kindlevel

Kindlevel is a concept in type theory and programming language design that refers to the level at which a kind resides within a hierarchy that classifies types and type constructors. Kinds are the "types of types," and, in systems that support multiple universes, kinds themselves can be organized into layers. The lowest level typically describes ordinary types (often called Type0 or Set0), while higher levels describe kinds of type constructors and beyond, forming a universe-like structure that prevents circularities and paradoxes.

In practice, kindlevel helps manage the complexity of polymorphism and higher-order abstractions. A plain type, such as a concrete data type, sits at a base level. A type constructor that takes a type and yields another type, such as a generic List, has a higher kind (a type constructor of arity greater than zero) and is associated with a higher kindlevel. More abstract operators that map type constructors to other type constructors sit at even higher levels. Languages with explicit universe hierarchies use labels like Type0, Type1, Type2 (or Set0, Set1, Set2) to denote these levels and to enforce consistency across definitions.

Examples appear in dependently typed languages such as Coq, Agda, and Lean, which employ universe polymorphism to allow definitions to be instantiated at different kindlevels. Haskell’s higher-kinded types also illustrate the idea, with kinds such as * -> * indicating a type constructor that takes a type and returns a type. The term kindlevel is not universally standardized but is commonly used to discuss the depth of a kind within a universe hierarchy. See also type theory, kinds, universes, and higher-kinded types.