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Concept
Tagged union
Summary
In computer science, a tagged union, also called a variant, variant record, choice type, discriminated union, disjoint union, sum type or coproduct, 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. This is critical in defining recursive datatypes, in which some component of a value may have the same type as that value, for example in defining a type for representing trees, where it is necessary to distinguish multi-node subtrees and leaves. 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 programming 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 programming language, and are much safer than untagged unions, often simply called unions, which are similar but do not explicitly track which member of a union is in use currently.
Tagged unions are often accompanied by the concept of a type constructor, which is similar but not the same as a constructor for a class. Type constructors produce a tagged union type, given the initial tag type and 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. Sum types are the dual of product types.
Official source
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