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6.1 Sequences

This section describes functions that accept any kind of sequence.

function sequencep object​

This function returns t if object is a list, vector, string, bool-vector, or char-table, nil otherwise. See also seqp below.

function length sequence​

This function returns the number of elements in sequence. The function signals the wrong-type-argument error if the argument is not a sequence or is a dotted list; it signals the circular-list error if the argument is a circular list. For a char-table, the value returned is always one more than the maximum Emacs character code.

See Definition of safe-length, for the related function safe-length.

(length '(1 2 3))
    ⇒ 3
(length ())
    ⇒ 0
(length "foobar")
    ⇒ 6
(length [1 2 3])
    ⇒ 3
(length (make-bool-vector 5 nil))
    ⇒ 5

See also string-bytes, in Text Representations.

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

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, out-of-range values behave as for nth. See Definition of nth. Otherwise, out-of-range values trigger an args-out-of-range error.

(elt [1 2 3 4] 2)
     ⇒ 3
(elt '(1 2 3 4) 2)
     ⇒ 3
;; We use string to show clearly which character elt returns.
(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 Array Functions) and nth (see Definition of nth).

function copy-sequence seqr​

This function returns a copy of 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. However, if seqr is empty, like a string or a vector of zero length, the value returned by this function might not be a copy, but an empty object of the same type and identical to seqr.

Storing a new element into the copy does not affect the original seqr, and vice versa. However, the elements of the copy are not copies; they are identical (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. See Text Properties.

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

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

(setq bar (list 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 reverse sequence​

This function creates a new sequence whose elements are the elements of sequence, but in reverse order. The original argument sequence is not altered. Note that char-tables cannot be reversed.

(setq x '(1 2 3 4))
     ⇒ (1 2 3 4)
(reverse x)
     ⇒ (4 3 2 1)
x
     ⇒ (1 2 3 4)
(setq x [1 2 3 4])
     ⇒ [1 2 3 4]
(reverse x)
     ⇒ [4 3 2 1]
x
     ⇒ [1 2 3 4]
(setq x "xyzzy")
     ⇒ "xyzzy"
(reverse x)
     ⇒ "yzzyx"
x
     ⇒ "xyzzy"

function nreverse sequence​

This function reverses the order of the elements of sequence. Unlike reverse the original sequence may be modified.

For example:

(setq x (list 'a 'b 'c))
     ⇒ (a b c)
x
     ⇒ (a b c)
(nreverse x)
     ⇒ (c b a)
;; The cons cell that was first is now last.
x
     ⇒ (a)

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

(setq x (nreverse x))

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

Original list head:                       Reversed list:
 -------------        -------------        ------------
| car  | cdr  |      | car  | cdr  |      | car | cdr  |
|   a  |  nil |<--   |   b  |   o  |<--   |   c |   o  |
|      |      |   |  |      |   |  |   |  |     |   |  |
 -------------    |   --------- | -    |   -------- | -
                  |             |      |            |
                   -------------        ------------

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

(setq x (copy-sequence [1 2 3 4]))
     ⇒ [1 2 3 4]
(nreverse x)
     ⇒ [4 3 2 1]
x
     ⇒ [4 3 2 1]

Note that unlike reverse, this function doesn’t work with strings. Although you can alter string data by using aset, it is strongly encouraged to treat strings as immutable even when they are mutable. See Mutability.

function sort sequence predicate​

This function sorts sequence stably. Note that this function doesn’t work for all sequences; it may be used only for lists and vectors. If sequence is a list, it is modified destructively. This functions returns the sorted sequence and compares elements using 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 predicate must be a function that accepts two arguments. It is called with two elements of sequence. To get an increasing order sort, the predicate should return non-nil if the first element is “less" than the second, or nil if not.

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

The destructive aspect of sort for lists is that it rearranges the cons cells forming sequence by changing CDRs. 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 copy-sequence and then sort.

Sorting does not change the CARs of the cons cells in sequence; the cons cell that originally contained the element a in sequence still has a in its CAR after sorting, but it now appears in a different position in the list due to the change of CDRs. For example:

(setq nums (list 1 3 2 6 5 4 0))
     ⇒ (1 3 2 6 5 4 0)
(sort nums #'<)
     ⇒ (0 1 2 3 4 5 6)
nums
     ⇒ (1 2 3 4 5 6)

Warning: Note that the list in 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 sort and use that. Most often we store the result back into the variable that held the original list:

(setq nums (sort nums #'<))

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

(setq
  vector
  (vector '(8 . "xxx") '(9 . "aaa") '(8 . "bbb") '(9 . "zzz")
          '(9 . "ppp") '(8 . "ttt") '(8 . "eee") '(9 . "fff")))
     ⇒ [(8 . "xxx") (9 . "aaa") (8 . "bbb") (9 . "zzz")
         (9 . "ppp") (8 . "ttt") (8 . "eee") (9 . "fff")]
(sort vector (lambda (x y) (< (car x) (car y))))
     ⇒ [(8 . "xxx") (8 . "bbb") (8 . "ttt") (8 . "eee")
         (9 . "aaa") (9 . "zzz") (9 . "ppp") (9 . "fff")]

See Sorting, for more functions that perform sorting. See documentation in Accessing Documentation, for a useful example of sort.

The seq.el library provides the following additional sequence manipulation macros and functions, prefixed with seq-. To use them, you must first load the 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 seq.el library can be extended to work with additional types of sequential data-structures. For that purpose, all functions are defined using cl-defgeneric. See Generic Functions, for more details about using cl-defgeneric for adding extensions.

function seq-elt sequence index​

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

(seq-elt [1 2 3 4] 2)
⇒ 3

seq-elt returns places settable using setf (see Setting Generalized Variables).

(setq vec [1 2 3 4])
(setf (seq-elt vec 2) 5)
vec
⇒ [1 2 5 4]

function seq-length sequence​

This function returns the number of elements in sequence. For built-in sequence types, seq-length behaves like length. See Definition of length.

function seqp object​

This function returns non-nil if object is a sequence (a list or array), or any additional type of sequence defined via seq.el generic functions. This is an extensible variant of sequencep.

(seqp [1 2])
⇒ t
(seqp 2)
⇒ nil

function seq-drop sequence n​

This function returns all but the first n (an integer) elements of sequence. If n is negative or zero, the result is sequence.

(seq-drop [1 2 3 4 5 6] 3)
⇒ [4 5 6]
(seq-drop "hello world" -4)
⇒ "hello world"

function seq-take sequence n​

This function returns the first n (an integer) elements of sequence. If n is negative or zero, the result is nil.

(seq-take '(1 2 3 4) 3)
⇒ (1 2 3)
(seq-take [1 2 3 4] 0)
⇒ []

function seq-take-while predicate sequence​

This function returns the members of sequence in order, stopping before the first one for which predicate returns nil.

(seq-take-while (lambda (elt) (> elt 0)) '(1 2 3 -1 -2))
⇒ (1 2 3)
(seq-take-while (lambda (elt) (> elt 0)) [-1 4 6])
⇒ []

function seq-drop-while predicate sequence​

This function returns the members of sequence in order, starting from the first one for which predicate returns nil.

(seq-drop-while (lambda (elt) (> elt 0)) '(1 2 3 -1 -2))
⇒ (-1 -2)
(seq-drop-while (lambda (elt) (< elt 0)) [1 4 6])
⇒ [1 4 6]

function seq-do function sequence​

This function applies function to each element of sequence in turn (presumably for side effects), and returns sequence.

function seq-map function sequence​

This function returns the result of applying function to each element of sequence. The returned value is a list.

(seq-map #'1+ '(2 4 6))
⇒ (3 5 7)
(seq-map #'symbol-name [foo bar])
⇒ ("foo" "bar")

function seq-map-indexed function sequence​

This function returns the result of applying function to each element of sequence and its index within seq. The returned value is a list.

(seq-map-indexed (lambda (elt idx)
                   (list idx elt))
                 '(a b c))
⇒ ((0 a) (1 b) (2 c))

function seq-mapn function \&rest sequences​

This function returns the result of applying function to each element of sequences. The arity (see subr-arity) of function must match the number of sequences. Mapping stops at the end of the shortest sequence, and the returned value is a list.

(seq-mapn #'+ '(2 4 6) '(20 40 60))
⇒ (22 44 66)
(seq-mapn #'concat '("moskito" "bite") ["bee" "sting"])
⇒ ("moskitobee" "bitesting")

function seq-filter predicate sequence​

This function returns a list of all the elements in sequence for which predicate returns non-nil.

(seq-filter (lambda (elt) (> elt 0)) [1 -1 3 -3 5])
⇒ (1 3 5)
(seq-filter (lambda (elt) (> elt 0)) '(-1 -3 -5))
⇒ nil

function seq-remove predicate sequence​

This function returns a list of all the elements in sequence for which predicate returns nil.

(seq-remove (lambda (elt) (> elt 0)) [1 -1 3 -3 5])
⇒ (-1 -3)
(seq-remove (lambda (elt) (< elt 0)) '(-1 -3 -5))
⇒ nil

function seq-reduce function sequence initial-value​

This function returns the result of calling function with initial-value and the first element of sequence, then calling function with that result and the second element of sequence, then with that result and the third element of sequence, etc. function should be a function of two arguments.

function is called with two arguments. intial-value (and then the accumulated value) is used as the first argument, and the elements in sequence are used for the second argument.

If sequence is empty, this returns initial-value without calling function.

(seq-reduce #'+ [1 2 3 4] 0)
⇒ 10
(seq-reduce #'+ '(1 2 3 4) 5)
⇒ 15
(seq-reduce #'+ '() 3)
⇒ 3

function seq-some predicate sequence​

This function returns the first non-nil value returned by applying predicate to each element of sequence in turn.

(seq-some #'numberp ["abc" 1 nil])
⇒ t
(seq-some #'numberp ["abc" "def"])
⇒ nil
(seq-some #'null ["abc" 1 nil])
⇒ t
(seq-some #'1+ [2 4 6])
⇒ 3

function seq-find predicate sequence \&optional default​

This function returns the first element in sequence for which predicate returns non-nil. If no element matches predicate, the function returns default.

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

(seq-find #'numberp ["abc" 1 nil])
⇒ 1
(seq-find #'numberp ["abc" "def"])
⇒ nil

function seq-every-p predicate sequence​

This function returns non-nil if applying predicate to every element of sequence returns non-nil.

(seq-every-p #'numberp [2 4 6])
⇒ t
(seq-every-p #'numberp [2 4 "6"])
⇒ nil

function seq-empty-p sequence​

This function returns non-nil if sequence is empty.

(seq-empty-p "not empty")
⇒ nil
(seq-empty-p "")
⇒ t

function seq-count predicate sequence​

This function returns the number of elements in sequence for which predicate returns non-nil.

(seq-count (lambda (elt) (> elt 0)) [-1 2 0 3 -2])
⇒ 2

function seq-sort function sequence​

This function returns a copy of sequence that is sorted according to function, a function of two arguments that returns non-nil if the first argument should sort before the second.

function seq-sort-by function predicate sequence​

This function is similar to seq-sort, but the elements of sequence are transformed by applying function on them before being sorted. function is a function of one argument.

(seq-sort-by #'seq-length #'> ["a" "ab" "abc"])
⇒ ["abc" "ab" "a"]

function seq-contains-p sequence elt \&optional function​

This function returns non-nil if at least one element in sequence is equal to elt. If the optional argument function is non-nil, it is a function of two arguments to use instead of the default equal.

(seq-contains-p '(symbol1 symbol2) 'symbol1)
⇒ t
(seq-contains-p '(symbol1 symbol2) 'symbol3)
⇒ nil

function seq-set-equal-p sequence1 sequence2 \&optional testfn​

This function checks whether sequence1 and sequence2 contain the same elements, regardless of the order. If the optional argument testfn is non-nil, it is a function of two arguments to use instead of the default equal.

(seq-set-equal-p '(a b c) '(c b a))
⇒ t
(seq-set-equal-p '(a b c) '(c b))
⇒ nil
(seq-set-equal-p '("a" "b" "c") '("c" "b" "a"))
⇒ t
(seq-set-equal-p '("a" "b" "c") '("c" "b" "a") #'eq)
⇒ nil

function seq-position sequence elt \&optional function​

This function returns the index of the first element in sequence that is equal to elt. If the optional argument function is non-nil, it is a function of two arguments to use instead of the default equal.

(seq-position '(a b c) 'b)
⇒ 1
(seq-position '(a b c) 'd)
⇒ nil

function seq-uniq sequence \&optional function​

This function returns a list of the elements of sequence with duplicates removed. If the optional argument function is non-nil, it is a function of two arguments to use instead of the default equal.

(seq-uniq '(1 2 2 1 3))
⇒ (1 2 3)
(seq-uniq '(1 2 2.0 1.0) #'=)
⇒ (1 2)

function seq-subseq sequence start \&optional end​

This function returns a subset of sequence from start to end, both integers (end defaults to the last element). If start or end is negative, it counts from the end of sequence.

(seq-subseq '(1 2 3 4 5) 1)
⇒ (2 3 4 5)
(seq-subseq '[1 2 3 4 5] 1 3)
⇒ [2 3]
(seq-subseq '[1 2 3 4 5] -3 -1)
⇒ [3 4]

function seq-concatenate type \&rest sequences​

This function returns a sequence of type type made of the concatenation of sequences. type may be: vector, list or string.

(seq-concatenate 'list '(1 2) '(3 4) [5 6])
⇒ (1 2 3 4 5 6)
(seq-concatenate 'string "Hello " "world")
⇒ "Hello world"

function seq-mapcat function sequence \&optional type​

This function returns the result of applying seq-concatenate to the result of applying function to each element of sequence. The result is a sequence of type type, or a list if type is nil.

(seq-mapcat #'seq-reverse '((3 2 1) (6 5 4)))
⇒ (1 2 3 4 5 6)

function seq-partition sequence n​

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

(seq-partition '(0 1 2 3 4 5 6 7) 3)
⇒ ((0 1 2) (3 4 5) (6 7))

function seq-intersection sequence1 sequence2 \&optional function​

This function returns a list of the elements that appear both in sequence1 and sequence2. If the optional argument function is non-nil, it is a function of two arguments to use to compare elements instead of the default equal.

(seq-intersection [2 3 4 5] [1 3 5 6 7])
⇒ (3 5)

function seq-difference sequence1 sequence2 \&optional function​

This function returns a list of the elements that appear in sequence1 but not in sequence2. If the optional argument function is non-nil, it is a function of two arguments to use to compare elements instead of the default equal.

(seq-difference '(2 3 4 5) [1 3 5 6 7])
⇒ (2 4)

function seq-group-by function sequence​

This function separates the elements of sequence into an alist whose keys are the result of applying function to each element of sequence. Keys are compared using equal.

(seq-group-by #'integerp '(1 2.1 3 2 3.2))
⇒ ((t 1 3 2) (nil 2.1 3.2))
(seq-group-by #'car '((a 1) (b 2) (a 3) (c 4)))
⇒ ((b (b 2)) (a (a 1) (a 3)) (c (c 4)))

function seq-into sequence type​

This function converts the sequence sequence into a sequence of type type. type can be one of the following symbols: vector, string or list.

(seq-into [1 2 3] 'list)
⇒ (1 2 3)
(seq-into nil 'vector)
⇒ []
(seq-into "hello" 'vector)
⇒ [104 101 108 108 111]

function seq-min sequence​

This function returns the smallest element of sequence. The elements of sequence must be numbers or markers (see Markers).

(seq-min [3 1 2])
⇒ 1
(seq-min "Hello")
⇒ 72

function seq-max sequence​

This function returns the largest element of sequence. The elements of sequence must be numbers or markers.

(seq-max [1 3 2])
⇒ 3
(seq-max "Hello")
⇒ 111

macro seq-doseq (var sequence) body…​

This macro is like dolist (see dolist), except that sequence can be a list, vector or string. This is primarily useful for side-effects.

macro seq-let var-sequence val-sequence body…​

This macro binds the variables defined in var-sequence to the values that are the corresponding elements of val-sequence. This is known as destructuring binding. The elements of var-sequence can themselves include sequences, allowing for nested destructuring.

The var-sequence sequence can also include the &rest marker followed by a variable name to be bound to the rest of val-sequence.

(seq-let [first second] [1 2 3 4]
  (list first second))
⇒ (1 2)
(seq-let (_ a _ b) '(1 2 3 4)
  (list a b))
⇒ (2 4)
(seq-let [a [b [c]]] [1 [2 [3]]]
  (list a b c))
⇒ (1 2 3)
(seq-let [a b &rest others] [1 2 3 4]
  others)
⇒ [3 4]

The pcase patterns provide an alternative facility for destructuring binding, see Destructuring with pcase Patterns.

function seq-random-elt sequence​

This function returns an element of sequence taken at random.

(seq-random-elt [1 2 3 4])
⇒ 3
(seq-random-elt [1 2 3 4])
⇒ 2
(seq-random-elt [1 2 3 4])
⇒ 4
(seq-random-elt [1 2 3 4])
⇒ 2
(seq-random-elt [1 2 3 4])
⇒ 1

If sequence is empty, this function signals an error.