In computer programming, particularly functional programming and type theory, an algebraic data type is a kind of composite type, i.e. a type formed by combining other types. Two common classes of algebraic type are product types, i.e. tuples and records, and sum types, also called tagged unions or variant types.
The values of a product type typically contain several values, called fields. All values of that type have the same combination of field types. The set of all possible values of a product type is the set-theoretical product of the sets of all possible values of its field types.
The values of a sum type are typically grouped into several classes, called variants. A value of a variant type is usually created with a quasi-functional entity called a constructor. Each variant has its own constructor, which takes a specified number of arguments with specified types. The set of all possible values of a sum type is the set-theoretical sum, i.e. the disjoint union, of the sets of all possible values of its variants. enumerated types are a special case of sum types in which the constructors take no arguments.
Values of algebraic types are analyzed with pattern matching, which identifies a value by its constructor or field names and extracts the data it contains.
Algebraic data types were introduced in Hope, a small functional programming language developed in the 1970s at Edinburgh University.
Read more about Algebraic Data Type: Examples, Explanation, Theory, Programming Languages With Algebraic Data Types
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