2 @c This is part of the GNU Emacs Lisp Reference Manual.
3 @c Copyright (C) 1990, 1991, 1992, 1993, 1994, 1995, 1998, 1999
4 @c 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 * Lists as Boxes:: Graphical notation to explain lists.
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.
30 @section Lists and Cons Cells
31 @cindex lists and cons cells
32 @cindex @code{nil} and lists
34 Lists in Lisp are not a primitive data type; they are built up from
35 @dfn{cons cells}. A cons cell is a data object that represents an
36 ordered pair. That is, it has two slots, and each slot @dfn{holds}, or
37 @dfn{refers to}, some Lisp object. One slot is known as the @sc{car},
38 and the other is known as the @sc{cdr}. (These names are traditional;
39 see @ref{Cons Cell Type}.) @sc{cdr} is pronounced ``could-er.''
41 We say that ``the @sc{car} of this cons cell is'' whatever object
42 its @sc{car} slot currently holds, and likewise for the @sc{cdr}.
44 A list is a series of cons cells ``chained together,'' so that each
45 cell refers to the next one. There is one cons cell for each element of
46 the list. By convention, the @sc{car}s of the cons cells hold the
47 elements of the list, and the @sc{cdr}s are used to chain the list: the
48 @sc{cdr} slot of each cons cell refers to the following cons cell. The
49 @sc{cdr} of the last cons cell is @code{nil}. This asymmetry between
50 the @sc{car} and the @sc{cdr} is entirely a matter of convention; at the
51 level of cons cells, the @sc{car} and @sc{cdr} slots have the same
54 @cindex list structure
55 Because most cons cells are used as part of lists, the phrase
56 @dfn{list structure} has come to mean any structure made out of cons
59 The symbol @code{nil} is considered a list as well as a symbol; it is
60 the list with no elements. For convenience, the symbol @code{nil} is
61 considered to have @code{nil} as its @sc{cdr} (and also as its
64 The @sc{cdr} of any nonempty list @var{l} is a list containing all the
65 elements of @var{l} except the first.
68 @comment node-name, next, previous, up
69 @section Lists as Linked Pairs of Boxes
70 @cindex box representation for lists
71 @cindex lists represented as boxes
72 @cindex cons cell as box
74 A cons cell can be illustrated as a pair of boxes. The first box
75 represents the @sc{car} and the second box represents the @sc{cdr}.
76 Here is an illustration of the two-element list, @code{(tulip lily)},
77 made from two cons cells:
81 --------------- ---------------
82 | car | cdr | | car | cdr |
83 | tulip | o---------->| lily | nil |
85 --------------- ---------------
89 Each pair of boxes represents a cons cell. Each box ``refers to'',
90 ``points to'' or ``holds'' a Lisp object. (These terms are
91 synonymous.) The first box, which describes the @sc{car} of the first
92 cons cell, contains the symbol @code{tulip}. The arrow from the
93 @sc{cdr} box of the first cons cell to the second cons cell indicates
94 that the @sc{cdr} of the first cons cell is the second cons cell.
96 The same list can be illustrated in a different sort of box notation
102 | | |--> | | |--> nil
110 Here is a more complex illustration, showing the three-element list,
111 @code{((pine needles) oak maple)}, the first element of which is a
116 --- --- --- --- --- ---
117 | | |--> | | |--> | | |--> nil
118 --- --- --- --- --- ---
124 --> | | |--> | | |--> nil
132 The same list represented in the first box notation looks like this:
136 -------------- -------------- --------------
137 | car | cdr | | car | cdr | | car | cdr |
138 | o | o------->| oak | o------->| maple | nil |
140 -- | --------- -------------- --------------
143 | -------------- ----------------
144 | | car | cdr | | car | cdr |
145 ------>| pine | o------->| needles | nil |
147 -------------- ----------------
151 @xref{Cons Cell Type}, for the read and print syntax of cons cells and
152 lists, and for more ``box and arrow'' illustrations of lists.
154 @node List-related Predicates
155 @section Predicates on Lists
157 The following predicates test whether a Lisp object is an atom, is a
158 cons cell or is a list, or whether it is the distinguished object
159 @code{nil}. (Many of these predicates can be defined in terms of the
160 others, but they are used so often that it is worth having all of them.)
163 This function returns @code{t} if @var{object} is a cons cell, @code{nil}
164 otherwise. @code{nil} is not a cons cell, although it @emph{is} a list.
169 This function returns @code{t} if @var{object} is an atom, @code{nil}
170 otherwise. All objects except cons cells are atoms. The symbol
171 @code{nil} is an atom and is also a list; it is the only Lisp object
175 (atom @var{object}) @equiv{} (not (consp @var{object}))
180 This function returns @code{t} if @var{object} is a cons cell or
181 @code{nil}. Otherwise, it returns @code{nil}.
196 This function is the opposite of @code{listp}: it returns @code{t} if
197 @var{object} is not a list. Otherwise, it returns @code{nil}.
200 (listp @var{object}) @equiv{} (not (nlistp @var{object}))
205 This function returns @code{t} if @var{object} is @code{nil}, and
206 returns @code{nil} otherwise. This function is identical to @code{not},
207 but as a matter of clarity we use @code{null} when @var{object} is
208 considered a list and @code{not} when it is considered a truth value
209 (see @code{not} in @ref{Combining Conditions}).
226 @section Accessing Elements of Lists
227 @cindex list elements
230 This function returns the value referred to by the first slot of the
231 cons cell @var{cons-cell}. Expressed another way, this function
232 returns the @sc{car} of @var{cons-cell}.
234 As a special case, if @var{cons-cell} is @code{nil}, then @code{car}
235 is defined to return @code{nil}; therefore, any list is a valid argument
236 for @code{car}. An error is signaled if the argument is not a cons cell
252 This function returns the value referred to by the second slot of
253 the cons cell @var{cons-cell}. Expressed another way, this function
254 returns the @sc{cdr} of @var{cons-cell}.
256 As a special case, if @var{cons-cell} is @code{nil}, then @code{cdr}
257 is defined to return @code{nil}; therefore, any list is a valid argument
258 for @code{cdr}. An error is signaled if the argument is not a cons cell
273 @defun car-safe object
274 This function lets you take the @sc{car} of a cons cell while avoiding
275 errors for other data types. It returns the @sc{car} of @var{object} if
276 @var{object} is a cons cell, @code{nil} otherwise. This is in contrast
277 to @code{car}, which signals an error if @var{object} is not a list.
281 (car-safe @var{object})
283 (let ((x @var{object}))
291 @defun cdr-safe object
292 This function lets you take the @sc{cdr} of a cons cell while
293 avoiding errors for other data types. It returns the @sc{cdr} of
294 @var{object} if @var{object} is a cons cell, @code{nil} otherwise.
295 This is in contrast to @code{cdr}, which signals an error if
296 @var{object} is not a list.
300 (cdr-safe @var{object})
302 (let ((x @var{object}))
312 This macro is a way of examining the @sc{car} of a list,
313 and taking it off the list, all at once. It is new in Emacs 21.
315 It operates on the list which is stored in the symbol @var{listname}.
316 It removes this element from the list by setting @var{listname}
317 to the @sc{cdr} of its old value---but it also returns the @sc{car}
318 of that list, which is the element being removed.
331 This function returns the @var{n}th element of @var{list}. Elements
332 are numbered starting with zero, so the @sc{car} of @var{list} is
333 element number zero. If the length of @var{list} is @var{n} or less,
334 the value is @code{nil}.
336 If @var{n} is negative, @code{nth} returns the first element of
352 (nth n x) @equiv{} (car (nthcdr n x))
356 The function @code{elt} is similar, but applies to any kind of sequence.
357 For historical reasons, it takes its arguments in the opposite order.
358 @xref{Sequence Functions}.
362 This function returns the @var{n}th @sc{cdr} of @var{list}. In other
363 words, it skips past the first @var{n} links of @var{list} and returns
366 If @var{n} is zero or negative, @code{nthcdr} returns all of
367 @var{list}. If the length of @var{list} is @var{n} or less,
368 @code{nthcdr} returns @code{nil}.
372 (nthcdr 1 '(1 2 3 4))
376 (nthcdr 10 '(1 2 3 4))
380 (nthcdr -3 '(1 2 3 4))
386 @defun safe-length list
387 This function returns the length of @var{list}, with no risk
388 of either an error or an infinite loop.
390 If @var{list} is not really a list, @code{safe-length} returns 0. If
391 @var{list} is circular, it returns a finite value which is at least the
392 number of distinct elements.
395 The most common way to compute the length of a list, when you are not
396 worried that it may be circular, is with @code{length}. @xref{Sequence
399 @defun caar cons-cell
400 This is the same as @code{(car (car @var{cons-cell}))}.
403 @defun cadr cons-cell
404 This is the same as @code{(car (cdr @var{cons-cell}))}
405 or @code{(nth 1 @var{cons-cell})}.
408 @defun cdar cons-cell
409 This is the same as @code{(cdr (car @var{cons-cell}))}.
412 @defun cddr cons-cell
413 This is the same as @code{(cdr (cdr @var{cons-cell}))}
414 or @code{(nthcdr 2 @var{cons-cell})}.
418 @comment node-name, next, previous, up
419 @section Building Cons Cells and Lists
421 @cindex building lists
423 Many functions build lists, as lists reside at the very heart of Lisp.
424 @code{cons} is the fundamental list-building function; however, it is
425 interesting to note that @code{list} is used more times in the source
426 code for Emacs than @code{cons}.
428 @defun cons object1 object2
429 This function is the fundamental function used to build new list
430 structure. It creates a new cons cell, making @var{object1} the
431 @sc{car}, and @var{object2} the @sc{cdr}. It then returns the new cons
432 cell. The arguments @var{object1} and @var{object2} may be any Lisp
433 objects, but most often @var{object2} is a list.
451 @code{cons} is often used to add a single element to the front of a
452 list. This is called @dfn{consing the element onto the list}. For
456 (setq list (cons newelt list))
459 Note that there is no conflict between the variable named @code{list}
460 used in this example and the function named @code{list} described below;
461 any symbol can serve both purposes.
465 @defmac push newelt listname
466 This macro provides an alternative way to write
467 @code{(setq @var{listname} (cons @var{newelt} @var{listname}))}.
468 It is new in Emacs 21.
471 @defun list &rest objects
472 This function creates a list with @var{objects} as its elements. The
473 resulting list is always @code{nil}-terminated. If no @var{objects}
474 are given, the empty list is returned.
479 @result{} (1 2 3 4 5)
482 (list 1 2 '(3 4 5) 'foo)
483 @result{} (1 2 (3 4 5) foo)
492 @defun make-list length object
493 This function creates a list of length @var{length}, in which all the
494 elements have the identical value @var{object}. Compare
495 @code{make-list} with @code{make-string} (@pxref{Creating Strings}).
500 @result{} (pigs pigs pigs)
509 @defun append &rest sequences
510 @cindex copying lists
511 This function returns a list containing all the elements of
512 @var{sequences}. The @var{sequences} may be lists, vectors,
513 bool-vectors, or strings, but the last one should usually be a list.
514 All arguments except the last one are copied, so none of the arguments
515 is altered. (See @code{nconc} in @ref{Rearrangement}, for a way to join
516 lists with no copying.)
518 More generally, the final argument to @code{append} may be any Lisp
519 object. The final argument is not copied or converted; it becomes the
520 @sc{cdr} of the last cons cell in the new list. If the final argument
521 is itself a list, then its elements become in effect elements of the
522 result list. If the final element is not a list, the result is a
523 ``dotted list'' since its final @sc{cdr} is not @code{nil} as required
526 The @code{append} function also allows integers as arguments. It
527 converts them to strings of digits, making up the decimal print
528 representation of the integer, and then uses the strings instead of the
529 original integers. @strong{Don't use this feature; we plan to eliminate
530 it. If you already use this feature, change your programs now!} The
531 proper way to convert an integer to a decimal number in this way is with
532 @code{format} (@pxref{Formatting Strings}) or @code{number-to-string}
533 (@pxref{String Conversion}).
536 Here is an example of using @code{append}:
540 (setq trees '(pine oak))
542 (setq more-trees (append '(maple birch) trees))
543 @result{} (maple birch pine oak)
550 @result{} (maple birch pine oak)
553 (eq trees (cdr (cdr more-trees)))
558 You can see how @code{append} works by looking at a box diagram. The
559 variable @code{trees} is set to the list @code{(pine oak)} and then the
560 variable @code{more-trees} is set to the list @code{(maple birch pine
561 oak)}. However, the variable @code{trees} continues to refer to the
568 | --- --- --- --- -> --- --- --- ---
569 --> | | |--> | | |--> | | |--> | | |--> nil
570 --- --- --- --- --- --- --- ---
573 --> maple -->birch --> pine --> oak
577 An empty sequence contributes nothing to the value returned by
578 @code{append}. As a consequence of this, a final @code{nil} argument
579 forces a copy of the previous argument:
587 (setq wood (append trees nil))
601 This once was the usual way to copy a list, before the function
602 @code{copy-sequence} was invented. @xref{Sequences Arrays Vectors}.
604 Here we show the use of vectors and strings as arguments to @code{append}:
608 (append [a b] "cd" nil)
609 @result{} (a b 99 100)
613 With the help of @code{apply} (@pxref{Calling Functions}), we can append
614 all the lists in a list of lists:
618 (apply 'append '((a b c) nil (x y z) nil))
619 @result{} (a b c x y z)
623 If no @var{sequences} are given, @code{nil} is returned:
632 Here are some examples where the final argument is not a list:
638 @result{} (x y . [z])
642 The second example shows that when the final argument is a sequence but
643 not a list, the sequence's elements do not become elements of the
644 resulting list. Instead, the sequence becomes the final @sc{cdr}, like
645 any other non-list final argument.
648 This function creates a new list whose elements are the elements of
649 @var{list}, but in reverse order. The original argument @var{list} is
666 @defun remq object list
667 This function returns a copy of @var{list}, with all elements removed
668 which are @code{eq} to @var{object}. The letter @samp{q} in @code{remq}
669 says that it uses @code{eq} to compare @var{object} against the elements
674 (setq sample-list '(a b c a b c))
675 @result{} (a b c a b c)
678 (remq 'a sample-list)
683 @result{} (a b c a b c)
687 The function @code{delq} offers a way to perform this operation
688 destructively. See @ref{Sets And Lists}.
691 @node Modifying Lists
692 @section Modifying Existing List Structure
693 @cindex destructive list operations
695 You can modify the @sc{car} and @sc{cdr} contents of a cons cell with the
696 primitives @code{setcar} and @code{setcdr}. We call these ``destructive''
697 operations because they change existing list structure.
699 @cindex CL note---@code{rplaca} vrs @code{setcar}
703 @b{Common Lisp note:} Common Lisp uses functions @code{rplaca} and
704 @code{rplacd} to alter list structure; they change structure the same
705 way as @code{setcar} and @code{setcdr}, but the Common Lisp functions
706 return the cons cell while @code{setcar} and @code{setcdr} return the
707 new @sc{car} or @sc{cdr}.
711 * Setcar:: Replacing an element in a list.
712 * Setcdr:: Replacing part of the list backbone.
713 This can be used to remove or add elements.
714 * Rearrangement:: Reordering the elements in a list; combining lists.
718 @subsection Altering List Elements with @code{setcar}
720 Changing the @sc{car} of a cons cell is done with @code{setcar}. When
721 used on a list, @code{setcar} replaces one element of a list with a
724 @defun setcar cons object
725 This function stores @var{object} as the new @sc{car} of @var{cons},
726 replacing its previous @sc{car}. In other words, it changes the
727 @sc{car} slot of @var{cons} to refer to @var{object}. It returns the
728 value @var{object}. For example:
746 When a cons cell is part of the shared structure of several lists,
747 storing a new @sc{car} into the cons changes one element of each of
748 these lists. Here is an example:
752 ;; @r{Create two lists that are partly shared.}
755 (setq x2 (cons 'z (cdr x1)))
760 ;; @r{Replace the @sc{car} of a shared link.}
761 (setcar (cdr x1) 'foo)
763 x1 ; @r{Both lists are changed.}
770 ;; @r{Replace the @sc{car} of a link that is not shared.}
773 x1 ; @r{Only one list is changed.}
774 @result{} (baz foo c)
780 Here is a graphical depiction of the shared structure of the two lists
781 in the variables @code{x1} and @code{x2}, showing why replacing @code{b}
786 --- --- --- --- --- ---
787 x1---> | | |----> | | |--> | | |--> nil
788 --- --- --- --- --- ---
802 Here is an alternative form of box diagram, showing the same relationship:
807 -------------- -------------- --------------
808 | car | cdr | | car | cdr | | car | cdr |
809 | a | o------->| b | o------->| c | nil |
811 -------------- | -------------- --------------
823 @subsection Altering the CDR of a List
825 The lowest-level primitive for modifying a @sc{cdr} is @code{setcdr}:
827 @defun setcdr cons object
828 This function stores @var{object} as the new @sc{cdr} of @var{cons},
829 replacing its previous @sc{cdr}. In other words, it changes the
830 @sc{cdr} slot of @var{cons} to refer to @var{object}. It returns the
834 Here is an example of replacing the @sc{cdr} of a list with a
835 different list. All but the first element of the list are removed in
836 favor of a different sequence of elements. The first element is
837 unchanged, because it resides in the @sc{car} of the list, and is not
838 reached via the @sc{cdr}.
855 You can delete elements from the middle of a list by altering the
856 @sc{cdr}s of the cons cells in the list. For example, here we delete
857 the second element, @code{b}, from the list @code{(a b c)}, by changing
858 the @sc{cdr} of the first cons cell:
864 (setcdr x1 (cdr (cdr x1)))
872 Here is the result in box notation:
878 -------------- | -------------- | --------------
879 | car | cdr | | | car | cdr | -->| car | cdr |
880 | a | o----- | b | o-------->| c | nil |
882 -------------- -------------- --------------
887 The second cons cell, which previously held the element @code{b}, still
888 exists and its @sc{car} is still @code{b}, but it no longer forms part
891 It is equally easy to insert a new element by changing @sc{cdr}s:
897 (setcdr x1 (cons 'd (cdr x1)))
904 Here is this result in box notation:
908 -------------- ------------- -------------
909 | car | cdr | | car | cdr | | car | cdr |
910 | a | o | -->| b | o------->| c | nil |
911 | | | | | | | | | | |
912 --------- | -- | ------------- -------------
925 @subsection Functions that Rearrange Lists
926 @cindex rearrangement of lists
927 @cindex modification of lists
929 Here are some functions that rearrange lists ``destructively'' by
930 modifying the @sc{cdr}s of their component cons cells. We call these
931 functions ``destructive'' because they chew up the original lists passed
932 to them as arguments, relinking their cons cells to form a new list that
933 is the returned value.
936 See @code{delq}, in @ref{Sets And Lists}, for another function
937 that modifies cons cells.
940 The function @code{delq} in the following section is another example
941 of destructive list manipulation.
944 @defun nconc &rest lists
945 @cindex concatenating lists
946 @cindex joining lists
947 This function returns a list containing all the elements of @var{lists}.
948 Unlike @code{append} (@pxref{Building Lists}), the @var{lists} are
949 @emph{not} copied. Instead, the last @sc{cdr} of each of the
950 @var{lists} is changed to refer to the following list. The last of the
951 @var{lists} is not altered. For example:
960 @result{} (1 2 3 4 5)
964 @result{} (1 2 3 4 5)
968 Since the last argument of @code{nconc} is not itself modified, it is
969 reasonable to use a constant list, such as @code{'(4 5)}, as in the
970 above example. For the same reason, the last argument need not be a
980 @result{} (1 2 3 . z)
984 @result{} (1 2 3 . z)
988 However, the other arguments (all but the last) must be lists.
990 A common pitfall is to use a quoted constant list as a non-last
991 argument to @code{nconc}. If you do this, your program will change
992 each time you run it! Here is what happens:
996 (defun add-foo (x) ; @r{We want this function to add}
997 (nconc '(foo) x)) ; @r{@code{foo} to the front of its arg.}
1001 (symbol-function 'add-foo)
1002 @result{} (lambda (x) (nconc (quote (foo)) x))
1006 (setq xx (add-foo '(1 2))) ; @r{It seems to work.}
1010 (setq xy (add-foo '(3 4))) ; @r{What happened?}
1011 @result{} (foo 1 2 3 4)
1019 (symbol-function 'add-foo)
1020 @result{} (lambda (x) (nconc (quote (foo 1 2 3 4) x)))
1025 @defun nreverse list
1026 @cindex reversing a list
1027 This function reverses the order of the elements of @var{list}.
1028 Unlike @code{reverse}, @code{nreverse} alters its argument by reversing
1029 the @sc{cdr}s in the cons cells forming the list. The cons cell that
1030 used to be the last one in @var{list} becomes the first cons cell of the
1047 ;; @r{The cons cell that was first is now last.}
1053 To avoid confusion, we usually store the result of @code{nreverse}
1054 back in the same variable which held the original list:
1057 (setq x (nreverse x))
1060 Here is the @code{nreverse} of our favorite example, @code{(a b c)},
1061 presented graphically:
1065 @r{Original list head:} @r{Reversed list:}
1066 ------------- ------------- ------------
1067 | car | cdr | | car | cdr | | car | cdr |
1068 | a | nil |<-- | b | o |<-- | c | o |
1069 | | | | | | | | | | | | |
1070 ------------- | --------- | - | -------- | -
1072 ------------- ------------
1077 @defun sort list predicate
1079 @cindex sorting lists
1080 This function sorts @var{list} stably, though destructively, and
1081 returns the sorted list. It compares elements using @var{predicate}. A
1082 stable sort is one in which elements with equal sort keys maintain their
1083 relative order before and after the sort. Stability is important when
1084 successive sorts are used to order elements according to different
1087 The argument @var{predicate} must be a function that accepts two
1088 arguments. It is called with two elements of @var{list}. To get an
1089 increasing order sort, the @var{predicate} should return @code{t} if the
1090 first element is ``less than'' the second, or @code{nil} if not.
1092 The comparison function @var{predicate} must give reliable results for
1093 any given pair of arguments, at least within a single call to
1094 @code{sort}. It must be @dfn{antisymmetric}; that is, if @var{a} is
1095 less than @var{b}, @var{b} must not be less than @var{a}. It must be
1096 @dfn{transitive}---that is, if @var{a} is less than @var{b}, and @var{b}
1097 is less than @var{c}, then @var{a} must be less than @var{c}. If you
1098 use a comparison function which does not meet these requirements, the
1099 result of @code{sort} is unpredictable.
1101 The destructive aspect of @code{sort} is that it rearranges the cons
1102 cells forming @var{list} by changing @sc{cdr}s. A nondestructive sort
1103 function would create new cons cells to store the elements in their
1104 sorted order. If you wish to make a sorted copy without destroying the
1105 original, copy it first with @code{copy-sequence} and then sort.
1107 Sorting does not change the @sc{car}s of the cons cells in @var{list};
1108 the cons cell that originally contained the element @code{a} in
1109 @var{list} still has @code{a} in its @sc{car} after sorting, but it now
1110 appears in a different position in the list due to the change of
1111 @sc{cdr}s. For example:
1115 (setq nums '(1 3 2 6 5 4 0))
1116 @result{} (1 3 2 6 5 4 0)
1120 @result{} (0 1 2 3 4 5 6)
1124 @result{} (1 2 3 4 5 6)
1129 @strong{Warning}: Note that the list in @code{nums} no longer contains
1130 0; this is the same cons cell that it was before, but it is no longer
1131 the first one in the list. Don't assume a variable that formerly held
1132 the argument now holds the entire sorted list! Instead, save the result
1133 of @code{sort} and use that. Most often we store the result back into
1134 the variable that held the original list:
1137 (setq nums (sort nums '<))
1140 @xref{Sorting}, for more functions that perform sorting.
1141 See @code{documentation} in @ref{Accessing Documentation}, for a
1142 useful example of @code{sort}.
1145 @node Sets And Lists
1146 @section Using Lists as Sets
1147 @cindex lists as sets
1150 A list can represent an unordered mathematical set---simply consider a
1151 value an element of a set if it appears in the list, and ignore the
1152 order of the list. To form the union of two sets, use @code{append} (as
1153 long as you don't mind having duplicate elements). Other useful
1154 functions for sets include @code{memq} and @code{delq}, and their
1155 @code{equal} versions, @code{member} and @code{delete}.
1157 @cindex CL note---lack @code{union}, @code{intersection}
1159 @b{Common Lisp note:} Common Lisp has functions @code{union} (which
1160 avoids duplicate elements) and @code{intersection} for set operations,
1161 but GNU Emacs Lisp does not have them. You can write them in Lisp if
1165 @defun memq object list
1166 @cindex membership in a list
1167 This function tests to see whether @var{object} is a member of
1168 @var{list}. If it is, @code{memq} returns a list starting with the
1169 first occurrence of @var{object}. Otherwise, it returns @code{nil}.
1170 The letter @samp{q} in @code{memq} says that it uses @code{eq} to
1171 compare @var{object} against the elements of the list. For example:
1175 (memq 'b '(a b c b a))
1179 (memq '(2) '((1) (2))) ; @r{@code{(2)} and @code{(2)} are not @code{eq}.}
1185 @defun delq object list
1186 @cindex deletion of elements
1187 This function destructively removes all elements @code{eq} to
1188 @var{object} from @var{list}. The letter @samp{q} in @code{delq} says
1189 that it uses @code{eq} to compare @var{object} against the elements of
1190 the list, like @code{memq} and @code{remq}.
1193 When @code{delq} deletes elements from the front of the list, it does so
1194 simply by advancing down the list and returning a sublist that starts
1195 after those elements:
1199 (delq 'a '(a b c)) @equiv{} (cdr '(a b c))
1203 When an element to be deleted appears in the middle of the list,
1204 removing it involves changing the @sc{cdr}s (@pxref{Setcdr}).
1208 (setq sample-list '(a b c (4)))
1209 @result{} (a b c (4))
1212 (delq 'a sample-list)
1217 @result{} (a b c (4))
1220 (delq 'c sample-list)
1229 Note that @code{(delq 'c sample-list)} modifies @code{sample-list} to
1230 splice out the third element, but @code{(delq 'a sample-list)} does not
1231 splice anything---it just returns a shorter list. Don't assume that a
1232 variable which formerly held the argument @var{list} now has fewer
1233 elements, or that it still holds the original list! Instead, save the
1234 result of @code{delq} and use that. Most often we store the result back
1235 into the variable that held the original list:
1238 (setq flowers (delq 'rose flowers))
1241 In the following example, the @code{(4)} that @code{delq} attempts to match
1242 and the @code{(4)} in the @code{sample-list} are not @code{eq}:
1246 (delq '(4) sample-list)
1251 The following two functions are like @code{memq} and @code{delq} but use
1252 @code{equal} rather than @code{eq} to compare elements. @xref{Equality
1255 @defun member object list
1256 The function @code{member} tests to see whether @var{object} is a member
1257 of @var{list}, comparing members with @var{object} using @code{equal}.
1258 If @var{object} is a member, @code{member} returns a list starting with
1259 its first occurrence in @var{list}. Otherwise, it returns @code{nil}.
1261 Compare this with @code{memq}:
1265 (member '(2) '((1) (2))) ; @r{@code{(2)} and @code{(2)} are @code{equal}.}
1269 (memq '(2) '((1) (2))) ; @r{@code{(2)} and @code{(2)} are not @code{eq}.}
1273 ;; @r{Two strings with the same contents are @code{equal}.}
1274 (member "foo" '("foo" "bar"))
1275 @result{} ("foo" "bar")
1280 @defun delete object sequence
1281 If @code{sequence} is a list, this function destructively removes all
1282 elements @code{equal} to @var{object} from @var{sequence}. For lists,
1283 @code{delete} is to @code{delq} as @code{member} is to @code{memq}: it
1284 uses @code{equal} to compare elements with @var{object}, like
1285 @code{member}; when it finds an element that matches, it removes the
1286 element just as @code{delq} would.
1288 If @code{sequence} is a vector or string, @code{delete} returns a copy
1289 of @code{sequence} with all elements @code{equal} to @code{object}
1296 (delete '(2) '((2) (1) (2)))
1300 (delete '(2) [(2) (1) (2)])
1306 @defun remove object sequence
1307 This function is the non-destructive counterpart of @code{delete}. If
1308 returns a copy of @code{sequence}, a list, vector, or string, with
1309 elements @code{equal} to @code{object} removed. For example:
1313 (remove '(2) '((2) (1) (2)))
1317 (remove '(2) [(2) (1) (2)])
1324 @b{Common Lisp note:} The functions @code{member}, @code{delete} and
1325 @code{remove} in GNU Emacs Lisp are derived from Maclisp, not Common
1326 Lisp. The Common Lisp versions do not use @code{equal} to compare
1330 See also the function @code{add-to-list}, in @ref{Setting Variables},
1331 for another way to add an element to a list stored in a variable.
1333 @node Association Lists
1334 @section Association Lists
1335 @cindex association list
1338 An @dfn{association list}, or @dfn{alist} for short, records a mapping
1339 from keys to values. It is a list of cons cells called
1340 @dfn{associations}: the @sc{car} of each cons cell is the @dfn{key}, and the
1341 @sc{cdr} is the @dfn{associated value}.@footnote{This usage of ``key''
1342 is not related to the term ``key sequence''; it means a value used to
1343 look up an item in a table. In this case, the table is the alist, and
1344 the alist associations are the items.}
1346 Here is an example of an alist. The key @code{pine} is associated with
1347 the value @code{cones}; the key @code{oak} is associated with
1348 @code{acorns}; and the key @code{maple} is associated with @code{seeds}.
1358 The associated values in an alist may be any Lisp objects; so may the
1359 keys. For example, in the following alist, the symbol @code{a} is
1360 associated with the number @code{1}, and the string @code{"b"} is
1361 associated with the @emph{list} @code{(2 3)}, which is the @sc{cdr} of
1368 Sometimes it is better to design an alist to store the associated
1369 value in the @sc{car} of the @sc{cdr} of the element. Here is an
1373 '((rose red) (lily white) (buttercup yellow))
1377 Here we regard @code{red} as the value associated with @code{rose}. One
1378 advantage of this kind of alist is that you can store other related
1379 information---even a list of other items---in the @sc{cdr} of the
1380 @sc{cdr}. One disadvantage is that you cannot use @code{rassq} (see
1381 below) to find the element containing a given value. When neither of
1382 these considerations is important, the choice is a matter of taste, as
1383 long as you are consistent about it for any given alist.
1385 Note that the same alist shown above could be regarded as having the
1386 associated value in the @sc{cdr} of the element; the value associated
1387 with @code{rose} would be the list @code{(red)}.
1389 Association lists are often used to record information that you might
1390 otherwise keep on a stack, since new associations may be added easily to
1391 the front of the list. When searching an association list for an
1392 association with a given key, the first one found is returned, if there
1395 In Emacs Lisp, it is @emph{not} an error if an element of an
1396 association list is not a cons cell. The alist search functions simply
1397 ignore such elements. Many other versions of Lisp signal errors in such
1400 Note that property lists are similar to association lists in several
1401 respects. A property list behaves like an association list in which
1402 each key can occur only once. @xref{Property Lists}, for a comparison
1403 of property lists and association lists.
1405 @defun assoc key alist
1406 This function returns the first association for @var{key} in
1407 @var{alist}. It compares @var{key} against the alist elements using
1408 @code{equal} (@pxref{Equality Predicates}). It returns @code{nil} if no
1409 association in @var{alist} has a @sc{car} @code{equal} to @var{key}.
1413 (setq trees '((pine . cones) (oak . acorns) (maple . seeds)))
1414 @result{} ((pine . cones) (oak . acorns) (maple . seeds))
1416 @result{} (oak . acorns)
1417 (cdr (assoc 'oak trees))
1419 (assoc 'birch trees)
1423 Here is another example, in which the keys and values are not symbols:
1426 (setq needles-per-cluster
1427 '((2 "Austrian Pine" "Red Pine")
1431 (cdr (assoc 3 needles-per-cluster))
1432 @result{} ("Pitch Pine")
1433 (cdr (assoc 2 needles-per-cluster))
1434 @result{} ("Austrian Pine" "Red Pine")
1438 The functions @code{assoc-ignore-representation} and
1439 @code{assoc-ignore-case} are much like @code{assoc} except using
1440 @code{compare-strings} to do the comparison. @xref{Text Comparison}.
1442 @defun rassoc value alist
1443 This function returns the first association with value @var{value} in
1444 @var{alist}. It returns @code{nil} if no association in @var{alist} has
1445 a @sc{cdr} @code{equal} to @var{value}.
1447 @code{rassoc} is like @code{assoc} except that it compares the @sc{cdr} of
1448 each @var{alist} association instead of the @sc{car}. You can think of
1449 this as ``reverse @code{assoc}'', finding the key for a given value.
1452 @defun assq key alist
1453 This function is like @code{assoc} in that it returns the first
1454 association for @var{key} in @var{alist}, but it makes the comparison
1455 using @code{eq} instead of @code{equal}. @code{assq} returns @code{nil}
1456 if no association in @var{alist} has a @sc{car} @code{eq} to @var{key}.
1457 This function is used more often than @code{assoc}, since @code{eq} is
1458 faster than @code{equal} and most alists use symbols as keys.
1459 @xref{Equality Predicates}.
1462 (setq trees '((pine . cones) (oak . acorns) (maple . seeds)))
1463 @result{} ((pine . cones) (oak . acorns) (maple . seeds))
1465 @result{} (pine . cones)
1468 On the other hand, @code{assq} is not usually useful in alists where the
1469 keys may not be symbols:
1473 '(("simple leaves" . oak)
1474 ("compound leaves" . horsechestnut)))
1476 (assq "simple leaves" leaves)
1478 (assoc "simple leaves" leaves)
1479 @result{} ("simple leaves" . oak)
1483 @defun rassq value alist
1484 This function returns the first association with value @var{value} in
1485 @var{alist}. It returns @code{nil} if no association in @var{alist} has
1486 a @sc{cdr} @code{eq} to @var{value}.
1488 @code{rassq} is like @code{assq} except that it compares the @sc{cdr} of
1489 each @var{alist} association instead of the @sc{car}. You can think of
1490 this as ``reverse @code{assq}'', finding the key for a given value.
1495 (setq trees '((pine . cones) (oak . acorns) (maple . seeds)))
1497 (rassq 'acorns trees)
1498 @result{} (oak . acorns)
1499 (rassq 'spores trees)
1503 Note that @code{rassq} cannot search for a value stored in the @sc{car}
1504 of the @sc{cdr} of an element:
1507 (setq colors '((rose red) (lily white) (buttercup yellow)))
1509 (rassq 'white colors)
1513 In this case, the @sc{cdr} of the association @code{(lily white)} is not
1514 the symbol @code{white}, but rather the list @code{(white)}. This
1515 becomes clearer if the association is written in dotted pair notation:
1518 (lily white) @equiv{} (lily . (white))
1522 @defun assoc-default key alist test default
1523 This function searches @var{alist} for a match for @var{key}. For each
1524 element of @var{alist}, it compares the element (if it is an atom) or
1525 the element's @sc{car} (if it is a cons) against @var{key}, by calling
1526 @var{test} with two arguments: the element or its @sc{car}, and
1527 @var{key}. The arguments are passed in that order so that you can get
1528 useful results using @code{string-match} with an alist that contains
1529 regular expressions (@pxref{Regexp Search}). If @var{test} is omitted
1530 or @code{nil}, @code{equal} is used for comparison.
1532 If an alist element matches @var{key} by this criterion,
1533 then @code{assoc-default} returns a value based on this element.
1534 If the element is a cons, then the value is the element's @sc{cdr}.
1535 Otherwise, the return value is @var{default}.
1537 If no alist element matches @var{key}, @code{assoc-default} returns
1541 @defun copy-alist alist
1542 @cindex copying alists
1543 This function returns a two-level deep copy of @var{alist}: it creates a
1544 new copy of each association, so that you can alter the associations of
1545 the new alist without changing the old one.
1549 (setq needles-per-cluster
1550 '((2 . ("Austrian Pine" "Red Pine"))
1551 (3 . ("Pitch Pine"))
1553 (5 . ("White Pine"))))
1555 ((2 "Austrian Pine" "Red Pine")
1559 (setq copy (copy-alist needles-per-cluster))
1561 ((2 "Austrian Pine" "Red Pine")
1565 (eq needles-per-cluster copy)
1567 (equal needles-per-cluster copy)
1569 (eq (car needles-per-cluster) (car copy))
1571 (cdr (car (cdr needles-per-cluster)))
1572 @result{} ("Pitch Pine")
1574 (eq (cdr (car (cdr needles-per-cluster)))
1575 (cdr (car (cdr copy))))
1580 This example shows how @code{copy-alist} makes it possible to change
1581 the associations of one copy without affecting the other:
1585 (setcdr (assq 3 copy) '("Martian Vacuum Pine"))
1586 (cdr (assq 3 needles-per-cluster))
1587 @result{} ("Pitch Pine")
1592 @defun assoc-delete-all key alist
1593 @tindex assoc-delete-all
1594 This function deletes from @var{alist} all the elements whose @sc{car}
1595 is @var{key}. It returns the modified alist.
1598 (assoc-delete-all 'foo
1599 '((foo 1) (bar 2) (foo 3) (lose 4)))
1600 @result{} ((bar 2) (lose 4))