We develop the Scott model of the programming language PCF in univalent type theory. Moreover, we work constructively and predicatively. To account for the non-termination in PCF, we use the lifting monad (also known as the partial map classifier monad) from topos theory, which has been extended to univalent type theory by Escardó and Knapp. Our results show that lifting is a viable approach to partiality in univalent type theory. Moreover, we show that the Scott model can be constructed in a predicative and constructive setting. Other approaches to partiality either require some form of choice or quotient inductive-inductive types. We show that one can do without these extensions.

我们在单价类型理论中开发了编程语言 PCF 的 Scott 模型。此外，我们进行建设性和预测性的工作。为了解释 PCF 中的非终止，我们使用来自 topos 理论的提升单子（也称为部分映射分类器单子），该理论已被 Escardó 和 Knapp 扩展到单价类型理论。我们的结果表明，提升是单价类型理论中偏向性的一种可行方法。此外，我们表明斯科特模型可以在预测性和建设性的环境中构建。其他偏向性方法要么需要某种形式的选择，要么需要商归纳归纳类型。我们表明，没有这些扩展也可以。