Variance

Abstract

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• Let $C(T)$ be a complex type based on type $T$. The complex type $C$ can be Covariant, Contravariant and Invariant

Covariant

• Given two datatypes $S$ and $T$ and $C()$ as the complex type, $S:<T\to C(S)<:C(T)$

Covariance in Java arrays can lead to runtime errors

Java Arrays are Covariant.

• Imagine you have an array of Integer.
• Due to covariance, you can assign this array to a variable declared as an array of Object.
• Now, you might try to add a String to this array (which seems okay since it’s an array of Object).
• However, at runtime, Java discovers you’re trying to put a String into an array meant for Integer, causing an error.

Contravariant

• Given two datatypes $S$ and $T$ and $C()$ as the complex type, $S:<T\to C(T)<:C(S)$

Invariant

• If complex type $C$ is neither Covariant nor Contravariant

Invariants in Java

Primitive arrays and Generics are invariant.