e-mail nour@univ-savoie.fr\
**

Introduction
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In 1990, J.L. Krivine introduced the notion of storage operators (see \[4\]). They are closed $\l$-terms which allow, for a given data type (the type of integers, for example), to simulate in $\l$-calculus the “call by value” in a context of a “call by name” (the head reduction) and they can be used in order to modelize assignment instructions. J.L. Krivine has shown that the formula $\q x
\{ N$\*$[x] \f \neg\neg N[x] \}$ is a specification for storage operators for Church integers : where $N[x]$ is the type of integers in $AF2$ type system, and the operation $*$ is the simple Gődel translation from classical to intuitionistic logic which associates to every formula $F$ the formula $F$\* obtained by replacing in $F$ every atomic formula by its negation (see \[3\]).\
The latter result suggests many questions :

-   Why do we need a Gődel translation ?

-   Why do we need the type $N$\*$[x]$ which characterize a class larger than integers ?

In order to modelize the control operators, J-L. Krivine has extended the system $AF2$ to the classical logic (see \[6\]). His method is very simple : it consists of adding a new 