Complete restrictions of the intersection type discipline
Theoretical Computer Science
Intersection and union types: syntax and semantics
Information and Computation
Intersection type assignment systems
Selected papers of the thirteenth conference on Foundations of software technology and theoretical computer science
A symmetric lambda calculus for classical program extraction
Information and Computation - special issue: symposium on theoretical aspects of computer software TACS '94
ICFP '00 Proceedings of the fifth ACM SIGPLAN international conference on Functional programming
Completeness and Soundness Results for X with Intersection and Union Types
Fundamenta Informaticae - Intersection Types and Related Systems ITRS
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This paper presents a notion of intersection and union type assignment for the calculus X, a substitution free language that can be used to describe the behaviour of functional programming languages at a very low level of granularity, and has first been defined in [Stephane Lengrand. Call-by-value, call-by-name, and strong normalization for the classical sequent calculus. In Bernhard Gramlich and Salvador Lucas, editors, Electronic Notes in Theoretical Computer Science, volume 86. Elsevier, 2003, S. van Bakel, S. Lengrand, and P. Lescanne. The language &: computation and sequent calculus in classical logic. Submitted, 2004]. X has been designed to give a Curry-Howard-de Bruijn correspondence to the sequent calculus for classical logic. In this paper we will define a notion of sequent-style intersection type assignment on X that needs union types, and show that this notion is closed for both subject-reduction and subject-expansion. We will also show that it is an extension of the Strict system for lc.