1-- function closures are powerful
2
3-- traditional fixed-point operator from functional programming
4Y = function (g)
5      local a = function (f) return f(f) end
6      return a(function (f)
7                 return g(function (x)
8                             local c=f(f)
9                             return c(x)
10                           end)
11               end)
12end
13
14
15-- factorial without recursion
16F = function (f)
17      return function (n)
18               if n == 0 then return 1
19               else return n*f(n-1) end
20             end
21    end
22
23factorial = Y(F)   -- factorial is the fixed point of F
24
25-- now test it
26function test(x)
27	io.write(x,"! = ",factorial(x),"\n")
28end
29
30for n=0,16 do
31	test(n)
32end
33