Covariance, Invariance, and Contravariance: How Do Subtype Relationships Transform?

Understanding Covariance, Invariance, and Contravariance

Understanding the intricacies of covariance, invariance, and contravariance is crucial for mastering type relationships in programming.

What Are They?

In essence, these terms describe how the relationship between types and subtypes transforms. Let's consider a scenario where we have two types, A and B, and a transformation function f. Suppose ≤ denotes the subtype relation (with A ≤ B indicating that A is a subtype of B).

• Covariant: f is covariant if A ≤ B implies f(A) ≤ f(B).
• Contravariant: f is contravariant if A ≤ B implies f(B) ≤ f(A).
• Invariant: f is invariant if neither of the above conditions holds.

Examples in Java

Let's explore some Java examples to clarify these concepts:

• Covariance: Consider f(A) = List. Since a List is not a subtype of List
• Contravariance: Consider f(A) = A[]. In Java, arrays are covariant, meaning that String[] is a subtype of Object[].

Application in Programming

Subtyping plays a crucial role in:

• Assignment: x = y is valid only if typeof(y) ≤ typeof(x).

  • In Java, ArrayList cannot be assigned to ArrayList

• Method Invocation: result = method(a) requires typeof(a) ≤ typeof(parameter) and returntype ≤ typeof(result).

  • Number[] cannot be returned by method(ArrayList) because Number[] ≠ ArrayList[].

• Overriding: The method parameter of the overriding method must be a supertype of the overridden method, and the return type a subtype.

  • In Java 1.4, return types must be identical in overridden methods.
  • In Java 1.5 and later, covariant return types are allowed (e.g., Iterator in Collection and ListIterator in List).

Understanding these concepts is essential for navigating the complexities of type relationships effectively.

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