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 store. We adopt the monadic approach to model side-effects and treat read and write as algebraic operations over a monad. We introduce operational and denotational semantics and a type assignment system of intersection types and prove that types are invariant under the reduction and expansion of term and state configurations. Finally, we characterize convergent terms via their typings, establishing the adequacy of the denotational semantics w.r.t. the operational semantics.