Module Sequence

module Sequence: sig .. end

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 a sequence can be iterated on as many times as needed; this choice allows for high performance of many combinators. However, for transient iterators, the Sequence.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 sequences (e.g. group). The transformation is computed on the fly every time one iterates over the resulting sequence. If a transformation performs heavy computation, Sequence.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 on a sequence, one gets a new sequence, but nothing else happens until this new sequence is used (by folding or iterating on it).

If a sequence 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 Sequence.t object is also repeatable. For one-time iter functions such as iteration on a file descriptor or a Stream, the Sequence.persistent function can be used to iterate and store elements in a memory structure; the result is a sequence that iterates on the elements of this memory structure, cheaply and repeatably.

type 'a t = ('a -> unit) -> unit 
A sequence of values of type 'a. If you give it a function 'a -> unit it will be applied to every element of the sequence successively.
type 'a sequence = 'a t 
type ('a, 'b) t2 = ('a -> 'b -> unit) -> unit 
Sequence of pairs of values of type 'a and 'b.
type 'a equal = 'a -> 'a -> bool 
type 'a hash = 'a -> int 

Build a sequence

val from_iter : (('a -> unit) -> unit) -> 'a t
Build a sequence from a iter function
val from_fun : (unit -> 'a option) -> 'a t
Call the function repeatedly until it returns None. This sequence is transient, use Sequence.persistent if needed!
val empty : 'a t
Empty sequence. It contains no element.
val singleton : 'a -> 'a t
Singleton sequence, with exactly one element.
val doubleton : 'a -> 'a -> 'a t
Sequence with exactly two elements
val init : (int -> 'a) -> 'a t
init f is the infinite sequence 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
val snoc : 'a t -> 'a -> 'a t
Same as Sequence.cons but yields the element after iterating on l
val return : 'a -> 'a t
Synonym to Sequence.singleton
val pure : 'a -> 'a t
Synonym to Sequence.singleton
val repeat : 'a -> 'a t
Infinite sequence of the same element. You may want to look at Sequence.take and the likes if you iterate on it.
val iterate : ('a -> 'a) -> 'a -> 'a t
iterate f x is the infinite sequence x, f(x), f(f(x)), ...
val forever : (unit -> 'b) -> 'b t
Sequence that calls the given function to produce elements. The sequence may be transient (depending on the function), and definitely is infinite. You may want to use Sequence.take and Sequence.persistent.
val cycle : 'a t -> 'a t
Cycle forever through the given sequence. Assume the given sequence can be traversed any amount of times (not transient). This yields an infinite sequence, you should use something like Sequence.take not to loop forever.

Consume a sequence

val iter : ('a -> unit) -> 'a t -> unit
Consume the sequence, 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 sequence
val fold : ('a -> 'b -> 'a) -> 'a -> 'b t -> 'a
Fold over elements of the sequence, consuming it
val foldi : ('a -> int -> 'b -> 'a) -> 'a -> 'b t -> 'a
Fold over elements of the sequence and their index, consuming it
val fold_map : ('acc -> 'a -> 'acc * 'b) -> 'acc -> 'a t -> 'b t
fold_map f acc l is like, but it carries some state as in Sequence.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 Sequence.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 sequence into other elements, lazily
val mapi : (int -> 'a -> 'b) -> 'a t -> 'b t
Map objects, along with their index in the sequence
val map_by_2 : ('a -> 'a -> 'a) -> 'a t -> 'a t
Map objects two by two. lazily. The last element is kept in the sequence 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 sequence?
Since 0.5
eq : the equality predicate to use (default (=))
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 Sequence.find
Since 0.10
val findi : (int -> 'a -> 'b option) -> 'a t -> 'b option
Indexed version of Sequence.find
Since 0.9
val find_mapi : (int -> 'a -> 'b option) -> 'a t -> 'b option
Alias to Sequence.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 Sequence.find_pred
Since 0.9
Raises Not_found if no such element is found
val length : 'a t -> int
How long is the sequence? Forces the sequence.
val is_empty : 'a t -> bool
Is the sequence empty? Forces the sequence.

Transform a sequence

val filter : ('a -> bool) -> 'a t -> 'a t
Filter on elements of the sequence
val append : 'a t -> 'a t -> 'a t
Append two sequences. Iterating on the result is like iterating on the first, then on the second.
val concat : 'a t t -> 'a t
Concatenate a sequence of sequences into one sequence.
val flatten : 'a t t -> 'a t
Alias for Sequence.concat
val flat_map : ('a -> 'b t) -> 'a t -> 'b t
Monadic bind. Intuitively, it applies the function to every element of the initial sequence, and calls Sequence.concat. Formerly flatMap
Since 0.5
val flat_map_l : ('a -> 'b list) -> 'a t -> 'b t
Convenience function combining Sequence.flat_map and Sequence.of_list
Since 0.9
val filter_map : ('a -> 'b option) -> 'a t -> 'b t
Map and only keep non-None elements Formerly fmap
Since 0.5
val intersperse : 'a -> 'a t -> 'a t
Insert the single element between every element of the sequence


val persistent : 'a t -> 'a t
Iterate on the sequence, storing elements in an efficient internal structure.. The resulting sequence can be iterated on as many times as needed. Note: calling persistent on an already persistent sequence will still make a new copy of the sequence!
val persistent_lazy : 'a t -> 'a t
Lazy version of Sequence.persistent. When calling persistent_lazy s, a new sequence 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 (Sequence.take, etc.) then s' will not be memorized, and the next call to s' will traverse s again.


val sort : ?cmp:('a -> 'a -> int) -> 'a t -> 'a t
Sort the sequence. Eager, O(n) ram and O(n ln(n)) time. It iterates on elements of the argument sequence immediately, before it sorts them.
val sort_uniq : ?cmp:('a -> 'a -> int) -> 'a t -> 'a t
Sort the sequence and remove duplicates. Eager, same as sort
val sorted : ?cmp:('a -> 'a -> int) -> 'a t -> bool
Checks whether the sequence is sorted. Eager, same as Sequence.sort.
Since 0.9
val group_succ_by : ?eq:('a -> 'a -> bool) -> 'a t -> 'a list t
Group equal consecutive elements. Formerly synonym to group.
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. The result sequence is traversable as many times as required.
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)
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 the sequences. When calling product a b, the caller MUST ensure that b can be traversed as many times as required (several times), possibly by calling Sequence.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 sequence 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 sequence. Iterates only once on the sequence, which must be finite.
Since 0.9
val product2 : 'a t -> 'b t -> ('a, 'b) t2
Binary version of Sequence.product. Same requirements.
Since 0.5
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 sequences 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.
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 sequences a and b, projects their elements resp. with key1 and key2, and, for each key k occurring in at least one of them:
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 sequence, all the elements y of the second sequence such that eq x (key y). Elements of the first sequences without corresponding values in the second one are mapped to []
Since 0.10
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.
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.
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.
Since 0.10
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
Sequence of intermediate results
val max : ?lt:('a -> 'a -> bool) -> 'a t -> 'a option
Max element of the sequence, using the given comparison function.
Returns None if the sequence is empty, Some m where m is the maximal element otherwise
val max_exn : ?lt:('a -> 'a -> bool) -> 'a t -> 'a
Unsafe version of Sequence.max
Since 0.10
Raises Not_found if the sequence is empty
val min : ?lt:('a -> 'a -> bool) -> 'a t -> 'a option
Min element of the sequence, using the given comparison function. see Sequence.max for more details.
val min_exn : ?lt:('a -> 'a -> bool) -> 'a t -> 'a
Unsafe version of Sequence.min
Since 0.10
Raises Not_found if the sequence is empty
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
Since 0.5.1
Raises Invalid_argument if the sequence is empty
val take : int -> 'a t -> 'a t
Take at most n elements from the sequence. Works on infinite sequences.
val take_while : ('a -> bool) -> 'a t -> 'a t
Take elements while they satisfy the predicate, then stops iterating. Will work on an infinite sequence s if the predicate is false for at least one element of s.
val fold_while : ('a -> 'b -> 'a * [ `Continue | `Stop ]) -> 'a -> 'b t -> 'a
Folds over elements of the sequence, 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 sequence. Lazy.
val drop_while : ('a -> bool) -> 'a t -> 'a t
Predicate version of Sequence.drop
val rev : 'a t -> 'a t
Reverse the sequence. O(n) memory and time, needs the sequence to be finite. The result is persistent and does not depend on the input being repeatable.

Binary sequences

val empty2 : ('a, 'b) t2
val is_empty2 : ('a, 'b) t2 -> bool
val length2 : ('a, 'b) t2 -> int
val zip : ('a, 'b) t2 -> ('a * 'b) t
val unzip : ('a * 'b) t -> ('a, 'b) t2
val zip_i : 'a t -> (int, 'a) t2
Zip elements of the sequence with their index in the sequence
val fold2 : ('c -> 'a -> 'b -> 'c) -> 'c -> ('a, 'b) t2 -> 'c
val iter2 : ('a -> 'b -> unit) -> ('a, 'b) t2 -> unit
val map2 : ('a -> 'b -> 'c) -> ('a, 'b) t2 -> 'c t
val map2_2 : ('a -> 'b -> 'c) ->
('a -> 'b -> 'd) -> ('a, 'b) t2 -> ('c, 'd) t2
map2_2 f g seq2 maps each x, y of seq2 into f x y, g x y

Basic data structures converters

val to_list : 'a t -> 'a list
Convert the sequence 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 Sequence.to_rev_list.
val to_rev_list : 'a t -> 'a list
Get the list of the reversed sequence (more efficient than Sequence.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 to_opt : 'a t -> 'a option
Alias to Sequence.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 of_array2 : 'a array -> (int, 'a) t2
val array_slice : 'a array -> int -> int -> 'a t
array_slice a i j Sequence 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_stream : 'a Stream.t -> 'a t
Sequence of elements of a stream (usable only once)
val to_stream : 'a t -> 'a Stream.t
Convert to a stream. linear in memory and time (a copy is made in memory)
val to_stack : 'a Stack.t -> 'a t -> unit
Push elements of the sequence on the stack
val of_stack : 'a Stack.t -> 'a t
Sequence of elements of the stack (same order as Stack.iter)
val to_queue : 'a Queue.t -> 'a t -> unit
Push elements of the sequence into the queue
val of_queue : 'a Queue.t -> 'a t
Sequence of elements contained in the queue, FIFO order
val hashtbl_add : ('a, 'b) Hashtbl.t -> ('a * 'b) t -> unit
Add elements of the sequence to the hashtable, with Hashtbl.add
val hashtbl_replace : ('a, 'b) Hashtbl.t -> ('a * 'b) t -> unit
Add elements of the sequence to the hashtable, with Hashtbl.replace (erases conflicting bindings)
val to_hashtbl : ('a * 'b) t -> ('a, 'b) Hashtbl.t
Build a hashtable from a sequence of key/value pairs
val to_hashtbl2 : ('a, 'b) t2 -> ('a, 'b) Hashtbl.t
Build a hashtable from a sequence of key/value pairs
val of_hashtbl : ('a, 'b) Hashtbl.t -> ('a * 'b) t
Sequence of key/value pairs from the hashtable
val of_hashtbl2 : ('a, 'b) Hashtbl.t -> ('a, 'b) t2
Sequence 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 Sequence.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 : Pervasives.in_channel -> char t
Iterates on characters of the input (can block when one iterates over the sequence). If you need to iterate several times on this sequence, use Sequence.persistent.
Raises OneShotSequence when used more than once.
val to_buffer : char t -> Buffer.t -> unit
Copy content of the sequence 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 sequence.
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 a sequence. 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 sequence to a set, given the proper set module
type 'a gen = unit -> 'a option 
type 'a klist = unit -> [ `Cons of 'a * 'a klist | `Nil ] 
val of_gen : 'a gen -> 'a t
Traverse eagerly the generator and build a sequence from it
val to_gen : 'a t -> 'a gen
Make the sequence persistent (O(n)) and then iterate on it. Eager.
val of_klist : 'a klist -> 'a t
Iterate on the lazy list
val to_klist : 'a t -> 'a klist
Make the sequence persistent and then iterate on it. Eager.

Functorial conversions between sets and sequences

module Set: sig .. end

Conversion between maps and sequences.

module Map: sig .. end

Infinite sequences of random values

val random_int : int -> int t
Infinite sequence of random integers between 0 and the given higher bound (see
val random_bool : bool t
Infinite sequence of random bool values
val random_float : float -> float t
val random_array : 'a array -> 'a t
Sequence of choices of an element in the array
val random_list : 'a list -> 'a t
Infinite sequence of random elements of the list. Basically the same as Sequence.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 a sequence of element of seq in random order. The shuffling is *not* uniform. Uses O(n) memory.

The first n elements of the sequence are consumed immediately. The rest is consumed lazily.
Since 0.7


val sample : int -> 'a t -> 'a array
sample n seq returns k samples of seq, with uniform probability. It will consume the sequence and use O(n) memory.

It returns an array of size min (length seq) n.
Since 0.7

Infix functions

module Infix: sig .. end
include Sequence.Infix

Pretty printing of sequences

val pp_seq : ?sep:string ->
(Format.formatter -> 'a -> unit) -> Format.formatter -> 'a t -> unit
Pretty print a sequence of 'a, using the given pretty printer to print each elements. An optional separator string can be provided.
val pp_buf : ?sep:string -> (Buffer.t -> 'a -> unit) -> Buffer.t -> 'a t -> unit
Print into a buffer
val to_string : ?sep:string -> ('a -> string) -> 'a t -> string
Print into a string

Basic IO

Very basic interface to manipulate files as sequence of chunks/lines. The sequences take care of opening and closing files properly; every time one iterates over a sequence, the file is opened/closed again.

Example: copy a file "a" into file "b", removing blank lines:

      Sequence.(IO.lines_of "a" |> filter (fun l-> l<> "") |> IO.write_lines "b");;

By chunks of 4096 bytes:

      Sequence.IO.(chunks_of ~size:4096 "a" |> write_to "b");;

Read the lines of a file into a list:

      Sequence.IO.lines "a" |> Sequence.to_list

module IO: sig .. end