Intersection types for a λ-calculus with global store

We study the semantics of an untyped λ-calculus equipped with operators representing read and write operations from and to a global store. We adopt the monadic approach to model side effects and treat read and write as algebraic operations over a 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.