Module Stdlib.Iarray

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.

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.

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

Same as 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 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 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 fold_left and 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.

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))|].

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 for_all, but for a two-argument predicate.

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

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

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 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, Stdlib.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 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 sort.

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

Same as sort or 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