assq 3 copy) '("Martian Vacuum Pine"))
1646 (cdr (assq 3 needles-per-cluster))
1647 @result{} ("Pitch Pine")
1652 @defun assq-delete-all key alist
1653 @tindex assq-delete-all
1654 This function deletes from @var{alist} all the elements whose @sc{car}
1655 is @code{eq} to @var{key}, much as if you used @code{delq} to delete
1656 each such element one by one. It returns the shortened alist, and
1657 often modifies the original list structure of @var{alist}. For
1658 correct results, use the return value of @code{assq-delete-all} rather
1659 than looking at the saved value of @var{alist}.
1662 (setq alist '((foo 1) (bar 2) (foo 3) (lose 4)))
1663 @result{} ((foo 1) (bar 2) (foo 3) (lose 4))
1664 (assq-delete-all 'foo alist)
1665 @result{} ((bar 2) (lose 4))
1667 @result{} ((foo 1) (bar 2) (lose 4))
1671 @defun rassq-delete-all value alist
1672 This function deletes from @var{alist} all the elements whose @sc{cdr}
1673 is @code{eq} to @var{value}. It returns the shortened alist, and
1674 often modifies the original list structure of @var{alist}.
1675 @code{rassq-delete-all} is like @code{assq-delete-all} except that it
1676 compares the @sc{cdr} of each @var{alist} association instead of the
1681 @section Managing a Fixed-Size Ring of Objects
1683 @cindex ring data structure
1684 This section describes functions for operating on rings. A
1685 @dfn{ring} is a fixed-size data structure that supports insertion,
1686 deletion, rotation, and modulo-indexed reference and traversal.
1688 @defun make-ring size
1689 This returns a new ring capable of holding @var{size} objects.
1690 @var{size} should be an integer.
1693 @defun ring-p object
1694 This returns @code{t} if @var{object} is a ring, @code{nil} otherwise.
1697 @defun ring-size ring
1698 This returns the maximum capacity of the @var{ring}.
1701 @defun ring-length ring
1702 This returns the number of objects that @var{ring} currently contains.
1703 The value will never exceed that returned by @code{ring-size}.
1706 @defun ring-elements ring
1707 This returns a list of the objects in @var{ring}, in order, newest first.
1710 @defun ring-copy ring
1711 This returns a new ring which is a copy of @var{ring}.
1712 The new ring contains the same (@code{eq}) objects as @var{ring}.
1715 @defun ring-empty-p ring
1716 This returns @code{t} if @var{ring} is empty, @code{nil} otherwise.
1719 The newest element in the ring always has index 0. Higher indices
1720 correspond to older elements. Indices are computed modulo the ring
1721 length. Index @minus{}1 corresponds to the oldest element, @minus{}2
1722 to the next-oldest, and so forth.
1724 @defun ring-ref ring index
1725 This returns the object in @var{ring} found at index @var{index}.
1726 @var{index} may be negative or greater than the ring length. If
1727 @var{ring} is empty, @code{ring-ref} signals an error.
1730 @defun ring-insert ring object
1731 This inserts @var{object} into @var{ring}, making it the newest
1732 element, and returns @var{object}.
1734 If the ring is full, insertion removes the oldest element to
1735 make room for the new element.
1738 @defun ring-remove ring &optional index
1739 Remove an object from @var{ring}, and return that object. The
1740 argument @var{index} specifies which item to remove; if it is
1741 @code{nil}, that means to remove the oldest item. If @var{ring} is
1742 empty, @code{ring-remove} signals an error.
1745 @defun ring-insert-at-beginning ring object
1746 This inserts @var{object} into @var{ring}, treating it as the oldest
1747 element. The return value is not significant.
1749 If the ring is full, this function removes the newest element to make
1750 room for the inserted element.
1753 @cindex fifo data structure
1754 If you are careful not to exceed the ring size, you can
1755 use the ring as a first-in-first-out queue. For example:
1758 (let ((fifo (make-ring 5)))
1759 (mapc (lambda (obj) (ring-insert fifo obj))
1761 (list (ring-remove fifo) t
1762 (ring-remove fifo) t
1763 (ring-remove fifo)))
1764 @result{} (0 t one t "two")
1768 arch-tag: 31fb8a4e-4aa8-4a74-a206-aa00451394d4