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Functional and Fixed Point

• Partial functions

  fac_i+1 = F(fac_i) = Fⁱ(_|_)
  _|_:= (lambda n._|_)

• Function graph

  graph(factorial) = union_i=0^oo graph(Fⁱ(_|_))

• Fixed point property

  graph(F(factorial)) = graph(factorial)
  F(factorial) = factorial

The function factorial is a fixed point of the functional F!