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module Sequence

: sig

A sequence of elements that can be produced one at a time, on demand, normally with no sharing.

The elements are computed on demand, possibly repeating work if they are demanded multiple times. A sequence can be built by unfolding from some initial state, which will in practice often be other containers.

Most functions constructing a sequence will not immediately compute any elements of the sequence. These functions will always return in O(1), but traversing the resulting sequence may be more expensive. The most they will do immediately is generate a new internal state and a new step function.

Functions that transform existing sequences sometimes have to reconstruct some suffix of the input sequence, even if it is unmodified. For example, calling drop 1 will return a sequence with a slightly larger state and whose elements all cost slightly more to traverse. Because this is sometimes undesirable (for example, applying drop 1 n times will cost O(n) per element traversed in the result), there are also more eager versions of many functions (whose names are suffixed with _eagerly) that do more work up front. A function has the _eagerly suffix iff it matches both of these conditions:

It might consume an element from an input t before returning.

It only returns a t (not paired with something else, not wrapped in an option, etc.). If it returns anything other than a t and it has at least one t input, it's probably demanding elements from the input t anyway.

Only *_exn functions can raise exceptions, except if the function underlying the sequence (the f passed to unfold) raises, in which case the exception will cascade.

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type +'a t
#
type 'a sequence = 'a t
include Container.S1 with type 'a t := 'a t
include Monad.S with type 'a t := 'a t
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val empty : _ t

empty is a sequence with no elements.

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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.

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module Step : sig

A Step describes the next step of the sequence construction. Done indicates the sequence is finished. Skip indicates the sequence continues with another state without producing the next element yet. Yield outputs an element and introduces a new state.

Modifying 's doesn't violate any *internal* invariants, but it may violate some undocumented expectations. For example, one might expect that producing an element from the same point in the sequence would always give the same value, but if the state can mutate, that is not so.

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type ('a, 's) t =
# | Done
# | Skip of 's
# | Yield of 'a * 's
end
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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.

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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.

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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

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

return the nth element

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

merge t1 t2 ~cmp produces the interleaved elements of t1 and t2, always picking the smallest of the two available elements from t1 and t2, according to cmp. When the two available elements are equal, the one from t1 is preferred.

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

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

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

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

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

concat tt produces the elements of each inner sequence sequentially.

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

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

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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.

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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.

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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.

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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.

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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.

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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.

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val reduce : 'a t -> f:('a -> 'a -> 'a) -> 'a option
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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.

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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.

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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).

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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.

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

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

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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.

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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

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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.

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

take t n produces the first n elements of t.

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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.

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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.

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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.

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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.

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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).

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

split_n_eagerly t n immediately consumes the first n elements of t and returns the consumed prefix, as a new stream, along with the unevaluated tail of t.

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

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

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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 later O(n) work per element produced.

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

shift_left t n is a synonym for drop t n.

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module Infix : sig
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val (@) : 'a t -> 'a t -> 'a t
end
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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.

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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]

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val cycle : 'a t -> 'a t

cycle t repeats the sequence t forever. The elements of t will be recomputed for each repetition in the cycle.

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val repeat : 'a -> 'a t

repeat a repeats a forever.

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val singleton : 'a -> 'a t

singleton a produces a exactly once.

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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.

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

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

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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.

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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.

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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)
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module Generator : sig
include Monad.S2
#
val yield : 'elt -> (unit, 'elt) t
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val run : (unit, 'elt) t -> 'elt sequence
end
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val sexp_of_t : ('a -> Sexplib.Sexp.t) -> 'a t -> Sexplib.Sexp.t
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val compare : ('a -> 'a -> int) -> 'a t -> 'a t -> int
end