Closedtype

Closedtype is a term used in programming language theory to describe a type whose set of values is fixed by its declaration and cannot be extended by external modules. It is often described as a closed algebraic data type or a sealed type. The defining property is that all constructors and operations for the type are determined at compile time, so new cases or variants cannot be introduced outside the defining scope.

In functional languages with algebraic data types, a datatype declaration yields a closed type: clients can use the provided constructors, but cannot add new ones without editing the type definition. This makes pattern matching on values of the type exhaustively checkable by the compiler. In languages that support sealed or closed hierarchies, such as Java with sealed classes, the set of allowed subtypes is restricted to a known, finite list, providing similar guarantees about openness and extensibility.

Examples help illustrate the idea. Haskell and ML commonly define closed types via data or datatype declarations (for instance, Color = Red | Green | Blue). In object-oriented contexts, a sealed class or interface constrains subclassing to a predetermined set of implementations. By contrast, open types or extensible variants permit new cases to be added outside the original scope, often complicating safety guarantees.

Applications of closedtypes include ensuring exhaustiveness in pattern matching, enabling optimizations, and facilitating modular design and security by preventing external code from extending critical types. See also sealed classes, algebraic data types, abstract data types, and opaque types.