La Valeur d'un Entier Classique en $\lambda\mu$-Calcul

TL;DR

This paper introduces three methods to determine the value of classical integers in lambda-mu calculus, including an external approach, a new reduction rule, and an existing method using storage operators.

Contribution

It presents novel techniques for extracting classical integer values in lambda-mu calculus, including a new reduction rule and an adaptation of existing storage operator methods.

Findings

The external method identifies the value and false part of a classical integer.

The new reduction rule yields the corresponding Church integer.

Parigot's method with Krivine's storage operators is adapted for classical integers.

Abstract

In this paper, we present three methods to give the value of a classical integer in $\lambda\mu$-calculus. The first method is an external method and gives the value and the false part of a normal classical integer. The second method uses a new reduction rule and gives as result the corresponding Church integer. The third method is the M. Parigot's method which uses the J.L. Krivine's storage operators.