X combinator (like the Y combinator) in Lua

x_combinator.lua

-- traditional fixed-point operator from functional programming
Y = function (f)
    return (function (x)
            return x(x)
            end)(function (x)
                 return f(function (v)
                          return (x(x))(v)
                          end)
                 end)
    end

-- The above is actually the X combinator, according to Wikipedia:
--   X = λf.(λx.x x) (λx.f (x x))
-- except that
--   (x x)
-- has been beta-expanded, yielding
--   (λv.((x x) v))
-- which is a necessary change because Lua is call-by-value and strict.
-- Without this beta-expansion, the combinator would cause a stack overflow.
--
-- Based on code from https://github.com/mherkender/lua.js/blob/master/tests/factorial.lua