Add C# as another examples

[Phyllee]

Hi!
so when I eventually looked at the rust and java code... I realized there is no virtual and override (well it does show in java, but not explicit)

so why not add C# as another examples of polymorphism in appendix B

// C# implementation of the Taylor series example program based on
// subtyping given in Appendix B of the proposal "Improved run-time
// polymorphism for Fortran".
//

using System;

public interface IDeriv {
    void Deriv1();
}

public interface IHDeriv : IDeriv {
    void Deriv2();
}

public abstract class DerivativeBase : IDeriv {
    public virtual void Deriv1() {
        Console.WriteLine(" Default derivative implementation.");
    }
}

public class DerivF : DerivativeBase {
    public override void Deriv1() {
        Console.WriteLine(" 1st derivative of function F!");
    }
}

public class HDerivF : DerivativeBase, IHDeriv {
    public override void Deriv1() {
        Console.WriteLine(" 1st derivative of function F!");
    }

    public void Deriv2() {
        Console.WriteLine(" 2nd derivative of function F!");
    }
}

public class DerivG : DerivativeBase
{
    public override void Deriv1() {
        Console.WriteLine(" 1st derivative of function G!");
    }
}

public class HDerivG : DerivativeBase, IHDeriv {
    public override void Deriv1() {
        Console.WriteLine(" 1st derivative of function G!");
    }

    public void Deriv2() {
        Console.WriteLine(" 2nd derivative of function G!");
    }
}

public class Taylor {
    private readonly IDeriv _calc;

    public Taylor(IDeriv calc) {
        _calc = calc;
    }

    public void Term1() {
        _calc.Deriv1();
    }

    public void Evaluate() {
        Console.WriteLine("Evaluating Taylor series using");
        Term1();
    }
}

public class HTaylor {
    private readonly IHDeriv _calc;

    public HTaylor(IHDeriv calc) {
        _calc = calc;
    }

    public void Term1() {
        _calc.Deriv1();
    }

    public void Term2() {
        _calc.Deriv2();
    }

    public void Evaluate() {
        Console.WriteLine("Evaluating Taylor series using");
        Term1();
        Term2();
    }
}

class Program {
    static void Main() {
        IDeriv derivg = new DerivG();
        IDeriv derivf = new DerivF();
        IHDeriv hderivg = new HDerivG();
        IHDeriv hderivf = new HDerivF();

        Taylor evalG = new Taylor(derivg);
        Taylor evalF = new Taylor(derivf);
        HTaylor hevalG = new HTaylor(hderivg);
        HTaylor hevalF = new HTaylor(hderivf);

        evalG.Evaluate();
        Console.WriteLine();
        evalF.Evaluate();
        Console.WriteLine();
        hevalG.Evaluate();
        Console.WriteLine();
        hevalF.Evaluate();
    }
}