Functional Style Boolean Logic in C#

Are their any issues with this approach?  I'm also trying to follow a very function first style so am I doing that correctly.  Also can anyone see a way to make this shorter.  For instance I hate having to repeat the signatures twice every time.  var will not work here.  I'm trying to do something similar to what Erik did here. 

http://channel9.msdn.com/shows/Going+Deep/C9-Lectures-Dr-Erik-Meijer-Functional-Programming-Fundamentals-Chapter-4-of-13/ 

Thanks.

    abstract class Bool
    {
        public static readonly Bool True = new True();
        public static readonly Bool False = new False();

        public static readonly Func<Bool, Bool> Not =
            new Func<Bool, Bool>(a => a is True ? False : True );

        public static readonly Func<Bool, Func<Bool, Bool>> And =
            new Func<Bool, Func<Bool, Bool>>(a => b => a is True ? b : a);
    }
    class True : Bool {}
    class False : Bool {}

Actually after looking more carefully it looks like the And function might be more like below, which is better?

        public static readonly Func<Bool, Func<Bool, Bool>> And =
            new Func<Bool, Func<Bool, Bool>>(a =>
                a is True ?
                new Func<Bool, Bool>(b => b) :
                new Func<Bool, Bool>(_ => False));