Well, thanks everyone, I think I understand now why it doesn't work when 
specifying Array{Any}, and your answers completed each other.
What I still fail to understand is why how Julia manages to choose the 
correct function, assume I still have:

function f(s)
  println(s.x)
end

function f{T}(sl::Array{T})
  for s in sl
    f(s)
  end
end

If I call f on an Array of state, how does Julia know that it has to choose 
the second function... After all, the argument of the first function could 
still be an Array of state...

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