scratch.lua

function map(func, array)
   local new_array = {}
   for i,v in ipairs(array) do
      new_array[i] = func(v)
   end
   return new_array
end

function fix(u)
   return u(u)
end

function y_star(...)
   local l={...}
   return fix(
      function (p)
         return map(
            function (li)
               return (function (...)
                     return li(unpack(p(p)))(unpack({...}))
               end)
            end,
            l)
      end)
end

function odd_maker(odd, even)
   return function (n)
      return not(even(n))
   end
end

function even_maker(odd, even)
   return function (n)
      if n == 0 then
         return true
      else
         return odd(n-1)
      end
   end
end

x = y_star(odd_maker, even_maker)

oddp = x[1]

evenp = x[2]

print(512, evenp(512), oddp(512))
print(513, evenp(513), oddp(513))