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Algebraic Data Types
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- Snippet from Wikipedia: Algebraic data type
In computer programming, especially in functional programming and type theory, an algebraic data type (ADT) is a composite data type—a type formed by combining other types.
An algebraic data type is defined by two key constructions: a sum and a product. These are sometimes referred to as "OR" and "AND" types.
A sum type is a choice between possibilities. The value of a sum type can match one of several defined variants. For example, a type representing the state of a traffic light could be either
Red,Amber, orGreen. A shape type could be either aCircle(which stores a radius) or aSquare(which stores a width). In formal terms, these variants are known as tagged unions or disjoint unions. Each variant has a name, called a constructor, which can also carry data. Enumerated types are a simple form of sum type where the constructors carry no data.A product type combines types together. A value of a product type will contain a value for each of its component types. For example, a
Pointtype might be defined to contain anxcoordinate (an integer) and aycoordinate (also an integer). Formal examples of product types include tuples and records. The set of all possible values of a product type is the Cartesian product of the sets of its component types.Values of algebraic data types are typically handled using pattern matching. This feature allows a programmer to check which constructor a value was made with and extract the data it contains in a convenient and type-safe way.
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