# Sequences, Arrays, and Vectors

Recall that the sequence type is the union of three other Lisp types: lists, vectors, and strings. In other words, any list is a sequence, any 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 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 and vectors are the two 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 nth element requires looking through 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:

```          ___________________________________
|                                   |
|          Sequence                 |
|  ______   ______________________  |
| |      | |                      | |
| | List | |         Array        | |
| |      | |  ________   _______  | |
| |______| | |        | |       | | |
|          | | Vector | | String| | |
|          | |________| |_______| | |
|          |______________________| |
|___________________________________|
```

The elements of vectors and lists may be any Lisp objects. The elements of strings are all characters.

## Sequences

In Emacs Lisp, a sequence is either a list, a 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.

Function: sequencep object
Returns `t` if object is a list, vector, or string, `nil` otherwise.

Function: copy-sequence sequence
Returns a copy of 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 sequence, and vice versa. However, the elements of the new sequence are not copies; they are identical (`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 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. See section Text Properties.

See also `append` in section Building Cons Cells and Lists, `concat` in section Creating Strings, and `vconcat` in section Vectors, for others ways to copy sequences.

```(setq bar '(1 2))
=> (1 2)
(setq x (vector 'foo bar))
=> [foo (1 2)]
(setq y (copy-sequence x))
=> [foo (1 2)]

(eq x y)
=> nil
(equal x y)
=> t
(eq (elt x 1) (elt y 1))
=> t

;; Replacing an element of one sequence.
(aset x 0 'quux)
x => [quux (1 2)]
y => [foo (1 2)]

;; Modifying the inside of a shared element.
(setcar (aref x 1) 69)
x => [quux (69 2)]
y => [foo (69 2)]
```

Function: length sequence
Returns the number of elements in sequence. If sequence is a cons cell that is not a list (because the final CDR is not `nil`), a `wrong-type-argument` error is signaled.

```(length '(1 2 3))
=> 3
(length ())
=> 0
(length "foobar")
=> 6
(length [1 2 3])
=> 3
```

Function: elt sequence index
This function returns the element of sequence indexed by index. Legitimate values of index are integers ranging from 0 up to one less than the length of sequence. If sequence is a list, then out-of-range values of index return `nil`; otherwise, they trigger an `args-out-of-range` error.

```(elt [1 2 3 4] 2)
=> 3
(elt '(1 2 3 4) 2)
=> 3
(char-to-string (elt "1234" 2))
=> "3"
(elt [1 2 3 4] 4)
error-->Args out of range: [1 2 3 4], 4
(elt [1 2 3 4] -1)
error-->Args out of range: [1 2 3 4], -1
```

This function generalizes `aref` (see section Functions that Operate on Arrays) and `nth` (see section Accessing Elements of Lists).

## Arrays

An 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.

Emacs defines two types of array, both of which are one-dimensional: strings and 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 (i.e., integers between 0 and 255). Each type of array has its own read syntax. See section String Type, and section Vector Type.

Both kinds of array share these characteristics:

• The first element of an array has index zero, the second element has index 1, and so on. This is called zero-origin indexing. For example, an array of four elements has indices 0, 1, 2, and 3.
• The elements of an array may be referenced or changed with the functions `aref` and `aset`, respectively (see section Functions that Operate on Arrays).

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:

• They occupy one-fourth the space of a vector of the same elements.
• Strings are printed in a way that shows the contents more clearly as characters.
• Strings can hold text properties. See section Text Properties.
• 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. See section Strings and Characters.

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. See section Key Sequence Input.

## Functions that Operate on Arrays

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

Function: arrayp object
This function returns `t` if object is an array (i.e., either a vector or a string).

```(arrayp [a])
=> t
(arrayp "asdf")
=> t
```

Function: aref array index
This function returns the indexth element of array. The first element is at index zero.

```(setq primes [2 3 5 7 11 13])
=> [2 3 5 7 11 13]
(aref primes 4)
=> 11
(elt primes 4)
=> 11

(aref "abcdefg" 1)
=> 98           ; `b' is ASCII code 98.
```

See also the function `elt`, in section Sequences.

Function: aset array index object
This function sets the indexth element of array to be object. It returns object.

```(setq w [foo bar baz])
=> [foo bar baz]
(aset w 0 'fu)
=> fu
w
=> [fu bar baz]

(setq x "asdfasfd")
=> "asdfasfd"
(aset x 3 ?Z)
=> 90
x
=> "asdZasfd"
```

If array is a string and object is not a character, a `wrong-type-argument` error results.

Function: fillarray array object
This function fills the array array with object, so that each element of array is object. It returns array.

```(setq a [a b c d e f g])
=> [a b c d e f g]
(fillarray a 0)
=> [0 0 0 0 0 0 0]
a
=> [0 0 0 0 0 0 0]
(setq s "When in the course")
=> "When in the course"
(fillarray s ?-)
=> "------------------"
```

If array is a string and object is not a character, a `wrong-type-argument` error results.

The general sequence functions `copy-sequence` and `length` are often useful for objects known to be arrays. See section Sequences.

## Vectors

Arrays in Lisp, like arrays in most languages, are blocks of memory whose elements can be accessed in constant time. A vector is a general-purpose array; its elements can be any Lisp objects. (The other kind of array in Emacs Lisp is the string, whose elements must be characters.) Vectors in Emacs serve as syntax tables (vectors of integers), as obarrays (vectors of symbols), and in keymaps (vectors of commands). 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 Emacs 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 `a`, `b` and `a` is printed as `[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. See section Self-Evaluating Forms.

Here are examples of these principles:

```(setq avector [1 two '(three) "four" [five]])
=> [1 two (quote (three)) "four" [five]]
(eval avector)
=> [1 two (quote (three)) "four" [five]]
(eq avector (eval avector))
=> t
```

## Functions That Operate on Vectors

Here are some functions that relate to vectors:

Function: vectorp object
This function returns `t` if object is a vector.

```(vectorp [a])
=> t
(vectorp "asdf")
=> nil
```

Function: vector &rest objects
This function creates and returns a vector whose elements are the arguments, objects.

```(vector 'foo 23 [bar baz] "rats")
=> [foo 23 [bar baz] "rats"]
(vector)
=> []
```

Function: make-vector length object
This function returns a new vector consisting of length elements, each initialized to object.

```(setq sleepy (make-vector 9 'Z))
=> [Z Z Z Z Z Z Z Z Z]
```

Function: vconcat &rest sequences
This function returns a new vector containing all the elements of the sequences. The arguments sequences may be lists, vectors, or strings. If no sequences are given, an empty vector is returned.

The value is a newly constructed vector that is not `eq` to any existing vector.

```(setq a (vconcat '(A B C) '(D E F)))
=> [A B C D E F]
(eq a (vconcat a))
=> nil
(vconcat)
=> []
(vconcat [A B C] "aa" '(foo (6 7)))
=> [A B C 97 97 foo (6 7)]
```

The `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. 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 `format` (see section Formatting Strings) or `number-to-string` (see section Conversion of Characters and Strings).

For other concatenation functions, see `mapconcat` in section Mapping Functions, `concat` in section Creating Strings, and `append` in section Building Cons Cells and Lists.

The `append` function provides a way to convert a vector into a list with the same elements (see section Building Cons Cells and Lists):

```(setq avector [1 two (quote (three)) "four" [five]])
=> [1 two (quote (three)) "four" [five]]
(append avector nil)
=> (1 two (quote (three)) "four" [five])
```