Reflexivetype

Reflexivetype is a term used in type theory and programming languages to denote a type that refers to itself, either directly within its definition or via a fixed-point construction. In this sense, reflexivetype supports recursion at the type level, enabling definitions where a type is built in terms of itself.

In programming, reflexivetype concepts appear as self-types, this-type, or fixed-point encodings that allow methods to return the most specific subtype or to express constraints that reference the implementing type. This enables patterns such as fluent interfaces, the Curiously Recurring Template Pattern (CRTP), and precise typing of self-referential structures. Languages differ in how they expose reflexivetype features: for example, Scala provides this.type and self-types to constrain and refine types in terms of the implementing class; Rust uses the Self type to refer to the implementing type within trait definitions; TypeScript exposes a this type to describe methods that return the exact runtime type. Many functional or ML-style languages implement reflexivetype indirectly through recursive or fixed-point type constructors.

From a type-theory perspective, reflexivetype often requires recursive or guarded type definitions, such as mu X. F(X), which denote the least fixed point of a type operator F. These recursive types enable the modeling of endlessly nested or self-similar data structures, such as linked lists or self-referential records, while preserving type safety.

Practical use of reflexivetype involves trade-offs: it can increase expressiveness and type precision but may complicate type inference and lead to more complex error messages. Correct usage typically requires explicit annotations or language-supported facilities for self-referential typing.

See also: self-type, this type, recursive type, fixed-point type, CRTP, mu type, type safety.