Storage operators and \(\forall\)-positive types. (Opérateurs de mise en mémoire et types \(\forall\)-positifs.) (French) Zbl 0869.03009

In 1990, J.-L. Krivine introduced the notion of storage operator to simulate the “call by value” in a context of “call by name”. He has shown that, using Gödel’s translation from classical to intuitionistic logic, we can find a very simple type of AF2 type system for the storage operators [see J.-L. Krivine, Arch. Math. Logic 30, No. 4, 241-267 (1990; Zbl 0712.03009)]. In this paper, we study the \(\forall\)-positive types (the universal second-order quantifier appears positively in the types) and the Gödel transformations (a generalization of classical Gödel translation) of the system AF2. We generalize, by using a purely syntactic method, J.-L. Krivine’s theorem about these types and for these transformations.


03B40 Combinatory logic and lambda calculus


Zbl 0712.03009
Full Text: DOI EuDML


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