@c -*-texinfo-*-
@c This is part of the GNU Emacs Lisp Reference Manual.
@c Copyright (C) 1990-1995, 1998-1999, 2001-2017 Free Software
@c Foundation, Inc.
@c See the file elisp.texi for copying conditions.
@node Sequences Arrays Vectors
@chapter Sequences, Arrays, and Vectors
@cindex sequence

  The @dfn{sequence} type is the union of two other Lisp types: lists
and arrays.  In other words, any list is a sequence, and any array is
a sequence.  The common property that all sequences have is that each
is an ordered collection of elements.

  An @dfn{array} is a fixed-length object with a slot for each of its
elements.  All the elements are accessible in constant time.  The four
types of arrays are strings, vectors, char-tables and bool-vectors.

  A list is a sequence of elements, but it is not a single primitive
object; it is made of cons cells, one cell per element.  Finding the
@var{n}th element requires looking through @var{n} cons cells, so
elements farther from the beginning of the list take longer to access.
But it is possible to add elements to the list, or remove elements.

  The following diagram shows the relationship between these types:

@example
@group
          _____________________________________________
         |                                             |
         |          Sequence                           |
         |  ______   ________________________________  |
         | |      | |                                | |
         | | List | |             Array              | |
         | |      | |    ________       ________     | |
         | |______| |   |        |     |        |    | |
         |          |   | Vector |     | String |    | |
         |          |   |________|     |________|    | |
         |          |  ____________   _____________  | |
         |          | |            | |             | | |
         |          | | Char-table | | Bool-vector | | |
         |          | |____________| |_____________| | |
         |          |________________________________| |
         |_____________________________________________|
@end group
@end example

@menu
* Sequence Functions::    Functions that accept any kind of sequence.
* Arrays::                Characteristics of arrays in Emacs Lisp.
* Array Functions::       Functions specifically for arrays.
* Vectors::               Special characteristics of Emacs Lisp vectors.
* Vector Functions::      Functions specifically for vectors.
* Char-Tables::           How to work with char-tables.
* Bool-Vectors::          How to work with bool-vectors.
* Rings::                 Managing a fixed-size ring of objects.
@end menu

@node Sequence Functions
@section Sequences

  This section describes functions that accept any kind of sequence.

@defun sequencep object
This function returns @code{t} if @var{object} is a list, vector,
string, bool-vector, or char-table, @code{nil} otherwise.
@end defun

@defun length sequence
@cindex string length
@cindex list length
@cindex vector length
@cindex sequence length
@cindex char-table length
@anchor{Definition of length}
This function returns the number of elements in @var{sequence}.  If
@var{sequence} is a dotted list, a @code{wrong-type-argument} error is
signaled.  Circular lists may cause an infinite loop.  For a
char-table, the value returned is always one more than the maximum
Emacs character code.

@xref{Definition of safe-length}, for the related function @code{safe-length}.

@example
@group
(length '(1 2 3))
    @result{} 3
@end group
@group
(length ())
    @result{} 0
@end group
@group
(length "foobar")
    @result{} 6
@end group
@group
(length [1 2 3])
    @result{} 3
@end group
@group
(length (make-bool-vector 5 nil))
    @result{} 5
@end group
@end example
@end defun

@noindent
See also @code{string-bytes}, in @ref{Text Representations}.

If you need to compute the width of a string on display, you should use
@code{string-width} (@pxref{Size of Displayed Text}), not @code{length},
since @code{length} only counts the number of characters, but does not
account for the display width of each character.

@defun elt sequence index
@anchor{Definition of elt}
@cindex elements of sequences
This function returns the element of @var{sequence} indexed by
@var{index}.  Legitimate values of @var{index} are integers ranging
from 0 up to one less than the length of @var{sequence}.  If
@var{sequence} is a list, out-of-range values behave as for
@code{nth}.  @xref{Definition of nth}.  Otherwise, out-of-range values
trigger an @code{args-out-of-range} error.

@example
@group
(elt [1 2 3 4] 2)
     @result{} 3
@end group
@group
(elt '(1 2 3 4) 2)
     @result{} 3
@end group
@group
;; @r{We use @code{string} to show clearly which character @code{elt} returns.}
(string (elt "1234" 2))
     @result{} "3"
@end group
@group
(elt [1 2 3 4] 4)
     @error{} Args out of range: [1 2 3 4], 4
@end group
@group
(elt [1 2 3 4] -1)
     @error{} Args out of range: [1 2 3 4], -1
@end group
@end example

This function generalizes @code{aref} (@pxref{Array Functions}) and
@code{nth} (@pxref{Definition of nth}).
@end defun

@defun copy-sequence seqr
@cindex copying sequences
This function returns a copy of @var{seqr}, which should be either a
sequence or a record.  The copy is the same type of object as the
original, and it has the same elements in the same order.

Storing a new element into the copy does not affect the original
@var{seqr}, and vice versa.  However, the elements of the copy
are not copies; they are identical (@code{eq}) to the elements
of the original.  Therefore, changes made within these elements, as
found via the copy, are also visible in the original.

If the argument is a string with text properties, the property list in
the copy is itself a copy, not shared with the original's property
list.  However, the actual values of the properties are shared.
@xref{Text Properties}.

This function does not work for dotted lists.  Trying to copy a
circular list may cause an infinite loop.

See also @code{append} in @ref{Building Lists}, @code{concat} in
@ref{Creating Strings}, and @code{vconcat} in @ref{Vector Functions},
for other ways to copy sequences.

@example
@group
(setq bar '(1 2))
     @result{} (1 2)
@end group
@group
(setq x (vector 'foo bar))
     @result{} [foo (1 2)]
@end group
@group
(setq y (copy-sequence x))
     @result{} [foo (1 2)]
@end group

@group
(eq x y)
     @result{} nil
@end group
@group
(equal x y)
     @result{} t
@end group
@group
(eq (elt x 1) (elt y 1))
     @result{} t
@end group

@group
;; @r{Replacing an element of one sequence.}
(aset x 0 'quux)
x @result{} [quux (1 2)]
y @result{} [foo (1 2)]
@end group

@group
;; @r{Modifying the inside of a shared element.}
(setcar (aref x 1) 69)
x @result{} [quux (69 2)]
y @result{} [foo (69 2)]
@end group
@end example
@end defun

@defun reverse sequence
@cindex string reverse
@cindex list reverse
@cindex vector reverse
@cindex sequence reverse
This function creates a new sequence whose elements are the elements
of @var{sequence}, but in reverse order.  The original argument @var{sequence}
is @emph{not} altered.  Note that char-tables cannot be reversed.

@example
@group
(setq x '(1 2 3 4))
     @result{} (1 2 3 4)
@end group
@group
(reverse x)
     @result{} (4 3 2 1)
x
     @result{} (1 2 3 4)
@end group
@group
(setq x [1 2 3 4])
     @result{} [1 2 3 4]
@end group
@group
(reverse x)
     @result{} [4 3 2 1]
x
     @result{} [1 2 3 4]
@end group
@group
(setq x "xyzzy")
     @result{} "xyzzy"
@end group
@group
(reverse x)
     @result{} "yzzyx"
x
     @result{} "xyzzy"
@end group
@end example
@end defun

@defun nreverse sequence
@cindex reversing a string
@cindex reversing a list
@cindex reversing a vector
  This function reverses the order of the elements of @var{sequence}.
Unlike @code{reverse} the original @var{sequence} may be modified.

  For example:

@example
@group
(setq x '(a b c))
     @result{} (a b c)
@end group
@group
x
     @result{} (a b c)
(nreverse x)
     @result{} (c b a)
@end group
@group
;; @r{The cons cell that was first is now last.}
x
     @result{} (a)
@end group
@end example

  To avoid confusion, we usually store the result of @code{nreverse}
back in the same variable which held the original list:

@example
(setq x (nreverse x))
@end example

  Here is the @code{nreverse} of our favorite example, @code{(a b c)},
presented graphically:

@smallexample
@group
@r{Original list head:}                       @r{Reversed list:}
 -------------        -------------        ------------
| car  | cdr  |      | car  | cdr  |      | car | cdr  |
|   a  |  nil |<--   |   b  |   o  |<--   |   c |   o  |
|      |      |   |  |      |   |  |   |  |     |   |  |
 -------------    |   --------- | -    |   -------- | -
                  |             |      |            |
                   -------------        ------------
@end group
@end smallexample

  For the vector, it is even simpler because you don't need setq:

@example
(setq x [1 2 3 4])
     @result{} [1 2 3 4]
(nreverse x)
     @result{} [4 3 2 1]
x
     @result{} [4 3 2 1]
@end example

Note that unlike @code{reverse}, this function doesn't work with strings.
Although you can alter string data by using @code{aset}, it is strongly
encouraged to treat strings as immutable.

@end defun

@defun sort sequence predicate
@cindex stable sort
@cindex sorting lists
@cindex sorting vectors
This function sorts @var{sequence} stably.  Note that this function doesn't work
for all sequences; it may be used only for lists and vectors.  If @var{sequence}
is a list, it is modified destructively.  This functions returns the sorted
@var{sequence} and compares elements using @var{predicate}.  A stable sort is
one in which elements with equal sort keys maintain their relative order before
and after the sort.  Stability is important when successive sorts are used to
order elements according to different criteria.

The argument @var{predicate} must be a function that accepts two
arguments.  It is called with two elements of @var{sequence}.  To get an
increasing order sort, the @var{predicate} should return non-@code{nil} if the
first element is ``less'' than the second, or @code{nil} if not.

The comparison function @var{predicate} must give reliable results for
any given pair of arguments, at least within a single call to
@code{sort}.  It must be @dfn{antisymmetric}; that is, if @var{a} is
less than @var{b}, @var{b} must not be less than @var{a}.  It must be
@dfn{transitive}---that is, if @var{a} is less than @var{b}, and @var{b}
is less than @var{c}, then @var{a} must be less than @var{c}.  If you
use a comparison function which does not meet these requirements, the
result of @code{sort} is unpredictable.

The destructive aspect of @code{sort} for lists is that it rearranges the
cons cells forming @var{sequence} by changing @sc{cdr}s.  A nondestructive
sort function would create new cons cells to store the elements in their
sorted order.  If you wish to make a sorted copy without destroying the
original, copy it first with @code{copy-sequence} and then sort.

Sorting does not change the @sc{car}s of the cons cells in @var{sequence};
the cons cell that originally contained the element @code{a} in
@var{sequence} still has @code{a} in its @sc{car} after sorting, but it now
appears in a different position in the list due to the change of
@sc{cdr}s.  For example:

@example
@group
(setq nums '(1 3 2 6 5 4 0))
     @result{} (1 3 2 6 5 4 0)
@end group
@group
(sort nums '<)
     @result{} (0 1 2 3 4 5 6)
@end group
@group
nums
     @result{} (1 2 3 4 5 6)
@end group
@end example

@noindent
@strong{Warning}: Note that the list in @code{nums} no longer contains
0; this is the same cons cell that it was before, but it is no longer
the first one in the list.  Don't assume a variable that formerly held
the argument now holds the entire sorted list!  Instead, save the result
of @code{sort} and use that.  Most often we store the result back into
the variable that held the original list:

@example
(setq nums (sort nums '<))
@end example

For the better understanding of what stable sort is, consider the following
vector example.  After sorting, all items whose @code{car} is 8 are grouped
at the beginning of @code{vector}, but their relative order is preserved.
All items whose @code{car} is 9 are grouped at the end of @code{vector},
but their relative order is also preserved:

@example
@group
(setq
  vector
  (vector '(8 . "xxx") '(9 . "aaa") '(8 . "bbb") '(9 . "zzz")
          '(9 . "ppp") '(8 . "ttt") '(8 . "eee") '(9 . "fff")))
     @result{} [(8 . "xxx") (9 . "aaa") (8 . "bbb") (9 . "zzz")
         (9 . "ppp") (8 . "ttt") (8 . "eee") (9 . "fff")]
@end group
@group
(sort vector (lambda (x y) (< (car x) (car y))))
     @result{} [(8 . "xxx") (8 . "bbb") (8 . "ttt") (8 . "eee")
         (9 . "aaa") (9 . "zzz") (9 . "ppp") (9 . "fff")]
@end group
@end example

@xref{Sorting}, for more functions that perform sorting.
See @code{documentation} in @ref{Accessing Documentation}, for a
useful example of @code{sort}.
@end defun

@cindex sequence functions in seq
@cindex seq library
  The @file{seq.el} library provides the following additional sequence
manipulation macros and functions, prefixed with @code{seq-}.  To use
them, you must first load the @file{seq} library.

  All functions defined in this library are free of side-effects;
i.e., they do not modify any sequence (list, vector, or string) that
you pass as an argument.  Unless otherwise stated, the result is a
sequence of the same type as the input.  For those functions that take
a predicate, this should be a function of one argument.

  The @file{seq.el} library can be extended to work with additional
types of sequential data-structures.  For that purpose, all functions
are defined using @code{cl-defgeneric}.  @xref{Generic Functions}, for
more details about using @code{cl-defgeneric} for adding extensions.

@defun seq-elt sequence index
  This function returns the element of @var{sequence} at the specified
@var{index}, which is an integer whose valid value range is zero to
one less than the length of @var{sequence}.  For out-of-range values
on built-in sequence types, @code{seq-elt} behaves like @code{elt}.
For the details, see @ref{Definition of elt}.

@example
@group
(seq-elt [1 2 3 4] 2)
@result{} 3
@end group
@end example

  @code{seq-elt} returns places settable using @code{setf}
(@pxref{Setting Generalized Variables}).

@example
@group
(setq vec [1 2 3 4])
(setf (seq-elt vec 2) 5)
vec
@result{} [1 2 5 4]
@end group
@end example
@end defun

@defun seq-length sequence
  This function returns the number of elements in @var{sequence}.  For
built-in sequence types, @code{seq-length} behaves like @code{length}.
@xref{Definition of length}.
@end defun

@defun seqp sequence
  This function returns non-@code{nil} if @var{sequence} is a sequence
(a list or array), or any additional type of sequence defined via
@file{seq.el} generic functions.

@example
@group
(seqp [1 2])
@result{} t
@end group
@group
(seqp 2)
@result{} nil
@end group
@end example
@end defun

@defun seq-drop sequence n
  This function returns all but the first @var{n} (an integer)
elements of @var{sequence}.  If @var{n} is negative or zero,
the result is @var{sequence}.

@example
@group
(seq-drop [1 2 3 4 5 6] 3)
@result{} [4 5 6]
@end group
@group
(seq-drop "hello world" -4)
@result{} "hello world"
@end group
@end example
@end defun

@defun seq-take sequence n
  This function returns the first @var{n} (an integer) elements of
@var{sequence}.  If @var{n} is negative or zero, the result
is @code{nil}.

@example
@group
(seq-take '(1 2 3 4) 3)
@result{} (1 2 3)
@end group
@group
(seq-take [1 2 3 4] 0)
@result{} []
@end group
@end example
@end defun

@defun seq-take-while predicate sequence
  This function returns the members of @var{sequence} in order,
stopping before the first one for which @var{predicate} returns @code{nil}.

@example
@group
(seq-take-while (lambda (elt) (> elt 0)) '(1 2 3 -1 -2))
@result{} (1 2 3)
@end group
@group
(seq-take-while (lambda (elt) (> elt 0)) [-1 4 6])
@result{} []
@end group
@end example
@end defun

@defun seq-drop-while predicate sequence
  This function returns the members of @var{sequence} in order,
starting from the first one for which @var{predicate} returns @code{nil}.

@example
@group
(seq-drop-while (lambda (elt) (> elt 0)) '(1 2 3 -1 -2))
@result{} (-1 -2)
@end group
@group
(seq-drop-while (lambda (elt) (< elt 0)) [1 4 6])
@result{} [1 4 6]
@end group
@end example
@end defun

@defun seq-do function sequence
  This function applies @var{function} to each element of
@var{sequence} in turn (presumably for side effects), and returns
@var{sequence}.
@end defun

@defun seq-map function sequence
  This function returns the result of applying @var{function} to each
element of @var{sequence}.  The returned value is a list.

@example
@group
(seq-map #'1+ '(2 4 6))
@result{} (3 5 7)
@end group
@group
(seq-map #'symbol-name [foo bar])
@result{} ("foo" "bar")
@end group
@end example
@end defun

@defun seq-map-indexed function sequence
  This function returns the result of applying @var{function} to each
element of @var{sequence} and its index within @var{seq}.  The
returned value is a list.

@example
@group
(seq-map-indexed (lambda (elt idx)
                   (list idx elt))
                 '(a b c))
@result{} ((0 a) (b 1) (c 2))
@end group
@end example
@end defun

@defun seq-mapn function &rest sequences
  This function returns the result of applying @var{function} to each
element of @var{sequences}.  The arity (@pxref{What Is a Function,
sub-arity}) of @var{function} must match the number of sequences.
Mapping stops at the end of the shortest sequence, and the returned
value is a list.

@example
@group
(seq-mapn #'+ '(2 4 6) '(20 40 60))
@result{} (22 44 66)
@end group
@group
(seq-mapn #'concat '("moskito" "bite") ["bee" "sting"])
@result{} ("moskitobee" "bitesting")
@end group
@end example
@end defun

@defun seq-filter predicate sequence
@cindex filtering sequences
  This function returns a list of all the elements in @var{sequence}
for which @var{predicate} returns non-@code{nil}.

@example
@group
(seq-filter (lambda (elt) (> elt 0)) [1 -1 3 -3 5])
@result{} (1 3 5)
@end group
@group
(seq-filter (lambda (elt) (> elt 0)) '(-1 -3 -5))
@result{} nil
@end group
@end example
@end defun

@defun seq-remove predicate sequence
@cindex removing from sequences
  This function returns a list of all the elements in @var{sequence}
for which @var{predicate} returns @code{nil}.

@example
@group
(seq-remove (lambda (elt) (> elt 0)) [1 -1 3 -3 5])
@result{} (-1 -3)
@end group
@group
(seq-remove (lambda (elt) (< elt 0)) '(-1 -3 -5))
@result{} nil
@end group
@end example
@end defun

@defun seq-reduce function sequence initial-value
@cindex reducing sequences
  This function returns the result of calling @var{function} with
@var{initial-value} and the first element of @var{sequence}, then calling
@var{function} with that result and the second element of @var{sequence},
then with that result and the third element of @var{sequence}, etc.
@var{function} should be a function of two arguments.  If
@var{sequence} is empty, this returns @var{initial-value} without
calling @var{function}.

@example
@group
(seq-reduce #'+ [1 2 3 4] 0)
@result{} 10
@end group
@group
(seq-reduce #'+ '(1 2 3 4) 5)
@result{} 15
@end group
@group
(seq-reduce #'+ '() 3)
@result{} 3
@end group
@end example
@end defun

@defun seq-some predicate sequence
  This function returns the first non-@code{nil} value returned by
applying @var{predicate} to each element of @var{sequence} in turn.

@example
@group
(seq-some #'numberp ["abc" 1 nil])
@result{} t
@end group
@group
(seq-some #'numberp ["abc" "def"])
@result{} nil
@end group
@group
(seq-some #'null ["abc" 1 nil])
@result{} t
@end group
@group
(seq-some #'1+ [2 4 6])
@result{} 3
@end group
@end example
@end defun

@defun seq-find predicate sequence &optional default
  This function returns the first element in @var{sequence} for which
@var{predicate} returns non-@code{nil}.  If no element matches
@var{predicate}, the function returns @var{default}.

Note that this function has an ambiguity if the found element is
identical to @var{default}, as in that case it cannot be known whether
an element was found or not.

@example
@group
(seq-find #'numberp ["abc" 1 nil])
@result{} 1
@end group
@group
(seq-find #'numberp ["abc" "def"])
@result{} nil
@end group
@end example
@end defun

@defun seq-every-p predicate sequence
  This function returns non-@code{nil} if applying @var{predicate}
to every element of @var{sequence} returns non-@code{nil}.

@example
@group
(seq-every-p #'numberp [2 4 6])
@result{} t
@end group
@group
(seq-some #'numberp [2 4 "6"])
@result{} nil
@end group
@end example
@end defun

@defun seq-empty-p sequence
  This function returns non-@code{nil} if @var{sequence} is empty.

@example
@group
(seq-empty-p "not empty")
@result{} nil
@end group
@group
(seq-empty-p "")
@result{} t
@end group
@end example
@end defun

@defun seq-count predicate sequence
  This function returns the number of elements in @var{sequence} for which
@var{predicate} returns non-@code{nil}.

@example
(seq-count (lambda (elt) (> elt 0)) [-1 2 0 3 -2])
@result{} 2
@end example
@end defun

@cindex sorting sequences
@defun seq-sort function sequence
  This function returns a copy of @var{sequence} that is sorted
according to @var{function}, a function of two arguments that returns
non-@code{nil} if the first argument should sort before the second.
@end defun

@defun seq-sort-by function predicate sequence
  This function is similar to @code{seq-sort}, but the elements of
@var{sequence} are transformed by applying @var{function} on them
before being sorted.  @var{function} is a function of one argument.

@example
(seq-sort-by #'seq-length #'> ["a" "ab" "abc"])
@result{} ["abc" "ab" "a"]
@end example
@end defun


@defun seq-contains sequence elt &optional function
  This function returns the first element in @var{sequence} that is equal to
@var{elt}.  If the optional argument @var{function} is non-@code{nil},
it is a function of two arguments to use instead of the default @code{equal}.

@example
@group
(seq-contains '(symbol1 symbol2) 'symbol1)
@result{} symbol1
@end group
@group
(seq-contains '(symbol1 symbol2) 'symbol3)
@result{} nil
@end group
@end example

@end defun

@defun seq-set-equal sequence1 sequence2 &optional testfn
This function checks whether every element of @var{sequence1} also
appears in @var{sequence2} and if every element of @var{sequence2}
also appears in @var{sequence1}.  If the optional argument
@var{testfn} is non-@code{nil}, it is a function of two arguments to
use instead of the default @code{equal}.

@example
@group
(seq-set-equal '(a b c) '(c b a))
@result{} t
@end group
@group
(seq-set-equal '(a b c) '(c b))
@result{} nil
@end group
@group
(seq-set-equal '("a" "b" "c") '("c" "b" "a"))
@result{} t
@end group
@group
(seq-set-equal '("a" "b" "c") '("c" "b" "a") #'eq)
@result{} nil
@end group
@end example

@end defun

@defun seq-position sequence elt &optional function
  This function returns the index of the first element in
@var{sequence} that is equal to @var{elt}.  If the optional argument
@var{function} is non-@code{nil}, it is a function of two arguments to
use instead of the default @code{equal}.

@example
@group
(seq-position '(a b c) 'b)
@result{} 1
@end group
@group
(seq-position '(a b c) 'd)
@result{} nil
@end group
@end example
@end defun


@defun seq-uniq sequence &optional function
  This function returns a list of the elements of @var{sequence} with
duplicates removed.  If the optional argument @var{function} is non-@code{nil},
it is a function of two arguments to use instead of the default @code{equal}.

@example
@group
(seq-uniq '(1 2 2 1 3))
@result{} (1 2 3)
@end group
@group
(seq-uniq '(1 2 2.0 1.0) #'=)
@result{} [3 4]
@end group
@end example
@end defun

@defun seq-subseq sequence start &optional end
  This function returns a subset of @var{sequence} from @var{start}
to @var{end}, both integers (@var{end} defaults to the last element).
If @var{start} or @var{end} is negative, it counts from the end of
@var{sequence}.

@example
@group
(seq-subseq '(1 2 3 4 5) 1)
@result{} (2 3 4 5)
@end group
@group
(seq-subseq '[1 2 3 4 5] 1 3)
@result{} [2 3]
@end group
@group
(seq-subseq '[1 2 3 4 5] -3 -1)
@result{} [3 4]
@end group
@end example
@end defun

@defun seq-concatenate type &rest sequences
  This function returns a sequence of type @var{type} made of the
concatenation of @var{sequences}.  @var{type} may be: @code{vector},
@code{list} or @code{string}.

@example
@group
(seq-concatenate 'list '(1 2) '(3 4) [5 6])
@result{} (1 2 3 4 5 6)
@end group
@group
(seq-concatenate 'string "Hello " "world")
@result{} "Hello world"
@end group
@end example
@end defun

@defun seq-mapcat function sequence &optional type
  This function returns the result of applying @code{seq-concatenate}
to the result of applying @var{function} to each element of
@var{sequence}.  The result is a sequence of type @var{type}, or a
list if @var{type} is @code{nil}.

@example
@group
(seq-mapcat #'seq-reverse '((3 2 1) (6 5 4)))
@result{} (1 2 3 4 5 6)
@end group
@end example
@end defun

@defun seq-partition sequence n
  This function returns a list of the elements of @var{sequence}
grouped into sub-sequences of length @var{n}.  The last sequence may
contain less elements than @var{n}.  @var{n} must be an integer.  If
@var{n} is a negative integer or 0, the return value is @code{nil}.

@example
@group
(seq-partition '(0 1 2 3 4 5 6 7) 3)
@result{} ((0 1 2) (3 4 5) (6 7))
@end group
@end example
@end defun

@defun seq-intersection sequence1 sequence2 &optional function
  This function returns a list of the elements that appear both in
@var{sequence1} and @var{sequence2}.  If the optional argument
@var{function} is non-@code{nil}, it is a function of two arguments to
use to compare elements instead of the default @code{equal}.

@example
@group
(seq-intersection [2 3 4 5] [1 3 5 6 7])
@result{} (3 5)
@end group
@end example
@end defun


@defun seq-difference sequence1 sequence2 &optional function
  This function returns a list of the elements that appear in
@var{sequence1} but not in @var{sequence2}.  If the optional argument
@var{function} is non-@code{nil}, it is a function of two arguments to
use to compare elements instead of the default @code{equal}.

@example
@group
(seq-difference '(2 3 4 5) [1 3 5 6 7])
@result{} (2 4)
@end group
@end example
@end defun

@defun seq-group-by function sequence
  This function separates the elements of @var{sequence} into an alist
whose keys are the result of applying @var{function} to each element
of @var{sequence}.  Keys are compared using @code{equal}.

@example
@group
(seq-group-by #'integerp '(1 2.1 3 2 3.2))
@result{} ((t 1 3 2) (nil 2.1 3.2))
@end group
@group
(seq-group-by #'car '((a 1) (b 2) (a 3) (c 4)))
@result{} ((b (b 2)) (a (a 1) (a 3)) (c (c 4)))
@end group
@end example
@end defun

@defun seq-into sequence type
  This function converts the sequence @var{sequence} into a sequence
of type @var{type}.  @var{type} can be one of the following symbols:
@code{vector}, @code{string} or @code{list}.

@example
@group
(seq-into [1 2 3] 'list)
@result{} (1 2 3)
@end group
@group
(seq-into nil 'vector)
@result{} []
@end group
@group
(seq-into "hello" 'vector)
@result{} [104 101 108 108 111]
@end group
@end example
@end defun

@defun seq-min sequence
  This function returns the smallest element of @var{sequence}.  The
elements of @var{sequence} must be numbers or markers
(@pxref{Markers}).

@example
@group
(seq-min [3 1 2])
@result{} 1
@end group
@group
(seq-min "Hello")
@result{} 72
@end group
@end example
@end defun

@defun seq-max sequence
  This function returns the largest element of @var{sequence}.  The
elements of @var{sequence} must be numbers or markers.

@example
@group
(seq-max [1 3 2])
@result{} 3
@end group
@group
(seq-max "Hello")
@result{} 111
@end group
@end example
@end defun

@defmac seq-doseq (var sequence) body@dots{}
@cindex sequence iteration
  This macro is like @code{dolist} (@pxref{Iteration, dolist}), except
that @var{sequence} can be a list, vector or string.  This is
primarily useful for side-effects.
@end defmac

@defmac seq-let arguments sequence body@dots{}
@cindex sequence destructuring
  This macro binds the variables defined in @var{arguments} to the
elements of @var{sequence}.  @var{arguments} can themselves include
sequences, allowing for nested destructuring.

The @var{arguments} sequence can also include the @code{&rest} marker
followed by a variable name to be bound to the rest of
@code{sequence}.

@example
@group
(seq-let [first second] [1 2 3 4]
  (list first second))
@result{} (1 2)
@end group
@group
(seq-let (_ a _ b) '(1 2 3 4)
  (list a b))
@result{} (2 4)
@end group
@group
(seq-let [a [b [c]]] [1 [2 [3]]]
  (list a b c))
@result{} (1 2 3)
@end group
@group
(seq-let [a b &rest others] [1 2 3 4]
  others)
@end group
@result{} [3 4]
@end example
@end defmac

@defun seq-random-elt sequence
  This function returns an element of @var{sequence} taken at random.

@example
@group
(seq-random-elt [1 2 3 4])
@result{} 3
(seq-random-elt [1 2 3 4])
@result{} 2
(seq-random-elt [1 2 3 4])
@result{} 4
(seq-random-elt [1 2 3 4])
@result{} 2
(seq-random-elt [1 2 3 4])
@result{} 1
@end group
@end example

  If @var{sequence} is empty, this function signals an error.
@end defun

@node Arrays
@section Arrays
@cindex array

  An @dfn{array} object has slots that hold a number of other Lisp
objects, called the elements of the array.  Any element of an array
may be accessed in constant time.  In contrast, the time to access an
element of a list is proportional to the position of that element in
the list.

  Emacs defines four types of array, all one-dimensional:
@dfn{strings} (@pxref{String Type}), @dfn{vectors} (@pxref{Vector
Type}), @dfn{bool-vectors} (@pxref{Bool-Vector Type}), and
@dfn{char-tables} (@pxref{Char-Table Type}).  Vectors and char-tables
can hold elements of any type, but strings can only hold characters,
and bool-vectors can only hold @code{t} and @code{nil}.

  All four kinds of array share these characteristics:

@itemize @bullet
@item
The first element of an array has index zero, the second element has
index 1, and so on.  This is called @dfn{zero-origin} indexing.  For
example, an array of four elements has indices 0, 1, 2, @w{and 3}.

@item
The length of the array is fixed once you create it; you cannot
change the length of an existing array.

@item
For purposes of evaluation, the array is a constant---i.e.,
it evaluates to itself.

@item
The elements of an array may be referenced or changed with the functions
@code{aref} and @code{aset}, respectively (@pxref{Array Functions}).
@end itemize

    When you create an array, other than a char-table, you must specify
its length.  You cannot specify the length of a char-table, because that
is determined by the range of character codes.

  In principle, if you want an array of text characters, you could use
either a string or a vector.  In practice, we always choose strings for
such applications, for four reasons:

@itemize @bullet
@item
They occupy one-fourth the space of a vector of the same elements.

@item
Strings are printed in a way that shows the contents more clearly
as text.

@item
Strings can hold text properties.  @xref{Text Properties}.

@item
Many of the specialized editing and I/O facilities of Emacs accept only
strings.  For example, you cannot insert a vector of characters into a
buffer the way you can insert a string.  @xref{Strings and Characters}.
@end itemize

  By contrast, for an array of keyboard input characters (such as a key
sequence), a vector may be necessary, because many keyboard input
characters are outside the range that will fit in a string.  @xref{Key
Sequence Input}.

@node Array Functions
@section Functions that Operate on Arrays

  In this section, we describe the functions that accept all types of
arrays.

@defun arrayp object
This function returns @code{t} if @var{object} is an array (i.e., a
vector, a string, a bool-vector or a char-table).

@example
@group
(arrayp [a])
     @result{} t
(arrayp "asdf")
     @result{} t
(arrayp (syntax-table))    ;; @r{A char-table.}
     @result{} t
@end group
@end example
@end defun

@defun aref arr index
@cindex array elements
This function returns the @var{index}th element of the array or record
@var{arr}.  The first element is at index zero.

@example
@group
(setq primes [2 3 5 7 11 13])
     @result{} [2 3 5 7 11 13]
(aref primes 4)
     @result{} 11
@end group
@group
(aref "abcdefg" 1)
     @result{} 98           ; @r{@samp{b} is @acronym{ASCII} code 98.}
@end group
@end example

See also the function @code{elt}, in @ref{Sequence Functions}.
@end defun

@defun aset array index object
This function sets the @var{index}th element of @var{array} to be
@var{object}.  It returns @var{object}.

@example
@group
(setq w [foo bar baz])
     @result{} [foo bar baz]
(aset w 0 'fu)
     @result{} fu
w
     @result{} [fu bar baz]
@end group

@group
(setq x "asdfasfd")
     @result{} "asdfasfd"
(aset x 3 ?Z)
     @result{} 90
x
     @result{} "asdZasfd"
@end group
@end example

If @var{array} is a string and @var{object} is not a character, a
@code{wrong-type-argument} error results.  The function converts a
unibyte string to multibyte if necessary to insert a character.
@end defun

@defun fillarray array object
This function fills the array @var{array} with @var{object}, so that
each element of @var{array} is @var{object}.  It returns @var{array}.

@example
@group
(setq a [a b c d e f g])
     @result{} [a b c d e f g]
(fillarray a 0)
     @result{} [0 0 0 0 0 0 0]
a
     @result{} [0 0 0 0 0 0 0]
@end group
@group
(setq s "When in the course")
     @result{} "When in the course"
(fillarray s ?-)
     @result{} "------------------"
@end group
@end example

If @var{array} is a string and @var{object} is not a character, a
@code{wrong-type-argument} error results.
@end defun

The general sequence functions @code{copy-sequence} and @code{length}
are often useful for objects known to be arrays.  @xref{Sequence Functions}.

@node Vectors
@section Vectors
@cindex vector (type)

  A @dfn{vector} is a general-purpose array whose elements can be any
Lisp objects.  (By contrast, the elements of a string can only be
characters.  @xref{Strings and Characters}.)  Vectors are used in
Emacs for many purposes: as key sequences (@pxref{Key Sequences}), as
symbol-lookup tables (@pxref{Creating Symbols}), as part of the
representation of a byte-compiled function (@pxref{Byte Compilation}),
and more.

  Like other arrays, vectors use zero-origin indexing: the first
element has index 0.

  Vectors are printed with square brackets surrounding the elements.
Thus, a vector whose elements are the symbols @code{a}, @code{b} and
@code{a} is printed as @code{[a b a]}.  You can write vectors in the
same way in Lisp input.

  A vector, like a string or a number, is considered a constant for
evaluation: the result of evaluating it is the same vector.  This does
not evaluate or even examine the elements of the vector.
@xref{Self-Evaluating Forms}.

  Here are examples illustrating these principles:

@example
@group
(setq avector [1 two '(three) "four" [five]])
     @result{} [1 two (quote (three)) "four" [five]]
(eval avector)
     @result{} [1 two (quote (three)) "four" [five]]
(eq avector (eval avector))
     @result{} t
@end group
@end example

@node Vector Functions
@section Functions for Vectors

  Here are some functions that relate to vectors:

@defun vectorp object
This function returns @code{t} if @var{object} is a vector.

@example
@group
(vectorp [a])
     @result{} t
(vectorp "asdf")
     @result{} nil
@end group
@end example
@end defun

@defun vector &rest objects
This function creates and returns a vector whose elements are the
arguments, @var{objects}.

@example
@group
(vector 'foo 23 [bar baz] "rats")
     @result{} [foo 23 [bar baz] "rats"]
(vector)
     @result{} []
@end group
@end example
@end defun

@defun make-vector length object
This function returns a new vector consisting of @var{length} elements,
each initialized to @var{object}.

@example
@group
(setq sleepy (make-vector 9 'Z))
     @result{} [Z Z Z Z Z Z Z Z Z]
@end group
@end example
@end defun

@defun vconcat &rest sequences
@cindex copying vectors
This function returns a new vector containing all the elements of
@var{sequences}.  The arguments @var{sequences} may be true lists,
vectors, strings or bool-vectors.  If no @var{sequences} are given,
the empty vector is returned.

The value is either the empty vector, or is a newly constructed
nonempty vector that is not @code{eq} to any existing vector.

@example
@group
(setq a (vconcat '(A B C) '(D E F)))
     @result{} [A B C D E F]
(eq a (vconcat a))
     @result{} nil
@end group
@group
(vconcat)
     @result{} []
(vconcat [A B C] "aa" '(foo (6 7)))
     @result{} [A B C 97 97 foo (6 7)]
@end group
@end example

The @code{vconcat} function also allows byte-code function objects as
arguments.  This is a special feature to make it easy to access the entire
contents of a byte-code function object.  @xref{Byte-Code Objects}.

For other concatenation functions, see @code{mapconcat} in @ref{Mapping
Functions}, @code{concat} in @ref{Creating Strings}, and @code{append}
in @ref{Building Lists}.
@end defun

  The @code{append} function also provides a way to convert a vector into a
list with the same elements:

@example
@group
(setq avector [1 two (quote (three)) "four" [five]])
     @result{} [1 two (quote (three)) "four" [five]]
(append avector nil)
     @result{} (1 two (quote (three)) "four" [five])
@end group
@end example

@node Char-Tables
@section Char-Tables
@cindex char-tables
@cindex extra slots of char-table

  A char-table is much like a vector, except that it is indexed by
character codes.  Any valid character code, without modifiers, can be
used as an index in a char-table.  You can access a char-table's
elements with @code{aref} and @code{aset}, as with any array.  In
addition, a char-table can have @dfn{extra slots} to hold additional
data not associated with particular character codes.  Like vectors,
char-tables are constants when evaluated, and can hold elements of any
type.

@cindex subtype of char-table
  Each char-table has a @dfn{subtype}, a symbol, which serves two
purposes:

@itemize @bullet
@item
The subtype provides an easy way to tell what the char-table is for.
For instance, display tables are char-tables with @code{display-table}
as the subtype, and syntax tables are char-tables with
@code{syntax-table} as the subtype.  The subtype can be queried using
the function @code{char-table-subtype}, described below.

@item
The subtype controls the number of @dfn{extra slots} in the
char-table.  This number is specified by the subtype's
@code{char-table-extra-slots} symbol property (@pxref{Symbol
Properties}), whose value should be an integer between 0 and 10.  If
the subtype has no such symbol property, the char-table has no extra
slots.
@end itemize

@cindex parent of char-table
  A char-table can have a @dfn{parent}, which is another char-table.  If
it does, then whenever the char-table specifies @code{nil} for a
particular character @var{c}, it inherits the value specified in the
parent.  In other words, @code{(aref @var{char-table} @var{c})} returns
the value from the parent of @var{char-table} if @var{char-table} itself
specifies @code{nil}.

@cindex default value of char-table
  A char-table can also have a @dfn{default value}.  If so, then
@code{(aref @var{char-table} @var{c})} returns the default value
whenever the char-table does not specify any other non-@code{nil} value.

@defun make-char-table subtype &optional init
Return a newly-created char-table, with subtype @var{subtype} (a
symbol).  Each element is initialized to @var{init}, which defaults to
@code{nil}.  You cannot alter the subtype of a char-table after the
char-table is created.

There is no argument to specify the length of the char-table, because
all char-tables have room for any valid character code as an index.

If @var{subtype} has the @code{char-table-extra-slots} symbol
property, that specifies the number of extra slots in the char-table.
This should be an integer between 0 and 10; otherwise,
@code{make-char-table} raises an error.  If @var{subtype} has no
@code{char-table-extra-slots} symbol property (@pxref{Property
Lists}), the char-table has no extra slots.
@end defun

@defun char-table-p object
This function returns @code{t} if @var{object} is a char-table, and
@code{nil} otherwise.
@end defun

@defun char-table-subtype char-table
This function returns the subtype symbol of @var{char-table}.
@end defun

There is no special function to access default values in a char-table.
To do that, use @code{char-table-range} (see below).

@defun char-table-parent char-table
This function returns the parent of @var{char-table}.  The parent is
always either @code{nil} or another char-table.
@end defun

@defun set-char-table-parent char-table new-parent
This function sets the parent of @var{char-table} to @var{new-parent}.
@end defun

@defun char-table-extra-slot char-table n
This function returns the contents of extra slot @var{n} (zero based)
of @var{char-table}.  The number of extra slots in a char-table is
determined by its subtype.
@end defun

@defun set-char-table-extra-slot char-table n value
This function stores @var{value} in extra slot @var{n} (zero based) of
@var{char-table}.
@end defun

  A char-table can specify an element value for a single character code;
it can also specify a value for an entire character set.

@defun char-table-range char-table range
This returns the value specified in @var{char-table} for a range of
characters @var{range}.  Here are the possibilities for @var{range}:

@table @asis
@item @code{nil}
Refers to the default value.

@item @var{char}
Refers to the element for character @var{char}
(supposing @var{char} is a valid character code).

@item @code{(@var{from} . @var{to})}
A cons cell refers to all the characters in the inclusive range
@samp{[@var{from}..@var{to}]}.
@end table
@end defun

@defun set-char-table-range char-table range value
This function sets the value in @var{char-table} for a range of
characters @var{range}.  Here are the possibilities for @var{range}:

@table @asis
@item @code{nil}
Refers to the default value.

@item @code{t}
Refers to the whole range of character codes.

@item @var{char}
Refers to the element for character @var{char}
(supposing @var{char} is a valid character code).

@item @code{(@var{from} . @var{to})}
A cons cell refers to all the characters in the inclusive range
@samp{[@var{from}..@var{to}]}.
@end table
@end defun

@defun map-char-table function char-table
This function calls its argument @var{function} for each element of
@var{char-table} that has a non-@code{nil} value.  The call to
@var{function} is with two arguments, a key and a value.  The key
is a possible @var{range} argument for @code{char-table-range}---either
a valid character or a cons cell @code{(@var{from} . @var{to})},
specifying a range of characters that share the same value.  The value is
what @code{(char-table-range @var{char-table} @var{key})} returns.

Overall, the key-value pairs passed to @var{function} describe all the
values stored in @var{char-table}.

The return value is always @code{nil}; to make calls to
@code{map-char-table} useful, @var{function} should have side effects.
For example, here is how to examine the elements of the syntax table:

@example
(let (accumulator)
   (map-char-table
    #'(lambda (key value)
        (setq accumulator
              (cons (list
                     (if (consp key)
                         (list (car key) (cdr key))
                       key)
                     value)
                    accumulator)))
    (syntax-table))
   accumulator)
@result{}
(((2597602 4194303) (2)) ((2597523 2597601) (3))
 ... (65379 (5 . 65378)) (65378 (4 . 65379)) (65377 (1))
 ... (12 (0)) (11 (3)) (10 (12)) (9 (0)) ((0 8) (3)))
@end example
@end defun

@node Bool-Vectors
@section Bool-vectors
@cindex Bool-vectors

  A bool-vector is much like a vector, except that it stores only the
values @code{t} and @code{nil}.  If you try to store any non-@code{nil}
value into an element of the bool-vector, the effect is to store
@code{t} there.  As with all arrays, bool-vector indices start from 0,
and the length cannot be changed once the bool-vector is created.
Bool-vectors are constants when evaluated.

  Several functions work specifically with bool-vectors; aside
from that, you manipulate them with same functions used for other kinds
of arrays.

@defun make-bool-vector length initial
Return a new bool-vector of @var{length} elements,
each one initialized to @var{initial}.
@end defun

@defun bool-vector &rest objects
This function creates and returns a bool-vector whose elements are the
arguments, @var{objects}.
@end defun

@defun bool-vector-p object
This returns @code{t} if @var{object} is a bool-vector,
and @code{nil} otherwise.
@end defun

There are also some bool-vector set operation functions, described below:

@defun bool-vector-exclusive-or a b &optional c
Return @dfn{bitwise exclusive or} of bool vectors @var{a} and @var{b}.
If optional argument @var{c} is given, the result of this operation is
stored into @var{c}.  All arguments should be bool vectors of the same length.
@end defun

@defun bool-vector-union a b &optional c
Return @dfn{bitwise or} of bool vectors @var{a} and @var{b}.  If
optional argument @var{c} is given, the result of this operation is
stored into @var{c}.  All arguments should be bool vectors of the same length.
@end defun

@defun bool-vector-intersection a b &optional c
Return @dfn{bitwise and} of bool vectors @var{a} and @var{b}.  If
optional argument @var{c} is given, the result of this operation is
stored into @var{c}.  All arguments should be bool vectors of the same length.
@end defun

@defun bool-vector-set-difference a b &optional c
Return @dfn{set difference} of bool vectors @var{a} and @var{b}.  If
optional argument @var{c} is given, the result of this operation is
stored into @var{c}.  All arguments should be bool vectors of the same length.
@end defun

@defun bool-vector-not a &optional b
Return @dfn{set complement} of bool vector @var{a}.  If optional
argument @var{b} is given, the result of this operation is stored into
@var{b}.  All arguments should be bool vectors of the same length.
@end defun

@defun bool-vector-subsetp a b
Return @code{t} if every @code{t} value in @var{a} is also t in
@var{b}, @code{nil} otherwise.  All arguments should be bool vectors of the
same length.
@end defun

@defun bool-vector-count-consecutive a b i
Return the number of consecutive elements in @var{a} equal @var{b}
starting at @var{i}.  @code{a} is a bool vector, @var{b} is @code{t}
or @code{nil}, and @var{i} is an index into @code{a}.
@end defun

@defun bool-vector-count-population a
Return the number of elements that are @code{t} in bool vector @var{a}.
@end defun

  The printed form represents up to 8 boolean values as a single
character:

@example
@group
(bool-vector t nil t nil)
     @result{} #&4"^E"
(bool-vector)
     @result{} #&0""
@end group
@end example

You can use @code{vconcat} to print a bool-vector like other vectors:

@example
@group
(vconcat (bool-vector nil t nil t))
     @result{} [nil t nil t]
@end group
@end example

  Here is another example of creating, examining, and updating a
bool-vector:

@example
(setq bv (make-bool-vector 5 t))
     @result{} #&5"^_"
(aref bv 1)
     @result{} t
(aset bv 3 nil)
     @result{} nil
bv
     @result{} #&5"^W"
@end example

@noindent
These results make sense because the binary codes for control-_ and
control-W are 11111 and 10111, respectively.

@node Rings
@section Managing a Fixed-Size Ring of Objects

@cindex ring data structure
  A @dfn{ring} is a fixed-size data structure that supports insertion,
deletion, rotation, and modulo-indexed reference and traversal.  An
efficient ring data structure is implemented by the @code{ring}
package.  It provides the functions listed in this section.

  Note that several rings in Emacs, like the kill ring and the
mark ring, are actually implemented as simple lists, @emph{not} using
the @code{ring} package; thus the following functions won't work on
them.

@defun make-ring size
This returns a new ring capable of holding @var{size} objects.
@var{size} should be an integer.
@end defun

@defun ring-p object
This returns @code{t} if @var{object} is a ring, @code{nil} otherwise.
@end defun

@defun ring-size ring
This returns the maximum capacity of the @var{ring}.
@end defun

@defun ring-length ring
This returns the number of objects that @var{ring} currently contains.
The value will never exceed that returned by @code{ring-size}.
@end defun

@defun ring-elements ring
This returns a list of the objects in @var{ring}, in order, newest first.
@end defun

@defun ring-copy ring
This returns a new ring which is a copy of @var{ring}.
The new ring contains the same (@code{eq}) objects as @var{ring}.
@end defun

@defun ring-empty-p ring
This returns @code{t} if @var{ring} is empty, @code{nil} otherwise.
@end defun

  The newest element in the ring always has index 0.  Higher indices
correspond to older elements.  Indices are computed modulo the ring
length.  Index @minus{}1 corresponds to the oldest element, @minus{}2
to the next-oldest, and so forth.

@defun ring-ref ring index
This returns the object in @var{ring} found at index @var{index}.
@var{index} may be negative or greater than the ring length.  If
@var{ring} is empty, @code{ring-ref} signals an error.
@end defun

@defun ring-insert ring object
This inserts @var{object} into @var{ring}, making it the newest
element, and returns @var{object}.

If the ring is full, insertion removes the oldest element to
make room for the new element.
@end defun

@defun ring-remove ring &optional index
Remove an object from @var{ring}, and return that object.  The
argument @var{index} specifies which item to remove; if it is
@code{nil}, that means to remove the oldest item.  If @var{ring} is
empty, @code{ring-remove} signals an error.
@end defun

@defun ring-insert-at-beginning ring object
This inserts @var{object} into @var{ring}, treating it as the oldest
element.  The return value is not significant.

If the ring is full, this function removes the newest element to make
room for the inserted element.
@end defun

@cindex fifo data structure
  If you are careful not to exceed the ring size, you can
use the ring as a first-in-first-out queue.  For example:

@lisp
(let ((fifo (make-ring 5)))
  (mapc (lambda (obj) (ring-insert fifo obj))
        '(0 one "two"))
  (list (ring-remove fifo) t
        (ring-remove fifo) t
        (ring-remove fifo)))
     @result{} (0 t one t "two")
@end lisp