English

A conjecture on numeral systems

Logic 2009-05-07 v1

Abstract

A numeral system is an infinite sequence of different closed normal λ\lambda-terms intended to code the integers in λ\lambda-calculus. H. Barendregt has shown that if we can represent, for a numeral system, the functions : Successor, Predecessor, and Zero Test, then all total recursive functions can be represented. In this paper we prove the independancy of these particular three functions. We give at the end a conjecture on the number of unary functions necessary to represent all total recursive functions.

Keywords

Cite

@article{arxiv.0905.0755,
  title  = {A conjecture on numeral systems},
  author = {Karim Nour},
  journal= {arXiv preprint arXiv:0905.0755},
  year   = {2009}
}
R2 v1 2026-06-21T12:58:40.401Z