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 ω ; —the higher-order types and context-free session types. Type equivalence is given by a standard bisimulation defined over novel labelled transition system for Our subsumes contractive fragment _\omega as studied in literature. Decidability results various languages are obtained translation into objects an appropriate computational model: finite-state automata, simple grammars deterministic pushdown automata. show that decidable significant language. further propose message-passing, concurrent functional language equipped it enjoys preservation absence runtime errors typable processes.