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Partial Functions

• Answer is produced in a finite number of unfolding steps.
• Idea: place limit on number of unfoldings and investigate resulting graphs
  • zero: {}
  • one: {(zero, one)}
  • two: {(zero, one), (one, one)}
  • i+1: {(zero, one), (one, one), ...(i, i!)}
• Graph at stage i defines function fac_i.
  • Consistency with each other:

    graph(fac_i) c graph(fac_i+1)

  • Consistency with ultimate solution:

    graph(fac_i) c graph(factorial)

  • Consequently

    union_i=0^oo graph(fac_i) c graph(factorial)