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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