# Regressive Recursion

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This Demonstration shows a definition by regressive recursion. The domain of the functions considered is the set of non-negative integers. Given an increasing function , define the predicate . Two other functions and are also given. The new function is defined by: if , then ; otherwise, .

Contributed by: Izidor Hafner (April 2018)

Open content licensed under CC BY-NC-SA

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## Details

If , and are primitive recursive functions, is also a primitive recursive function [1].

Reference

[1] I. Hafner, "Regressive Recursion," *Mathematica* *Balkanica*, 6(13), 1976 pp. 75–77.

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