// And = a => b => a(b)(False) public static Boolean And(this Boolean a, Boolean b) => ChurchBoolean.And(a)(b);
// IsNotHalting = f => If(IsHalting(f)(f))(_ => Sequence(Ω())(False))(_ => True)
internal Boolean IsNotHalting <T>
(ω <T> f) =>
ChurchBoolean <Boolean> .If(this.IsHalting(new Func <ω <T>, T>(f))(f))
(_ => Sequence <T, Boolean>(OmegaCombinators <T> .Ω(__ => __))(False))
(_ => True);
// Factorial = factorial => numeral => If(numeral.IsZero())(_ => One)(_ => factorial(numeral.Decrease()));
public static Func <NumeralWrapper, NumeralWrapper> Factorial(Func <NumeralWrapper, NumeralWrapper> factorial) => numeral =>
ChurchBoolean <NumeralWrapper> .If(numeral.IsZero())
(_ => NumeralWrapper.One)
(_ => factorial(numeral.Decrease()));