Question

I’ve been implementing an enhanced Shunting-Yard algorithm for parsing an arithmetic expression. One aspect of the algorithm, is that it maintains a Queue, and a Stack.

In my implementation, the Queue contains Expressions and Operators.
The Stack contains Operators and Parenthesis.

Expressions, Parenthesis, and Operators have nothing in common that warrants any two of them having a shared interface.

Approaches:

• My current implementation consists of Expression and Operator implementing a INotParanthesis. Operator and Paranthesis implement a INotExpression. I then declare Queue <INotParanthesis>, and Stack <INotExpression>.

  I don’t like this implementation – these interfaces seem very much a hack for the purpose of cleaner algorithm code. I also believe that interfaces should describe what an object is, as opposed to what it isn’t.

• On the other hand, I also don’t want to use collections of <Object>, as it can be difficult to be certain of the correctness of such code.

• The only one I’ve come up with, so far, is implementing my own NonParanthesisQueue and NonExpressionStack containers. This has the advantage of more consistent type checking on objects getting pulled out of those containers – and the disadvantage of a lot more code.

Are there any reasonable alternatives to my approaches?

Answer 1

It sounds like what you really want is a sum type. Although C# does not have these built in, there’s a trick from functional programming that you can use called Church encoding to achieve this. It’s completely type safe with no casts involved, however it’s a bit weird to use in C# mostly due to the limitations of the type inference.

The main trick is that instead of using properties and checks to retrieve one of the two alternatives, we have a higher order function Map that takes two functions as arguments and calls the appropriate one depending on which alternative was present. Here’s how you would use it:

var stack = new Stack<IEither<Operator, Parenthesis>>();

stack.Push(new Left<Operator, Parenthesis>(new Operator()));
stack.Push(new Right<Operator, Parenthesis>(new Parenthesis()));

while (stack.Count > 0)
{
    stack.Pop().Map(op  => Console.WriteLine("Found an operator: " + op),
                    par => Console.WriteLine("Found a parenthesis: " + par));
}

Here’s the implementation of IEither, Left and Right. They are fully generic and could be used anywhere you want a sum type.

public interface IEither<TLeft, TRight>
{
    TResult Map<TResult>(Func<TLeft, TResult> onLeft, Func<TRight, TResult> onRight);
    void Map(Action<TLeft> onLeft, Action<TRight> onRight);
}

public sealed class Left<TLeft, TRight> : IEither<TLeft, TRight>
{
    private readonly TLeft value;

    public Left(TLeft value)
    {
        this.value = value;
    }

    public TResult Map<TResult>(Func<TLeft, TResult> onLeft, Func<TRight, TResult> onRight)
    {
        return onLeft(value);
    }

    public void Map(Action<TLeft> onLeft, Action<TRight> onRight)
    {
        onLeft(value);
    }
}

public sealed class Right<TLeft, TRight> : IEither<TLeft, TRight>
{
    private readonly TRight value;

    public Right(TRight value)
    {
        this.value = value;
    }

    public TResult Map<TResult>(Func<TLeft, TResult> onLeft, Func<TRight, TResult> onRight)
    {
        return onRight(value);
    }

    public void Map(Action<TLeft> onLeft, Action<TRight> onRight)
    {
        onRight(value);
    }
}

---

References:

• Tagged union
• Algebraic data type
• Church encoding