System $$F^\mu _\omega $$ with Context-free Session Types

Abstract

We study increasingly expressive type systems, from $$F^\mu $$ F μ —an extension of the polymorphic lambda calculus with equirecursive types—to $$F^{\mu ;}_\omega $$ F ω μ ; —the higher-order polymorphic lambda calculus with equirecursive types and context-free session types. Type equivalence is given by a standard bisimulation defined over a novel labelled transition system for types. Our system subsumes the contractive fragment of $$F^\mu _\omega $$ F ω μ as studied in the literature. Decidability results for type equivalence of the various type languages are obtained from the translation of types into objects of an appropriate computational model: finite-state automata, simple grammars and deterministic pushdown automata. We show that type equivalence is decidable for a significant fragment of the type language. We further propose a message-passing, concurrent functional language equipped with the expressive type language and show that it enjoys preservation and absence of runtime errors for typable processes.