Subtyping
a form of type polymorphism
In programming language theory, subtyping (also called subtype polymorphism or inclusion polymorphism) is a form of type polymorphism. A subtype is a datatype that is related to another datatype (the supertype) by some notion of substitutability, meaning that program elements (typically subroutines or functions), written to operate on elements of the supertype, can also operate on elements of the subtype.
If S is a subtype of T, the subtyping relation (written as S <: T, S ⊑ T, or S ≤: T ) means that any term of type S can safely be used in any context where a term of type T is expected. The precise semantics of subtyping here crucially depends on the particulars of how "safely be used" and "any context" are defined by a given type formalism or programming language. The type system of a programming language essentially defines its own subtyping relation, which may well be trivial, should the language support no (or very little) conversion mechanisms.
Due to the subtyping relation, a term may belong to more than one type. Subtyping is therefore a form of type polymorphism. In object-oriented programming the term 'polymorphism' is commonly used to refer solely to this subtype polymorphism, while the techniques of parametric polymorphism would be considered generic programming.
Functional programming languages often allow the subtyping of records. Consequently, simply typed lambda calculus extended with record types is perhaps the simplest theoretical setting in which a useful notion of subtyping may be defined and studied.
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This entry incorporates text from “Subtyping” on English Wikipedia. Contributors are listed in the page history. Text is available under the Creative Commons Attribution-ShareAlike 4.0 License. Selected authority identifiers and statements are retrieved from Wikidata under CC0; their references and qualifiers remain part of the verification path.