#### oseq

Simple list of suspensions, as a composable lazy iterator that behaves like a value
IN THIS PACKAGE
Module

## OSeq: Functional Iterators

`type 'a t = unit -> 'a node`
`and 'a node = 'a Seq.node = `
 `| Nil` `| Cons of 'a * 'a t`
`type 'a seq = 'a t`
`type 'a sequence = ( 'a -> unit ) -> unit`
`type 'a gen = unit -> 'a option`
`type 'a equal = 'a -> 'a -> bool`
`type 'a ord = 'a -> 'a -> int`
`type 'a printer = Format.formatter -> 'a -> unit`
`val empty : 'a t`

Empty iterator, with no elements

`val return : 'a -> 'a t`

One-element iterator

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

Repeat same element endlessly

`val cycle : 'a t -> 'a t`

Cycle through the iterator infinitely. The iterator shouldn't be empty.

``````# OSeq.(cycle (1--3) |> take 10 |> to_list);;
- : int list = [1; 2; 3; 1; 2; 3; 1; 2; 3; 1]``````
`val iterate : 'a -> ( 'a -> 'a ) -> 'a t`

`iterate x f` is `[x; f x; f (f x); f (f (f x)); ...]`.

``````# OSeq.(iterate 0 succ |> take 10 |> to_list);;
- : int list = [0; 1; 2; 3; 4; 5; 6; 7; 8; 9]``````
`val unfold : ( 'b -> ('a * 'b) option ) -> 'b -> 'a t`

Dual of `fold`, with a deconstructing operation. It keeps on unfolding the `'b` value into a new `'b`, and a `'a` which is yielded, until `None` is returned.

``````# OSeq.(unfold (fun x -> if x<5 then Some (string_of_int x, x+1) else None) 0 |> to_list);;
- : string list = ["0"; "1"; "2"; "3"; "4"]``````
`val repeatedly : ( unit -> 'a ) -> 'a t`

Call the same function an infinite number of times (useful for instance if the function is a random iterator).

`val init : ?n:int -> ( int -> 'a ) -> 'a t`

Calls the function, starting from 0, on increasing indices. If `n` is provided and is a positive int, iteration will stop at the limit (excluded). For instance `init ~n:4 (fun x->x)` will yield 0, 1, 2, and 3.

### Basic combinators

`val is_empty : _ t -> bool`

Check whether the iterator is empty. Pops an element, if any

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

Fold on the iterator, tail-recursively.

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

Fold on the iterator, tail-recursively.

• since 0.3
`val reduce : ( 'a -> 'a -> 'a ) -> 'a t -> 'a`

Fold on non-empty iterators.

• raises Invalid_argument

on an empty iterator

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

Like `fold`, but keeping successive values of the accumulator.

``````# OSeq.(scan (+) 0 (1--5) |> to_list);;
- : int list = [0; 1; 3; 6; 10; 15]``````
`val unfold_scan : ( 'b -> 'a -> 'b * 'c ) -> 'b -> 'a t -> 'c t`

A mix of `unfold` and `scan`. The current state is combined with the current element to produce a new state, and an output value of type 'c.

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

Iterate on the iterator .

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

Iterate on elements with their index in the iterator, from 0.

`val length : _ t -> int`

Length of an iterator (linear time).

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

Lazy map. No iteration is performed now, the function will be called when the result is traversed.

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

Lazy map with indexing starting from 0. No iteration is performed now, the function will be called when the result is traversed.

`val app : ( 'a -> 'b ) t -> 'a t -> 'b t`

Applicative

`val fold_map : ( 'b -> 'a -> 'b ) -> 'b -> 'a t -> 'b t`

Lazy fold and map. No iteration is performed now, the function will be called when the result is traversed. The result is an iterator over the successive states of the fold. The final accumulator is discarded. Unlike `scan`, fold_map does not return the first accumulator.

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

Append the two iterators; the result contains the elements of the first, then the elements of the second iterator.

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

Flatten the iterator of iterators

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

Monadic bind; each element is transformed to a sub-iterator which is then iterated on, before the next element is processed, and so on.

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

Is the given element, member of the iterator?

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

Take at most n elements

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

Drop n elements

`val nth : int -> 'a t -> 'a`

n-th element, or Not_found

• raises Not_found

if the iterator contains less than `n` arguments

`val take_nth : int -> 'a t -> 'a t`

`take_nth n g` returns every element of `g` whose index is a multiple of `n`. For instance `take_nth 2 (1--10) |> to_list` will return `[1;3;5;7;9]`

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

Filter out elements that do not satisfy the predicate.

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

Take elements while they satisfy the predicate.

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

Fold elements until (`'a, `Stop`) is indicated by the accumulator.

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

Drop elements while they satisfy the predicate.

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

Maps some elements to 'b, drop the other ones

`val zip_index : 'a t -> (int * 'a) t`

Zip elements with their index in the iterator

`val unzip : ('a * 'b) t -> 'a t * 'b t`

Unzip into two iterators, splitting each pair

`val partition : ( 'a -> bool ) -> 'a t -> 'a t * 'a t`

`partition p l` returns the elements that satisfy `p`, and the elements that do not satisfy `p`

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

Is the predicate true for all elements?

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

Is the predicate true for at least one element?

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

Minimum element, according to the given comparison function.

• raises Invalid_argument

if the iterator is empty

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

Maximum element, see `min`

• raises Invalid_argument

if the iterator is empty

`val equal : eq:( 'a -> 'a -> bool ) -> 'a t -> 'a t -> bool`

Equality of iterators.

`val compare : cmp:( 'a -> 'a -> int ) -> 'a t -> 'a t -> int`

Lexicographic comparison of iterators. If a iterator is a prefix of the other one, it is considered smaller.

`val find : ( 'a -> bool ) -> 'a t -> 'a option`

`find p e` returns the first element of `e` to satisfy `p`, or None.

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

`find_map f e` returns the result of `f` on the first element of `e` for which it returns `Some _`, or `None` otherwise.

• since 0.3
`val sum : int t -> int`

Sum of all elements

### Multiple iterators

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

Map on the two iterators. Stops once one of them is exhausted.

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

Iterate on the two iterators. Stops once one of them is exhausted.

`val fold2 : ( 'acc -> 'a -> 'b -> 'acc ) -> 'acc -> 'a t -> 'b t -> 'acc`

Fold the common prefix of the two iterators

`val for_all2 : ( 'a -> 'b -> bool ) -> 'a t -> 'b t -> bool`

Succeeds if all pairs of elements satisfy the predicate. Ignores elements of an iterator if the other runs dry.

`val exists2 : ( 'a -> 'b -> bool ) -> 'a t -> 'b t -> bool`

Succeeds if some pair of elements satisfy the predicate. Ignores elements of an iterator if the other runs dry.

`val zip_with : ( 'a -> 'b -> 'c ) -> 'a t -> 'b t -> 'c t`

Combine common part of the gens (stops when one is exhausted)

`val zip : 'a t -> 'b t -> ('a * 'b) t`

Zip together the common part of the gens

### Complex combinators

`val merge : 'a t t -> 'a t`

Pick elements fairly in each sub-iterator. The merge of gens `e1, e2, ... ` picks elements in `e1`, `e2`, in `e3`, `e1`, `e2` .... Once an iterator is empty, it is skipped; when they are all empty, and none remains in the input, their merge is also empty. For instance, `merge [1;3;5] [2;4;6]` will be, in disorder, `1;2;3;4;5;6`.

`val intersection : cmp:( 'a -> 'a -> int ) -> 'a t -> 'a t -> 'a t`

Intersection of two sorted iterators. Only elements that occur in both inputs appear in the output

`val sorted_merge : cmp:( 'a -> 'a -> int ) -> 'a t -> 'a t -> 'a t`

Merge two sorted iterators into a sorted iterator

`val round_robin : ?n:int -> 'a t -> 'a t list`

Split the iterator into `n` iterators in a fair way. Elements with `index = k mod n` with go to the k-th iterator. `n` default value is 2.

`val interleave : 'a t -> 'a t -> 'a t`

`interleave a b` yields an element of `a`, then an element of `b`, and so on. When a iterator is exhausted, this behaves like the other iterator.

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

Put the separator element between all elements of the given iterator

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

Cartesian product, in no predictable order. Works even if some of the arguments are infinite.

`val product3 : 'a t -> 'b t -> 'c t -> ('a * 'b * 'c) t`

Cartesian product of three iterators, see product.

• since 0.2
`val product4 : 'a t -> 'b t -> 'c t -> 'd t -> ('a * 'b * 'c * 'd) t`

Cartesian product of four iterators, see product.

• since 0.2
```val product5 : 'a t -> 'b t -> 'c t -> 'd t -> 'e t -> ('a * 'b * 'c * 'd * 'e) t```

Cartesian product of five iterators, see product.

• since 0.2
```val product6 : 'a t -> 'b t -> 'c t -> 'd t -> 'e t -> 'f t -> ('a * 'b * 'c * 'd * 'e * 'f) t```

Cartesian product of six iterators, see product.

• since 0.2
```val product7 : 'a t -> 'b t -> 'c t -> 'd t -> 'e t -> 'f t -> 'g t -> ('a * 'b * 'c * 'd * 'e * 'f * 'g) t```

Cartesian product of seven iterators, see product.

• since 0.2
`val cartesian_product : 'a t t -> 'a list t`

Produce the cartesian product of this list of lists, by returning all the ways of picking one element per sublist. NOTE the order of the returned list is unspecified. For example:

``````# cartesian_product [[1;2];[3];[4;5;6]] |> sort =
[[1;3;4];[1;3;5];[1;3;6];[2;3;4];[2;3;5];[2;3;6]];;
# cartesian_product [[1;2];[];[4;5;6]] = [];;
# cartesian_product [[1;2];[3];[4];[5];[6]] |> sort =
[[1;3;4;5;6];[2;3;4;5;6]];;``````

invariant: `cartesian_product l = map_product_l id l`.

• since 0.2
`val map_product_l : ( 'a -> 'b t ) -> 'a t -> 'b list t`

`map_product_l f l` maps each element of `l` to a list of objects of type `'b` using `f`. We obtain `[l1;l2;...;ln]` where `length l=n` and `li : 'b list`. Then, it returns all the ways of picking exactly one element per `li`.

• since 0.2
`val group : eq:( 'a -> 'a -> bool ) -> 'a t -> 'a t t`

Group equal consecutive elements together.

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

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

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

Sort according to the given comparison function. The iterator must be finite.

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

Sort and remove duplicates. The iterator must be finite.

`val chunks : int -> 'a t -> 'a array t`

`chunks n e` returns a iterator of arrays of length `n`, composed of successive elements of `e`. The last array may be smaller than `n`

`val permutations : 'a list -> 'a list t`

Permutations of the list.

`val combinations : int -> 'a t -> 'a list t`

Combinations of given length. The ordering of the elements within each combination is unspecified. Example (ignoring ordering): `combinations 2 (1--3) |> to_list = [[1;2]; [1;3]; [2;3]]`

`val power_set : 'a t -> 'a list t`

All subsets of the iterator (in no particular order). The ordering of the elements within each subset is unspecified.

### Basic conversion functions

`val of_list : 'a list -> 'a t`

Enumerate elements of the list

`val to_list : 'a t -> 'a list`

non tail-call trasnformation to list, in the same order

`val to_rev_list : 'a t -> 'a list`

Tail call conversion to list, in reverse order (more efficient)

`val to_array : 'a t -> 'a array`

Convert the iterator to an array (not very efficient). The iterator must be memoized, as it's traversed twice.

`val of_array : ?start:int -> ?len:int -> 'a array -> 'a t`

Iterate on (a slice of) the given array

`val of_gen : 'a gen -> 'a t`

Build a functional iterator from a mutable, imperative generator. The result is properly memoized and can be iterated on several times, as a normal functional value.

`val of_gen_transient : 'a gen -> 'a t`

Build a functional iterator from a mutable, imperative generator. Note that the resulting iterator is not going to be really functional because the underlying generator can be consumed only once. Use `memoize` to recover the proper semantics, or use `of_gen` directly.

`val of_string : ?start:int -> ?len:int -> string -> char t`

Iterate on bytes of the string

`val to_string : char t -> string`

Convert into a string

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

Traverse the iterator and writes its content to the buffer

`val concat_string : sep:string -> string t -> string`

`concat_string ~sep s` concatenates all strings of `i`, separated with `sep`. The iterator must be memoized.

• since 0.3
`val lines : char t -> string t`

Group together chars belonging to the same line

`val unlines : string t -> char t`

Explode lines into their chars, adding a `'\n'` after each one

`module Infix : sig ... end`
`include module type of Infix`
`val (--) : int -> int -> int t`
`val (--^) : int -> int -> int t`
`val (>>=) : 'a t -> ( 'a -> 'b t ) -> 'b t`

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

Infix map operator

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

Infix map operator

`val (<*>) : ( 'a -> 'b ) t -> 'a t -> 'b t`
`val pp : ?sep:string -> 'a printer -> 'a t printer`

Pretty print the content of the iterator on a formatter.

`val memoize : 'a t -> 'a t`

Store content of the transient iterator in memory, to be able to iterate on it several times later.

### Easy interface to Produce Iterators

`module Generator : sig ... end`

This interface is designed to make it easy to build complex streams of values in a way that resembles Python's generators (using "yield").

`module IO : sig ... end`
`module type MONAD = sig ... end`
`module Traverse (M : MONAD) : sig ... end`