Number of sealed / unsealed types in the framework

A Console application to determine the number of sealed and unsealed types in the framework

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static class Program
{
    static void Main(string[] args)
    {
        var publicFrameworkTypes = new HashSet<Type>(
            from assembly in AppDomain.CurrentDomain.GetAssemblies()
            from type in assembly.GetTypes()
            where type.FullName.StartsWith("System")
            where type.IsPublic
            where !type.IsValueType
            where !type.IsInterface
            where !type.IsPointer
            where !type.IsPrimitive
            select type);

        Console.WriteLine("publicFrameworkTypes.Count: " + publicFrameworkTypes.Count());

        // Non-leaf types are types that have descendents within the framework.
        var nonLeafTypes = new HashSet<Type>(
            from type in publicFrameworkTypes
            from nonLeafType in type.GetBaseTypes()
            where nonLeafType.IsPublic
            where publicFrameworkTypes.Contains(nonLeafType)
            select nonLeafType);

        Console.WriteLine("nonLeafTypes.Count: " + nonLeafTypes.Count());

        // Leaf types are types that don't have any descendents within the framwork.
        var leafTypes = new HashSet<Type>(publicFrameworkTypes);
        leafTypes.ExceptWith(nonLeafTypes);

        Console.WriteLine("leafTypes.Count: " + leafTypes.Count());

        var sealedLeafTypes = (
            from leafType in leafTypes
            where leafType.IsSealed || !leafType.HasPublicConstructors()
            select leafType).ToArray();

        var openLeafTypes = (
            from leafType in leafTypes
            where !(leafType.IsSealed || !leafType.HasPublicConstructors())
            select leafType).ToArray();

        Console.WriteLine("Open types: {0} = {1:p}", openLeafTypes.Length,
            (double)openLeafTypes.Length / (double)leafTypes.Count);
        Console.WriteLine("Sealed types: {0} = {1:p}", sealedLeafTypes.Length,
            (double)sealedLeafTypes.Length / (double)leafTypes.Count);

        Console.WriteLine("Done");
        Console.ReadLine();
    }

    private static IEnumerable<Type> GetBaseTypes(this Type type)
    {
        var baseType = GetGenericTypeDefinition(type.BaseType);

        while (baseType != null)
        {
            yield return baseType;
            baseType = GetGenericTypeDefinition(baseType.BaseType);
        }
    }

    private static Type GetGenericTypeDefinition(Type type)
    {
        return type != null && type.IsGenericType ? type.GetGenericTypeDefinition() : type;
    }

    private static bool HasPublicConstructors(this Type type)
    {
        return type.GetConstructors(BindingFlags.Instance | BindingFlags.Public).Any();
    }
}