Concept of C# polymorphism-Collection of common programming errors

Use ‘new’ modifier, which function will be called is determined when it is compiled.The program will choose the object’s declared type to call its function.(As above, the f’s declared type is father ,so using ‘new’ modifier make the output to show ‘father’.

Not really. The decision is still made at execution time, but the new method does not override the virtual method in the base class. This is most easily shown by extending your example somewhat:

using System;

class Base
{
    public virtual void Foo()
    {
        Console.WriteLine("Base.Foo");
    }
}

class Derived : Base
{
    public override void Foo()
    {
        Console.WriteLine("Derived.Foo");
    }
}

class MoreDerived : Derived
{
    public new void Foo()
    {
        Console.WriteLine("MoreDerived.Foo");
    }
}

class Test
{
    static void Main()
    {
        Base x = new MoreDerived();
        x.Foo(); // Prints Derived.Foo
    }
}

Here, at compile time the decision is made to call the most overridden implementation of Base.Foo – if there were multiple Foo signatures, the decision about which signature to use would be taken, for example. Which implementation will be “the most overridden” is unknown at this point, of course.

At execution time, the CLR will find that most overridden implementation based on the actual type of the target object – which is MoreDerived. But MoreDerived.Foo doesn’t override Base.Foo… whereas Derived.Foo does, so the implementation in Derived is the one which is actually executed.