subtyping

Subtyping is a relation between types in a programming language where one type, called a subtype, is considered a more specific version of another type, its supertype. Values of the subtype can be used wherever a value of the supertype is expected, without altering the program’s correctness. Subtyping enables polymorphism and code reuse by allowing operations to be written in terms of the supertype and applied to any of its subtypes.

The relationship is often described in terms of substitutability. The Liskov Substitution Principle specifies that objects of a subtype should be usable wherever objects of the supertype are expected, preserving expected behavior. This principle supports safe extension and refinement of types in object-oriented and related paradigms.

Subtyping systems can be nominal or structural. In nominal typing, subtyping is declared explicitly through inheritance or interface implementation. In structural typing, subtyping is determined by the shape of types, such as the presence of compatible members, regardless of explicit declarations. Languages vary in whether they adopt nominal or structural subtyping; for example, Java uses nominal typing, while many typing systems for functional or scripting languages use structural rules or a mix of both.

Subtyping interacts closely with generics and variance. Variance describes how subtyping relates to type parameters: covariant, contravariant, or invariant, affecting how subtypes propagate through parameterized types. Subtyping also interfaces with type safety and language design, influencing how easily code can be reused and how robust the type system remains.

Common considerations include coercions and upcasts, where values are treated as their supertype, and the potential for runtime type errors if subtyping rules are violated.