When Types Intersect and Effects Get Handled

2026-06-08

AI Summary

This work addresses the challenge of precisely characterizing terminating programs and enabling reachability analysis in a λ-calculus enriched with algebraic effects and handlers. To this end, we introduce the first intersection type system that simultaneously captures program termination and supports reachability reductions. Its behavioral semantics accommodates both reduction and expansion, and it reduces termination checking to a type inference problem. Building upon this system, we derive a type-safe simple-type subsystem and prove that its higher-order model checking (HOMC) problem is decidable. Our approach yields an exact type-theoretic characterization of terminating programs and establishes a novel foundation for static analysis of higher-order programs with algebraic effects.

Abstract

We introduce a novel intersection type system for a $λ$-calculus with algebraic effects and handlers. The system, inherently behavioral in nature, enjoys the classical properties of intersection type systems, in particular subject reduction and expansion. It thus characterizes the set of terms whose evaluation process terminates and, at the same time, allows reducing the reachability problem to type inference. This new system, the first with these features for a calculus with handlers, induces a system of simple types which, although not guaranteeing termination, is type sound and admits a decidable HOMC problem, unlike similar type systems like Dal Lago and Ghyselen's HEPCF.

Problem

• intersection types
• algebraic effects
• type inference
• termination
• reachability

Innovation

• intersection types
• algebraic effects
• effect handlers
• type inference
• decidable HOMC