3 research outputs found
Uniform Proofs of Normalisation and Approximation for Intersection Types
We present intersection type systems in the style of sequent calculus,
modifying the systems that Valentini introduced to prove normalisation
properties without using the reducibility method. Our systems are more natural
than Valentini's ones and equivalent to the usual natural deduction style
systems. We prove the characterisation theorems of strong and weak
normalisation through the proposed systems, and, moreover, the approximation
theorem by means of direct inductive arguments. This provides in a uniform way
proofs of the normalisation and approximation theorems via type systems in
sequent calculus style.Comment: In Proceedings ITRS 2014, arXiv:1503.0437
Strong Normalization through Intersection Types and Memory
AbstractWe characterize β-strongly normalizing λ-terms by means of a non-idempotent intersection type system. More precisely, we first define a memory calculus K together with a non-idempotent intersection type system K, and we show that a K-term t is typable in K if and only if t is K-strongly normalizing. We then show that β-strong normalization is equivalent to K-strong normalization. We conclude since λ-terms are strictly included in K-terms