Higher-order Context-free Session Types in System F

TL;DR

This paper extends System F with higher-order context-free session types, unifying functional and session type equivalence, and proves decidability of type equivalence for these complex types.

Contribution

It introduces a unified approach to handle functional and session type equivalence, including three notions and a decidability result for higher-order context-free session types.

Findings

Three notions of type equivalence are shown to coincide.

Decidability of type equivalence for higher-order context-free session types.

A reduction algorithm to bisimulation of simple grammars.

Abstract

We present an extension of System F with higher-order context-free session types. The mixture of functional types with session types has proven to be a challenge for type equivalence formalization: whereas functional type equivalence is often rule-based, session type equivalence usually follows a semantic approach based on bisimulations. We propose a unifying approach that handles the equivalence of functional and session types together. We present three notions of type equivalence: a syntactic rule-based version, a semantic bisimulation-based version, and an algorithmic version by reduction to the problem of bisimulation of simple grammars. We prove that the three notions coincide and derive a decidability result for the type equivalence problem of higher-order context-free session types.