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functional-programmingalgebraic-data-types

What type of algebraic data type is Option[T] or Optional<T>

So it's my understanding there are two types of Algebraic Data Types (ADTs). For the case of Option[T] in Scala or Optional<T> in Java, would this be an example of a sum type or a product type?

Solution

  • Defining the Option[T] type in Haskell makes it clear that it's a sum type.

    data Option t = None | Some t

    Values of type Option t can be one of 2 things:

    1. None
    2. Some t

    So Option[T] and Optional<T> both take a type T and then add 1 more possible value (None).

    For fun, we can also translate this ADT into an algebraic equation:

    Option(t) = 1 + t

    To see why, see this question: Abusing the algebra of algebraic data types - why does this work?