C#: Getting Names of properties in a chain from lambda expression

Something like this?

public void Foo<T, P>(Expression<Func<T, P>> expr)
{
    MemberExpression me;
    switch (expr.Body.NodeType)
    {
        case ExpressionType.Convert:
        case ExpressionType.ConvertChecked:
            var ue = expr.Body as UnaryExpression;
            me = ((ue != null) ? ue.Operand : null) as MemberExpression;
            break;
        default:
            me = expr.Body as MemberExpression;
            break;
    }

    while (me != null)
    {
        string propertyName = me.Member.Name;
        Type propertyType = me.Type;

        Console.WriteLine(propertyName + ": " + propertyType);

        me = me.Expression as MemberExpression;
    }
}

I played a little with ExpressionVisitor:

public static class PropertyPath<TSource>
{
    public static IReadOnlyList<MemberInfo> Get<TResult>(Expression<Func<TSource, TResult>> expression)
    {
        var visitor = new PropertyVisitor();
        visitor.Visit(expression.Body);
        visitor.Path.Reverse();
        return visitor.Path;
    }

    private class PropertyVisitor : ExpressionVisitor
    {
        internal readonly List<MemberInfo> Path = new List<MemberInfo>();

        protected override Expression VisitMember(MemberExpression node)
        {
            if (!(node.Member is PropertyInfo))
            {
                throw new ArgumentException("The path can only contain properties", nameof(node));
            }

            this.Path.Add(node.Member);
            return base.VisitMember(node);
        }
    }
}

Usage:

var path = string.Join(".", PropertyPath<string>.Get(x => x.Length).Select(p => p.Name));