definition agrees with the following:

:A (vector-valued) function is primitive recursive if it can be written as
::
:where each component is a (scalar-valued) primitive recursive function.

Loop nesting

The central significance of the LOOP language lies in its stratification by maximum loop nesting depth. Writing Loop_k(L) for the class of functions computable by programs in variant L with at most k-nested LOOP constructs, the

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