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 (Maybe (Maybe A)Maybe A), while nullable types do not (String?? = String?).

Theoretical aspects

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 maybeNothing>>=f=Nothing-- Fails if the previous monad fails(Justx)>>=f=fx-- 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.



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.TypeElement_Typeisprivate;PackageOptional_Typeis-- When the discriminant, Has_Element, is true there is an element field,-- when it is false, there are no fields (hence the null keyword).TypeOptional(Has_Element: Boolean)isrecordcaseHas_ElementiswhenFalse=>Null;whenTrue=>Element:Element_Type;endcase;end record;endOptional_Type;


Scala implements Option as a parameterized type, so a variable can be an Option, accessed as follows: [7]

objectMain{// This function uses pattern matching to deconstruct `Option`sdefcomputeV1(opt:Option[Int]):String=optmatch{caseSome(x)=>s"The value is: $x"caseNone=>"No value"}// This function uses the built-in `fold` methoddefcomputeV2(opt:Option[Int]):String=opt.fold("No value")(x=>s"The value is: $x")defmain(args:Array[String]):Unit={// Define variables that are `Option`s of type `Int`valfull=Some(42)valempty:Option[Int]=None// computeV1(full) -> The value is: 42println(s"computeV1(full) -> ${computeV1(full)}")// computeV1(empty) -> No valueprintln(s"computeV1(empty) -> ${computeV1(empty)}")// computeV2(full) -> The value is: 42println(s"computeV2(full) -> ${computeV2(full)}")// computeV2(empty) -> No valueprintln(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 type-safe alternative to the null value.


OCaml implements Option as a parameterized variant type. Options are constructed and deconstructed as follows:

(* This function uses pattern matching to deconstruct `option`s *)letcompute_v1=function|Somex->"The value is: "^string_of_intx|None->"No value"(* This function uses the built-in `fold` function *)letcompute_v2=Option.fold~none:"No value"~some:(funx->"The value is: "^string_of_intx)let()=(* Define variables that are `option`s of type `int` *)letfull=Some42inletempty=Nonein(* compute_v1 full -> The value is: 42 *)print_endline("compute_v1 full -> "^compute_v1full);(* compute_v1 empty -> No value *)print_endline("compute_v1 empty -> "^compute_v1empty);(* compute_v2 full -> The value is: 42 *)print_endline("compute_v2 full -> "^compute_v2full);(* compute_v2 empty -> No value *)print_endline("compute_v2 empty -> "^compute_v2empty)


// This function uses pattern matching to deconstruct `option`sletcompute_v1=function|Somex->sprintf"The value is: %d"x|None->"No value"// This function uses the built-in `fold` functionletcompute_v2=Option.fold(fun_x->sprintf"The value is: %d"x)"No value"// Define variables that are `option`s of type `int`letfull=Some42letempty=None// compute_v1 full -> The value is: 42compute_v1full|>printfn"compute_v1 full -> %s"// compute_v1 empty -> No valuecompute_v1empty|>printfn"compute_v1 empty -> %s"// compute_v2 full -> The value is: 42compute_v2full|>printfn"compute_v2 full -> %s"// compute_v2 empty -> No valuecompute_v2empty|>printfn"compute_v2 empty -> %s"


-- This function uses pattern matching to deconstruct `Maybe`scomputeV1::MaybeInt->StringcomputeV1(Justx)="The value is: "++showxcomputeV1Nothing="No value"-- This function uses the built-in `foldl` functioncomputeV2::MaybeInt->StringcomputeV2=foldl(\_x->"The value is: "++showx)"No value"main::IO()main=do-- Define variables that are `Maybe`s of type `Int`letfull=Just42letempty=Nothing-- computeV1 full -> The value is: 42putStrLn$"computeV1 full -> "++computeV1full-- computeV1 full -> No valueputStrLn$"computeV1 empty -> "++computeV1empty-- computeV2 full -> The value is: 42putStrLn$"computeV2 full -> "++computeV2full-- computeV2 full -> No valueputStrLn$"computeV2 empty -> "++computeV2empty


// This function uses a `switch` statement to deconstruct `Optional`sfunccomputeV1(_opt:Int?)->String{switchopt{case.some(letx):return"The value is: \(x)"case.none:return"No value"}}// This function uses optional binding to deconstruct `Optional`sfunccomputeV2(_opt:Int?)->String{ifletx=opt{return"The value is: \(x)"}else{return"No value"}}// Define variables that are `Optional`s of type `Int`letfull:Int?=42letempty:Int?=nil// computeV1(full) -> The value is: 42print("computeV1(full) -> \(computeV1(full))")// computeV1(empty) -> No valueprint("computeV1(empty) -> \(computeV1(empty))")// computeV2(full) -> The value is: 42print("computeV2(full) -> \(computeV2(full))")// computeV2(empty) -> No valueprint("computeV2(empty) -> \(computeV2(empty))")


// This function uses a `match` expression to deconstruct `Option`sfncompute_v1(opt: &Option<i32>)-> String{matchopt{Some(x)=>format!("The value is: {}",x),None=>"No value".to_owned(),}}// This function uses an `if let` expression to deconstruct `Option`sfncompute_v2(opt: &Option<i32>)-> String{ifletSome(x)=opt{format!("The value is: {}",x)}else{"No value".to_owned()}}// This function uses the built-in `map_or` methodfncompute_v3(opt: &Option<i32>)-> String{opt.map_or("No value".to_owned(),|x|format!("The value is: {}",x))}fnmain(){// Define variables that are `Option`s of type `i32`letfull=Some(42);letempty: Option<i32>=None;// compute_v1(&full) -> The value is: 42println!("compute_v1(&full) -> {}",compute_v1(&full));// compute_v1(&empty) -> No valueprintln!("compute_v1(&empty) -> {}",compute_v1(&empty));// compute_v2(&full) -> The value is: 42println!("compute_v2(&full) -> {}",compute_v2(&full));// compute_v2(&empty) -> No valueprintln!("compute_v2(&empty) -> {}",compute_v2(&empty));// compute_v3(&full) -> The value is: 42println!("compute_v3(&full) -> {}",compute_v3(&full));// compute_v3(&empty) -> No valueprintln!("compute_v3(&empty) -> {}",compute_v3(&empty))}


importoptions# This proc uses the built-in `isSome` and `get` procs to deconstruct `Option`sproc compute(opt:Option[int]):string=ifopt.isSome:"The Value is: "&$opt.getelse:"No value"# Define variables that are `Optional`s of type `Int`letfull=some(42)empty=none(int)# compute(full) -> The Value is: 42echo"compute(full) -> ",compute(full)# compute(empty) -> No valueecho"compute(empty) -> ",compute(empty)

See also

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