Course-of-values recursion
Course-of-value recursion allows the use of any number of values for previous arguments, as opposed to the primitive recursion where only the value for the immediately preceding argument can be used. Although apparently more general, this notion actually turns out to be reducible to the usual primitive recursion as well (see Odifreddi, 1989, I.7.1).
References
Odifreddi, P.G., 1989, Classical Recursion Theory, North Holland; second edition, 1999.
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