Option type

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  or  ), or which encapsulates the original data type   (often written   or  ).

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

Theoretical aspects
In type theory, it may be written as: $$A^{?} = A + 1$$. This expresses the fact that for a given set of values in $$A$$, an option type adds exactly one additional value (the empty value) to the set of valid values for $$A$$. 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.

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.

The option type is also a monad where:

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

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 std::optional.

Coq
In Coq, the option type is defined as Some : A -> option A.

Elm
In Elm, the option type is defined as Nothing.

Haskell
In Haskell, the option type is defined as Just a.

Idris
In Idris, the option type is defined as Just a.

OCaml
In OCaml, the option type is defined as Some of 'a.

Rust
In Rust, the option type is defined as enum Option { None, Some(T) }.

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.

Standard ML
In Standard ML, the option type is defined as SOME of 'a.

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

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

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