package regular

empty is a sequence with no elements.

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.

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.

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.

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

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

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).

return the nth element

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.

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.

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

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

Like for_all, but passes the index as an argument.

Like exists, but passes the index as an argument.

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

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.

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

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

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.

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.

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.

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

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

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

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.

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

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).

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

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

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

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

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.

take t n produces the first n elements of 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.

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

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

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.

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).

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.

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

• deprecated [since 2015-11] Use {!Sequence.split_n} instead.

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.

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

shift_left t n is a synonym for drop t n.

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.

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.

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

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

repeat a repeats a forever.

singleton a produces a exactly once.

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.

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

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

of_lazy t_lazy produces a sequence that forces t_lazy the first time it needs to compute an element.

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.

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.

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.

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.