sumptype

Sumptype is a type construction used in programming languages and type theory to represent a value that may be one of several distinct types. It is commonly called a sum type or tagged union, emphasizing its additive nature: the type is a disjoint union of its variants, each with its own payload.

Construction and syntax often involve declaring multiple variants, each carrying its own data. In pseudocode, a sumptype can be written as a type with several constructors, for example a variant carrying an integer or a string. In Haskell, a similar concept appears as data SumType = IntCase Int | StringCase String. In OCaml, a corresponding form is type sumtype = IntCase of int | StringCase of string. In TypeScript, a practical representation uses discriminated unions, for instance type SumType = { tag: "IntCase", value: number } | { tag: "StringCase", value: string }. These constructions allow values to be created with different shapes while remaining within a single, composable type.

Semantics and usage revolve around pattern matching or case analysis. Programs typically inspect the tag or variant to determine how to operate on the contained payload, with exhaustive matching ensuring all variants are handled. Sumptypes are widely used for error handling (as in Result or Either types), optional values, and abstract syntax trees, where different node kinds must be combined within a uniform type.

Relation to other concepts: sumptype is the dual of product types and closely mirrors coproducts in category theory. It is a foundational concept in algebraic data types and discriminated or variant unions in modern programming languages. See also algebraic data type, tagged union, coproduct, pattern matching.