The heart of intersection type assignment: Normalisation proofs revisited

This paper gives a new proof for the approximation theorem and the characterisation of normalisability using intersection types for a system with ω and a ≤-relation that is contravariant over arrow types. The technique applied is to define reduction on derivations and to show a strong normalisation result for this reduction. From this result, the characterisation of strong normalisation and the approximation result will follow easily; the latter, in its turn, will lead to the characterisation of (head-) normalisability.