Type Systems: Covariance, Contravariance, Bivariance, and Invariance explained

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Variance is a topic that comes up fairly often in type systems and can be a bit confusing the first time you hear it. Let’s walk through each form of variance.

First we’ll setup a couple of classes that extend one another.

class Noun {}
class City extends Noun {}
class SanFrancisco extends City {}

We’ll use these classes to write a method that has each kind of variance.

Invariance

function method(value: <strong><em>Invariant</em><City></strong>) {...}

method(new Noun());         // error...
method(new City());         // okay
method(new SanFrancisco()); // error...

Invariance does not accept supertypes .

Invariance does not accept subtypes .

Covariance

function method(value: <strong><em>Covariant</em><City></strong>) {...}

method(new Noun());         // error...
method(new City());         // okay
method(new SanFrancisco()); // okay

Covariance does not accept supertypes .

Covariance does accept subtypes .

Contravariance

function method(value: <strong><em>Contravariant</em><City></strong>) {...}

method(new Noun());         // okay
method(new City());         // okay
method(new SanFrancisco()); // error...

Contravariance does accept supertypes .

Contravariance does not accept subtypes .

Bivariance

function method(value: <strong><em>Bivariant</em><City></strong>) {...}

method(new Noun());         // okay
method(new City());         // okay
method(new SanFrancisco()); // okay

Bivariance does accept supertypes .

Bivariance does accept subtypes .