Typesubtype

Typesubtype, commonly referred to simply as subtyping, is a relationship between types in a type system. If type A is a subtype of type B, values of A can be used wherever a value of B is expected without causing type errors. This containment means every value of A is also a value of B, but B may have additional values that A does not possess.

In programming languages with inheritance, subtyping often comes from class hierarchies: if A extends B, then A is a subtype of B. For example, a Dog is a subtype of Animal, so a function that expects an Animal can be given a Dog. Subtyping supports polymorphism, enabling code that works with a general type to also work with its specific subtypes.

Formal rules of subtyping can vary. A common notation is A ≤ B to denote that A is a subtype of B. In addition to nominal typing based on declared inheritance, some systems use structural typing where subtyping depends on the actual shape or members of a type rather than its name.

When parameterized types are involved, subtyping becomes more nuanced. Variance explains how subtyping propagates through type constructors: covariant, contravariant, or invariant positions determine whether a container of A can be used where a container of B is expected. For example, function types and generic collections rely on these rules to preserve type safety.

Subtyping is central to type safety and language design. It supports flexible interfaces and code reuse while requiring careful handling of casts and conversions. Related concepts include the Liskov substitution principle, type hierarchies, and both nominal and structural type systems.