General recursive function: Difference between revisions

Revision as of 05:35, 2 June 2004

Revision as of 21:44, 2 June 2004

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The unbounded search operator is not definable by the rules of primitive recursion as those do not provide a mechanism for "infinite loops" (undefined values).

It is interesting to note that if the application of the unbounded search operator in the definition above is limited strictly to ''regular functions'' (functions which are guaranteed to be total when the unbounded search operator is applied to them), the resulting set (historically called the ''general recursive functions'') is the same as the set of recursive functions -- in other words, the requirement for partial functions can be partially obviated.