A programming language is an artificial language designed to communicate instructions to a machine, particularly a computer. Programming languages can be used to create programs that control the behavior of a machine and/or to express algorithms precisely....
In computer science, functional programming is a programming paradigm that treats computation as the evaluation of mathematical functions and avoids state and mutable data. It emphasizes the application of functions, in contrast to the imperative programming style, which emphasizes changes in state...
In mathematics, logic and computer science, type theory is any of several formal systems that can serve as alternatives to naive set theory, or the study of such formalisms in general...
In programming languages and type theory, parametric polymorphism is a way to make a language more expressive, while still maintaining full static type-safety. Using parametric polymorphism, a function or a data type can be written generically so that it can handle values identically without...
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're applied. It consists of either an empty constructor (called None or Nothing), or a constructor encapsulating the original data type A (written Just A or Some A).
In the Haskell language, the option type (called Maybe) is defined as data Maybe a = Just a | Nothing. In the OCaml language, the option type is defined as type 'a option = None | Some of 'a. In the Scala language, Option is defined as parametrized abstract class '.. Option[A] = if (x null) None else Some(x)... In the Standard ML
Standard ML
Standard ML is a general-purpose, modular, functional programming language with compile-time type checking and type inference. It is popular among compiler writers and programming language researchers, as well as in the development of theorem provers.SML is a modern descendant of the ML...
language, the option type is defined as datatype 'a option = NONE | SOME of 'a.
In mathematics, logic and computer science, type theory is any of several formal systems that can serve as alternatives to naive set theory, or the study of such formalisms in general...
In computer science, functional programming is a programming paradigm that treats computation as the evaluation of mathematical functions and avoids state and mutable data. It emphasizes the application of functions, in contrast to the imperative programming style, which emphasizes changes in state...
languages, option types can be expressed as the union of a unit type
Unit type
In the area of mathematical logic, and computer science known as type theory, a unit type is a type that allows only one value . The carrier associated with a unit type can be any singleton set. There is an isomorphism between any two such sets, so it is customary to talk about the unit type and...
plus the encapsulated type.
In the Curry-Howard correspondence, option types are related to the annihilation law
Absorption law
In algebra, the absorption law or absorption identity is an identity linking a pair of binary operations.Two binary operations, say ¤ and *, are said to be connected by the absorption law if:...
In computer science, a collection is a grouping of some variable number of data items that have some shared significance to the problem being solved and need to be operated upon together in some controlled fashion. Generally, the data items will be of the same type or, in languages supporting...
containing either a single element or zero elements.
The option monad
The option type is a monad
Monads in functional programming
In functional programming, a monad is a programming structure that represents computations. Monads are a kind of abstract data type constructor that encapsulate program logic instead of data in the domain model...
under the following functions:
We may also describe the option monad in terms of functions return, fmap and join, where the latter two are given by:
The option monad is an additive monad: it has Nothing as a zero constructor and the following function as a monadic sum:
In fact, the resulting structure is an idempotent monoid
Monoid
In abstract algebra, a branch of mathematics, a monoid is an algebraic structure with a single associative binary operation and an identity element. Monoids are studied in semigroup theory as they are naturally semigroups with identity. Monoids occur in several branches of mathematics; for...
.
Scala
Scala implements the Option type using Java generics, so you can specify the type of a variable as an Option and then access it as follows:
.
