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Immutability, part 2: Creating a simple immutable stack

Posted on Sunday, June 23, 2013

Last time, I explained the basic meaning of immutability. The simplest useful example of an immutable class is an immutable stack. Immutable stacks work just like regular stacks – with Push(), Pop(), and Peek() methods – except that instead of mutating the original instance, Push() and Pop() return a new, modified, instance.

In code, that looks like

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

IStack<int> myStack = empty;
myStack = myStack.Push(1).Push(2).Push(3);

while (!myStack.IsEmpty) {
    Console.WriteLine(myStack.Peek());
    myStack = myStack.Pop();
}

Each implementation of this interface would supply a singleton empty instance; since they are immutable; there is no need to have more than one empty instance. Thus, there is no need for a constructor. Since Pop() needs to return the new stack, it cannot return the removed item; therefore, Peek() is the only way to get the item.

As a side benefit, this pattern naturally enables and encourages fluent interfaces, since each mutation methods returns a new instance. (eg, myStack.Push(1).Push(2).Push(3))

The naive implementation of this interface would use a list, and copy the list when creating a new stack:

public class NaiveStack<T> : IStack<T> {
    private readonly ReadOnlyCollection<T> items;
    private NaiveStack(IList<T> items) {
        this.items = new ReadOnlyCollection<T>(items);
    }

    public static readonly NaiveStack<T> Empty 
        = new NaiveStack<T>(new T[0]);

    public IStack<T> Push(T element) {
        var list = new List<T>(items);
        list.Add(element);
        return new NaiveStack<T>(list);
    }

    public IStack<T> Pop() {
        if (IsEmpty)
            throw new InvalidOperationException("Stack is empty");
        var list = new List<T>(items);
        list.RemoveAt(list.Count - 1);
        return new NaiveStack<T>(list);
    }

    public T Peek() { return items.Last(); }
    public bool IsEmpty { 
        get { return items.Count == 0; } 
    }
}

The problem with this approach is that each mutation requires an O(n) copy to create the list behind the new instance. This makes Push() and Pop() awfully slow, and vastly increases the memory footprint until the intermediate instances can be GCd.

To solve these problems, we can design the stack as a persistent data structure. Instead of copying anything when pushing on to a stack, we cab make the new stack instance hold only the newly added item, and maintain a reference to the previous instance storing the rest of the items. Popping from the stack can then simply return the previous instance. Basically, the stack becomes an immutable single-linked list.

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

    public IStack<T> Push(T element) {
        return new LinkNode(this, element);
    }

    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; } }
    }

    private 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; }
}

In this implementation, the empty and non-empty nodes are different enough that I decided to use polymorphism rather than if statements. The PersistentStack<T> type contains the only common logic (Push()); everything else is implement by the two concrete classes.

Here, the empty stack truly is a singleton; only one instance will ever be created for each element type. It can only be used as a starting point to create new stacks; the other methods simply throw exceptions. It also serves as the final node in the chain for all non-empty stacks.

Pushing onto any stack (empty or not) returns a new node that holds the new item and points to the previous stack; popping a non-empty stack simply returns that reference.

Like other linked lists, this approach implements both Push() and Pop() in O(1) in both memory and time.

Next time: Adding covariance

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

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