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.

翻译：我们研究一个不类型的羊羔计算器的语义,该计算器配备了代表全球状态的读写操作的操作员;我们采用修道院方法来模拟副作用,并将读写作为计算式月球的代数操作处理;我们引入一个操作性语义和交叉类型类型类型类型分配系统,并证明各种类型在缩短和扩大期限和状态配置方面是无差异的,并通过打字对趋同的术语进行定性。