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Linear types, anyone?The following is from von Neumann's early account of selfreproducing automata ("Theory and Organization of Complicated Automata", 1949):
Arthur Burks who brought von Neumann's lectures to print goes on to explain that the final result is two automata (A + B + C) and (A + B + C) + \phi(A + B +C), and that if B were to copy the description thrice, the process would start with one copy of (A + B + C) + \phi(A + B + C) and terminate with two copies of this automaton. von Neumann himself is quick to note that the procedure he outlines is not circular: "It is true that I argued with a variable X first, describing what C is supposed to do, and then put something which involved C for X. But I defined A and B exactly, before I even mentioned this particular X, and I defined C in terms which apply to any X." Can you formalize von Neumann's construction so that the two arguments that follow will be derivable (provable) from the description of the construction? By Ehud Lamm at 20110108 07:58  LtU Forum  previous forum topic  next forum topic  other blogs  6055 reads

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