# Mixed Logic and Storage Operators - Mathematics > Logic

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Abstract: In 1990 J-L. Krivine introduced the notion of storage operators. They are$\lambda$-terms which simulate call-by-value in the call-by-name strategy andthey can be used in order to modelize assignment instructions. J-L. Krivine hasshown that there is a very simple second order type in AF2 type system forstorage operators using G\-odel translation of classical to intuitionisticlogic. In order to modelize the control operators, J-L. Krivine has extendedthe system AF2 to the classical logic. In his system the property of theunicity of integers representation is lost, but he has shown that storageoperators typable in the system AF2 can be used to find the values of classicalintegers. In this paper, we present a new classical type system based on alogical system called mixed logic. We prove that in this system we cancharacterize, by types, the storage operators and the control operators. Wepresent also a similar result in the M. Parigot-s $\lambda\mu$-calculus.

Author: ** Karim Nour LAMA**

Source: https://arxiv.org/