Replicate, Reuse, Repeat: Capturing Non-Linear Communication via Session Types and Graded Modal Types

Abstract

Session types provide guarantees about concurrent behaviour and can be understood through their correspondence with linear logic, with propositions as sessions and proofs as processes. However, a strictly linear setting is somewhat limiting, since there exist various useful patterns of communication that rely on non-linear behaviours. For example, shared channels provide a way to repeatedly spawn a process with binary communication along a fresh linear session-typed channel. Non-linearity can be introduced in a controlled way in programming through the general concept of graded modal types, which are a framework encompassing various kinds of coeffect typing (describing how computations make demands on their context). This paper shows how graded modal types can be leveraged alongside session types to enable various non-linear concurrency behaviours to be re-introduced in a precise manner in a type system with a linear basis. The ideas here are demonstrated using Granule, a functional programming language with linear, indexed, and graded modal types.

Dependent Type Refinements for Futures

“…Another line of work seeks to embed session type systems into existing dependent type theories, allowing meta-level reasoning about processes and the exploitation of existing language infrastructure [7,72,20,57,29,43]. Embedded implementation is certainly not opposed by DRSAX nor the line of work above, but moving the burden of proof to the meta level requires explicit reasoning about the typing and operational semantics of programs to an extent determined by the embedding depth.…”