General recursive function: Difference between revisions

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The set of ''partial recursive functions'' is defined as the smallest set of partial functions of any [[arity]] from natural numbers to natural numbers which contains the zero, successor, and projection functions, and which is closed under composition, primitive recursion, and unbounded search.

The set of ''total recursive functions'' is the subset of partial recursive functions which are [[total function|total]].

In the [[equivalence of models of computability]] the parallel is drawn between [[Turing machine|Turing machines]] which do not terminate for certain inputs and an undefined result for that input in the corresponding partial recursive function.