Kindfunction

Kindfunction is a theoretical construct in type theory and programming languages describing a function whose inputs and outputs are kinds rather than types. In languages with sophisticated kind systems, kinds classify types; a kindfunction operates at that level, producing new kinds from existing ones. It is the kind-level analogue of a type-level function (such as a type family or type operator) that maps types to types.

In formal terms, a kindfunction F has kind K1 -> K2, where K1 and K2 are kinds. Applying F to a specific kind k1 yields a new kind F k1 of kind K2. Many languages with higher-kinded types support such constructs indirectly via type operators and type families. They enable encoding generic abstractions that manipulate type constructors themselves, not only concrete types.

Usage and interpretation: Kindfunctions enable higher-level abstractions such as composing type constructors, abstracting over the arity of type constructors, or expressing generic pipelines that transform one kind into another. They are essential in discussions of type-level programming, dependent types, and language design.

Limitations: Not all languages expose kind-level computation; many implement it using type-level features like type families, type operators, or dependent types. The practical form of kindfunctions varies between languages and may be restricted to certain universes or levels to avoid inconsistencies.

See also: Kind, Type, Type-level programming, Type family, Higher-kinded types, Dependent type.