# Module Batteries.Seq

    module Seq: BatSeq

A sequence represent a collection of elements, for which you never construct the complete representation.

Basically you should use a sequence when you would prefer using a list or a lazy-list but constructing the whole list explicitly would explode your memory.

All functions returning a sequence operates in time and space O(1).

Note that if you want a ``consumable sequence'', you should prefer using enumerations (from module `BatEnum`).

    type 'a t = unit -> 'a node

A sequence is a computation which returns a list-like node

    type 'a node =

`|` | `Nil`
`|` | `Cons of `'a * 'a t``

    include BatInterfaces.Mappable

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

`enum s` returns the enumeration of all element of `s`.

Since enumerations are consumable and sequence are not, it is not possible to have the inverse operations, i.e. `of_enum`

###### Base operations

    val length : 'a t -> int

Return the number of elements of the given sequence. This may never return if the sequence is infinite.

    val hd : 'a t -> 'a

Returns the first element of the sequence or raise `Invalid_argument` if the sequence is empty.

    val tl : 'a t -> 'a t

Returns the sequence without its first elements or raise `Invalid_argument` if the sequence is empty.

    val is_empty : 'a t -> bool

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

    val first : 'a t -> 'a

Same as `BatSeq.hd`

    val last : 'a t -> 'a

Returns the last element of the sequence, or raise `Invalid_argument` if the sequence is empty.

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

`at l n` returns the element at index `n` (starting from `0`) in the sequence `l` or raise `Invalid_argument` is the index is outside of `l` bounds.

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

`append s1 s2` returns the sequence which first returns all elements of `s1` then all elements of `s2`.

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

`concat s` returns the sequence which returns all the elements of all the elements of `s`, in the same order.

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

Same as `BatSeq.concat`.

###### Constructors

    val nil : 'a t

`nil = fun () -> Nil`

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

`cons e s = fun () -> Cons(e, s)`

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

`make n e` returns the sequence of length `n` where all elements are `e`

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

`init n f` returns the sequence returning the results of `f 0`, `f 1`.... `f (n-1)`.
Raises `Invalid_argument` if `n < 0`.

###### Iterators

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

`iter f s` applies `f` to all the elements of the sequence. Eager.

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

`map f s` returns the sequence where elements are elements of `s` mapped with `f`. Lazy.

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

`fold_left f a (cons b0 (... bn))` is `f (... (f (f a b0) b1) ...) bn`. Tail-recursive, eager.

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

`fold_right f (cons a0 (cons a1 (cons a2 ...))) b` is `f a0 (f a1 (f a2 ...))`. Not tail-recursive, eager.

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

`reduce f (cons e s)` is `fold_left f e s`.
Raises `Invalid_argument` on empty sequences.

    val max : 'a t -> 'a

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

    val min : 'a t -> 'a

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

###### Sequence scanning

Most functions in the following sections have a shortcut semantic similar to the behavior of the usual (&&) and (||) operators : they will force the sequence until they find an satisfying element, and then return immediately.

For example, `for_all` will only diverge if the sequence begins with an infinite number of true elements --- elements for which the predicate `p` returns `true`.

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

`for_all p (cons a0 (cons a1 ...))` checks if all elements of the given sequence satisfy the predicate `p`. That is, it returns `(p a0) && (p a1) && ...`. Eager, shortcut.

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

`exists p (cons a0 (cons a1 ...))` checks if at least one element of the sequence satisfies the predicate `p`. That is, it returns `(p a0) || (p a1) || ...`. Eager, shortcut.

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

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

###### Sequence searching

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

`find p s` returns the first element of `s` such as `p e` returns `true`, if any. Eager, shortcut.

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

`find_map p s` finds the first element of `s` for which `p e` returns `Some r`, if any. Eager, short-cut.

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

`filter p s` returns the sequence of elements of `s` satisfying `p`. Lazy.

Note filter is lazy in that it returns a lazy sequence, but each element in the result is eagerly searched in the input sequence. Therefore, the access to a given element in the result will diverge if it is preceded, in the input sequence, by infinitely many false elements (elements on which the predicate `p` returns `false`).

Other functions that may drop an unbound number of elements (`filter_map`, `take_while`, etc.) have the same behavior.

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

`filter_map f s` returns the sequence of elements filtered and mapped by `f`. Lazy.

###### Association sequences

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

`assoc a s` returns the value associated with key `a` in the sequence of pairs `s`. Eager, shortcut.

###### Sequence transformations

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

`take n s` returns up to the `n` first elements from sequence `s`, if available. Lazy.

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

`drop n s` returns `s` without the first `n` elements, or the empty sequence if `s` have less than `n` elements. Lazy.

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

`take_while f s` returns the first elements of sequence `s` which satisfy the predicate `f`. Lazy.

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

`drop_while f s` returns the sequence `s` with the first elements satisfying the predicate `f` dropped. Lazy.

###### Sequence of pairs

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

`split s = (map fst s, map snd s)`. Lazy.

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

Transform a pair of sequences into a sequence of pairs. Lazy.
Raises `Invalid_argument` if given sequences of different length.

###### Printing

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

Print the contents of a sequence

    module Infix: sig .. end

    include BatSeq.Infix

    module Exceptionless: sig .. end