We present a fully abstract model of a call-by-value language with higher-order functions, recursion and natural numbers, as an exponential ideal in a topos. Our model is inspired by the fully abstract models of O'Hearn, Riecke and Sandholm, and Marz and Streicher. In contrast with semantics based on cpo's, we treat recursion as just one feature in a model built by combining a choice of modular components.

中文翻译：

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滑轮类别中的递归和顺序

我们提出了一个具有高阶函数，递归和自然数的按值调用语言的完全抽象模型，作为topos中的指数理想。我们的模型的灵感来自O'Hearn，Riecke和Sandholm以及Marz和Streicher的完全抽象模型。与基于cpo的语义相反，我们将递归视为通过组合各种模块化组件而构建的模型中的一个功能。