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In computer programming, an enumerated type (also called enumeration or enum, or factor in the R programming language, and a categorical variable in statistics) is a data type consisting of a set of named values called elements, members or enumerators of the type. The enumerator names are usually identifiers that behave as constants in the language. A variable that has been declared as having an enumerated type can be assigned any of the enumerators as a value. In other words, an enumerated type has values that are different from each other, and that can be compared and assigned, but which are not specified by the programmer as having any particular concrete representation in the computer's memory; compilers and interpreters can represent them arbitrarily. For example, the four suits in a deck of playing cards may be four enumerators named CLUB, DIAMOND, HEART, SPADE, belonging to an enumerated type named suit. If a variable V is declared having suit as its data type, one can assign any of those four values to it. Although the enumerators are usually distinct, some languages may allow the same enumerator to be listed twice in the type's declaration. The names of enumerators need not be semantically complete or compatible in any sense. For example, an enumerated type called color may be defined to consist of the enumerators RED, GREEN, ZEBRA, MISSING, and BACON. In some languages, the declaration of an enumerated type also intentionally defines an ordering of its members; in others, the enumerators are unordered; in others still, an implicit ordering arises from the compiler concretely representing enumerators as integers. Some enumerator types may be built into the language. The Boolean type, for example is often a pre-defined enumeration of the values FALSE and TRUE. Many languages allow the user to define new enumerated types. Values and variables of an enumerated type are usually implemented as fixed-length bit strings, often in a format and size compatible with some integer type. Some languages, especially system programming languages, allow the user to specify the bit combination to be used for each enumerator. In type theory, enumerated types are often regarded as tagged unions of unit types. Since such types are of the form , they may also be written as natural numbers.
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