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Hmmm... so, If I understand correctly, the closure is "frozen" or "closed" once the local x is out of scope.
I find this one also interesting:

function fie() local x=789
      f = function() return x end --global f
print(f()); x=123; print(f());

fie() -- will print 789 newline 123

Apparently, you can still change the contents of the closure's x whilst the local x is in scope, because they are the same x. Which makes sense due to the lexical scoping.

You can change it even later ;-)

function fie()
  local x=123;
  function f() return x end
  function g(y) x=y end


print(f()); --prints 123
print(f()); --prints 321

This is powerfull stuff....
(Were upvalues read-only?)

Btw. I became curious about what Peter had suggested
year ago. I think that what he wanted (protected datatypes
in Lua) might be implementable with closures. Create an object
which has its internals in a closure, which can only be
accessed by the interface functions, hmmm, I don't know if there
are any holes here.