Disjoint Polymorphism

The combination of intersection types, a merge operator and parametric polymorphism enables important applications for programming. However, such combination makes it hard to achieve the desirable property of a coherent semantics: all valid reductions for the same expression should have the same value. Recent work proposed disjoint intersections types as a means to ensure coherence in a simply typed setting. However, the addition of parametric polymorphism was not studied. This paper presents Fi: a calculus with disjoint intersection types, a variant of parametric polymorphism and a merge operator. Fi is both typesafe and coherent. The key difficulty in adding polymorphism is that, when a type variable occurs in an intersection type, it is not statically known whether the instantiated type will be disjoint to other components of the intersection. To address this problem we propose disjoint polymorphism: a constrained form of parametric polymorphism, which allows disjointness constraints for type variables. With disjoint polymorphism the calculus remains very flexible in terms of programs that can be written, while retaining coherence.