Strong storage operators and data types

The storage operators were introduced by J.L. Krivine (6]); they are closed -terms which, for some fixed data type (the integers for example), allow to simulate call by value while using call by name. J.L. Krivine showed that such operators can be typed, in the type system, using Gödel's translation from classical to intuitionistic logic (8]).This paper studies the existence of storage operators which give a normal form as result (strong storage operators) for recursive and iterative representation of data in -calculus. We obtain the following result: We can find typed strong storage operators for the recursive representations of data type, but that is not the case for the iterative representations of an infinite data type.We give the proof of this result in the case of integers.