Abstract
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 [Stéphane 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.
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