sequence 1.1 · 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 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 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, 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 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 t object is also repeatable. For one-time iter functions such as iteration on a file descriptor or a Stream, the 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

NOTE Type ('a, 'b) t2 = ('a -> 'b -> unit) -> unit has been removed and subsumed by ('a * 'b) t

since 1.0

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 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 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 sequence 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 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 take and 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 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 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 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?

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 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 append_l : 'a t list -> 'a t

Append sequences. Iterating on the result is like iterating on the each sequence of the list in order.

since 0.11

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

Concatenate a sequence of sequences into one sequence.

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 sequence, 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-sequence in l. Assumes the sub-sequences 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 sequence

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.result t -> 'a t

keep_ok l retains only elements of the form Ok x.

since 1.0

val keep_error : (_, 'e) Result.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 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 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 (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 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 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.

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. precondition: for any x and y, if eq x y then hash x=hash y must hold.

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 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 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 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. 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 sequences 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 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 [] precondition: for any x and y, if eq x y then hash x=hash y must hold.

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. 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

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 max

raises Not_found
if the sequence is empty

since 0.10

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

Min element of the sequence, 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 sequence 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

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 sequence is empty

since 0.5.1

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 * [ `Stop | `Continue ]) -> '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 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.

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

Zip elements of the sequence with their index in the sequence. Changed type

since 1.0 to just give a sequence of pairs

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

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 to_rev_list.

val to_rev_list : 'a t -> 'a list

Get the list of the reversed sequence (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 sequence 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 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 of_hashtbl : ('a, 'b) Hashtbl.t -> ('a * 'b) t

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 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 sequence). If you need to iterate several times on this sequence, use 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 -> [ `Nil | `Cons of 'a * 'a klist ]

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 Random.int)

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 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

Sampling

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 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 sequences

since 0.5

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

since 0.5.1

module IO : sig ... end

package sequence