# Option type

Short description: Encapsulation of an optional value in programming or type theory

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?).

## Theoretical aspects

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]

In the Curry–Howard correspondence, option types are related to the annihilation law for ∨: x∨1=1.

An option type can also be seen as a collection containing either one or zero elements.[original research?]

The option type is also a monad where:[2]

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.[3]

## Examples

### Agda

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

### C++

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

### Coq

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

### Elm

In Elm, the option type is defined as type Maybe a = Just a | Nothing.[4]

### F#

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.[5]

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

### Idris

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

### Nim

import std/options

proc showValue(opt: Option[int]): string =
opt.map(proc (x: int): string = "The value is: " & $x).get("No value") let full = some(42) empty = none(int) echo "showValue(full) -> ", showValue(full) echo "showValue(empty) -> ", showValue(empty) showValue(full) -> The Value is: 42 showValue(empty) -> No value ### OCaml In OCaml, the option type is defined as type 'a option = None | Some of 'a.[6] let show_value = Option.fold ~none:"No value" ~some:(fun x -> "The value is: " ^ string_of_int x) let () = let full = Some 42 in let empty = None in print_endline ("show_value full -> " ^ show_value full); print_endline ("show_value empty -> " ^ show_value empty) show_value full -> The value is: 42 show_value empty -> No value ### Rust In Rust, the option type is defined as enum Option<T> { None, Some(T) }.[7] fn show_value(opt: Option<i32>) -> String { opt.map_or("No value".to_owned(), |x| format!("The value is: {}", x)) } fn main() { let full = Some(42); let empty = None; println!("show_value(full) -> {}", show_value(full)); println!("show_value(empty) -> {}", show_value(empty)); } show_value(full) -> The value is: 42 show_value(empty) -> No value ### Scala In Scala, the option type is defined as sealed abstract class Option[+A], a type extended by final case class Some[+A](value: A) and case object None. object Main { def showValue(opt: Option[Int]): String = opt.fold("No value")(x => s"The value is:$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

### Standard ML

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

### Swift

In Swift, the option type is defined as enum Optional<T> { case none, some(T) } but is generally written as T?.[8]

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

### Zig

In Zig, add ? before the type name like ?32 to make it 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.GeneralPurposeAllocator(.{}){};
defer std.debug.assert(!gpa.deinit());
const allocator = gpa.allocator();

// Prepare the standard output stream.
const stdout = std.io.getStdOut().writer();

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