When Types Intersect and Effects Get Handled

We introduce a novel intersection type system for a $\lambda$-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.