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Immutability, part 2.5: Adding covariance to the immutable stack

Posted on Friday, June 28, 2013

Last time, I showed how to create a simple immutable stack. However, this stack is not covariant. Ideally, we should be able (for example) to implicitly convert IStack<string> to IStack<object>.

Most collection types cannot be co-variant. Had List<string> been convertible to List<object>, you would then be able to add an int (or any other type) to the converted List<object>, even though it can’t fit in List<string> (which the casted instance actually is). To be precise, covariance is only type-safe for immutable types.

Since our Stack<T> class is immutable, we should be able to simply change it to public interface Stack<out T> and get co-variance instantly.

In practice, it’s not so simple. Even though the class is immutable, it still has a method that takes T as a parameter (namely, Push(T)). Even though the method doesn’t mutate anything, it still wouldn’t be type safe:

IStack<string> stringStack = PersistentStack<string>.Empty;
IStack<object> objectStack = stringStack;
objectStack = objectStack.Push(4);
Console.WriteLine(objectStack.GetType());	// This is PersistentStack<string>

This isn’t safe because covariance is a property of the interface, not the implementing class. Even when casted to IStack<object>, the instance is still an IStack<string>, and therefore its Push(T) method can still only take a string. Similarly, the return value of Push() would still have been IStack<string>, which would be implicitly converted to IStack<object> to fit in the variable.

The actual behavior that we want for Push() is a little more subtle. If we have an IStack<string>, we should be able to push any object onto it, resulting in a new stack whose type is the least common ancestor between the type of the original stack and the type that we pushed. For example, Stack<Button>.Push(new TextBox()) should return a Stack<Control>.

Therefore, the desired signature for Push() would look like this:

public interface IStack<out T> {
	IStack<U> Push<U>(U element) where T : U;
	// Other members...

In other words, Push() can return a stack of any supertype of our element type. Unfortunately, this won’t work; C# (unlike Java) does not support upper bounds on a generic type parameter. You can write X<T> where T : SomeType, but not X<T> where SomeType : T.
Java, by contrast, would allow us to write Stack<U> <U super T> push(U element);.

However, all is not lost. Although we can’t constrain Push() based on the parent type’s type parameter, we can constrain it on its own type parameter. Specifically, we can make it an extension method:

public static IStack<U> Push<T, U>(this IStack<T> stack, U element) where T : U;

In fact, once we move it out of the class itself, we don’t even need a second type parameter. Since the stack is covariant, the IStack<T> parameter is convertible to IStack<U>, so we can simplify it to take just one generic parameter:

public static IStack<U> Push<U>(this IStack<U> stack, U element);

This way, you can write stringStack.Push(new object()), and the compiler will infer U to be object, then covariantly convert the IStack<string> to IStack<object> to pass as the first parameter.

Note that C#’s type inference algorithm will not attempt to find the least-common-ancestor when presented with two types (unless one is a descendant of the other), so you would need to specify the type parameter explicitly: buttonStack.Push<Control>(new TextBox()). Rather, it can only infer ancestral relationships can be inferred, such as buttonStack.Push(new Control()).

The only remaining problem is that the extension method must be specific to one implementation. It can extend (and return) the IStack interface, but it must create a specific implementing type. There is no elegant type-safe way for it to return whatever implementing type was passed to it.

Here is the code for a fully covariant immutable stack:

public interface IStack<out T> {
	IStack<T> Pop();
	T Peek();
	bool IsEmpty { get; }

public static class PersistentStackExtensions {
	public static IStack<TNew> Push<TNew>(this IStack<TNew> stack, TNew element)  {
		return new PersistentStack<TNew>.LinkNode(stack, element);

public abstract class PersistentStack<T> : IStack<T> {
	public static readonly PersistentStack<T> Empty = new EmptyNode();

	private class EmptyNode : PersistentStack<T> {
		public override IStack<T> Pop() {
			throw new InvalidOperationException("Stack is empty");
		public override T Peek() { 
			throw new InvalidOperationException("Stack is empty");
		public override bool IsEmpty { get { return true; } }

	internal class LinkNode : PersistentStack<T> {
		readonly IStack<T> previous;
		readonly T element;
		public LinkNode(IStack<T> previous, T element) {
			this.previous = previous;
			this.element = element;

		public override IStack<T> Pop() {
			return previous;
		public override T Peek() { return element; }
		public override bool IsEmpty { get { return false; } }
	public abstract IStack<T> Pop();
	public abstract T Peek();
	public abstract bool IsEmpty { get; }

IStack<string> stringStack = PersistentStack<string>.Empty;
stringStack = stringStack.Push("A").Push("B");

IStack<object> objectStack = stringStack.Push<object>(42);
while (!objectStack.IsEmpty) {
	objectStack = objectStack.Pop();

The private PersistentStack<T>.LinkNode class now needs to be internal so that the extension method can instantiate it.

Next time: Swapping immutable objects without losing thread-safety

Categories: C#, variance, oop, thread-safety, immutability Tweet this post

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