WPF DataGrid not updating - is it one-way binding?

Question

C#, WPF. I am using a Datagrid with binding. My understanding is that with INotifyPropertyChanged implemented, object properties should update in the Datagrid if they are changed.

Currently this is not happening, although I I have implemented INotifyPropertyChanged and I know from testing that the PropertyChanged event is firing. My guess is that binding is not two-way(?) If that is the case I'm not sure how to set it to two-way. The binding is set in XAML, and the ItemsSource is set later in code-behind:

<DataGrid Name="dataGridxyz" ItemsSource="{Binding}">

---

dataGridxyz.ItemsSource = foo;

Adding two-way binding in XAML using this syntax causes an error:

<DataGrid Name="dataGridxyz" ItemsSource="{Binding, Mode=TwoWay}">

So I was looking for something like this:

dataGridxyz.ItemsSource = foo;
dataGridxyz.Binding.Mode = TwoWay;

It may be that I could set it to two-way binding either in XAML or code-behind... but I can't see how to do either.

EDIT:

The following is minimal functional example to show the problem. It is a much-simplified version of the real thing which is part of a much bigger project.

When the button is clicked, the Name property is changed but it does not update in the PropertyGrid.

<Window x:Class="testBinding.MainWindow"
        xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
        xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
        xmlns:d="http://schemas.microsoft.com/expression/blend/2008"
        xmlns:mc="http://schemas.openxmlformats.org/markup-compatibility/2006"
        mc:Ignorable="d"
        Title="MainWindow">
    <Grid>
        <StackPanel Orientation="Vertical">
            <DataGrid Name="dg" ItemsSource="{Binding}" AutoGenerateColumns="True"/>
            <Button Name="btn" Width="100" Height="20" Content="Test" Click="btn_Click"/>
        </StackPanel>
    </Grid>

---

namespace testBinding
{
    public partial class MainWindow : Window
    {
        BindingList<foo> bar = new BindingList<foo>() { new foo() };
        public MainWindow()
        {
            InitializeComponent();
            dg.ItemsSource = bar;
        }

        private void btn_Click(object sender, RoutedEventArgs e)
        {
            bar[0].Name = "Paul";
        }
    }

    class foo : genericClass, INotifyPropertyChanged
    {
        public event PropertyChangedEventHandler PropertyChanged;
    }

    class genericClass : INotifyPropertyChanged
    {
        private string _name = "John";
        public string EyeColor = "Blue";
        public bool Child = false;

        public event PropertyChangedEventHandler PropertyChanged;
        protected virtual void OnPropertyChanged([CallerMemberName] string propertyName = null)
        {
            PropertyChanged?.Invoke(this, new PropertyChangedEventArgs(propertyName));
        }

        public string Name
        {
            get { return _name; }
            set
            {
                _name = value;
                MessageBox.Show("Name changed!"); // !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
                OnPropertyChanged("Name");
            }
        }
    }
}

Answer 1

I figured out what was happening here through a combination of guesswork and trial and error. Thanks to those who commented.

It was not caused by one-way binding as I had originally surmised.

This problem was caused by the fact that the foo object in the example above inherits from another class (genericClass) and both implement INotifyPropertyChanged. It seems clear that the existence of the PropertyChanged event in the foo class prevents the DataGrid from updating. I had not expected this behavior since I know that the PropertyChanged event in the inherited class does fire and does update the Name property.

If I remove the PropertyChanged event from foo, then the name updates in the PropertyGrid as expected.

class foo : genericClass, INotifyPropertyChanged
    {
        //public event PropertyChangedEventHandler PropertyChanged;
    }

It leaves me with the problem of how to handle property changes at more than one level of inheritance (i.e. both in a class and in one it inherits from, which seems a valid thing to do) ... but that is perhaps a different question.