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+-- function closures are powerful
+
+-- traditional fixed-point operator from functional programming
+Y = function (g)
+ local a = function (f) return f(f) end
+ return a(function (f)
+ return g(function (x)
+ local c=f(f)
+ return c(x)
+ end)
+ end)
+end
+
+
+-- factorial without recursion
+F = function (f)
+ return function (n)
+ if n == 0 then return 1
+ else return n*f(n-1) end
+ end
+ end
+
+factorial = Y(F) -- factorial is the fixed point of F
+
+-- now test it
+function test(x)
+ io.write(x,"! = ",factorial(x),"\n")
+end
+
+for n=0,16 do
+ test(n)
+end