Practical Refinement Session Type Inference (Extended Version)

2026-02-06

AI Summary

While session types with arithmetic refinements enable precise specification of concurrent communication protocols, their heavy annotation burden has hindered practical adoption. This work proposes the first practical type inference algorithm for such refined session types, leveraging a semantic subtyping theory based on type simulation, combined with a constraint generation mechanism and the Z3 SMT solver to automatically infer both types and associated arithmetic constraints. We introduce three key optimizations that substantially improve inference efficiency. A fully implemented inference engine in the Rast language demonstrates the approach’s effectiveness across six complex benchmarks—including unary/binary natural numbers and the linear λ-calculus—significantly reducing solving times and establishing the practical feasibility of refined session type inference.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Search and Optimization: Sampling/Simulation-based Search
• Knowledge Representation and Reasoning: Automated Reasoning and Theorem Proving

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

Abstract

Session types express and enforce safe communication in concurrent message-passing systems by statically capturing the interaction protocols between processes in the type. Recent works extend session types with arithmetic refinements, which enable additional fine-grained description of communication, but impose additional annotation burden on the programmer. To alleviate this burden, we propose a type inference algorithm for a session type system with arithmetic refinements. We develop a theory of subtyping for session types, including an algorithm which we prove sound with respect to a semantic definition based on type simulation. We also provide a formal inference algorithm that generates type and arithmetic constraints, which are then solved using the Z3 SMT solver. The algorithm has been implemented on top of the Rast language, and includes 3 key optimizations that make inference feasible and practical. We evaluate the efficacy of our inference engine by evaluating it on 6 challenging benchmarks, ranging from unary and binary natural numbers to linear $\lambda$-calculus. We show the performance benefits provided by our optimizations in coercing Z3 into solving the arithmetic constraints in reasonable time.

Problem

• session types
• arithmetic refinements
• type inference
• annotation burden
• concurrent message-passing systems

Innovation

• session types
• arithmetic refinements
• type inference
• subtyping
• SMT solving