S-storage operators

TL;DR

This paper introduces the concept of S-storage operators for lambda calculus, extending Krivine's storage operators, and analyzes their properties and differences.

Contribution

Defines S-storage operators for lambda terms realizing successor functions and compares them to traditional storage operators.

Findings

Every storage operator is an S-storage operator.

Not all S-storage operators are storage operators.

S-storage operators generalize storage operators for successor functions.

Abstract

In 1990, J.L. Krivine introduced the notion of storage operator to simulate, for Church integers, the "call by value" in a context of a "call by name" strategy. In this present paper, we define, for every $\lambda$-term S which realizes the successor function on Church integers, the notion of S-storage operator. We prove that every storage operator is a $S-storage operator. But the converse is not always true.