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.
Checks whether the provided element is there, using polymorphic compare if equal
is not provided
fold t ~init ~f
returns f (... f (f (f init e1) e2) e3 ...) en
, where e1..en
are the elements of t
Returns true
if and only if there exists an element for which the provided
function evaluates to true
. This is a short-circuiting operation.
Returns true
if and only if the provided function evaluates to true
for all
elements. This is a short-circuiting operation.
Returns the number of elements for which the provided function evaluates to true.
Returns as an option
the first element for which f
evaluates to true.
Returns the first evaluation of f
that returns Some
, and returns None
if there
is no such element.
Returns a minimum (resp maximum) element from the collection using the provided
cmp
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
.
A monad is an abstraction of the concept of sequencing of computations. A value of type 'a monad represents a computation that returns a value of type 'a.
return v
returns the (trivial) computation that returns v.
empty
is a sequence with no elements.
Step
describes the next step of the sequence construction.
unfold ~init f
is a simplified version of unfold_step
that does not allow
Skip
.
unfold_with_and_finish t ~init ~running_step ~inner_finished ~finishing_step
folds a
state through the sequence t
to create a new sequence. The new sequence can
continue once t
has finished.
return the nth element
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
.
find_exn t ~f
returns the first element of t
that satisfies f
. It raises if
there is no such element.
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.
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
.
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
.
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
).
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.
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.
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.
to_list_rev t
returns a list of the elements of t
, in reverse order. It is faster
than to_list
.
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.
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)