# Module BatLazyList

    module BatLazyList: sig .. end

Lazy lists of elements.

Lazy lists are similar to lists, with the exception that their contents are only computed whenever requested. This makes them particularly useful in contexts where streams of data are to be handled.

Note For this documentation, we will assume the existence of a lazy list syntax extension such that `[^ ^]` is the empty lazy list and `[^ a;b;c ^]` is the lazy list containing elements `a`, `b`, `c`.

Note Enumerations (as featured in module `BatEnum`) and lazy lists (as featured in this module) are quite similar in purpose. Lazy lists are slightly higher level, insofar as no cloning is required to get them to work, which makes them slightly more useful in contexts where backtracking is common. Enumerations, on the other hand, are closer to traditional stream processing, and require more low-level marking whenever backtracking is required, but may be faster and more memory-efficient when used properly. Either choice is recommended over OCaml's built-in `Stream`.
Author(s): David Teller

###### Exceptions

    exception Empty_list

`Empty_list` is raised when an operation applied on an empty list is invalid. For instance, `hd nil` will raise `Empty_list`.

    exception Invalid_index of int

`Invalid_index` is raised when an indexed access on a list is out of list bounds.

    exception Different_list_size of string

`Different_list_size` is raised when applying functions such as `iter2` on two lists having different size.

    exception No_more_elements

See `BatLazyList.from` and `BatLazyList.from_loop` for more information on this exception.

###### Type

Note The types are kept concrete so as to allow pattern-matching. However, it is generally easier to manipulate `BatLazyList.nil` and `BatLazyList.cons`.

    type 'a t = 'a node_t Lazy.t

The type of a lazy list.

    type 'a node_t =

`|` | `Nil`
`|` | `Cons of `'a * 'a t`` | `(*` | The type of an item in the list. | `*)`

    include BatEnum.Enumerable

    include BatInterfaces.Mappable

###### Access

    val nil : 'a t

The empty list.

    val cons : 'a -> 'a t -> 'a t

Build a list from a head and a tail.

    val (^:^) : 'a -> 'a t -> 'a t

As `cons`: `x^:^l` is the lazy list with head `x` and tail `l`

    val peek : 'a t -> 'a option

`peek l` returns the first element of `l`, if it exists.

    val get : 'a t -> ('a * 'a t) option

`get l` returns the head and tail of `l`, if `l` is not empty.

###### List creation

    val from : (unit -> 'a) -> 'a t

`from next` creates a (possibly infinite) lazy list from the successive results of `next`.
Raises `LazyList.No_more_elements` to denote the end of the list.

    val from_while : (unit -> 'a option) -> 'a t

`from next` creates a (possibly infinite) lazy list from the successive results of `next`. The list ends whenever `next` returns `None`.

    val from_loop : 'b -> ('b -> 'a * 'b) -> 'a t

`from_loop data next` creates a (possibly infinite) lazy list from the successive results of applying `next` to `data`, then to the result, etc. The list ends whenever the function raises `LazyList.No_more_elements`.

    val seq : 'a -> ('a -> 'a) -> ('a -> bool) -> 'a t

`seq init step cond` creates a sequence of data, which starts from `init`, extends by `step`, until the condition `cond` fails. E.g. `seq 1 ((+) 1) ((>) 100)` returns `[^1, 2, ... 99^]`. If `cond init` is false, the result is empty.

    val unfold : 'b -> ('b -> ('a * 'b) option) -> 'a t

`unfold data next` creates a (possibly infinite) lazy list from the successive results of applying `next` to `data`, then to the result, etc. The list ends whenever the function returns `None`

    val init : int -> (int -> 'a) -> 'a t

Similar to `Array.init`, `init n f` returns the lazy list containing the results of (f 0),(f 1).... (f (n-1)).
Raises `Invalid_argument` `"LazyList.init"` if n < 0.

    val make : int -> 'a -> 'a t

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

    val range : int -> int -> int t

Compute lazily a range of integers a .. b as a lazy list.

The range is empty if a <= b.

###### Higher-order functions

    val iter : ('a -> 'b) -> 'a t -> unit

Eager iteration

`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`. In particular, it causes all the elements of the list to be evaluated.

    val iteri : (int -> 'a -> unit) -> 'a t -> unit

Eager iteration, with indices

`iteri f [^ a0; a1; ...; an ^]` applies function `f` in turn to `a0; a1;...; an`, along with the corresponding `0,1..n` index. It is equivalent to `begin f 0 a0; f 1 a1; ...; f n an; () end`. In particular, it causes all the elements of the list to be evaluated.

    val map : ('a -> 'b) -> 'a t -> 'b t

Lazy map

`map f [^ a0; a1; ... ^]` builds the list `[^ f a0; f a1; ... ^]` with the results returned by `f`. Not tail-recursive. Evaluations of `f` take place only when the contents of the list are forced.

    val mapi : (int -> 'a -> 'b) -> 'a t -> 'b t

Lazy map, with indices

`mapi f [^ a0; a1; ... ^]` builds the list `[^ f 0 a0; f 1 a1; ... ^]` with the results returned by `f`. Not tail-recursive. Evaluations of `f` take place only when the contents of the list are forced.

    val fold_left : ('a -> 'b -> 'a) -> 'a -> 'b t -> 'a

Eager fold_left

`LazyList.fold_left f a [^ b0; b1; ...; bn ^]` is `f (... (f (f a b0) b1) ...) bn`. This causes evaluation of all the elements of the list.

    val fold_right : ('a -> 'b -> 'b) -> 'b -> 'a t -> 'b

Eager fold_right

`fold_right f b [^ a0; a1; ...; an ^]` is `f a0 (f a1 (... (f an b) ...))`. This causes evaluation of all the elements of the list. Not tail-recursive.

Note that the argument order of this function is the same as `fold_left` above, but inconsistent with other `fold_right` functions in Batteries. We hope to fix this inconsistency in the next compatibility-breaking release, so you should rather use the more consistent `eager_fold_right`.
Since 2.2.0

    val eager_fold_right : ('a -> 'b -> 'b) -> 'a t -> 'b -> 'b

Eager fold_right

As `fold_right` above, but with the usual argument order for a fold_right.

Just as `fold_left` on a structure `'a t` turns an element-level function of type `('b -> 'a -> 'b)`, with the accumulator argument `'b` on the left, into a structure-level function `'b -> 'a t -> 'b`, `fold_right` turns a function `('a -> 'b -> 'b)` (accumulator on the right) into a `'a t -> 'b -> 'b`.

    val lazy_fold_right : ('a -> 'b Lazy.t -> 'b) -> 'a t -> 'b Lazy.t -> 'b Lazy.t

Lazy fold_right `lazy_fold_right f (Cons (a0, Cons (a1, Cons (a2, nil)))) b` is `lazy (f a0 (lazy (f a1 (lazy (f a2 b)))))`.

Forcing the result of `lazy_fold_right` forces the first element of the list; the rest is forced only if/when the function `f` forces its accumulator argument.
Since 2.1

###### Finding

    val mem : 'a -> 'a t -> bool

`mem x l` determines if `x` is part of `l`. Evaluates all the elements of `l` which appear before `x`.

    val memq : 'a -> 'a t -> bool

As `mem`, but with physical equality

    val find : ('a -> bool) -> 'a t -> 'a

`find p l` returns the first element of `l` such as `p x` returns `true`.
Raises `Not_found` if such an element has not been found.

    val rfind : ('a -> bool) -> 'a t -> '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 find_exn : ('a -> bool) -> exn -> 'a t -> '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 rfind_exn : ('a -> bool) -> exn -> 'a t -> 'a

`find_exn p e l` returns the last 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 t -> 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.
Raises `Not_found` if no such element has been found.

    val rfindi : (int -> 'a -> bool) -> 'a t -> int * 'a

`findi p e l` returns the last 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 index_of : 'a -> 'a t -> 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 t -> int option

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

    val rindex_of : 'a -> 'a t -> int option

`index_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 t -> int option

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

###### Common functions

    val next : 'a t -> 'a node_t

Compute and return the next value of the list

    val length : 'a t -> int

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

Causes the evaluation of all the elements of the list.

    val is_empty : 'a t -> bool

Returns `true` if the list is empty, false otherwise.

    val would_at_fail : 'a t -> int -> bool

`would_at_fail l n` returns `true` if `l` contains strictly less than `n` elements, `false` otherwise

    val hd : 'a t -> 'a

Return the first element of the given list.
Raises `Empty_list` if the list is empty.

Note: this function does not comply with the usual exceptionless error-management recommendations, as doing so would essentially render it useless.

    val tl : 'a t -> 'a t

Return the given list without its first element.
Raises `Empty_list` if the list is empty.

Note: this function does not comply with the usual exceptionless error-management recommendations, as doing so would essentially render it useless.

    val first : 'a t -> 'a

As `hd`

    val last : 'a t -> 'a

Returns the last element of the list.
Raises `Empty_list` if the list is empty. This function takes linear time and causes the evaluation of all elements of the list

    val at : 'a t -> int -> 'a

`at l n` returns the element at index `n` (starting from `0`) in the list `l`.
Raises `Invalid_index` is the index is outside of `l` bounds.

    val nth : 'a t -> int -> 'a

Obsolete. As `at`

###### Association lists

These lists behave essentially as `HashMap`, although they are typically faster for short number of associations, and much slower for for large number of associations.

    val assoc : 'a -> ('a * 'b) t -> '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 assq : 'a -> ('a * 'b) t -> 'b

As `BatLazyList.assoc` but with physical equality

    val mem_assoc : 'a -> ('a * 'b) t -> bool

As `BatLazyList.assoc` but simply returns `true` if a binding exists, `false` otherwise.

    val mem_assq : 'a -> ('a * 'b) t -> bool

As `BatLazyList.mem_assoc` but with physical equality.

    val rev : 'a t -> 'a t

Eager list reversal.

###### Transformations

    val eager_append : 'a t -> 'a t -> 'a t

Evaluate a list and append another list after this one.

Cost is linear in the length of the first list, not tail-recursive.

    val rev_append : 'a t -> 'a t -> 'a t

Eager reverse-and-append

Cost is linear in the length of the first list, tail-recursive.

    val append : 'a t -> 'a t -> 'a t

Lazy append

Cost is constant. All evaluation is delayed until the contents of the list are actually read. Reading itself is delayed by a constant.

    val (^@^) : 'a t -> 'a t -> 'a t

As lazy append

    val concat : 'a t t -> 'a t

Lazy concatenation of a lazy list of lazy lists

    val flatten : 'a t list -> 'a t

Lazy concatenation of a list of lazy lists

    val split_at : int -> 'a t -> 'a t * 'a t

`split_at n l` returns two lists `l1` and `l2`, `l1` containing the first `n` elements of `l` and `l2` the others.
Raises `Invalid_index` if `n` is outside of `l` size bounds.

    val split_nth : int -> 'a t -> 'a t * 'a t

Obsolete. As `split_at`.

###### Dropping elements

    val unique : ?cmp:('a -> 'a -> int) -> 'a t -> 'a t

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

    val unique_eq : ?eq:('a -> 'a -> bool) -> 'a t -> 'a t

as `unique` except only uses an equality function. Use for short lists when comparing is expensive compared to equality testing
Since 1.3.0

    val remove : 'a -> 'a t -> 'a t

`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 t -> 'a t

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

    val remove_all : 'a -> 'a t -> 'a t

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

    val remove_all_such : ('a -> bool) -> 'a t -> 'a t

`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 t -> 'a t

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

    val drop : int -> 'a t -> 'a t

`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 t -> 'a t

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

    val drop_while : ('a -> bool) -> 'a t -> 'a t

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

###### Conversions

    val to_list : 'a t -> 'a list

Eager conversion to string.

    val to_stream : 'a t -> 'a Stream.t

Lazy conversion to stream.

    val to_array : 'a t -> 'a array

Eager conversion to array.

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

Lazy conversion to enumeration

    val of_list : 'a list -> 'a t

Lazy conversion from lists

Albeit slower than eager conversion, this is the default mechanism for converting from regular lists to lazy lists. This for two reasons : * if you're using lazy lists, total speed probably isn't as much an issue as start-up speed * this will let you convert regular infinite lists to lazy lists.

    val of_stream : 'a Stream.t -> 'a t

Lazy conversion from stream.

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

Lazy conversion from enum.

    val eager_of_list : 'a list -> 'a t

Eager conversion from lists.

This function is much faster than `BatLazyList.of_list` but will freeze on cyclic lists.

    val of_array : 'a array -> 'a t

Eager conversion from array

###### Predicates

    val filter : ('a -> bool) -> 'a t -> 'a t

Lazy filtering.

`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 exists : ('a -> bool) -> 'a t -> bool

Eager existential.

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

    val for_all : ('a -> bool) -> 'a t -> bool

Eager universal.

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

    val filter_map : ('a -> 'b option) -> 'a t -> 'b t

Lazily eliminate some elements and transform others.

`filter_map f [^ a0; a1; ... ^]` applies lazily `f` to each `a0`, `a1`... If `f ai` evaluates to `None`, the element is not included in the result. Otherwise, if `f ai` evaluates to `Some x`, element `x` is included in the result.

This is equivalent to `match f a0 with | Some x0 -> x0 ^:^ (match f a1 with | Some x1 -> x1 ^:^ ... | None -> [^ ^]) | None -> [^ ^]` .

###### Misc.

    val eternity : unit t

An infinite list of nothing

###### Sorting

    val sort : ?cmp:('a -> 'a -> int) -> 'a t -> 'a t

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

    val stable_sort : ('a -> 'a -> int) -> 'a t -> 'a t

###### Operations on two lists

    val map2 : ('a -> 'b -> 'c) -> 'a t -> 'b t -> 'c t

`map2 f [^ a0; a1; ...^] [^ b0; b1; ... ^]` is `[^ f a0 b0; f a1 b1; ... ^]`.
Raises `Different_list_size` if the two lists have different lengths. Not tail-recursive, lazy. In particular, the exception is raised only after the shortest list has been entirely consumed.

    val iter2 : ('a -> 'b -> unit) -> 'a t -> 'b t -> unit

`iter2 f [^ a0; ...; an ^] [^ b0; ...; bn ^]` calls in turn `f a0 b0; ...; f an bn`. Tail-recursive, eager.
Raises `Different_list_size` if the two lists have different lengths.

    val fold_left2 : ('a -> 'b -> 'c -> 'a) -> 'a -> 'b t -> 'c t -> 'a

`fold_left2 f a [^ b0; b1; ...; bn ^] [^ c0; c1; ...; cn ^]` is `f (... (f (f a b0 c0) b1 c1) ...) bn cn`. Eager.
Raises `Different_list_size` if the two lists have different lengths.

    val fold_right2 : ('a -> 'b -> 'c -> 'c) -> 'a t -> 'b t -> 'c -> 'c

`fold_right2 f [^ a0; a1; ...; an ^] [^ b0; b1; ...; bn ^] c` is `f a0 b0 (f a1 b1 (... (f an bn c) ...))`. Eager.
Raises `Different_list_size` if the two lists have different lengths. Tail-recursive.

    val for_all2 : ('a -> 'b -> bool) -> 'a t -> 'b t -> bool

Same as `BatLazyList.for_all`, but for a two-argument predicate.
Raises `Different_list_size` if the two lists have different lengths.

    val exists2 : ('a -> 'b -> bool) -> 'a t -> 'b t -> bool

Same as `BatLazyList.exists`, but for a two-argument predicate.
Raises `Different_list_size` if the two lists have different lengths.

    val combine : 'a t -> 'b t -> ('a * 'b) t

Transform a pair of lists into a list of pairs: `combine [^ a0; a1; ... ^] [^ b0; b1; ... ^]` is `[^ (a0, b0); (a1, b1); ... ^]`.
Raises `Different_list_size` if the two lists have different lengths. Tail-recursive, lazy.

    val uncombine : ('a * 'b) t -> 'a t * 'b t

Divide a list of pairs into a pair of lists.

    module Infix: sig .. end

Infix submodule regrouping all infix operators

###### Boilerplate code

Printing

    val print : ?first:string ->
           ?last:string ->
           ?sep:string ->
           ('a BatInnerIO.output -> 'b -> unit) ->
           'a BatInnerIO.output -> 'b t -> unit

###### Override modules

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

    module Exceptionless: sig .. end

Exceptionless counterparts for error-raising operations

    module Labels: sig .. end

Operations on `LazyList` with labels.