My brain seems to be in masochistic mode, so after being drowned in this, this and this, it wanted to mess around with some DIY in C#.

I came up with the following, which I don't think is the Y-combinator, but it does seem to manage to make a non-recursive function recursive, without referring to itself:

Func<Func<dynamic, dynamic>, Func<dynamic, dynamic>> Y = x => x(x);

So given these:

Func<dynamic, Func<dynamic, dynamic>> fact = 
                  self => n => n == 0 ? 1 : n * self(self)(n - 1);
Func<dynamic, Func<dynamic, dynamic>> fib = 
                  self => n => n < 2 ? n : self(self)(n-1) + self(self)(n-2);

We can generate these:

Func<dynamic, dynamic> Fact = Y(fact);
Func<dynamic, dynamic> Fib = Y(fib);

Enumerable.Range(0, 10)
          .ToList()
          .ForEach(i => Console.WriteLine("Fact({0})={1}", i, Fact(i)));

Enumerable.Range(0, 10)
          .ToList()
          .ForEach(i => Console.WriteLine("Fib({0})={1}", i, Fib(i)));
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