Regressive Recursion

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

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



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


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

Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.