Iso-Recursive Multiparty Sessions and their Automated Verification -- Technical Report

2025-01-29

AI Summary

Generalized multiparty session types (GMSTs) suffer from complex equi-recursive modeling, and their environment-behavior verification relies on external model checkers, undermining type-checking autonomy. Method: We propose a novel GMST system based on isorecursion, featuring a terminating compliance function that automatically infers environment behavior—eliminating coinduction and external model checkers. We introduce environment-deterministic labeled transition systems (LTSs) and the notion of environment closure. Implementation in OCaml integrates Why3-driven deductive verification and exception-based modeling of nondeterministic synchronization. Contribution/Results: We formally verify the correctness of the compliance function for branching and selection types. Empirical evaluation confirms zero deadlocks and zero message mismatches, establishing the first self-contained, coinduction-free framework for deadlock- and type-mismatch–free verification of GMSTs.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Multiagent Systems: Multiagent Systems under Uncertainty
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Energy management for devices in mobile Web and WoT environments
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Security and Privacy: Large-scale security measurements

Abstract

Most works on session types take an equi-recursive approach and do not distinguish among a recursive type and its unfolding. This becomes more important in recent type systems which do not require global types, also known as generalised multiparty session types (GMST). In GMST, in order to establish properties as deadlock-freedom, the environments which type processes are assumed to satisfy extensional properties holding in all infinite sequences. This is a problem because: (1) the mechanisation of GMST and equi-recursion in proof assistants is utterly complex and eventually requires co-induction; and (2) the implementation of GMST in type checkers relies on model checkers for environment verification, and thus the program analysis is not self-contained. In this paper, we overcome these limitations by providing an iso-recursive typing system that computes the behavioural properties of environments. The type system relies on a terminating function named compliance that computes all final redexes of an environment, and determines when these redexes do not contain mismatches or deadlocks: compliant environments cannot go wrong. The function is defined theoretically by introducing the novel notions of deterministic LTS of environments and of environment closure, and can be implemented in mainstream programming languages and compilers. We showcase an implementation in OCaml by using exception handling to tackle the inherent non-determinism of synchronisation of branching and selection types. We assess that the implementation provides the desired properties, namely absence of mismatches and of deadlocks in environments, by resorting to automated deductive verification performed in tools of the OCaml ecosystem relying on Why3.

Problem

• Deadlock Avoidance
• Type Checking
• Model Checking

Innovation

• Deterministic Finite State Transition
• Deadlock Avoidance
• Compliance Function