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ModuleSequence = Sequence

Signature

type +'a t
val sexp_of_t : ('a -> Sexplib.Sexp.t) -> 'a t -> Sexplib.Sexp.t
val compare : ('a -> 'a -> int) -> 'a t -> 'a t -> int
type 'a sequence = 'a t
include Container.S1 with type 'a t := 'a t
type 'a t
val mem : ?equal:('a -> 'a -> bool) -> 'a t -> 'a -> bool

Checks whether the provided element is there, using polymorphic compare if `equal` is not provided

val length : 'a t -> int
val is_empty : 'a t -> bool
val iter : 'a t -> f:('a -> unit) -> unit
val fold : 'a t -> init:'accum -> f:('accum -> 'a -> 'accum) -> 'accum

`fold t ~init ~f` returns `f (... f (f (f init e1) e2) e3 ...) en`, where `e1..en` are the elements of `t`

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

Returns `true` if and only if there exists an element for which the provided function evaluates to `true`. This is a short-circuiting operation.

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

Returns `true` if and only if the provided function evaluates to `true` for all elements. This is a short-circuiting operation.

val count : 'a t -> f:('a -> bool) -> int

Returns the number of elements for which the provided function evaluates to true.

val sum : (module Commutative_group.S with type t = 'sum) -> 'a t -> f:('a -> 'sum) -> 'sum

Returns the sum of `f i` for i in the container

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

Returns as an `option` the first element for which `f` evaluates to true.

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

Returns the first evaluation of `f` that returns `Some`, and returns `None` if there is no such element.

val to_list : 'a t -> 'a list
val to_array : 'a t -> 'a array
val min_elt : 'a t -> cmp:('a -> 'a -> int) -> 'a option

Returns a minimum (resp maximum) element from the collection using the provided `cmp` function, or `None` if the collection is empty. In case of a tie, the first element encountered while traversing the collection is returned. The implementation uses `fold` so it has the same complexity as `fold`.

val max_elt : 'a t -> cmp:('a -> 'a -> int) -> 'a option
include Monad.S with type 'a t := 'a t
type 'a t
include Monad_intf.S_without_syntax with type 'a t := 'a t
type 'a t

A monad is an abstraction of the concept of sequencing of computations. A value of type 'a monad represents a computation that returns a value of type 'a.

include Monad_intf.Infix with type 'a t := 'a t
type 'a t
val (>>=) : 'a t -> ('a -> 'b t) -> 'b t

`t >>= f` returns a computation that sequences the computations represented by two monad elements. The resulting computation first does `t` to yield a value `v`, and then runs the computation returned by `f v`.

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

`t >>| f` is `t >>= (fun a -> return (f a))`.

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

`bind t f` = `t >>= f`

val return : 'a -> 'a t

`return v` returns the (trivial) computation that returns v.

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

`map t ~f` is t >>| f.

val join : 'a t t -> 'a t

`join t` is `t >>= (fun t' -> t')`.

val ignore_m : 'a t -> unit t

`ignore_m t` is `map t ~f:(fun _ -> ())`. `ignore_m` used to be called `ignore`, but we decided that was a bad name, because it shadowed the widely used `Pervasives.ignore`. Some monads still do `let ignore = ignore_m` for historical reasons.

val all : 'a t list -> 'a list t
val all_ignore : unit t list -> unit t
include Monad_intf.Syntax with type 'a t := 'a t
type 'a t
module Let_syntax : sig .. end
val empty : _ t

`empty` is a sequence with no elements.

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

`next` returns the next element of a sequence and the next tail if the sequence is not finished. It is the most primitive way to walk over a sequence.

module Step : sig .. end
A `Step` describes the next step of the sequence construction.
val unfold_step : init:'s -> f:('s -> ('a, 's) Step.t) -> 'a t

`unfold_step ~init ~f` constructs a sequence by giving an initial state `init` and a function `f` explaining how to continue the next step from a given state.

val unfold : init:'s -> f:('s -> ('a * 's) option) -> 'a t

`unfold ~init f` is a simplified version of `unfold_step` that does not allow `Skip`.

val unfold_with : 'a t -> init:'s -> f:('s -> 'a -> ('b, 's) Step.t) -> 'b t

`unfold_with t ~init ~f` folds a state through the sequence `t` to create a new sequence

val unfold_with_and_finish : 'a t -> init:'s_a -> running_step:('s_a -> 'a -> ('b, 's_a) Step.t) -> inner_finished:('s_a -> 's_b) -> finishing_step:('s_b -> ('b, 's_b) Step.t) -> 'b t

`unfold_with_and_finish t ~init ~running_step ~inner_finished ~finishing_step` folds a state through the sequence `t` to create a new sequence. The new sequence can continue once `t` has finished.

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

return the nth element

val nth_exn : 'a t -> int -> 'a
val mapi : 'a t -> f:(int -> 'a -> 'b) -> 'b t
val filteri : 'a t -> f:(int -> 'a -> bool) -> 'a t
val filter : 'a t -> f:('a -> bool) -> 'a t
val merge : 'a t -> 'a t -> cmp:('a -> 'a -> int) -> 'a t

`merge t1 t2 ~cmp` merges two sorted sequences `t1` and `t2`, returning a sorted sequence, all according to `cmp`. If two elements are equal, the one from `t1` is preferred. The behavior is undefined if the inputs aren't sorted.

module Merge_with_duplicates_element : sig .. end
val merge_with_duplicates : 'a t -> 'a t -> cmp:('a -> 'a -> int) -> 'a Merge_with_duplicates_element.t t

`merge_with_duplicates_element t1 t2 ~cmp` is like `merge`, except that for each element it indicates which input(s) the element comes from, using `Merge_with_duplicates_element`.

val hd : 'a t -> 'a option
val hd_exn : 'a t -> 'a
val tl : 'a t -> 'a t option

`tl t` and `tl_eagerly_exn t` immediately evaluate the first element of `t` and return the unevaluated tail.

val tl_eagerly_exn : 'a t -> 'a t
val findi : 'a t -> f:(int -> 'a -> bool) -> (int * 'a) option
val find_exn : 'a t -> f:('a -> bool) -> 'a

`find_exn t ~f` returns the first element of `t` that satisfies `f`. It raises if there is no such element.

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

`append t1 t2` first produces the elements of `t1`, then produces the elements of `t2`.

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

`concat tt` produces the elements of each inner sequence sequentially. If any inner sequences are infinite, elements of subsequent inner sequences will not be reached.

val concat_map : 'a t -> f:('a -> 'b t) -> 'b t

`concat_map t ~f` is `concat (map t ~f)`.

val concat_mapi : 'a t -> f:(int -> 'a -> 'b t) -> 'b t

`concat_mapi t ~f` is like concat_map, but passes the index as an argument.

val interleave : 'a t t -> 'a t

`interleave tt` produces each element of the inner sequences of `tt` eventually, even if any or all of the inner sequences are infinite. The elements of each inner sequence are produced in order with respect to that inner sequence. The manner of interleaving among the separate inner sequences is deterministic but unspecified.

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

Transforms a pair of sequences into a sequence of pairs. The length of the returned sequence is the length of the shorter input. The remaining elements of the longer input are discarded.

WARNING: Unlike `List.zip`, this will not error out if the two input sequences are of different lengths, because `zip` may have already returned some elements by the time this becomes apparent.

val zip_full : 'a t -> 'b t -> [
| `Left of 'a
| `Both of 'a * 'b
| `Right of 'b
] t

`zip_full` is like `zip`, but if one sequence ends before the other, then it keeps producing elements from the other sequence until it has ended as well.

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

`iteri` is just like `iter`, but it also passes in the index of each element to `f`.

val foldi : 'a t -> f:(int -> 'b -> 'a -> 'b) -> init:'b -> 'b

`foldi` is just like `fold`, but it also passes in the index of each element to `f`.

val reduce_exn : 'a t -> f:('a -> 'a -> 'a) -> 'a

`reduce_exn f [a1; ...; an]` is `f (... (f (f a1 a2) a3) ...) an`. It fails on the empty sequence.

val reduce : 'a t -> f:('a -> 'a -> 'a) -> 'a option
val find_consecutive_duplicate : 'a t -> equal:('a -> 'a -> bool) -> ('a * 'a) option

`find_consecutive_duplicate t ~equal` returns the first pair of consecutive elements `(a1, a2)` in `t` such that `equal a1 a2`. They are returned in the same order as they appear in `t`.

val remove_consecutive_duplicates : 'a t -> equal:('a -> 'a -> bool) -> 'a t

The same sequence with consecutive duplicates removed. The relative order of the other elements is unaffected.

val range : ?stride:int -> ?start:[
| `inclusive
| `exclusive
] -> ?stop:[
| `inclusive
| `exclusive
] -> int -> int -> int t

`range ?stride ?start ?stop start_i stop_i` is the sequence of integers from `start_i` to `stop_i`, stepping by `stride`. If `stride` < 0 then we need `start_i` > `stop_i` for the result to be nonempty (or `start_i` >= `stop_i` in the case where both bounds are inclusive).

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

`init n ~f` is `[(f 0); (f 1); ...; (f (n-1))]`. It is an error if `n < 0`.

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

`filter_map t ~f` produce mapped elements of `t` which are not `None`.

val filter_mapi : 'a t -> f:(int -> 'a -> 'b option) -> 'b t

`filter_mapi` is just like `filter_map`, but it also passes in the index of each element to `f`.

val filter_opt : 'a option t -> 'a t

`filter_opt t` produces the elements of `t` which are not `None`. `filter_opt t` = `filter_map t ~f:ident`

val sub : 'a t -> pos:int -> len:int -> 'a t

`sub t ~pos ~len` is the `len`-element subsequence of `t`, starting at `pos`. If the sequence is shorter than `pos + len`, it returns ` t[pos] ... t[l-1] `, where `l` is the length of the sequence.

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

`take t n` produces the first `n` elements of `t`.

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

`drop t n` produces all elements of `t` except the first `n` elements. If there are fewer than `n` elements in `t`, there is no error; the resulting sequence simply produces no elements. Usually you will probably want to use `drop_eagerly` because it can be significantly cheaper.

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

`drop_eagerly t n` immediately consumes the first `n` elements of `t` and returns the unevaluated tail of `t`.

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

`take_while t ~f` produces the longest prefix of `t` for which `f` applied to each element is `true`.

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

`drop_while t ~f` produces the suffix of `t` beginning with the first element of `t` for which `f` is `false`. Usually you will probably want to use `drop_while_option` because it can be significantly cheaper.

val drop_while_option : 'a t -> f:('a -> bool) -> ('a * 'a t) option

`drop_while_option t ~f` immediately consumes the elements from `t` until the predicate `f` fails and returns the first element that failed along with the unevaluated tail of `t`. The first element is returned separately because the alternatives would mean forcing the consumer to evaluate the first element again (if the previous state of the sequence is returned) or take on extra cost for each element (if the element is added to the final state of the sequence using `shift_right`).

val split_n : 'a t -> int -> 'a list * 'a t

`split_n t n` immediately consumes the first `n` elements of `t` and returns the consumed prefix, as a list, along with the unevaluated tail of `t`.

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

`split_n_eagerly t n` behaves as `split_n t n`, but converts the prefix into a sequence.

val chunks_exn : 'a t -> int -> 'a list t

`chunks_exn t n` produces lists of elements of `t`, up to `n` elements at a time. The last list may contain fewer than `n` elements. No list contains zero elements. If `n` is not positive, it raises.

val shift_right : 'a t -> 'a -> 'a t

`shift_right t a` produces `a` and then produces each element of `t`.

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

`shift_right_with_list t l` produces the elements of `l`, then produces the elements of `t`. It is better to call `shift_right_with_list` with a list of size n than `shift_right` n times; the former will require O(1) work per element produced and the latter O(n) work per element produced.

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

`shift_left t n` is a synonym for `drop t n`.

module Infix : sig .. end
val cartesian_product : 'a t -> 'b t -> ('a * 'b) t

Returns a sequence with all possible pairs. The stepper function of the second sequence passed as argument may be applied to the same state multiple times, so be careful using `cartesian_product` with expensive or side-effecting functions. If the second sequence is infinite, some values in the first sequence may not be reached.

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

Returns a sequence that eventually reaches every possible pair of elements of the inputs, even if either or both are infinite. The step function of both inputs may be applied to the same state repeatedly, so be careful using `interleaved_cartesian_product` with expensive or side-effecting functions.

val intersperse : 'a t -> sep:'a -> 'a t

`intersperse xs ~sep` produces `sep` between adjacent elements of `xs`. e.g. `intersperse [1;2;3] ~sep:0 = [1;0;2;0;3]`

val cycle_list_exn : 'a list -> 'a t

`cycle_list_exn xs` repeats the elements of `xs` forever. If `xs` is empty, it raises.

val repeat : 'a -> 'a t

`repeat a` repeats `a` forever.

val singleton : 'a -> 'a t

`singleton a` produces `a` exactly once.

val delayed_fold : 'a t -> init:'s -> f:('s -> 'a -> k:('s -> 'r) -> 'r) -> finish:('s -> 'r) -> 'r

`delayed_fold` allows to do an on-demand fold, while maintaining a state. This function is sufficient to implement `fold_m` in any monad.

``````
let fold_m t ~init ~f =
let open M in
delayed_fold t ~init
~f:(fun s a ~k -> f s a >>= k)
~finish:return
``````

It is possible to exit early by not calling `k` in `f`. It is also possible to call `k` multiple times. This results in the rest of the sequence being folded over multiple times, independently.

val to_list : 'a t -> 'a list
val to_list_rev : 'a t -> 'a list

`to_list_rev t` returns a list of the elements of `t`, in reverse order. It is faster than `to_list`.

val of_list : 'a list -> 'a t
val memoize : 'a t -> 'a t

`memoize t` produces each element of `t`, but also memoizes them so that if you consume the same element multiple times it is only computed once. It's a non-eager version of `force_eagerly`.

val force_eagerly : 'a t -> 'a t

`force_eagerly t` precomputes the sequence. It is behaviorally equivalent to ```of_list (to_list t)```, but may at some point have a more efficient implementation. It's an eager version of `memoize`.

val bounded_length : _ t -> at_most:int -> [
| `Is of int
| `Greater
]

`bounded_length ~at_most t` returns ``Is len` if `len = length t <= at_most`, and otherwise returns ``Greater`. Walks through only as much of the sequence as necessary. Always returns ``Greater` if `at_most < 0`.

val length_is_bounded_by : ?min:int -> ?max:int -> _ t -> bool

`length_is_bounded_by ~min ~max t` returns true if `min <= length t` and ```length t <= max``` When `min` or `max` are not provided, the check for that bound is omitted. Walks through only as much of the sequence as necessary.

`Generator` is a monadic interface to generate sequences in a direct style, similar to Python's generators.

Here are some examples:

``````
open Generator

let rec traverse_list = function
| [] -> return ()
| x :: xs -> yield x >>= fun () -> traverse_list xs

let traverse_option = function
| None -> return ()
| Some x -> yield x

let traverse_array arr =
let n = Array.length arr in
let rec loop i =
if i >= n then return () else yield arr.(i) >>= fun () -> loop (i + 1)
in
loop 0

let rec traverse_bst = function
| Node.Empty -> return ()
| Node.Branch (left, value, right) ->
traverse_bst left  >>= fun () ->
yield        value >>= fun () ->
traverse_bst right

let sequence_of_list   x = Generator.run (traverse_list   x)
let sequence_of_option x = Generator.run (traverse_option x)
let sequence_of_array  x = Generator.run (traverse_array  x)
let sequence_of_bst    x = Generator.run (traverse_bst    x)
``````
module Generator : sig .. end