@c -*-texinfo-*-
@c This is part of the XEmacs Lisp Reference Manual.
@c Copyright (C) 1990, 1991, 1992, 1993, 1994 Free Software Foundation, Inc.
@c Copyright (C) 1996 Ben Wing.
@c See the file lispref.texi for copying conditions.
@setfilename ../../info/sequences.info
@node Sequences Arrays Vectors, Symbols, Lists, Top
@chapter Sequences, Arrays, and Vectors
@cindex sequence

  Recall that the @dfn{sequence} type is the union of four other Lisp
types: lists, vectors, bit vectors, and strings.  In other words, any
list is a sequence, any vector is a sequence, any bit vector is a
sequence, and any string is a sequence.  The common property that all
sequences have is that each is an ordered collection of elements.

  An @dfn{array} is a single primitive object that has a slot for each
elements.  All the elements are accessible in constant time, but the
length of an existing array cannot be changed.  Strings, vectors, and
bit vectors are the three types of arrays.

  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| | |
         |          | |________| |_______| | |
         |          |  __________________  | |
         |          | |                  | | |
         |          | |    Bit Vector    | | |
         |          | |__________________| | |
         |          |______________________| |
         |___________________________________|
@end group
@end example

  The elements of vectors and lists may be any Lisp objects.  The
elements of strings are all characters.  The elements of bit vectors
are the numbers 0 and 1.

@menu
* Sequence Functions::    Functions that accept any kind of sequence.
* Arrays::                Characteristics of arrays in XEmacs Lisp.
* Array Functions::       Functions specifically for arrays.
* Vectors::               Special characteristics of XEmacs Lisp vectors.
* Vector Functions::      Functions specifically for vectors.
* Bit Vectors::           Special characteristics of XEmacs Lisp bit vectors.
* Bit Vector Functions::  Functions specifically for bit vectors.
@end menu

@node Sequence Functions
@section Sequences

  In XEmacs Lisp, a @dfn{sequence} is either a list, a vector, a bit
vector, or a string.  The common property that all sequences have is
that each is an ordered collection of elements.  This section describes
functions that accept any kind of sequence.

@defun sequencep object
Returns @code{t} if @var{object} is a list, vector, bit vector, or
string, @code{nil} otherwise.
@end defun

@defun copy-sequence sequence
@cindex copying sequences
Returns a copy of @var{sequence}.  The copy is the same type of object
as the original sequence, and it has the same elements in the same order.

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

If the sequence is a string with extents or text properties, the extents
and text properties in the copy are also copied, not shared with the
original. (This means that modifying the extents or text properties of
the original will not affect the copy.) However, the actual values of
the properties are shared.  @xref{Extents}, @xref{Text Properties}.

See also @code{append} in @ref{Building Lists}, @code{concat} in
@ref{Creating Strings}, @code{vconcat} in @ref{Vectors}, and
@code{bvconcat} in @ref{Bit Vectors}, 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

@group
;; @r{Creating a bit vector.}
(bit-vector 1 0 1 1 0 1 0 0)
     @result{} #*10110100
@end group
@end example
@end defun

@defun length sequence
@cindex string length
@cindex list length
@cindex vector length
@cindex bit vector length
@cindex sequence length
Returns the number of elements in @var{sequence}.  If @var{sequence} is
a cons cell that is not a list (because the final @sc{cdr} is not
@code{nil}), a @code{wrong-type-argument} error is signaled.

@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 #*01101)
    @result{} 5
@end group
@end example
@end defun

@defun elt sequence index
@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, then out-of-range values of @var{index} return @code{nil};
otherwise, they 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
(char-to-string (elt "1234" 2))
     @result{} "3"
@end group
@group
(elt #*00010000 3)
     @result{} 1
@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{List Elements}).
@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, an element of a list
requires access time that is proportional to the position of the element
in the list.

  When you create an array, you must specify how many elements it has.
The amount of space allocated depends on the number of elements.
Therefore, it is impossible to change the size of an array once it is
created; you cannot add or remove elements.  However, you can replace an
element with a different value.

  XEmacs defines three types of array, all of which are one-dimensional:
@dfn{strings}, @dfn{vectors}, and @dfn{bit vectors}.  A vector is a
general array; its elements can be any Lisp objects.  A string is a
specialized array; its elements must be characters.  A bit vector is
another specialized array; its elements must be bits (an integer, either
0 or 1).  Each type of array has its own read syntax.  @xref{String
Type}, @ref{Vector Type}, and @ref{Bit Vector Type}.

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

  In principle, if you wish to have 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 usually occupy one-fourth the space of a vector of the same
elements.  (This is one-eighth the space for 64-bit machines such as the
DEC Alpha, and may also be different when @sc{mule} support is compiled
into XEmacs.)

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

@item
Strings can hold extent and text properties.  @xref{Extents}, @xref{Text
Properties}.

@item
Many of the specialized editing and I/O facilities of XEmacs 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 non-printable and are represented with symbols rather than
with characters.  @xref{Key Sequence Input}.

  Similarly, when representing an array of bits, a bit vector has
the following advantages over a regular vector:

@itemize @bullet
@item
They occupy 1/32nd the space of a vector of the same elements.
(1/64th on 64-bit machines such as the DEC Alpha.)

@item
Bit vectors are printed in a way that shows the contents more clearly
as bits.
@end itemize

@node Array Functions
@section Functions that Operate on Arrays

  In this section, we describe the functions that accept strings, vectors,
and bit vectors.

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

@example
@group
(arrayp "asdf")
@result{} t
(arrayp [a])
@result{} t
(arrayp #*101)
@result{} t
@end group
@end example
@end defun

@defun aref array index
@cindex array elements
This function returns the @var{index}th element of @var{array}.  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
(elt primes 4)
     @result{} 11
@end group

@group
(aref "abcdefg" 1)
     @result{} ?b
@end group

@group
(aref #*1101 2)
     @result{} 0
@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{} ?Z
x
     @result{} "asdZasfd"
@end group

@group
(setq bv #*1111)
     @result{} #*1111
(aset bv 2 0)
     @result{} 0
bv
     @result{} #*1101
@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

@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

@group
(setq bv #*1101)
     @result{} #*1101
(fillarray bv 0)
     @result{} #*0000
@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

  Arrays in Lisp, like arrays in most languages, are blocks of memory
whose elements can be accessed in constant time.  A @dfn{vector} is a
general-purpose array; its elements can be any Lisp objects.  (The other
kind of array in XEmacs Lisp is the @dfn{string}, whose elements must be
characters.)  Vectors in XEmacs serve as obarrays (vectors of symbols),
although this is a shortcoming that should be fixed.  They are also used
internally as part of the representation of a byte-compiled function; if
you print such a function, you will see a vector in it.

  In XEmacs Lisp, the indices of the elements of a vector start from zero
and count up from there.

  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 of 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 That Operate on 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 the
@var{sequences}.  The arguments @var{sequences} may be lists, vectors,
or strings.  If no @var{sequences} are given, an empty vector is
returned.

The value is a newly constructed 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 integers as arguments.  It
converts them to strings of digits, making up the decimal print
representation of the integer, and then uses the strings instead of the
original integers.  @strong{Don't use this feature; we plan to eliminate
it.  If you already use this feature, change your programs now!}  The
proper way to convert an integer to a decimal number in this way is with
@code{format} (@pxref{Formatting Strings}) or @code{number-to-string}
(@pxref{String Conversion}).

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

  The @code{append} function provides a way to convert a vector into a
list with the same elements (@pxref{Building Lists}):

@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 Bit Vectors
@section Bit Vectors
@cindex bit vector

  Bit vectors are specialized vectors that can only represent arrays
of 1's and 0's.  Bit vectors have a very efficient representation
and are useful for representing sets of boolean (true or false) values.

  There is no limit on the size of a bit vector.  You could, for example,
create a bit vector with 100,000 elements if you really wanted to.

  Bit vectors have a special printed representation consisting of
@samp{#*} followed by the bits of the vector.  For example, a bit vector
whose elements are 0, 1, 1, 0, and 1, respectively, is printed as

@example
#*01101
@end example

  Bit vectors are considered constants for evaluation, like vectors,
strings, and numbers.  @xref{Self-Evaluating Forms}.

@node Bit Vector Functions
@section Functions That Operate on Bit Vectors

  Here are some functions that relate to bit vectors:

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

@example
@group
(bit-vector-p #*01)
     @result{} t
(bit-vector-p [0 1])
     @result{} nil
(bit-vector-p "01")
     @result{} nil
@end group
@end example
@end defun

@defun bitp object
This function returns @code{t} if @var{object} is either 0 or 1.
@end defun

@defun bit-vector &rest bits
This function creates and returns a bit vector whose elements are the
arguments @var{bits}.  Each argument must be a bit, i.e. one of the two
integers 0 or 1.

@example
@group
(bit-vector 0 0 0 1 0 0 0 0 1 0)
     @result{} #*0001000010
(bit-vector)
     @result{} #*
@end group
@end example
@end defun

@defun make-bit-vector length bit
This function creates and returns a bit vector consisting of
@var{length} elements, each initialized to @var{bit}, which must be
one of the two integers 0 or 1.

@example
@group
(setq picket-fence (make-bit-vector 9 1))
     @result{} #*111111111
@end group
@end example
@end defun

@defun bvconcat &rest sequences
@cindex copying bit vectors
This function returns a new bit vector containing all the elements of
the @var{sequences}.  The arguments @var{sequences} may be lists,
vectors, or bit vectors, all of whose elements are the integers 0 or 1.
If no @var{sequences} are given, an empty bit vector is returned.

The value is a newly constructed bit vector that is not @code{eq} to any
existing bit vector.

@example
@group
(setq a (bvconcat '(1 1 0) '(0 0 1)))
     @result{} #*110001
(eq a (bvconcat a))
     @result{} nil
@end group
@group
(bvconcat)
     @result{} #*
(bvconcat [1 0 0 0 0] #*111 '(0 0 0 0 1))
     @result{} #*1000011100001
@end group
@end example

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

  The @code{append} function provides a way to convert a bit vector into a
list with the same elements (@pxref{Building Lists}):

@example
@group
(setq bv #*00001110)
     @result{} #*00001110
(append bv nil)
     @result{} (0 0 0 0 1 1 1 0)
@end group
@end example