Intersection types for explicit substitutions

Stéphane Lengrand (1, 2) , Pierre Lescanne (2) , Dan Dougherty (3) , Mariangiola Dezani (4) , Steffen van Bakel (5)

1 PPS - Preuves, Programmes et Systèmes
2 LIP - Laboratoire de l'Informatique du Parallélisme
3 WPI CS - Department of Computer Science
4 Dipartimento di Informatica [Torino]
5 Department of Computing [London]

We present a new system of intersection types for a composition-free calculus of explicit substitutions with a rule for garbage collection, and show that it characterizes those terms which are strongly normalizing. This system extends previous work on the natural generalization of the classical intersection types system, which characterized head normalization and weak normalization, but was not complete for strong normalization. An important role is played by the notion of available variable in a term, which is a generalization of the classical notion of free variable.

Mots clés: Calculi of explicit substitutions; intersection types; strong normalization.; strong normalization

Domaines: Logique en informatique [cs.LO]

Stéphane Lengrand, Pierre Lescanne, Dan Dougherty, Mariangiola Dezani, Steffen van Bakel. Intersection types for explicit substitutions. Information and Computation, 2004, 189 (1), pp.17 - 42. ⟨hal-00150285⟩