subtyper

Subtyper is a term used in type theory and programming to describe the relationship that makes one type a subtype of another. In a subtyping relation, a type A is a subtype of type B if every value of A can be used wherever a value of B is expected, without causing type errors. The relation is typically denoted A <: B and is defined to be reflexive (A <: A) and transitive (if A <: B and B <: C, then A <: C).

Subtyping arises from the need to reason about polymorphism and code reuse. It enables upcasting, where a value of a more specific type is treated as a value of a more general type, and supports safe substitution in programs. Subtyping can be nominal, where the relation is declared by explicit inheritance or interface implementation, or structural, where the relation is determined by the shape of the types’ members.

Key aspects of subtyping include variance in generic types. For function types, parameters are contravariant and return types are covariant: a function that accepts a more general parameter type and returns a more specific type can be a subtype of another function type, under certain rules. For container types, variance (covariant, contravariant, or invariant) determines whether a container of one type can be substituted for a container of another.

Common examples include class hierarchies in object-oriented languages (Dog is a subtype of Animal) and, with varying rules, generic collections (e.g., List<Dog> versus List<Animal>).

Subtyping is enforced by a language’s type system or a dedicated subtyping checker, ensuring type safety while enabling flexible and reusable code. See also type system, variance, covariance, contravariance, and polymorphism.