A conjecture on numeral systems

Karim Nour

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arXiv · 0905.0755

A conjecture on numeral systems

Karim Nour

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Abstract

A numeral system is an infinite sequence of different closed normal $λ$-terms intended to code the integers in $λ$-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.

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BibTeX RIS

Karim Nour. 2009-05-06. A conjecture on numeral systems. https://arxiv.org/abs/0905.0755

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