Option type

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In programming languages (especially functional programming languages) and type theory, an option type or maybe type is a polymorphic type that represents encapsulation of an optional value; e.g., it is used as the return type of functions which may or may not return a meaningful value when they are applied. It consists of a constructor which either is empty (often named None or Nothing), or which encapsulates the original data type A (often written Just A or Some A).

A distinct, but related concept outside of functional programming, which is popular in object-oriented programming, is called nullable types (often expressed as A?). The core difference between option types and nullable types is that option types support nesting (e.g. Maybe (Maybe String) ≠ Maybe String), while nullable types do not (e.g. String?? = String?).

In type theory, it may be written as: ${\displaystyle A^{?}=A+1}$. This expresses the fact that for a given set of values in ${\displaystyle A}$, an option type adds exactly one additional value (the empty value) to the set of valid values for ${\displaystyle A}$. This is reflected in programming by the fact that in languages having tagged unions, option types can be expressed as the tagged union of the encapsulated type plus a unit type.^[1] An option type is a particular case of a tagged union, where the Nothing is taken as (nullary constructor for a) singleton type. Tagged unions can generally be implemented by a combination of union types and record types using occurrence typing.^[2]

The option type is also a monad where:^[3]

return = Just -- Wraps the value into a maybe

Nothing  >>= f = Nothing -- Fails if the previous monad fails
(Just x) >>= f = f x     -- Succeeds when both monads succeed

The monadic nature of the option type is useful for efficiently tracking failure and errors.^[4]

Ada does not implement option-types directly, however it provides discriminated types which can be used to parameterize a record. To implement a Option type, a Boolean type is used as the discriminant; the following example provides a generic to create an option type from any non-limited constrained type:

generic
  -- Any constrained & non-limited type.
  type Element_Type is private;
package Optional_Type is
  -- When the discriminant, Has_Element, is true there is an element field,
  -- when it is false, there are no fields (hence the null keyword).
  type Optional (Has_Element : Boolean) is record
    case Has_Element is
      when False => Null;
      when True  => Element : Element_Type;
    end case;
  end record;
end Optional_Type;

Example usage:

   package Optional_Integers is new Optional_Type
      (Element_Type => Integer);
   Foo : Optional_Integers.Optional :=
      (Has_Element => True, Element => 5);
   Bar : Optional_Integers.Optional := 
      (Has_Element => False);

This section needs expansion with: example usage. You can help by adding to it. (July 2022)

In Agda, the option type is named Maybe with variants nothing and just a.

In ATS, the option type is defined as

datatype option_t0ype_bool_type (a: t@ype+, bool) = 
	| Some(a, true) of a
 	| None(a, false)
stadef option = option_t0ype_bool_type
typedef Option(a: t@ype) = [b:bool] option(a, b)

#include "share/atspre_staload.hats"

fn show_value (opt: Option int): string =
	case+ opt of
	| None() => "No value"
	| Some(s) => tostring_int s

implement main0 (): void = let
	val full = Some 42
	and empty = None
in
	println!("show_value full → ", show_value full);
	println!("show_value empty → ", show_value empty);
end

show_value full → 42
show_value empty → No value

Since C++17, the option type is defined in the standard library as template <typename T> std::optional<T>.

import std;

using std::nullopt;
using std::optional;

constexpr optional<double> divide(double x, double y) noexcept {
	if (y != 0.0) {
		return x / y;
    }

	return nullopt;
}

void readDivisionResults(int x, int y) {
    optional<double> result = divide(x, y);
    if (result) {
        std::println("The quotient of x: {} and y: {} is {}.", x, y, result.value());
    } else {
        std::println("The quotient of x: {} and y: {} is undefined!");
    }
}

int main(int argc, char* argv[]) {
    readDivisionResults(1, 5);
    readDivisionResults(8, 0);
}

This section needs expansion with: example usage. You can help by adding to it. (July 2022)

In Elm, the option type is defined as type Maybe a = Just a | Nothing.^[5]

In F#, the option type is defined as type 'a option = None | Some of 'a.^[6]

let showValue =
    Option.fold (fun _ x -> sprintf "The value is: %d" x) "No value"

let full = Some 42
let empty = None

showValue full |> printfn "showValue full -> %s"
showValue empty |> printfn "showValue empty -> %s"

showValue full -> The value is: 42
showValue empty -> No value

In Haskell, the option type is defined as data Maybe a = Nothing | Just a.^[7]

showValue :: Maybe Int -> String
showValue = foldl (\_ x -> "The value is: " ++ show x) "No value"

main :: IO ()
main = do
    let full = Just 42
    let empty = Nothing

    putStrLn $ "showValue full -> " ++ showValue full
    putStrLn $ "showValue empty -> " ++ showValue empty

showValue full -> The value is: 42
showValue empty -> No value

In Idris, the option type is defined as data Maybe a = Nothing | Just a.

showValue : Maybe Int -> String
showValue = foldl (\_, x => "The value is " ++ show x) "No value"

main : IO ()
main = do
    let full = Just 42
    let empty = Nothing

    putStrLn $ "showValue full -> " ++ showValue full
    putStrLn $ "showValue empty -> " ++ showValue empty

showValue full -> The value is: 42
showValue empty -> No value

In Java, the option type is defined the standard library by the java.util.Optional<T> class.

import java.util.Optional;

public class OptionExample {
    static String showValue(Optional<Integer> opt) {
        return opt.map(x -> String.format("The value is: %d", x)).orElse("No value");
    }

    public static void main(String[] args) {
        Optional<Integer> full = Optional.of(42);
        Optional<Integer> empty = Optional.empty();

        System.out.printf("showValue(full): %s\n", showValue(full));
        System.out.printf("showValue(empty): %s\n", showValue(empty));
    }
}

showValue full -> The value is: 42
showValue empty -> No value

This section needs expansion with: the definition. You can help by adding to it. (July 2022)

import std/options

proc showValue(opt: Option[int]): string =
  opt.map(proc (x: int): string = "The value is: " & $x).get("No value")

let
  full = some(42)
  empty = none(int)

echo "showValue(full) -> ", showValue(full)
echo "showValue(empty) -> ", showValue(empty)

showValue(full) -> The Value is: 42
showValue(empty) -> No value

In OCaml, the option type is defined as type 'a option = None | Some of 'a.^[8]

let show_value =
  Option.fold ~none:"No value" ~some:(fun x -> "The value is: " ^ string_of_int x)

let () =
  let full = Some 42 in
  let empty = None in

  print_endline ("show_value full -> " ^ show_value full);
  print_endline ("show_value empty -> " ^ show_value empty)

show_value full -> The value is: 42
show_value empty -> No value

This section needs expansion with: example usage. You can help by adding to it. (July 2022)

In Rocq, the option type is defined as Inductive option (A:Type) : Type := | Some : A -> option A | None : option A..

In Rust, the option type is defined as enum Option<T> { None, Some(T) }.^[9]

fn show_value(opt: Option<i32>) -> String {
    opt.map_or("No value".to_owned(), |x: i32| format!("The value is: {}", x))
}

fn main() {
    let full: Option<i32> = Some(42);
    let empty: Option<i32> = None;

    println!("show_value(full) -> {}", show_value(full));
    println!("show_value(empty) -> {}", show_value(empty));
}

show_value(full) -> The value is: 42
show_value(empty) -> No value

In Scala, the option type is defined as sealed abstract class Option[+A], a type extended by final case class Some[+A](value: A) and case object None.

object Main:
  def showValue(opt: Option[Int]): String =
    opt.fold("No value")(x => s"The value is: $x")

  def main(args: Array[String]): Unit =
    val full = Some(42)
    val empty = None

    println(s"showValue(full) -> ${showValue(full)}")
    println(s"showValue(empty) -> ${showValue(empty)}")

showValue(full) -> The value is: 42
showValue(empty) -> No value

This section needs expansion with: example usage. You can help by adding to it. (July 2022)

In Standard ML, the option type is defined as datatype 'a option = NONE | SOME of 'a.

In Swift, the option type is defined as enum Optional<T> { case none, some(T) } but is generally written as T?.^[10]

func showValue(_ opt: Int?) -> String {
    return opt.map { "The value is: \($0)" } ?? "No value"
}

let full = 42
let empty: Int? = nil

print("showValue(full) -> \(showValue(full))")
print("showValue(empty) -> \(showValue(empty))")

showValue(full) -> The value is: 42
showValue(empty) -> No value

In Zig, add ? before the type name like ?i32 to make it an optional type.

Payload n can be captured in an if or while statement, such as if (opt) |n| { ... } else { ... }, and an else clause is evaluated if it is null.

const std = @import("std");

fn showValue(allocator: std.mem.Allocator, opt: ?i32) ![]u8 {
    return if (opt) |n|
        std.fmt.allocPrint(allocator, "The value is: {}", .{n})
    else
        allocator.dupe(u8, "No value");
}

pub fn main() !void {
    // Set up an allocator, and warn if we forget to free any memory.
    var gpa: std.heap.DebugAllocator(.{}) = .init;
    defer std.debug.assert(gpa.deinit() == .ok);
    const allocator = gpa.allocator();

    // Prepare the standard output stream.
    var buffer: [1024]u8 = undefined;
    var writer = std.fs.File.stdout().writer(&buffer);
    const stdout = &writer.interface;

    // Perform our example.
    const full = 42;
    const empty = null;

    const full_msg = try showValue(allocator, full);
    defer allocator.free(full_msg);
    try stdout.print("showValue(allocator, full) -> {s}\n", .{full_msg});

    const empty_msg = try showValue(allocator, empty);
    defer allocator.free(empty_msg);
    try stdout.print("showValue(allocator, empty) -> {s}\n", .{empty_msg});

    try stdout.flush();
}

showValue(allocator, full) -> The value is: 42 
showValue(allocator, empty) -> No value

• Result type
• Tagged union
• Nullable type
• Null object pattern
• Exception handling
• Pattern matching