package coq

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package coq
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type 'a t = 'a array

An alias for the type of arrays.

val length : 'a array -> int

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

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

get a n returns the element number n of array a. The first element has number 0. The last element has number length a - 1. You can also write a.(n) instead of get a n.

val set : 'a array -> int -> 'a -> unit

set a n x modifies array a in place, replacing element number n with x. You can also write a.(n) <- x instead of set a n x.

val make : int -> 'a -> 'a array

make n x returns a fresh array of length n, initialized with x. All the elements of this new array are initially physically equal to x (in the sense of the == predicate). Consequently, if x is mutable, it is shared among all elements of the array, and modifying x through one of the array entries will modify all other entries at the same time.

  • raises Invalid_argument

    if n < 0 or n > Sys.max_array_length. If the value of x is a floating-point number, then the maximum size is only Sys.max_array_length / 2.

val create : int -> 'a -> 'a array
  • deprecated

    create is an alias for make.

val create_float : int -> float array

create_float n returns a fresh float array of length n, with uninitialized data.

  • since 4.03
val make_float : int -> float array
val init : int -> (int -> 'a) -> 'a array

init n f returns a fresh 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 make_matrix : int -> int -> 'a -> 'a array array

make_matrix dimx dimy e returns a two-dimensional array (an array of arrays) with first dimension dimx and second dimension dimy. All the elements of this new matrix are initially physically equal to e. The element (x,y) of a matrix m is accessed with the notation m.(x).(y).

  • raises Invalid_argument

    if dimx or dimy is negative or greater than Sys.max_array_length. If the value of e is a floating-point number, then the maximum size is only Sys.max_array_length / 2.

val create_matrix : int -> int -> 'a -> 'a array array
val append : 'a array -> 'a array -> 'a array

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

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

Same as append, but concatenates a list of arrays.

val sub : 'a array -> int -> int -> 'a array

sub a pos len returns a fresh array of length len, containing the elements number pos to pos + len - 1 of array a.

  • 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 copy : 'a array -> 'a array

copy a returns a copy of a, that is, a fresh array containing the same elements as a.

val fill : 'a array -> int -> int -> 'a -> unit

fill a pos len x modifies the array a in place, storing x in elements number pos to pos + len - 1.

val blit : 'a array -> int -> 'a array -> int -> int -> unit

blit src src_pos dst dst_pos len copies len elements from array src, starting at element number src_pos, to array dst, starting at element number dst_pos. It works correctly even if src and dst are the same array, and the source and destination chunks overlap.

  • raises Invalid_argument

    if src_pos and len do not designate a valid subarray of src, or if dst_pos and len do not designate a valid subarray of dst.

val to_list : 'a array -> 'a list

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

val of_list : 'a list -> 'a array

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

  • raises Invalid_argument

    if the length of l is greater than Sys.max_array_length.

Iterators

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

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

val iteri : (int -> 'a -> unit) -> 'a array -> 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 array -> 'b array

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

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

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 array -> 'a

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

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

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

Iterators on two arrays

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

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

  • since 4.03.0 (4.05.0 in ArrayLabels)
val map2 : ('a -> 'b -> 'c) -> 'a array -> 'b array -> 'c array

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

  • since 4.03.0 (4.05.0 in ArrayLabels)

Array scanning

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

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

  • since 4.03.0
val exists : ('a -> bool) -> 'a array -> bool

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

  • since 4.03.0
val mem : 'a -> 'a array -> 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).

  • since 4.03.0
val memq : 'a -> 'a array -> bool

Same as mem, but uses physical equality instead of structural equality to compare list elements.

  • since 4.03.0
val find_opt : ('a -> bool) -> 'a array -> 'a option

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

  • since 4.13.0
val find_map : ('a -> 'b option) -> 'a array -> '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.

  • since 4.13.0

Arrays of pairs

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

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

  • since 4.13.0

Sorting

val sort : ('a -> 'a -> int) -> 'a array -> unit

Sort an 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. After calling sort, the array is sorted in place in increasing order. 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 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

When sort returns, a contains the same elements as before, reordered in such a way that for all i and j valid indices of a :

  • cmp a.(i) a.(j) >= 0 if and only if i >= j
val stable_sort : ('a -> 'a -> int) -> 'a array -> unit

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 array. It is usually faster than the current implementation of sort.

val fast_sort : ('a -> 'a -> int) -> 'a array -> unit

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

Arrays and Sequences

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

Iterate on the array, in increasing order. Modifications of the array during iteration will be reflected in the sequence.

  • since 4.07
val to_seqi : 'a array -> (int * 'a) Seq.t

Iterate on the array, in increasing order, yielding indices along elements. Modifications of the array during iteration will be reflected in the sequence.

  • since 4.07
val of_seq : 'a Seq.t -> 'a array

Create an array from the generator

  • since 4.07
val compare : ('a -> 'a -> int) -> 'a array -> 'a array -> int

First size comparison, then lexicographic order.

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

Lift equality to array type.

val equal_norefl : ('a -> 'a -> bool) -> 'a array -> 'a array -> bool

Like equal but does not assume that equality is reflexive: no optimisation is performed if both arrays are physically the same.

val is_empty : 'a array -> bool

True whenever the array is empty.

val exists2 : ('a -> 'b -> bool) -> 'a array -> 'b array -> bool
val for_all2 : ('a -> 'b -> bool) -> 'a array -> 'b array -> bool
val for_all3 : ('a -> 'b -> 'c -> bool) -> 'a array -> 'b array -> 'c array -> bool
val for_all4 : ('a -> 'b -> 'c -> 'd -> bool) -> 'a array -> 'b array -> 'c array -> 'd array -> bool
val for_all_i : (int -> 'a -> bool) -> int -> 'a array -> bool
val findi : (int -> 'a -> bool) -> 'a array -> int option
val hd : 'a array -> 'a

First element of an array, or Failure "Array.hd" if empty.

val tl : 'a array -> 'a array

Remaining part of hd, or Failure "Array.tl" if empty.

val last : 'a array -> 'a

Last element of an array, or Failure "Array.last" if empty.

val cons : 'a -> 'a array -> 'a array

Append an element on the left.

val rev : 'a array -> unit

In place reversal.

val fold_right_i : (int -> 'b -> 'a -> 'a) -> 'b array -> 'a -> 'a
val fold_left_i : (int -> 'a -> 'b -> 'a) -> 'a -> 'b array -> 'a
val fold_right2 : ('a -> 'b -> 'c -> 'c) -> 'a array -> 'b array -> 'c -> 'c
val fold_right3 : ('a -> 'b -> 'c -> 'd -> 'd) -> 'a array -> 'b array -> 'c array -> 'd -> 'd
val fold_left2 : ('a -> 'b -> 'c -> 'a) -> 'a -> 'b array -> 'c array -> 'a
val fold_left3 : ('a -> 'b -> 'c -> 'd -> 'a) -> 'a -> 'b array -> 'c array -> 'd array -> 'a
val fold_left4 : ('a -> 'b -> 'c -> 'd -> 'e -> 'a) -> 'a -> 'b array -> 'c array -> 'd array -> 'e array -> 'a
val fold_left2_i : (int -> 'a -> 'b -> 'c -> 'a) -> 'a -> 'b array -> 'c array -> 'a
val fold_left_from : int -> ('a -> 'b -> 'a) -> 'a -> 'b array -> 'a
val map_to_list : ('a -> 'b) -> 'a array -> 'b list

Composition of map and to_list.

val map_of_list : ('a -> 'b) -> 'a list -> 'b array

Composition of map and of_list.

val chop : int -> 'a array -> 'a array * 'a array

chop i a returns (a1, a2) s.t. a = a1 + a2 and length a1 = n. Raise Failure "Array.chop" if i is not a valid index.

val split : ('a * 'b) array -> 'a array * 'b array
val map2_i : (int -> 'a -> 'b -> 'c) -> 'a array -> 'b array -> 'c array
val map3 : ('a -> 'b -> 'c -> 'd) -> 'a array -> 'b array -> 'c array -> 'd array
val map3_i : (int -> 'a -> 'b -> 'c -> 'd) -> 'a array -> 'b array -> 'c array -> 'd array
val map_left : ('a -> 'b) -> 'a array -> 'b array

As map but guaranteed to be left-to-right.

val iter2_i : (int -> 'a -> 'b -> unit) -> 'a array -> 'b array -> unit

Iter on two arrays. Raise Invalid_argument "Array.iter2_i" if sizes differ.

val iter3 : ('a -> 'b -> 'c -> unit) -> 'a array -> 'b array -> 'c array -> unit

Iter on three arrays. Raise Invalid_argument "Array.iter3" if sizes differ.

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

fold_left_map f e_0 [|l_1...l_n|] = e_n,[|k_1...k_n|] where (e_i,k_i)=f e_{i-1} l_i; see also Smart.fold_left_map

val fold_right_map : ('a -> 'c -> 'b * 'c) -> 'a array -> 'c -> 'b array * 'c

Same, folding on the right

val fold_left2_map : ('a -> 'b -> 'c -> 'a * 'd) -> 'a -> 'b array -> 'c array -> 'a * 'd array

Same with two arrays, folding on the left; see also Smart.fold_left2_map

val fold_left2_map_i : (int -> 'a -> 'b -> 'c -> 'a * 'd) -> 'a -> 'b array -> 'c array -> 'a * 'd array

Same than fold_left2_map but passing the index of the array

val fold_right2_map : ('a -> 'b -> 'c -> 'd * 'c) -> 'a array -> 'b array -> 'c -> 'd array * 'c

Same with two arrays, folding on the right

val distinct : 'a array -> bool

Return true if every element of the array is unique (for default equality).

val rev_of_list : 'a list -> 'a array

rev_of_list l is equivalent to Array.of_list (List.rev l).

val rev_to_list : 'a array -> 'a list

rev_to_list a is equivalent to List.rev (List.of_array a).

val filter_with : bool list -> 'a array -> 'a array

filter_with b a selects elements of a whose corresponding element in b is true. Raise Invalid_argument _ when sizes differ.

module Smart : sig ... end

The functions defined in this module are optimized specializations of the main ones, when the returned array is of same type as one of the original array.

module Fun1 : sig ... end

The functions defined in this module are the same as the main ones, except that they are all higher-order, and their function arguments have an additional parameter. This allows us to prevent closure creation in critical cases.

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