On isomorphisms of intersection types

Provable Isomorphisms of Types

A constructive characterization is given of the isomorphisms which must hold in all models of the typed lambda calculus with surjective pairing. By the close relation between closed Cartesian categories and models of these calculi, we also produce a characterization of those isomorphisms which hold in all CCC’s. By the correspondence between these calculi and proofs in intuitionistic positive p...

Classical isomorphisms of types

The study of isomorphisms of types has been mainly carried out in an intuitionistic setting. We extend some of these works to classical logic for both call-by-name and call-by-value computations by means of polarized linear logic and game semantics. This leads to equational characterizations of these isomorphisms for all the propositional connectives.

Remarks on isomorphisms of simple inductive types

Randomised algorithms for isomorphisms of simple types

We give the first linear time (yet randomized) algorithm for the first order isomorphism problem, i.e., the isomorphism of non-recursive types involving productand functiontype constructors, under the axioms of commutativity and associativity of products, currying and distributivity of functions over products. This problem can also be thought of as the problem of formal equality-testing of mult...

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...