# Module `Base.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 sequence`

`= 'a t`

`include Indexed_container.S1 with type 'a t := 'a t`

`include Container.S1`

`val mem : 'a t -> 'a -> equal:('a -> 'a -> bool) -> bool`

Checks whether the provided element is there, using

`equal`

.

`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 fold_result : 'a t -> init:'accum -> f:('accum -> 'a -> ('accum, 'e) Result.t) -> ('accum, 'e) Result.t`

`fold_result t ~init ~f`

is a short-circuiting version of`fold`

that runs in the`Result`

monad. If`f`

returns an`Error _`

, that value is returned without any additional invocations of`f`

.

`val fold_until : 'a t -> init:'accum -> f:('accum -> 'a -> ('accum, 'final) Base__.Container_intf.Continue_or_stop.t) -> finish:('accum -> 'final) -> 'final`

`fold_until t ~init ~f ~finish`

is a short-circuiting version of`fold`

. If`f`

returns`Stop _`

the computation ceases and results in that value. If`f`

returns`Continue _`

, the fold will proceed. If`f`

never returns`Stop _`

, the final result is computed by`finish`

.Example:

`type maybe_negative = | Found_negative of int | All_nonnegative of { sum : int } (** [first_neg_or_sum list] returns the first negative number in [list], if any, otherwise returns the sum of the list. *) let first_neg_or_sum = List.fold_until ~init:0 ~f:(fun sum x -> if x < 0 then Stop (Found_negative x) else Continue (sum + x)) ~finish:(fun sum -> All_nonnegative { sum }) ;; let x = first_neg_or_sum [1; 2; 3; 4; 5] val x : maybe_negative = All_nonnegative {sum = 15} let y = first_neg_or_sum [1; 2; -3; 4; 5] val y : maybe_negative = Found_negative -3`

`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 Base__.Container_intf.Summable with type t = 'sum) -> 'a t -> f:('a -> 'sum) -> 'sum`

Returns the sum of

`f i`

for all`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 -> compare:('a -> 'a -> int) -> 'a option`

Returns a minimum (resp maximum) element from the collection using the provided

`compare`

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 -> compare:('a -> 'a -> int) -> 'a option`

`val foldi : ('a t, 'a, _) Base__.Indexed_container_intf.foldi`

`val iteri : ('a t, 'a) Base__.Indexed_container_intf.iteri`

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

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

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

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

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

`include Monad.S with type 'a t := 'a t`

`include Base__.Monad_intf.S_without_syntax with type 'a t := 'a t`

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

`val return : 'a -> 'a t`

`return v`

returns the (trivial) computation that returns v.

`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.

`module Step : sig ... end`

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.

`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`t`

to create a new sequence (like`unfold_with t ~init ~f:running_step`

), and then continues the new sequence by unfolding the final state (like`unfold_step ~init:(inner_finished final_state) ~f:finishing_step`

).

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

Returns the nth element.

`val nth_exn : 'a t -> int -> 'a`

`val folding_map : 'a t -> init:'b -> f:('b -> 'a -> 'b * 'c) -> 'c t`

`folding_map`

is a version of`map`

that threads an accumulator through calls to`f`

.

`val folding_mapi : 'a t -> init:'b -> f:(int -> 'b -> 'a -> 'b * 'c) -> 'c t`

`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 -> compare:('a -> 'a -> int) -> 'a t`

`merge t1 t2 ~compare`

merges two sorted sequences`t1`

and`t2`

, returning a sorted sequence, all according to`compare`

. 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 -> 'b t -> compare:('a -> 'b -> int) -> ('a, 'b) Merge_with_duplicates_element.t t`

`merge_with_duplicates_element t1 t2 ~compare`

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 evaluates the first element of`t`

and returns the unevaluated tail.

`val tl_eagerly_exn : 'a t -> 'a t`

`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 for_alli : 'a t -> f:(int -> 'a -> bool) -> bool`

Like

`for_all`

, but passes the index as an argument.

`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_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 round_robin : 'a t list -> 'a t`

`round_robin list`

is like`interleave (of_list list)`

, except that the manner of interleaving among the inner sequences is guaranteed to be round-robin. The input sequences may be of different lengths; an empty sequence is dropped from subsequent rounds of interleaving.

`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 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 group : 'a t -> break:('a -> 'a -> bool) -> 'a list t`

`group l ~break`

returns a sequence of lists (i.e., groups) whose concatenation is equal to the original sequence. Each group is broken where`break`

returns true on a pair of successive elements.Example:

`group ~break:(<>) (of_list ['M';'i';'s';'s';'i';'s';'s';'i';'p';'p';'i']) -> of_list [['M'];['i'];['s';'s'];['i'];['s';'s'];['i'];['p';'p'];['i']]`

`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 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 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_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.

`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.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.Note that

`delayed_fold`

, when targeting JavaScript, can result in stack overflow as JavaScript doesn't generally have tail call optimization.

`val fold_m : bind:('acc_m -> f:('acc -> 'acc_m) -> 'acc_m) -> return:('acc -> 'acc_m) -> 'elt t -> init:'acc -> f:('acc -> 'elt -> 'acc_m) -> 'acc_m`

`fold_m`

is a monad-friendly version of`fold`

. Supply it with the monad's`return`

and`bind`

, and it will chain them through the computation.

`val iter_m : bind:('unit_m -> f:(unit -> 'unit_m) -> 'unit_m) -> return:(unit -> 'unit_m) -> 'elt t -> f:('elt -> 'unit_m) -> 'unit_m`

`iter_m`

is a monad-friendly version of`iter`

. Supply it with the monad's`return`

and`bind`

, and it will chain them through the computation.

`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 of_lazy : 'a t Lazy.t -> 'a t`

`of_lazy t_lazy`

produces a sequence that forces`t_lazy`

the first time it needs to compute an element.

`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.

`module Generator : sig ... end`

`module Expert : sig ... end`

The functions in

`Expert`

expose internal structure which is normally meant to be hidden. For example, at least when`f`

is purely functional, it is not intended for client code to distinguish between