iter 1.8 · OCaml Package

Simple and Efficient Iterators.

The iterators are designed to allow easy transfer (mappings) between data structures, without defining n^2 conversions between the n types. The implementation relies on the assumption that an iterator can be iterated on as many times as needed; this choice allows for high performance of many combinators. However, for transient iterators, the persistent function is provided, storing elements of a transient iterator in memory; the iterator can then be used several times (See further).

Note that some combinators also return iterators (e.g. group). The transformation is computed on the fly every time one iterates over the resulting iterator. If a transformation performs heavy computation, persistent can also be used as intermediate storage.

Most functions are lazy, i.e. they do not actually use their arguments until their result is iterated on. For instance, if one calls map on an iterator, one gets a new iterator, but nothing else happens until this new iterator is used (by folding or iterating on it).

If an iterator is built from an iteration function that is repeatable (i.e. calling it several times always iterates on the same set of elements, for instance List.iter or Map.iter), then the resulting t object is also repeatable. For one-time iter functions such as iteration on a file descriptor or a Seq, the persistent function can be used to iterate and store elements in a memory structure; the result is an iterator that iterates on the elements of this memory structure, cheaply and repeatably.

type +'a t = ('a -> unit) -> unit

An iterator of values of type 'a. If you give it a function 'a -> unit it will be applied to every element of the iterator successively.

type +'a iter = 'a t

type 'a equal = 'a -> 'a -> bool

type 'a hash = 'a -> int

Creation

val from_iter : (('a -> unit) -> unit) -> 'a t

Build an iterator from a iter function

val from_labelled_iter : (f:('a -> unit) -> unit) -> 'a t

Build an iterator from a labelled iter function

since 1.2

val from_fun : (unit -> 'a option) -> 'a t

Call the function repeatedly until it returns None. This iterator is transient, use persistent if needed!

val empty : 'a t

Empty iterator. It contains no element.

val singleton : 'a -> 'a t

Singleton iterator, with exactly one element.

val doubleton : 'a -> 'a -> 'a t

Iterator with exactly two elements

val init : (int -> 'a) -> 'a t

init f is the infinite iterator f 0; f 1; f 2; ….

since 0.9

val cons : 'a -> 'a t -> 'a t

cons x l yields x, then yields from l. Same as append (singleton x) l.

Caution: it is advised not to build long iterators out of cons, because it's inefficient. Each additional cons x i adds one layer of function call per item traversed in i.

val snoc : 'a t -> 'a -> 'a t

Same as cons but yields the element after iterating on l.

val return : 'a -> 'a t

Synonym to singleton

val pure : 'a -> 'a t

Synonym to singleton

val repeat : 'a -> 'a t

Infinite iterator of the same element. You may want to look at take and the likes if you iterate on it.

val iterate : ('a -> 'a) -> 'a -> 'a t

iterate f x is the infinite iterator x, f(x), f(f(x)), ...

val forever : (unit -> 'b) -> 'b t

Iterator that calls the given function to produce elements. The iterator may be transient (depending on the function), and definitely is infinite. You may want to use take and persistent.

val cycle : 'a t -> 'a t

Cycle forever through the given iterator. Assume the given iterator can be traversed any amount of times (not transient). This yields an infinite iterator, you should use something like take not to loop forever.

val unfoldr : ('b -> ('a * 'b) option) -> 'b -> 'a t

unfoldr f b will apply f to b. If it yields Some (x,b') then x is returned and unfoldr recurses with b'.

val scan : ('b -> 'a -> 'b) -> 'b -> 'a t -> 'b t

Iterator of intermediate results

Consumption

val iter : ('a -> unit) -> 'a t -> unit

Consume the iterator, passing all its arguments to the function. Basically iter f seq is just seq f.

val iteri : (int -> 'a -> unit) -> 'a t -> unit

Iterate on elements and their index in the iterator

val for_each : 'a t -> ('a -> unit) -> unit

Consume the iterator, passing all its arguments to the function. for_each seq f is the same as iter f seq, i.e., iter with arguments reversed.

since 1.4

val for_eachi : 'a t -> (int -> 'a -> unit) -> unit

Iterate on elements and their index in the iterator. for_eachi seq f is the same as iteri f seq, i.e., iteri with arguments reversed.

since 1.4

val fold : ('a -> 'b -> 'a) -> 'a -> 'b t -> 'a

Fold over elements of the iterator, consuming it

val foldi : ('a -> int -> 'b -> 'a) -> 'a -> 'b t -> 'a

Fold over elements of the iterator and their index, consuming it

val fold_map : ('acc -> 'a -> 'acc * 'b) -> 'acc -> 'a t -> 'b t

fold_map f acc l is like map, but it carries some state as in fold. The state is not returned, it is just used to thread some information to the map function.

since 0.9

val fold_filter_map : ('acc -> 'a -> 'acc * 'b option) -> 'acc -> 'a t -> 'b t

fold_filter_map f acc l is a fold_map-like function, but the function can choose to skip an element by retuning None.

since 0.9

val map : ('a -> 'b) -> 'a t -> 'b t

Map objects of the iterator into other elements, lazily

val mapi : (int -> 'a -> 'b) -> 'a t -> 'b t

Map objects, along with their index in the iterator

val map_by_2 : ('a -> 'a -> 'a) -> 'a t -> 'a t

Map objects two by two. lazily. The last element is kept in the iterator if the count is odd.

since 0.7

val for_all : ('a -> bool) -> 'a t -> bool

Do all elements satisfy the predicate?

val exists : ('a -> bool) -> 'a t -> bool

Exists there some element satisfying the predicate?

val mem : ?eq:('a -> 'a -> bool) -> 'a -> 'a t -> bool

Is the value a member of the iterator?

parameter eq
the equality predicate to use (default (=))

since 0.5

val find : ('a -> 'b option) -> 'a t -> 'b option

Find the first element on which the function doesn't return None

since 0.5

val find_map : ('a -> 'b option) -> 'a t -> 'b option

Alias to find

since 0.10

val findi : (int -> 'a -> 'b option) -> 'a t -> 'b option

Indexed version of find

since 0.9

val find_mapi : (int -> 'a -> 'b option) -> 'a t -> 'b option

Alias to findi

since 0.10

val find_pred : ('a -> bool) -> 'a t -> 'a option

find_pred p l finds the first element of l that satisfies p, or returns None if no element satisfies p

since 0.9

val find_pred_exn : ('a -> bool) -> 'a t -> 'a

Unsafe version of find_pred

raises Not_found
if no such element is found

since 0.9

val length : 'a t -> int

How long is the iterator? Forces the iterator.

val is_empty : 'a t -> bool

Is the iterator empty? Forces the iterator.

Transformation

val filter : ('a -> bool) -> 'a t -> 'a t

Filter on elements of the iterator

val append : 'a t -> 'a t -> 'a t

Append two iterators. Iterating on the result is like iterating on the first, then on the second.

val append_l : 'a t list -> 'a t

Append iterators. Iterating on the result is like iterating on the each iterator of the list in order.

since 0.11

val concat : 'a t t -> 'a t

Concatenate an iterator of iterators into one iterator.

val flatten : 'a t t -> 'a t

Alias for concat

val flat_map : ('a -> 'b t) -> 'a t -> 'b t

Monadic bind. Intuitively, it applies the function to every element of the initial iterator, and calls concat. Formerly flatMap

since 0.5

val flat_map_l : ('a -> 'b list) -> 'a t -> 'b t

Convenience function combining flat_map and of_list

since 0.9

val seq_list : 'a t list -> 'a list t

seq_list l returns all the ways to pick one element in each sub-iterator in l. Assumes the sub-iterators can be iterated on several times.

since 0.11

val seq_list_map : ('a -> 'b t) -> 'a list -> 'b list t

seq_list_map f l maps f over every element of l, then calls seq_list

since 0.11

val filter_map : ('a -> 'b option) -> 'a t -> 'b t

Map and only keep non-None elements Formerly fmap

since 0.5

val filter_mapi : (int -> 'a -> 'b option) -> 'a t -> 'b t

Map with indices, and only keep non-None elements

since 0.11

val filter_count : ('a -> bool) -> 'a t -> int

Count how many elements satisfy the given predicate

since 1.0

val intersperse : 'a -> 'a t -> 'a t

Insert the single element between every element of the iterator

val keep_some : 'a option t -> 'a t

filter_some l retains only elements of the form Some x. Same as filter_map (fun x->x)

since 1.0

val keep_ok : ('a, _) result t -> 'a t

keep_ok l retains only elements of the form Ok x.

since 1.0

val keep_error : (_, 'e) result t -> 'e t

keep_error l retains only elements of the form Error x.

since 1.0

Caching

val persistent : 'a t -> 'a t

Iterate on the iterator, storing elements in an efficient internal structure.. The resulting iterator can be iterated on as many times as needed. Note: calling persistent on an already persistent iterator will still make a new copy of the iterator!

val persistent_lazy : 'a t -> 'a t

Lazy version of persistent. When calling persistent_lazy s, a new iterator s' is immediately returned (without actually consuming s) in constant time; the first time s' is iterated on, it also consumes s and caches its content into a inner data structure that will back s' for future iterations.

warning: on the first traversal of s', if the traversal is interrupted prematurely (take, etc.) then s' will not be memorized, and the next call to s' will traverse s again.

Misc

val sort : ?cmp:('a -> 'a -> int) -> 'a t -> 'a t

Sort the iterator. Eager, O(n) ram and O(n ln(n)) time. It iterates on elements of the argument iterator immediately, before it sorts them.

val sort_uniq : ?cmp:('a -> 'a -> int) -> 'a t -> 'a t

Sort the iterator and remove duplicates. Eager, same as sort

val sorted : ?cmp:('a -> 'a -> int) -> 'a t -> bool

Checks whether the iterator is sorted. Eager, same as sort.

since 0.9

val group_succ_by : ?eq:('a -> 'a -> bool) -> 'a t -> 'a list t

Group equal consecutive elements. Linear time. Formerly synonym to group. note: Order of items in each list is unspecified.

since 0.6

val group_by : ?hash:('a -> int) -> ?eq:('a -> 'a -> bool) -> 'a t -> 'a list t

Group equal elements, disregarding their order of appearance. precondition: for any x and y, if eq x y then hash x=hash y must hold. note: Order of items in each list is unspecified.

since 0.6

val count : ?hash:('a -> int) -> ?eq:('a -> 'a -> bool) -> 'a t -> ('a * int) t

Map each distinct element to its number of occurrences in the whole seq. Similar to group_by seq |> map (fun l->List.hd l, List.length l) precondition: for any x and y, if eq x y then hash x=hash y must hold.

since 0.10

val uniq : ?eq:('a -> 'a -> bool) -> 'a t -> 'a t

Remove consecutive duplicate elements. Basically this is like fun seq -> map List.hd (group seq).

val product : 'a t -> 'b t -> ('a * 'b) t

Cartesian product of iterators. When calling product a b, the caller MUST ensure that b can be traversed as many times as required (several times), possibly by calling persistent on it beforehand.

val diagonal_l : 'a list -> ('a * 'a) t

All pairs of distinct positions of the list. diagonal l will return the iterator of all List.nth i l, List.nth j l if i < j.

since 0.9

val diagonal : 'a t -> ('a * 'a) t

All pairs of distinct positions of the iterator. Iterates only once on the iterator, which must be finite.

since 0.9

val join : join_row:('a -> 'b -> 'c option) -> 'a t -> 'b t -> 'c t

join ~join_row a b combines every element of a with every element of b using join_row. If join_row returns None, then the two elements do not combine. Assume that b allows for multiple iterations.

val join_by : 
  ?eq:'key equal ->
  ?hash:'key hash ->
  ('a -> 'key) ->
  ('b -> 'key) ->
  merge:('key -> 'a -> 'b -> 'c option) ->
  'a t ->
  'b t ->
  'c t

join key1 key2 ~merge is a binary operation that takes two iterators a and b, projects their elements resp. with key1 and key2, and combine values (x,y) from (a,b) with the same key using merge. If merge returns None, the combination of values is discarded. precondition: for any x and y, if eq x y then hash x=hash y must hold.

since 0.10

val join_all_by : 
  ?eq:'key equal ->
  ?hash:'key hash ->
  ('a -> 'key) ->
  ('b -> 'key) ->
  merge:('key -> 'a list -> 'b list -> 'c option) ->
  'a t ->
  'b t ->
  'c t

join_all_by key1 key2 ~merge is a binary operation that takes two iterators a and b, projects their elements resp. with key1 and key2, and, for each key k occurring in at least one of them:

compute the list l1 of elements of a that map to k
compute the list l2 of elements of b that map to k
call merge k l1 l2. If merge returns None, the combination of values is discarded, otherwise it returns Some c and c is inserted in the result.

since 0.10

val group_join_by : 
  ?eq:'a equal ->
  ?hash:'a hash ->
  ('b -> 'a) ->
  'a t ->
  'b t ->
  ('a * 'b list) t

group_join_by key2 associates to every element x of the first iterator, all the elements y of the second iterator such that eq x (key y). Elements of the first iterators without corresponding values in the second one are mapped to [] precondition: for any x and y, if eq x y then hash x=hash y must hold.

since 0.10

Set-like

val inter : ?eq:'a equal -> ?hash:'a hash -> 'a t -> 'a t -> 'a t

Intersection of two collections. Each element will occur at most once in the result. Eager. precondition: for any x and y, if eq x y then hash x=hash y must hold.

since 0.10

val union : ?eq:'a equal -> ?hash:'a hash -> 'a t -> 'a t -> 'a t

Union of two collections. Each element will occur at most once in the result. Eager. precondition: for any x and y, if eq x y then hash x=hash y must hold.

since 0.10

val diff : ?eq:'a equal -> ?hash:'a hash -> 'a t -> 'a t -> 'a t

Set difference. Eager.

since 0.10

val subset : ?eq:'a equal -> ?hash:'a hash -> 'a t -> 'a t -> bool

subset a b returns true if all elements of a belong to b. Eager. precondition: for any x and y, if eq x y then hash x=hash y must hold.

since 0.10

Arithmetic

val max : ?lt:('a -> 'a -> bool) -> 'a t -> 'a option

Max element of the iterator, using the given comparison function.

returns
None if the iterator is empty, Some m where m is the maximal element otherwise

val max_exn : ?lt:('a -> 'a -> bool) -> 'a t -> 'a

Unsafe version of max

raises Not_found
if the iterator is empty

since 0.10

val min : ?lt:('a -> 'a -> bool) -> 'a t -> 'a option

Min element of the iterator, using the given comparison function. see max for more details.

val min_exn : ?lt:('a -> 'a -> bool) -> 'a t -> 'a

Unsafe version of min

raises Not_found
if the iterator is empty

since 0.10

val sum : int t -> int

Sum of elements

since 0.11

val sumf : float t -> float

Sum of elements, using Kahan summation

since 0.11

List-like

val head : 'a t -> 'a option

First element, if any, otherwise None

since 0.5.1

val head_exn : 'a t -> 'a

First element, if any, fails

raises Invalid_argument
if the iterator is empty

since 0.5.1

val take : int -> 'a t -> 'a t

Take at most n elements from the iterator. Works on infinite iterators.

val take_while : ('a -> bool) -> 'a t -> 'a t

Take elements while they satisfy the predicate, then stops iterating. Will work on an infinite iterator s if the predicate is false for at least one element of s.

val map_while : 
  ('a -> [ `Yield of 'b | `Return of 'b | `Stop ]) ->
  'a t ->
  'b t

Maps over elements of the iterator, stopping early if the mapped function returns `Stop or `Return x. At each iteration:

If f returns `Yield y, y is added to the sequence and the iteration continues.
If f returns `Stop, nothing is added to the sequence and the iteration stops.
If f returns `Return y, y is added to the sequence and the iteration stops.

since 1.8

val fold_while : ('a -> 'b -> 'a * [ `Stop | `Continue ]) -> 'a -> 'b t -> 'a

Folds over elements of the iterator, stopping early if the accumulator returns ('a, `Stop)

since 0.5.5

val drop : int -> 'a t -> 'a t

Drop the n first elements of the iterator. Lazy.

val drop_while : ('a -> bool) -> 'a t -> 'a t

Predicate version of drop

val rev : 'a t -> 'a t

Reverse the iterator. O(n) memory and time, needs the iterator to be finite. The result is persistent and does not depend on the input being repeatable.

val zip_i : 'a t -> (int * 'a) t

Zip elements of the iterator with their index in the iterator.

since 1.0 Changed type to just give an iterator of pairs

Pair iterators

val fold2 : ('c -> 'a -> 'b -> 'c) -> 'c -> ('a * 'b) t -> 'c

val iter2 : ('a -> 'b -> unit) -> ('a * 'b) t -> unit

val map2 : ('a -> 'b -> 'c) -> ('a * 'b) t -> 'c t

val map2_2 : ('a -> 'b -> 'c) -> ('a -> 'b -> 'd) -> ('a * 'b) t -> ('c * 'd) t

map2_2 f g seq2 maps each x, y of seq2 into f x y, g x y

Data structures converters

val to_list : 'a t -> 'a list

Convert the iterator into a list. Preserves order of elements. This function is tail-recursive, but consumes 2*n memory. If order doesn't matter to you, consider to_rev_list.

val to_rev_list : 'a t -> 'a list

Get the list of the reversed iterator (more efficient than to_list)

val of_list : 'a list -> 'a t

val on_list : ('a t -> 'b t) -> 'a list -> 'b list

on_list f l is equivalent to to_list @@ f @@ of_list l.

since 0.5.2

val pair_with_idx : 'a t -> (int * 'a) t

Similar to zip_i but returns a normal iterator of tuples

since 0.11

val to_opt : 'a t -> 'a option

Alias to head

since 0.5.1

val to_array : 'a t -> 'a array

Convert to an array. Currently not very efficient because an intermediate list is used.

val of_array : 'a array -> 'a t

val of_array_i : 'a array -> (int * 'a) t

Elements of the array, with their index

val array_slice : 'a array -> int -> int -> 'a t

array_slice a i j Iterator of elements whose indexes range from i to j

val of_opt : 'a option -> 'a t

Iterate on 0 or 1 values.

since 0.5.1

val of_seq : 'a Seq.t -> 'a t

Iterator of elements of a Seq.t.

since 1.5

val to_seq_persistent : 'a t -> 'a Seq.t

Convert to a Seq. Linear in memory and time (a copy is made in memory). This does not work on infinite iterators.

since 1.5

val to_stack : 'a Stack.t -> 'a t -> unit

Push elements of the iterator on the stack

val of_stack : 'a Stack.t -> 'a t

Iterator of elements of the stack (same order as Stack.iter)

val to_queue : 'a Queue.t -> 'a t -> unit

Push elements of the iterator into the queue

val of_queue : 'a Queue.t -> 'a t

Iterator of elements contained in the queue, FIFO order

val hashtbl_add : ('a, 'b) Hashtbl.t -> ('a * 'b) t -> unit

Add elements of the iterator to the hashtable, with Hashtbl.add

val hashtbl_replace : ('a, 'b) Hashtbl.t -> ('a * 'b) t -> unit

Add elements of the iterator to the hashtable, with Hashtbl.replace (erases conflicting bindings)

val to_hashtbl : ('a * 'b) t -> ('a, 'b) Hashtbl.t

Build a hashtable from an iterator of key/value pairs

val of_hashtbl : ('a, 'b) Hashtbl.t -> ('a * 'b) t

Iterator of key/value pairs from the hashtable

val hashtbl_keys : ('a, 'b) Hashtbl.t -> 'a t

val hashtbl_values : ('a, 'b) Hashtbl.t -> 'b t

val of_str : string -> char t

val to_str : char t -> string

val concat_str : string t -> string

Concatenate strings together, eagerly. Also see intersperse to add a separator.

since 0.5

exception OneShotSequence

Raised when the user tries to iterate several times on a transient iterator

val of_in_channel : in_channel -> char t

Iterates on characters of the input (can block when one iterates over the iterator). If you need to iterate several times on this iterator, use persistent.

raises OneShotIterator
when used more than once.

val to_buffer : char t -> Buffer.t -> unit

Copy content of the iterator into the buffer

val int_range : start:int -> stop:int -> int t

Iterator on integers in start...stop by steps 1. Also see (--) for an infix version.

val int_range_dec : start:int -> stop:int -> int t

Iterator on decreasing integers in stop...start by steps -1. See (--^) for an infix version

val int_range_by : step:int -> int -> int -> int t

int_range_by ~step i j is the range starting at i, including j, where the difference between successive elements is step. use a negative step for a decreasing iterator.

raises Invalid_argument
if step=0

val bools : bool t

Iterates on true and false

since 0.7

val of_set : (module Set.S with type elt = 'a and type t = 'b) -> 'b -> 'a t

Convert the given set to an iterator. The set module must be provided.

val to_set : (module Set.S with type elt = 'a and type t = 'b) -> 'a t -> 'b

Convert the iterator to a set, given the proper set module

type 'a gen = unit -> 'a option

val of_gen : 'a gen -> 'a t

Traverse eagerly the generator and build an iterator from it

val of_gen_once : 'a gen -> 'a t

One shot iterator using this generator. It must not be traversed twice.

since 1.5

val to_gen : 'a t -> 'a gen

Make the iterator persistent (O(n)) and then iterate on it. Eager.

Sets

module Set : sig ... end

Maps

module Map : sig ... end

Random iterators

Generating

val random_int : int -> int t

Infinite iterator of random integers between 0 and the given higher bound (see Random.int)

val random_bool : bool t

Infinite iterator of random bool values

val random_float : float -> float t

val random_array : 'a array -> 'a t

Iterator of choices of an element in the array

val random_list : 'a list -> 'a t

Infinite iterator of random elements of the list. Basically the same as random_array.

val shuffle : 'a t -> 'a t

shuffle seq returns a perfect shuffle of seq. Uses O(length seq) memory and time. Eager.

since 0.7

val shuffle_buffer : int -> 'a t -> 'a t

shuffle_buffer n seq returns an iterator of element of seq in random order. The shuffling is *not* uniform. Uses O(n) memory.

The first n elements of the iterator are consumed immediately. The rest is consumed lazily.

since 0.7

Sampling

val sample : int -> 'a t -> 'a array

sample n seq returns k samples of seq, with uniform probability. It will consume the iterator and use O(n) memory.

It returns an array of size min (length seq) n.

since 0.7

Seeding

Random iterators use Random.int, Random.float, Random.bool, etc., under the hood, so they will respect seeding of the random generator in the usual way. I.e., if you do not initialize the random generator with one of Random.init, Random.full_init, or Random.self_init before calling these functions, they will yield the same values across seperate invocations of your program.

Example:

(* Ensure a fresh random seed each time the program is executed. *)
let () = Random.self_init ()

(* Generate random values. *)
let l = Iter.random_int 1000 |> Iter.take 3 |> Iter.to_list

Infix functions

module Infix : sig ... end

include module type of Infix

val (--) : int -> int -> int t

a -- b is the range of integers from a to b, both included, in increasing order. It will therefore be empty if a > b.

val (--^) : int -> int -> int t

a --^ b is the range of integers from b to a, both included, in decreasing order (starts from a). It will therefore be empty if a < b.

val (>>=) : 'a t -> ('a -> 'b t) -> 'b t

Monadic bind (infix version of flat_map

since 0.5

val (>|=) : 'a t -> ('a -> 'b) -> 'b t

Infix version of map

since 0.5

val (<*>) : ('a -> 'b) t -> 'a t -> 'b t

Applicative operator (product+application)

since 0.5

val (<+>) : 'a t -> 'a t -> 'a t

Concatenation of iterators

since 0.5

val let+ : 'a t -> ('a -> 'b) -> 'b t

Alias for map

since 1.7

val and+ : 'a t -> 'b t -> ('a * 'b) t

Alias for product

since 1.7

val let* : 'a t -> ('a -> 'b t) -> 'b t

Alias for flat_map

since 1.7

val and* : 'a t -> 'b t -> ('a * 'b) t