Module Stdlib.List

List operations.

Some functions are flagged as not tail-recursive. A tail-recursive function uses constant stack space, while a non-tail-recursive function uses stack space proportional to the length of its list argument, which can be a problem with very long lists. When the function takes several list arguments, an approximate formula giving stack usage (in some unspecified constant unit) is shown in parentheses.

The above considerations can usually be ignored if your lists are not longer than about 10000 elements.

The labeled version of this module can be used as described in the StdLabels module.

type 'a t = 'a list =

type t('a) = list('a) =

| []

| :: of 'a * 'a list

| ::('a, list('a))

;

An alias for the type of lists.

val length : 'a list -> int

let length: list('a) => int;

Return the length (number of elements) of the given list.

val compare_lengths : 'a list -> 'b list -> int

let compare_lengths: list('a) => list('b) => int;

Compare the lengths of two lists. compare_lengths l1 l2 is equivalent to compare (length l1) (length l2), except that the computation stops after reaching the end of the shortest list.

since 4.05

val compare_length_with : 'a list -> int -> int

let compare_length_with: list('a) => int => int;

Compare the length of a list to an integer. compare_length_with l len is equivalent to compare (length l) len, except that the computation stops after at most len iterations on the list.

since 4.05

val is_empty : 'a list -> bool

let is_empty: list('a) => bool;

is_empty l is true if and only if l has no elements. It is equivalent to compare_length_with l 0 = 0.

since 5.1

val cons : 'a -> 'a list -> 'a list

let cons: 'a => list('a) => list('a);

cons x xs is x :: xs

since 4.03 (4.05 in ListLabels)

val singleton : 'a -> 'a list

let singleton: 'a => list('a);

singleton x returns the one-element list [x].

since 5.4

val hd : 'a list -> 'a

let hd: list('a) => 'a;

Return the first element of the given list.

raises Failure if the list is empty.

val tl : 'a list -> 'a list

let tl: list('a) => list('a);

Return the given list without its first element.

raises Failure if the list is empty.

val nth : 'a list -> int -> 'a

let nth: list('a) => int => 'a;

Return the n-th element of the given list. The first element (head of the list) is at position 0.

raises Failure if the list is too short. raises Invalid_argument if n is negative.

val nth_opt : 'a list -> int -> 'a option

let nth_opt: list('a) => int => option('a);

Return the n-th element of the given list. The first element (head of the list) is at position 0. Return None if the list is too short.

raises Invalid_argument if n is negative. since 4.05

val rev : 'a list -> 'a list

let rev: list('a) => list('a);

List reversal.

val init : int -> (int -> 'a) -> 'a list

let init: int => (int => 'a) => list('a);

init len f is [f 0; f 1; ...; f (len-1)], evaluated left to right.

raises Invalid_argument if len < 0. since 4.06

val append : 'a list -> 'a list -> 'a list

let append: list('a) => list('a) => list('a);

append l0 l1 appends l1 to l0. Same function as the infix operator @.

since 5.1 this function is tail-recursive.

val rev_append : 'a list -> 'a list -> 'a list

let rev_append: list('a) => list('a) => list('a);

rev_append l1 l2 reverses l1 and concatenates it with l2. This is equivalent to (rev l1) @ l2.

val concat : 'a list list -> 'a list

let concat: list(list('a)) => list('a);

Concatenate a list of lists. The elements of the argument are all concatenated together (in the same order) to give the result. Not tail-recursive (length of the argument + length of the longest sub-list).

val flatten : 'a list list -> 'a list

let flatten: list(list('a)) => list('a);

Same as concat. Not tail-recursive (length of the argument + length of the longest sub-list).

Comparison

val equal : ('a -> 'a -> bool) -> 'a list -> 'a list -> bool

let equal: ('a => 'a => bool) => list('a) => list('a) => bool;

equal eq [a1; ...; an] [b1; ..; bm] holds when the two input lists have the same length, and for each pair of elements ai, bi at the same position we have eq ai bi.

Note: the eq function may be called even if the lists have different length. If you know your equality function is costly, you may want to check compare_lengths first.

since 4.12

val compare : ('a -> 'a -> int) -> 'a list -> 'a list -> int

let compare: ('a => 'a => int) => list('a) => list('a) => int;

compare cmp [a1; ...; an] [b1; ...; bm] performs a lexicographic comparison of the two input lists, using the same 'a -> 'a -> int('a, 'a) => int interface as Stdlib.compare:

• a1 :: l1 is smaller than a2 :: l2 (negative result) if a1 is smaller than a2, or if they are equal (0 result) and l1 is smaller than l2
• the empty list [] is strictly smaller than non-empty lists Note: the cmp function will be called even if the lists have different lengths.

since 4.12

Iterators

val iter : ('a -> unit) -> 'a list -> unit

let iter: ('a => unit) => list('a) => unit;

iter f [a1; ...; an] applies function f in turn to [a1; ...; an]. It is equivalent to f a1; f a2; ...; f an.

val iteri : (int -> 'a -> unit) -> 'a list -> unit

let iteri: (int => 'a => unit) => list('a) => unit;

Same as iter, but the function is applied to the index of the element as first argument (counting from 0), and the element itself as second argument.

since 4.00

val map : ('a -> 'b) -> 'a list -> 'b list

let map: ('a => 'b) => list('a) => list('b);

map f [a1; ...; an] applies function f to a1, ..., an, and builds the list [f a1; ...; f an] with the results returned by f.

val mapi : (int -> 'a -> 'b) -> 'a list -> 'b list

let mapi: (int => 'a => 'b) => list('a) => list('b);

Same as map, but the function is applied to the index of the element as first argument (counting from 0), and the element itself as second argument.

since 4.00

val rev_map : ('a -> 'b) -> 'a list -> 'b list

let rev_map: ('a => 'b) => list('a) => list('b);

rev_map f l gives the same result as rev (map f l), but is more efficient.

val filter_map : ('a -> 'b option) -> 'a list -> 'b list

let filter_map: ('a => option('b)) => list('a) => list('b);

filter_map f l applies f to every element of l, filters out the None elements and returns the list of the arguments of the Some elements.

since 4.08

val concat_map : ('a -> 'b list) -> 'a list -> 'b list

let concat_map: ('a => list('b)) => list('a) => list('b);

concat_map f l gives the same result as concat (map f l). Tail-recursive.

since 4.10

val fold_left_map : 
  ('acc -> 'a -> 'acc * 'b) ->
  'acc ->
  'a list ->
  'acc * 'b list

let fold_left_map: 
  ('acc => 'a => ('acc, 'b)) =>
  'acc =>
  list('a) =>
  ('acc, list('b));

fold_left_map is a combination of fold_left and map that threads an accumulator through calls to f.

since 4.11

val fold_left : ('acc -> 'a -> 'acc) -> 'acc -> 'a list -> 'acc

let fold_left: ('acc => 'a => 'acc) => 'acc => list('a) => 'acc;

fold_left f init [b1; ...; bn] is f (... (f (f init b1) b2) ...) bn.

val fold_right : ('a -> 'acc -> 'acc) -> 'a list -> 'acc -> 'acc

let fold_right: ('a => 'acc => 'acc) => list('a) => 'acc => 'acc;

fold_right f [a1; ...; an] init is f a1 (f a2 (... (f an init) ...)). Not tail-recursive.

Iterators on two lists

val iter2 : ('a -> 'b -> unit) -> 'a list -> 'b list -> unit

let iter2: ('a => 'b => unit) => list('a) => list('b) => unit;

iter2 f [a1; ...; an] [b1; ...; bn] calls in turn f a1 b1; ...; f an bn.

raises Invalid_argument if the two lists are determined to have different lengths.

val map2 : ('a -> 'b -> 'c) -> 'a list -> 'b list -> 'c list

let map2: ('a => 'b => 'c) => list('a) => list('b) => list('c);

map2 f [a1; ...; an] [b1; ...; bn] is [f a1 b1; ...; f an bn].

raises Invalid_argument if the two lists are determined to have different lengths.

val rev_map2 : ('a -> 'b -> 'c) -> 'a list -> 'b list -> 'c list

let rev_map2: ('a => 'b => 'c) => list('a) => list('b) => list('c);

rev_map2 f l1 l2 gives the same result as rev (map2 f l1 l2), but is more efficient.

val fold_left2 : 
  ('acc -> 'a -> 'b -> 'acc) ->
  'acc ->
  'a list ->
  'b list ->
  'acc

let fold_left2: 
  ('acc => 'a => 'b => 'acc) =>
  'acc =>
  list('a) =>
  list('b) =>
  'acc;

fold_left2 f init [a1; ...; an] [b1; ...; bn] is f (... (f (f init a1 b1) a2 b2) ...) an bn.

raises Invalid_argument if the two lists are determined to have different lengths.

val fold_right2 : 
  ('a -> 'b -> 'acc -> 'acc) ->
  'a list ->
  'b list ->
  'acc ->
  'acc

let fold_right2: 
  ('a => 'b => 'acc => 'acc) =>
  list('a) =>
  list('b) =>
  'acc =>
  'acc;

fold_right2 f [a1; ...; an] [b1; ...; bn] init is f a1 b1 (f a2 b2 (... (f an bn init) ...)).

raises Invalid_argument if the two lists are determined to have different lengths. Not tail-recursive.

List scanning

val for_all : ('a -> bool) -> 'a list -> bool

let for_all: ('a => bool) => list('a) => bool;

for_all f [a1; ...; an] checks if all elements of the list satisfy the predicate f. That is, it returns (f a1) && (f a2) && ... && (f an) for a non-empty list and true if the list is empty.

val exists : ('a -> bool) -> 'a list -> bool

let exists: ('a => bool) => list('a) => bool;

exists f [a1; ...; an] checks if at least one element of the list satisfies the predicate f. That is, it returns (f a1) || (f a2) || ... || (f an) for a non-empty list and false if the list is empty.

val for_all2 : ('a -> 'b -> bool) -> 'a list -> 'b list -> bool

let for_all2: ('a => 'b => bool) => list('a) => list('b) => bool;

Same as for_all, but for a two-argument predicate.

raises Invalid_argument if the two lists are determined to have different lengths.

val exists2 : ('a -> 'b -> bool) -> 'a list -> 'b list -> bool

let exists2: ('a => 'b => bool) => list('a) => list('b) => bool;

Same as exists, but for a two-argument predicate.

raises Invalid_argument if the two lists are determined to have different lengths.

val mem : 'a -> 'a list -> bool

let mem: 'a => list('a) => bool;

mem a set is true if and only if a is equal to an element of set.

val memq : 'a -> 'a list -> bool

let memq: 'a => list('a) => bool;

Same as mem, but uses physical equality instead of structural equality to compare list elements.

List searching

val find : ('a -> bool) -> 'a list -> 'a

let find: ('a => bool) => list('a) => 'a;

find f l returns the first element of the list l that satisfies the predicate f.

raises Not_found if there is no value that satisfies f in the list l.

val find_opt : ('a -> bool) -> 'a list -> 'a option

let find_opt: ('a => bool) => list('a) => option('a);

find f l returns the first element of the list l that satisfies the predicate f. Returns None if there is no value that satisfies f in the list l.

since 4.05

val find_index : ('a -> bool) -> 'a list -> int option

let find_index: ('a => bool) => list('a) => option(int);

find_index f xs returns Some i, where i is the index of the first element of the list xs that satisfies f x, if there is such an element.

It returns None if there is no such element.

since 5.1

val find_map : ('a -> 'b option) -> 'a list -> 'b option

let find_map: ('a => option('b)) => list('a) => option('b);

find_map f l applies f to the elements of l in order, and returns the first result of the form Some v, or None if none exist.

since 4.10

val find_mapi : (int -> 'a -> 'b option) -> 'a list -> 'b option

let find_mapi: (int => 'a => option('b)) => list('a) => option('b);

Same as find_map, but the predicate is applied to the index of the element as first argument (counting from 0), and the element itself as second argument.

since 5.1

val filter : ('a -> bool) -> 'a list -> 'a list

let filter: ('a => bool) => list('a) => list('a);

filter f l returns all the elements of the list l that satisfy the predicate f. The order of the elements in the input list is preserved.

val find_all : ('a -> bool) -> 'a list -> 'a list

let find_all: ('a => bool) => list('a) => list('a);

find_all is another name for filter.

val filteri : (int -> 'a -> bool) -> 'a list -> 'a list

let filteri: (int => 'a => bool) => list('a) => list('a);

Same as filter, but the predicate is applied to the index of the element as first argument (counting from 0), and the element itself as second argument.

since 4.11

List manipulation

val take : int -> 'a list -> 'a list

let take: int => list('a) => list('a);

take n l returns the prefix of l of length n, or a copy of l if n > length l. This is the empty list if n is negative.

Warning. In version 5.3 only, this function raises Invalid_argument for negative n values.

since 5.3

val drop : int -> 'a list -> 'a list

let drop: int => list('a) => list('a);

drop n l returns the suffix of l after n elements, or [] if n > length l. This is l if n is negative.

Warning. In version 5.3 only, this function raises Invalid_argument for negative n values.

since 5.3

val take_while : ('a -> bool) -> 'a list -> 'a list

let take_while: ('a => bool) => list('a) => list('a);

take_while p l is the longest (possibly empty) prefix of l containing only elements that satisfy p.

since 5.3

val drop_while : ('a -> bool) -> 'a list -> 'a list

let drop_while: ('a => bool) => list('a) => list('a);

drop_while p l is the longest (possibly empty) suffix of l starting at the first element that does not satisfy p.

since 5.3

val partition : ('a -> bool) -> 'a list -> 'a list * 'a list

let partition: ('a => bool) => list('a) => (list('a), list('a));

partition f l returns a pair of lists (l1, l2), where l1 is the list of all the elements of l that satisfy the predicate f, and l2 is the list of all the elements of l that do not satisfy f. The order of the elements in the input list is preserved.

val partition_map : ('a -> ('b, 'c) Either.t) -> 'a list -> 'b list * 'c list

let partition_map: 
  ('a => Either.t('b, 'c)) =>
  list('a) =>
  (list('b), list('c));

partition_map f l returns a pair of lists (l1, l2) such that, for each element x of the input list l:

• if f x is Left y1, then y1 is in l1, and
• if f x is Right y2, then y2 is in l2. The output elements are included in l1 and l2 in the same relative order as the corresponding input elements in l.

In particular, partition_map (fun x -> if f x then Left x else Right x) l is equivalent to partition f l.

since 4.12

Association lists

val assoc : 'a -> ('a * 'b) list -> 'b

let assoc: 'a => list(('a, 'b)) => 'b;

assoc a l returns the value associated with key a in the list of pairs l. That is, assoc a [ ...; (a,b); ...] = b if (a,b) is the leftmost binding of a in list l.

raises Not_found if there is no value associated with a in the list l.

val assoc_opt : 'a -> ('a * 'b) list -> 'b option

let assoc_opt: 'a => list(('a, 'b)) => option('b);

assoc_opt a l returns the value associated with key a in the list of pairs l. That is, assoc_opt a [ ...; (a,b); ...] = Some b if (a,b) is the leftmost binding of a in list l. Returns None if there is no value associated with a in the list l.

since 4.05

val assq : 'a -> ('a * 'b) list -> 'b

let assq: 'a => list(('a, 'b)) => 'b;

Same as assoc, but uses physical equality instead of structural equality to compare keys.

val assq_opt : 'a -> ('a * 'b) list -> 'b option

let assq_opt: 'a => list(('a, 'b)) => option('b);

Same as assoc_opt, but uses physical equality instead of structural equality to compare keys.

since 4.05

val mem_assoc : 'a -> ('a * 'b) list -> bool

let mem_assoc: 'a => list(('a, 'b)) => bool;

Same as assoc, but simply return true if a binding exists, and false if no bindings exist for the given key.

val mem_assq : 'a -> ('a * 'b) list -> bool

let mem_assq: 'a => list(('a, 'b)) => bool;

Same as mem_assoc, but uses physical equality instead of structural equality to compare keys.

val remove_assoc : 'a -> ('a * 'b) list -> ('a * 'b) list

let remove_assoc: 'a => list(('a, 'b)) => list(('a, 'b));

remove_assoc a l returns the list of pairs l without the first pair with key a, if any. Not tail-recursive.

val remove_assq : 'a -> ('a * 'b) list -> ('a * 'b) list

let remove_assq: 'a => list(('a, 'b)) => list(('a, 'b));

Same as remove_assoc, but uses physical equality instead of structural equality to compare keys. Not tail-recursive.

Lists of pairs

val split : ('a * 'b) list -> 'a list * 'b list

let split: list(('a, 'b)) => (list('a), list('b));

Transform a list of pairs into a pair of lists: split [(a1,b1); ...; (an,bn)] is ([a1; ...; an], [b1; ...; bn]). Not tail-recursive.

val combine : 'a list -> 'b list -> ('a * 'b) list

let combine: list('a) => list('b) => list(('a, 'b));

Transform a pair of lists into a list of pairs: combine [a1; ...; an] [b1; ...; bn] is [(a1,b1); ...; (an,bn)].

raises Invalid_argument if the two lists have different lengths. Not tail-recursive.

Sorting

val sort : ('a -> 'a -> int) -> 'a list -> 'a list

let sort: ('a => 'a => int) => list('a) => list('a);

Sort a list in increasing order according to a comparison function. The comparison function must return 0 if its arguments compare as equal, a positive integer if the first is greater, and a negative integer if the first is smaller (see Array.sort for a complete specification). For example, Stdlib.compare is a suitable comparison function. The resulting list is sorted in increasing order. sort is guaranteed to run in constant heap space (in addition to the size of the result list) and logarithmic stack space.

The current implementation uses Merge Sort. It runs in constant heap space and logarithmic stack space.

val stable_sort : ('a -> 'a -> int) -> 'a list -> 'a list

let stable_sort: ('a => 'a => int) => list('a) => list('a);

Same as sort, but the sorting algorithm is guaranteed to be stable (i.e. elements that compare equal are kept in their original order).

The current implementation uses Merge Sort. It runs in constant heap space and logarithmic stack space.

val fast_sort : ('a -> 'a -> int) -> 'a list -> 'a list

let fast_sort: ('a => 'a => int) => list('a) => list('a);

Same as sort or stable_sort, whichever is faster on typical input.

val sort_uniq : ('a -> 'a -> int) -> 'a list -> 'a list

let sort_uniq: ('a => 'a => int) => list('a) => list('a);

Same as sort, but also remove duplicates: if multiple elements compare equal, keep only the first.

since 4.02 (4.03 in ListLabels) before 5.4 the element kept was not necessarily the first one.

val merge : ('a -> 'a -> int) -> 'a list -> 'a list -> 'a list

let merge: ('a => 'a => int) => list('a) => list('a) => list('a);

Merge two lists: Assuming that l1 and l2 are sorted according to the comparison function cmp, merge cmp l1 l2 will return a sorted list containing all the elements of l1 and l2. If several elements compare equal, the elements of l1 will be before the elements of l2. Not tail-recursive (sum of the lengths of the arguments).

Lists and Sequences

val to_seq : 'a list -> 'a Seq.t

let to_seq: list('a) => Seq.t('a);

Iterate on the list.

since 4.07

val of_seq : 'a Seq.t -> 'a list

let of_seq: Seq.t('a) => list('a);

Create a list from a sequence.

since 4.07