[論文レビュー] Practical Refinement Session Type Inference (Extended Version)

Ueno, Toby, Das, Ankush|arXiv (Cornell University)|Feb 6, 2026

Logic, programming, and type systems被引用数 0

ひとこと要約

The paper presents a type inference algorithm for refinement session types with arithmetic refinements, proves a sound subtyping framework, and implements it with three optimizations evaluated on six Rast benchmarks.

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 $λ$-calculus. We show the performance benefits provided by our optimizations in coercing Z3 into solving the arithmetic constraints in reasonable time.

研究の動機と目的

• Motivate the need for refining session types to express richer protocols with arithmetic constraints.
• Develop a declarative and algorithmic subtyping framework for refinement session types.
• Provide a two-stage inference algorithm that first infers base session types then arithmetic indices.
• Implement the inference engine with optimizations to ensure practicality.
• Evaluate the approach on challenging benchmarks and analyze performance gains from the optimizations.

提案手法

• Define a semantic notion of type simulation and a sound subtyping algorithm for refinement session types.
• Extend subtyping with arithmetic refinements and derive algorithmic rules that generate typing and arithmetic constraints.
• Propose a two-stage inference process: infer base session types, then extract and solve arithmetic constraints.
• Generate constraints that are solved by unification (base types) and the Z3 SMT solver (arithmetic refinements).
• Introduce three optimizations: transitivity to reduce intermediate types, polynomial templates for arithmetic expressions, and theory of reals to speed up solving.

実験結果

リサーチクエスチョン

• RQ1 How can refinement session types be subtyped in a sound manner with arithmetic refinements?
• RQ2 Can a practical inference algorithm be designed to infer process types and refinements from definitions?
• RQ3 What optimizations are necessary to make SMT-based inference scalable for real-world examples?
• RQ4 How does the inferred typing enable reconstruction of program assertions automatically?

主な発見

• The authors define a declarative subtyping and prove soundness with respect to a semantic type simulation.
• They present an inference algorithm that produces typing and arithmetic constraints and prove its soundness.
• An implementation on top of the Rast language demonstrates feasibility of inference despite undecidability.
• Three optimizations are shown to be essential: transitivity to reduce types, polynomial templates to bound arithmetic search space, and a theory-of-reals approach to accelerate SMT solving.
• Evaluations on six Rast benchmarks (including unary/binary naturals, lists, and linear lambda-calculus) show the practical benefits of the optimizations.
• Without the optimizations, Z3 often times out on simple examples; with all optimizations, inference remains scalable.