Covariance and contravariance (computer science): Difference between revisions

Revision as of 01:05, 23 December 2023

Revision as of 21:42, 23 December 2023

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Depending on the variance of the [[type constructor]], the subtyping relation of the simple types may be either preserved, reversed, or ignored for the respective complex types. In the [[OCaml]] programming language, for example, "list of Cat" is a subtype of "list of Animal" because the list type constructor is '''covariant'''. This means that the subtyping relation of the simple types is preserved for the complex types.

On the other hand, "function offrom Animal to String" is a subtype of "function offrom Cat to String" because the function type constructor is '''contravariant''' in the [[parameter (computer science)|parameter]] type. Here, the subtyping relation of the simple types is reversed for the complex types.

A programming language designer will consider variance when devising [[typing rule]]s for language features such as [[Array (data type)|array]]s, [[Inheritance (object-oriented programming)|inheritance]], and [[generic datatype]]s. By making type constructors covariant or contravariant instead of '''invariant''', more programs will be accepted as well-typed. On the other hand, programmers often find contravariance unintuitive, and accurately tracking variance to avoid [[runtime errors|runtime type errors]] can lead to complex typing rules.