typet

Typet is a term used in programming language theory and type systems to denote a meta-type, the type of types rather than of values. In this sense typet refers to the kind of a type, and is thus positioned above conventional data types in the hierarchy of a language's type system. While not standardized across languages, typet is often encountered in educational discussions to illustrate higher-level abstractions such as higher-kinded types, type constructors, and universes.

In practice, typet is closely related to the concept of kinds or universes. A typet may classify types by their shape, arity, or the collection of type constructors they support. In dependently typed or higher-order type systems, typet can enable type-level computation, allowing programs to manipulate and reason about types themselves rather than only values.

Usage examples tend to revolve around type constructors that operate on other types. For instance, a parameterized container type might be described as mapping a typet to a concrete type, enabling generic programming and code reuse. Typet also supports language features such as higher-kinded polymorphism, where functions can be abstracted over type constructors, not just plain types.

Limitations and debates around typet focus on coherence, consistency of universes, and the potential for paradoxes in unrestricted type-level programming. Some languages choose to enforce a hierarchy of universes or to separate value-level and type-level computation to maintain soundness.

Typet remains a teaching tool and a conceptual construct rather than a universally standardized feature. See also kinds, universes, type theory, parametric polymorphism.