# Module Batteries.List

    module List: BatList

List operations.

    type 'a t = 'a list

The type of lists

    include BatEnum.Enumerable

    include BatInterfaces.Mappable

###### 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 first : 'a list -> 'a

Returns the first element of the list, or
Raises `Empty_list` if the list is empty (similar to `hd`).

    val hd : 'a list -> 'a

Similar to `first`, but
Raises `Failure` if the list is empty.

    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, or
Raises `Empty_list` 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 at : 'a list -> int -> 'a

`at l n` returns the n-th element of the list `l` or
Raises `Invalid_argument` is the index is outside of `l` bounds. O(l)

    val rev : 'a list -> 'a list

List reversal.

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

Catenate two lists. Same function as the infix operator `@`. Tail-recursive O(length of the first argument).

    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 (length of the argument + length of the longest sub-list).

    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 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

###### Iterators

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

`List.iter f [a1; ...; an]` applies function `f` in turn to `a1; ...; an`. It is equivalent to `begin f a1; f a2; ...; 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 [b1; ...; bn]` is `f (... (f (f a b1) b2) ...) bn`.

    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 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 max : 'a list -> 'a

`max l` returns the largest value in `l` as judged by `Pervasives.compare`

    val min : 'a list -> 'a

`min l` returns the smallest value in `l` as judged by `Pervasives.compare`

    val sum : int list -> int

`sum l` returns the sum of the integers of `l`
Raises `Invalid_argument` on the empty list.

    val fsum : float list -> float

`fsum l` returns the sum of the floats of `l`
Raises `Invalid_argument` on the empty list.

    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.
Since 2.1
Raises `Invalid_argument` on an empty list.

###### 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 `Different_list_size` if the 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 `Different_list_size` if the 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 `Different_list_size` if the 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 `Different_list_size` if the 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 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 [a1; ...; an]` checks if all elements of the list satisfy the predicate `p`. That is, it returns `(p a1) && (p a2) && ... && (p an)`.

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

`exists p [a1; ...; an]` checks if at least one element of the list satisfies the predicate `p`. That is, it returns `(p a1) || (p a2) || ... || (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 the 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 the two lists have different lengths.

###### 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_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 e l` returns the first element `ai` of `l` along with its index `i` such that `p i ai` is true, or
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 or
Raises `Not_found` if no element matches the predicate. See also `BatList.filter_map`.

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

`rfind p l` returns the last element `x` of `l` such as `p x` returns `true` or
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 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 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 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.
Since 2.0
See also `sort_unique` to save time in cases when reordering the list is acceptable

    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_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_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 associated to key `a` replaced with `f a`.
Since 2.1
Raises `Not_found` if no value is associated with `a` in `l`

    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 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_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 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 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 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 `Different_list_size` if the 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 containting 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_unique : ('a -> 'a -> int) -> 'a list -> 'a list

`sort_unique 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.

###### 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: functor (T : BatOrd.Eq) -> Eq  with type t = T.t list

    module Ord: functor (T : BatOrd.Ord) -> Ord  with type t = T.t list

    module Comp: functor (T : BatOrd.Comp) -> Comp  with type t = T.t list

###### Obsolete functions

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

Obsolete. As `at`.

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

obsolete, as `BatList.take_while`

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

obsolete, as `BatList.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 meant to override the corresponding functions of `List`.

    module Exceptionless: sig .. end

Exceptionless counterparts for error-raising operations

    module Infix: sig .. end

Infix submodule regrouping all infix operators

    module Labels: sig .. end

Operations on `List` with labels.

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

Tail recursive `List.append`.