Y y

Y.cs

void Main()
{
    foreach(var t in typeof(test).Assembly.GetTypes().Where(t => t.IsSubclassOf(typeof(test))))
        ((test)(Activator.CreateInstance(t))).TestMethod();
}

private abstract class test
{
    public abstract void TestMethod();
}

private class test1 : test
{

    delegate Action<T> Continuation<T>(Continuation<T> r);

    //[TestMethod]
    //The fixed point operator, very slow also.
    public override void TestMethod()
    {
        IObject root = BuildComposite();

        Performance.Measure(1000000, () =>
        {
            Apply(root, h => t =>
            {
                foreach (IObject item in t.Children)
                {
                    //Console.WriteLine(item.Name);
                    h(item);
                }
            });
        }, "Time " + this.GetType().Name);
    }

    private static void Apply(IObject root, Func<Action<IObject>, Action<IObject>> g)
    {
        Continuation<IObject> action = c => thing => { g(c(c))(thing); };

        Action<IObject> target = action(action);

        target(root);
    }

}

private class test2 : test
{

    delegate void Continuation<T>(Continuation<T> r, T n);

    //[TestMethod]
    //Without curry, curring makes things go slow.
    public override void TestMethod()
    {
        var root = BuildComposite();

        Performance.Measure(1000000, () =>
        {
            Apply(root, (c, thing) =>
            {
                foreach (var item in thing.Children)
                {
                    //Console.WriteLine(item.Name);
                    c(c, item);
                }
            });
        }, "Time " + this.GetType().Name);
    }

    void Apply(IObject root, Continuation<IObject> f)
    {
        f(f, root);
    }

}

private class test3 : test
{

    //[TestMethod]
    //Another common definition found on web, this is worse of then all.
    //https://stackoverflow.com/questions/4763690/alternative-y-combinator-definition
    public override void TestMethod()
    {
        var root = BuildComposite();

        Performance.Measure(1000000, () =>
        {
            Y<IObject, int>(f => thing =>
            {
                foreach (var item in thing.Children)
                {
                    //Console.WriteLine(item.Name);
                    f(item);
                }
                return 0;
            })(root);
        }, "Time " + this.GetType().Name);
    }

    public delegate TResult SelfApplicable<TResult>(SelfApplicable<TResult> r);

    public static TResult U<TResult>(SelfApplicable<TResult> r)
    {
        return r(r);
    }

    public static Func<TArg1, TReturn> Y<TArg1, TReturn>(Func<Func<TArg1, TReturn>, Func<TArg1, TReturn>> f)
    {
        return U<Func<TArg1, TReturn>>(r => arg1 => f(U(r))(arg1));
    }

}

private class test4 : test
{

    //[TestMethod]
    //Simpler definition, taken from this SO.
    //This uses inherent compiler recursion, lets see if it speed things up.
    //https://stackoverflow.com/questions/4763690/alternative-y-combinator-definition
    public override void TestMethod()
    {
        var root = BuildComposite();

        Performance.Measure(1000000, () =>
        {
            Y<IObject, int>(f => thing =>
            {
                foreach (var item in thing.Children)
                {
                    //Console.WriteLine(item.Name);
                    f(item);
                }
                return 0;
            })(root);
        }, "Time " + this.GetType().Name);
    }

    public static Func<TArg1, TReturn> Y<TArg1, TReturn>(Func<Func<TArg1, TReturn>, Func<TArg1, TReturn>> f)
    {
        return f(n => Y(f)(n));
    }

}

private class test5 : test
{

    //[TestMethod]
    //Simple way to recurse, is also the fastest
    //but then its no more an anonymous lambda.
    //This defeats the game purpose.
    public override void TestMethod()
    {
        var root = BuildComposite();

        Action<IObject> a = null;
        a = thing =>
            {
                foreach (var item in thing.Children)
                {
                    //Console.WriteLine(item.Name);
                    a(item);
                }
            };

        Performance.Measure(1000000, () =>
        {
            a(root);
        }, "Time " + this.GetType().Name);
    }

}

private class test6 : test
{

    //[TestMethod]
    //Reference test, direct method call
    //There should be no way to get faster than this.
    public override void TestMethod()
    {
        var root = BuildComposite();

        Performance.Measure(1000000, () =>
        {
            a(root);
        }, "Time " + this.GetType().Name);
    }

    public static void a(IObject thing)
    {
        foreach (var item in thing.Children)
        {
            //Console.WriteLine(item.Name);
            a(item);
        }
    }

}

private class test7 : test
{

    //[TestMethod]
    //Lets try some memoization.
    public override void TestMethod()
    {
        var root = BuildComposite();

        Performance.Measure(1000000, () =>
        {
            Y<IObject, int>.Combinator(f => thing =>
            {
                foreach (var item in thing.Children)
                {
                    //Console.WriteLine(item.Name);
                    f(item);
                }
                return 0;
            })(root);
        }, "Time " + this.GetType().Name);
    }

    private class Y<TArg1, TReturn>
    {
        public static Func<TArg1, TReturn> Combinator(Func<Func<TArg1, TReturn>, Func<TArg1, TReturn>> f)
        {
            return f(n => 
                {
                    if (memoized == null) memoized = Combinator(f);
                    return memoized(n);
                });
        }
        private static Func<TArg1, TReturn> memoized;
    }

}

private interface IObject
{
    List<IObject> Children { get; }
}

private class CObject : IObject
{
    private int lvl;
    public CObject(int lvl)
    {
        this.lvl = lvl;
    }
    public List<IObject> Children 
    { 
        get
        {
            var l = new List<IObject>() { BuildComposite(lvl + 1) }; 
            if (lvl > 2) l.Clear();
            return l;
        }
    }
}

private static IObject BuildComposite()
{
    return new CObject(0);
}

private static IObject BuildComposite(int lvl)
{
    return new CObject(lvl);
}

private class Performance
{
    public static void Measure(int count, Action a, string msg)
    {
        using(new WallClock(msg))
            Enumerable.Range(1, count).ToList().ForEach(_ => a());
    }
}

private class WallClock : IDisposable
{   
    private string name;
    private Stopwatch w;
    public WallClock(string name)
    {
        this.name = name;
        w = Stopwatch.StartNew();
    }
    public void Dispose()
    {
        w.Stop();
        Console.WriteLine(name + " : " + w.ElapsedMilliseconds);
    }
}