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12. Sequences, Arrays, and Vectors

Recall that the 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 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 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| | |
         |          | |________| |_______| | |
         |          |  __________________  | |
         |          | |                  | | |
         |          | |    Bit Vector    | | |
         |          | |__________________| | |
         |          |______________________| |

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.

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12.1 Sequences

In XEmacs Lisp, a 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.

Function: sequencep object

Returns t if object is a list, vector, bit 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 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. See section Extents, See section Text Properties.

See also append in Building Cons Cells and Lists, concat in Creating Strings, vconcat in Vectors, and bvconcat in Bit Vectors, for other 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)]
;; Creating a bit vector.
(bit-vector 1 0 1 1 0 1 0 0)
     ⇒ #*10110100
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
(length #*01101)
    ⇒ 5
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 #*00010000 3)
     ⇒ 1
(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).

Function: fill sequence object &key :start :end

This function fills the sequence sequence with object, so that each element of sequence between the indices specified by :start (inclusive) and :end (exclusive), is object. It returns sequence.

(setq a [a b c d e f g])
     ⇒ [a b c d e f g]
(fill a 0 :end 2)
     ⇒ [0 0 c d e f g]
(fill a 0)
     ⇒ [0 0 0 0 0 0 0]
     ⇒ [0 0 0 0 0 0 0]
(setq s "When in the course")
     ⇒ "When in the course"
(fill s ?-)
     ⇒ "------------------"
(setq bv #*1101)
     ⇒ #*1101
(fill bv 0)
     ⇒ #*0000

If sequence is of a type that cannot hold object ( bit-vector can only hold the integers one or zero, strings can only hold characters) a wrong-type-argument error results.

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12.2 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.

XEmacs defines three types of array, all of which are one-dimensional: strings, vectors, and 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. See section String Type, Vector Type, and Bit Vector Type.

All kinds of array share these characteristics:

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:

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. See section Key Sequence Input.

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

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12.3 Functions that Operate on Arrays

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

Function: arrayp object

This function returns t if object is an array (i.e., a string, vector, or bit vector).

(arrayp "asdf")
⇒ t
(arrayp [a])
⇒ t
(arrayp #*101)
⇒ 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)
     ⇒ ?b
(aref #*1101 2)
     ⇒ 0

See also the function elt, in 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
     ⇒ [fu bar baz]
(setq x "asdfasfd")
     ⇒ "asdfasfd"
(aset x 3 ?Z)
     ⇒ ?Z
     ⇒ "asdZasfd"
(setq bv #*1111)
     ⇒ #*1111
(aset bv 2 0)
     ⇒ 0
     ⇒ #*1101

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.

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12.4 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 XEmacs Lisp is the 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 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

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12.5 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"]
     ⇒ []
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 [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 Mapping Functions, concat in Creating Strings, append in Building Cons Cells and Lists, and bvconcat in Functions That Operate on Bit Vectors.

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])

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12.6 Bit Vectors

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 ‘#*’ 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


Bit vectors are considered constants for evaluation, like vectors, strings, and numbers. See section Self-Evaluating Forms.

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