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:
t before returning.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.
include sig ... endval sexp_of_t : ('a ‑> Base.Sexp.t) ‑> 'a t ‑> Base.Sexp.tinclude Base.Indexed_container.S1 with type a t := a tinclude Base.Container.S1val mem : 'a t ‑> 'a ‑> equal:('a ‑> 'a ‑> bool) ‑> boolChecks whether the provided element is there, using equal.
val length : 'a t ‑> intval is_empty : 'a t ‑> boolval iter : 'a t ‑> f:('a ‑> unit) ‑> unitval fold : 'a t ‑> init:'accum ‑> f:('accum ‑> 'a ‑> 'accum) ‑> 'accumfold 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) Base.Result.t) ‑> ('accum, 'e) Base.Result.tfold_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) ‑> 'finalfold_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.
val exists : 'a t ‑> f:('a ‑> bool) ‑> boolReturns 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) ‑> boolReturns 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) ‑> intReturns the number of elements for which the provided function evaluates to true.
val sum : (module Base.Commutative_group.S with type t = 'sum) ‑> 'a t ‑> f:('a ‑> 'sum) ‑> 'sumReturns the sum of f i for all i in the container.
val find : 'a t ‑> f:('a ‑> bool) ‑> 'a optionReturns as an option the first element for which f evaluates to true.
val find_map : 'a t ‑> f:('a ‑> 'b option) ‑> 'b optionReturns the first evaluation of f that returns Some, and returns None if there
is no such element.
val to_list : 'a t ‑> 'a listval to_array : 'a t ‑> 'a arrayval min_elt : 'a t ‑> compare:('a ‑> 'a ‑> int) ‑> 'a optionReturns 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 optionThese are all like their equivalents in Container except that an index starting at
0 is added as the first argument to f.
val foldi : ('a t, 'a, _) Base__.Indexed_container_intf.foldival iteri : ('a t, 'a) Base__.Indexed_container_intf.iterival existsi : 'a t ‑> f:(int ‑> 'a ‑> bool) ‑> boolval for_alli : 'a t ‑> f:(int ‑> 'a ‑> bool) ‑> boolval counti : 'a t ‑> f:(int ‑> 'a ‑> bool) ‑> intval findi : 'a t ‑> f:(int ‑> 'a ‑> bool) ‑> (int * 'a) optionval find_mapi : 'a t ‑> f:(int ‑> 'a ‑> 'b option) ‑> 'b optioninclude Base.Monad.S with type a t := a tinclude Base__.Monad_intf.S_without_syntax with type a t := a tinclude Base__.Monad_intf.Infix with type a t := a tmodule Monad_infix : Base__.Monad_intf.Infix with type a t := a tmodule Step : sig ... endA 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 tunfold ~init f is a simplified version of unfold_step that does not allow
Skip.
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 tunfold_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_exn : 'a t ‑> int ‑> 'amerge 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.
module Merge_with_duplicates_element : sig ... endval merge_with_duplicates : 'a t ‑> 'b t ‑> cmp:('a ‑> 'b ‑> int) ‑> ('a, 'b) Merge_with_duplicates_element.t tmerge_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.
val hd : 'a t ‑> 'a optionval hd_exn : 'a t ‑> 'atl 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) ‑> 'afind_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) ‑> boolLike for_all, but passes the index as an argument.
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.
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.
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.
val reduce_exn : 'a t ‑> f:('a ‑> 'a ‑> 'a) ‑> 'areduce_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 optiongroup 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) optionfind_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.
val range : ?stride:int ‑> ?start:[ `inclusive | `exclusive ] ‑> ?stop:[ `inclusive | `exclusive ] ‑> int ‑> int ‑> int trange ?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 tinit n ~f is [(f 0); (f 1); ...; (f (n-1))]. It is an error if n < 0.
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 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.
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.
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 ... endReturns 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].
val cycle_list_exn : 'a list ‑> 'a tcycle_list_exn xs repeats the elements of xs forever. If xs is empty, it
raises.
val delayed_fold : 'a t ‑> init:'s ‑> f:('s ‑> 'a ‑> k:('s ‑> 'r) ‑> 'r) ‑> finish:('s ‑> 'r) ‑> 'rdelayed_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_mfold_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_miter_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 listto_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 tval of_lazy : 'a t Base.Lazy.t ‑> 'a tof_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.
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 ‑> boollength_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)module Generator : sig ... endmodule Expert : sig ... endThe 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