## Program Self-Reference in Constructive Scott Subdomains

- John Case, Samuel E. Moelius
- Theory of Computing Systems
- 2009

1 Excerpt

- Published 2009 in FCT

The n-ary first and second recursion theorems formalize two distinct, yet similar, notions of self-reference. Roughly, the n-ary first recursion theorem says that, for any n algorithmic tasks (of an appropriate type), there exist n partial computable functions that use their own graphs in the manner prescribed by those tasks; the n-ary second recursion theorem says that, for any n algorithmic tasks (of an appropriate type), there exist n programs that use their own source code in the manner prescribed by those tasks. Results include the following. The constructive 1-ary form of the first recursion theorem is independent of either 1-ary form of the second recursion theorem. The constructive 1-ary form of the first recursion theorem does not imply the constructive 2-ary form; however , the constructive 2-ary form does imply the constructive n-ary form, for each n ≥ 1. For each n ≥ 1, the not-necessarily-constructive n-ary form of the second recursion theorem does not imply the (n+ 1)-ary form.

@inproceedings{Case2009IndependenceRF,
title={Independence Results for n-Ary Recursion Theorems},
author={John Case and Samuel E. Moelius},
booktitle={FCT},
year={2009}
}