Module Sequence

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.


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)).

module Monad_infix : Monad_intf.Infix with type 'a t := 'a t
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 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.

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)

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)
        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