# Module Iarray

    module Iarray: sig .. end

Operations on immutable arrays. This module mirrors the API of `Array`, but omits functions that assume mutability; in addition to obviously mutating functions, it omits `copy` along with the functions `make`, `create_float`, and `make_matrix` that produce all-constant arrays. The exception is the sorting functions, which are given a copying API to replace the in-place one.

    type 'a t = 'a iarray

An alias for the type of immutable arrays.

    val length : 'a iarray -> int

Return the length (number of elements) of the given immutable array.

    val get : 'a iarray -> int -> 'a

`get a n` returns the element number `n` of immutable array `a`. The first element has number 0. The last element has number `length a - 1`.

- Raises `Invalid_argument` if `n` is outside the range 0 to `(length a - 1)`.

    val init : int -> (int -> 'a) -> 'a iarray

`init n f` returns a fresh immutable array of length `n`, with element number `i` initialized to the result of `f i`. In other terms, `init n f` tabulates the results of `f` applied to the integers `0` to `n-1`.

- Raises `Invalid_argument` if `n < 0` or `n > Sys.max_array_length`. If the return type of `f` is `float`, then the maximum size is only `Sys.max_array_length / 2`.

    val append : 'a iarray -> 'a iarray -> 'a iarray

`append v1 v2` returns a fresh immutable array containing the concatenation of the immutable arrays `v1` and `v2`.

- Raises `Invalid_argument` if `length v1 + length v2 > Sys.max_array_length`.

    val concat : 'a iarray list -> 'a iarray

Same as `Iarray.append`, but concatenates a list of immutable arrays.

    val sub : 'a iarray -> pos:int -> len:int -> 'a iarray

`sub a ~pos ~len` returns a fresh immutable array of length `len`, containing the elements number `pos` to `pos + len - 1` of immutable array `a`. This creates a copy of the selected portion of the immutable array.

- Raises `Invalid_argument` if `pos` and `len` do not designate a valid subarray of `a`; that is, if `pos < 0`, or `len < 0`, or `pos + len > length a`.

    val to_list : 'a iarray -> 'a list

`to_list a` returns the list of all the elements of `a`.

    val of_list : 'a list -> 'a iarray

`of_list l` returns a fresh immutable array containing the elements of `l`.

- Raises `Invalid_argument` if the length of `l` is greater than `Sys.max_array_length`.

## Converting to and from mutable arrays

    val to_array : 'a iarray -> 'a array

`to_array a` returns a mutable copy of the immutable array `a`; that is, a fresh (mutable) array containing the same elements as `a`

    val of_array : 'a array -> 'a iarray

`of_array ma` returns an immutable copy of the mutable array `ma`; that is, a fresh immutable array containing the same elements as `ma`

## Comparison

    val equal : ('a -> 'a -> bool) -> 'a iarray -> 'a iarray -> bool

`eq [|a1; ...; an|] [|b1; ..; bm|]` holds when the two input immutable arrays have the same length, and for each pair of elements `ai, bi` at the same position we have `eq ai bi`.

    val compare : ('a -> 'a -> int) -> 'a iarray -> 'a iarray -> int

Provided the function `cmp` defines a preorder on elements, `compare cmp a b` compares first `a` and `b` by their length, and then, if equal, by their elements according to the lexicographic preorder.

For more details on comparison functions, see `Iarray.sort`.

## Iterators

    val iter : ('a -> unit) -> 'a iarray -> unit

`iter f a` applies function `f` in turn to all the elements of `a`. It is equivalent to `f (get a 0); f (get a 1); ...; f (get a (length a - 1)); ()`.

    val iteri : (int -> 'a -> unit) -> 'a iarray -> unit

Same as `Iarray.iter`, but the function is applied to the index of the element as first argument, and the element itself as second argument.

    val map : ('a -> 'b) -> 'a iarray -> 'b iarray

`map f a` applies function `f` to all the elements of `a`, and builds an immutable array with the results returned by `f`: `[| f (get a 0); f (get a 1); ...; f (get a (length a - 1)) |]`.

    val mapi : (int -> 'a -> 'b) -> 'a iarray -> 'b iarray

Same as `Iarray.map`, but the function is applied to the index of the element as first argument, and the element itself as second argument.

    val fold_left : ('a -> 'b -> 'a) -> 'a -> 'b iarray -> 'a

`fold_left f init a` computes `f (... (f (f init (get a 0)) (get a 1)) ...) (get a n-1)`, where `n` is the length of the immutable array `a`.

    val fold_left_map : ('a -> 'b -> 'a * 'c) -> 'a -> 'b iarray -> 'a * 'c iarray

`fold_left_map` is a combination of `Iarray.fold_left` and `Iarray.map` that threads an accumulator through calls to `f`.

    val fold_right : ('b -> 'a -> 'a) -> 'b iarray -> 'a -> 'a

`fold_right f a init` computes `f (get a 0) (f (get a 1) ( ... (f (get a (n-1)) init) ...))`, where `n` is the length of the immutable array `a`.

## Iterators on two arrays

    val iter2 : ('a -> 'b -> unit) -> 'a iarray -> 'b iarray -> unit

`iter2 f a b` applies function `f` to all the elements of `a` and `b`.

- Raises `Invalid_argument` if the immutable arrays are not the same size.

    val map2 : ('a -> 'b -> 'c) -> 'a iarray -> 'b iarray -> 'c iarray

`map2 f a b` applies function `f` to all the elements of `a` and `b`, and builds an immutable array with the results returned by `f`: `[| f (get a 0) (get b 0);
...;
f (get a (length a - 1)) (get b (length b - 1))|]`.

- Raises `Invalid_argument` if the immutable arrays are not the same size.

## Array scanning

    val for_all : ('a -> bool) -> 'a iarray -> bool

`for_all f [|a1; ...; an|]` checks if all elements of the immutable array satisfy the predicate `f`. That is, it returns `(f a1) && (f a2) && ... && (f an)`.

    val exists : ('a -> bool) -> 'a iarray -> bool

`exists f [|a1; ...; an|]` checks if at least one element of the immutable array satisfies the predicate `f`. That is, it returns `(f a1) || (f a2) || ... || (f an)`.

    val for_all2 : ('a -> 'b -> bool) -> 'a iarray -> 'b iarray -> bool

Same as `Iarray.for_all`, but for a two-argument predicate.

- Raises `Invalid_argument` if the two immutable arrays have different lengths.

    val exists2 : ('a -> 'b -> bool) -> 'a iarray -> 'b iarray -> bool

Same as `Iarray.exists`, but for a two-argument predicate.

- Raises `Invalid_argument` if the two immutable arrays have different lengths.

    val mem : 'a -> 'a iarray -> bool

`mem a set` is true if and only if `a` is structurally equal to an element of `l` (i.e. there is an `x` in `l` such that `compare a x = 0`).

    val memq : 'a -> 'a iarray -> bool

Same as `Iarray.mem`, but uses physical equality instead of structural equality to compare array elements.

    val find_opt : ('a -> bool) -> 'a iarray -> 'a option

`find_opt f a` returns the first element of the immutable array `a` that satisfies the predicate `f`, or `None` if there is no value that satisfies `f` in the array `a`.

    val find_index : ('a -> bool) -> 'a iarray -> int option

`find_index f a` returns `Some i`, where `i` is the index of the first element of the array `a` that satisfies `f x`, if there is such an element.

It returns `None` if there is no such element.

    val find_map : ('a -> 'b option) -> 'a iarray -> 'b option

`find_map f a` applies `f` to the elements of `a` in order, and returns the first result of the form `Some v`, or `None` if none exist.

    val find_mapi : (int -> 'a -> 'b option) -> 'a iarray -> 'b option

Same as `find_map`, but the predicate is applied to the index of the element as first argument (counting from 0), and the element itself as second argument.

## Arrays of pairs

    val split : ('a * 'b) iarray -> 'a iarray * 'b iarray

`split [|(a1,b1); ...; (an,bn)|]` is `([|a1; ...; an|], [|b1; ...; bn|])`.

    val combine : 'a iarray -> 'b iarray -> ('a * 'b) iarray

`combine [|a1; ...; an|] [|b1; ...; bn|]` is `[|(a1,b1); ...; (an,bn)|]`. Raise `Invalid_argument` if the two immutable arrays have different lengths.

## Sorting

    val sort : ('a -> 'a -> int) -> 'a iarray -> 'a iarray

Sort an immutable array in increasing order according to a comparison function. The comparison function must return 0 if its arguments compare as equal, a positive integer if the first is greater, and a negative integer if the first is smaller (see below for a complete specification). For example, `compare` is a suitable comparison function. The result of calling `sort` is a fresh immutable array containing the same elements as the original sorted in increasing order. Other than this fresh array, `sort` is guaranteed to run in constant heap space and (at most) logarithmic stack space.

The current implementation uses Heap Sort. It runs in constant stack space.

Specification of the comparison function: Let `a` be the immutable array and `cmp` the comparison function. The following must be true for all `x`, `y`, `z` in `a` :

- `cmp x y` > 0 if and only if `cmp y x` < 0
- if `cmp x y` >= 0 and `cmp y z` >= 0 then `cmp x z` >= 0

The result of `sort`, which we'll call `a'`, contains the same elements as `a`, reordered in such a way that for all i and j valid indices of `a` (or equivalently, of `a'`):

- `cmp (get a' i) (get a' j)` >= 0 if and only if i >= j

    val stable_sort : ('a -> 'a -> int) -> 'a iarray -> 'a iarray

Same as `Iarray.sort`, but the sorting algorithm is stable (i.e. elements that compare equal are kept in their original order) and not guaranteed to run in constant heap space.

The current implementation uses Merge Sort. It uses a temporary array of length `n/2`, where `n` is the length of the immutable array. It is usually faster than the current implementation of `Iarray.sort`.

    val fast_sort : ('a -> 'a -> int) -> 'a iarray -> 'a iarray

Same as `Iarray.sort` or `Iarray.stable_sort`, whichever is faster on typical input.

## Iterators

    val to_seq : 'a iarray -> 'a Seq.t

Iterate on the immutable array, in increasing order.

    val to_seqi : 'a iarray -> (int * 'a) Seq.t

Iterate on the immutable array, in increasing order, yielding indices along elements.

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

Create an immutable array from the generator