Annotations for Intersection Typechecking

TL;DR

This paper investigates the design of annotation mechanisms for intersection type systems in functional programming, introducing new annotation forms and clarifying their roles in context management.

Contribution

It introduces a refined set of annotation mechanisms, including a novel left-hand annotation, to better handle intersection types and contextual information in typechecking.

Findings

Separated annotations into elementary mechanisms

Introduced a new left-hand annotation for context guarding

Clarified the role of annotations in intersection type systems

Abstract

In functional programming languages, the classic form of annotation is a single type constraint on a term. Intersection types add complications: a single term may have to be checked several times against different types, in different contexts, requiring annotation with several types. Moreover, it is useful (in some systems, necessary) to indicate the context in which each such type is to be used. This paper explores the technical design space of annotations in systems with intersection types. Earlier work (Dunfield and Pfenning 2004) introduced contextual typing annotations, which we now tease apart into more elementary mechanisms: a "right hand" annotation (the standard form), a "left hand" annotation (the context in which a right-hand annotation is to be used), a merge that allows for multiple annotations, and an existential binder for index variables. The most novel element is the left-hand annotation, which guards terms (and right-hand annotations) with a judgment that must follow from the current context.