package batteries

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package batteries
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Sequence of elements

A sequence represents 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).

  • author Jeremie Dimino
type 'a t = 'a Seq.t

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

and 'a node = 'a Seq.node =
  1. | Nil
  2. | Cons of 'a * 'a t
include BatInterfaces.Mappable with type 'a mappable = 'a t
type 'a mappable = 'a t

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

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 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 first : 'a t -> 'a

Same as 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 concat.

Constructors
val nil : 'a t

nil = fun () -> Nil

val empty : 'a t

the empty sequence, containing no elements

  • since 3.3.0
val return : 'a -> 'a t

the singleton sequence, containing only the given element

  • since 3.3.0
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 of_list : 'a list -> 'a t

Convenience function to build a seq from a list.

  • since 2.2.0
val unfold : ('b -> ('a * 'b) option) -> 'b -> 'a t

Build a sequence from a step function and an initial value. unfold f u returns empty if f u returns None, or fun () -> Cons (x, unfold f y) if f u returns Some (x, y).

For example, unfold (function [] -> None | h::t -> Some (h,t)) l is equivalent to List.to_seq l.

  • since 3.3.0
val flat_map : ('a -> 'b t) -> 'a t -> 'b t

Map each element to a subsequence, then return each element of this sub-sequence in turn. This transformation is lazy, it only applies when the result is traversed.

  • since 3.3.0
val concat_map : ('a -> 'b t) -> 'a t -> 'b t

Alias for flat_map.

  • since 3.4.0
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.

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

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

equal ~eq s1 s2 compares elements of s1 and s2 pairwise using eq

  • since 2.2.0
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 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 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
Sequence of pairs
val combine : 'a t -> 'b t -> ('a * 'b) t

Transform a pair of sequences into a sequence of pairs. Lazy.

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

val to_buffer : ?first:string -> ?last:string -> ?sep:string -> ('a -> string) -> Buffer.t -> (unit -> 'a node) -> unit

Convert a sequence to a string in the given buffer; eager.

  • since 2.10.0
val to_string : ?first:string -> ?last:string -> ?sep:string -> ('a -> string) -> 'a t -> string

Convert the sequence to a string; eager.

  • since 2.10.0
val of_string : ?first:string -> ?last:string -> ?sep:string -> (string -> 'a) -> string -> 'a t

Create a sequence by parsing a string.

  • since 2.10.0
module Infix : sig ... end

Infix operators matching those provided by BatEnum.Infix

include module type of Infix
val (--) : int -> int -> int t
val (--^) : int -> int -> int t
val (--.) : (float * float) -> float -> float t
val (---) : int -> int -> int t
val (--~) : char -> char -> char t
val (//) : 'a t -> ('a -> bool) -> 'a t
val (/@) : 'a t -> ('a -> 'b) -> 'b t
val (@/) : ('a -> 'b) -> 'a t -> 'b t
val (//@) : 'a t -> ('a -> 'b option) -> 'b t
val (@//) : ('a -> 'b option) -> 'a t -> 'b t
module Exceptionless : sig ... end
val is_empty : 'a t -> bool

is_empty xs determines whether the sequence xs is empty.

It is recommended that the sequence xs be persistent. Indeed, is_empty xs demands the head of the sequence xs, so, if xs is ephemeral, it may be the case that xs cannot be used any more after this call has taken place.

  • since 4.14
val uncons : 'a t -> ('a * 'a t) option

If xs is empty, then uncons xs is None.

If xs is nonempty, then uncons xs is Some (head xs, tail xs), that is, a pair of the head and tail of the sequence xs.

This equivalence holds if xs is persistent. If xs is ephemeral, then uncons must be preferred over separate calls to head and tail, which would cause xs to be queried twice.

  • since 4.14
val length : 'a t -> int

length xs is the length of the sequence xs.

The sequence xs must be finite.

  • since 4.14
val iteri : (int -> 'a -> unit) -> 'a t -> unit

iteri f xs invokes f i x successively for every element x located at index i in the sequence xs.

It terminates only if the sequence xs is finite.

iteri f xs is equivalent to iter (fun (i, x) -> f i x) (zip (ints 0) xs).

  • since 4.14
val fold_lefti : ('b -> int -> 'a -> 'b) -> 'b -> 'a t -> 'b

fold_lefti f _ xs invokes f _ i x successively for every element x located at index i of the sequence xs.

An accumulator of type 'b is threaded through the calls to f.

It terminates only if the sequence xs is finite.

fold_lefti f accu xs is equivalent to fold_left (fun accu (i, x) -> f accu i x) accu (zip (ints 0) xs).

  • since 4.14
val for_all : ('a -> bool) -> 'a t -> bool

for_all p xs determines whether all elements x of the sequence xs satisfy p x.

The sequence xs must be finite.

  • since 4.14
val exists : ('a -> bool) -> 'a t -> bool

exists xs p determines whether at least one element x of the sequence xs satisfies p x.

The sequence xs must be finite.

  • since 4.14
val find : ('a -> bool) -> 'a t -> 'a option

find p xs returns Some x, where x is the first element of the sequence xs that satisfies p x, if there is such an element.

It returns None if there is no such element.

The sequence xs must be finite.

  • since 4.14
val find_map : ('a -> 'b option) -> 'a t -> 'b option

find_map f xs returns Some y, where x is the first element of the sequence xs such that f x = Some _, if there is such an element, and where y is defined by f x = Some y.

It returns None if there is no such element.

The sequence xs must be finite.

  • since 4.14
val iter2 : ('a -> 'b -> unit) -> 'a t -> 'b t -> unit

iter2 f xs ys invokes f x y successively for every pair (x, y) of elements drawn synchronously from the sequences xs and ys.

If the sequences xs and ys have different lengths, then iteration stops as soon as one sequence is exhausted; the excess elements in the other sequence are ignored.

Iteration terminates only if at least one of the sequences xs and ys is finite.

iter2 f xs ys is equivalent to iter (fun (x, y) -> f x y) (zip xs ys).

  • since 4.14
val fold_left2 : ('a -> 'b -> 'c -> 'a) -> 'a -> 'b t -> 'c t -> 'a

fold_left2 f _ xs ys invokes f _ x y successively for every pair (x, y) of elements drawn synchronously from the sequences xs and ys.

An accumulator of type 'a is threaded through the calls to f.

If the sequences xs and ys have different lengths, then iteration stops as soon as one sequence is exhausted; the excess elements in the other sequence are ignored.

Iteration terminates only if at least one of the sequences xs and ys is finite.

fold_left2 f accu xs ys is equivalent to fold_left (fun accu (x, y) -> f accu x y) (zip xs ys).

  • since 4.14
val for_all2 : ('a -> 'b -> bool) -> 'a t -> 'b t -> bool

for_all2 p xs ys determines whether all pairs (x, y) of elements drawn synchronously from the sequences xs and ys satisfy p x y.

If the sequences xs and ys have different lengths, then iteration stops as soon as one sequence is exhausted; the excess elements in the other sequence are ignored. In particular, if xs or ys is empty, then for_all2 p xs ys is true. This is where for_all2 and equal differ: equal eq xs ys can be true only if xs and ys have the same length.

At least one of the sequences xs and ys must be finite.

for_all2 p xs ys is equivalent to for_all (fun b -> b) (map2 p xs ys).

  • since 4.14
val exists2 : ('a -> 'b -> bool) -> 'a t -> 'b t -> bool

exists2 p xs ys determines whether some pair (x, y) of elements drawn synchronously from the sequences xs and ys satisfies p x y.

If the sequences xs and ys have different lengths, then iteration must stop as soon as one sequence is exhausted; the excess elements in the other sequence are ignored.

At least one of the sequences xs and ys must be finite.

exists2 p xs ys is equivalent to exists (fun b -> b) (map2 p xs ys).

  • since 4.14
val equal_stdlib : ('a -> 'b -> bool) -> 'a t -> 'b t -> bool

Provided the function eq defines an equality on elements, equal eq xs ys determines whether the sequences xs and ys are pointwise equal.

At least one of the sequences xs and ys must be finite.

  • since 4.14
val compare : ('a -> 'b -> int) -> 'a t -> 'b t -> int

Provided the function cmp defines a preorder on elements, compare cmp xs ys compares the sequences xs and ys according to the lexicographic preorder.

For more details on comparison functions, see Array.sort.

At least one of the sequences xs and ys must be finite.

  • since 4.14
val init : int -> (int -> 'a) -> 'a t

init n f is the sequence f 0; f 1; ...; f (n-1).

n must be nonnegative.

If desired, the infinite sequence f 0; f 1; ... can be defined as map f (ints 0).

  • since 4.14
val repeat : 'a -> 'a t

repeat x is the infinite sequence where the element x is repeated indefinitely.

repeat x is equivalent to cycle (return x).

  • since 4.14
val forever : (unit -> 'a) -> 'a t

forever f is an infinite sequence where every element is produced (on demand) by the function call f().

For instance, forever Random.bool is an infinite sequence of random bits.

forever f is equivalent to map f (repeat ()).

  • since 4.14
val cycle : 'a t -> 'a t

cycle xs is the infinite sequence that consists of an infinite number of repetitions of the sequence xs.

If xs is an empty sequence, then cycle xs is empty as well.

Consuming (a prefix of) the sequence cycle xs once can cause the sequence xs to be consumed more than once. Therefore, xs must be persistent.

  • since 4.14
val iterate : ('a -> 'a) -> 'a -> 'a t

iterate f x is the infinite sequence whose elements are x, f x, f (f x), and so on.

In other words, it is the orbit of the function f, starting at x.

  • since 4.14
val mapi : (int -> 'a -> 'b) -> 'a t -> 'b t

mapi is analogous to map, but applies the function f to an index and an element.

mapi f xs is equivalent to map2 f (ints 0) xs.

  • since 4.14
val scan : ('b -> 'a -> 'b) -> 'b -> 'a t -> 'b t

If xs is a sequence [x0; x1; x2; ...], then scan f a0 xs is a sequence of accumulators [a0; a1; a2; ...] where a1 is f a0 x0, a2 is f a1 x1, and so on.

Thus, scan f a0 xs is conceptually related to fold_left f a0 xs. However, instead of performing an eager iteration and immediately returning the final accumulator, it returns a sequence of accumulators.

For instance, scan (+) 0 transforms a sequence of integers into the sequence of its partial sums.

If xs has length n then scan f a0 xs has length n+1.

  • since 4.14
val take : int -> 'a t -> 'a t

take n xs is the sequence of the first n elements of xs.

If xs has fewer than n elements, then take n xs is equivalent to xs.

n must be nonnegative.

  • since 4.14
val drop : int -> 'a t -> 'a t

drop n xs is the sequence xs, deprived of its first n elements.

If xs has fewer than n elements, then drop n xs is empty.

n must be nonnegative.

drop is lazy: the first n+1 elements of the sequence xs are demanded only when the first element of drop n xs is demanded. For this reason, drop 1 xs is not equivalent to tail xs, which queries xs immediately.

  • since 4.14
val take_while : ('a -> bool) -> 'a t -> 'a t

take_while p xs is the longest prefix of the sequence xs where every element x satisfies p x.

  • since 4.14
val drop_while : ('a -> bool) -> 'a t -> 'a t

drop_while p xs is the sequence xs, deprived of the prefix take_while p xs.

  • since 4.14
val group : ('a -> 'a -> bool) -> 'a t -> 'a t t

Provided the function eq defines an equality on elements, group eq xs is the sequence of the maximal runs of adjacent duplicate elements of the sequence xs.

Every element of group eq xs is a nonempty sequence of equal elements.

The concatenation concat (group eq xs) is equal to xs.

Consuming group eq xs, and consuming the sequences that it contains, can cause xs to be consumed more than once. Therefore, xs must be persistent.

  • since 4.14
val memoize : 'a t -> 'a t

The sequence memoize xs has the same elements as the sequence xs.

Regardless of whether xs is ephemeral or persistent, memoize xs is persistent: even if it is queried several times, xs is queried at most once.

The construction of the sequence memoize xs internally relies on suspensions provided by the module Lazy. These suspensions are not thread-safe. Therefore, the sequence memoize xs must not be queried by multiple threads concurrently.

  • since 4.14
exception Forced_twice

This exception is raised when a sequence returned by once (or a suffix of it) is queried more than once.

  • since 4.14
val once : 'a t -> 'a t

The sequence once xs has the same elements as the sequence xs.

Regardless of whether xs is ephemeral or persistent, once xs is an ephemeral sequence: it can be queried at most once. If it (or a suffix of it) is queried more than once, then the exception Forced_twice is raised. This can be useful, while debugging or testing, to ensure that a sequence is consumed at most once.

  • raises Forced_twice

    if once xs, or a suffix of it, is queried more than once.

  • since 4.14
val transpose : 'a t t -> 'a t t

If xss is a matrix (a sequence of rows), then transpose xss is the sequence of the columns of the matrix xss.

The rows of the matrix xss are not required to have the same length.

The matrix xss is not required to be finite (in either direction).

The matrix xss must be persistent.

  • since 4.14
val zip : 'a t -> 'b t -> ('a * 'b) t

zip xs ys is the sequence of pairs (x, y) drawn synchronously from the sequences xs and ys.

If the sequences xs and ys have different lengths, then the sequence ends as soon as one sequence is exhausted; the excess elements in the other sequence are ignored.

zip xs ys is equivalent to map2 (fun a b -> (a, b)) xs ys.

  • since 4.14
val map2 : ('a -> 'b -> 'c) -> 'a t -> 'b t -> 'c t

map2 f xs ys is the sequence of the elements f x y, where the pairs (x, y) are drawn synchronously from the sequences xs and ys.

If the sequences xs and ys have different lengths, then the sequence ends as soon as one sequence is exhausted; the excess elements in the other sequence are ignored.

map2 f xs ys is equivalent to map (fun (x, y) -> f x y) (zip xs ys).

  • since 4.14
val interleave : 'a t -> 'a t -> 'a t

interleave xs ys is the sequence that begins with the first element of xs, continues with the first element of ys, and so on.

When one of the sequences xs and ys is exhausted, interleave xs ys continues with the rest of the other sequence.

  • since 4.14
val sorted_merge : ('a -> 'a -> int) -> 'a t -> 'a t -> 'a t

If the sequences xs and ys are sorted according to the total preorder cmp, then sorted_merge cmp xs ys is the sorted sequence obtained by merging the sequences xs and ys.

For more details on comparison functions, see Array.sort.

  • since 4.14
val product : 'a t -> 'b t -> ('a * 'b) t

product xs ys is the Cartesian product of the sequences xs and ys.

For every element x of xs and for every element y of ys, the pair (x, y) appears once as an element of product xs ys.

The order in which the pairs appear is unspecified.

The sequences xs and ys are not required to be finite.

The sequences xs and ys must be persistent.

  • since 4.14
val map_product : ('a -> 'b -> 'c) -> 'a t -> 'b t -> 'c t

The sequence map_product f xs ys is the image through f of the Cartesian product of the sequences xs and ys.

For every element x of xs and for every element y of ys, the element f x y appears once as an element of map_product f xs ys.

The order in which these elements appear is unspecified.

The sequences xs and ys are not required to be finite.

The sequences xs and ys must be persistent.

map_product f xs ys is equivalent to map (fun (x, y) -> f x y) (product xs ys).

  • since 4.14
val unzip : ('a * 'b) t -> 'a t * 'b t

unzip transforms a sequence of pairs into a pair of sequences.

unzip xs is equivalent to (map fst xs, map snd xs).

Querying either of the sequences returned by unzip xs causes xs to be queried. Therefore, querying both of them causes xs to be queried twice. Thus, xs must be persistent and cheap. If that is not the case, use unzip (memoize xs).

  • since 4.14
val split : ('a * 'b) t -> 'a t * 'b t

split is an alias for unzip.

  • since 4.14
val partition_map : ('a -> ('b, 'c) Either.t) -> 'a t -> 'b t * 'c t

partition_map f xs returns a pair of sequences (ys, zs), where:

  • ys is the sequence of the elements y such that f x = Left y, where x ranges over xs;
  • zs is the sequence of the elements z such that f x = Right z, where x ranges over xs.

partition_map f xs is equivalent to a pair of filter_map Either.find_left (map f xs) and filter_map Either.find_right (map f xs).

Querying either of the sequences returned by partition_map f xs causes xs to be queried. Therefore, querying both of them causes xs to be queried twice. Thus, xs must be persistent and cheap. If that is not the case, use partition_map f (memoize xs).

  • since 4.14
val partition : ('a -> bool) -> 'a t -> 'a t * 'a t

partition p xs returns a pair of the subsequence of the elements of xs that satisfy p and the subsequence of the elements of xs that do not satisfy p.

partition p xs is equivalent to filter p xs, filter (fun x -> not (p x)) xs.

Consuming both of the sequences returned by partition p xs causes xs to be consumed twice and causes the function f to be applied twice to each element of the list. Therefore, f should be pure and cheap. Furthermore, xs should be persistent and cheap. If that is not the case, use partition p (memoize xs).

  • since 4.14

Converting between sequences and dispensers

A dispenser is a representation of a sequence as a function of type unit -> 'a option. Every time this function is invoked, it returns the next element of the sequence. When there are no more elements, it returns None. A dispenser has mutable internal state, therefore is ephemeral: the sequence that it represents can be consumed at most once.

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

of_dispenser it is the sequence of the elements produced by the dispenser it. It is an ephemeral sequence: it can be consumed at most once. If a persistent sequence is needed, use memoize (of_dispenser it).

  • since 4.14
val to_dispenser : 'a t -> unit -> 'a option

to_dispenser xs is a fresh dispenser on the sequence xs.

This dispenser has mutable internal state, which is not protected by a lock; so, it must not be used by several threads concurrently.

  • since 4.14

Sequences of integers

val ints : int -> int t

ints i is the infinite sequence of the integers beginning at i and counting up.

  • since 4.14