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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 objectoriented programming, is called nullable types (often expressed as A?
). The core difference between option types and nullable types is that option types support nesting (Maybe (Maybe A)
≠ Maybe A
), while nullable types do not (String??
= String?
).
Theoretical aspects
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In type theory, it may be written as: . This expresses the fact that for a given set of values in , an option type adds exactly one additional value (the empty value) to the set of valid values for . 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.^{[how?]}
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]}
Names and definitions
In different programming languages, the option type has various names and definitions.
 In Agda, it is named
Maybe
with variantsnothing
andjust a
.  In C++17 it is defined as the template class
std::optional<T>
,optional()
can be used to create an empty option. (Might break monad laws due to the heavy overloading of constructors.)  In C#, it is defined as
Nullable<T>
but is generally written asT?
. (Breaks monad laws.)  In Coq, it is defined as
Inductive option (A:Type) : Type :=  Some : A > option A  None : option A.
.  In Elm, it is named
Maybe
, and defined astype Maybe a = Just a  Nothing
.^{[4]}  In Haskell, it is named
Maybe
, and defined asdata Maybe a = Nothing  Just a
.  In Idris, it is defined as
data Maybe a = Nothing  Just a
.  In Java, since version 8, it is defined as parameterized final class
Optional<T>
. (Breaks monad laws (map is implemented incorrectly).)  In Julia, it is named
Nullable{T}
. (However, this has been deprecated.^{[5]})  In OCaml, it is defined as
type 'a option = None  Some of 'a
.  In Perl 6, this is the default, but you can add a
:D
"smiley" to opt into a non option type. (Breaks monad laws (does not support nesting.))  In Rust, it is defined as
enum Option<T> { None, Some(T) }
.  In Scala, it is defined as
sealed abstract class Option[+A]
, a type extended byfinal case class Some[+A](value: A)
andcase object None
.  In Standard ML, it is defined as
datatype 'a option = NONE  SOME of 'a
.  In Swift, it is defined as
enum Optional<T> { case none, some(T) }
but is generally written asT?
.^{[6]}
Examples
Ada
Ada does not implement optiontypes 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 nonlimited constrained type:
Generic
 Any constrained & nonlimited 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;
Scala
Scala implements Option
as a parameterized type, so a variable can be an Option
, accessed as follows:^{[7]}
object Main {
// This function uses pattern matching to deconstruct `Option`s
def computeV1(opt: Option[Int]): String =
opt match {
case Some(x) => s"The value is: $x"
case None => "No value"
}
// This function uses the builtin `fold` method
def computeV2(opt: Option[Int]): String =
opt.fold("No value")(x => s"The value is: $x")
def main(args: Array[String]): Unit = {
// Define variables that are `Option`s of type `Int`
val full = Some(42)
val empty: Option[Int] = None
// computeV1(full) > The value is: 42
println(s"computeV1(full) > ${computeV1(full)}")
// computeV1(empty) > No value
println(s"computeV1(empty) > ${computeV1(empty)}")
// computeV2(full) > The value is: 42
println(s"computeV2(full) > ${computeV2(full)}")
// computeV2(empty) > No value
println(s"computeV2(empty) > ${computeV2(empty)}")
}
}
Two main ways to use an Option
value exist. The first, not the best, is the pattern matching, as in the first example. The second, the best practice is a monadic approach, as in the second example. In this way, a program is safe, as it can generate no exception or error (e.g., by trying to obtain the value of an Option
variable that is equal to None
). Thus, it essentially works as a typesafe alternative to the null value.
OCaml
OCaml implements Option
as a parameterized variant type. Option
s are constructed and deconstructed as follows:
(* This function uses pattern matching to deconstruct `option`s *)
let compute_v1 = function
 Some x > "The value is: " ^ string_of_int x
 None > "No value"
(* This function uses the builtin `fold` function *)
let compute_v2 =
Option.fold ~none:"No value" ~some:(fun x > "The value is: " ^ string_of_int x)
let () =
(* Define variables that are `option`s of type `int` *)
let full = Some 42 in
let empty = None in
(* compute_v1 full > The value is: 42 *)
print_endline ("compute_v1 full > " ^ compute_v1 full);
(* compute_v1 empty > No value *)
print_endline ("compute_v1 empty > " ^ compute_v1 empty);
(* compute_v2 full > The value is: 42 *)
print_endline ("compute_v2 full > " ^ compute_v2 full);
(* compute_v2 empty > No value *)
print_endline ("compute_v2 empty > " ^ compute_v2 empty)
F#
// This function uses pattern matching to deconstruct `option`s
let compute_v1 = function
 Some x > sprintf "The value is: %d" x
 None > "No value"
// This function uses the builtin `fold` function
let compute_v2 =
Option.fold (fun _ x > sprintf "The value is: %d" x) "No value"
// Define variables that are `option`s of type `int`
let full = Some 42
let empty = None
// compute_v1 full > The value is: 42
compute_v1 full > printfn "compute_v1 full > %s"
// compute_v1 empty > No value
compute_v1 empty > printfn "compute_v1 empty > %s"
// compute_v2 full > The value is: 42
compute_v2 full > printfn "compute_v2 full > %s"
// compute_v2 empty > No value
compute_v2 empty > printfn "compute_v2 empty > %s"
Haskell
 This function uses pattern matching to deconstruct `Maybe`s
computeV1 :: Maybe Int > String
computeV1 (Just x) = "The value is: " ++ show x
computeV1 Nothing = "No value"
 This function uses the builtin `foldl` function
computeV2 :: Maybe Int > String
computeV2 = foldl (\_ x > "The value is: " ++ show x) "No value"
main :: IO ()
main = do
 Define variables that are `Maybe`s of type `Int`
let full = Just 42
let empty = Nothing
 computeV1 full > The value is: 42
putStrLn $ "computeV1 full > " ++ computeV1 full
 computeV1 full > No value
putStrLn $ "computeV1 empty > " ++ computeV1 empty
 computeV2 full > The value is: 42
putStrLn $ "computeV2 full > " ++ computeV2 full
 computeV2 full > No value
putStrLn $ "computeV2 empty > " ++ computeV2 empty
Swift
// This function uses a `switch` statement to deconstruct `Optional`s
func computeV1(_ opt: Int?) > String {
switch opt {
case .some(let x):
return "The value is: \(x)"
case .none:
return "No value"
}
}
// This function uses optional binding to deconstruct `Optional`s
func computeV2(_ opt: Int?) > String {
if let x = opt {
return "The value is: \(x)"
} else {
return "No value"
}
}
// Define variables that are `Optional`s of type `Int`
let full: Int? = 42
let empty: Int? = nil
// computeV1(full) > The value is: 42
print("computeV1(full) > \(computeV1(full))")
// computeV1(empty) > No value
print("computeV1(empty) > \(computeV1(empty))")
// computeV2(full) > The value is: 42
print("computeV2(full) > \(computeV2(full))")
// computeV2(empty) > No value
print("computeV2(empty) > \(computeV2(empty))")
Rust
// This function uses a `match` expression to deconstruct `Option`s
fn compute_v1(opt: &Option<i32>) > String {
match opt {
Some(x) => format!("The value is: {}", x),
None => "No value".to_owned(),
}
}
// This function uses an `if let` expression to deconstruct `Option`s
fn compute_v2(opt: &Option<i32>) > String {
if let Some(x) = opt {
format!("The value is: {}", x)
} else {
"No value".to_owned()
}
}
// This function uses the builtin `map_or` method
fn compute_v3(opt: &Option<i32>) > String {
opt.map_or("No value".to_owned(), x format!("The value is: {}", x))
}
fn main() {
// Define variables that are `Option`s of type `i32`
let full = Some(42);
let empty: Option<i32> = None;
// compute_v1(&full) > The value is: 42
println!("compute_v1(&full) > {}", compute_v1(&full));
// compute_v1(&empty) > No value
println!("compute_v1(&empty) > {}", compute_v1(&empty));
// compute_v2(&full) > The value is: 42
println!("compute_v2(&full) > {}", compute_v2(&full));
// compute_v2(&empty) > No value
println!("compute_v2(&empty) > {}", compute_v2(&empty));
// compute_v3(&full) > The value is: 42
println!("compute_v3(&full) > {}", compute_v3(&full));
// compute_v3(&empty) > No value
println!("compute_v3(&empty) > {}", compute_v3(&empty))
}
Nim
import options
# This proc uses the builtin `isSome` and `get` procs to deconstruct `Option`s
proc compute(opt: Option[int]): string =
if opt.isSome:
"The Value is: " & $opt.get
else:
"No value"
# Define variables that are `Optional`s of type `Int`
let
full = some(42)
empty = none(int)
# compute(full) > The Value is: 42
echo "compute(full) > ", compute(full)
# compute(empty) > No value
echo "compute(empty) > ", compute(empty)
See also
References
 ^ Milewski, Bartosz (20150113). "Simple Algebraic Data Types". Bartosz Milewski's Programming Cafe. Sum types. "We could have encoded Maybe as: data Maybe a = Either () a". Archived from the original on 20190818. Retrieved 20190818.
 ^ "A Fistful of Monads  Learn You a Haskell for Great Good!". www.learnyouahaskell.com. Retrieved 20190818.
 ^ Hutton, Graham (Nov 25, 2017). "What is a Monad?". Computerphile Youtube. Retrieved Aug 18, 2019.
 ^ "Maybe · An Introduction to Elm". guide.elmlang.org.
 ^ "Julia v0.7.0 Release Notes · The Julia Language". docs.julialang.org.
 ^ "Apple Developer Documentation". developer.apple.com. Retrieved 20200906.
 ^ Martin Odersky; Lex Spoon; Bill Venners (2008). Programming in Scala. Artima Inc. pp. 282–284. ISBN 9780981531601. Retrieved 6 September 2011.