Polymorphic Subtyping Without Distributivity

Consistent Subtyping for All

Consistent subtyping is employed in some gradual type systems to validate type conversions. The original definition by Siek and Taha serves as a guideline for designing gradual type systems with subtyping. Polymorphic types à la System F also induce a subtyping relation that relates polymorphic types to their instantiations. However Siek and Taha’s definition is not adequate for polymorphic sub...

Subtyping First-Class Polymorphic Components

We present a statically typed, class-based object oriented language where classes are first class polymorphic values. A main contribution of this work is the design of a type system that combines first class polymorphic values with structural equirecursive types and admits a subtyping algorithm which is arguably much simpler than existing alternatives. Our development is modular and can be easi...

Polymorphic Subtyping: a Semantic Perspective Based on Abtract Interpretation

System F with Width-Subtyping and Record Updating

It is a well-known problem that F { the polymorphic lambda calculus F extended with subtyping { does not provide so-called polymor-phic updates, and that the standard PER model for F does not provide interpretations for these operations. The polymorphic updates are interesting because they play an important role in some type-theoretic models of object-oriented languages. We present an extension...

Decidability of Higher-Order Subtyping with Intersection Types

The combination of higher-order subtyping with intersection types yields a typed model of object-oriented programming with multiple inheritance 11]. The target calculus, F ! ^ , a natural generalization of Girard's system F ! with intersection types and bounded polymorphism, is of independent interest, and is our subject of study. Our main contribution is the proof that subtyping in F ! ^ is de...