højtype

Højtype is a term used in Danish computer science, mathematics and logic to refer to higher-order types—types that describe or parameterize other types. The concept appears in discussions of type systems, lambda calculus, and functional programming, where types can operate on types themselves rather than only on values.

Etymology and usage

The word combines høj meaning “high” and type, and is closely related to the English term “higher-type.” In Danish technical writing, it is sometimes rendered as højere type or higher-type, depending on author preference. The term is most common in specialized texts rather than in everyday programming language discussions.

Contexts and examples

- In type theory and semantics, higher-type concepts describe categories of types or types of type constructors. For example, a type constructor that takes a type and returns a new type is a higher-type construct, because it takes types as input and yields types as output.

- In functional programming, higher-order types underlie parametric polymorphism and generic programming. A type constructor like List, which can be applied to different element types (List<Integer>, List<String>), is often discussed in the context of higher-type reasoning.

- In logic and proof theory, higher-type concepts relate to the hierarchy of propositions and functions that can quantify over other functions or predicates.

Related terms

Højere ordre (higher-order) and højere-type functionality are closely related. The field also intersects with higher-order logic, type theory, and category theory, where hierarchical type structures are analyzed.

See also

Higher-order function, type theory, lambda calculus, type system, generic programming.