# Module type `Sek.ITER`

The signature `ITER` is the core iterator API. It is common to ephemeral and persistent sequences. Please follow the link for details.

### Types

`type 'a t`

`'a t` is the type of the sequence that the iterator navigates.

`type 'a iter`

`'a iter` is the type of an iterator. If the sequence has n elements, then an iterator can be thought of as an integer index that lies in the closed interval `[-1, n]`. The special indices `-1` and `n` designate the two sentinel elements, while the ordinary indices in the semi-open interval `[0, n)` designate the actual elements of the sequence.

`type direction`

Many operations on iterators are parameterized with a direction, which is either `forward` or `backward`.

### Creation Operations

`val create : direction -> 'a t -> 'a iter`

`create forward s` creates an iterator that points to index `0`. This means that the iterator points to the first element of the sequence, if the sequence is nonempty, and points to the back sentinel if the sequence is empty. Symmetrically, `create backward s` creates an iterator that points to index `n-1`, where `n` is the length of the sequence. This means that the iterator points to the last element of the sequence, if the sequence is nonempty, and points to the front sentinel if the sequence is empty.

Time complexity: O(1).

`val reset : direction -> 'a iter -> unit`

`reset dir it` resets the iterator `it` to the same initial state that is established when a new iterator is created by ```create dir (sequence it)```. Thus, `reset forward it` is equivalent to `reach it 0`, and ```reset backward it``` is equivalent to `reach it (length it - 1)`.

Time complexity: O(1).

`val copy : 'a iter -> 'a iter`

`copy it` creates a new iterator on the sequence `sequence it`, at the same position as the iterator `it`. Thus, if `copy it` returns `it'`, then the equality `index it = index it'` holds.

Time complexity: O(log n).

### Accessors

`val sequence : 'a iter -> 'a t`

`sequence it` is the sequence that the iterator `it` navigates. Throughout its lifetime, an iterator remains attached to the same sequence.

Time complexity: O(1).

`val length : 'a iter -> length`

`length it` is the length of the sequence that the iterator `it` navigates. It is a short-hand for `length (sequence it)`.

Time complexity: O(1).

`val index : 'a iter -> index`

`index it` is the index that the iterator `it` currently points to. It lies in the closed interval `[-1, length it]`. The special indices `-1` and `n` designate the two sentinel elements, while the ordinary indices in the semi-open interval `[0, n)` designate the actual elements of the sequence.

Time complexity: O(1).

`val finished : 'a iter -> bool`

`finished it` tests whether the iterator `it` currently points to the front or back sentinel. Thus, `finished it` is equivalent to `index it = -1 || index it = length it`. Its use is recommended, as it is both more readable and more efficient than testing a condition based on `index it`. The condition `not (finished it)` corresponds to `it.hasNext()` in Java's iterator API.

Time complexity: O(1).

`val get : 'a iter -> 'a`

If `finished it` is `false`, then `get it` reads and returns the element that the iterator `it` currently points to, that is, the element at index `index it`. In that case, `get it` is equivalent to accessing the sequence via `get (sequence it) (index it)`, yet is much cheaper. If `finished it` is `true`, which means that the iterator points to a sentinel, then `get it` raises the exception `End`.

Time complexity: O(1).

`val get_opt : 'a iter -> 'a option`

`get_opt it` is analogous to `get it`, but returns an option instead of possibly raising the exception `End`. It is equivalent to ```if finished it then None else Some (get it)```.

Time complexity: O(1).

`val get_segment : direction -> 'a iter -> 'a segment`

If `finished it` is `false`, then `get_segment dir it` returns a nonempty array segment, which contains a range of sequence elements. An array segment is a triple `(a, j, k)`, where `a` is an array, `j` is the start index of the segment in the array `a`, and `k` is the length of the segment. `k` must be positive. The segment covers the array indices in the semi-open interval `[j, j + k)`. You are allowed to read this array segment. You are not allowed to modify the array `a` in any way.

• If `dir` is `forward`, then the array element `a.(j)` is the current element, that is, the element that would be returned by `get it`. It is the first element of the segment. The last element of the segment is `a.(j + k - 1)`. A loop of the form ```for j = j to j + k - 1``` can be used to enumerate these elements in the forward direction.
• If `dir` is `backward`, then the array element `a.(j + k - 1)` is the current element, that is, the element that would be returned by `get it`. It is the first element of the segment. The last element of the segment is `a.(j)`. A loop of the form `for j = j + k - 1 downto j` can be used to enumerate these elements in the backward direction.

If `finished it` is `true`, which means that the iterator points to a sentinel, then `get_segment dir it` raises the exception `End`.

Time complexity: O(1).

`val get_segment_opt : direction -> 'a iter -> 'a segment option`

`get_segment_opt dir it` is analogous to `get_segment dir it`, but returns an option instead of possibly raising the exception `End`. It is equivalent to `if finished it then None else Some (get_segment dir it)`.

Time complexity: O(1).

### Move Operations

`val move : direction -> 'a iter -> unit`

`move dir it` moves the iterator `it` by one element in the direction `dir`. An attempt to move the iterator forward when it already points to the back sentinel, or to move it backward when it already points to the front sentinel, is forbidden: in such a situation, `move` must not be called. In other words, the new index `index it + sign dir` must lie in the closed interval `[-1, length it]`.

Time complexity: O(log n) in the worst case. However, the amortized time complexity of `move` is only O(1), in the following sense: the cost of iterating over a sequence using n successive `move` operations is O(n).

`val jump : direction -> 'a iter -> length -> unit`

`jump dir it k` moves the iterator `it` by `k` elements in the direction `dir`. The value of `k` may be positive, null, or negative. The new index `index it + sign dir * k` must lie in the closed interval ```[-1, length it]```. When `k` is positive, `jump dir it k` is equivalent to a series of `k` calls to `move dir it`. When `k` is negative, `jump dir it k` is equivalent to a series of `k` calls to `move (opposite dir) it`. The operation `jump dir it 0` has no effect.

Time complexity: O(log n). In the particular where `abs k = 1`, `jump` is optimized using `move`.

`val reach : 'a iter -> index -> unit`

`reach it i` moves the iterator `it` so as to point to the element at index `i`. Thus, after this operation, `index it` is `i`. The index `i` must lie in the closed interval `[-1, length it]`.

Time complexity: O(log n). In the particular case where `i = -1` or `i = length it`, `reach` is optimized and its complexity is O(1). In the particular case where one moves to the next or previous item, `reach` is optimized using `move`.

`val get_and_move : direction -> 'a iter -> 'a`

`get_and_move` combines `get` and `move`. `get_and_move dir it` is equivalent to `let x = get it in move dir it; x`. Therefore, it raises the exception `End` if (before the move) the iterator points to a sentinel. It corresponds to `it.next()` in Java's iterator API.

Time complexity: same as `move`.

`val get_and_move_opt : direction -> 'a iter -> 'a option`

`get_and_move_opt dir it` is analogous to `get_and_move dir it`, but returns an option instead of possibly raising the exception `End`. It is equivalent to `if finished it then None else Some (get_and_move it)`.

Time complexity: same as `move`.

`val get_segment_and_jump : direction -> 'a iter -> 'a segment`

`get_segment_and_jump` combines `get_segment` and a `jump` of the length of the segment. `get_segment_and_jump dir it` is equivalent to ```let (_, _, k) as seg = get_segment dir it in jump dir it k; seg```. Therefore, it raises the exception `End` if (before the move) the iterator points to a sentinel.

Time complexity: same as `jump`. Furthermore, the total cost of iterating over a sequence of n elements using `get_segment_and_jump` is O(n/K).

`val get_segment_and_jump_opt : direction -> 'a iter -> 'a segment option`

`get_segment_and_jump_opt dir it` is analogous to ```get_segment_and_jump dir it```, but returns an option instead of possibly raising the exception `End`. It is equivalent to ```if finished it then None else Some (get_segment_and_jump dir it)```.

Time complexity: same as `get_segment_and_jump`.

### Miscellaneous Operations

`val check : 'a iter -> unit`

In a release build, `check it` does nothing. In a development build, it checks that the iterator's internal invariant is satisfied.

`val format : Stdlib.Format.formatter -> int iter -> unit`

`format` is a printer for iterators over sequences of integers. It can be installed in the OCaml toplevel loop by `#install_printer format`. It is intended to be used only while debugging the library.