Authors: Søren Debois ; Thomas Hildebrandt ; Tijs Slaats ; Nobuko Yoshida

We present the first session typing system guaranteeing request-response liveness properties for possibly non-terminating communicating processes. The types augment the branch and select types of the standard binary session types with a set of required responses, indicating that whenever a particular label is selected, a set of other labels, its responses, must eventually also be selected. We prove that these extended types are strictly more expressive than standard session types. We provide a type system for a process calculus similar to a subset of collaborative BPMN processes with internal (data-based) and external (event-based) branching, message passing, bounded and unbounded looping. We prove that this type system is sound, i.e., it guarantees request-response liveness for dead-lock free processes. We exemplify the use of the calculus and type system on a concrete example of an infinite state system.

• 03B25 - Decidability of theories and sets of sentences
• 03D05 - Automata and formal grammars in connection with logical questions
• 20M35 - Semigroups in automata theory, linguistics, etc.
• 68Q45 - Formal languages and automata
• 68Q70 - Algebraic theory of languages and automata