Intersection Types for a Computational Lambda-Calculus with Global State

We study the semantics of an untyped lambda-calculus equipped with operators representing read and write operations from and to a global state. We adopt the monadic approach to model side effects and treat read and write as algebraic operations over a computational monad. We introduce an operational semantics and a type assignment system of intersection types, and prove that types are invariant under reduction and expansion of term and state configurations, and characterize convergent terms via their typings.