# Arrays and Loops

Arrays are fixed-length mutable sequences with constant-time access and update. So they are similar in various ways to refs, lists, and tuples. Like refs, they are mutable. Like lists, they are (finite) sequences. Like tuples, their length is fixed in advance and cannot be resized.

The syntax for arrays is similar to lists:

# let v = [|0.; 1.|];;
val v : float array = [|0.; 1.|]


That code creates an array whose length is fixed to be 2 and whose contents are initialized to 0. and 1.. The keyword array is a type constructor, much like list.

Later those contents can be changed using the <- operator:

# v.(0) <- 5.;;
- : unit = ()

# v;;
- : float array = [|5.; 1.|]


As you can see in that example, indexing into an array uses the syntax array.(index), where the parentheses are mandatory.

The Array module has many useful functions on arrays.

## Syntax and Semantics

Syntax.

• Array creation: [|e0; e1; ...; en|]

• Array indexing: e1.(e2)

• Array assignment: e1.(e2) <- e3

Dynamic semantics.

• To evaluate [|e0; e1; ...; en|], evaluate each ei to a value vi, create a new array of length n+1, and store each value in the array at its index.

• To evaluate e1.(e2), evaluate e1 to an array value v1, and e2 to an integer v2. If v2 is not within the bounds of the array (i.e., 0 to n-1, where n is the length of the array), raise Invalid_argument. Otherwise, index into v1 to get the value v at index v2, and return v.

• To evaluate e1.(e2) <- e3, evaluate each expression ei to a value vi. Check that v2 is within bounds, as in the semantics of indexing. Mutate the element of v1 at index v2 to be v3.

Static semantics.

• [|e0; e1; ...; en|] : t array if ei : t for all the ei.

• e1.(e2) : t if e1 : t array and e2 : int.

• e1.(e2) <- e3 : unit if e1 : t array and e2 : int and e3 : t.

## Loops

OCaml has while loops and for loops. Their syntax is as follows:

while e1 do e2 done
for x=e1 to e2 do e3 done
for x=e1 downto e2 do e3 done


Each of these three expressions evaluates the expression between do and done for each iteration of the loop; while loops terminate when e1 becomes false; for loops execute once for each integer from e1 to e2; for..to loops evaluate starting at e1 and incrementing x each iteration; for..downto loops evaluate starting at e1 and decrementing x each iteration. All three expressions evaluate to () after the termination of the loop. Because they always evaluate to (), they are less general than folds, maps, or recursive functions.

Loops are themselves not inherently mutable, but they are most often used in conjunction with mutable features like arrays—typically, e causes side effects. We can also use functions like Array.iter, Array.map, and Array.fold_left instead of loops.

The "Expressions" page of OCaml manual contains the syntax and semantics of loops.