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
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
- It only returns a
t(not paired with something else, not wrapped in an
option, etc.). If it returns anything other than a
tand it has at least one
tinput, it's probably demanding elements from the input
*_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 with type 'a t := 'a t
val mem : 'a t -> 'a -> equal:('a -> 'a -> bool) -> bool
Checks whether the provided element is there, using
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
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
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
Stop _ the computation ceases and results in that value. If
Continue _, the fold will proceed. If
f never returns
Stop _, the final result is computed by
val exists : 'a t -> f:('a -> bool) -> bool
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
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.
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
val max_elt : 'a t -> compare:('a -> 'a -> int) -> 'a option
These are all like their equivalents in
Container except that an index starting at 0 is added as the first argument to
val foldi : 'a t -> init:_ -> f:(int -> _ -> 'a -> _) -> _
val iteri : 'a t -> f:(int -> 'a -> unit) -> unit
val existsi : '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
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
module Monad_infix : sig ... end
val return : 'a -> 'a t
return v returns the (trivial) computation that returns v.
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.
module Let_syntax : sig ... end
These are convenient to have in scope when programming with a monad:
val empty : _ t
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.
module Step : sig ... end
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.
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
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
folding_map is a version of
map that threads an accumulator through calls to
merge t1 t2 ~cmp merges two sorted sequences
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 -> 'b t -> cmp:('a -> 'b -> int) -> ('a, 'b) 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
val hd : 'a t -> 'a option
val hd_exn : 'a t -> 'a
tl t and
tl_eagerly_exn t immediately evaluates the first element of
t and returns the unevaluated tail.
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
for_all, but passes the index as an argument.
append t1 t2 first produces the elements of
t1, then produces the elements of
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_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.
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.
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.
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.
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
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.
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
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
stop_i, stepping by
stride < 0 then we need
stop_i for the result to be nonempty (or
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.
filter_map t ~f produce mapped elements of
t which are not
filter_mapi is just like
filter_map, but it also passes in the index of each element to
filter_opt t produces the elements of
t which are not
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.
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
take_while t ~f produces the longest prefix of
t for which
f applied to each element is
drop_while t ~f produces the suffix of
t beginning with the first element of
t for which
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
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
split_n_eagerly t n behaves as
split_n t n, but converts the prefix into a sequence.
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_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
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
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
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
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 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
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
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
val of_list : 'a list -> 'a t
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 t precomputes the sequence. It is behaviorally equivalent to
(to_list t), but may at some point have a more efficient implementation. It's an eager version of
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
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 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
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