@c -*-texinfo-*-
@c This is part of the GNU Emacs Lisp Reference Manual.
@c Copyright (C) 1990--1995, 1998--1999, 2001--2022 Free Software
@c Foundation, Inc.
@c See the file elisp.texi for copying conditions.
@node Lists
@chapter Lists
@cindex lists
@cindex element (of list)

  A @dfn{list} represents a sequence of zero or more elements (which may
be any Lisp objects).  The important difference between lists and
vectors is that two or more lists can share part of their structure; in
addition, you can insert or delete elements in a list without copying
the whole list.

@menu
* Cons Cells::          How lists are made out of cons cells.
* List-related Predicates::        Is this object a list?  Comparing two lists.
* List Elements::       Extracting the pieces of a list.
* Building Lists::      Creating list structure.
* List Variables::      Modifying lists stored in variables.
* Modifying Lists::     Storing new pieces into an existing list.
* Sets And Lists::      A list can represent a finite mathematical set.
* Association Lists::   A list can represent a finite relation or mapping.
* Property Lists::      A list of paired elements.
@end menu

@node Cons Cells
@section Lists and Cons Cells
@cindex lists and cons cells

  Lists in Lisp are not a primitive data type; they are built up from
@dfn{cons cells} (@pxref{Cons Cell Type}).  A cons cell is a data
object that represents an ordered pair.  That is, it has two slots,
and each slot @dfn{holds}, or @dfn{refers to}, some Lisp object.  One
slot is known as the @sc{car}, and the other is known as the @sc{cdr}.
(These names are traditional; see @ref{Cons Cell Type}.)  @sc{cdr} is
pronounced ``could-er''.

  We say that ``the @sc{car} of this cons cell is'' whatever object
its @sc{car} slot currently holds, and likewise for the @sc{cdr}.

  A list is a series of cons cells chained together, so that each
cell refers to the next one.  There is one cons cell for each element
of the list.  By convention, the @sc{car}s of the cons cells hold the
elements of the list, and the @sc{cdr}s are used to chain the list
(this asymmetry between @sc{car} and @sc{cdr} is entirely a matter of
convention; at the level of cons cells, the @sc{car} and @sc{cdr}
slots have similar properties).  Hence, the @sc{cdr} slot of each cons
cell in a list refers to the following cons cell.

@cindex proper list
@cindex true list
  Also by convention, the @sc{cdr} of the last cons cell in a list is
@code{nil}.  We call such a @code{nil}-terminated structure a
@dfn{proper list}@footnote{It is sometimes also referred to as a
@dfn{true list}, but we generally do not use this terminology in this
manual.}.  In Emacs Lisp, the symbol @code{nil} is both a symbol and a
list with no elements.  For convenience, the symbol @code{nil} is
considered to have @code{nil} as its @sc{cdr} (and also as its
@sc{car}).

  Hence, the @sc{cdr} of a proper list is always a proper list.  The
@sc{cdr} of a nonempty proper list is a proper list containing all the
elements except the first.

@cindex dotted list
@cindex circular list
  If the @sc{cdr} of a list's last cons cell is some value other than
@code{nil}, we call the structure a @dfn{dotted list}, since its
printed representation would use dotted pair notation (@pxref{Dotted
Pair Notation}).  There is one other possibility: some cons cell's
@sc{cdr} could point to one of the previous cons cells in the list.
We call that structure a @dfn{circular list}.

  For some purposes, it does not matter whether a list is proper,
circular or dotted.  If a program doesn't look far enough down the
list to see the @sc{cdr} of the final cons cell, it won't care.
However, some functions that operate on lists demand proper lists and
signal errors if given a dotted list.  Most functions that try to find
the end of a list enter infinite loops if given a circular list.

@cindex list structure
  Because most cons cells are used as part of lists, we refer to any
structure made out of cons cells as a @dfn{list structure}.

@node List-related Predicates
@section Predicates on Lists
@cindex predicates for lists
@cindex list predicates

  The following predicates test whether a Lisp object is an atom,
whether it is a cons cell or is a list, or whether it is the
distinguished object @code{nil}.  (Many of these predicates can be
defined in terms of the others, but they are used so often that it is
worth having them.)

@defun consp object
This function returns @code{t} if @var{object} is a cons cell, @code{nil}
otherwise.  @code{nil} is not a cons cell, although it @emph{is} a list.
@end defun

@defun atom object
This function returns @code{t} if @var{object} is an atom, @code{nil}
otherwise.  All objects except cons cells are atoms.  The symbol
@code{nil} is an atom and is also a list; it is the only Lisp object
that is both.

@example
(atom @var{object}) @equiv{} (not (consp @var{object}))
@end example
@end defun

@defun listp object
This function returns @code{t} if @var{object} is a cons cell or
@code{nil}.  Otherwise, it returns @code{nil}.

@example
@group
(listp '(1))
     @result{} t
@end group
@group
(listp '())
     @result{} t
@end group
@end example
@end defun

@defun nlistp object
This function is the opposite of @code{listp}: it returns @code{t} if
@var{object} is not a list.  Otherwise, it returns @code{nil}.

@example
(listp @var{object}) @equiv{} (not (nlistp @var{object}))
@end example
@end defun

@defun null object
This function returns @code{t} if @var{object} is @code{nil}, and
returns @code{nil} otherwise.  This function is identical to @code{not},
but as a matter of clarity we use @code{null} when @var{object} is
considered a list and @code{not} when it is considered a truth value
(see @code{not} in @ref{Combining Conditions}).

@example
@group
(null '(1))
     @result{} nil
@end group
@group
(null '())
     @result{} t
@end group
@end example
@end defun

@defun proper-list-p object
This function returns the length of @var{object} if it is a proper
list, @code{nil} otherwise (@pxref{Cons Cells}).  In addition to
satisfying @code{listp}, a proper list is neither circular nor dotted.

@example
@group
(proper-list-p '(a b c))
    @result{} 3
@end group
@group
(proper-list-p '(a b . c))
    @result{} nil
@end group
@end example
@end defun

@node List Elements
@section Accessing Elements of Lists
@cindex list elements

@defun car cons-cell
This function returns the value referred to by the first slot of the
cons cell @var{cons-cell}.  In other words, it returns the @sc{car} of
@var{cons-cell}.

As a special case, if @var{cons-cell} is @code{nil}, this function
returns @code{nil}.  Therefore, any list is a valid argument.  An
error is signaled if the argument is not a cons cell or @code{nil}.

@example
@group
(car '(a b c))
     @result{} a
@end group
@group
(car '())
     @result{} nil
@end group
@end example
@end defun

@defun cdr cons-cell
This function returns the value referred to by the second slot of the
cons cell @var{cons-cell}.  In other words, it returns the @sc{cdr} of
@var{cons-cell}.

As a special case, if @var{cons-cell} is @code{nil}, this function
returns @code{nil}; therefore, any list is a valid argument.  An error
is signaled if the argument is not a cons cell or @code{nil}.

@example
@group
(cdr '(a b c))
     @result{} (b c)
@end group
@group
(cdr '())
     @result{} nil
@end group
@end example
@end defun

@defun car-safe object
This function lets you take the @sc{car} of a cons cell while avoiding
errors for other data types.  It returns the @sc{car} of @var{object} if
@var{object} is a cons cell, @code{nil} otherwise.  This is in contrast
to @code{car}, which signals an error if @var{object} is not a list.

@example
@group
(car-safe @var{object})
@equiv{}
(let ((x @var{object}))
  (if (consp x)
      (car x)
    nil))
@end group
@end example
@end defun

@defun cdr-safe object
This function lets you take the @sc{cdr} of a cons cell while
avoiding errors for other data types.  It returns the @sc{cdr} of
@var{object} if @var{object} is a cons cell, @code{nil} otherwise.
This is in contrast to @code{cdr}, which signals an error if
@var{object} is not a list.

@example
@group
(cdr-safe @var{object})
@equiv{}
(let ((x @var{object}))
  (if (consp x)
      (cdr x)
    nil))
@end group
@end example
@end defun

@defmac pop listname
This macro provides a convenient way to examine the @sc{car} of a
list, and take it off the list, all at once.  It operates on the list
stored in @var{listname}.  It removes the first element from the list,
saves the @sc{cdr} into @var{listname}, then returns the removed
element.

In the simplest case, @var{listname} is an unquoted symbol naming a
list; in that case, this macro is equivalent to @w{@code{(prog1
(car listname) (setq listname (cdr listname)))}}.

@example
x
     @result{} (a b c)
(pop x)
     @result{} a
x
     @result{} (b c)
@end example

More generally, @var{listname} can be a generalized variable.  In that
case, this macro saves into @var{listname} using @code{setf}.
@xref{Generalized Variables}.

For the @code{push} macro, which adds an element to a list,
@xref{List Variables}.
@end defmac

@defun nth n list
@anchor{Definition of nth}
This function returns the @var{n}th element of @var{list}.  Elements
are numbered starting with zero, so the @sc{car} of @var{list} is
element number zero.  If the length of @var{list} is @var{n} or less,
the value is @code{nil}.

@c Behavior for -ve n undefined since 2013/08; see bug#15059.
@ignore
If @var{n} is negative, @code{nth} returns the first element of @var{list}.
@end ignore

@example
@group
(nth 2 '(1 2 3 4))
     @result{} 3
@end group
@group
(nth 10 '(1 2 3 4))
     @result{} nil

(nth n x) @equiv{} (car (nthcdr n x))
@end group
@end example

The function @code{elt} is similar, but applies to any kind of sequence.
For historical reasons, it takes its arguments in the opposite order.
@xref{Sequence Functions}.
@end defun

@defun nthcdr n list
This function returns the @var{n}th @sc{cdr} of @var{list}.  In other
words, it skips past the first @var{n} links of @var{list} and returns
what follows.

@c "or negative" removed 2013/08; see bug#15059.
If @var{n} is zero, @code{nthcdr} returns all of
@var{list}.  If the length of @var{list} is @var{n} or less,
@code{nthcdr} returns @code{nil}.

@example
@group
(nthcdr 1 '(1 2 3 4))
     @result{} (2 3 4)
@end group
@group
(nthcdr 10 '(1 2 3 4))
     @result{} nil
@end group
@group
(nthcdr 0 '(1 2 3 4))
     @result{} (1 2 3 4)
@end group
@end example
@end defun

@defun last list &optional n
This function returns the last link of @var{list}.  The @code{car} of
this link is the list's last element.  If @var{list} is null,
@code{nil} is returned.  If @var{n} is non-@code{nil}, the
@var{n}th-to-last link is returned instead, or the whole of @var{list}
if @var{n} is bigger than @var{list}'s length.
@end defun

@defun safe-length list
@anchor{Definition of safe-length}
This function returns the length of @var{list}, with no risk of either
an error or an infinite loop.  It generally returns the number of
distinct cons cells in the list.  However, for circular lists,
the value is just an upper bound; it is often too large.

If @var{list} is not @code{nil} or a cons cell, @code{safe-length}
returns 0.
@end defun

  The most common way to compute the length of a list, when you are not
worried that it may be circular, is with @code{length}.  @xref{Sequence
Functions}.

@defun caar cons-cell
This is the same as @code{(car (car @var{cons-cell}))}.
@end defun

@defun cadr cons-cell
This is the same as @code{(car (cdr @var{cons-cell}))}
or @code{(nth 1 @var{cons-cell})}.
@end defun

@defun cdar cons-cell
This is the same as @code{(cdr (car @var{cons-cell}))}.
@end defun

@defun cddr cons-cell
This is the same as @code{(cdr (cdr @var{cons-cell}))}
or @code{(nthcdr 2 @var{cons-cell})}.
@end defun

@findex caaar
@findex caadr
@findex cadar
@findex caddr
@findex cdaar
@findex cdadr
@findex cddar
@findex cdddr
@findex caaaar
@findex caaadr
@findex caadar
@findex caaddr
@findex cadaar
@findex cadadr
@findex caddar
@findex cadddr
@findex cdaaar
@findex cdaadr
@findex cdadar
@findex cdaddr
@findex cddaar
@findex cddadr
@findex cdddar
@findex cddddr
In addition to the above, 24 additional compositions of @code{car} and
@code{cdr} are defined as @code{c@var{xxx}r} and @code{c@var{xxxx}r},
where each @code{@var{x}} is either @code{a} or @code{d}.  @code{cadr},
@code{caddr}, and @code{cadddr} pick out the second, third or fourth
elements of a list, respectively.  @file{cl-lib} provides the same
under the names @code{cl-second}, @code{cl-third}, and
@code{cl-fourth}.  @xref{List Functions,,, cl, Common Lisp
Extensions}.

@defun butlast x &optional n
This function returns the list @var{x} with the last element,
or the last @var{n} elements, removed.  If @var{n} is greater
than zero it makes a copy of the list so as not to damage the
original list.  In general, @code{(append (butlast @var{x} @var{n})
(last @var{x} @var{n}))} will return a list equal to @var{x}.
@end defun

@defun nbutlast x &optional n
This is a version of @code{butlast} that works by destructively
modifying the @code{cdr} of the appropriate element, rather than
making a copy of the list.
@end defun

@node Building Lists
@section Building Cons Cells and Lists
@cindex cons cells
@cindex building lists

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

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

@example
@group
(cons 1 '(2))
     @result{} (1 2)
@end group
@group
(cons 1 '())
     @result{} (1)
@end group
@group
(cons 1 2)
     @result{} (1 . 2)
@end group
@end example

@cindex consing
@code{cons} is often used to add a single element to the front of a
list.  This is called @dfn{consing the element onto the list}.
@footnote{There is no strictly equivalent way to add an element to
the end of a list.  You can use @code{(append @var{listname} (list
@var{newelt}))}, which creates a whole new list by copying @var{listname}
and adding @var{newelt} to its end.  Or you can use @code{(nconc
@var{listname} (list @var{newelt}))}, which modifies @var{listname}
by following all the @sc{cdr}s and then replacing the terminating
@code{nil}.  Compare this to adding an element to the beginning of a
list with @code{cons}, which neither copies nor modifies the list.}
For example:

@example
(setq list (cons newelt list))
@end example

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

@defun list &rest objects
This function creates a list with @var{objects} as its elements.  The
resulting list is always @code{nil}-terminated.  If no @var{objects}
are given, the empty list is returned.

@example
@group
(list 1 2 3 4 5)
     @result{} (1 2 3 4 5)
@end group
@group
(list 1 2 '(3 4 5) 'foo)
     @result{} (1 2 (3 4 5) foo)
@end group
@group
(list)
     @result{} nil
@end group
@end example
@end defun

@defun make-list length object
This function creates a list of @var{length} elements, in which each
element is @var{object}.  Compare @code{make-list} with
@code{make-string} (@pxref{Creating Strings}).

@example
@group
(make-list 3 'pigs)
     @result{} (pigs pigs pigs)
@end group
@group
(make-list 0 'pigs)
     @result{} nil
@end group
@group
(setq l (make-list 3 '(a b)))
     @result{} ((a b) (a b) (a b))
(eq (car l) (cadr l))
     @result{} t
@end group
@end example
@end defun

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

More generally, the final argument to @code{append} may be any Lisp
object.  The final argument is not copied or converted; it becomes the
@sc{cdr} of the last cons cell in the new list.  If the final argument
is itself a list, then its elements become in effect elements of the
result list.  If the final element is not a list, the result is a
dotted list since its final @sc{cdr} is not @code{nil} as required
in a proper list (@pxref{Cons Cells}).
@end defun

  Here is an example of using @code{append}:

@example
@group
(setq trees '(pine oak))
     @result{} (pine oak)
(setq more-trees (append '(maple birch) trees))
     @result{} (maple birch pine oak)
@end group

@group
trees
     @result{} (pine oak)
more-trees
     @result{} (maple birch pine oak)
@end group
@group
(eq trees (cdr (cdr more-trees)))
     @result{} t
@end group
@end example

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

@smallexample
@group
more-trees                trees
|                           |
|     --- ---      --- ---   -> --- ---      --- ---
 --> |   |   |--> |   |   |--> |   |   |--> |   |   |--> nil
      --- ---      --- ---      --- ---      --- ---
       |            |            |            |
       |            |            |            |
        --> maple    -->birch     --> pine     --> oak
@end group
@end smallexample

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

@example
@group
trees
     @result{} (pine oak)
@end group
@group
(setq wood (append trees nil))
     @result{} (pine oak)
@end group
@group
wood
     @result{} (pine oak)
@end group
@group
(eq wood trees)
     @result{} nil
@end group
@end example

@noindent
This once was the usual way to copy a list, before the function
@code{copy-sequence} was invented.  @xref{Sequences Arrays Vectors}.

  Here we show the use of vectors and strings as arguments to @code{append}:

@example
@group
(append [a b] "cd" nil)
     @result{} (a b 99 100)
@end group
@end example

  With the help of @code{apply} (@pxref{Calling Functions}), we can append
all the lists in a list of lists:

@example
@group
(apply 'append '((a b c) nil (x y z) nil))
     @result{} (a b c x y z)
@end group
@end example

  If no @var{sequences} are given, @code{nil} is returned:

@example
@group
(append)
     @result{} nil
@end group
@end example

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

@example
(append '(x y) 'z)
     @result{} (x y . z)
(append '(x y) [z])
     @result{} (x y . [z])
@end example

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

@defun copy-tree tree &optional vecp
This function returns a copy of the tree @var{tree}.  If @var{tree} is a
cons cell, this makes a new cons cell with the same @sc{car} and
@sc{cdr}, then recursively copies the @sc{car} and @sc{cdr} in the
same way.

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

@defun flatten-tree tree
This function returns a ``flattened'' copy of @var{tree}, that is,
a list containing all the non-@code{nil} terminal nodes, or leaves, of
the tree of cons cells rooted at @var{tree}.  Leaves in the returned
list are in the same order as in @var{tree}.
@end defun

@example
(flatten-tree '(1 (2 . 3) nil (4 5 (6)) 7))
    @result{}(1 2 3 4 5 6 7)
@end example

@defun ensure-list object
This function returns @var{object} as a list.  If @var{object} is
already a list, the function returns it; otherwise, the function
returns a one-element list containing @var{object}.

This is usually useful if you have a variable that may or may not be a
list, and you can then say, for instance:

@lisp
(dolist (elem (ensure-list foo))
  (princ elem))
@end lisp
@end defun

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

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

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

Some examples:

@example
(number-sequence 4 9)
     @result{} (4 5 6 7 8 9)
(number-sequence 9 4 -1)
     @result{} (9 8 7 6 5 4)
(number-sequence 9 4 -2)
     @result{} (9 7 5)
(number-sequence 8)
     @result{} (8)
(number-sequence 8 5)
     @result{} nil
(number-sequence 5 8 -1)
     @result{} nil
(number-sequence 1.5 6 2)
     @result{} (1.5 3.5 5.5)
@end example
@end defun

@node List Variables
@section Modifying List Variables
@cindex modify a list
@cindex list modification

  These functions, and one macro, provide convenient ways
to modify a list which is stored in a variable.

@defmac push element listname
This macro creates a new list whose @sc{car} is @var{element} and
whose @sc{cdr} is the list specified by @var{listname}, and saves that
list in @var{listname}.  In the simplest case, @var{listname} is an
unquoted symbol naming a list, and this macro is equivalent
to @w{@code{(setq @var{listname} (cons @var{element} @var{listname}))}}.

@example
(setq l '(a b))
     @result{} (a b)
(push 'c l)
     @result{} (c a b)
l
     @result{} (c a b)
@end example

More generally, @code{listname} can be a generalized variable.  In
that case, this macro does the equivalent of @w{@code{(setf
@var{listname} (cons @var{element} @var{listname}))}}.
@xref{Generalized Variables}.

For the @code{pop} macro, which removes the first element from a list,
@xref{List Elements}.
@end defmac

  Two functions modify lists that are the values of variables.

@defun add-to-list symbol element &optional append compare-fn
This function sets the variable @var{symbol} by consing @var{element}
onto the old value, if @var{element} is not already a member of that
value.  It returns the resulting list, whether updated or not.  The
value of @var{symbol} had better be a list already before the call.
@code{add-to-list} uses @var{compare-fn} to compare @var{element}
against existing list members; if @var{compare-fn} is @code{nil}, it
uses @code{equal}.

Normally, if @var{element} is added, it is added to the front of
@var{symbol}, but if the optional argument @var{append} is
non-@code{nil}, it is added at the end.

The argument @var{symbol} is not implicitly quoted; @code{add-to-list}
is an ordinary function, like @code{set} and unlike @code{setq}.  Quote
the argument yourself if that is what you want.

Do not use this function when @var{symbol} refers to a lexical
variable.
@end defun

Here's a scenario showing how to use @code{add-to-list}:

@example
(setq foo '(a b))
     @result{} (a b)

(add-to-list 'foo 'c)     ;; @r{Add @code{c}.}
     @result{} (c a b)

(add-to-list 'foo 'b)     ;; @r{No effect.}
     @result{} (c a b)

foo                       ;; @r{@code{foo} was changed.}
     @result{} (c a b)
@end example

  An equivalent expression for @code{(add-to-list '@var{var}
@var{value})} is this:

@example
(if (member @var{value} @var{var})
    @var{var}
  (setq @var{var} (cons @var{value} @var{var})))
@end example

@defun add-to-ordered-list symbol element &optional order
This function sets the variable @var{symbol} by inserting
@var{element} into the old value, which must be a list, at the
position specified by @var{order}.  If @var{element} is already a
member of the list, its position in the list is adjusted according
to @var{order}.  Membership is tested using @code{eq}.
This function returns the resulting list, whether updated or not.

The @var{order} is typically a number (integer or float), and the
elements of the list are sorted in non-decreasing numerical order.

@var{order} may also be omitted or @code{nil}.  Then the numeric order
of @var{element} stays unchanged if it already has one; otherwise,
@var{element} has no numeric order.  Elements without a numeric list
order are placed at the end of the list, in no particular order.

Any other value for @var{order} removes the numeric order of @var{element}
if it already has one; otherwise, it is equivalent to @code{nil}.

The argument @var{symbol} is not implicitly quoted;
@code{add-to-ordered-list} is an ordinary function, like @code{set}
and unlike @code{setq}.  Quote the argument yourself if necessary.

The ordering information is stored in a hash table on @var{symbol}'s
@code{list-order} property.
@var{symbol} cannot refer to a lexical variable.
@end defun

Here's a scenario showing how to use @code{add-to-ordered-list}:

@example
(setq foo '())
     @result{} nil

(add-to-ordered-list 'foo 'a 1)     ;; @r{Add @code{a}.}
     @result{} (a)

(add-to-ordered-list 'foo 'c 3)     ;; @r{Add @code{c}.}
     @result{} (a c)

(add-to-ordered-list 'foo 'b 2)     ;; @r{Add @code{b}.}
     @result{} (a b c)

(add-to-ordered-list 'foo 'b 4)     ;; @r{Move @code{b}.}
     @result{} (a c b)

(add-to-ordered-list 'foo 'd)       ;; @r{Append @code{d}.}
     @result{} (a c b d)

(add-to-ordered-list 'foo 'e)       ;; @r{Add @code{e}}.
     @result{} (a c b e d)

foo                       ;; @r{@code{foo} was changed.}
     @result{} (a c b e d)
@end example

@node Modifying Lists
@section Modifying Existing List Structure
@cindex destructive list operations
@cindex mutable lists

  You can modify the @sc{car} and @sc{cdr} contents of a cons cell with the
primitives @code{setcar} and @code{setcdr}.  These are destructive
operations because they change existing list structure.
Destructive operations should be applied only to mutable lists,
that is, lists constructed via @code{cons}, @code{list} or similar
operations.  Lists created by quoting are part of the program and
should not be changed by destructive operations.  @xref{Mutability}.

@cindex CL note---@code{rplaca} vs @code{setcar}
@quotation
@findex rplaca
@findex rplacd
@b{Common Lisp note:} Common Lisp uses functions @code{rplaca} and
@code{rplacd} to alter list structure; they change structure the same
way as @code{setcar} and @code{setcdr}, but the Common Lisp functions
return the cons cell while @code{setcar} and @code{setcdr} return the
new @sc{car} or @sc{cdr}.
@end quotation

@menu
* Setcar::          Replacing an element in a list.
* Setcdr::          Replacing part of the list backbone.
                      This can be used to remove or add elements.
* Rearrangement::   Reordering the elements in a list; combining lists.
@end menu

@node Setcar
@subsection Altering List Elements with @code{setcar}
@cindex replace list element
@cindex list, replace element

  Changing the @sc{car} of a cons cell is done with @code{setcar}.  When
used on a list, @code{setcar} replaces one element of a list with a
different element.

@defun setcar cons object
This function stores @var{object} as the new @sc{car} of @var{cons},
replacing its previous @sc{car}.  In other words, it changes the
@sc{car} slot of @var{cons} to refer to @var{object}.  It returns the
value @var{object}.  For example:

@example
@group
(setq x (list 1 2))
     @result{} (1 2)
@end group
@group
(setcar x 4)
     @result{} 4
@end group
@group
x
     @result{} (4 2)
@end group
@end example
@end defun

  When a cons cell is part of the shared structure of several lists,
storing a new @sc{car} into the cons changes one element of each of
these lists.  Here is an example:

@example
@group
;; @r{Create two lists that are partly shared.}
(setq x1 (list 'a 'b 'c))
     @result{} (a b c)
(setq x2 (cons 'z (cdr x1)))
     @result{} (z b c)
@end group

@group
;; @r{Replace the @sc{car} of a shared link.}
(setcar (cdr x1) 'foo)
     @result{} foo
x1                           ; @r{Both lists are changed.}
     @result{} (a foo c)
x2
     @result{} (z foo c)
@end group

@group
;; @r{Replace the @sc{car} of a link that is not shared.}
(setcar x1 'baz)
     @result{} baz
x1                           ; @r{Only one list is changed.}
     @result{} (baz foo c)
x2
     @result{} (z foo c)
@end group
@end example

  Here is a graphical depiction of the shared structure of the two lists
in the variables @code{x1} and @code{x2}, showing why replacing @code{b}
changes them both:

@example
@group
        --- ---        --- ---      --- ---
x1---> |   |   |----> |   |   |--> |   |   |--> nil
        --- ---        --- ---      --- ---
         |        -->   |            |
         |       |      |            |
          --> a  |       --> b        --> c
                 |
       --- ---   |
x2--> |   |   |--
       --- ---
        |
        |
         --> z
@end group
@end example

  Here is an alternative form of box diagram, showing the same relationship:

@example
@group
x1:
 --------------       --------------       --------------
| car   | cdr  |     | car   | cdr  |     | car   | cdr  |
|   a   |   o------->|   b   |   o------->|   c   |  nil |
|       |      |  -->|       |      |     |       |      |
 --------------  |    --------------       --------------
                 |
x2:              |
 --------------  |
| car   | cdr  | |
|   z   |   o----
|       |      |
 --------------
@end group
@end example

@node Setcdr
@subsection Altering the CDR of a List
@cindex replace part of list

  The lowest-level primitive for modifying a @sc{cdr} is @code{setcdr}:

@defun setcdr cons object
This function stores @var{object} as the new @sc{cdr} of @var{cons},
replacing its previous @sc{cdr}.  In other words, it changes the
@sc{cdr} slot of @var{cons} to refer to @var{object}.  It returns the
value @var{object}.
@end defun

  Here is an example of replacing the @sc{cdr} of a list with a
different list.  All but the first element of the list are removed in
favor of a different sequence of elements.  The first element is
unchanged, because it resides in the @sc{car} of the list, and is not
reached via the @sc{cdr}.

@example
@group
(setq x (list 1 2 3))
     @result{} (1 2 3)
@end group
@group
(setcdr x '(4))
     @result{} (4)
@end group
@group
x
     @result{} (1 4)
@end group
@end example

  You can delete elements from the middle of a list by altering the
@sc{cdr}s of the cons cells in the list.  For example, here we delete
the second element, @code{b}, from the list @code{(a b c)}, by changing
the @sc{cdr} of the first cons cell:

@example
@group
(setq x1 (list 'a 'b 'c))
     @result{} (a b c)
(setcdr x1 (cdr (cdr x1)))
     @result{} (c)
x1
     @result{} (a c)
@end group
@end example

  Here is the result in box notation:

@smallexample
@group
                   --------------------
                  |                    |
 --------------   |   --------------   |    --------------
| car   | cdr  |  |  | car   | cdr  |   -->| car   | cdr  |
|   a   |   o-----   |   b   |   o-------->|   c   |  nil |
|       |      |     |       |      |      |       |      |
 --------------       --------------        --------------
@end group
@end smallexample

@noindent
The second cons cell, which previously held the element @code{b}, still
exists and its @sc{car} is still @code{b}, but it no longer forms part
of this list.

  It is equally easy to insert a new element by changing @sc{cdr}s:

@example
@group
(setq x1 (list 'a 'b 'c))
     @result{} (a b c)
(setcdr x1 (cons 'd (cdr x1)))
     @result{} (d b c)
x1
     @result{} (a d b c)
@end group
@end example

  Here is this result in box notation:

@smallexample
@group
 --------------        -------------       -------------
| car  | cdr   |      | car  | cdr  |     | car  | cdr  |
|   a  |   o   |   -->|   b  |   o------->|   c  |  nil |
|      |   |   |  |   |      |      |     |      |      |
 --------- | --   |    -------------       -------------
           |      |
     -----         --------
    |                      |
    |    ---------------   |
    |   | car   | cdr   |  |
     -->|   d   |   o------
        |       |       |
         ---------------
@end group
@end smallexample

@node Rearrangement
@subsection Functions that Rearrange Lists
@cindex rearrangement of lists
@cindex reordering, of elements in lists
@cindex modification of lists

  Here are some functions that rearrange lists destructively by
modifying the @sc{cdr}s of their component cons cells.  These functions
are destructive because they chew up the original lists passed
to them as arguments, relinking their cons cells to form a new list that
is the returned value.

@ifnottex
  See @code{delq}, in @ref{Sets And Lists}, for another function
that modifies cons cells.
@end ifnottex
@iftex
   The function @code{delq} in the following section is another example
of destructive list manipulation.
@end iftex

@defun nconc &rest lists
@cindex concatenating lists
@cindex joining lists
This function returns a list containing all the elements of @var{lists}.
Unlike @code{append} (@pxref{Building Lists}), the @var{lists} are
@emph{not} copied.  Instead, the last @sc{cdr} of each of the
@var{lists} is changed to refer to the following list.  The last of the
@var{lists} is not altered.  For example:

@example
@group
(setq x (list 1 2 3))
     @result{} (1 2 3)
@end group
@group
(nconc x '(4 5))
     @result{} (1 2 3 4 5)
@end group
@group
x
     @result{} (1 2 3 4 5)
@end group
@end example

   Since the last argument of @code{nconc} is not itself modified, it is
reasonable to use a constant list, such as @code{'(4 5)}, as in the
above example.  For the same reason, the last argument need not be a
list:

@example
@group
(setq x (list 1 2 3))
     @result{} (1 2 3)
@end group
@group
(nconc x 'z)
     @result{} (1 2 3 . z)
@end group
@group
x
     @result{} (1 2 3 . z)
@end group
@end example

However, the other arguments (all but the last) should be mutable
lists.

A common pitfall is to use a constant list as a non-last argument to
@code{nconc}.  If you do this, the resulting behavior is undefined
(@pxref{Self-Evaluating Forms}).  It is possible that your program
will change each time you run it!  Here is what might happen (though
this is not guaranteed to happen):

@smallexample
@group
(defun add-foo (x)            ; @r{We want this function to add}
  (nconc '(foo) x))           ;   @r{@code{foo} to the front of its arg.}
@end group

@group
(symbol-function 'add-foo)
     @result{} (lambda (x) (nconc '(foo) x))
@end group

@group
(setq xx (add-foo '(1 2)))    ; @r{It seems to work.}
     @result{} (foo 1 2)
@end group
@group
(setq xy (add-foo '(3 4)))    ; @r{What happened?}
     @result{} (foo 1 2 3 4)
@end group
@group
(eq xx xy)
     @result{} t
@end group

@group
(symbol-function 'add-foo)
     @result{} (lambda (x) (nconc '(foo 1 2 3 4) x))
@end group
@end smallexample
@end defun

@node Sets And Lists
@section Using Lists as Sets
@cindex lists as sets
@cindex sets

  A list can represent an unordered mathematical set---simply consider
a value an element of a set if it appears in the list, and ignore the
order of the list.  To form the union of two sets, use @code{append}
(as long as you don't mind having duplicate elements).  You can remove
@code{equal} duplicates using @code{delete-dups} or @code{seq-uniq}.
Other useful functions for sets include @code{memq} and @code{delq},
and their @code{equal} versions, @code{member} and @code{delete}.

@cindex CL note---lack @code{union}, @code{intersection}
@quotation
@b{Common Lisp note:} Common Lisp has functions @code{union} (which
avoids duplicate elements) and @code{intersection} for set operations.
In Emacs Lisp, variants of these facilities are provided by the
@file{cl-lib} library.  @xref{Lists as Sets,,,cl,Common Lisp Extensions}.
@end quotation

@defun memq object list
@cindex membership in a list
This function tests to see whether @var{object} is a member of
@var{list}.  If it is, @code{memq} returns a list starting with the
first occurrence of @var{object}.  Otherwise, it returns @code{nil}.
The letter @samp{q} in @code{memq} says that it uses @code{eq} to
compare @var{object} against the elements of the list.  For example:

@example
@group
(memq 'b '(a b c b a))
     @result{} (b c b a)
@end group
@group
(memq '(2) '((1) (2)))    ; @r{The two @code{(2)}s need not be @code{eq}.}
     @result{} @r{Unspecified; might be @code{nil} or @code{((2))}.}
@end group
@end example
@end defun

@defun delq object list
@cindex deleting list elements
This function destructively removes all elements @code{eq} to
@var{object} from @var{list}, and returns the resulting list.  The
letter @samp{q} in @code{delq} says that it uses @code{eq} to compare
@var{object} against the elements of the list, like @code{memq} and
@code{remq}.

Typically, when you invoke @code{delq}, you should use the return
value by assigning it to the variable which held the original list.
The reason for this is explained below.
@end defun

The @code{delq} function deletes elements from the front of the list
by simply advancing down the list, and returning a sublist that starts
after those elements.  For example:

@example
@group
(delq 'a '(a b c)) @equiv{} (cdr '(a b c))
@end group
@end example

@noindent
When an element to be deleted appears in the middle of the list,
removing it involves changing the @sc{cdr}s (@pxref{Setcdr}).

@example
@group
(setq sample-list (list 'a 'b 'c '(4)))
     @result{} (a b c (4))
@end group
@group
(delq 'a sample-list)
     @result{} (b c (4))
@end group
@group
sample-list
     @result{} (a b c (4))
@end group
@group
(delq 'c sample-list)
     @result{} (a b (4))
@end group
@group
sample-list
     @result{} (a b (4))
@end group
@end example

Note that @code{(delq 'c sample-list)} modifies @code{sample-list} to
splice out the third element, but @code{(delq 'a sample-list)} does not
splice anything---it just returns a shorter list.  Don't assume that a
variable which formerly held the argument @var{list} now has fewer
elements, or that it still holds the original list!  Instead, save the
result of @code{delq} and use that.  Most often we store the result back
into the variable that held the original list:

@example
(setq flowers (delq 'rose flowers))
@end example

In the following example, the @code{(list 4)} that @code{delq} attempts to match
and the @code{(4)} in the @code{sample-list} are @code{equal} but not @code{eq}:

@example
@group
(delq (list 4) sample-list)
     @result{} (a c (4))
@end group
@end example

If you want to delete elements that are @code{equal} to a given value,
use @code{delete} (see below).

@defun remq object list
This function returns a copy of @var{list}, with all elements removed
which are @code{eq} to @var{object}.  The letter @samp{q} in @code{remq}
says that it uses @code{eq} to compare @var{object} against the elements
of @code{list}.

@example
@group
(setq sample-list (list 'a 'b 'c 'a 'b 'c))
     @result{} (a b c a b c)
@end group
@group
(remq 'a sample-list)
     @result{} (b c b c)
@end group
@group
sample-list
     @result{} (a b c a b c)
@end group
@end example
@end defun

@defun memql object list
The function @code{memql} tests to see whether @var{object} is a member
of @var{list}, comparing members with @var{object} using @code{eql},
so floating-point elements are compared by value.
If @var{object} is a member, @code{memql} returns a list starting with
its first occurrence in @var{list}.  Otherwise, it returns @code{nil}.

Compare this with @code{memq}:

@example
@group
(memql 1.2 '(1.1 1.2 1.3))  ; @r{@code{1.2} and @code{1.2} are @code{eql}.}
     @result{} (1.2 1.3)
@end group
@group
(memq 1.2 '(1.1 1.2 1.3))  ; @r{The two @code{1.2}s need not be @code{eq}.}
     @result{} @r{Unspecified; might be @code{nil} or @code{(1.2 1.3)}.}
@end group
@end example
@end defun

The following three functions are like @code{memq}, @code{delq} and
@code{remq}, but use @code{equal} rather than @code{eq} to compare
elements.  @xref{Equality Predicates}.

@defun member object list
The function @code{member} tests to see whether @var{object} is a member
of @var{list}, comparing members with @var{object} using @code{equal}.
If @var{object} is a member, @code{member} returns a list starting with
its first occurrence in @var{list}.  Otherwise, it returns @code{nil}.

Compare this with @code{memq}:

@example
@group
(member '(2) '((1) (2)))  ; @r{@code{(2)} and @code{(2)} are @code{equal}.}
     @result{} ((2))
@end group
@group
(memq '(2) '((1) (2)))    ; @r{The two @code{(2)}s need not be @code{eq}.}
     @result{} @r{Unspecified; might be @code{nil} or @code{(2)}.}
@end group
@group
;; @r{Two strings with the same contents are @code{equal}.}
(member "foo" '("foo" "bar"))
     @result{} ("foo" "bar")
@end group
@end example
@end defun

@defun delete object sequence
This function removes all elements @code{equal} to @var{object} from
@var{sequence}, and returns the resulting sequence.

If @var{sequence} is a list, @code{delete} is to @code{delq} as
@code{member} is to @code{memq}: it uses @code{equal} to compare
elements with @var{object}, like @code{member}; when it finds an
element that matches, it cuts the element out just as @code{delq}
would.  As with @code{delq}, you should typically use the return value
by assigning it to the variable which held the original list.

If @code{sequence} is a vector or string, @code{delete} returns a copy
of @code{sequence} with all elements @code{equal} to @code{object}
removed.

For example:

@example
@group
(setq l (list '(2) '(1) '(2)))
(delete '(2) l)
     @result{} ((1))
l
     @result{} ((2) (1))
;; @r{If you want to change @code{l} reliably,}
;; @r{write @code{(setq l (delete '(2) l))}.}
@end group
@group
(setq l (list '(2) '(1) '(2)))
(delete '(1) l)
     @result{} ((2) (2))
l
     @result{} ((2) (2))
;; @r{In this case, it makes no difference whether you set @code{l},}
;; @r{but you should do so for the sake of the other case.}
@end group
@group
(delete '(2) [(2) (1) (2)])
     @result{} [(1)]
@end group
@end example
@end defun

@defun remove object sequence
This function is the non-destructive counterpart of @code{delete}.  It
returns a copy of @code{sequence}, a list, vector, or string, with
elements @code{equal} to @code{object} removed.  For example:

@example
@group
(remove '(2) '((2) (1) (2)))
     @result{} ((1))
@end group
@group
(remove '(2) [(2) (1) (2)])
     @result{} [(1)]
@end group
@end example
@end defun

@quotation
@b{Common Lisp note:} The functions @code{member}, @code{delete} and
@code{remove} in GNU Emacs Lisp are derived from Maclisp, not Common
Lisp.  The Common Lisp versions do not use @code{equal} to compare
elements.
@end quotation

@defun member-ignore-case object list
This function is like @code{member}, except that @var{object} should
be a string and that it ignores differences in letter-case and text
representation: upper-case and lower-case letters are treated as
equal, and unibyte strings are converted to multibyte prior to
comparison.
@end defun

@defun delete-dups list
This function destructively removes all @code{equal} duplicates from
@var{list}, stores the result in @var{list} and returns it.  Of
several @code{equal} occurrences of an element in @var{list},
@code{delete-dups} keeps the first one.  See @code{seq-uniq} for
non-destructive operation (@pxref{Sequence Functions}).
@end defun

  See also the function @code{add-to-list}, in @ref{List Variables},
for a way to add an element to a list stored in a variable and used as a
set.

@node Association Lists
@section Association Lists
@cindex association list
@cindex alist

  An @dfn{association list}, or @dfn{alist} for short, records a mapping
from keys to values.  It is a list of cons cells called
@dfn{associations}: the @sc{car} of each cons cell is the @dfn{key}, and the
@sc{cdr} is the @dfn{associated value}.@footnote{This usage of ``key''
is not related to the term ``key sequence''; it means a value used to
look up an item in a table.  In this case, the table is the alist, and
the alist associations are the items.}

  Here is an example of an alist.  The key @code{pine} is associated with
the value @code{cones}; the key @code{oak} is associated with
@code{acorns}; and the key @code{maple} is associated with @code{seeds}.

@example
@group
((pine . cones)
 (oak . acorns)
 (maple . seeds))
@end group
@end example

  Both the values and the keys in an alist may be any Lisp objects.
For example, in the following alist, the symbol @code{a} is
associated with the number @code{1}, and the string @code{"b"} is
associated with the @emph{list} @code{(2 3)}, which is the @sc{cdr} of
the alist element:

@example
((a . 1) ("b" 2 3))
@end example

  Sometimes it is better to design an alist to store the associated
value in the @sc{car} of the @sc{cdr} of the element.  Here is an
example of such an alist:

@example
((rose red) (lily white) (buttercup yellow))
@end example

@noindent
Here we regard @code{red} as the value associated with @code{rose}.  One
advantage of this kind of alist is that you can store other related
information---even a list of other items---in the @sc{cdr} of the
@sc{cdr}.  One disadvantage is that you cannot use @code{rassq} (see
below) to find the element containing a given value.  When neither of
these considerations is important, the choice is a matter of taste, as
long as you are consistent about it for any given alist.

  The same alist shown above could be regarded as having the
associated value in the @sc{cdr} of the element; the value associated
with @code{rose} would be the list @code{(red)}.

  Association lists are often used to record information that you might
otherwise keep on a stack, since new associations may be added easily to
the front of the list.  When searching an association list for an
association with a given key, the first one found is returned, if there
is more than one.

  In Emacs Lisp, it is @emph{not} an error if an element of an
association list is not a cons cell.  The alist search functions simply
ignore such elements.  Many other versions of Lisp signal errors in such
cases.

  Note that property lists are similar to association lists in several
respects.  A property list behaves like an association list in which
each key can occur only once.  @xref{Property Lists}, for a comparison
of property lists and association lists.

@defun assoc key alist &optional testfn
This function returns the first association for @var{key} in
@var{alist}, comparing @var{key} against the alist elements using
@var{testfn} if it is a function, and @code{equal} otherwise
(@pxref{Equality Predicates}).  If @var{testfn} is a function, it is
called with two arguments: the @sc{car} of an element from @var{alist}
and @var{key}.  The function returns @code{nil} if no
association in @var{alist} has a @sc{car} equal to @var{key}, as
tested by @var{testfn}.  For example:

@smallexample
(setq trees '((pine . cones) (oak . acorns) (maple . seeds)))
     @result{} ((pine . cones) (oak . acorns) (maple . seeds))
(assoc 'oak trees)
     @result{} (oak . acorns)
(cdr (assoc 'oak trees))
     @result{} acorns
(assoc 'birch trees)
     @result{} nil
@end smallexample

Here is another example, in which the keys and values are not symbols:

@smallexample
(setq needles-per-cluster
      '((2 "Austrian Pine" "Red Pine")
        (3 "Pitch Pine")
        (5 "White Pine")))

(cdr (assoc 3 needles-per-cluster))
     @result{} ("Pitch Pine")
(cdr (assoc 2 needles-per-cluster))
     @result{} ("Austrian Pine" "Red Pine")
@end smallexample
@end defun

  The function @code{assoc-string} is much like @code{assoc} except
that it ignores certain differences between strings.  @xref{Text
Comparison}.

@defun rassoc value alist
This function returns the first association with value @var{value} in
@var{alist}.  It returns @code{nil} if no association in @var{alist} has
a @sc{cdr} @code{equal} to @var{value}.

@code{rassoc} is like @code{assoc} except that it compares the @sc{cdr} of
each @var{alist} association instead of the @sc{car}.  You can think of
this as reverse @code{assoc}, finding the key for a given value.
@end defun

@defun assq key alist
This function is like @code{assoc} in that it returns the first
association for @var{key} in @var{alist}, but it makes the comparison
using @code{eq}.  @code{assq} returns @code{nil} if no association in
@var{alist} has a @sc{car} @code{eq} to @var{key}.  This function is
used more often than @code{assoc}, since @code{eq} is faster than
@code{equal} and most alists use symbols as keys.  @xref{Equality
Predicates}.

@smallexample
(setq trees '((pine . cones) (oak . acorns) (maple . seeds)))
     @result{} ((pine . cones) (oak . acorns) (maple . seeds))
(assq 'pine trees)
     @result{} (pine . cones)
@end smallexample

On the other hand, @code{assq} is not usually useful in alists where the
keys may not be symbols:

@smallexample
(setq leaves
      '(("simple leaves" . oak)
        ("compound leaves" . horsechestnut)))

(assq "simple leaves" leaves)
     @result{} @r{Unspecified; might be @code{nil} or @code{("simple leaves" . oak)}.}
(assoc "simple leaves" leaves)
     @result{} ("simple leaves" . oak)
@end smallexample
@end defun

@defun alist-get key alist &optional default remove testfn
This function is similar to @code{assq}.  It finds the first
association @w{@code{(@var{key} . @var{value})}} by comparing
@var{key} with @var{alist} elements, and, if found, returns the
@var{value} of that association.  If no association is found, the
function returns @var{default}.  Comparison of @var{key} against
@var{alist} elements uses the function specified by @var{testfn},
defaulting to @code{eq}.

This is a generalized variable (@pxref{Generalized Variables})
that can be used to change a value with @code{setf}.  When
using it to set a value, optional argument @var{remove} non-@code{nil}
means to remove @var{key}'s association from @var{alist} if the new
value is @code{eql} to @var{default}.
@end defun

@defun rassq value alist
This function returns the first association with value @var{value} in
@var{alist}.  It returns @code{nil} if no association in @var{alist} has
a @sc{cdr} @code{eq} to @var{value}.

@code{rassq} is like @code{assq} except that it compares the @sc{cdr} of
each @var{alist} association instead of the @sc{car}.  You can think of
this as reverse @code{assq}, finding the key for a given value.

For example:

@smallexample
(setq trees '((pine . cones) (oak . acorns) (maple . seeds)))

(rassq 'acorns trees)
     @result{} (oak . acorns)
(rassq 'spores trees)
     @result{} nil
@end smallexample

@code{rassq} cannot search for a value stored in the @sc{car}
of the @sc{cdr} of an element:

@smallexample
(setq colors '((rose red) (lily white) (buttercup yellow)))

(rassq 'white colors)
     @result{} nil
@end smallexample

In this case, the @sc{cdr} of the association @code{(lily white)} is not
the symbol @code{white}, but rather the list @code{(white)}.  This
becomes clearer if the association is written in dotted pair notation:

@smallexample
(lily white) @equiv{} (lily . (white))
@end smallexample
@end defun

@defun assoc-default key alist &optional test default
This function searches @var{alist} for a match for @var{key}.  For each
element of @var{alist}, it compares the element (if it is an atom) or
the element's @sc{car} (if it is a cons) against @var{key}, by calling
@var{test} with two arguments: the element or its @sc{car}, and
@var{key}.  The arguments are passed in that order so that you can get
useful results using @code{string-match} with an alist that contains
regular expressions (@pxref{Regexp Search}).  If @var{test} is omitted
or @code{nil}, @code{equal} is used for comparison.

If an alist element matches @var{key} by this criterion,
then @code{assoc-default} returns a value based on this element.
If the element is a cons, then the value is the element's @sc{cdr}.
Otherwise, the return value is @var{default}.

If no alist element matches @var{key}, @code{assoc-default} returns
@code{nil}.
@end defun

@defun copy-alist alist
@cindex copying alists
This function returns a two-level deep copy of @var{alist}: it creates a
new copy of each association, so that you can alter the associations of
the new alist without changing the old one.

@smallexample
@group
(setq needles-per-cluster
      '((2 . ("Austrian Pine" "Red Pine"))
        (3 . ("Pitch Pine"))
@end group
        (5 . ("White Pine"))))
@result{}
((2 "Austrian Pine" "Red Pine")
 (3 "Pitch Pine")
 (5 "White Pine"))

(setq copy (copy-alist needles-per-cluster))
@result{}
((2 "Austrian Pine" "Red Pine")
 (3 "Pitch Pine")
 (5 "White Pine"))

(eq needles-per-cluster copy)
     @result{} nil
(equal needles-per-cluster copy)
     @result{} t
(eq (car needles-per-cluster) (car copy))
     @result{} nil
(cdr (car (cdr needles-per-cluster)))
     @result{} ("Pitch Pine")
@group
(eq (cdr (car (cdr needles-per-cluster)))
    (cdr (car (cdr copy))))
     @result{} t
@end group
@end smallexample

  This example shows how @code{copy-alist} makes it possible to change
the associations of one copy without affecting the other:

@smallexample
@group
(setcdr (assq 3 copy) '("Martian Vacuum Pine"))
(cdr (assq 3 needles-per-cluster))
     @result{} ("Pitch Pine")
@end group
@end smallexample
@end defun

@defun assq-delete-all key alist
This function deletes from @var{alist} all the elements whose @sc{car}
is @code{eq} to @var{key}, much as if you used @code{delq} to delete
each such element one by one.  It returns the shortened alist, and
often modifies the original list structure of @var{alist}.  For
correct results, use the return value of @code{assq-delete-all} rather
than looking at the saved value of @var{alist}.

@example
(setq alist (list '(foo 1) '(bar 2) '(foo 3) '(lose 4)))
     @result{} ((foo 1) (bar 2) (foo 3) (lose 4))
(assq-delete-all 'foo alist)
     @result{} ((bar 2) (lose 4))
alist
     @result{} ((foo 1) (bar 2) (lose 4))
@end example
@end defun

@defun assoc-delete-all key alist &optional test
This function is like @code{assq-delete-all} except that it accepts
an optional argument @var{test}, a predicate function to compare the
keys in @var{alist}.  If omitted or @code{nil}, @var{test} defaults to
@code{equal}.  As @code{assq-delete-all}, this function often modifies
the original list structure of @var{alist}.
@end defun

@defun rassq-delete-all value alist
This function deletes from @var{alist} all the elements whose @sc{cdr}
is @code{eq} to @var{value}.  It returns the shortened alist, and
often modifies the original list structure of @var{alist}.
@code{rassq-delete-all} is like @code{assq-delete-all} except that it
compares the @sc{cdr} of each @var{alist} association instead of the
@sc{car}.
@end defun

@defmac let-alist alist body
Creates a binding for each symbol used as keys the association list
@var{alist}, prefixed with dot.  This can be useful when accessing
several items in the same association list, and it's best understood
through a simple example:

@lisp
(setq colors '((rose . red) (lily . white) (buttercup . yellow)))
(let-alist colors
  (if (eq .rose 'red)
      .lily))
     @result{} white
@end lisp

The @var{body} is inspected at compilation time, and only the symbols
that appear in @var{body} with a @samp{.} as the first character in
the symbol name will be bound.  Finding the keys is done with
@code{assq}, and the @code{cdr} of the return value of this
@code{assq} is assigned as the value for the binding.

Nested association lists is supported:

@lisp
(setq colors '((rose . red) (lily (belladonna . yellow) (brindisi . pink))))
(let-alist colors
  (if (eq .rose 'red)
      .lily.belladonna))
     @result{} yellow
@end lisp

Nesting @code{let-alist} inside each other is allowed, but the code in
the inner @code{let-alist} can't access the variables bound by the
outer @code{let-alist}.
@end defmac

@node Property Lists
@section Property Lists
@cindex property list
@cindex plist

  A @dfn{property list} (@dfn{plist} for short) is a list of paired
elements.  Each of the pairs associates a property name (usually a
symbol) with a property or value.  Here is an example of a property
list:

@example
(pine cones numbers (1 2 3) color "blue")
@end example

@noindent
This property list associates @code{pine} with @code{cones},
@code{numbers} with @code{(1 2 3)}, and @code{color} with
@code{"blue"}.  The property names and values can be any Lisp objects,
but the names are usually symbols (as they are in this example).

  Property lists are used in several contexts.  For instance, the
function @code{put-text-property} takes an argument which is a
property list, specifying text properties and associated values which
are to be applied to text in a string or buffer.  @xref{Text
Properties}.

  Another prominent use of property lists is for storing symbol
properties.  Every symbol possesses a list of properties, used to
record miscellaneous information about the symbol; these properties
are stored in the form of a property list.  @xref{Symbol Properties}.

@menu
* Plists and Alists::           Comparison of the advantages of property
                                  lists and association lists.
* Plist Access::                Accessing property lists stored elsewhere.
@end menu

@node Plists and Alists
@subsection Property Lists and Association Lists
@cindex plist vs. alist
@cindex alist vs. plist

@cindex property lists vs association lists
  Association lists (@pxref{Association Lists}) are very similar to
property lists.  In contrast to association lists, the order of the
pairs in the property list is not significant, since the property
names must be distinct.

  Property lists are better than association lists for attaching
information to various Lisp function names or variables.  If your
program keeps all such information in one association list, it will
typically need to search that entire list each time it checks for an
association for a particular Lisp function name or variable, which
could be slow.  By contrast, if you keep the same information in the
property lists of the function names or variables themselves, each
search will scan only the length of one property list, which is
usually short.  This is why the documentation for a variable is
recorded in a property named @code{variable-documentation}.  The byte
compiler likewise uses properties to record those functions needing
special treatment.

  However, association lists have their own advantages.  Depending on
your application, it may be faster to add an association to the front of
an association list than to update a property.  All properties for a
symbol are stored in the same property list, so there is a possibility
of a conflict between different uses of a property name.  (For this
reason, it is a good idea to choose property names that are probably
unique, such as by beginning the property name with the program's usual
name-prefix for variables and functions.)  An association list may be
used like a stack where associations are pushed on the front of the list
and later discarded; this is not possible with a property list.

@node Plist Access
@subsection Property Lists Outside Symbols
@cindex plist access
@cindex accessing plist properties

  The following functions can be used to manipulate property lists.
They all compare property names using @code{eq}.

@defun plist-get plist property
This returns the value of the @var{property} property stored in the
property list @var{plist}.  It accepts a malformed @var{plist}
argument.  If @var{property} is not found in the @var{plist}, it
returns @code{nil}.  For example,

@example
(plist-get '(foo 4) 'foo)
     @result{} 4
(plist-get '(foo 4 bad) 'foo)
     @result{} 4
(plist-get '(foo 4 bad) 'bad)
     @result{} nil
(plist-get '(foo 4 bad) 'bar)
     @result{} nil
@end example
@end defun

@defun plist-put plist property value
This stores @var{value} as the value of the @var{property} property in
the property list @var{plist}.  It may modify @var{plist} destructively,
or it may construct a new list structure without altering the old.  The
function returns the modified property list, so you can store that back
in the place where you got @var{plist}.  For example,

@example
(setq my-plist (list 'bar t 'foo 4))
     @result{} (bar t foo 4)
(setq my-plist (plist-put my-plist 'foo 69))
     @result{} (bar t foo 69)
(setq my-plist (plist-put my-plist 'quux '(a)))
     @result{} (bar t foo 69 quux (a))
@end example
@end defun

@defun lax-plist-get plist property
Like @code{plist-get} except that it compares properties
using @code{equal} instead of @code{eq}.
@end defun

@defun lax-plist-put plist property value
Like @code{plist-put} except that it compares properties
using @code{equal} instead of @code{eq}.
@end defun

@defun plist-member plist property
This returns non-@code{nil} if @var{plist} contains the given
@var{property}.  Unlike @code{plist-get}, this allows you to distinguish
between a missing property and a property with the value @code{nil}.
The value is actually the tail of @var{plist} whose @code{car} is
@var{property}.
@end defun
