Resource control and intersection types: an intrinsic connection

In this paper we investigate the λ-calculus, a λ-calculus enriched with resource control. Explicit control of resources is enabled by the presence of erasure and duplication operators, which correspond to thinning and contraction rules in the type assignment system. We introduce directly the class of λ-terms and we provide a new treatment of substitution by its decomposition into atomic steps. We propose an intersection type assignment system for λ-calculus which makes a clear correspondence between three roles of variables and three kinds of intersection types. Finally, we provide the characterisation of strong normalisation in λ-calculus by means of an intersection type assignment system. This process uses typeability of normal forms, redex subject expansion and reducibility method.