Storage Operators and ∀-positive Types in TTR Type System

✍ Scribed by Karim Nour

• Publisher: John Wiley and Sons
• Year: 1996
• Tongue: English
• Weight: 1013 KB
• Volume: 42
• Category: Article
• ISSN: 0044-3050
• DOI: 10.1002/malq.19960420130

✦ Synopsis

In 1990, J. L. Krivine introduced the notion of storage operator to simulate "call by value" in the "call by name" strategy. J. L. Krivine has showed that, using Glidel translation of classical into intuitionistic logic, one can find a simple type for the storage operators in AF2 type system. This paper studies the V-positive types (the universal second order quantifier appears positively in these types) and the Glidel transformations (a generalization of classical Glidel translation) of TTR type system. We generalize by using syntactical methods Krivine's theorem about these types and for these transformations. We give a proof of this result in the case of the type of recursive integers.