Why I could not serialize a tuple in C#? [duplicate]

For XmlSerializer to be able to do its job it needs a default contructor. That is a constructor that takes no arguments. All the Tuple<...> classes have a single constructor and that constructor takes a number of arguments. One for each value in the tuple. So in your case the sole constructor is

Tuple(T1 value1, T2 value2)

The serializer is looking for a constructor with no arguments and because it can't find it, you get the exception.

you could create a mutable class, that could be substituted for tuples for the purpose of serialization

class MyTuple<T1, T2>
{
    MyTuple() { }

    public T1 Item1 { get; set; }
    public T2 Item2 { get; set; }

    public static implicit operator MyTuple<T1, T2>(Tuple<T1, T2> t)
    {
         return new MyTuple<T1, T2>(){
                      Item1 = t.Item1,
                      Item2 = t.Item2
                    };
    }

    public static implicit operator Tuple<T1, T2>(MyTuple<T1, T2> t)
    {
        return Tuple.Create(t.Item1, t.Item2);
    }
}

You could then use it the following way

XmlSerializer formatter = new XmlSerializer(
    typeof(List<List<MyTuple<String, CodeExtractor.StatementNode>>>));

formatter.Serialize(fs, results.SelectMany(
                              lst => lst.Select(
                                        t => (MyTuple)t
                                     ).ToList()
                              ).ToList());

As the exception tells you: The Tuple<T1, T2> has NO parameterless constructor which is needed by the serializer.