Infinite intersection types

Intersection of Infinite Cylinders

Session Types = Intersection Types + Union Types

We propose a semantically grounded theory of session types which relies on intersection and union types. We argue that intersection and union types are natural candidates for modeling branching points in session types and we show that the resulting theory overcomes some important defects of related behavioral theories. In particular, intersections and unions provide a native solution to the pro...

Liquid Intersection Types

We present a new type system combining refinement types and the expressiveness of intersection type discipline. The use of such features makes it possible to derive more precise types than in the original refinement system. We have been able to prove several interesting properties for our system (including subject reduction) and developed an inference algorithm, which we proved to be sound.

Retractions in Intersection Types

This paper deals with retraction intended as isomorphic embedding in intersection types building left and right inverses as terms of a λ-calculus with a ⊥ constant. The main result is a necessary and sufficient condition two strict intersection types must satisfy in order to assure the existence of two terms showing the first type to be a retract of the second one. Moreover, the characterisatio...

Intersection Types and Counting

We present a new approach to the following meta-problem: given a quantitative property of trees, design a type system such that the desired property for the tree generated by an infinitary ground λ -term corresponds to some property of a derivation of a type for this λ -term, in this type system. Our approach is presented in the particular case of the language finiteness problem for nondetermin...