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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.
val fold : 'at->init:'acc->f:('acc->'a->'acc)->'acc
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 :
'at->init:'acc->f:('acc->'a->('acc, 'e)Result.t)->('acc, '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 :
'at->init:'acc->f:('acc->'a->('acc, 'final)Container.Continue_or_stop.t)->finish:('acc->'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 min_elt : 'at->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 : 'at->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 f.
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.
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 Stdlib.ignore. Some monads still do let ignore = ignore_m for historical reasons.
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)->'at
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)->'at
unfold ~init f is a simplified version of unfold_step that does not allow Skip.
val unfold_with : 'at->init:'s->f:('s->'a->('b, 's)Step.t)->'bt
unfold_with t ~init ~f folds a state through the sequence t to create a new sequence
val unfold_with_and_finish :
'at->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)->'bt
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 merge_deduped_and_sorted :
'at->'at->compare:('a->'a-> int)->'at
If t1 and t2 are each sorted without duplicates, merge_deduped_and_sorted t1 t2
~compare merges t1 and t2 into a sorted sequence without duplicates. Whenever identical elements are found in both t1 and t2, the one from t1 is used and the one from t2 is discarded. The behavior is undefined if the inputs aren't sorted or contain duplicates.
val merge_sorted : 'at->'at->compare:('a->'a-> int)->'at
If t1 and t2 are each sorted, merge_sorted t1 t2 ~compare merges t1 and t2 into a sorted sequence. Whenever identical elements are found in both t1 and t2, the one from t1 is used first. The behavior is undefined if the inputs aren't sorted.
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.
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.
val zip_full :
'at->'bt->[ `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.
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 :
'at->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 : 'at->equal:('a->'a-> bool)->'at
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).
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_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 : 'at->f:('a-> bool)->('a * 'at) 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).
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.
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 : 'at->'bt->('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 delayed_fold :
'at->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)->'eltt->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)->'eltt->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.
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-> 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)
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)
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