Work

Non-linear communication via graded modal session types

Year: 2024

Type: article

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, strict linearity is limiting since there exist useful communication patterns that rely on non-linear behaviours. For example, shared channels can repeatedly spawn a process with binary communication along a fresh linear channel. Non-linearity can be introduced in a controlled way through the concept of graded modal types, which are a framework encompassing various kinds of coeffect (describing how computations make demands on their context). This paper shows how graded modalities can work alongside session types, enabling various non-linear concurrency behaviours to be re-introduced precisely. The ideas are demonstrated using Granule, a functional language with linear, indexed, and graded modal types. We define a core calculus capturing the requisite features and our new graded primitives, then present an operational model and establish various key properties.

Source: Information and Computation

DOI: 10.1016/j.ic.2024.105234

Authors: Danielle Marshall, Dominic Orchard

Language: English

Topic: Logic, programming, and type systems

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,630

Funder: Engineering and Physical Sciences Research Council

Awards: G363745060, DTP 2020-2021 University of Kent, Verifying Resource-like Data Use in Programs via Types, G8214229692