Integrate Algebraic Subtyping to achieve better type inference

[be5invis]

Thesis : https://www.cl.cam.ac.uk/~sd601/thesis.pdf
A shorter one : http://www.cl.cam.ac.uk/~sd601/papers/mlsub-preprint.pdf

Type inference gives programmers the benefit of static, compile-time type checking without the cost of manually specifying types, and has long been a standard feature of functional programming languages. However, it has proven difficult to integrate type inference with subtyping, since the unification engine at the core of classical type inference accepts only equations, not subtyping constraints.

This thesis presents a type system combining ML-style parametric polymorphism and subtyping, with type inference, principal types, and decidable type subsumption. Type inference is based on biunification, an analogue of unification that works with subtyping constraints. Making this possible are several contributions, beginning with the notion of an “extensible” type system, in which an open world of types is assumed, so that no typeable program becomes untypeable by the addition of new types to the language. While previous formulations of subtyping fail to be extensible, this thesis shows that adopting a more algebraic approach can remedy this.

Using such an approach, this thesis develops the theory of biunification, shows how it is used to infer types, and shows how it can be efficiently implemented, exploiting deep connections between the algebra of regular languages and polymorphic subtyping.