A complete type inference system for subtyped recursive types

Abstract

Since record polymorphism is one of essential factors for object-oriented languages, various approaches to incorporate record polymorphism into type systems have been proposed to lay the foundation for object-oriented languages. Recursive types, which are essentially types of lists or trees, are major programming tools. In object-oriented languages, a pseudo variable “self” has a recursive type, which requires that type systems be able to treat recursive types. The purpose of this paper is to provide a type system and its type inference algorithm which can handle subtyping, recursive types and parametric polymorphism without any kind of type declaration or unnatural restrictions. We prove soundness and completeness of the type inference algorithm. Our system integrates subtyping and recursive types into Damas and Milner's type system and preserves important properties such as existence of principal typing. The basic idea is that we consider a type as a regular tree.