Tagged Union

In computer science, a tagged union, also called a variant, variant record, discriminated union, disjoint union, or sum type, is a data structure used to hold a value that could take on several different, but fixed types. Only one of the types can be in use at any one time, and a tag field explicitly indicates which one is in use. It can be thought of as a type that has several "cases," each of which should be handled correctly when that type is manipulated. Like ordinary unions, tagged unions can save storage by overlapping storage areas for each type, since only one is in use at a time.

Tagged unions are most important in functional languages such as ML and Haskell, where they are called datatypes (see algebraic data type) and the compiler is able to verify that all cases of a tagged union are always handled, avoiding many types of errors. They can, however, be constructed in nearly any language, and are much safer than untagged unions, often simply called unions, which are similar but do not explicitly keep track of which member of the union is currently in use.

Tagged unions are often accompanied by the concept of a constructor, which is similar but not the same as a constructor for a class. Constructors produce a tagged union value, given the initial tag value and a value of the corresponding type.

Mathematically, tagged unions correspond to disjoint or discriminated unions, usually written using +. Given an element of a disjoint union A + B, it is possible to determine whether it came from A or B. If an element lies in both, there will be two effectively distinct copies of the value in A + B, one from A and one from B.

In type theory, a tagged union is called a sum type. Notations vary, but usually the sum type comes with two introduction forms and . The elimination form is case analysis, known as pattern matching in ML-style programming languages: if has type and and have type under the assumptions and respectively, then the term has type . The sum type corresponds to intuitionistic logical disjunction under the Curry-Howard correspondence.

An enumerated type can be seen as a degenerate case: a tagged union of unit types. It corresponds to a set of nullary constructors and may be implemented as a simple tag variable, since it holds no additional data besides the value of the tag.