Resource control and intersection types: an intrinsic connection

S Ghilezan (1) , J Ivetic (1) , P Lescanne (2) , S Likavec (3)

1 Faculty of engineering, University of Novi Sad
2 LIP - Laboratoire de l'Informatique du Parallélisme
3 Dipartimento di Informatica [Torino]

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 con-traction rules in the type assignment system. We introduce directly the class of λ -terms and we provide a new treatment of substitution by its decompo-sition 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 in-tersection type assignment system. This process uses typeability of normal forms, redex subject expansion and reducibility method.

Mots clés: lambda calculus; resource control; intersection types; strong normalisation; typeability

Domaines: Logique en informatique [cs.LO]; Logique [math.LO]

S Ghilezan, J Ivetic, P Lescanne, S Likavec. Resource control and intersection types: an intrinsic connection. 2014. ⟨ensl-01091753⟩