Abstract

Linear types, derived from Girard’s Linear Logic, provide a means to expose safe interfaces to stateful protocols and language features, e.g. channels and file handles. Data is delineated into two camps: unconstrained values which can be consumed or discarded arbitrarily and ‘resources’ which must be used exactly once. Bounded Linear Logic (BLL) [1], allows tracking a more nuanced notion of nonlinearity via the natural numbers semiring which is baked into its proof rules. Our system of Graded Modal Types generalises BLL by parameterising over the resource algebra, thus allowing a wide array of analyses to be captured in the type system.

In this talk we will explore how graded modal types and linearity conveniently extend our typical toolkit of parametric polymorphism and indexed types, allowing us to reason about pure and effectful programs in a novel, resource-oriented, manner. Session typed channels and mutable arrays are just two examples of programming idioms that can be provided in such a language without having to give up safety and compositionality. We will see this in action via Granule [2], our implementation of a functional language with a type system which supports all these features.

1. Girard, Scedrov, Scott (1992)

2. https://github.com/granule-project/granule