A conjecture on numeral systems
Year: 2009
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Nour, Karim
Institution: Le LAMA
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6891782219
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