Recursion-free modular arithmetic in the lambda-calculus

We investigate encodings for modular arithmetic in the lambda-calculus. There are two approaches: adapting well-known numeral systems, and building a new one. This paper focuses on providing original techniques to encode modular arithmetic directly. We present a modular arithmetic numeral system complete with multiplication and an implementation of the Chinese remainder theorem, all without recursion i.e., without using fixed-point operators.

Automated summary

This research investigates encodings for modular arithmetic in the lambda-calculus. Two approaches are considered: adapting existing numeral systems and creating a new one. The focus of this paper is to provide original techniques for encoding modular arithmetic directly. A modular arithmetic numeral system is presented, complete with multiplication and an implementation of the Chinese remainder theorem, all without recursion i.e., without using fixed-point operators.