A graphical presentation of ML ^F types with a linear-time unification algorithm

Abstract

MLF is a language that extends ML and System SF and combines the benefits of both. We propose a dag representation of MLF types that superposes a term-dag, encoding the underlying term-structure with sharing, and a binding tree encoding the binding-structure. Compared to the original definition, this representation is more canonical as it factors out most of the notational details; it is also closely related to first-order terms. Moreover, it permits a simpler and more direct definition of type instance that combines type instance on first-order term-dags, simple operations on dags, and a control that allows or rejects potential instances. Using this representation, we build a linear-time unification algorithm for MLF types, which we prove sound and complete with respect to the specification.