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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