For any fixed k, iterators that stop after k length or lookahead revisions are lambda-P equivalent to the Cook-Urquhart recursor over type-one polynomial-time functions.
Cook (1992): Computability and complexity of higher type functions
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Type-two Iteration with Bounded Query Revision
For any fixed k, iterators that stop after k length or lookahead revisions are lambda-P equivalent to the Cook-Urquhart recursor over type-one polynomial-time functions.