A general storage theorem for integers in call-by-name λ-calculus

Jean-Louis Krivine
1994 Theoretical Computer Science  
Krivine, J.-L., A general storage theorem for integers in call-by-name /I-calculus, Theoretical Computer Science 129 (1994) 79994. The notion of storage operator introduced in J.-L. Krivine, 1991 Krivine, , 1990 appears to be an important tool in the study of data types in second-order i-calculus. These operators are I-terms which simulate call by value in the call-by-name strategy, and they can be used in order to modelize assignment instructions. The main result about storage operators is
more » ... there is a very simple second-order type for them, using Giidel's "not-not translation" of classical into intuitionistic logic. We give here a new and simpler proof of a strengthened version of this theorem, which contains all previous result in intuitionistic and in classical logic (J.-L. Krivine, 1990 Krivine, , 1992, and gives rise to new "storage theorems". Morever, this result has a simple and intuitive meaning, in terms of realizability. Correspondence to: J.-L. Krivine, Equipe de Logique Mathematique, CNRS URA 753, Universite Paris VII, 2 place Jussieu, Tour 45-55 (5eme &age),
doi:10.1016/0304-3975(94)90081-7 fatcat:ah3ikn7r6fapjmj4bsyz2qeqdu