`module Pervasives := Stdlib`

Additional and modified functions for lists.

The OCaml standard library provides a module for list functions. This BatList module can be used to extend the List module or as a standalone module. It provides new functions and modify the behavior of some other ones (in particular all functions are now tail-recursive).

The following functions have the same behavior as the `List` module ones but are tail-recursive: `map`, `append`, `concat`, `flatten`, `fold_right`, `remove_assoc`, `remove_assq`, `split`. That means they will not cause a `Stack_overflow` when used on very long list.

The implementation might be a little more slow in bytecode, but compiling in native code will not affect performances.

This module extends Stdlib's List module, go there for documentation on the rest of the functions and types.

List operations.

@documents List

- author Xavier Leroy (base module)

- author Brian Hurt

- author Nicolas Cannasse

- author Richard W.M. Jones

- author David Teller

`type 'a t = 'a list =`

1. `| []`
2. `| :: of 'a * 'a list`

The type of lists

`include BatEnum.Enumerable with type 'a enumerable = 'a t`
`type 'a enumerable = 'a t`

The data structure, e.g. `'a List.t`

`include BatInterfaces.Mappable with type 'a mappable = 'a t`
`type 'a mappable = 'a t`

The data structure, e.g. `'a List.t`

## Base operations

`val is_empty : 'a list -> bool`

`is_empty e` returns true if `e` does not contains any element.

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

`cons h t` returns the list starting with `h` and continuing as `t`.

`val hd : 'a list -> 'a`

Returns the first element of the list.

- raises `Failure`

  if the list is empty.

`val first : 'a list -> 'a`

Alias to hd

`val tl : 'a list -> 'a list`

Return the given list without its first element.

- raises `Failure`

  if the list is empty.

`val last : 'a list -> 'a`

Returns the last element of the list.

- raises `Invalid_argument`

  if the list is empty.

This function takes linear time.

`val length : 'a list -> int`

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

`val compare_lengths : 'a list -> 'b list -> 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 itering on the shortest list.

- since 2.7.0

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

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

- since 2.7.0

`val at : 'a list -> int -> 'a`

`at l n` returns the n-th element of the list `l` or

- raises `Invalid_argument`

  if the index is outside of `l` bounds. O(l)

`val at_opt : 'a list -> int -> 'a option`

`at_opt` returns the n-th element of the list `l` or None if the index is beyond the length of `l`.

- since 2.7.0

- raises `Invalid_argument`

  if the index is negative

`val rev : 'a list -> 'a list`

List reversal.

`val shuffle : ?state:Stdlib.Random.State.t -> 'a list -> 'a list`

`shuffle ~state:rs l` randomly shuffles the elements of `l`. The optional random state `rs` allows to control the random numbers being used during shuffling (for reproducibility).

Shuffling is implemented using the Fisher-Yates algorithm on an array and works in O(n), where n is the number of elements of `l`.

- since 2.6.0

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

`append l1 l2` is a concatenation of `l1` and `l2`. Same function as the infix operator `@`. Tail-recursive. This function takes O(`length l1`) time.

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

`List.rev_append l1 l2` reverses `l1` and concatenates it to `l2`.

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

Concatenate a list of lists. The elements of the argument are all concatenated together (in the same order) to give the result. Tail-recursive.

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

Same as `concat`.

`val singleton : 'a -> 'a list`

Create a list consisting of exactly one element.

- since 2.1

## Constructors

`val make : int -> 'a -> 'a list`

Similar to `String.make`, `make n x` returns a list containing `n` elements `x`.

`val range : int -> [< `To | `Downto ] -> int -> int list`

`range 1 `To 3` = `[1; 2; 3]`. `range 3 `Downto 1` = `[3; 2; 1]`.

- raises `Invalid_argument`

  in (`range i `To j`) if (i > j).

- raises `Invalid_argument`

  in (`range i `Downto j`) if (i < j).

- since 2.2.0

`val frange : float -> [< `To | `Downto ] -> float -> int -> float list`

`frange start `To stop n` generates (without accumulating floating point errors) `n` floats in the range `[start..stop]`. `n` must be >= 2. At each step, floats in an increasing (resp. decreasing) range increase (resp. decrease) by approximately (stop - start) / (n - 1).

- raises `Invalid_argument`

  in (`frange i _ j n`) if (n < 2).

- raises `Invalid_argument`

  in (`frange i `To j _`) if (i >= j).

- raises `Invalid_argument`

  in (`frange i `Downto j _`) if (i <= j). Examples: `frange 1.0 `To 3.0 3` = `[1.0; 2.0; 3.0]`. `frange 3.0 `Downto 1.0 3` = `[3.0; 2.0; 1.0]`.

- since 2.6.0

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

Similar to `Array.init`, `init n f` returns the list containing the results of (f 0),(f 1).... (f (n-1)).

- raises `Invalid_argument`

  if n < 0.

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

`unfold init f` creates a list by repeatedly applying `f` to the second element of its own result, starting from the initial value `init`. The first element of each result is accumulated in a list. The list is terminated and returned as soon as `f` returns `None`.

Example: `List.unfold 0 (fun x -> if x = 3 then None else Some (string_of_int x, x+1))` will return `["0";"1";"2"]`

- since 2.1

`val unfold_exn : (unit -> 'a) -> 'a list * exn`

Creates a list containing the results of sequential calls to `f()`. `f()` is called repeatedly until it throws an exception. Both the results list, as well as the exception thrown are returned in a `(results_list, exn)` pair. Warning: if calls to `f()` never throw an exception, unfold_exn is an infinite loop.

- since 3.2.0

`val unfold_exc : (unit -> 'a) -> 'a list * exn`

Alias for `unfold_exn`.

- deprecated

  use `unfold_exn`

- since 2.3.0

## Comparison

`val equal : ('a -> 'a -> bool) -> 'a list -> 'a list -> 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 3.3.0 and 4.12.0

## Iterators

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

`List.iter f [a0; a1; ...; an]` applies function `f` in turn to `a0; a1; ...; an`. It is equivalent to `begin f a0; f a1; ...; f an; () end`.

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

`iteri f l` will call `(f 0 a0); (f 1 a1) ... (f n an)` where `a0..an` are the elements of the list `l`.

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

`map f [a0; a1; ...; an]` applies function `f` to `a0, a1, ..., an`, and builds the list `[f a0; f a1; ...; f an]` with the results returned by `f`. Tail-recursive.

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

`List.rev_map f l` gives the same result as `List.rev``(``List.map` `f l)`.

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

`mapi f l` will build the list containing `(f 0 a0); (f 1 a1) ... (f n an)` where `a0..an` are the elements of the list `l`.

`val fold_left : ('a -> 'b -> 'a) -> 'a -> 'b list -> 'a`

`List.fold_left f a [b0; b1; ...; bn]` is `f (... (f (f a b0) b1) ...) bn`.

`val fold : ('a -> 'b -> 'a) -> 'a -> 'b list -> 'a`

Alias for `fold_left`.

`val fold_lefti : ('a -> int -> 'b -> 'a) -> 'a -> 'b list -> 'a`

As `fold_left`, but with the index of the element, from `0` to `length li - 1`, as additional argument.

- since 2.3.0

`val fold_right : ('a -> 'b -> 'b) -> 'a list -> 'b -> 'b`

`List.fold_right f [a0; a1; ...; an] b` is `f a0 (f a1 (... (f an b) ...))`. Tail-recursive.

`val fold_righti : (int -> 'b -> 'a -> 'a) -> 'b list -> 'a -> 'a`

As `fold_right`, but with the index of the element, from `0` to `length li - 1`, as additional argument.

- since 2.3.0

`val reduce : ('a -> 'a -> 'a) -> 'a list -> 'a`

`List.reduce f h::t` is `fold_left f h t`.

- raises `Invalid_argument`

  on empty list.

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

Combines `fold_left` and `map`. Tail-recursive.

More precisely :

    fold_left_map f acc [] = (acc, [])

    fold_left_map f acc (x :: xs) =
      let (acc', y) = f acc x in
      let (res, ys) = fold_left_map acc' xs in
      (res, y :: ys)

- since 2.6.0

`val max : ?cmp:('a -> 'a -> int) -> 'a list -> 'a`

`max l` returns the largest value in `l` as judged by `Pervasives.compare` (by default). You can provide another comparison function via the optional `cmp` parameter.

- raises `Invalid_argument`

  on an empty list.

`val min : ?cmp:('a -> 'a -> int) -> 'a list -> 'a`

`min l` returns the smallest value in `l` as judged by `Pervasives.compare` (by default). You can provide another comparison function via the optional `cmp` parameter.

- raises `Invalid_argument`

  on an empty list.

`val sum : int list -> int`

`sum l` returns the sum of the integers of `l`. Returns `0` on the empty list. Note: prior to 2.11.0, used to raise Invalid_argument on the empty list.

`val fsum : float list -> float`

`fsum l` returns the sum of the floats of `l`. Returns `0.` on the empty list. Note: prior to 2.11.0, used to raise Invalid_argument on the empty list.

`val favg : float list -> float`

`favg l` returns the average of the floats of `l`

- raises `Invalid_argument`

  on the empty list.

- since 2.6.0

`val kahan_sum : float list -> float`

`kahan_sum l` returns a numerically-accurate sum of the floats of `l`. See `BatArray.fsum` for more details.

- since 2.2.0

`val min_max : ?cmp:('a -> 'a -> int) -> 'a list -> 'a * 'a`

`min_max l` returns the pair (smallest, largest) from `l` as judged by `Pervasives.compare` (by default). You can provide another comparison function via the optional `cmp` parameter.

- raises `Invalid_argument`

  on an empty list.

- since 2.1

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

Iterate on the list

- since 2.10.0 and OCaml 4.07

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

Create a list from the iterator

- since 2.10.0 and OCaml 4.07

## Iterators on two lists

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

`List.iter2 f [a0; a1; ...; an] [b0; b1; ...; bn]` calls in turn `f a0 b0; f a1 b1; ...; f an bn`.

- raises `Invalid_argument`

  if two lists have different lengths.

`val iter2i : (int -> 'a -> 'b -> unit) -> 'a list -> 'b list -> unit`

`List.iter2i f [a0; a1; ...; an] [b0; b1; ...; bn]` calls in turn `f 0 a0 b0; f 1 a1 b1; ...; f n an bn`.

- raises `Invalid_argument`

  if two lists have different lengths.

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

`List.map2 f [a0; a1; ...; an] [b0; b1; ...; bn]` is `[f a0 b0; f a1 b1; ...; f an bn]`.

- raises `Invalid_argument`

  if two lists have different lengths. Tail-recursive.

`val map2i : (int -> 'a -> 'b -> 'c) -> 'a list -> 'b list -> 'c list`

`List.map2i f [a0; a1; ...; an] [b0; b1; ...; bn]` is `[f 0 a0 b0; f 1 a1 b1; ...; f n an bn]`.

- raises `Invalid_argument`

  if two lists have different lengths. Tail-recursive.

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

`List.rev_map2 f l1 l2` gives the same result as `List.rev``(``List.map2` `f l1 l2)`, but is tail-recursive and more efficient.

`val fold_left2 : ('a -> 'b -> 'c -> 'a) -> 'a -> 'b list -> 'c list -> 'a`

`List.fold_left2 f a [b0; b1; ...; bn] [c0; c1; ...; cn]` is `f (... (f (f a b0 c0) b1 c1) ...) bn cn`.

- raises `Invalid_argument`

  if two lists have different lengths.

`val fold_right2 : ('a -> 'b -> 'c -> 'c) -> 'a list -> 'b list -> 'c -> 'c`

`List.fold_right2 f [a0; a1; ...; an] [b0; b1; ...; bn] c` is `f a0 b0 (f a1 b1 (... (f an bn c) ...))`.

- raises `Invalid_argument`

  if two lists have different lengths. Tail-recursive.

## List scanning

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

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

`val mem_cmp : ('a -> 'a -> int) -> 'a -> 'a list -> bool`

Same as `List.mem`, but the comparator function is explicitly provided.

- since 2.2.0

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

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

### Unary predicate, One list

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

`for_all p [a0; a1; ...; an]` checks if all elements of the list satisfy the predicate `p`. That is, it returns `(p a0) && (p a1) && ... && (p an)`.

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

`exists p [a0; a1; ...; an]` checks if at least one element of the list satisfies the predicate `p`. That is, it returns `(p a0) || (p a1) || ... || (p an)`.

### Binary predicate, Two lists

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

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

- raises `Invalid_argument`

  if two lists have different lengths.

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

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

- raises `Invalid_argument`

  if two lists have different lengths.

`val subset : ('a -> 'b -> int) -> 'a list -> 'b list -> bool`

`subset cmp l l'` check if all elements of the list `l` is contained in the list `l'` by applying `cmp` as comparator.

- since 2.2.0

## List searching

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

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

- raises `Not_found`

  if there is no value that satisfies `p` in the list `l`.

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

`find_opt p l` returns the first element of the list `l` that satisfies the predicate `p`, or `None` if there is no value that satisfies `p` in the list `l`.

- since 2.7.0

`val find_map_opt : ('a -> 'b option) -> 'a list -> 'b option`

`find_map_opt 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 2.12.0 and OCaml 4.10

`val find_exn : ('a -> bool) -> exn -> 'a list -> 'a`

`find_exn p e l` returns the first element of `l` such as `p x` returns `true` or raises `e` if such an element has not been found.

`val findi : (int -> 'a -> bool) -> 'a list -> int * 'a`

`findi p l` returns the first element `ai` of `l` along with its index `i` such that `p i ai` is true.

- raises `Not_found`

  if no such element has been found.

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

`find_map pred list` finds the first element of `list` for which `pred element` returns `Some r`. It returns `r` immediately once found.

- raises `Not_found`

  if no element matches the predicate.

See also `filter_map`.

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

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

- since 2.12.0 and OCaml 4.10

`val rfind : ('a -> bool) -> 'a list -> 'a`

`rfind p l` returns the last element `x` of `l` such as `p x` returns `true`.

- raises `Not_found`

  if such element as not been found.

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

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

`val count_matching : ('a -> bool) -> 'a list -> int`

`count_matching p l` returns the number of elements in `l` that satisfy `p`. Semantically equivalent but faster than `length (filter p l)`.

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

`filteri p [a0; a1; ...; an]` returns all the elements `ai` of index `i` that satisfy the predicate `p i ai`. The order of the elements in the input list is preserved.

- since 2.2.0

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

`filter_map f l` calls `(f a0) (f a1).... (f an)` where `a0,a1..an` are the elements of `l`. It returns the list of elements `bi` such as `f ai = Some bi` (when `f` returns `None`, the corresponding element of `l` is discarded).

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

`filteri_map f l` calls `(f 0 a0) (f 1 a1).... (f n an)` where `a0,a1..an` are the elements of `l`. It returns the list of elements `bi` such as `f ai = Some bi` (when `f` returns `None`, the corresponding element of `l` is discarded).

- since 2.2.0

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

`find_all` is another name for `List.filter`.

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

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

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

`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 3.3.0

`val index_of : 'a -> 'a list -> int option`

`index_of e l` returns the index of the first occurrence of `e` in `l`, or `None` if there is no occurrence of `e` in `l`

`val index_ofq : 'a -> 'a list -> int option`

`index_ofq e l` behaves as `index_of e l` except it uses physical equality

`val rindex_of : 'a -> 'a list -> int option`

`rindex_of e l` returns the index of the last occurrence of `e` in `l`, or `None` if there is no occurrence of `e` in `l`

`val rindex_ofq : 'a -> 'a list -> int option`

`rindex_ofq e l` behaves as `rindex_of e l` except it uses physical equality

`val unique : ?eq:('a -> 'a -> bool) -> 'a list -> 'a list`

`unique cmp l` returns the list `l` without any duplicate element. The default comparator ( = ) is used if no comparison function specified.

Implementation Note: The current implementation removes any elements where the tail of the list contains an equal element, thus it keeps the *last* copy of each equal element.

This function takes O(n^2) time.

- see `sort_unique`

  to save time in cases when reordering the list is acceptable

- since 2.0

`val unique_cmp : ?cmp:('a -> 'a -> int) -> 'a list -> 'a list`

As `unique`, except comparator parameter returns an int. Default comparator is `Pervasives.compare`. This function takes O(n log n) time.

Implementation Note: The current implementation removes subsequent elements that compare as equal to earlier elements in the list, thus it keeps the *first* copy of each equal element.

- since 1.3.0

`val unique_hash : ?hash:('a -> int) -> ?eq:('a -> 'a -> bool) -> 'a list -> 'a list`

As `unique`, except uses a hash table to cut down the expected runtime to linear, assuming a good hash function. `?hash` defaults to `Hashtbl.hash` and `?eq` defaults to `(=)`.

Implementation Note: The current implementation removes subsequent elements that hash and compare as equal to earlier elements in the list, thus it keeps the *first* copy of each equal element.

- since 2.0.0

## Association lists

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

`assoc_opt a l` returns the value associated with key `a` in the list of pairs `l`. That is, `assoc_opt a [ ...; (a,b); ...] = 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 2.7.0

`val assoc_inv : 'b -> ('a * 'b) list -> 'a`

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

- raises `Not_found`

  if there is no key associated with `b` in the list `l`.

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

`remove_assoc a l` returns the list of pairs `l` without the first pair with key `a`, if any. Tail-recursive.

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

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

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

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

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

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

- since 2.7.0

`val assq_inv : 'b -> ('a * 'b) list -> 'a`

Same as `List.assoc_inv`, but uses physical equality instead of structural equality to compare keys.

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

Same as `List.remove_assoc`, but uses physical equality instead of structural equality to compare keys. Tail-recursive.

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

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

`val modify : 'a -> ('b -> 'b) -> ('a * 'b) list -> ('a * 'b) list`

`modify a f l` returns the same list as `l` but with value `b` associated to key `a` replaced with `f b`.

- raises `Not_found`

  if no value is associated with `a` in `l`

- since 2.1

`val modify_def : 'b -> 'a -> ('b -> 'b) -> ('a * 'b) list -> ('a * 'b) list`

`modify_def dfl a f l` performs as `modify a f l` except that it add an association from `a` to `f dfl` instead of raising `Not_found`.

- since 2.1

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

`modify_opt a f l` allows to modify the binding for `a` in `l` or absence thereof.

- since 2.1

## List transformations

`val modify_at : int -> ('a -> 'a) -> 'a list -> 'a list`

`modify_at n f l` returns the same list as `l` but with nth-value `a` replaced with `f a`.

- raises `Invalid_argument`

  if the index is outside of `l` bounds

- since 2.3.0

`val modify_opt_at : int -> ('a -> 'a option) -> 'a list -> 'a list`

`modify_opt_at n f l` returns the same list as `l` but with nth-value `a` removed if `f a` is `None`, and replaced by `v` if it is `Some v`.

- raises `Invalid_argument`

  if the index is outside of `l` bounds

- since 2.3.0

`val split_at : int -> 'a list -> 'a list * 'a list`

`split_at n l` returns two lists `l1` and `l2`, `l1` containing the first `n` elements of `l` and `l2` the others.

- raises `Invalid_argument`

  if `n` is outside of `l` size bounds.

`val split_nth : int -> 'a list -> 'a list * 'a list`

Obsolete. As `split_at`.

`val remove : 'a list -> 'a -> 'a list`

`remove l x` returns the list `l` without the first element `x` found or returns `l` if no element is equal to `x`. Elements are compared using ( = ).

`val remove_if : ('a -> bool) -> 'a list -> 'a list`

`remove_if cmp l` is similar to `remove`, but with `cmp` used instead of ( = ).

`val remove_at : int -> 'a list -> 'a list`

`remove_at i l` returns the list `l` without the element at index `i`.

- raises `Invalid_argument`

  if `i` is outside of `l` size bounds.

- since 2.3.0

`val remove_all : 'a list -> 'a -> 'a list`

`remove_all l x` is similar to `remove` but removes all elements that are equal to `x` and not only the first one.

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

`take n l` returns up to the `n` first elements from list `l`, if available.

`val ntake : int -> 'a list -> 'a list list`

`ntake n l` cuts `l` into lists of size at most `n`. `n` must be > 0.

- raises `Invalid_argument`

  if `n` <= 0. Each list in the result has size n, except the last one which may have fewer elements in case `l` was too short. Example: `ntake 2 [1; 2; 3; 4; 5] = [[1; 2]; [3; 4]; [5]]`

- since 2.2.0

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

`drop n l` returns `l` without the first `n` elements, or the empty list if `l` have less than `n` elements.

`val takedrop : int -> 'a list -> 'a list * 'a list`

`takedrop n l` is equivalent to `(take n l, drop n l)` but is done in one pass.

- since 2.2.0

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

`take_while p xs` returns the (possibly empty) longest prefix of elements of `xs` that satisfy the predicate `p`.

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

`drop_while p xs` returns the suffix remaining after `take_while p xs`.

`val span : ('a -> bool) -> 'a list -> 'a list * 'a list`

`span`, applied to a predicate `p` and a list `xs`, returns a tuple where first element is longest prefix (possibly empty) of xs of elements that satisfy p and second element is the remainder of the list. This is equivalent to `(take_while p xs, drop_while p xs)`, but is done in one pass.

- since 2.1

`val fold_while : ('acc -> 'a -> bool) -> ('acc -> 'a -> 'acc) -> 'acc -> 'a list -> 'acc * 'a list`

`fold_while p f init l`, accumulates elements `x` of list `l` using function `f`, as long as predicate `p acc x` holds. At the end, the accumulated value along with the remaining part of the list are returned.

- since 2.10.0

`val nsplit : ('a -> bool) -> 'a list -> 'a list list`

`nsplit`, applied to a predicate `p` and a list `xs`, returns a list of lists. `xs` is split when `p x` is true and `x` is excluded from the result.

If elements that satisfy `p` are consecutive, or at the beginning or end of the input list, the output list will contain empty lists marking their position. For example, `split (fun n -> n<0) [-1;2;-2;-3;4;-5]` is `[[];[2];[];[4];[]]`. This is consistent with the behavior of `String.nsplit`, where `String.nsplit ";" "1;2;;3;" = ["1";"2";"";"3";""]`.

Note that for any `xss : 'a list list` and `sep : 'a`, we always have that `flatten (interleave [sep] (nsplit ((=) sep) xss))` is `xss`.

- since 2.1

`val group_consecutive : ('a -> 'a -> bool) -> 'a list -> 'a list list`

The `group_consecutive` function takes a list and returns a list of lists such that the concatenation of the result is equal to the argument. Moreover, each sublist in the result contains only equal elements. For example, `group_consecutive (=) [3;3;4;3;3] = [[3;3];[4];[3;3]]`.

Note: In the next major version, this function is intended to replace the current `group`, which also sorts its input before grouping, and which will therefore be renamed into something more pertinent, such as `classify`, `regroup`, or `group_sort`.

- since 2.1

`val interleave : ?first:'a -> ?last:'a -> 'a -> 'a list -> 'a list`

`interleave ~first ~last sep [a0;a1;a2;...;an]` returns `first; a0; sep; a1; sep; a2; sep; ...; sep; an; last`.

## BatEnum functions

Abstraction layer.

`val enum : 'a list -> 'a BatEnum.t`

Returns an enumeration of the elements of a list. This enumeration may be used to visit elements of the list in forward order (i.e. from the first element to the last one).

`val of_enum : 'a BatEnum.t -> 'a list`

Build a list from an enumeration. In the result, elements appear in the same order as they did in the source enumeration.

`val backwards : 'a list -> 'a BatEnum.t`

Returns an enumeration of the elements of a list. This enumeration may be used to visit elements of the list in backwards order (i.e. from the last element to the first one).

`val of_backwards : 'a BatEnum.t -> 'a list`

Build a list from an enumeration. The first element of the enumeration becomes the last element of the list, the second element of the enumeration becomes the second-to-last element of the list...

## List of pairs

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

Transform a list of pairs into a pair of lists: `split [(a0,b0); (a1,b1); ...; (an,bn)]` is `([a0; a1; ...; an], [b0; b1; ...; bn])`. Tail-recursive.

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

Transform a pair of lists into a list of pairs: `combine [a0; a1; ...; an] [b0; b1; ...; bn]` is `[(a0,b0); (a1,b1); ...; (an,bn)]`.

- raises `Invalid_argument`

  if two lists have different lengths. Tail-recursive.

## Sorting

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

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, `Pervasives.compare` is a suitable comparison function. The resulting list is sorted in increasing order. `List.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`

Same as `List.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`

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

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

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).

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

`sort_uniq cmp l` returns the list `l` sorted and without any duplicate element. `cmp` is a usual comparison function providing total order.

This function takes O(n log n) time.

- since 2.3.0

`val sort_unique : ('a -> 'a -> int) -> 'a list -> 'a list`

synonym for `sort_uniq`

## Utilities

`val group : ('a -> 'a -> int) -> 'a list -> 'a list list`

`group cmp l` returns list of groups and each group consists of elements judged equal by comparison function `cmp`. Groups in the resulting list appear in order given by `cmp`. All groups are always nonempty. `group` returns `[]` only if `l` is empty.

For example `group cmp [f;c;b;e;d;a]` can give `[[a;b];[c];[d;e;f]]` if following conditions are met: `cmp a b = 0`, `cmp b c = -1`, `cmp c d = -1`, `cmp d e = 0`, ...

See the note on `group_consecutive`.

`val cartesian_product : 'a list -> 'b list -> ('a * 'b) list`

Different from `List.combine`, this returns every pair of elements formed out of the two lists. `cartesian_product [a0; a1; ...; an] [b0; b1; ...; bn] = [(a0,b0);(a0,b1); ...; (a0,bn); (a1,b0); ..; (a1, bn); ...; (an,bn)]`. The lists can be of unequal size.

`val n_cartesian_product : 'a list list -> 'a list list`

Given n lists, return the n-way cartesian product of these lists. Given `[a;b];[c];[d;e;f]`, returns `[a;c;d];[a;c;e];[a;c;f];[b;c;d];[b;c;e];[b;c;f]`, all ways of choosing one element from each input list.

`val transpose : 'a list list -> 'a list list`

Transposes a list of lists, turning rows of the input into columns of the output and vice versa.

- since 2.0.0

## Boilerplate code

### Printing

`val print : ?first:string -> ?last:string -> ?sep:string -> ('a BatInnerIO.output -> 'b -> unit) -> 'a BatInnerIO.output -> 'b list -> unit`

Print the contents of a list

`val eq : 'a BatOrd.eq -> 'a list BatOrd.eq`
`val ord : 'a BatOrd.ord -> 'a list BatOrd.ord`
`val compare : 'a BatOrd.comp -> 'a list BatOrd.comp`

Comparison and equality for lists based on element comparison and equality

`module Eq (T : BatOrd.Eq) : BatOrd.Eq with type t = T.t list`
`module Ord (T : BatOrd.Ord) : BatOrd.Ord with type t = T.t list`
`module Comp (T : BatOrd.Comp) : BatOrd.Comp with type t = T.t list`

## Obsolete functions

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

Obsolete. As `at`.

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

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. Raise `Invalid_argument "List.nth"` if `n` is negative.

- since 2.7.0

`val takewhile : ('a -> bool) -> 'a list -> 'a list`

obsolete, as `take_while`

`val dropwhile : ('a -> bool) -> 'a list -> 'a list`

obsolete, as `drop_while`

## Override modules

The following modules replace functions defined in `List` with functions behaving slightly differently but having the same name. This is by design: the functions are meant to override the corresponding functions of `List`.

`module Exceptionless : sig ... end`

Exceptionless counterparts for error-raising operations

`module Infix : sig ... end`
`module Labels : sig ... end`

Operations on `List` with labels.

`val (@) : 'a list -> 'a list -> 'a list`

Tail recursive `List.append`.

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