# Module BatList

    module BatList: sig .. end

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.

    type 'a t = 'a list

List operations.

The type of lists
Author(s): Xavier Leroy (base module), Brian Hurt, Nicolas Cannasse, Richard W.M. Jones, David Teller

    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 raise `Empty_list` if the list is empty (similar to `hd`).

    val last : 'a list -> 'a

Returns the last element of the list, or raise `Empty_list` if the list is empty. This function takes linear time.

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

`at l n` returns the n-th element of the list `l` or raise `Invalid_index` is the index is outside of `l` bounds.

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

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

    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`.

###### 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)). Raise `Invalid_arg "BatList.init"` if n < 0.

###### Iterators

    val iteri : (int -> 'a -> 'b) -> '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 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_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 `Empty_list` on empty lists.

    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 elements of `l`

    val fsum : float list -> float

`sum l` returns the sum of the elements of `l`

###### 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 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 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_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 : ?cmp:('a -> 'a -> bool) -> 'a list -> 'a list

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

This function takes O(n²) time.
See also `sort_unique` to save time in cases when reordering the list is acceptable

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

As `unique` except comparator label is ~eq.
Since 1.3.0

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

As `unique`, except comparator parameter returns an int
Since 1.3.0

###### Association lists

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

`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`. Raise `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 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.

###### 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. Raise `Invalid_index` 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

`takewhile f xs` returns the first elements of list `xs` which satisfy the predicate `f`.

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

`dropwhile f xs` returns the list `xs` with the first elements satisfying the predicate `f` dropped.

    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`

###### 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.

###### Utilities

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

`make_compare c` generates the lexicographical order on lists induced by `c`

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

Sort the list using optional comparator (by default `compare`).

    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 linear order.

This function takes O(n log n) time.

    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`,...

    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.

###### 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 sprint : ?first:string ->
           ?last:string ->
           ?sep:string -> ('a BatInnerIO.output -> 'b -> unit) -> 'b list -> string

Deprecated.use `BatIO.to_string`.
Using a string printer, print a list to a string (as sprintf vs. printf)

    val t_printer : 'a BatValue_printer.t -> 'a t BatValue_printer.t

###### 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

the new implementation for ( @ ) operator, see `List.append`.