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.

翻译：我们研究一个非型式羊羔计算仪的语义,该计算仪配备的操作员代表全球商店的阅读和写作操作;我们采用修道院方法模拟副作用,并将读和写作作为代数操作处理;我们采用操作和分解的语义以及交叉类型类型类型类型分配系统,并证明在缩短和扩大期限和状态配置下,类型是无差异的。最后,我们通过打字对趋同术语进行定性。