Supertypesubtype

Supertypesubtype is a term describing the core relationship in type systems between a type that is more general (the supertype) and a type that is more specific (the subtype). The subtyping relation is typically reflexive and transitive: every type is a subtype of itself, and if B is a subtype of A and C is a subtype of B, then C is a subtype of A. In practice, values of a subtype can be used wherever a value of the supertype is expected, a principle known as substitutability.

In common programming languages, subtyping underpins polymorphism. For example, in Java or C#, Integer is a subtype of Number, and Number is a subtype of Object; an Integer value can be treated as a Number or an Object. Similarly, ArrayList implements the List interface, making ArrayList a subtype of List. The exact rules vary by language and typing discipline, influencing whether subtyping applies to classes, interfaces, or generic types.

Subtyping interacts with variance, especially in function types and generics. For function values, parameter types are often contravariant and return types covariant. Some languages enforce invariance for generic type parameters to preserve type safety. Nominal typing bases subtyping on declared relationships (such as class inheritance), while structural typing derives subtyping from the compatibility of members rather than declarations.

Practical implications include code reuse, API design, and safety guarantees. Subtyping enables abstraction and polymorphic behavior, while also requiring careful design to avoid unintended substitutions or runtime errors. The supertypesubtype concept thus organizes understanding of how more general interfaces and concrete implementations relate and how values flow through a type hierarchy.