Variance Describes When a Subtype Can Be Used in Place of a Supertype, Covariant, Invariant, or Contravariant

Variance describes what types are subtypes of other types and when a type can be used in place of a supertype (and viceversa).
For example, Turtle is a subtype of Animal and in Java you can pass Turtle to a function that accepts an Animal.

All types with generic parameters have a variance with respect to those parameters.
There are three kinds of variance:

• covariant, a subtype can be used in place of the type. If Turtle <: Animal, then List<Turtle> <: List<Animal>
• invariant, you must provide exactly the given type; neither subtype nor supertype is accepted
• contravariant — a supertype can be used in place of the type. Function argument types are contravariant: a function that accepts Animal can be used where a function that accepts Turtle is expected, because it handles more

See also

• Chomsky hierarchy - Regular < Context-Free < Context-Sensitive < Recursively Enumerable — the Chomsky hierarchy is a subtype relationship between language classes: a Regular language is a subtype of Context-Free; covariance applies here too
• Functional Programming programs are trees of expressions, not sequences of steps — contravariance of function arguments is most visible in functional programming: a more general function (Animal -> Bool) can safely replace a more specific one (Turtle -> Bool)

References

• J. Gjengset, Rust for Rustaceans: Idiomatic Programming for Experienced Developers. No Starch Press, 2021.