We introduce an intersection type system which is a restriction of the intersection type discipline. This restriction leads to a principal type property for normal forms in the classical sense, while retaining the expressivity of the classical discipline. We characterize the structure of principal types of normal forms and give an algorithm that reconstructs normal forms from types. Having shown the equivalence between principal types and normal forms, we define an expansion operation on types which allows us to recover all possible types for any normalizable -term. The contribution of this work is a new and simpler presentation of the intersection type discipline through a purely syntactic and completely characterized notion of principal types.

Abstract. We build a lambda model which characterizes completely (persistently) normalizing, (persistently) head normalizing, and (persistently) weak head normalizing terms. This is proved by using the finitary logical description of the model obtained by defining a suitable intersection type assignment system.

Conditions on type preorders are provided in order to characterize the induced filter models for the #-calculus and some of its restrictions. Besides, two examples are given of filter models in which not all the continuous functions are representable. 1.